# Integrated control and fault detection of air-handling units.

INTRODUCTION

The development of fault detection and diagnosis (FDD) methods for HVAC applications has been an area that has been actively researched for more than a decade. Numerous studies report methods developed for application to central air-handling units (AHUs) based on either passive monitoring, where data are collected without interrupting the normal operation of the system (e.g., Haves et al. 1996; Dexter and Benouarets 1996; Lee et al. 1996a, 1996b, and 1997; Katipamula et al. 1999; House et al. 1999 and 2001; Norford et al. 2002), or active testing, where data are collected that result from overrides of control signals and setpoints (e.g., Kelso and Wright 2005; Xu et al. 2005; Haves et al. 2007; Katipamula and Brambley 2007). Katipamula and Brambley (2005a and 2005b) provide a review of the literature on the topic of FDD methods for HVAC applications published prior to 2005.

The development and implementation of an FDD method involves a trade-off between the sensitivity of the method to faults and the number of false alarms that it will generate (Reddy 2007; Katipamula and Brambley 2007). The development of robust FDD methods for the HVAC industry is challenged by the fact that there are limited sensors available for use in analyses (due to cost considerations, only those necessary to control the equipment are commonly installed), the equipment and systems have nonlinear characteristics, and the loads on the system are time varying. Methods can be made more sensitive to faults and less likely to create false alarms if the data they process are collected under well-defined and well-controlled conditions. For this reason, AHU FDD methods are commonly based on analyses of data collected while operating in steady state. For AHU FDD methods implemented as on-line monitoring tools, a filtering algorithm, commonly referred to as a steady-state detector, is often used to collect data while the system operates in steady state and to discard data from transient operation (e.g., Haves et al. 1996; House et al. 1999 and 2001). For AHU FDD methods implemented as commissioning tools (i.e., those that utilize active testing), steady-state data can be obtained by overriding a control signal and forcing the AHU into a particular operating state until steady-state conditions prevail (Kelso and Wright 2005; Xu et al. 2005; Haves et al. 2007; Katipamula and Brambley 2007).

Both approaches to obtaining steady-state data have drawbacks. Because unstable operation is prevalent in AHUs, a well-designed steady-state detector could discard large portions of the operational data, leaving little data for an on-line FDD method to process. FDD methods that rely on injected test signals would be used intermittently and may require an operator to either manually introduce the test signals or to monitor the test as it progresses. Thus, faults could exist for significant periods of time before they are discovered, because data are being discarded or collected infrequently.

This paper describes a simulation study of a new method for integrated control and fault detection of AHUs that overcomes these drawbacks. The method uses sensors commonly installed in AHUs and collects much of the key diagnostic information at times when steady-state conditions are imposed on the AHU by the sequencing logic, thereby eliminating the need for a steady-state detector. This enables the method to continuously monitor the AHU operation and over time produces a rich data set collected under controlled conditions. A model-based fault detection method processes these data and generates residual values that can be further processed to identify faults. In parallel, an algorithm monitors the saturation status of control loops for the processes used for sequential control of the AHU.

The paper is organized in the following manner. First, the AHU system description and finite state machine sequencing control are described. This is followed by descriptions of the integrated control and fault detection method and the simulation environment used to evaluate the method. Results obtained for six faults are then discussed in detail, and a table summarizing the results for all faults considered in the study is presented. Finally, conclusions and recommendations for future work are provided.

AHU SYSTEM DESCRIPTION

Figure 1 is a schematic diagram of a single-duct central AHU. Outdoor air enters the AHU and is mixed in the mixed air plenum with recirculated air returned from the building. The supply fan draws mixed air through the heating and cooling coils where it is conditioned, if necessary, prior to being distributed to the building through the supply duct. Return air from the building is either exhausted or recirculated to mix with outdoor air. The outdoor, recirculation, and relief airflow rates are controlled by their respective dampers (collectively called the mixing-box dampers) and by the supply and return fans.

[FIGURE 1 OMITTED]

In variable-air-volume (VAV) AHUs, the supply air temperature is commonly controlled to satisfy a setpoint value. Feedback control is used to modulate the heating coil valve, cooling coil valve, and mixing-box dampers to achieve the setpoint. An AHU controller uses sequencing control logic to determine the proper component(s) to use to control the temperature at any given time. Seem et al. (1999) and ASHRAE (2007) describe a sequencing strategy for AHUs based on finite state machine logic. A state transition diagram illustrating the logic for the sequencing strategy is shown in Figure 2. The description of each operating state is summarized in the rounded boxes and described further below. The conditions necessary for transitions between states are provided adjacent to the arrows connecting the states.

[FIGURE 2 OMITTED]

State 1

In State 1, feedback control is used to modulate the amount of energy transferred from the heating coil to the air. The mixing-box dampers are positioned to provide the minimum outdoor airflow rate required for ventilation and the cooling coil valve is closed. The transition to State 2 occurs after the control signal has saturated in the no-heating position (i.e., closed). The control signal is considered saturated in the no-heating position when it has been continuously at this position for a time period equal to the state transition delay. A state transition delay of five minutes was used in this study.

State 2

In State 2, feedback control is used to modulate the mixing-box dampers in order to maintain the supply air temperature at the setpoint value. Adjusting the positions of the dampers varies the relative amounts of outdoor air and return air in the supply airstream. In State 2, the heating and cooling coil valves are closed. The transition to State 1 occurs after the control signal for the dampers has been at the minimum outdoor air position for a time period equal to the state transition delay. Transition to State 3 occurs after the control signal for the dampers has been at the 100% outdoor air position for a time period equal to the state transition delay.

State 3

In State 3, feedback control is used to modulate the flow of chilled water to the cooling coil, thereby controlling the amount of energy extracted from the air. The mixing-box dampers are positioned for 100% outdoor air, and the heating coil valve is closed. Transition to State 2 occurs after the control signal for mechanical cooling has been saturated at the no-cooling position for a time period equal to the state transition delay. Economizer logic is used to determine the transition to State 4. Enthalpy-based, temperature-based or combined enthalpy and temperature economizer logic may be used. In the state transition diagram shown in Figure 2, logic based on the outdoor air temperature is used to determine the transition point. Transition to State 4 occurs when the outdoor air temperature is greater than the switchover temperature plus the deadband temperature. Typically, the switchover temperature is equal to the return air temperature, and the deadband is about 0.56[degrees]C (1[degrees]F). The deadband prevents cycling from State 3 to State 4 caused by noise in the return and outdoor air temperature sensor readings.

State 4

State 4 also uses feedback control to modulate the flow of chilled water to the cooling coil, thereby controlling the amount of energy extracted from the air. However, in this case, the mixing-box dampers are set at the minimum outdoor air position. Economizer logic is used to determine the transition to State 3. In the state transition diagram shown in Figure 2, transition to State 3 occurs when the outdoor air temperature is less than the switchover temperature.

INTEGRATED CONTROL AND FAULT DETECTION SYSTEM

FDD methods can be classified as either model-free methods or model-based methods (Gertler 1998). Model-free methods include methods based on: 1) physical redundancy, in which multiple sensors are installed to measure the same physical quantity; 2) special sensors installed to specifically detect and diagnose particular faults; 3) limit checking, in which process variables are compared to thresholds; 4) spectrum analysis to detect and identify faults in rotating machinery; and 5) logic reasoning approaches. As the name implies, model-based methods use a model of a process to calculate expected values of specific variables. The expected values are compared to measured values and the differences, or residuals, are evaluated to determine if a fault exists.

The overall structure of the integrated control and fault detection system is shown in the block diagram in Figure 3. A finite state machine is used to provide sequential control of the devices. Based on the current state or state transition, observations are passed from the finite state machine to the model-based residual generation block. This block determines residuals based on mass and energy balances of the system. Within the finite state machine, a control performance monitor calculates state-based performance indices for the control loops. The residuals and state-based performance indices are passed to the fault analysis block. The following sections describe the model-based residual calculations and the control performance monitor.

[FIGURE 3 OMITTED]

Model-Based Residuals

The ability to detect faults in HVAC systems is limited by the available measurement and control points. While AHUs commonly have sensors for measuring the supply, return, outdoor, and mixed air temperatures, one or more of these sensors may be missing in a particular system. Thus, fault detection systems based on model-based residuals are presented for combinations of sensors as outlined below:

* supply and outdoor air temperature sensors

* supply, return, and outdoor air temperature sensors

* supply, return, outdoor, and mixed air temperature sensors

System 1: Supply and Outdoor Air Temperature Sensors. For AHUs having only supply and outdoor air temperature sensors, model-based residuals are determined only at transitions between States 2 and 3. From Figure 2, a transition from State 2 to State 3 occurs after the damper control signal has been saturated in the 100% outdoor air position for a period of time equal to the state transition delay. At this condition, the AHU is assumed to be in steady state. A similar assumption of steady-state operation is used for all residuals calculated at a state transition. Assuming steady-state conditions prevail, mass balances on the dry air and water vapor entering and leaving the control volume in Figure 4 yield

[FIGURE 4 OMITTED]

[m.sub.o] = [m.sub.s] (1)

and

[m.sub.o][[omega].sub.o] = [m.sub.s][[omega].sub.s], (2)

where [m.sub.o] is the mass of dry air entering the control volume, [m.sub.s] is the mass of dry air leaving the control volume through the supply air duct, and [omega.sub.o] and [omega.sub.s] are the humidity ratios of the outdoor air and supply air, respectively. Using Equation 1, Equation 2 simplifies to

[[omega].sub.o] = [[omega].sub.s]. (3)

Performing an energy balance on the control volume with the assumption that the kinetic and potential energy of the air entering and leaving the control volume are the same (an assumption applied throughout the development of the model-based residuals) gives the following:

[m.sub.o][h.sub.o] + [W.sub.fan] = [m.sub.s][h.sub.s] (4)

where [h.sub.o] and [h.sub.s] are the enthalpy of the outdoor air and supply air, respectively, [W.sub.fan] and is the power input to the fan. Air can be modeled as an ideal gas at the temperatures found in HVAC systems (Kuehn et al. 1998). Using the ideal-gas assumption, the enthalpy of air is given by

h = [c.sub.p]T + [omega][h.sub.g0], (5)

where [c.sub.p] is the specific heat of the moist air mixture, and [h.sub.g0] is the enthalpy of water vapor at the reference state. The specific heat of the mixture is determined from

[c.sub.p] = [c.sub.pa] + [omega][c.sub.pw], (6)

where [c.sub.pa] is the specific heat at constant pressure of dry air and [c.sub.pw] is the specific heat at constant pressure of water vapor. Substituting Equation 5 into Equation 4 gives

[m.sub.o]([c.sub.p][T.sub.o] + [[omega].sub.o][h.sub.g0]) + [W.sub.fan] = [m.sub.s]([c.sub.p][T.sub.s] + [[omega].sub.s][h.sub.g0]). (7)

Substituting Equation 1 and Equation 3 into Equation 7 and solving for the difference between the supply and outdoor air temperatures gives

[T.sub.s]-[T.sub.o] = [[W.sub.fan]/[[m.sub.s][c.sub.p]]]. (8)

Thus, at the transition from State 2 to State 3, the difference between the supply and outdoor air temperatures is due to the energy gained from the fan. The supply airflow rate and fan power will vary with the load in a VAV air-handling system, and while the volumetric airflow rate may be measured, the fan power typically is not. Thus, to evaluate Equation 8, the specific heat of the moist air mixture, the fan power, and possibly the supply air mass flow rate will need to be estimated. The specific heat can be estimated for typical operating conditions and the fan power and mass flow rate can be estimated from design data. Residual [R.sub.1] is then computed from

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where [[T.sub.s,2[right arrow]3]] and [[T.sub.o,2[right arrow]3]] are the supply and outdoor air temperatures recorded immediately prior to the transition (i.e., at the end of the state transition delay) from State 2 to State 3 when steady-state conditions are expected to prevail, and the symbol ^ over the variables on the right-hand side of Equation 9 indicates an estimated value.

The transition from State 3 to State 2 occurs after the cooling coil valve control signal is saturated in the no-cooling position for a period of time equal to the state transition delay. Equations 1-8 can again be applied, and residual [R.sub.2] is defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [[T.sub.s,3[right arrow]2]] and [[T.sub.o,3[right arrow]2]] are the supply and outdoor air temperatures recorded immediately prior to the transition from State 3 to State 2.

For a properly controlled AHU, transitions between States 2 and 3 should be closely tied to the outdoor air temperature, which generally increases monotonically in the morning and decreases monotonically in the late afternoon or evening. Thus, there may only be one transition from State 2 to State 3 and one transition from State 3 to State 2 in a day, or there may be none at all, so the number of data points accumulated in a given day or week for residuals [R.sub.1] and [R.sub.2] is expected to be small. The same is true for the six additional residuals to be defined in the ensuing sections that are calculated at state transitions. Although limited in number, these residuals are collected under well-controlled conditions, making the data quality similar to that resulting from a manual override of the AHU into a specific operating mode. Furthermore, the residuals are collected on a continuous and automatic basis (i.e., whenever the appropriate state transition occurs) as part of the normal control sequence, which is an advantage over an approach that overrides the normal control of the AHU, even if it is done automatically.

