Development and evaluation of a simple model-based automated fault detection and diagnosis (FDD) method suitable for process faults of large chillers.

BACKGROUND AND OBJECTIVES

During the past several years, there has been growing interest in applying fault detection and diagnosis (FDD) methods, which are fairly mature in such engineering disciplines as nuclear, aeronautical, and automotive, to the HVAC&R industry. Indeed, several articles (for example, Moran [2006]) have identified FDD as one of the most urgent needs along with such measures as more stringent energy-efficiency standards, developing high-performance heating and cooling residential units, and improved training programs for operation and maintenance personnel. Braun (1999) pointed out that high reliability and safety are relatively less critical in building operations compared to operating cost and capital investment; therefore, FDD did not receive the same level of interest among the building researchers, owners, and operators. Although FDD has been an active area of research among the building and the HVAC&R community for several years, it is not widely deployed in the field. The primary reasons for slow adoption of FDD in buildings and the HVAC&R area are numerous, and the major ones are described below:

* The cost-to-benefit ratio for an FDD implementation is relatively high, partly caused by the lack of extensive instrumentation in the building and HVAC&R systems and lack of data to quantify the benefits (Braun 1999).

* Dexter and Ngo (2001) point out that the problems associated with identifying and isolating faults in HVAC systems are more severe than those that occur in most process control applications. The behavior of HVAC plants and buildings is more difficult to predict due to lack of accurate mathematical models because most HVAC designs are unique and financial considerations restrict the amount of time and effort that can be put in deriving a model.

* Detailed design information is seldom available, and measured data from an actual plant are often inadequate indicators of the overall behavior, since test signals cannot be injected during normal operation because of potential occupant discomfort, unacceptable energy penalties, and possibility of equipment damage (Haves et al. 1996).

* Another problem is that many inputs to the FDD model cannot be measured accurately with commercial-grade sensors, and some measurements (such as flow rates) are often not even available. Finally, the issue of fault diagnosis can be problematic since several faults may have the same symptoms.

The objective of this paper is to propose and demonstrate a simple model-based FDD method for medium-to-large chillers that uses available sensors, allows tuning of specific thresholds so as to attain the desired compromise between robustness (i.e., low false alarm rate) and sensitivity (i.e., low missed opportunity rate for detecting faulty operation), and has the potential to be automated and implemented online. Since proper field-monitored data from actual chillers under both fault-free and known faulty operation were unavailable, the performance of the proposed FDD method is demonstrated with labeled data from a laboratory chiller (Comstock and Braun 1999). Since large chillers are not prepackaged as is unitary equipment, their design and assembly allow selecting different subsystems for a stipulated maximum cooling capacity. In such a case, selection of specific variables likely to be impacted by different faults depends on several aspects unique to the chiller installation: the type of chiller load control (thermostatic expansion valve [TXV] or inlet guide vane), the specific choice of the relative heat exchanger (HX) size, and the load level at which the chiller is usually operated. Hence, some customization would be needed to adapt the FDD thresholds and associated rules for each chiller installation. This paper describes the FDD method proposed in a manner clear enough for it to be implemented and evaluated by facility energy managers, chiller manufacturers, control equipment companies, chiller service companies, and independent software developers.

The scope of the proposed method is limited to process fault detection as against sensor faults (see, for example, Wang and Cui [2006]) or actuator faults or control loop or controller faults and relying on continuous thermal/pressure/electrical measurements as against one-time diagnostic measurements or other tests (such as vibration and electrical signature analysis, visual inspection checks, oil wear debris analysis, and surface and internal defect detection tests as described in Davies [1998]).

Large chillers and chiller plants are a natural choice for FDD implementation. There are several published articles on FDD applied to HVAC&R equipment such as air handlers, unitary vapor-compression systems, and a few medium-to-large chillers. The reader can refer to review articles by Comstock et al. (1999), Katipamula et al. (2001), Katipamula and Brambley (2005a, 2005b), and Reddy (2006). The focus of this paper is on medium-to-large chillers. Katipamula and Gaines (2003) analyzed published data and determined that central chillers and district cooling serve about 28% of the commercial building floor area and consume about 0.3 quads of primary energy per year. Assuming a power plant conversion efficiency of 33%, cooling equipment, they inferred, consumes about 30 TWh of electricity. If savings of 10% are attributable to FDD systems being in place, the net value of the energy savings would be $300M/yr at $0.10/kWh.

Further, only centrifugal chillers are considered. This limits the size of chillers to sizes above 80 tons or so and excludes unitary equipment such as rooftop units. Medium-to-large chillers come equipped with elaborate safety control mechanisms for critical/catastrophic faults. This paper is not targeted toward such faults or to the detection of hard faults (such as fan belt breakage or a burnt motor) but toward incipient faults that lead to energy waste and gradually damage equipment. Further, such medium-to-large chillers come equipped with numerous sensors, usually temperature, pressure, and electrical measurements, on individual subcomponents and loops, such as the condenser and evaporator loops, refrigerant loops, and cooling oil loops. Thus, any FDD method should explicitly make use of such data-rich environment for which component isolation methods (McIntosh et al. 2000; Jia and Reddy 2003; Wang and Cui 2006) seem particularly appropriate. On the other hand, calibrated simulation model approaches for FDD are best suited for systems where limited sensor data are available (such as those for unitary rooftop cooling equipment addressed by Rossi and Braun [1997], Brueker and Braun [1998a, 1998b], and Castro 2002).

