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Evolutionary tuning of building models to monthly electrical consumption.

INTRODUCTION

Sustainability, with its connections to energy and climate change, is perhaps the defining challenge of our time. With only 5% of the world's population, the U.S. consumes 25% of the world's primary energy and contributes 21% of the world's greenhouse gas emissions (DOE 2011). The largest sector of energy consumption is the ~119 million buildings in the U.S. that consume 40% of the U.S. primary energy (73% of the electrical energy). It is estimated that, by 2030, 60% of the urban building floor space to be in China and 67% will be in India. With the economic growth and modernization of highly populous regions of the Earth, energy security and sustainability will become increasingly important in a world whose global energy consumption is estimated to increase 50% by 2030. With buildings being the largest single sector of energy consumption, building efficiency is one of the fastest, easiest, and most cost-effective avenues toward achieving reduction in energy use.

There are many tools available that are used to project how specific policies or retrofit packages would maximize return on investment (ROI) with subsidies through federal, state, local, and utility tax incentives, rebates, and loan programs. Resolving issues such as principle-agent, first cost, ROI, and the cost/performance tradeoff between state-of-the-art versus standard equipment fall in the domain of these tools. Like all software tools, the Achilles heel is often "garbage in, garbage out" (GIGO); these tools rely on an accurate representation of the building being analyzed in order to perform an accurate analysis. A central challenge in the domain of energy efficiency for buildings is being able to realistically model specific building types; however, differences from actual monthly utility bills on the order of 24%-97% (Earth Advantage 2008; Roberts et al. 2012) are currently common. Many measurement and verification (M&V) protocols require accuracy of the coefficient of variation of the root mean squared error (CV [RMSE]) of 15%, relative to monthly calibration data, or 30% for hourly data (ASHRAE 2002). Achieving this accuracy is complicated by the fact that--unlike vehicles or airplanes, which are designed and built according to strict schematics--buildings are typically manufactured in the field based on one-off designs. This significant variability from prototypical buildings complicates even further the fact that there are thousands of parameters that must be known about a building to accurately model it using modern simulation engines.

There are several simulation engines, and tools that leverage those simulation engines, that are actively supported (DOE 2012d). The major simulation engine supported by the U.S. Department of Energy is EnergyPlus (DOE 2012e), with OpenStudio (DOE 2012f) serving as the primary interoperability middleware for communication between various tools and file formats. Graphical and other text-based user interfaces for E+ allow a user to provide parameters that fully describe a given building from which E+ calculates the detailed energy use of the building. These parameters are extensive, and their sensitivities are not yet fully explored. It is unrealistic to expect even an advanced user to be capable of providing accurate values for every parameter expected by E+. To mitigate this issue, users often use reference or template buildings already in a tool that are similar to their own as default points for parameter values. These values are then corrected to more closely match the actual building under consideration. In addition, average material properties are typically used from ASHRAE Handbook--Fundamentals, which next year will begin to publish the significant variances in material properties from controlled laboratory tests (ASHRAE 2013). However, the corrections currently made to building simulation parameters generally involve user intuition and experience and, thus, are not scientifically rigorous, repeatable, defensible, or transferrable. The Autotune project (New et al. 2012) aims to resolve these issues with an automated process.

If a user has accurate sensor information regarding the state of a building, it is possible to perform a search for more accurate parameters whose E+ output most closely matches the corresponding sensor data. The search space in such a problem is extremely large. Even if each parameter were a simple binary value (e.g., a categorical whose values were "yes" or "no"), the search space for a relatively small 3000-parameter building would contain [2.sup.3000] possibilities, which is unfathomably larger than the number of atoms believed to exist in the observable universe (about [2.sup.270]). This is a best-case scenario; the actual size of the search space is effectively infinite because many of the parameters are continuous-valued.