System 2: Supply, Return, and Outdoor Air Temperature Sensors. System 2 utilizes supply, return, and outdoor air temperature sensors. Adding a return air temperature sensor enables the calculation of residuals at transitions between States 1 and 2 as the AHU operates with minimum outdoor air and the heating and cooling coil valves are closed. Figure 5 shows a control volume used to perform steady-state mass and energy balances at transitions between States 1 and 2. Performing a mass balance for the dry air and water vapor entering and leaving the control volume gives the following:

[FIGURE 5 OMITTED]

[m.sub.o] + [m.sub.r] = [m.sub.s] (11)

and

[m.sub.o][[omega].sub.o] + [m.sub.r][[omega].sub.r] = [m.sub.s][[omega].sub.s] (12)

Performing a steady-state energy balance on the control volume in Figure 5 gives

[m.sub.o][h.sub.o] + [m.sub.r][h.sub.r] + [W.sub.fan] = [m.sub.s][h.sub.s]. (13)

Substituting Equation 5 into Equation 13 and simplifying using Equation 12 yields

[m.sub.o][c.sub.p][T.sub.o] + [m.sub.r][c.sub.p][T.sub.r] + [W.sub.fan] = [m.sub.s][c.sub.p][T.sub.s]. (14)

Solving Equation 11 for [m.sub.r] and substituting into Equation 14 gives

[m.sub.o][c.sub.p]([T.sub.o]-[T.sub.r]) = [m.sub.s][c.sub.p]([T.sub.s]-[T.sub.r])-[W.sub.fan]. (15)

Finally, rearranging Equation 15 yields an equation for the fraction of outdoor air, f, entering the AHU:

f = [[m.sub.o]/[m.sub.s]] = [[[T.sub.s]-[T.sub.r]-[[W.sub.fan]/[[m.sub.s][c.sub.p]]]]/[[T.sub.o]-[T.sub.r]]] (16)

where the final term in the numerator is the temperature rise across the supply fan. Residual [R.sub.3] is based on the outdoor air fraction in Equation 16 and is calculated by using the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

where [f.sub.design] is the design outdoor air fraction and [T.sub.s,1[right arrow]2], [T.sub.r,1[right arrow]2] and [T.sub.o,1[right arrow]2] are the supply, return, and outdoor air temperatures recorded immediately prior to a transition from State 1 to State 2.

In the same way, residual [R.sub.4] is calculated using temperatures recorded immediately prior to a transition from State 2 to State 1 and is calculated by using the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

System 3: Supply, Return, Outdoor, and Mixed Air Temperature Sensors. System 3 utilizes the supply, return, outdoor, and mixed air temperature sensors for calculating model-based residuals. The addition of a mixed air temperature sensor enables the calculation of nine more residuals during operation in various states and at state transitions. In State 1, the supply air temperature is maintained by controlling the heating coil valve and the dampers are positioned to allow the minimum amount of outdoor air required for ventilation. Performing mass balances on the dry air and water vapor entering and leaving the control volume in Figure 6 yields

[FIGURE 6 OMITTED]

[m.sub.o] + [m.sub.r] = [m.sub.m] (19)

and

[m.sub.o][[omega].sub.o] + [m.sub.r][[omega].sub.r] = [m.sub.m][[omega].sub.m], (20)

where steady-state conditions are assumed for the control volume because the dampers are maintained in the minimum outdoor air position. Performing an energy balance on the control volume in Figure 6 gives

[m.sub.o][h.sub.o] + [m.sub.r][h.sub.r] = [m.sub.m][h.sub.m]. (21)

Substituting Equation 5 into Equation 21 and simplifying using Equation 20 yields

[m.sub.o][c.sub.p][T.sub.o] + [m.sub.r][c.sub.p][T.sub.r] = [m.sub.m][c.sub.p][T.sub.m]. (22)

Solving Equation 19 for [m.sub.r] and substituting into Equation 22 gives

[m.sub.o][c.sub.p]([T.sub.o]-[T.sub.r]) = [m.sub.m][c.sub.p]([T.sub.m]-[T.sub.r]). (23)

Solving for the fraction of outdoor air to mixed air yields

f = [[m.sub.o]/[m.sub.m]] = [[[T.sub.m]-[T.sub.r]]/[[T.sub.o]-[T.sub.r]]]. (24)

Using the design minimum fraction of outdoor air and measurements of the return air, outdoor air, and mixed air temperatures in State 1, residual [R.sub.5] is computed using the following:

[R.sub.5] = [f.sub.design]-[[[T.sub.m,1]-[T.sub.r,1]]/[[T.sub.o,1]-[T.sub.r,1]]] (25)

Because the dampers are stationary in State 1 and the temperatures are measured upstream of the heating coil, steady-state conditions are assumed to prevail, and [R.sub.5] can be evaluated as frequently as desired. However, since the outdoor and return air temperatures tend to vary somewhat slowly, there is little to be gained by evaluating the residual at the sampling frequency of the AHU controller (typically 10-20 s). In this study, [R.sub.5] is evaluated at 30 minute intervals while the AHU operates in State 1.

In State 2, the supply air temperature is controlled by modulating the mixing-box dampers, and the heating and cooling coil valves are closed. Because the mixed air and supply air temperatures are located downstream of the mixing-box dampers and the heating and cooling coil valves are closed, steady-state conditions are assumed to prevail for the control volume in Figure 7. Performing a mass balance on the dry air and water vapor entering and leaving the control volume in Figure 7 gives

[FIGURE 7 OMITTED]

[m.sub.m] = [m.sub.s] (26)

and

[m.sub.m][[omega].sub.m] = [m.sub.s][[omega].sub.s]. (27)

Substituting Equation 26 into Equation 27 yields

[[omega].sub.m] = [[omega].sub.s]. (28)

Performing an energy balance on the control volume in Figure 7 gives

[m.sub.m][h.sub.m] + [W.sub.fan] = [m.sub.s][h.sub.s]. (29)

Substituting Equations 5, 26, and 28 into Equation 29 and rearranging results in

[T.sub.s]-[T.sub.m] = [[W.sub.fan]/[[m.sub.s][c.sub.p]]]. (30)

Using measured values of the supply and mixed air temperatures obtained in State 2, residual [R.sub.6] is computed using the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (31)

Residual [R.sub.6] is evaluated at 30 minute intervals in State 2.

In State 3, the cooling coil valve is controlled to maintain the supply air temperature at set-point and the mixing-box dampers are at the 100% outdoor air position. Although there should be no recirculation flow for State 3, the control volume in Figure 6 and the associated analysis can be applied and Equation 25 adapted to yield the limiting case where the recirculation damper is closed. The result is

[R.sub.7] = 1-[[[T.sub.m,3]-[T.sub.r,3]]/[[T.sub.o,3]-[T.sub.r,3]]], (32)

where an outdoor air fraction equal to unity is assumed in State 3. Residual [R.sub.7] is evaluated at 30-minute intervals in State 3; however, because a transition from State 4 to State 3 requires the mixing-box dampers to stroke from the minimum to the 100% outdoor air position, which may take a minute or more, [R.sub.7] should not be evaluated immediately after such a transition. In this study, [R.sub.7] was not evaluated until the AHU had operated in State 3 for at least five minutes after a transition from State 4. A similar limitation on residual [R.sub.7] is not necessary when the AHU transitions from State 2 to State 3, because in this case the dampers are not making an abrupt transition.

A second residual in State 3 is determined from mass and energy balances on control volume CV-1 in Figure 8. Figure 8 illustrates that the recirculation air damper is closed, and there is no recirculation flow. Since control volume CV-1 is located upstream of the cooling coil and the dampers are fixed in the 100% outdoor air position, steady-state conditions are assumed. Performing a mass balance on the dry air and water vapor entering and leaving control volume CV-1 gives

[FIGURE 8 OMITTED]

[m.sub.o] = [m.sub.m] (33)

and

[m.sub.o][[omega].sub.o] = [m.sub.m][[omega].sub.m]. (34)

Next, performing an energy balance on control volume CV-1 yields

[m.sub.o][h.sub.o] = [m.sub.m][h.sub.m]. (35)

Substituting Equations 5, 33, and 34 into Equation 35 gives

[T.sub.o] = [T.sub.m]. (36)

Thus, residual [R.sub.8] is computed from

[R.sub.8] = [T.sub.o,3]-[T.sub.m,3], (37)

where [T.sub.o,3] and [T.sub.m,3] are the outdoor air and mixed air temperatures while in State 3. Residual [R.sub.8] is evaluated at 30 minute intervals in State 3. However, like residual [R.sub.7], [R.sub.8] is not evaluated until the AHU has operated in State 3 for at least five minutes following a transition from State 4 to enable the mixing-box dampers to stroke to their new positions.

In State 4, the dampers are positioned to allow the minimum outdoor air required for ventilation, and the cooling coil is used to maintain the supply air temperature at setpoint. For this situation, the control volume in Figure 6 and the associated analysis can be applied, and Equation 25 adapted to yield the following:

[R.sub.9] = [f.sub.design]-[[[T.sub.m,4]-[T.sub.r,4]]/[[T.sub.o,4]-[T.sub.r,4]]] (38)

Residual [R.sub.9] is evaluated at 30 minute intervals in State 4. However, like residuals [R.sub.7] and [R.sub.8], [R.sub.9] should not be evaluated immediately after a transition to State 4, because the dampers will be stroking from the 100% outdoor air position to the minimum position. In this study, [R.sub.9] was not evaluated until the AHU had operated in State 4 for at least five minutes.

Although residuals [R.sub.5], [R.sub.7], and [R.sub.9] are based on the same equation, the variances of the residuals will likely be different because the outdoor air fraction calculation is sensitive to small variations in temperature, particularly when the temperatures in the denominator (outdoor and return air temperatures) are close to one another, which can occur in States 3 and 4. In the simulation results (presented later in the paper), values of the outdoor air fraction residuals ([R.sub.3], [R.sub.4], [R.sub.5], [R.sub.7], and [R.sub.9]) were discarded if the outdoor and return air temperatures used to calculate them differed by less than 5[degrees]C (9[degrees]F).

During transitions from State 2 to State 3, the dampers are positioned for 100% outdoor air, and residual [R.sub.1] is determined using Equation 9. In addition, mass and energy balances applied to control volumes CV-1 and CV-2 in Figure 8 yield the following residuals:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (39)

[R.sub.11] = [T.sub.o,2[right arrow]3]-[T.sub.m,2[right arrow]3]-[T.sub.m,2[right arrow]3] (40)

Equation 39 is developed in a manner similar to Equation 31, and Equation 40 is developed in a manner similar to Equation 37. Residual [R.sub.10] could be eliminated, since it can be derived by combining residual [R.sub.1] and residual [R.sub.11]. However, it will be retained so that a fault with any of the temperature sensors used in the residuals (supply air, outdoor air, and mixed air temperatures) will affect at least two residuals. Residuals [R.sub.10] and [R.sub.11] are evaluated using temperatures recorded immediately prior to transition from State 2 to State 3.

In the same way, during transitions from State 3 to State 2, residual [R.sub.2] is determined using Equation 10. In addition, the following residuals are defined:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (41)

[R.sub.13] = [T.sub.o,3[right arrow]2]-[T.sub.m,3[right arrow]2] (42)

Residual [R.sub.12] could be eliminated since it can be derived by combining residual [R.sub.2] and residual [R.sub.13], however, as in the case of residual [R.sub.10], it will be retained so that a fault with any of the temperature sensors used in the residuals will affect at least two residuals. Residuals [R.sub.12] and [R.sub.13] are evaluated using temperatures recorded immediately prior to a transition from State 3 to State 2.

Residual Summary. Table 1 lists the residuals, the sensor requirements to compute the residuals, and the operational state or state transition for which each residual is applicable.

[TABLE OMITTED]

Control Performance Monitor

The control performance monitor algorithm uses exponentially weighted moving averages (EWMAs) to compute indices that quantify local-loop control system performance. The equation for computing an EWMA (Hunter 1986) is given by

[[bar.X].sub.t] = [[[infinity].summation over (j = 0)][lambda](1-[lambda]).sup.j][X.sub.t-j[delta]], (43)

where [[bar.X].sub.t]] is the EWMA of performance index X at time t, [lambda] is the exponential smoothing constant, [[X.sub.t-j[delta]]] is the value of performance index X at discrete time t-j[delta], and [delta] is the sample time for the analog-to-digital converter.

The term [lambda][(1-[lambda]).sup.j] is referred to as an exponential smoothing weight. As j increases, the contribution of [X.sub.t-j[delta]] in Equation 43 decreases exponentially. To determine an EWMA using Equation 43, all previous values of X must be stored. A recursive formula for calculating EWMAs is given by

[[bar.X].sub.t] = [[bar.X].sub.t-[delta]] + [lambda]([X.sub.t]-[[bar.X].sub.t-[delta]]), (44)

for which only the immediate past value of the EWMA (i.e., [[bar.X].sub.t-[delta]]) must be stored. The smoothing constant is selected based on the response characteristics of the feedback control system being monitored. Seem et al. (1997) provides guidelines for the upper and lower bounds of the smoothing constant as

[[delta]/[20[t.sub.s]]]<[lambda]<[[delta]/[5[t.sub.s]]],(45)

where [t.sub.s] is the settling time of the controller.

When [[lambda] = [delta]/5[t.sub.s]], the summation of the exponential smoothing weights between times t and t-5[t.sub.s] is approximately 0.632, which indicates that approximately 63.2% of the EWMA is based on the data between times t and t-5[t.sub.s]. When [[lamda] = [delta]/(20[t.sub.s])], approximately 63.2% of the EWMA is based on the data between times t and t-20[t.sub.s].