Finally, most of the FDD work to date in the HVAC&R area is limited to steady-state data. Notable exceptions are studies by Bruecker and Braun (1998a, 1998b) and Stylianou (1997), but these use such data only cursorily and in a manner lacking in rigor. This is logical given the relative infancy of such FDD tools in the HVAC&R industry. Figure 1 is our attempt at a broad classification of FDD methods. It is our opinion that a strict real-time online FDD method (which detects and flags faults within, say, minutes of their appearance) is both unwarranted and probably infeasible. Certain faults appear momentarily and disappear (such as equipment surging) and others may be caused by short-lived transients in the overall system. It would be more practical in the early stages of FDD adoption, during which valuable field experience is imperative, to structure FDD methods more suited to off-line batch analysis using a certain number of steady-state performance points over a one-to two-day (or even a week) latency period, i.e., time from which data are collected to the time they are analyzed in batch mode.

[FIGURE 1 OMITTED]

REVIEW OF PERTINENT CHILLER FDD STUDIES

A final research report by Reddy (2006) summarizes the various studies published with respect to FDD of unitary cooling equipment and chillers. Information such as author, year of publication, type and size of equipment, number of faults studied, and type of action performed during both fault detection and diagnosis stages are summarized. We briefly describe some of the pertinent and more recent ones below. For example, the recent papers by Chen and Braun (2001) and Li and Braun (2003) build upon studies by Rossi and Braun (1997) and Brueker and Braun (1998a, 1998b) and so only the first two are reviewed.

Grimmelius et al. (1995) developed an empirical multivariate model-based fault diagnostic system for a chiller using residuals. This involves using a reference model along with the measured variables for FDD, which are carried out in a single step. Twenty-two different measurements were used, including temperature, pressure, power consumption, and compressor oil level, along with derived value of liquid subcooling, superheat, and pressure drop. The chiller was classified into seven regions. Fault modes were associated with any component that was serviceable, which led to 58 different fault modes. The cause and effect study of the 58 fault modes helped establish the expected influence on the components and subsequent chiller behavior. The symptoms associated with the 58 fault modes on the measured and derived variables were generated. In the resulting symptom matrix, some of the fault modes were indistinguishable in terms of their respective symptoms because they either had identical or empty patterns. As a result, the symptom matrix was reduced from 58 to 37 fault modes and symptom patterns.

To diagnose a fault, scores are assigned to each known fault mode in the matrix. The score for a given symptom is not a constant but is determined based on knowledge about the particular fault symptoms. A variable that shows a very distinct reaction to a fault mode becomes a higher score than a variable that shows only a limited reaction to the fault mode. Using the symptom matrix, a total score is generated by adding the individual scores of all expected symptoms that match the measured symptoms. A normalized score is calculated by dividing the total score by the total number of points per pattern. A normalized score of 0.9 or higher is used to indicate a probable fault, and a score between 0.5 and 0.9 is used to indicate a possible fault. Although the method proved effective in identifying faults in the systems before the system failed completely, faults with only a few symptoms tended to get high scores more often. Because the reference model is a simple regression model that was developed with the data from the test chiller, the same model cannot be used on another chiller.

Stylianou and Nikanpour (1996) used the reciprocating chiller model developed by Gordon and Ng (2000) and the pattern-matching approach outlined in Grimmelius et al. (1995) as part of their FDD system. Like Grimmelius et al. (1995), Stylianou and Nikanpour also perform the detection and diagnosis in a single step, and their approach lacks the evaluation and decision steps. The methods used in the FDD system included a thermodynamic model for fault detection and pattern recognition from expert knowledge for diagnosis of selected faults. The diagnoses of the faults are performed by an approach similar to that outlined by Grimmelius et al. (1995). Seventeen different measurements (pressures, temperatures, and flow rates) were used to detect four different faults: refrigerant leak, refrigerant line flow restriction, condenser water-side flow resistance, and evaporator waterside flow resistance.

The start-up module is deployed once the chiller is started and is left in operation for 15 minutes. The module used four measured inputs (discharge temperature, the crankcase oil temperature, and refrigerant temperature entering and leaving the evaporator) scanned at five-second intervals to detect refrigerant flow faults that are easier to detect before the system reaches steady state. To detect faults, the responses of the measured variables are compared to the baseline responses. For example, a shift (in time or magnitude) in the peak of the discharge temperature may indicate liquid refrigerant flood back, refrigerant loss, or refrigerant line restriction. Because the ambient conditions affect the baseline response, the response may have to be normalized before a comparison is made. The steady-state module is deployed after the chiller reaches steady state and stays deployed until the chiller is turned off. The fault diagnostics linear regression models are used to generate estimates of pressure and temperature variables, similar to the approach outlined by Grimmelius et al. (1995). To diagnose faults, the estimated variables are compared to the measured values, and the residuals are matched using a rule-based pattern matrix. Although Stylianou and Nikanpour (1996) extended the previous work of Gordon and Ng (2000) and Grimmelius et al. (1995), the evaluation of the FDD systems was not comprehensive and lacked several key elements, including sensitivity and false alarm. In addition, it is not clear whether the start-up module can easily be generalized.