Evolutionary algorithms have been shown to efficiently search such extremely large spaces (Michalewicz and Fogel 2004). They generally avoid the problem of local optima by maintaining a population of possible solutions, rather than performing a strictly gradient-based approach. Regardless of the search algorithm employed, the massive size of the search space necessitates that large samples be drawn from which to determine promising areas to explore. This particular requirement is complicated here by the fact that a single E+ simulation (i.e., one sample) requires several minutes of computation time on a single processor core. Once again, however, evolutionary algorithms are uniquely suited to such problems because they are inherently parallel. For instance, each member of the population of solutions can be evaluated independently of the others. It is also possible to allow multiple versions of an evolutionary algorithm to run in parallel and share solutions with one another. These variants are collectively known as island models (Eiben and Smith 2007), and they have the potential for each population to explore different regions of the search space in different ways.

A part of the current E+ research effort has been directed toward developing a machine learning model that approximates the E+ system. In other words, given a set of E+ parameters, the model provides an approximation of the energy use output. Such a model can execute in a fraction of the time of the actual E+ system. An island model evolutionary algorithm could be used to maintain a large population of approximate solutions that are evaluated by the machine learning model, while at the same time maintaining a much smaller population of exact solutions that are evaluated with the actual E+ system. The best solutions found so far in the approximate island could migrate to the exact island where they can drive the search toward promising areas. In this way, cheap and fast approximations can be used to focus the search for accurate solutions.

A final complication of this search problem is that there are likely many different parameter settings that provide accurate matches for the true energy use, especially when limited sensor data is available and leaves the problem underdetermined (i.e., the search space is multimodal). Any search algorithm must be able to deal with such problems efficiently so that the user can have access to a set of near-optimal solutions from which to choose the most preferred. However, even more than being multimodal, the problem presented here is also multiobjective. The primary objective is the minimization of the difference between the E+ software state and the real-world (sensed) state of the building. Other objectives might include minimization in the number of parameter changes from a given reference building, minimization of changes to the most sensitive parameters, and/or maximal use of traditionally used parameters for software calibration. Once again, evolutionary algorithms are an excellent choice in such situations. Several widely used evolutionary multiobjective optimization algorithms exist, such as NSGA-II and SPEA2. These algorithms maintain a repository of candidate solutions that each represents different parameter settings and different objective values. The user can, at any point, stop the algorithm and choose from this repository the near-optimal solution that best meets their needs.

BACKGROUND

This section discusses the EnergyPlus simulation system, highlights previous work in the tuning of building models, and provides an introduction to evolutionary computation.

EnergyPlus

The EnergyPlus whole-building energy simulation engine was consolidated from diverse involvement circa 1996 with functionality traceable back to DOE-2 and the U.S. Department of Energy's Building Loads Analysis and System Thermodynamics (BLAST) from the late 1970s (EnergyPlus 2012). Its original design goals were to provide a more consistent software structure for development and modification, to allow third-party programs and components to easily interface with the core system, and to fully integrate the loads, systems, and plants into the simulation (DOE 2012e). The workflow for a building modeler using a system like EnergyPlus is to create a building's geometry using external software, layer it with detailed metrics encoding material properties, and add equipment currently or expected to be in the building, including anticipated operational schedules. A typical residential building model in EnergyPlus has approximately 3000 input parameters that must be specified.

Tuning of Building Models

Although even inaccurate models can be tremendously useful, specific business applications require sufficiently-accurate building energy models according to established guidelines (ASHRAE 2002). Modification of simulation algorithms can help address this, but the process of tuning virtual building models to match real data remains the most tractable way to meet such requirements. Unfortunate for the advancement of the field, this tuning process has remained an art that even the practitioners most often do not enjoy. Informal interviews and surveys have indicated less than 1% of people actually enjoy the tuning process and, instead, see it as necessary and laborious. These practitioners often indicate the use of infiltration and schedules (of many types) as the primary "knobs" by which to tune the simulation to measured data. However, laboratory research has shown significant variance in the building materials used throughout the envelope of a building and will be incorporated in the latest edition of ASHRAE Handbook--Fundamentals (2013). As a starting point, this research paper will focus on tuning these critical envelope material properties before tuning based on properties such as infiltration, which is currently very difficult to measure over time and schedules (for which adequate smart-home emulation and sensing is not yet widely prevalent).