Seem et al. (1997) used performance indices to detect a number of AHU and VAV-box faults in laboratory and field testing. This paper emphasizes the use of performance indices for the control input to the heating coil valve and cooling coil valve for identifying faults in the AHU. The control input performance index is defined as

[[bar.u].sub.t] = [[bar.u].sub.t-[delta]] + [lambda]([u.sub.t]-[[bar.u].sub.t-[delta]]), (46)

where u is the control signal sent to the valve actuator. Saturated values of the control signal (either at the minimum or maximum value) indicate that the AHU is unable to satisfy the supply air temperature setpoint in the present state. Under typical operating conditions, the AHU will then transition to a new state that can satisfy the setpoint; however, design conditions and certain faults can cause the AHU to saturate at positions where transitions are not possible. There are four such positions associated with the finite state machine sequencing logic in Figure 2, namely:

* State 1 -- Heating coil valve control signal saturated in the maximum heating position. For example, a stuck damper could cause excess outdoor air to be introduced that could cause the heating load to exceed the heating coil capacity. Design conditions could also cause the heating (or cooling) load to exceed the coil capacity, but design conditions occur infrequently, and oversizing of equipment makes it unlikely that a saturated control signal would occur under normal operating conditions. This makes saturated control signals very useful as signatures of faulty operation.

* State 3 -- Cooling coil valve control signal saturated in the maximum cooling position. For example, a leaking heating coil valve could cause the cooling load to exceed the cooling coil capacity.

* State 4 -- Cooling coil valve control signal saturated in the minimum cooling position and conditions for transition to State 3 are not satisfied. For example, the cooling coil valve could be stuck open at a position that produces too much cooling, but the economizer switching logic may prevent a transition to State 3, which would eventually enable the AHU to transition to State 2 and then State 1 if necessary to regain control of the supply air temperature.

* State 4 -- Cooling coil valve control signal saturated in the maximum cooling position. The example described for State 3 is also applicable here.

State Transition Diagram

Figure 9 shows the state transition diagram of Figure 2 modified to reflect the integration of the model-based residuals and the saturation status of performance indices with the sequencing control strategy. This figure illustrates the well-defined conditions under which the model-based residuals and performance indices are computed.

DESCRIPTION OF THE SIMULATION TESTBED

The simulation testbed is based on established component and system models (Norford and Haves 1997; Haves et al. 1998; DeSimone 1995). The models are based on idealized flow relationships of a single-duct VAV AHU and the zones it serves and are implemented in HVACSIM+ (Park et al. 1985). Significant changes to the simulation testbed described by Norford and Haves (1997) are outlined below.

* The sequencing logic for supply air temperature control was replaced by an implementation of the finite state machine logic in Figure 2 (Seem et al. 1999), which was adapted to include calculations of residuals and performance indices. The supply air temperature reset strategy was altered to produce a fixed supply air temperature setpoint of 12.78[degrees]C (55[degrees]F) from April 1 through October 31, and a fixed setpoint of 15.56[degrees]C (60[degrees]F) for the remainder of the year.

* The mixing-box model, with separate minimum and modulating outdoor air dampers, was replaced with a model that has a single modulating outdoor air damper. In addition, the control was altered to keep the outdoor air damper 100% open at all times when the supply fan is running (Seem et al. 2000). The recirculation air damper modulates between 0% and 65% open, and the relief air damper modulates between 35% and 100% open. The recirculation and relief air damper positions correspond to how the dampers would be modulated in a traditional mixing-box control system with an outdoor air damper minimum position of 35% open.

* A heating coil, valve, and actuator were added to enable heating coil valve faults to be simulated.

Faults were simulated by implementing parameter and output overrides in the simulation code. The following faults were simulated:

* supply air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* return air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* mixed air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* outdoor air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* recirculation air damper stuck open, stuck closed, stuck 50% open

* recirculation air damper leakage (10% of full flow)

* cooling coil valve stuck 20% open

* cooling coil valve leakage (3% of full flow)

* heating coil valve stuck 10% open

* heating coil valve leakage (3% of full flow)

The temperature sensor faults are introduced by linearly increasing or decreasing the temperature sensor model offset parameter as time increases. The initial offset is 0[degrees]C (0[degrees]F), increasing to [+ or -]2[degrees]C ([+ or -]3.6[degrees]F) over a three-month period. A positive offset will produce an artificially low sensor reading and a negative offset will produce an artificially high sensor reading. The faults simulated are representative of common AHU faults (Yoshida et al. 1996).

Design values used in the residual calculations were determined through numerical experiments. The design mass flow rate of supply air [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is 10.53 kg/s (23.21 [lb.sub.m]/s), the supply fan power [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is 7.14 kW (24.36 x [10.sup.3] Btu/h), and the outdoor air fraction [f.sub.design] is 0.3. At conditions typical for the operation of an AHU, the constant pressure specific heat of moist air [[^.c].sub.p] is estimated to be 1.02 kJ/kg*[degrees]C (0.24 Btu/[lb.sub.m]*[degrees]F). The smoothing constant [lambda] used in the calculation of the EWMAs was set equal to 8.33 x [10.sup.-4].

Year-long simulations were performed using Chicago Typical Meteorological Year weather data (National Climatic Data Center 1981). Initial conditions for all simulations were established from the final conditions obtained by simulating a complete year of operation under normal operating conditions. All simulations correspond to one complete year of operation under either normal conditions or with a fault condition implemented. A 2.5 s time step was used in the simulations.

RESULTS

Detailed results from simulations of six faults are described in this section. All 13 residuals from Table 1 were calculated during the simulations to identify the dominant residuals for a system having supply, return, outdoor, and mixed air temperature sensors. If one or more of these sensors is not installed, a smaller number of residuals will be available. Recall that the temperature sensor offset faults are introduced gradually, with the offset increasing linearly from 0 to the maximum offset after three months of the year. The residuals presented for sensor offset faults are computed only for the final nine months of the year (i.e., after the sensor offset has achieved its maximum value). For the other faults considered, the residuals are calculated for the entire year. Finally, as discussed in the development of the residual equations, the outdoor air fraction residuals ([R.sub.3], [R.sub.4], [R.sub.5], [R.sub.7], and [R.sub.9]) are sensitive to small variations in the temperatures used to calculate them. Therefore, in the simulation results, values of these residuals were discarded if the outdoor and return air temperatures differed by less than 5[degrees]C (9[degrees]F).

Supply Air Temperature Offset Fault

Residuals for normal operation and a supply air temperature sensor offset fault of -2[degrees]C (-3.6[degrees]F) are shown in Figure 10. The upper plot in Figure 10 includes all residuals that compare the calculated outdoor air fraction to an expected value. The dimensionless magnitudes of the residuals are shown on the x-axis. The lower plot consists of the remaining residuals, which all have units of temperature.

[FIGURE 10 OMITTED]

Figure 10 shows that the dominant temperature residuals for this supply air temperature sensor offset fault are [R.sub.1], [R.sub.2], [R.sub.6], [R.sub.10], and [R.sub.12]. The absolute value of the difference between the median values of these residuals for normal and faulty operation ranges from 2.00[degrees]C to 2.06[degrees]C (3.60[degrees]F to 3.71[degrees]F). The median values of the dominant outdoor air fraction residuals, [R.sub.3] and [R.sub.4], differ by only 0.08 from those for normal operation. The magnitudes of the residuals impacted by the fault will vary with the severity of the fault.

Although residuals [R.sub.5], [R.sub.7], and [R.sub.9] are based on the same equation, the range of values for these residuals for normal operation is considerably different. While perfect measurements (i.e., there are no sensor errors) are assumed for normal operation, the temperature sensors have time constants that differ, with the time constant of the outdoor air temperature sensor being ten times that of the supply, return, and mixed air temperature sensors (300 vs. 30 s). This difference and the fact that the outdoor and return air temperatures are much closer to one another in States 3 and 4 than they are in State 1 results in the larger range of values observed for [R.sub.7] and [R.sub.9], in comparison to [R.sub.5].

All of the dominant residuals correspond to operation when the heating and cooling coil valves are closed. In this operating state, the temperature rise or drop across the two coils should be 0 when steady-state conditions prevail, as happens at the end of the state transition delay. Thus, the expected value of the supply air temperature can be easily related to the mixed air temperature and, if the outdoor air dampers are 100% open, to the outdoor air temperature. Residuals [R.sub.11] and [R.sub.13] are also computed when the heating and cooling coil valves are closed, however, they utilize sensors that are not affected by this particular fault. If either the heating or cooling coil valve is open (partially or fully), the temperature rise or drop becomes difficult to predict in the absence of a coil model.

Outdoor Air Temperature Offset Fault

The residuals for normal operation and an outdoor air temperature sensor offset fault of -2[degrees]C (-3.6[degrees]F) are shown in Figure 11. For this fault, residuals [R.sub.1], [R.sub.2], [R.sub.7], [R.sub.8], [R.sub.11], and [R.sub.13] show a significant departure from their values for normal operation. Each of these residuals is computed when the AHU operates with 100% outdoor air (i.e., either in State 3 or at transitions between States 2 and 3). The median values of the data clusters for normal and faulty operation differ by approximately 2[degrees]C (3.6[degrees]F) for the temperature residuals ([R.sub.1], [R.sub.2], [R.sub.8], [R.sub.11], and [R.sub.13]) and by approximately 0.31 for the outdoor air fraction residual [R.sub.7]. The outdoor air fraction residuals [R.sub.3], [R.sub.4], [R.sub.5], and [R.sub.9] are also impacted to a small degree by the fault; however, the largest difference in the median values for normal and faulty operation is only 0.07 to 0.08 for residual [R.sub.9]. Furthermore, the data clusters for normal and faulty operation overlap, so [R.sub.9] will not always be a reliable indicator of the presence of this fault.

[FIGURE 11 OMITTED]

Stuck-Open Recirculation Air Damper

The residuals for normal operation and a stuck-open recirculation air damper fault are shown in Figure 12. The residuals affected by the fault are [R.sub.1], [R.sub.2][R.sub.7], [R.sub.8], [R.sub.11], and [R.sub.13], which are calculated when the control sequence calls for 100% outdoor air, and normal operation dictates that the recirculation air damper is closed. The mixing-box model includes damper leakage parameters that, when set to their default values for normal operation, allow approximately 2% leakage through the recirculation damper when 100% outdoor air is desired, and the recirculation damper is closed. In comparison, the stuck-open recirculation air damper fault causes mixing of approximately 34% return air and 66% outdoor air when 100% outdoor air is desired. The result is a mixed air temperature that is frequently significantly warmer than expected. With the exception of [R.sub.7], all of the residuals affected by the fault are temperature residuals having magnitudes that can exceed 4[degrees]C (7.2[degrees]F). The two distinct clusters of data points for residuals [R.sub.1], [R.sub.2], [R.sub.11], and [R.sub.13] result from the two supply air setpoint temperatures used in the simulation. Also, note that while the magnitude of residual [R.sub.8] frequently exceeds 4[degrees]C (7.2[degrees]F), this residual, which compares the outdoor and mixed air temperatures during operation in State 3, has a broad range of values, and the residual range for normal operation overlaps that for faulty operation. The overlap of data clusters for residual [R.sub.8] occurs when the outdoor air temperature approaches the return air temperature, which causes the mixed air temperature to be insensitive to the fault. The other dominant residuals have distinct gaps between the clusters of data corresponding to normal and faulty operation.

[FIGURE 12 OMITTED]

The only outdoor air fraction residual affected by the stuck-open recirculation air damper fault is [R.sub.7]. Instead of an outdoor air fraction equal to unity, as expected for normal operation, the outdoor air fraction is approximately 0.64. As a result, the median values of the data clusters for normal and faulty operation differ by 0.33.

Stuck-Closed Recirculation Air Damper

The residuals for normal operation and a stuck-closed recirculation air damper fault are shown in Figure 13. The dominant residuals are [R.sub.3], [R.sub.4], [R.sub.5], and [R.sub.9]. All are outdoor air fraction residuals calculated when the control sequence calls for minimum outdoor air, which corresponds to a recirculation air damper positioned fully open for a normally operating system. The stuck-closed recirculation air damper results in an outdoor air fraction that is approximately equal to 0.9, instead of the design value of 0.3 that is expected at minimum outdoor air. Thus, the dominant residuals differ in magnitude by approximately 0.6 from their corresponding values for normal operation. The fault cannot be identified using the temperature residuals because, with the exception of [R.sub.6], all of the temperature residuals are calculated when the dampers are positioned for 100% outdoor air (either in State 3 or at transitions between States 2 and 3), which corresponds to a closed recirculation damper for normal operation. Residual [R.sub.6] is computed from an energy balance across the coils and supply fan, so the fault does not affect this calculation.

[FIGURE 13 OMITTED]

A time series plot of the dominant residuals is shown in Figure 14. Because the dominant residuals are applicable in two operating states ([R.sub.5] in State 1 and [R.sub.9] in State 4) and at the transitions between States 1 and 2 ([R.sub.3] and [R.sub.4]), the fault can be detected throughout the year. Although difficult to see in Figure 14, the data reveal that the AHU operates in the heating mode for periods of time in late May to compensate for the excess outdoor air that enters due to the fault. Although not shown, for normal operation the heating mode is not needed after the end of March.