Subsequently, Stylianou (1997) replaced the rule-based model used to match the pattern with a statistical pattern-recognition algorithm. This algorithm uses the residuals generated from comparison of predicted (using linear regression) models and measured pressures and temperatures to generate patterns that identify faults. Because this approach relies on the availability of training data for normal and faulty operation, it may be difficult to implement this in the field, and only limited testing of the method has been done.

Peitsman and Bakker (1996) used two types of black-box models (ANNs and auto regressive with exogenous inputs, ARX) to detect faults at the system, as well as at the component level of a reciprocating chiller system. The inputs to the system models included condenser supply water temperature, evaporator supply glycol temperature, instantaneous power of compressor, and flow rate of cooling water entering the condenser (for ANN only). The choice of the inputs was only limited to those that are commonly available in the field. Using the inputs with both the ANN and ARX models, 14 outputs were estimated. For the ANN models, inputs from the current and the previous time step and outputs from two previous time steps were used. Altogether, 14 system-level models and 16 component-level models were developed to detect faults in a chiller. The intent was to use system models to detect the fault at the system level and then use the component models to isolate the fault. ANN models appeared to have a slightly better performance than the ARX models in detecting faults at both the system and the component level. The evaluation and decision steps were not implemented.

Bailey (1998) also used the ANN model to detect and diagnose faults in an air-cooled chiller with a screw compressor. The detection and diagnosis were carried out in a single step. The faults evaluated included refrigerant under-and overcharge, oil under- and overcharge, condenser fan loss, and condenser fouling. The measured data included superheat and subcooling temperatures, power consumption, compressor suction pressure, discharge pressures, chilled-water inlet and outlet temperatures from the evaporator, and chiller capacity. The main drawback of this approach is that extensive fault data must be available in order to identify robust ANN models for fault-free and faulty performance.

Castro (2002) suggested and evaluated an FDD method called MATCH for a 12 ton air-cooled liquid reciprocating chiller using simulation and experimental data that included both fault-free as well as faulty data with one fault at a time at different levels of severity. Five different faults were studied using 12 performance indices. A detailed simulation model was first calibrated to fault-free experimental data (a process the author pointed out as being rather problematic). Subsequently, this model was used along with faulty data to generate residuals, which were normalized by their mean values. For each fault, three of the largest residuals were identified, and these were used to determine cluster thresholds for different faults. Two different types of clustering methods were evaluated, namely, the k-nearest neighbor and k-nearest prototype. Evaluation of the FDD method was done with a steady-state data set other than the one used for training. The steady-state data were obtained by using a steady-state filter to performance data collected every minute under actual operating conditions.

Chen and Braun (2001) present two easy-to-implement FDD methods suitable for rooftop air conditioners with thermal expansion valves and demonstrate their accuracy with laboratory data collected from a 5 ton air-cooled scroll compressor. Six different faults were considered using seven different performance parameters. The first method, called the sensitivity ratio method, is to use a unique pair of residuals (actual minus model) for each fault, where one is fault insensitive and the other is sensitive. Fault sensitivity ratios are computed as the ratio of both of these residuals. If these residuals are not larger than a specified threshold, they are set to a small value. Thus, at no-fault condition, the ratios are unity and when a fault develops, the sensitivity ratio becomes less than unity. As soon as this ratio reaches a certain threshold, an alarm for that fault is given. The baseline models were first-order polynomial models using the return air dry-bulb temperature, relative humidity, and ambient dry-bulb temperature. About 40 data points were used to identify these models. Fault diagnosis rules were identified from the faulty data.

The simple rule-based method (SRBM) is the second FDD method developed by Chen and Braun. It does not use a model but directly compares performance indices determined from raw measurements with preset thresholds to detect and diagnose faults. However, only four (instead of six for the sensitivity ratio method) faults could be detected and diagnosed. The authors state that this method is more general since no model is used. However, the extent to which these thresholds are constant across equipment is not discussed.

Li and Braun (2003) present improvements to a previous statistical rule-based FDD method by Rossi and Braun (1997) and Brueker and Braun (1998a, 1998b) on rooftop air conditioners. One improvement is that the baseline model identification includes a low-order polynomial to fit the training data, which is used to generate data needed to train a general regression neural network model. A second improvement is that the new method does not assume a constant covariance matrix for both normal and faulty operations, which reduces the sensitivity and robustness of the previous studies. It uses two new classifiers, one called the normalized distance fault detection classifier, which is, in essence, a multivariate statistical test, and the other, the distance ratio fault diagnosis classifier, based on the distance ratio method. A case study is presented with the same data as used by Brueker and Braun (1998a, 1998b), which demonstrates the superiority of this approach as compared to the previous study.