It should come as no surprise that, in order to reduce the cost of business, the idea of self-calibrating energy models has been around for decades with initial attempts beginning around the early 1980s. Much of the motivations, history, different levels of thoroughness in calibration, and state-of-the-art approaches (sensitivity analysis, reducing the number of simulations necessary, optimization methods, etc.) are expertly consolidated in ASHRAE report RP-1051 on the subject (Reddy et al. 2006). The Autotune project (New et al. 2012) seeks to facilitate the realization of calibrated energy models by leveraging the world's current fastest supercomputer (299,000-core Jaguar/Titan) and several other supercomputers to increase the number of simulations possible, the latest advances in Web-oriented database storage for queryable and publicly sharable storage of 156 inputs and 96 outputs at 15-minute resolution for 8 million E+ simulations, extensive data-mining for agent-based encapsulation of knowledge for deployment of an automated tuning methodology on a desktop or via the Web, simulation comparisons to a robotically emulated-occupancy ZEBRAlliance (2012; Biswas et al. 2012) 2800 [ft.sup.2] (260 [m.sup.2]) research home with 269+ channels of 15-minute sensor data, and advancing the state of the art in several machine learning algorithms for optimization. The Autotune project, in an effort to promote open science, is making a portion of the 267TB (26.9 trillion data points) of E+ simulation data publicly available at http://autotune.roofcalc.com.

Evolutionary Computation

Evolutionary computation (DeJong and Spears 1993; Spears et al. 1993; Fogel 1994, 2000) has been shown to be a very effective stochastic optimization technique (Back et al. 1997; Michalewicz and Fogel 2004). Essentially, an evolutionary computation (EC) attempts to mimic the biological process of evolution to solve a given problem (DeJong 2006).

Evolutionary computations operate on potential solutions to a given problem. These potential solutions are called individuals. The quality of a particular individual is referred to as its fitness, which is used as a measure of survivability (DeJong 2006). Most evolutionary computations maintain a set of individuals (referred to as a population). During each generation, or cycle, of the evolutionary computation, individuals from the population are selected for modification, modified in some way using evolutionary operators (typically some type of recombination and/or mutation) to produce new solutions, and then some set of existing solutions is allowed to continue to the next generation (Fogel 2000). Viewed in this way, evolutionary computation essentially performs a parallel, or beam, search across the landscape defined by the fitness measure (Russell and Norvig 2000, Spears et al. 1993). Abeam search is simply a search algorithm that maintains k states, rather than just one state, at each iteration.

The particular evolutionary operators used in this work were heuristic crossover and Gaussian mutation. Heuristic crossover works as follows. Given two parents, [p.sub.1] and [p.sub.2], where the fitness of [p.sub.1] is greater than the fitness of [p.sub.2], create two children. The first child is simply [p.sub.1]. Each element of the second child is created according to the equation where r is a uniform random value between 0 and 1. Gaussian mutation works by randomly modifying each element of a candidate solution using a Gaussian distribution centered on the current element with a variance that becomes a parameter to the algorithm.

According to Back et al. (1997), the majority of current evolutionary computation implementations come from three different but related areas: genetic algorithms (Holland 1975; Goldberg 1989; Forrest 1993; Vose 1999), evolutionary programming (Back et al. 1997; Fogel et al. 1966; Fogel 1994), and evolution strategies (Fogel 1994; Back et al. 1991). Each area is defined by its choice of representation of potential solutions and/or evolutionary operators. However, DeJong (2006) suggests that attempting to categorize a particular EC under one of these labels is often both difficult and unnecessary. Instead, he recommends specifying the representation and operators, as this conveys much more information than simply saying that a genetic algorithm was used, for example. We adopt DeJong's approach in this work.

METHODOLOGY

The simplest set of data that is common among all energy consumers is that of monthly electrical use, typically in the form of a utility bill. The work presented here attempts to optimize the match between a model building and actual monthly electricity use data. The reference building used in this work is house number 1 in the Wolf Creek subdivision (WC1), an Oak Ridge National Labs ZEBRAlliance experimental energy efficient home. This home has a plethora of energy-efficient technologies: (1) standing seam metal roof with infrared reflective pigments to boost solar reflectance, (2) ENERGY STAR appliances, (3) triple-pane low emittance Argon-filled windows, (4) compact fluorescent lighting, (5) horizontal ground loop installation that leverages foundation and utility excavations, (6) high-efficiency water-to-air heat pump for space conditioning, (7) high-efficiency water-to-water heat pump for hot-water heating, (8) an energy recovery ventilator for transferring heat and moisture between fresh incoming and outgoing air, and (9) structurally insulated panel (SIP) walls filled with expanded polystyrene insulation (for more information see ZEBRAlliance [2012] and Biswas et al. [2012]). The home has been fitted with hundreds of sensors that are capable of collecting subhourly data.