[FIGURE 14 OMITTED]

Figure 15 is a time series plot of the EWMA of the control signal to the cooling coil valve, [[bar.u].sub.t,cc], for the stuck-closed recirculation air damper fault. This performance index saturates numerous times while operating in State 4 during the summer months, indicating the AHU has insufficient capacity to satisfy the load placed on it and is out of control. This will not happen with a properly sized and normally operating system, so the saturation status of [[bar.u].sub.t,cc] can also be used to detect the fault and provides redundancy for the information provided by the residuals.

[FIGURE 15 OMITTED]

Leaking Cooling Coil Valve

The residuals for normal operation and a leaking cooling coil valve fault are shown in Figure 16. For this fault the valve leakage parameter in the model was set equal to 3% but actually produces a leakage rate when the cooling coil valve is commanded closed that is approximately 5% of the flow when the valve is 100% open. By comparison, the normal leakage when the cooling coil valve is commanded closed is essentially zero. The residuals affected by this fault are [R.sub.1], [R.sub.2], [R.sub.3], [R.sub.4], [R.sub.6], [R.sub.10], and [R.sub.12]. The residuals all correspond to operating conditions for which the cooling coil and heating coil valves are closed (transitions between States 1 and 2, operation in State 2, and transitions between States 2 and 3). Furthermore, all of the residuals affected by the fault are functions of the supply air temperature. Note that the data points for the affected residuals are not clustered in tight groups as they have generally been for previous faults. This spread in the residuals is due to the variation of the airflow rate across the coil, which causes the temperature drop across the coil to vary and ultimately causes the compensation by the mixing-box dampers to vary. The supply airflow rate varies between 29% and 51% of the design flow rate during operation in State 2.

[FIGURE 16 OMITTED]

Stuck Heating Coil Valve

The residuals for normal operation and a stuck heating coil valve fault are shown in Figure 17. The valve is stuck 10% open, resulting in a constant flow rate of 0.09 kg/s (0.20 [lb.sub.m]/s) of heated water through the coil. This is approximately 47% of the largest flow through the heating coil under normal operating conditions (for normal operation, the control signal to the heating coil valve never exceeded 30% open). The stuck valve results in unnecessary and/or excessive heating at certain times and insufficient heating at other times. The same seven residuals ([R.sub.1], [R.sub.2], [R.sub.3], [R.sub.4], [R.sub.6], [R.sub.10], and [R.sub.12]) impacted by the cooling coil valve leakage fault are affected by the stuck heating coil valve fault. The dominant residuals all correspond to operating conditions for which the cooling coil and heating coil valves are closed. The dominant temperature residuals range in magnitude from approximately 2[degrees]C to 4[degrees]C (3.6[degrees]F to 7.2[degrees]F), with smaller residual values occurring at higher supply airflow rates.

[FIGURE 17 OMITTED]

The outdoor air fraction residuals impacted by the stuck heating coil valve ([R.sub.3], [R.sub.4]) have magnitudes approximately equal to 0.1 and are computed at transitions between State 1 and State 2 when the AHU operates with minimum outdoor air. The fault causes the AHU to operate in State 2 at lower outdoor air temperatures than it ordinarily would. For normal operation, the outdoor air temperature at transitions between States 1 and 2 ranges from approximately -2[degrees]C to 1.5[degrees]C (28.4[degrees]F to 34.7[degrees]F), whereas it ranges from approximately -13[degrees]C to -6[degrees]C (8.6[degrees]F to 21.2[degrees]F) for this fault. The result is that cold outdoor air in excess of the ventilation rate is introduced to the AHU to compensate for the fault.

Figure 18 is a time series plot of residual [R.sub.6], which compares the mixed air temperature and supply air temperature in State 2 and is one of the dominant residuals for the stuck heating coil valve fault. Figure 18 reveals that the fault can be detected using residual [R.sub.6] during the first five months and the last three months of the year. Although not shown, the other dominant residuals are calculated at transitions between States 2 and 3, which occur primarily during March through May as well as October and November.

[FIGURE 18 OMITTED]

Figure 19 is a time series plot of the EWMA of the control signal to the heating coil valve, [[bar.u].sub.t,hc], for the stuck heating coil valve fault. The performance index saturates once during winter operation (Time [approximately equal to] 30 days) while the AHU operates in State 1, indicating the AHU has insufficient capacity to satisfy the load placed on it and is out of control. It is important to recognize that the only residual that is applicable in State 1 is residual [R.sub.5], and it is unaffected by the fault. Thus, [[bar.u].sub.t,hc] detects the fault under conditions that the model-based residuals do not.

[FIGURE 19 OMITTED]

Summary of Model-Based Residual Results

Results for all of the faults considered in this study are summarized in Table 2 in terms of the absolute value of the difference between the median values of the residuals for normal and faulty operation. Symbols are used to designate different residual types and magnitudes of the differences. Squares represent outdoor air fraction residuals and circles represent temperature residuals. Large symbols represent large differences in magnitude (greater than 0.3 for the outdoor air fraction residuals and greater than 3.0[degrees]C [5.4[degrees]F] for the temperature residuals), and small symbols represent small differences (between 0.1 and 0.3 for the outdoor air fraction residuals and between 1.0[degrees]C [1.8[degrees]F] and 3.0[degrees]C [5.4[degrees]F] for the temperature residuals). Empty cells indicate the difference in magnitude is less than 0.1 for outdoor air fraction residuals and less than 1.0[degrees]C (1.8[degrees]F) for temperature residuals. The boundaries used to classify a change in a residual value as a large, small, or no difference are intended to enable readers to quickly identify residual differences of similar magnitudes. These boundaries are not intended to be used as thresholds for fault detection.

Table 2 shows that with the exception of the return air temperature sensor offset faults, each fault had four or more residuals for which the magnitude of the differences in the median values for normal and faulty operation exceeded 0.1 for outdoor air fraction residuals, and 1.0[degrees]C (1.8[degrees]F) for temperature residuals. In addition, the results indicate that residuals [R.sub.1] and [R.sub.2] may be adequate for detecting all of the damper and valve faults considered, except for the stuck-closed recirculation air damper fault. Residuals [R.sub.1] and [R.sub.2] only require measurements of the supply air and outdoor air temperatures. With the addition of return air temperature measurement, residuals [R.sub.3] and [R.sub.4] can be calculated and used to detect the stuck-closed recirculation air damper fault.

As noted in the discussion of the supply air temperature sensor fault, the magnitude of the residuals impacted by a particular fault will vary with the severity of the fault. As seen in the results for the cooling coil valve leakage fault and the stuck heating coil valve, the magnitudes will also vary with the operating condition of the AHU. In this study, the severities of the faults were selected to be large enough to enable the impacted residuals to be distinguished from those that are largely unaffected by a particular fault. In a field application of the method, it would be necessary to establish robust thresholds for the residuals separating normal and faulty operation. These thresholds would identify when a residual is too large, thereby signaling a fault, and would be broadly applicable in AHUs but would not be indicative of a particular severity of a fault (e.g., a 5% leakage through the cooling coil valve).

This study did not consider cases with multiple simultaneous faults; however, there is nothing inherent to the method that limits its applicability to single-fault cases.

CONCLUSIONS AND FUTURE WORK

This paper described an integrated control and fault detection method for AHUs. The method integrates the calculation of model-based residuals derived from mass and energy balances, and state-based performance indices of control loops, with the finite state machine sequencing logic of the AHU. The method uses available temperature sensor measurements, eliminates the need for a steady-state detector algorithm and, over time, provides a rich data set collected under very specific operating conditions for which expected operation is well defined. For a complete sensor suite that includes the supply, return, outdoor, and mixed air temperature sensors, a total of 13 residuals are calculated that form the basis for identifying operational faults.

The integrated control and fault detection method was assessed through simulations of 16 faults that consisted of temperature sensor offset faults, stuck and leaking damper faults, and stuck and leaking valve faults. With the exception of the return air temperature sensor offset faults, each fault impacted numerous residuals. In addition, two faults (stuck-closed recirculation air damper and heating coil valve stuck 10% open) caused control performance indices to saturate, which should not happen to a properly designed and operating system. In the case of the stuck-closed recirculation air damper, the saturated control signal to the cooling coil valve provided redundancy for the residuals. For the stuck heating coil valve fault, the performance index for the control signal to the heating coil valve saturated in State 1. The residuals were unaffected by this particular fault in State 1. Thus, the control performance monitor complements the model-based residuals by enabling the detection of certain faults under operating conditions for which the residuals cannot detect the fault.

The ultimate goal in the development of the integrated control and fault detection method is to enable the automatic detection of faults by establishing thresholds for each residual that separate normal and faulty operation. This study represents the first step in that development process. The next step will likely entail testing under controlled conditions in a physical test bed where faults can be introduced artificially. This would enable a better assessment of the robustness of the method to imperfect measurements and an evaluation of the adequacy of the state transition delay for establishing steady-state conditions, and would provide some insight into the selection of thresholds for fault detection. The final step in the development process would be to install and test the integrated control and fault detection method at a number of field sites. Data representative of normal operation and naturally occurring faults could then be collected and analyzed to establish robust statistical ranges for each residual under normal operation that would enable automatic detection of faults and would be generally applicable in single-duct AHUs.

Testing with multiple simultaneous faults is not planned and is considered less important than the steps outlined above because the method described here is concerned only with fault detection. Simultaneous faults could mask one another, and by doing so, might prevent their detection. If, on the other hand, one or more residuals indicate the presence of a fault, human intervention would be required to properly diagnose whether there was one or more than one fault. If the goal of a method is to automatically detect and diagnose a fault or faults, then testing with multiple simultaneous faults would be more important and perhaps even a requirement of a rigorous development process.

ACKNOWLEDGMENTS

The authors would like to thank Dr. Cheol Park of the National Institute of Standards and Technology in Gaithersburg, MD, for providing source code for the sequencing logic and fault cases that were adapted for this study.

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John E. Seem, PhD

Member ASHRAE

John M. House, PhD

Member ASHRAE

Received June 17, 2008; accepted October 10, 2008

John E. Seem is a research fellow and John House is a principal research engineer at Johnson Controls, Inc., Milwaukee, WI.

The development of fault detection and diagnosis (FDD) methods for HVAC applications has been an area that has been actively researched for more than a decade. Numerous studies report methods developed for application to central air-handling units (AHUs) based on either passive monitoring, where data are collected without interrupting the normal operation of the system (e.g., Haves et al. 1996; Dexter and Benouarets 1996; Lee et al. 1996a, 1996b, and 1997; Katipamula et al. 1999; House et al. 1999 and 2001; Norford et al. 2002), or active testing, where data are collected that result from overrides of control signals and setpoints (e.g., Kelso and Wright 2005; Xu et al. 2005; Haves et al. 2007; Katipamula and Brambley 2007). Katipamula and Brambley (2005a and 2005b) provide a review of the literature on the topic of FDD methods for HVAC applications published prior to 2005.

The development and implementation of an FDD method involves a trade-off between the sensitivity of the method to faults and the number of false alarms that it will generate (Reddy 2007; Katipamula and Brambley 2007). The development of robust FDD methods for the HVAC industry is challenged by the fact that there are limited sensors available for use in analyses (due to cost considerations, only those necessary to control the equipment are commonly installed), the equipment and systems have nonlinear characteristics, and the loads on the system are time varying. Methods can be made more sensitive to faults and less likely to create false alarms if the data they process are collected under well-defined and well-controlled conditions. For this reason, AHU FDD methods are commonly based on analyses of data collected while operating in steady state. For AHU FDD methods implemented as on-line monitoring tools, a filtering algorithm, commonly referred to as a steady-state detector, is often used to collect data while the system operates in steady state and to discard data from transient operation (e.g., Haves et al. 1996; House et al. 1999 and 2001). For AHU FDD methods implemented as commissioning tools (i.e., those that utilize active testing), steady-state data can be obtained by overriding a control signal and forcing the AHU into a particular operating state until steady-state conditions prevail (Kelso and Wright 2005; Xu et al. 2005; Haves et al. 2007; Katipamula and Brambley 2007).

Both approaches to obtaining steady-state data have drawbacks. Because unstable operation is prevalent in AHUs, a well-designed steady-state detector could discard large portions of the operational data, leaving little data for an on-line FDD method to process. FDD methods that rely on injected test signals would be used intermittently and may require an operator to either manually introduce the test signals or to monitor the test as it progresses. Thus, faults could exist for significant periods of time before they are discovered, because data are being discarded or collected infrequently.

This paper describes a simulation study of a new method for integrated control and fault detection of AHUs that overcomes these drawbacks. The method uses sensors commonly installed in AHUs and collects much of the key diagnostic information at times when steady-state conditions are imposed on the AHU by the sequencing logic, thereby eliminating the need for a steady-state detector. This enables the method to continuously monitor the AHU operation and over time produces a rich data set collected under controlled conditions. A model-based fault detection method processes these data and generates residual values that can be further processed to identify faults. In parallel, an algorithm monitors the saturation status of control loops for the processes used for sequential control of the AHU.

The paper is organized in the following manner. First, the AHU system description and finite state machine sequencing control are described. This is followed by descriptions of the integrated control and fault detection method and the simulation environment used to evaluate the method. Results obtained for six faults are then discussed in detail, and a table summarizing the results for all faults considered in the study is presented. Finally, conclusions and recommendations for future work are provided.