An ASHRAE-sponsored research project (Reddy 2006) was recently completed with the objectives of (a) proposing a general methodology for evaluating and grading FDD methods and tools using steady-state data, which would include issues such as the ability to correctly detect and diagnose faults, ease of use, amount of training data, robustness, sensitivity, practicality in terms of conversion to a tool that can be implemented (Reddy 2007a) and (b) to identify four different chiller FDD methods and evaluate them against steady-state chiller performance data (both fault-free and faulty) gathered from a laboratory chiller as part of RP-1043 (Comstock and Braun 1999) with the intention of identifying the "best" one for subsequent field evaluation (Reddy 2007b). The FDD method proposed in this paper is a different and simplified version of one of the four FDD methods evaluated (namely, the multivariate model-based FDD method).

Finally, Wang and Cui (2006) proposed an FDD method for centrifugal chillers that is similar to those of Rossi and Braun (1997) and Chen and Braun (2001) except that six performance indices (as suggested by McIntosh et al. [2000] and Jia and Reddy [2003]) were used rather than the basic measurements themselves. The proposed method is similar to the multivariate regression method evaluated by Reddy (2006) and involves a fault diagnostic classifier. The method was also validated with performance data from the RP-1043 chiller data sets (Comstock and Braun 1999).

CHILLER FAULTS AND DATA SETS

This study used the extensive performance data gathered by Comstock and Braun (1999) within the framework of RP-1043 for a 90 ton centrifugal water-cooled chiller:

a. Experimental data were collected under eight different chiller faults (however, only data from six faults are used in this study since an earlier study by Reddy [2006] found certain limitations with data collected under excess oil faults and faulty TXV operation).

b. Each fault was introduced at four levels of severity (10%- 40% fault levels in increments of about 10%).

c. The faults were tested at 27 different operating conditions of chiller thermal load ([Q.sub.ev]), chilled-water outlet temperature from chiller evaporator ([T.sub.evo]), and condenser-water inlet temperature ([T.sub.cdi]).

The test data were sampled at ten-second intervals, then used to generate steady-state data. Each performance condition collected included the four entering and leaving water temperatures, the subcooling, suction, and discharge temperatures of the refrigerant, the water flow rates in the evaporator and condenser, the refrigerant pressures in the evaporator and condenser, the heat transfer rates in the condenser and evaporator, and the compressor power consumption. Table 1 summarizes the numerous sets of tests performed under each of the six different faults under benchmark (or normal or fault-free or baseline conditions) and under four different fault severity levels (SL). Note that several replicate sets of tests had to be performed under fault-free conditions in order to reestablish the baseline each time a specific fault, which was previously introduced, had to be rectified prior to introducing another fault. Three such fault-free data sets were used in this study (Normal 1, Normal 2, and Normal CF). Table 1 also specifies the range of variation in the magnitude of the faults compared to the baseline condition.

Table 1. Summary of RP-1043 Lab Chiller Datasets (Comstock and Braun
1999)

   Description of    Normal             SL1        SL2
    Fault            Operation

1      Reduced       270gpm (0.98-1.0)  0.87-0.93  0.77-0.81
   condenser-water
         flow

2      Reduced       216gpm (0.99-1.0)  0.90-0.91  0.81-0.82
   evaporator-water
         flow

3  Refrigerant leak        300 lb            0.1        0.2

4    Refrigerant           300 lb            0.1        0.2
      overcharge

5      Condenser           164 tubes        0.06       0.12
       fouling             total

6  Noncondensables           No             0.01       0.017
     in system (by         nitrogen
       volume)

           Description of Fault              SL3        SL4

1      Reduced condenser-water flow       0.69-0.70  0.59-0.61

2      Reduced evaporator-water flow      0.72-0.72  0.63-0.65

3            Refrigerant leak              0.3        0.4

4          Refrigerant overcharge          0.3        0.4

5            Condenser fouling            0.20       0.30

6            Noncondensables in system   0.024      0.057
            (by volume)

Note: Fractional values indicate the level of fault severity. For
example, the range 0.59-0.61 under SL4 for reduced condenser water
flow indicates that the flow was reduced to about 60% of the normal
value.

TYPES OF VARIABLES

Experience gained from past studies (for example, Comstock and Braun [1999], McIntosh et al. [2000], and Wang and Cui [2006]) indicates that fault detection can be more sensitive if certain characteristic quantities (CQ) or characteristic parameters (CP) are used instead of the basic sensor measurements themselves. These CPs and CQs can be directly deduced from the sensor measurements using arithmetic operations and thermodynamic refrigerant property tables or correlations. A supposedly distinguishing trait between CPs and CFs is that the former are those that in some manner better capture the performance of the internal state of the system or its components than do the latter in response to specific values of forcing functions. Hence, we have also adopted the terminology characteristic features (CF), which would include both CQs and CPs.

Definitions of the seven CQs and seven CPs subsequently used in this research are provided in Table 2 and Figure 2 along with their symbols and computational definitions. The overall chiller COP is also considered as an additional CF. The report by Reddy (2006) also found that the primary chiller measurements presumed to be available in this study were consistent with those assumed in allied published studies on large chillers.