In the following experiments, two different model buildings are used. The first was last modified on March 29, 2012, and is stored in an E+ file named "House_1_V7_A2.idf," which matches whole-building annual electric consumption exactly but has a sum of absolute errors (1) (SAE) of 1276.34 kWh (4594.82 MJ) for monthly and 6242.04 kWh (22471.34 MJ) for hourly electrical data when summed for the entire year. An earlier version of the same model was completed on July 28, 2010, and is stored in a file named "House_1_07282010.idf," with SAE of annual electric consumption 1623.36 kWh (5844.10 MJ) for monthly and 8113.69 kWh (29209.28 MJ) for hourly electrical data when summed for the entire year. These two baseline models, which we shall henceforth refer to as the "refined" and "primitive" models, respectively, are separated by approximately four man-months of effort (consisting of two months of laboratory material testing and two months manually tuning the input file) over the course of nearly two calendar years, with the refined model being the recipient of that effort.

In this work, only a subset of the real-valued parameters of the models, as specified by domain experts, was used as a part of the tuning process, and the phrase "tuning parameters" will be used when referencing these variables. While all 156 tunable parameters provided through the project website are too extensive to list here, a majority of the parameters were for building material properties such as thickness, conductivity, density, specific heat, thermal absorptance, and solar absorptance, and visible absorptance for materials such as gypsum board, stone, concrete foundation wall, fiberglass insulation, metal roofing, plywood, insulation, gravel, oriented strand board (OSB), and cladding, as well as U-factor, solar heat gain coefficient, and visible transmittance for window glazing systems. Other parameters include fraction of latent and radiant for equipment, radiant and visible for lighting, flow coefficients for HVAC, heating and cooling air supply temperatures, building orientation, infiltration, and several others. It should also be noted while these are individual line changes in an E+ *.idf input file, several instances of each material, equipment, etc., may be used throughout a building. The Autotune system currently scales to tune any set of numerical parameters so the particular set of parameters can be customized according to the needs of a particular use case.

In 2010, the average U.S. residential building consumed enough energy to cost the homeowner $2201 (DOE 2012a). An average of 44.7% of the energy went to space heating and 9.2% toward space cooling (DOE 2012b), totaling 53.9% for space conditioning. However, primarily because of differing costs for various fuel types (DOE 2012c), 28.9% of cost was for heating and 14.0% for cooling, yielding 42.9% and amounting to $944/yr for space conditioning. However, the energy-efficient HVAC in WC1 actually consumed $472.62 for January 1 through November 30,2010. This cost may serve as a point of reference for the tuning results presented throughout the study.

For the all-electric WC1, the actual energy use data for all HVAC equipment was reliably collected from January 1 through November 28, 2010, at which point a new set of test HVAC equipment was installed. Therefore, in all experiments reported, the "yearly" electrical use will always refer to the electrical use from January 1 to November 28. The electrical use in this work was calculated as the sum of all of the heating and cooling ideal loads for every time period (in kilowatt-hours) divided by their respective unitless coefficients of performance (COPs). In this case, the COPs were 4.1 for heating and 4.62 for cooling in order to derive the anticipated HVAC electrical consumption (kWh). While higher-resolution COP measurements are available, the annual COP measures reported here are accurate for "yearly" electrical use. The conversion from heating and cooling loads to electrical consumption (load divided by annual COP) and subsequently cost (multiplying by utility rate) is solely for conveying the accuracy in traditional terms. For this reason, application of more advanced utility rate structures or rate-payer limitations to localize model accuracy in terms of U.S. dollars for a given region or occupant is still valid as a post-processing exercise.