AHU SYSTEM DESCRIPTION

Figure 1 is a schematic diagram of a single-duct central AHU. Outdoor air enters the AHU and is mixed in the mixed air plenum with recirculated air returned from the building. The supply fan draws mixed air through the heating and cooling coils where it is conditioned, if necessary, prior to being distributed to the building through the supply duct. Return air from the building is either exhausted or recirculated to mix with outdoor air. The outdoor, recirculation, and relief airflow rates are controlled by their respective dampers (collectively called the mixing-box dampers) and by the supply and return fans.

[FIGURE 1 OMITTED]

In variable-air-volume (VAV) AHUs, the supply air temperature is commonly controlled to satisfy a setpoint value. Feedback control is used to modulate the heating coil valve, cooling coil valve, and mixing-box dampers to achieve the setpoint. An AHU controller uses sequencing control logic to determine the proper component(s) to use to control the temperature at any given time. Seem et al. (1999) and ASHRAE (2007) describe a sequencing strategy for AHUs based on finite state machine logic. A state transition diagram illustrating the logic for the sequencing strategy is shown in Figure 2. The description of each operating state is summarized in the rounded boxes and described further below. The conditions necessary for transitions between states are provided adjacent to the arrows connecting the states.

[FIGURE 2 OMITTED]

State 1

In State 1, feedback control is used to modulate the amount of energy transferred from the heating coil to the air. The mixing-box dampers are positioned to provide the minimum outdoor airflow rate required for ventilation and the cooling coil valve is closed. The transition to State 2 occurs after the control signal has saturated in the no-heating position (i.e., closed). The control signal is considered saturated in the no-heating position when it has been continuously at this position for a time period equal to the state transition delay. A state transition delay of five minutes was used in this study.

State 2

In State 2, feedback control is used to modulate the mixing-box dampers in order to maintain the supply air temperature at the setpoint value. Adjusting the positions of the dampers varies the relative amounts of outdoor air and return air in the supply airstream. In State 2, the heating and cooling coil valves are closed. The transition to State 1 occurs after the control signal for the dampers has been at the minimum outdoor air position for a time period equal to the state transition delay. Transition to State 3 occurs after the control signal for the dampers has been at the 100% outdoor air position for a time period equal to the state transition delay.

State 3

In State 3, feedback control is used to modulate the flow of chilled water to the cooling coil, thereby controlling the amount of energy extracted from the air. The mixing-box dampers are positioned for 100% outdoor air, and the heating coil valve is closed. Transition to State 2 occurs after the control signal for mechanical cooling has been saturated at the no-cooling position for a time period equal to the state transition delay. Economizer logic is used to determine the transition to State 4. Enthalpy-based, temperature-based or combined enthalpy and temperature economizer logic may be used. In the state transition diagram shown in Figure 2, logic based on the outdoor air temperature is used to determine the transition point. Transition to State 4 occurs when the outdoor air temperature is greater than the switchover temperature plus the deadband temperature. Typically, the switchover temperature is equal to the return air temperature, and the deadband is about 0.56[degrees]C (1[degrees]F). The deadband prevents cycling from State 3 to State 4 caused by noise in the return and outdoor air temperature sensor readings.

State 4

State 4 also uses feedback control to modulate the flow of chilled water to the cooling coil, thereby controlling the amount of energy extracted from the air. However, in this case, the mixing-box dampers are set at the minimum outdoor air position. Economizer logic is used to determine the transition to State 3. In the state transition diagram shown in Figure 2, transition to State 3 occurs when the outdoor air temperature is less than the switchover temperature.

INTEGRATED CONTROL AND FAULT DETECTION SYSTEM

FDD methods can be classified as either model-free methods or model-based methods (Gertler 1998). Model-free methods include methods based on: 1) physical redundancy, in which multiple sensors are installed to measure the same physical quantity; 2) special sensors installed to specifically detect and diagnose particular faults; 3) limit checking, in which process variables are compared to thresholds; 4) spectrum analysis to detect and identify faults in rotating machinery; and 5) logic reasoning approaches. As the name implies, model-based methods use a model of a process to calculate expected values of specific variables. The expected values are compared to measured values and the differences, or residuals, are evaluated to determine if a fault exists.

The overall structure of the integrated control and fault detection system is shown in the block diagram in Figure 3. A finite state machine is used to provide sequential control of the devices. Based on the current state or state transition, observations are passed from the finite state machine to the model-based residual generation block. This block determines residuals based on mass and energy balances of the system. Within the finite state machine, a control performance monitor calculates state-based performance indices for the control loops. The residuals and state-based performance indices are passed to the fault analysis block. The following sections describe the model-based residual calculations and the control performance monitor.

[FIGURE 3 OMITTED]

Model-Based Residuals

The ability to detect faults in HVAC systems is limited by the available measurement and control points. While AHUs commonly have sensors for measuring the supply, return, outdoor, and mixed air temperatures, one or more of these sensors may be missing in a particular system. Thus, fault detection systems based on model-based residuals are presented for combinations of sensors as outlined below:

* supply and outdoor air temperature sensors

* supply, return, and outdoor air temperature sensors

* supply, return, outdoor, and mixed air temperature sensors

System 1: Supply and Outdoor Air Temperature Sensors. For AHUs having only supply and outdoor air temperature sensors, model-based residuals are determined only at transitions between States 2 and 3. From Figure 2, a transition from State 2 to State 3 occurs after the damper control signal has been saturated in the 100% outdoor air position for a period of time equal to the state transition delay. At this condition, the AHU is assumed to be in steady state. A similar assumption of steady-state operation is used for all residuals calculated at a state transition. Assuming steady-state conditions prevail, mass balances on the dry air and water vapor entering and leaving the control volume in Figure 4 yield

[FIGURE 4 OMITTED]

[m.sub.o] = [m.sub.s] (1)

and

[m.sub.o][[omega].sub.o] = [m.sub.s][[omega].sub.s], (2)

where [m.sub.o] is the mass of dry air entering the control volume, [m.sub.s] is the mass of dry air leaving the control volume through the supply air duct, and [omega.sub.o] and [omega.sub.s] are the humidity ratios of the outdoor air and supply air, respectively. Using Equation 1, Equation 2 simplifies to

[[omega].sub.o] = [[omega].sub.s]. (3)

Performing an energy balance on the control volume with the assumption that the kinetic and potential energy of the air entering and leaving the control volume are the same (an assumption applied throughout the development of the model-based residuals) gives the following:

[m.sub.o][h.sub.o] + [W.sub.fan] = [m.sub.s][h.sub.s] (4)

where [h.sub.o] and [h.sub.s] are the enthalpy of the outdoor air and supply air, respectively, [W.sub.fan] and is the power input to the fan. Air can be modeled as an ideal gas at the temperatures found in HVAC systems (Kuehn et al. 1998). Using the ideal-gas assumption, the enthalpy of air is given by

h = [c.sub.p]T + [omega][h.sub.g0], (5)

where [c.sub.p] is the specific heat of the moist air mixture, and [h.sub.g0] is the enthalpy of water vapor at the reference state. The specific heat of the mixture is determined from

[c.sub.p] = [c.sub.pa] + [omega][c.sub.pw], (6)

where [c.sub.pa] is the specific heat at constant pressure of dry air and [c.sub.pw] is the specific heat at constant pressure of water vapor. Substituting Equation 5 into Equation 4 gives

[m.sub.o]([c.sub.p][T.sub.o] + [[omega].sub.o][h.sub.g0]) + [W.sub.fan] = [m.sub.s]([c.sub.p][T.sub.s] + [[omega].sub.s][h.sub.g0]). (7)

Substituting Equation 1 and Equation 3 into Equation 7 and solving for the difference between the supply and outdoor air temperatures gives

[T.sub.s]-[T.sub.o] = [[W.sub.fan]/[[m.sub.s][c.sub.p]]]. (8)

Thus, at the transition from State 2 to State 3, the difference between the supply and outdoor air temperatures is due to the energy gained from the fan. The supply airflow rate and fan power will vary with the load in a VAV air-handling system, and while the volumetric airflow rate may be measured, the fan power typically is not. Thus, to evaluate Equation 8, the specific heat of the moist air mixture, the fan power, and possibly the supply air mass flow rate will need to be estimated. The specific heat can be estimated for typical operating conditions and the fan power and mass flow rate can be estimated from design data. Residual [R.sub.1] is then computed from

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where [[T.sub.s,2[right arrow]3]] and [[T.sub.o,2[right arrow]3]] are the supply and outdoor air temperatures recorded immediately prior to the transition (i.e., at the end of the state transition delay) from State 2 to State 3 when steady-state conditions are expected to prevail, and the symbol ^ over the variables on the right-hand side of Equation 9 indicates an estimated value.

The transition from State 3 to State 2 occurs after the cooling coil valve control signal is saturated in the no-cooling position for a period of time equal to the state transition delay. Equations 1-8 can again be applied, and residual [R.sub.2] is defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [[T.sub.s,3[right arrow]2]] and [[T.sub.o,3[right arrow]2]] are the supply and outdoor air temperatures recorded immediately prior to the transition from State 3 to State 2.

For a properly controlled AHU, transitions between States 2 and 3 should be closely tied to the outdoor air temperature, which generally increases monotonically in the morning and decreases monotonically in the late afternoon or evening. Thus, there may only be one transition from State 2 to State 3 and one transition from State 3 to State 2 in a day, or there may be none at all, so the number of data points accumulated in a given day or week for residuals [R.sub.1] and [R.sub.2] is expected to be small. The same is true for the six additional residuals to be defined in the ensuing sections that are calculated at state transitions. Although limited in number, these residuals are collected under well-controlled conditions, making the data quality similar to that resulting from a manual override of the AHU into a specific operating mode. Furthermore, the residuals are collected on a continuous and automatic basis (i.e., whenever the appropriate state transition occurs) as part of the normal control sequence, which is an advantage over an approach that overrides the normal control of the AHU, even if it is done automatically.

System 2: Supply, Return, and Outdoor Air Temperature Sensors. System 2 utilizes supply, return, and outdoor air temperature sensors. Adding a return air temperature sensor enables the calculation of residuals at transitions between States 1 and 2 as the AHU operates with minimum outdoor air and the heating and cooling coil valves are closed. Figure 5 shows a control volume used to perform steady-state mass and energy balances at transitions between States 1 and 2. Performing a mass balance for the dry air and water vapor entering and leaving the control volume gives the following:

[FIGURE 5 OMITTED]

[m.sub.o] + [m.sub.r] = [m.sub.s] (11)

and

[m.sub.o][[omega].sub.o] + [m.sub.r][[omega].sub.r] = [m.sub.s][[omega].sub.s] (12)

Performing a steady-state energy balance on the control volume in Figure 5 gives

[m.sub.o][h.sub.o] + [m.sub.r][h.sub.r] + [W.sub.fan] = [m.sub.s][h.sub.s]. (13)

Substituting Equation 5 into Equation 13 and simplifying using Equation 12 yields

[m.sub.o][c.sub.p][T.sub.o] + [m.sub.r][c.sub.p][T.sub.r] + [W.sub.fan] = [m.sub.s][c.sub.p][T.sub.s]. (14)

Solving Equation 11 for [m.sub.r] and substituting into Equation 14 gives

[m.sub.o][c.sub.p]([T.sub.o]-[T.sub.r]) = [m.sub.s][c.sub.p]([T.sub.s]-[T.sub.r])-[W.sub.fan]. (15)

Finally, rearranging Equation 15 yields an equation for the fraction of outdoor air, f, entering the AHU:

f = [[m.sub.o]/[m.sub.s]] = [[[T.sub.s]-[T.sub.r]-[[W.sub.fan]/[[m.sub.s][c.sub.p]]]]/[[T.sub.o]-[T.sub.r]]] (16)

where the final term in the numerator is the temperature rise across the supply fan. Residual [R.sub.3] is based on the outdoor air fraction in Equation 16 and is calculated by using the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

where [f.sub.design] is the design outdoor air fraction and [T.sub.s,1[right arrow]2], [T.sub.r,1[right arrow]2] and [T.sub.o,1[right arrow]2] are the supply, return, and outdoor air temperatures recorded immediately prior to a transition from State 1 to State 2.