[FIGURE 2 OMITTED]

[TABLE OMITTED]

PROPOSED FDD METHOD

The FDD method proposed is based on insight gathered from an exploratory analysis of the fault-free and faulty data sets of RP-1043, which revealed that of the fifteen CFs described above, only five are the most influential and fairly consistent across the four FDD methods evaluated by Reddy (2006). Further, these five CFs show a linear behavior with cooling load. Finally, we note that the behavior of these five CFs under fault-free and faulty operation are able to provide the necessary association rules for fault diagnostics. These observations are supported by the various subplots assembled in Figure 3. For example, under reduced condenser flow rate (Fault F1), CQ1 is affected, and though it does vary with load, its linear behavior is distinct enough from its fault-free linear behavior to allow FDD to be performed (see Figure 3a). Table 3 assembles the fault diagnosis rules. It is clear that except for F1, F2, and F5, the other faults rely on multiple CFs for diagnosis. Unfortunately, the residual patterns for F4 and F6 are identical, and so these two faults cannot be diagnosed uniquely.

Table 3. Fault Diagnosis Table Proposed for Model-free FDD (Method #1)

Fault Code  Fault Description             CQ1  CQ2  CQ5  CQ6  CP1

F1     Reduced condenser water flow rate         +
F2     Reduced evaporator water flow rate   +
F3     Refrigerant leak                               -    -    +
F4     Refrigerant overcharge                         +    +    -
F5     Condenser fouling                                        -
F6     Noncondensables in system                      +    +    -

Note: The + and - signs indicate directional change of the specific
measured CF compared to its fault-free state. For example, as the
condenser water flow rate decreases, CQ2 will increase from its
baseline fault-free value. Note that refrigerant overcharge and
noncondensables in system faults cannot be uniquely distinguished.

The proposed FDD method would rely on fault-free data in order to develop a regression model describing how each of the five CFs vary under different operating conditions. The model predictions can be compared with actual performance data, and the residuals or innovations can be used to determine not only the onset of faults, but also make a diagnosis as to the likely cause. Such model-based multivariate methods with the three influential regressors {[Q.sub.ev], [T.sub.cdi], and [T.sub.evo]} have been suggested in the past; for example, by Grimmelius et al. (1995), Comstock and Braun (1999), Wang and Cui (2006) and Reddy (2007b). What we propose here is a simple regression model with thermal load [Q.sub.ev] as the only regressor.

The FD method we propose would qualify as an analytical redundancy method (see any appropriate FDD textbook, for example, Himmelblau [1978]). For a specific chiller operating condition, the particular models are used to predict the values of the various CFs from which the residual for each CF is normalized by the fault-free model root mean square error (RMSE) so as to provide the well known student t-statistic:

t-statistic = [([y.sub.means,i][[^.y].sub.model,i])/[RMSE]] (1)

Note that different studies have normalized the residuals (or innovations) differently. House et al. (1999) and Castro (2002) have used the mean to normalize the residuals during their FDD studies related to air-handling unit and unitary air conditioners, respectively. On the other hand, Chen and Braun (2001) have normalized the residuals of a specific CQ that is sensitive to a particular fault by that of another CQ that is not. Finally, Comstock and Braun (1999) have normalized the CQ residuals by the maximum measurement error associated with the specific CQ using propagation of error formulae. It is our opinion that the two latter studies are similar in concept and should yield very similar results. Also, the most likely limiting value for the RMSE of an excellent model is the measurement error in the dependent variable. Hence, our manner of normalizing is conceptually similar to the Chen and Braun method and the Comstock and Braun method, though the specific t-statistic values may differ somewhat since the RMSE is rather specific to the baseline data set used to identify the fault-free model.

DEMONSTRATION OF THE PROPOSED FDD METHOD

The RP-1043 data sets described above were used to acquire preliminary insights into the selection of the t-statistic threshold for model residuals beyond which fault alarms will be triggered. Table 4 assembles the linear regression results of fitting the five CFs with thermal load using 27 fault-free data points (using Normal 2 data set). We note that the models for CQ1-CQ6 are excellent with RMSE values lower or comparable to the errors in temperature difference measurements. A mean model was deemed adequate for the condenser UA value characterized by CP1 (see Figure 3e).