In the following experiments, the primary metric used for measuring tuning accuracy is the monthly SAE. The SAE was calculated according to Equation 1, where Mi is the monthly heating plus cooling load of the model and Ai is the monthly heating plus cooling load of the actual ZEBRAlliance WC1 building. This equation only contains 11 months because actual data were not collected for December. The SAE was chosen for this study, instead of the RMSE, because of its immediate interpretability when converted to electric utility costs.

SAE = [11.summation over (i=1)][absolute value of [M.sub.i] - [A.sub.i]] (1)

Experiment 1--Abbreviating the Simulation Schedule

The E+ simulation requires a schedule that specifies temperatures and energy needs for every zone in the building being simulated for each time period. The full schedule for the reference building in this research extends for an entire year at one-hour intervals (8760 time periods). This type of finegrained schedule leads to a much more exact but computationally expensive simulation. In this case, a single simulation takes approximately eight minutes and cannot currently be efficiently parallelized.

It is possible to reduce the number of time periods in a given schedule by using representative time periods, rather than the entire year. In this case, four days were chosen spanning the year--January 1, April 1, August 1, and November 1--which produced only 96 time periods. This amounts to only 1% of the size of the full schedule. Likewise, running E+ on this abbreviated schedule requires only a matter of seconds. However, it is important to determine whether good performance (i.e., low error compared with the actual electrical use) on the abbreviated schedule correlates with good performance on the full schedule.

Experimental Setup. To determine the correlation between the error rate of the abbreviated schedule and that of the full schedule, the search space of E+ building parameters (using the abbreviated schedule) needed to be sampled and analyzed. However, these samples could not be truly random because random samples would almost certainly produce high error when compared to actual electrical use, which would provide little information. Instead, samples needed to span the range from high error to low error.

In this experiment, the actual electrical use is, in fact, the E+ output from running the refined model, which is modified by each candidate solution. To accomplish the sampling, an EC was created with a population size of 16 individuals and was allowed to run for 1024 simulations (64 generations). This allowed the EC to begin with a random sampling of the parameter space, which could be refined through the generations to produce parameters with lower error. To ensure against statistical anomalies, the EC was run four different times with different initial populations each time.

Though not entirely necessary or relevant for the purposes of this experiment, the full EC parameters are provided for completeness. Tournament selection (tournament size 4) was used for parent selection. Generational replacement with weak elitism (one elite) was used for survivor selection. Heuristic crossover (and Gaussian mutation) were used as the variation operators. The mutation use rate was set to 1.0, and the Gaussian mutation rate was set to 10% of the allowable range of each variable. The fitness of a candidate solution was calculated to be the SAE between its monthly electrical use and the actual monthly electrical use. For the four-day schedule, this monthly electrical use is zero in all months except January, April, August, and November, in which case it is only the total use for the first day of each month.

Results. The entire set of 1024 individuals for each of the four trials is plotted in Figure 1. This plot compares the SAE between the candidate solutions and the actual electrical use, both for the four-day schedule and the yearly schedule. Individuals from each of the four trials are colored black, red, green, and blue, respectively. It is clear from the graph that there is a strong linear correlation between the electrical use with the four-day schedule and that of the yearly schedule. More precisely, this correlation was 0.9603, 0.9421, 0.9015, and 0.9555 for each of the four trials, respectively, as seen in Table 1.

The high correlations between the abbreviated and full schedules reveal a possible solution to the issue of the high computational overhead of E+ simulations. It is possible, at least for the single building currently under investigation, to use a much faster abbreviated schedule as a reasonable surrogate for the more expensive full-year schedule. However, these correlations do deteriorate, sometimes dramatically, as the minimization process progresses. Table 1 shows the correlations between the four-day and yearly SAE as the data is focused more and more toward the final n% (i.e., the solutions produced later in the search, where 10% in the "Data Used" column means that only the final 10% of solutions was used for the correlations). The correlation tends to decrease, and in Trial 3 it decreases substantially. This means that using the four-day SAE may not be as effective as the evolutionary search progresses. However, certainly at the beginning, the four-day SAE is a very good (and fast) approximation.