In the same way, residual [R.sub.4] is calculated using temperatures recorded immediately prior to a transition from State 2 to State 1 and is calculated by using the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

System 3: Supply, Return, Outdoor, and Mixed Air Temperature Sensors. System 3 utilizes the supply, return, outdoor, and mixed air temperature sensors for calculating model-based residuals. The addition of a mixed air temperature sensor enables the calculation of nine more residuals during operation in various states and at state transitions. In State 1, the supply air temperature is maintained by controlling the heating coil valve and the dampers are positioned to allow the minimum amount of outdoor air required for ventilation. Performing mass balances on the dry air and water vapor entering and leaving the control volume in Figure 6 yields

[FIGURE 6 OMITTED]

[m.sub.o] + [m.sub.r] = [m.sub.m] (19)

and

[m.sub.o][[omega].sub.o] + [m.sub.r][[omega].sub.r] = [m.sub.m][[omega].sub.m], (20)

where steady-state conditions are assumed for the control volume because the dampers are maintained in the minimum outdoor air position. Performing an energy balance on the control volume in Figure 6 gives

[m.sub.o][h.sub.o] + [m.sub.r][h.sub.r] = [m.sub.m][h.sub.m]. (21)

Substituting Equation 5 into Equation 21 and simplifying using Equation 20 yields

[m.sub.o][c.sub.p][T.sub.o] + [m.sub.r][c.sub.p][T.sub.r] = [m.sub.m][c.sub.p][T.sub.m]. (22)

Solving Equation 19 for [m.sub.r] and substituting into Equation 22 gives

[m.sub.o][c.sub.p]([T.sub.o]-[T.sub.r]) = [m.sub.m][c.sub.p]([T.sub.m]-[T.sub.r]). (23)

Solving for the fraction of outdoor air to mixed air yields

f = [[m.sub.o]/[m.sub.m]] = [[[T.sub.m]-[T.sub.r]]/[[T.sub.o]-[T.sub.r]]]. (24)

Using the design minimum fraction of outdoor air and measurements of the return air, outdoor air, and mixed air temperatures in State 1, residual [R.sub.5] is computed using the following:

[R.sub.5] = [f.sub.design]-[[[T.sub.m,1]-[T.sub.r,1]]/[[T.sub.o,1]-[T.sub.r,1]]] (25)

Because the dampers are stationary in State 1 and the temperatures are measured upstream of the heating coil, steady-state conditions are assumed to prevail, and [R.sub.5] can be evaluated as frequently as desired. However, since the outdoor and return air temperatures tend to vary somewhat slowly, there is little to be gained by evaluating the residual at the sampling frequency of the AHU controller (typically 10-20 s). In this study, [R.sub.5] is evaluated at 30 minute intervals while the AHU operates in State 1.

In State 2, the supply air temperature is controlled by modulating the mixing-box dampers, and the heating and cooling coil valves are closed. Because the mixed air and supply air temperatures are located downstream of the mixing-box dampers and the heating and cooling coil valves are closed, steady-state conditions are assumed to prevail for the control volume in Figure 7. Performing a mass balance on the dry air and water vapor entering and leaving the control volume in Figure 7 gives

[FIGURE 7 OMITTED]

[m.sub.m] = [m.sub.s] (26)

and

[m.sub.m][[omega].sub.m] = [m.sub.s][[omega].sub.s]. (27)

Substituting Equation 26 into Equation 27 yields

[[omega].sub.m] = [[omega].sub.s]. (28)

Performing an energy balance on the control volume in Figure 7 gives

[m.sub.m][h.sub.m] + [W.sub.fan] = [m.sub.s][h.sub.s]. (29)

Substituting Equations 5, 26, and 28 into Equation 29 and rearranging results in

[T.sub.s]-[T.sub.m] = [[W.sub.fan]/[[m.sub.s][c.sub.p]]]. (30)

Using measured values of the supply and mixed air temperatures obtained in State 2, residual [R.sub.6] is computed using the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (31)

Residual [R.sub.6] is evaluated at 30 minute intervals in State 2.

In State 3, the cooling coil valve is controlled to maintain the supply air temperature at set-point and the mixing-box dampers are at the 100% outdoor air position. Although there should be no recirculation flow for State 3, the control volume in Figure 6 and the associated analysis can be applied and Equation 25 adapted to yield the limiting case where the recirculation damper is closed. The result is

[R.sub.7] = 1-[[[T.sub.m,3]-[T.sub.r,3]]/[[T.sub.o,3]-[T.sub.r,3]]], (32)

where an outdoor air fraction equal to unity is assumed in State 3. Residual [R.sub.7] is evaluated at 30-minute intervals in State 3; however, because a transition from State 4 to State 3 requires the mixing-box dampers to stroke from the minimum to the 100% outdoor air position, which may take a minute or more, [R.sub.7] should not be evaluated immediately after such a transition. In this study, [R.sub.7] was not evaluated until the AHU had operated in State 3 for at least five minutes after a transition from State 4. A similar limitation on residual [R.sub.7] is not necessary when the AHU transitions from State 2 to State 3, because in this case the dampers are not making an abrupt transition.

A second residual in State 3 is determined from mass and energy balances on control volume CV-1 in Figure 8. Figure 8 illustrates that the recirculation air damper is closed, and there is no recirculation flow. Since control volume CV-1 is located upstream of the cooling coil and the dampers are fixed in the 100% outdoor air position, steady-state conditions are assumed. Performing a mass balance on the dry air and water vapor entering and leaving control volume CV-1 gives

[FIGURE 8 OMITTED]

[m.sub.o] = [m.sub.m] (33)

and

[m.sub.o][[omega].sub.o] = [m.sub.m][[omega].sub.m]. (34)

Next, performing an energy balance on control volume CV-1 yields

[m.sub.o][h.sub.o] = [m.sub.m][h.sub.m]. (35)

Substituting Equations 5, 33, and 34 into Equation 35 gives

[T.sub.o] = [T.sub.m]. (36)

Thus, residual [R.sub.8] is computed from

[R.sub.8] = [T.sub.o,3]-[T.sub.m,3], (37)

where [T.sub.o,3] and [T.sub.m,3] are the outdoor air and mixed air temperatures while in State 3. Residual [R.sub.8] is evaluated at 30 minute intervals in State 3. However, like residual [R.sub.7], [R.sub.8] is not evaluated until the AHU has operated in State 3 for at least five minutes following a transition from State 4 to enable the mixing-box dampers to stroke to their new positions.

In State 4, the dampers are positioned to allow the minimum outdoor air required for ventilation, and the cooling coil is used to maintain the supply air temperature at setpoint. For this situation, the control volume in Figure 6 and the associated analysis can be applied, and Equation 25 adapted to yield the following:

[R.sub.9] = [f.sub.design]-[[[T.sub.m,4]-[T.sub.r,4]]/[[T.sub.o,4]-[T.sub.r,4]]] (38)

Residual [R.sub.9] is evaluated at 30 minute intervals in State 4. However, like residuals [R.sub.7] and [R.sub.8], [R.sub.9] should not be evaluated immediately after a transition to State 4, because the dampers will be stroking from the 100% outdoor air position to the minimum position. In this study, [R.sub.9] was not evaluated until the AHU had operated in State 4 for at least five minutes.

Although residuals [R.sub.5], [R.sub.7], and [R.sub.9] are based on the same equation, the variances of the residuals will likely be different because the outdoor air fraction calculation is sensitive to small variations in temperature, particularly when the temperatures in the denominator (outdoor and return air temperatures) are close to one another, which can occur in States 3 and 4. In the simulation results (presented later in the paper), values of the outdoor air fraction residuals ([R.sub.3], [R.sub.4], [R.sub.5], [R.sub.7], and [R.sub.9]) were discarded if the outdoor and return air temperatures used to calculate them differed by less than 5[degrees]C (9[degrees]F).

During transitions from State 2 to State 3, the dampers are positioned for 100% outdoor air, and residual [R.sub.1] is determined using Equation 9. In addition, mass and energy balances applied to control volumes CV-1 and CV-2 in Figure 8 yield the following residuals:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (39)

[R.sub.11] = [T.sub.o,2[right arrow]3]-[T.sub.m,2[right arrow]3]-[T.sub.m,2[right arrow]3] (40)

Equation 39 is developed in a manner similar to Equation 31, and Equation 40 is developed in a manner similar to Equation 37. Residual [R.sub.10] could be eliminated, since it can be derived by combining residual [R.sub.1] and residual [R.sub.11]. However, it will be retained so that a fault with any of the temperature sensors used in the residuals (supply air, outdoor air, and mixed air temperatures) will affect at least two residuals. Residuals [R.sub.10] and [R.sub.11] are evaluated using temperatures recorded immediately prior to transition from State 2 to State 3.

In the same way, during transitions from State 3 to State 2, residual [R.sub.2] is determined using Equation 10. In addition, the following residuals are defined:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (41)

[R.sub.13] = [T.sub.o,3[right arrow]2]-[T.sub.m,3[right arrow]2] (42)

Residual [R.sub.12] could be eliminated since it can be derived by combining residual [R.sub.2] and residual [R.sub.13], however, as in the case of residual [R.sub.10], it will be retained so that a fault with any of the temperature sensors used in the residuals will affect at least two residuals. Residuals [R.sub.12] and [R.sub.13] are evaluated using temperatures recorded immediately prior to a transition from State 3 to State 2.

Residual Summary. Table 1 lists the residuals, the sensor requirements to compute the residuals, and the operational state or state transition for which each residual is applicable.

[TABLE OMITTED]

Control Performance Monitor

The control performance monitor algorithm uses exponentially weighted moving averages (EWMAs) to compute indices that quantify local-loop control system performance. The equation for computing an EWMA (Hunter 1986) is given by

[[bar.X].sub.t] = [[[infinity].summation over (j = 0)][lambda](1-[lambda]).sup.j][X.sub.t-j[delta]], (43)

where [[bar.X].sub.t]] is the EWMA of performance index X at time t, [lambda] is the exponential smoothing constant, [[X.sub.t-j[delta]]] is the value of performance index X at discrete time t-j[delta], and [delta] is the sample time for the analog-to-digital converter.

The term [lambda][(1-[lambda]).sup.j] is referred to as an exponential smoothing weight. As j increases, the contribution of [X.sub.t-j[delta]] in Equation 43 decreases exponentially. To determine an EWMA using Equation 43, all previous values of X must be stored. A recursive formula for calculating EWMAs is given by

[[bar.X].sub.t] = [[bar.X].sub.t-[delta]] + [lambda]([X.sub.t]-[[bar.X].sub.t-[delta]]), (44)

for which only the immediate past value of the EWMA (i.e., [[bar.X].sub.t-[delta]]) must be stored. The smoothing constant is selected based on the response characteristics of the feedback control system being monitored. Seem et al. (1997) provides guidelines for the upper and lower bounds of the smoothing constant as

[[delta]/[20[t.sub.s]]]<[lambda]<[[delta]/[5[t.sub.s]]],(45)

where [t.sub.s] is the settling time of the controller.

When [[lambda] = [delta]/5[t.sub.s]], the summation of the exponential smoothing weights between times t and t-5[t.sub.s] is approximately 0.632, which indicates that approximately 63.2% of the EWMA is based on the data between times t and t-5[t.sub.s]. When [[lamda] = [delta]/(20[t.sub.s])], approximately 63.2% of the EWMA is based on the data between times t and t-20[t.sub.s].

Seem et al. (1997) used performance indices to detect a number of AHU and VAV-box faults in laboratory and field testing. This paper emphasizes the use of performance indices for the control input to the heating coil valve and cooling coil valve for identifying faults in the AHU. The control input performance index is defined as

[[bar.u].sub.t] = [[bar.u].sub.t-[delta]] + [lambda]([u.sub.t]-[[bar.u].sub.t-[delta]]), (46)

where u is the control signal sent to the valve actuator. Saturated values of the control signal (either at the minimum or maximum value) indicate that the AHU is unable to satisfy the supply air temperature setpoint in the present state. Under typical operating conditions, the AHU will then transition to a new state that can satisfy the setpoint; however, design conditions and certain faults can cause the AHU to saturate at positions where transitions are not possible. There are four such positions associated with the finite state machine sequencing logic in Figure 2, namely:

* State 1 -- Heating coil valve control signal saturated in the maximum heating position. For example, a stuck damper could cause excess outdoor air to be introduced that could cause the heating load to exceed the heating coil capacity. Design conditions could also cause the heating (or cooling) load to exceed the coil capacity, but design conditions occur infrequently, and oversizing of equipment makes it unlikely that a saturated control signal would occur under normal operating conditions. This makes saturated control signals very useful as signatures of faulty operation.

* State 3 -- Cooling coil valve control signal saturated in the maximum cooling position. For example, a leaking heating coil valve could cause the cooling load to exceed the cooling coil capacity.

* State 4 -- Cooling coil valve control signal saturated in the minimum cooling position and conditions for transition to State 3 are not satisfied. For example, the cooling coil valve could be stuck open at a position that produces too much cooling, but the economizer switching logic may prevent a transition to State 3, which would eventually enable the AHU to transition to State 2 and then State 1 if necessary to regain control of the supply air temperature.

* State 4 -- Cooling coil valve control signal saturated in the maximum cooling position. The example described for State 3 is also applicable here.

State Transition Diagram

Figure 9 shows the state transition diagram of Figure 2 modified to reflect the integration of the model-based residuals and the saturation status of performance indices with the sequencing control strategy. This figure illustrates the well-defined conditions under which the model-based residuals and performance indices are computed.

DESCRIPTION OF THE SIMULATION TESTBED

The simulation testbed is based on established component and system models (Norford and Haves 1997; Haves et al. 1998; DeSimone 1995). The models are based on idealized flow relationships of a single-duct VAV AHU and the zones it serves and are implemented in HVACSIM+ (Park et al. 1985). Significant changes to the simulation testbed described by Norford and Haves (1997) are outlined below.

* The sequencing logic for supply air temperature control was replaced by an implementation of the finite state machine logic in Figure 2 (Seem et al. 1999), which was adapted to include calculations of residuals and performance indices. The supply air temperature reset strategy was altered to produce a fixed supply air temperature setpoint of 12.78[degrees]C (55[degrees]F) from April 1 through October 31, and a fixed setpoint of 15.56[degrees]C (60[degrees]F) for the remainder of the year.