Table 4. Regression Model Results of Fitting the Influential
Characteristic Features (CF) with Thermal Load to the Fault-Free
Data Set Consisting of 27 Performance Points Using Normal 2 Dataset

CF       Units           Range of      R-square, %
                   Variation of CFs

CQ1   [degrees]C       1.51-6.24          99.99

CQ2   [degrees]C       1.56-5.95          99.80

CQ5   [degrees]C       1.97-5.80          97.40

CQ6   [degrees]C       0.87-3.38          96.98

CP1  kW/[m.sup.2]      68.2-83.1         0.0082
      [degrees]C

CF           Model             RMSE

CQ1  0.003418+0.01756 Q_ev  0.00836

CQ2   0.1689+0.01612. Q_ev   0.0667

CQ5   0.9351+0.01293. Q_ev    0.197

CQ6  0.1320+0.008891. Q_ev   0.1462

CP1          72.06            3.376

Increasing the thresholds of the t-value reduces false alarms but also reduces the sensitivity of the FDD process, i.e., faulty behavior will go unnoticed or undetected. At this time, there is no well-established procedure that can be used to set these thresholds. The current feeling among FDD researchers is that even a low false alarm rate of, say, 5% would still be unacceptably high and result in the operator disabling the system altogether. One could consider different implementation schemes. For example, one could use two different thresholds, one to indicate that a fault may have occurred, another to signal the onset of a fault with more certitude. An alternate option is to adopt control chart techniques used in industrial process control, where a small set of observations are analyzed together to detect departure from normal operation rather than a single point. Such multipoint alarm schemes are bound to be more robust than single-point schemes. A third practical option is to use different thresholds for different faults. For example, from Figure 3, we note that different CFs are affected to varying degree by the faults. The trend lines of CQ6 under fault-free and faulty behavior for F4 or those for CQ5 under F6 are distinctly different, while those for CP1 under F5 much less so. In this illustrative study, we have selected the threshold limits for the t-values rather arbitrarily by assuming values of 3.0 and 4.0 (which, if the residuals of the 27 data points were to follow the t-distribution with 26 degrees of freedom, would suggest a one-tailed probability or significance level or false alarm rate of about 0.30% and 0.02%).

Assuming these thresholds, we have computed the false alarms using three different fault-free data sets (note that only one of the data sets, namely, Normal 2, was used for fault-free model identification). The results are shown in Table 5. For example, under Normal CF data set, the false alarm occurrences reduce from four to one for CQ5 when the t-threshold is increased from 3.0 to 4.0. Looking at the "Total" column, we note that selecting a threshold value of t = 3.0 could result in five to six false alarms (in data sets Normal 1 and Normal CF) in a set of 27 performance points, which would be deemed excessive. Selecting a value of t = 4.0 reduces the range to a more acceptable range of two to three occurrences over 27 data points.

Table 5. Number of Incorrectly Signaled Fault Detection Occurrences
from Individual CFs Using the Simple Regression Model Approach with
Three Fault-Free Data Sets Consisting of 27 Performance Points Each

Dataset    CQ1  CQ2  CQ5  CQ6  CP1  Total

Normal 1   0/0  0/0  1/1  2/1  2/1   5/3
Normal 2   0/0  0/0  0/0  1/1  1/0   2/1
Normal CF  1/0  0/0  4/1  1/1  0/0   6/2

Notes:

Only Normal 2 data set was used to identify the fault-free simple
regression models.Two values are indicated, corresponding to two
different threshold values for the assumed t-statistic: 3.0 /4.0

The issue of missed opportunity is not straight-forward and is very specific to not only the chiller type but also to the specific installation (see Reddy [2007a] for details). Only a brief summary is provided here. Discussions with the engineering and service managers of a large capacity chiller unit of a major company on issues such as probability of occurrence of different faults, energy implications of various faults, and what other issues need to be considered during evaluation of different FDD methods revealed the following.

a. It is difficult to generalize the effect of different faults on centrifugal chillers. The specific chiller design, selection of specific components, and type of control (whether TXV or orifice plate) all have an important effect on the onset of faults in a chiller.

b. Fault severity levels are manufacturer specific. For example, certain chiller designs cannot be overcharged by 20% excess refrigerant (the RP-1043 chiller data includes 40% refrigerant overcharge tests). The same with refrigerant loss--surging and other undesirable phenomena would occur when even 20% refrigerant loss occurs in such machines. The importance of the noncondensables in system fault would depend on whether it is a low-or high-pressure machine (i.e., on the working refrigerant used).

c. Thermal load under which equipment is operated is a very important factor during faulty operation. The energy penalties are likely to be very different, with maximum penalty due to faults occurring at maximum cooling load.

d. Loss of cooling capacity is too intangible and plant specific. Though this is an important issue, it is difficult to quantify this effect and include it in the FDD process since it depends too much on the annual cooling load profiles of the buildings being served, the type of building (how critical it is to meet the desired cooling load), and specific cooling plant design (whether multiple chillers are used and what mix).

e. Heuristic ranking for frequency and importance/impact of different faults. Table 6 assembles some tentative ranking in terms of the frequency of different faults (related to probability of occurrence) and their importance/ impact in terms of associated effort for remedial action and occurrence frequency. Thus, condenser fouling (with a ranking of 1) is to be interpreted as the most critical in terms of cost of repair, with refrigerant overcharge (with a rank of 6) as the least critical since this is a fault that ought to be detected at start-up commissioning and not during routine operation.

f. Energy penalty of different faults. Service personnel from the large chiller manufacturing company kindly agreed to use an internal software program to simulate energy use under various faults at different fault severities and at the 27 operating points similar to those adopted during RP-1043 lab chiller tests. Table 6 assembles suggested values for use in the FDD evaluation for excess electric energy use (in percent) of different faults at different severity levels (as indicated in Table 1) along with their frequency of occurrence and their impact. However, it is important to note that these are preliminary suggestions and are bound to be different for different generic chiller types and sizes. In any case, whatever FDD method is used, a certain amount of customization to the specific chiller system would be required in the light of the issues discussed above. An important issue impacting experimental design can be gleaned from Table 6. We note that the severity levels selected by RP-1043 for faults F2, F3, and F5 are too small in terms of the associated energy penalties. An experimental design where the fault severity levels were chosen so as to result in a preselected energy penalty would have been the better procedure instead of the adopted one, which was based on physical considerations (such as a predetermined decrease in fluid flow rate or a certain percentage of condenser tube blockage to mimic fouling).