Experiment 2--Tuning the Refined Model

In this experiment, the four-day abbreviated schedule is applied to ascertain the time required and the accuracy of the tuning process between the refined E+ model and actual WC1 data.

Experimental Setup. An EC was created containing candidate solutions composed of real values representing, and bound to the ranges of, the real-valued tuning parameters. This means that each candidate solution was a list of real values that specified those parameters of the building model. The EC used a population size of 16, tournament selection with tournament size 4, generational replacement with weak elitism (one elite), heuristic crossover, and Gaussian mutation with a use rate of 1.0 and a mutation rate of 10% of the allowable range of each variable. The fitness reported is the SAE of the monthly electrical use between the model and WC1 (and load in Megajoules), and the EC was allowed to use only 1024 fitness evaluations (i.e., E+ simulations). Because of the stochastic nature of the evolutionary search, eight independent trials were performed.

[FIGURE 1 OMITTED]

Results. First, it is important to establish a baseline of performance. In this case, the obvious baseline is the SAE between the refined model E+ output and the actual electrical use. These were 12.813 kWh (46.1268 MJ) for the four-day and 1276.340 kWh (4594.824 MJ) for the yearly. The final average and minimum fitness values for each trial are presented in Table 2. The average minimum SAE across the eight trials was 10.259 kWh (36.9324 MJ) and 1078.842 kWh (3883.831 MJ) for the four-day and yearly electrical use, respectively. This amounts to a 20% reduction in the four-day SAE and a 15% reduction in the yearly SAE. The total computational time for all eight trials on an eight-core machine was approximately 12 hours, so it is likely that a single-core machine could process a single trial in a similar amount of time (overnight).

As stated previously, we use utility rates solely to convey the tuning accuracy in dollars; this does not affect our tuning methodology. Throughout this report, we'll use the 2010 national average utility rate of 11.5 cents per kilowatt-hour. In this case, the refined model produced a cumulative error of $147 per year while the average cumulative error across the eight tuned models was $124 per year. This corresponds to a reduction in error from 31% ($147 of $473 actual yearly use) to 26%.

Experiment 3--Tuning the Primitive Model

The refined model used in the previous experiment was constructed, as mentioned previously, through approximately four man-months over the course of two calendar years. Two of the primary research questions are whether such a model could be automatically created and with what degree of fidelity to the actual energy data. In order to test this, we leverage the primitive model from which the refined model was created. In this experiment, the primitive model is used as the base in order to determine whether the tuning results are competitive with the refined model.

Experimental Setup. The experimental setup was identical to that defined for the previous experiment.

Results. As before, it is important to establish a baseline for comparison. In this case, there are two building models--primitive and refined. Their (lack of) accuracy (SAE) compared to the actual WC1 data serves as the baseline. In this experiment, the primitive model produced a four-day SAE of 17.995 kWh (64.782 MJ) and a yearly SAE of 1623.364 kWh (5844.11 MJ). The refined model produced a four-day SAE of 12.813 kWh (46.1268 MJ) and a yearly SAE of 1276.340 kWh (4594.824 MJ). The final population statistics for the eight trials are presented in Table 3.

The average minimum SAE across all eight trials was 12.800 kWh (46.080 MJ) forthe four-day SAE and 1415.213 kWh (5094.767 MJ) for the yearly SAE. Compared to the newer refined model, the four-day SAE of the tuned model is actually slightly better, and its yearly SAE is only about

140 kWh (500 MJ) greater. In contrast, the yearly SAE of the primitive model is about 350 kWh (1260 MJ) greater than the refined model. That corresponds to a 60% reduction from the primitive model toward the refined model. Once again, the four-day SAE, on which the EC was evaluated, shows remarkable performance. The tuned yearly SAE is a definite improvement over the primitive model, but it is likely to perform even better if it is incorporated into the evolutionary process. It should be noted that this 60% reduction in yearly SAE was achieved, as in the previous experiment, in about 12 hours on a single-core machine, rather than four man-months. It should also be noted that the manual refinements between the primitive and refined files changed several properties of the model outside the scope of the envelope material properties being automatically tuned in these experiments, making 100% SAE reduction unachievable. Table 4 enumerates those changes. It should be noted that, of all of the properties listed in Table 4, only the zone infiltration flow coefficient was accessible to the tuning process.