* The mixing-box model, with separate minimum and modulating outdoor air dampers, was replaced with a model that has a single modulating outdoor air damper. In addition, the control was altered to keep the outdoor air damper 100% open at all times when the supply fan is running (Seem et al. 2000). The recirculation air damper modulates between 0% and 65% open, and the relief air damper modulates between 35% and 100% open. The recirculation and relief air damper positions correspond to how the dampers would be modulated in a traditional mixing-box control system with an outdoor air damper minimum position of 35% open.

* A heating coil, valve, and actuator were added to enable heating coil valve faults to be simulated.

Faults were simulated by implementing parameter and output overrides in the simulation code. The following faults were simulated:

* supply air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* return air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* mixed air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* outdoor air temperature sensor offset faults of 2[degrees]C (3.6[degrees]F) and -2[degrees]C (-3.6[degrees]F)

* recirculation air damper stuck open, stuck closed, stuck 50% open

* recirculation air damper leakage (10% of full flow)

* cooling coil valve stuck 20% open

* cooling coil valve leakage (3% of full flow)

* heating coil valve stuck 10% open

* heating coil valve leakage (3% of full flow)

The temperature sensor faults are introduced by linearly increasing or decreasing the temperature sensor model offset parameter as time increases. The initial offset is 0[degrees]C (0[degrees]F), increasing to [+ or -]2[degrees]C ([+ or -]3.6[degrees]F) over a three-month period. A positive offset will produce an artificially low sensor reading and a negative offset will produce an artificially high sensor reading. The faults simulated are representative of common AHU faults (Yoshida et al. 1996).

Design values used in the residual calculations were determined through numerical experiments. The design mass flow rate of supply air [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is 10.53 kg/s (23.21 [lb.sub.m]/s), the supply fan power [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is 7.14 kW (24.36 x [10.sup.3] Btu/h), and the outdoor air fraction [f.sub.design] is 0.3. At conditions typical for the operation of an AHU, the constant pressure specific heat of moist air [[^.c].sub.p] is estimated to be 1.02 kJ/kg*[degrees]C (0.24 Btu/[lb.sub.m]*[degrees]F). The smoothing constant [lambda] used in the calculation of the EWMAs was set equal to 8.33 x [10.sup.-4].

Year-long simulations were performed using Chicago Typical Meteorological Year weather data (National Climatic Data Center 1981). Initial conditions for all simulations were established from the final conditions obtained by simulating a complete year of operation under normal operating conditions. All simulations correspond to one complete year of operation under either normal conditions or with a fault condition implemented. A 2.5 s time step was used in the simulations.

RESULTS

Detailed results from simulations of six faults are described in this section. All 13 residuals from Table 1 were calculated during the simulations to identify the dominant residuals for a system having supply, return, outdoor, and mixed air temperature sensors. If one or more of these sensors is not installed, a smaller number of residuals will be available. Recall that the temperature sensor offset faults are introduced gradually, with the offset increasing linearly from 0 to the maximum offset after three months of the year. The residuals presented for sensor offset faults are computed only for the final nine months of the year (i.e., after the sensor offset has achieved its maximum value). For the other faults considered, the residuals are calculated for the entire year. Finally, as discussed in the development of the residual equations, the outdoor air fraction residuals ([R.sub.3], [R.sub.4], [R.sub.5], [R.sub.7], and [R.sub.9]) are sensitive to small variations in the temperatures used to calculate them. Therefore, in the simulation results, values of these residuals were discarded if the outdoor and return air temperatures differed by less than 5[degrees]C (9[degrees]F).

Supply Air Temperature Offset Fault

Residuals for normal operation and a supply air temperature sensor offset fault of -2[degrees]C (-3.6[degrees]F) are shown in Figure 10. The upper plot in Figure 10 includes all residuals that compare the calculated outdoor air fraction to an expected value. The dimensionless magnitudes of the residuals are shown on the x-axis. The lower plot consists of the remaining residuals, which all have units of temperature.

[FIGURE 10 OMITTED]

Figure 10 shows that the dominant temperature residuals for this supply air temperature sensor offset fault are [R.sub.1], [R.sub.2], [R.sub.6], [R.sub.10], and [R.sub.12]. The absolute value of the difference between the median values of these residuals for normal and faulty operation ranges from 2.00[degrees]C to 2.06[degrees]C (3.60[degrees]F to 3.71[degrees]F). The median values of the dominant outdoor air fraction residuals, [R.sub.3] and [R.sub.4], differ by only 0.08 from those for normal operation. The magnitudes of the residuals impacted by the fault will vary with the severity of the fault.

Although residuals [R.sub.5], [R.sub.7], and [R.sub.9] are based on the same equation, the range of values for these residuals for normal operation is considerably different. While perfect measurements (i.e., there are no sensor errors) are assumed for normal operation, the temperature sensors have time constants that differ, with the time constant of the outdoor air temperature sensor being ten times that of the supply, return, and mixed air temperature sensors (300 vs. 30 s). This difference and the fact that the outdoor and return air temperatures are much closer to one another in States 3 and 4 than they are in State 1 results in the larger range of values observed for [R.sub.7] and [R.sub.9], in comparison to [R.sub.5].

All of the dominant residuals correspond to operation when the heating and cooling coil valves are closed. In this operating state, the temperature rise or drop across the two coils should be 0 when steady-state conditions prevail, as happens at the end of the state transition delay. Thus, the expected value of the supply air temperature can be easily related to the mixed air temperature and, if the outdoor air dampers are 100% open, to the outdoor air temperature. Residuals [R.sub.11] and [R.sub.13] are also computed when the heating and cooling coil valves are closed, however, they utilize sensors that are not affected by this particular fault. If either the heating or cooling coil valve is open (partially or fully), the temperature rise or drop becomes difficult to predict in the absence of a coil model.

Outdoor Air Temperature Offset Fault

The residuals for normal operation and an outdoor air temperature sensor offset fault of -2[degrees]C (-3.6[degrees]F) are shown in Figure 11. For this fault, residuals [R.sub.1], [R.sub.2], [R.sub.7], [R.sub.8], [R.sub.11], and [R.sub.13] show a significant departure from their values for normal operation. Each of these residuals is computed when the AHU operates with 100% outdoor air (i.e., either in State 3 or at transitions between States 2 and 3). The median values of the data clusters for normal and faulty operation differ by approximately 2[degrees]C (3.6[degrees]F) for the temperature residuals ([R.sub.1], [R.sub.2], [R.sub.8], [R.sub.11], and [R.sub.13]) and by approximately 0.31 for the outdoor air fraction residual [R.sub.7]. The outdoor air fraction residuals [R.sub.3], [R.sub.4], [R.sub.5], and [R.sub.9] are also impacted to a small degree by the fault; however, the largest difference in the median values for normal and faulty operation is only 0.07 to 0.08 for residual [R.sub.9]. Furthermore, the data clusters for normal and faulty operation overlap, so [R.sub.9] will not always be a reliable indicator of the presence of this fault.

[FIGURE 11 OMITTED]

Stuck-Open Recirculation Air Damper

The residuals for normal operation and a stuck-open recirculation air damper fault are shown in Figure 12. The residuals affected by the fault are [R.sub.1], [R.sub.2][R.sub.7], [R.sub.8], [R.sub.11], and [R.sub.13], which are calculated when the control sequence calls for 100% outdoor air, and normal operation dictates that the recirculation air damper is closed. The mixing-box model includes damper leakage parameters that, when set to their default values for normal operation, allow approximately 2% leakage through the recirculation damper when 100% outdoor air is desired, and the recirculation damper is closed. In comparison, the stuck-open recirculation air damper fault causes mixing of approximately 34% return air and 66% outdoor air when 100% outdoor air is desired. The result is a mixed air temperature that is frequently significantly warmer than expected. With the exception of [R.sub.7], all of the residuals affected by the fault are temperature residuals having magnitudes that can exceed 4[degrees]C (7.2[degrees]F). The two distinct clusters of data points for residuals [R.sub.1], [R.sub.2], [R.sub.11], and [R.sub.13] result from the two supply air setpoint temperatures used in the simulation. Also, note that while the magnitude of residual [R.sub.8] frequently exceeds 4[degrees]C (7.2[degrees]F), this residual, which compares the outdoor and mixed air temperatures during operation in State 3, has a broad range of values, and the residual range for normal operation overlaps that for faulty operation. The overlap of data clusters for residual [R.sub.8] occurs when the outdoor air temperature approaches the return air temperature, which causes the mixed air temperature to be insensitive to the fault. The other dominant residuals have distinct gaps between the clusters of data corresponding to normal and faulty operation.

[FIGURE 12 OMITTED]

The only outdoor air fraction residual affected by the stuck-open recirculation air damper fault is [R.sub.7]. Instead of an outdoor air fraction equal to unity, as expected for normal operation, the outdoor air fraction is approximately 0.64. As a result, the median values of the data clusters for normal and faulty operation differ by 0.33.

Stuck-Closed Recirculation Air Damper

The residuals for normal operation and a stuck-closed recirculation air damper fault are shown in Figure 13. The dominant residuals are [R.sub.3], [R.sub.4], [R.sub.5], and [R.sub.9]. All are outdoor air fraction residuals calculated when the control sequence calls for minimum outdoor air, which corresponds to a recirculation air damper positioned fully open for a normally operating system. The stuck-closed recirculation air damper results in an outdoor air fraction that is approximately equal to 0.9, instead of the design value of 0.3 that is expected at minimum outdoor air. Thus, the dominant residuals differ in magnitude by approximately 0.6 from their corresponding values for normal operation. The fault cannot be identified using the temperature residuals because, with the exception of [R.sub.6], all of the temperature residuals are calculated when the dampers are positioned for 100% outdoor air (either in State 3 or at transitions between States 2 and 3), which corresponds to a closed recirculation damper for normal operation. Residual [R.sub.6] is computed from an energy balance across the coils and supply fan, so the fault does not affect this calculation.

[FIGURE 13 OMITTED]

A time series plot of the dominant residuals is shown in Figure 14. Because the dominant residuals are applicable in two operating states ([R.sub.5] in State 1 and [R.sub.9] in State 4) and at the transitions between States 1 and 2 ([R.sub.3] and [R.sub.4]), the fault can be detected throughout the year. Although difficult to see in Figure 14, the data reveal that the AHU operates in the heating mode for periods of time in late May to compensate for the excess outdoor air that enters due to the fault. Although not shown, for normal operation the heating mode is not needed after the end of March.

[FIGURE 14 OMITTED]

Figure 15 is a time series plot of the EWMA of the control signal to the cooling coil valve, [[bar.u].sub.t,cc], for the stuck-closed recirculation air damper fault. This performance index saturates numerous times while operating in State 4 during the summer months, indicating the AHU has insufficient capacity to satisfy the load placed on it and is out of control. This will not happen with a properly sized and normally operating system, so the saturation status of [[bar.u].sub.t,cc] can also be used to detect the fault and provides redundancy for the information provided by the residuals.

[FIGURE 15 OMITTED]

Leaking Cooling Coil Valve

The residuals for normal operation and a leaking cooling coil valve fault are shown in Figure 16. For this fault the valve leakage parameter in the model was set equal to 3% but actually produces a leakage rate when the cooling coil valve is commanded closed that is approximately 5% of the flow when the valve is 100% open. By comparison, the normal leakage when the cooling coil valve is commanded closed is essentially zero. The residuals affected by this fault are [R.sub.1], [R.sub.2], [R.sub.3], [R.sub.4], [R.sub.6], [R.sub.10], and [R.sub.12]. The residuals all correspond to operating conditions for which the cooling coil and heating coil valves are closed (transitions between States 1 and 2, operation in State 2, and transitions between States 2 and 3). Furthermore, all of the residuals affected by the fault are functions of the supply air temperature. Note that the data points for the affected residuals are not clustered in tight groups as they have generally been for previous faults. This spread in the residuals is due to the variation of the airflow rate across the coil, which causes the temperature drop across the coil to vary and ultimately causes the compensation by the mixing-box dampers to vary. The supply airflow rate varies between 29% and 51% of the design flow rate during operation in State 2.

[FIGURE 16 OMITTED]

Stuck Heating Coil Valve

The residuals for normal operation and a stuck heating coil valve fault are shown in Figure 17. The valve is stuck 10% open, resulting in a constant flow rate of 0.09 kg/s (0.20 [lb.sub.m]/s) of heated water through the coil. This is approximately 47% of the largest flow through the heating coil under normal operating conditions (for normal operation, the control signal to the heating coil valve never exceeded 30% open). The stuck valve results in unnecessary and/or excessive heating at certain times and insufficient heating at other times. The same seven residuals ([R.sub.1], [R.sub.2], [R.sub.3], [R.sub.4], [R.sub.6], [R.sub.10], and [R.sub.12]) impacted by the cooling coil valve leakage fault are affected by the stuck heating coil valve fault. The dominant residuals all correspond to operating conditions for which the cooling coil and heating coil valves are closed. The dominant temperature residuals range in magnitude from approximately 2[degrees]C to 4[degrees]C (3.6[degrees]F to 7.2[degrees]F), with smaller residual values occurring at higher supply airflow rates.