Table 6. Excess Electric Use Due to Different Faults and Severity
Levels Assumed in RP-1043 Research

                            Energy Penalty

    Fault                                        Impact Frequency

                      SL    SL2%     SL3%  SL
                      1%                   4%

F1  Reduced           0.70  1.9      3.0   5.3     3       4 (1/yr)
    condenser-water
    flow

F2  Reduced           0.0   0.0      0.40  0.90    4       3
    evaporator-water                                     (1-3/yr)
    low

F3  Refrigerant leak  0.14  0.31     0.47  0.71    2       1
                                                         (1-2/yr)

F4  Refrigerant       0.80  0.94     3.8   7.6     6
    overcharge

F5  Condenser         0.50  0.50     0.50  1.8     1       2 (1/yr)
    fouling

F6  Noncondensables   4.5   6.2      7.4   15.6    5       5 (1/yr or
    in refrigerant                                         rare)

* Ratings of 1 is highest

Notes:

A value of 5.3 implies that the electric use increased by 5.3% w.r.t
fault-free use.
The data sets selected for further analysis are shown bolded.
The values in the last column indicate the relative frequency of
occurrence of different faults (based on discussion with a large
company that manufactures chillers and also provides maintenance
service).

It would have been best if we could select fault severity levels with energy penalties in the range of 3%-4%, which is a realistic range in view of sensor errors. However, the data sets available to us did not allow this, and so we have selected one severity level for each faulty datum, which was deemed most appropriate (energy penalties in the range of 0.7%-4.5% as shown bolded in Table 6). Again, to demonstrate the working of the FDD method proposed, we have used the t-value thresholds of both 3.0 and 4.0 for fault detection to screen the six faulty-data sets. The results are assembled in Table 7 and denote the number (out of 27 data points) of correctly detected faulty data points. The fault detection is done even if the residual of one CF exceeds the selected t-threshold value. Note that an ideal detector would have scored 27 in the cells shown bolded. For example, consider the detection of faults in the data set labeled F5-SL4 using CP1. The detection rate decreases from 16 to 4 occurrences when t-thresholds are increased from 3.0 to 4.0, which clearly indicates that missed opportunity rates have increased. One can use these results to get a sense of how fault detection is impacted by selecting different t-value thresholds. Such results could be weighted by the impact and frequency rating of different faults (shown in Table 6) so as to assign an overall score. Future investigations involving practical implementation of the proposed FDD method would have to address such issues in the context when data labeled as fault-free and faulty are unavailable.

An important conclusion drawn from Table 7 is that the proposed method can be tuned to generate false alarms lower than a proportion selected by the user (in our case either 1 or 2 at most out of 27 performance points) while providing 100% fault detection under faulty operation (there is no row in the six faulty data sets that has 0.0 in all columns). The drawback is that not all faults can then be diagnosed uniquely and without misdiagnosis (see Table 8). For example, applying our FDD method to data set F4-SL3 with the t-threshold = 4.0 would have erroneously signaled faults F1 and F5 in 5 and 25 instances, respectively, while only providing the correct diagnosis of F4 (and F6, which has an identical fault pattern) in 23 instances. The most poorly diagnosed fault is condenser fouling F5 (4 out of 27 instances only). The merit of favoring robustness over sensitivity is that this would provide increased confidence to the user during the early adoption of FDD tools and thereby be beneficial to field adoption of FDD methods in the longer run. It is more important to be sure that a fault has indeed occurred in the system rather than try to avoid an occurrence of missed opportunity.

Table 7. Number of Faults Signaled by Different CFs (Out of a Total of
27 Performance Points)

Datasets   CQ1    CQ2    CQ5    CQ6    CP1
used

F1-SL2     0/0   27/27  20/12   0/0    4/2

F2-SL4    27/27   0/0    0/0    0/0    2/2

F3-SL4     2/0    0/0   27/27  26/24  27/27

F4-SL3     1/0    8/5   26/25  27/24  27/25

F5-SL4     1/1    3/0    4/2   16/8   16/4

F6-SL1     3/1    1/0   27/27  27/27  27/27

Notes:

Two values are indicated in each cell, corresponding to two different
threshold values for t-values: 3.0/4.0.
In an ideal case, only the bolded cells should show 27, while the
remainder should be 0.