[FIGURE 17 OMITTED]

The outdoor air fraction residuals impacted by the stuck heating coil valve ([R.sub.3], [R.sub.4]) have magnitudes approximately equal to 0.1 and are computed at transitions between State 1 and State 2 when the AHU operates with minimum outdoor air. The fault causes the AHU to operate in State 2 at lower outdoor air temperatures than it ordinarily would. For normal operation, the outdoor air temperature at transitions between States 1 and 2 ranges from approximately -2[degrees]C to 1.5[degrees]C (28.4[degrees]F to 34.7[degrees]F), whereas it ranges from approximately -13[degrees]C to -6[degrees]C (8.6[degrees]F to 21.2[degrees]F) for this fault. The result is that cold outdoor air in excess of the ventilation rate is introduced to the AHU to compensate for the fault.

Figure 18 is a time series plot of residual [R.sub.6], which compares the mixed air temperature and supply air temperature in State 2 and is one of the dominant residuals for the stuck heating coil valve fault. Figure 18 reveals that the fault can be detected using residual [R.sub.6] during the first five months and the last three months of the year. Although not shown, the other dominant residuals are calculated at transitions between States 2 and 3, which occur primarily during March through May as well as October and November.

[FIGURE 18 OMITTED]

Figure 19 is a time series plot of the EWMA of the control signal to the heating coil valve, [[bar.u].sub.t,hc], for the stuck heating coil valve fault. The performance index saturates once during winter operation (Time [approximately equal to] 30 days) while the AHU operates in State 1, indicating the AHU has insufficient capacity to satisfy the load placed on it and is out of control. It is important to recognize that the only residual that is applicable in State 1 is residual [R.sub.5], and it is unaffected by the fault. Thus, [[bar.u].sub.t,hc] detects the fault under conditions that the model-based residuals do not.

[FIGURE 19 OMITTED]

Summary of Model-Based Residual Results

Results for all of the faults considered in this study are summarized in Table 2 in terms of the absolute value of the difference between the median values of the residuals for normal and faulty operation. Symbols are used to designate different residual types and magnitudes of the differences. Squares represent outdoor air fraction residuals and circles represent temperature residuals. Large symbols represent large differences in magnitude (greater than 0.3 for the outdoor air fraction residuals and greater than 3.0[degrees]C [5.4[degrees]F] for the temperature residuals), and small symbols represent small differences (between 0.1 and 0.3 for the outdoor air fraction residuals and between 1.0[degrees]C [1.8[degrees]F] and 3.0[degrees]C [5.4[degrees]F] for the temperature residuals). Empty cells indicate the difference in magnitude is less than 0.1 for outdoor air fraction residuals and less than 1.0[degrees]C (1.8[degrees]F) for temperature residuals. The boundaries used to classify a change in a residual value as a large, small, or no difference are intended to enable readers to quickly identify residual differences of similar magnitudes. These boundaries are not intended to be used as thresholds for fault detection.

Table 2. Identification of the Dominant Residuals (Based on Median Values) for All Faults Fault Residual [R.sub.1] [R.sub.2] [R.sub.3] Supply Air [small circle] [small circle] [small sqare] Temperature Offset, 2[degrees]C (3.6[degrees]F) Supply Air [small circle] [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Return Air Temperature Offset, 2[degrees]C (3.6[degrees]F) Return Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Mixed Air Temperature Offset, 2[degrees]C (+3.6[degrees]F) Mixed Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Outdoor Air [small circle] [small circle] Temperature Offset, 2[degrees]C (3.6[degrees]F) Outdoor Air [small circle] [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Recirculation Air [large circle] [large circle] Damper Stuck Open Recirculation Air [large square] Damper Stuck Closed Recirculation Air [small circle] [small square] Damper Stuck Half-Way Recirculation Air [small circle] [small circle] Damper Leakage (10%) Cooling Coil [large circle] [large circle] [large square] Valve Stuck Open (20%) Cooling Coil [small circle] [small circle] [small square] Valve Leakage (3%) Heating Coil [large circle] [large circle] [small square] Valve Stuck Open (10%) Heating Coil [large circle] [large circle] [small square] Valve Leakage (3%) Fault Residual [R.sub.4] [R.sub.5] [R.sub.6] Supply Air [small square] [small circle] Temperature Offset, 2[degrees]C (3.6[degrees]F) Supply Air [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Return Air Temperature Offset, 2[degrees]C (3.6[degrees]F) Return Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Mixed Air [small circle] Temperature Offset, 2[degrees]C (+3.6[degrees]F) Mixed Air [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Outdoor Air Temperature Offset, 2[degrees]C (3.6[degrees]F) Outdoor Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Recirculation Air Damper Stuck Open Recirculation Air [large square] [large square] Damper Stuck Closed Recirculation Air [small square] [small square] Damper Stuck Half-Way Recirculation Air Damper Leakage (10%) Cooling Coil [large square] [large circle] Valve Stuck Open (20%) Cooling Coil [small square] [large circle] Valve Leakage (3%) Heating Coil [small square] [large circle] Valve Stuck Open (10%) Heating Coil [small square] [large circle] Valve Leakage (3%) Fault Residual [R.sub.7] [R.sub.8] [R.sub.9] Supply Air Temperature Offset, 2[degrees]C (3.6[degrees]F) Supply Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Return Air [small sqare] Temperature Offset, 2[degrees]C (3.6[degrees]F) Return Air [small sqare] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Mixed Air [small square] [small circle] [small square] Temperature Offset, 2[degrees]C (+3.6[degrees]F) Mixed Air [small square] [small circle] [small square] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Outdoor Air [small square] [small circle] Temperature Offset, 2[degrees]C (3.6[degrees]F) Outdoor Air [large square] [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Recirculation Air [large square] [small circle] Damper Stuck Open Recirculation Air [large square] Damper Stuck Closed Recirculation Air [small square] Damper Stuck Half-Way Recirculation Air [small square] Damper Leakage (10%) Cooling Coil Valve Stuck Open (20%) Cooling Coil Valve Leakage (3%) Heating Coil Valve Stuck Open (10%) Heating Coil Valve Leakage (3%) Fault Residual [R.sub.10] [R.sub.11] [R.sub.12] Supply Air [small circle] [small circle] Temperature Offset, 2[degrees]C (3.6[degrees]F) Supply Air [small circle] [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Return Air Temperature Offset, 2[degrees]C (3.6[degrees]F) Return Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Mixed Air [small circle] [small circle] [small circle] Temperature Offset, 2[degrees]C (+3.6[degrees]F) Mixed Air [small circle] [small circle] [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Outdoor Air [small circle] Temperature Offset, 2[degrees]C (3.6[degrees]F) Outdoor Air [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Recirculation Air [large circle] Damper Stuck Open Recirculation Air Damper Stuck Closed Recirculation Air [small circle] Damper Stuck Half-Way Recirculation Air [small circle] Damper Leakage (10%) Cooling Coil [large circle] [large circle] Valve Stuck Open (20%) Cooling Coil [large circle] [small circle] Valve Leakage (3%) Heating Coil [large circle] [large circle] Valve Stuck Open (10%) Heating Coil [large circle] [large circle] Valve Leakage (3%) Fault Residual [R.sub.13] Supply Air Temperature Offset, 2[degrees]C (3.6[degrees]F) Supply Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Return Air Temperature Offset, 2[degrees]C (3.6[degrees]F) Return Air Temperature Offset, -2[degrees]C (-3.6[degrees]F) Mixed Air [small circle] Temperature Offset, 2[degrees]C (+3.6[degrees]F) Mixed Air [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Outdoor Air [small circle] Temperature Offset, 2[degrees]C (3.6[degrees]F) Outdoor Air [small circle] Temperature Offset, -2[degrees]C (-3.6[degrees]F) Recirculation Air [large circle] Damper Stuck Open Recirculation Air Damper Stuck Closed Recirculation Air [small circle] Damper Stuck Half-Way Recirculation Air [small circle] Damper Leakage (10%) Cooling Coil Valve Stuck Open (20%) Cooling Coil Valve Leakage (3%) Heating Coil Valve Stuck Open (10%) Heating Coil Valve Leakage (3%) Notes: [small square] = outdoor air fraction residual differences for which 0.1[less than or equal to]|[[~.R].sub.i,normal]-[[~.R].sub.i,fault]| [less than or equal to]0.3, where [[~.R].sub.i,normal]] is the median value of residual i for normal operation, and [[~.R].sub.i,fault]] is the median value of residual i for faulty operation. [large square] = outdoor air fraction residual differences for which 0.3 < |[[~.R].sub.i,normal]-[[~.R].sub.i,fault]|. [small circle] = temperature residual differences for which 1[degrees]c (1.8[degrees]F)[less than or equal to] |[[~.R].sub.i,normal]-[[~.R].sub.i,fault]|[less than or equal to] 3[degrees]C (5.4[degrees]F). [large circle] = temperature residual differences for which 3[degrees]C (5.4[degrees]F)<|[[~.R].sub.i,normal]-[[~.R].sub.i,fault]|.

Table 2 shows that with the exception of the return air temperature sensor offset faults, each fault had four or more residuals for which the magnitude of the differences in the median values for normal and faulty operation exceeded 0.1 for outdoor air fraction residuals, and 1.0[degrees]C (1.8[degrees]F) for temperature residuals. In addition, the results indicate that residuals [R.sub.1] and [R.sub.2] may be adequate for detecting all of the damper and valve faults considered, except for the stuck-closed recirculation air damper fault. Residuals [R.sub.1] and [R.sub.2] only require measurements of the supply air and outdoor air temperatures. With the addition of return air temperature measurement, residuals [R.sub.3] and [R.sub.4] can be calculated and used to detect the stuck-closed recirculation air damper fault.

As noted in the discussion of the supply air temperature sensor fault, the magnitude of the residuals impacted by a particular fault will vary with the severity of the fault. As seen in the results for the cooling coil valve leakage fault and the stuck heating coil valve, the magnitudes will also vary with the operating condition of the AHU. In this study, the severities of the faults were selected to be large enough to enable the impacted residuals to be distinguished from those that are largely unaffected by a particular fault. In a field application of the method, it would be necessary to establish robust thresholds for the residuals separating normal and faulty operation. These thresholds would identify when a residual is too large, thereby signaling a fault, and would be broadly applicable in AHUs but would not be indicative of a particular severity of a fault (e.g., a 5% leakage through the cooling coil valve).

This study did not consider cases with multiple simultaneous faults; however, there is nothing inherent to the method that limits its applicability to single-fault cases.

CONCLUSIONS AND FUTURE WORK

This paper described an integrated control and fault detection method for AHUs. The method integrates the calculation of model-based residuals derived from mass and energy balances, and state-based performance indices of control loops, with the finite state machine sequencing logic of the AHU. The method uses available temperature sensor measurements, eliminates the need for a steady-state detector algorithm and, over time, provides a rich data set collected under very specific operating conditions for which expected operation is well defined. For a complete sensor suite that includes the supply, return, outdoor, and mixed air temperature sensors, a total of 13 residuals are calculated that form the basis for identifying operational faults.

The integrated control and fault detection method was assessed through simulations of 16 faults that consisted of temperature sensor offset faults, stuck and leaking damper faults, and stuck and leaking valve faults. With the exception of the return air temperature sensor offset faults, each fault impacted numerous residuals. In addition, two faults (stuck-closed recirculation air damper and heating coil valve stuck 10% open) caused control performance indices to saturate, which should not happen to a properly designed and operating system. In the case of the stuck-closed recirculation air damper, the saturated control signal to the cooling coil valve provided redundancy for the residuals. For the stuck heating coil valve fault, the performance index for the control signal to the heating coil valve saturated in State 1. The residuals were unaffected by this particular fault in State 1. Thus, the control performance monitor complements the model-based residuals by enabling the detection of certain faults under operating conditions for which the residuals cannot detect the fault.

The ultimate goal in the development of the integrated control and fault detection method is to enable the automatic detection of faults by establishing thresholds for each residual that separate normal and faulty operation. This study represents the first step in that development process. The next step will likely entail testing under controlled conditions in a physical test bed where faults can be introduced artificially. This would enable a better assessment of the robustness of the method to imperfect measurements and an evaluation of the adequacy of the state transition delay for establishing steady-state conditions, and would provide some insight into the selection of thresholds for fault detection. The final step in the development process would be to install and test the integrated control and fault detection method at a number of field sites. Data representative of normal operation and naturally occurring faults could then be collected and analyzed to establish robust statistical ranges for each residual under normal operation that would enable automatic detection of faults and would be generally applicable in single-duct AHUs.

Testing with multiple simultaneous faults is not planned and is considered less important than the steps outlined above because the method described here is concerned only with fault detection. Simultaneous faults could mask one another, and by doing so, might prevent their detection. If, on the other hand, one or more residuals indicate the presence of a fault, human intervention would be required to properly diagnose whether there was one or more than one fault. If the goal of a method is to automatically detect and diagnose a fault or faults, then testing with multiple simultaneous faults would be more important and perhaps even a requirement of a rigorous development process.

ACKNOWLEDGMENTS

The authors would like to thank Dr. Cheol Park of the National Institute of Standards and Technology in Gaithersburg, MD, for providing source code for the sequencing logic and fault cases that were adapted for this study.

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John E. Seem, PhD

Member ASHRAE

John M. House, PhD

Member ASHRAE

Received June 17, 2008; accepted October 10, 2008

John E. Seem is a research fellow and John House is a principal research engineer at Johnson Controls, Inc., Milwaukee, WI.

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Author: | Seem, John E.; House, John M. |
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Publication: | HVAC & R Research |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jan 1, 2009 |

Words: | 11805 |

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