Table 8. Number of Fault Diagnosis Outcomes Predicted by the FDD Scheme
Out of a Total of 27 Performance Points Using the Diagnosis Rules Shown
in Table 3

Data Set  F1  F2   F3   F4  F5  F6

F1-SL2   27    0    0    0   2   0

F2-SL4    0   27    0    0   0   0

F3-SL4    0    0   24    0   0   0

F4-SL3    5    0    0   23  25  23

F5-SL4    0    1    0    2   4   2

F6-SL1    0    1    0   27  27  27

Notes:
The threshold value for the t-statistic = 4.0.
For an unique diagnosis, only the cells shown bolded should be 27,
while the remaining cells should be 0.

CONCLUSION AND FUTURE WORK

Implementing the FDD scheme proposed involves a number of challenges. Data labeled as fault-free and faulty will generally be unavailable for a field chiller, and some sort of online tuning of the fault detection thresholds will have to be done over time starting from some loosely set heuristic limits. Further, even if the general trends of how specific CFs vary under specific faults may be consistent across chillers of the same generic type and control mechanism, the regression models will have to be customized for fault-free behavior of the specific chiller, and clean fault-free data would be required for this purpose. What this paper suggests is an FDD approach involving simple models for the fault-free behavior of five important characteristic features from which six process faults can be identified (though two cannot be done uniquely). The important contributions of this paper are not only the specific selection of the CFs and the diagnosis rules but the attempt to provide clear guidance to other researchers wishing to adopt and evaluate (and modify as appropriate) the methodology and analysis results against other chiller types and sizes. This is important since numerous field trials are necessary before this procedure (or its mutation) can be adopted with confidence for all chillers.

The scope of this research has been limited to process faults only. A good and practical FDD method should also consider other fault categories, such as sensor faults, actuator faults, and control loop or controller faults. Further, the FDD method proposed only relied on thermodynamic data (temperature, pressure, flow, and electric power), while it would be advantageous, even for an automated FDD process, to include other types of sensor data (such as vibration meters) as well as one-time measurements (such as oil debris analysis) that are used in condition monitoring programs of large mechanical and electrical equipment.

ACKNOWLEDGMENTS

This research was sponsored by ASHRAE TC 7.5, Smart Building Systems. Constructive comments and suggestions by the PMSC members are greatly appreciated. We acknowledge advice and helpful feedback from Ashish Singhal, John Seem, Bill McQuade, Justin Kauffman, Dennis Dietz, and John House.

NOMENCLATURE 

[C.sub.d][A.sub.0] = expansion valve blockage coefficient 

[C.sub.p] = specific heat at constant pressure

COP = coefficient of performance of chiller

E = electric power input to compressor motor

h = enthalpy 

m = mass flow rate

p = pressure

[Q.sub.ev] = thermal heat load or capacity

T = temperature

[T.sub.c] = saturated refrigerant temperature in condenser

[T.sub.cdi] = condenser-water inlet temperature

[T.sub.cdo] = condenser-water outlet temperature

[T.sub.co] = refrigerant temperature leaving condenser

[T.sub,cpi] = refrigerant temperature entering compressor or leaving evaporator

[T.sub.cpo] = refrigerant temperature at compressor discharge

[T.sub.e] = saturated refrigerant temperature in evaporator

[T.sub.evi] = evaporator-water inlet temperature

[T.sub.evo] = evaporator-water outlet temperature

t-value = student t-statistic

UA = overall heat conductance of heat exchanger

[W.sub.in] = mechanical power input to compressor

x = regressor variable

y = response variable

[nu] = specific volume

[eta] = efficiency

1, 2, 3, 4= state points as indicated on the pressure-enthalpy diagram of Figure 2

Subscripts

cd = condenser

ch = chiller, evaporator

ev = evaporator

r = refrigerant

Acronyms

CF = characteristic feature

CP = characteristic parameter

CQ = characteristic quantity

FD = fault detection

FDD = fault detection and diagnosis

RMSE = root mean square error

SL = severity level of a fault

TXV = thermostatic expansion valve

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DISCUSSION

Bill Mohs, R&D Engineer, Thermo King, Minneapolis, MN: The speaker mentioned five critical parameters (CQ1, CQ2, CQ5, CQ6, and CP7) but did not explicitly state them in the presentation.

T. Agami Reddy: The five parameters that were found to be most useful for the chiller default detection and diagnosis method presented are as follows:

1. Evaporator water temperature difference

2. Condenser water temperature difference

3. Refrigerant condenser subcooling (difference between refrigerant leaving temperature and refrigerant saturation temperature)

4. Condenser approach temperatured difference (between condenser refrigerant saturation temperature and condenser water outlet temperature)

5. Condenser overall heat loss coefficient

The exact details are discussed in the technical paper on which the presentation was based. Note that these are specific to the chiller studied, namely, a centrifugal chiller with TXV control. I suspect that the critical parameters will differ for other generic chillers and types of control.

T. Agami Reddy, PhD, PE

Member ASHRAE

T. Agami Reddy is a professor in the Civil, Architectural and Environmental Engineering Department at Drexel University, Philadelphia, PA.