Experiment 4--Combining Abbreviated and Full Schedules

The final experiment completely duplicates the methodology of those above, except in regards to the evaluation of the fitness. In this experiment, the first 768 fitness evaluations (E+ simulations) were performed using the four-day schedule and electrical use. At the end of those evaluations, the best half (8) of the final population's candidate solutions were inserted into a new initial population of 16 individuals that was evolved for the remaining 256 evaluations on the yearly electrical use and schedule. In this way, the yearly schedule could be incorporated into the evolution after near-optimal candidates had quickly been found using the abbreviated four-day schedule.

Recall that the yearly SAEs produced by the primitive model and the refined model were 1623.364 kWh (5844.11 MJ) and 1276.340 kWh (4594.824 MJ), respectively. Table 5 shows the statistics of the final populations of the evolutionary tuning. Recall that each of the trials produces a population of 16 tuned models, of which one will have the minimum yearly SAE (as listed in the "Minimum" columns in Table 5). The average of these eight minimum values is the most representative value for the performance of the tuning process for each of the primitive and refined models.

Compared to the refined model with average minimum yearly SAE of 1026.844 kWh (3696.638 MJ), the tuned refined model corresponds to an almost 25% reduction in yearly SAE using the yearly schedule, compared to the 15% reduction when using the four-day schedule. For the primitive base model, the average minimum yearly SAE was 1392.688 kWh (5013.677 MJ). Recall from above that the difference in yearly SAE between the primitive and refined models was about 350 kWh (1260 MJ). In the previous experiment, the EC was able to reduce that difference to about 140 kWh (500 MJ) (a 60% reduction). Here, the difference was reduced to about 116 kWh (418 MJ), which corresponds to a 67% reduction. It appears that there may be diminishing gains in continuing to tune the primitive model. As mentioned above, this is due to variables that were changed between the primitive and refined models to which the EC has no access. In such a case, no amount of tuning will be able to provide better performance than the refined model.

CONCLUSIONS AND FUTURE WORK

A portion of the results of the experiments in this work are summarized in Table 6. This table shows the baseline for each model, which is the yearly SAE produced between the E+ model output and the actual data from WC1. It includes results from tuning with the abbreviated four-day schedule as well as the serial four-day schedule followed by the full schedule evaluation.

Table 7 provides information about the CV(RMSE) of the baselines and different tuning approaches. Here, the CV(RMSE) is calculated as specified in Equation 2. While these values are not competitive with the ASHRAE Guideline 14 of 15% for monthly utility CV(RMSE), they do provide a starting point and a context for both the inadequacy of the primitive model and the ability of the tuning process to reduce the error noticeably.

CV(RMSE) = [square root of ([11.summation over (i=1)][([M.sub.i] - [A.sub.i]).sup.2]/11)]/[11.summation over (i=1)][A.sub.i]/11 (2)

These experiments have shown that an evolutionary search can provide effective tuning to an existing model, in acceptable time (e.g., overnight), when judged on monthly electrical use. The primitive and refined models under consideration were both significantly improved upon by the EC in comparison to actual measured data. In the first experiment, justification was given, and experimentation verified the use of an accelerated tuning methodology using abbreviated schedules. In the second experiment, operating only on the four day surrogate simulations, the EC was capable of reducing the SAE by 15%. In the third experiment, the tuned primitive model's SAE was reduced by 13%, replacing ~60% of the ~4 man-months with an overnight computation on a single core. In the final experiment, the yearly simulations were brought into the evolutionary process directly by allowing the final quarter of the search process to specifically use the yearly, rather than the four-day, simulations as part of a serial process to measure fitness. The tuned primitive model reduced SAE by 14%, which was a 67% move toward the refined model (with 100% unachievable since properties outside the scope of tuning material properties were used to change the files between the primitive and refined models). Tuning the refined model resulted in a 25% reduction in SAE.

These experiments do not address central tuning questions regarding tuning of properties other than electrical data for HVAC consumption using envelope material properties, whether the modifications made to the input file are physically realistic, and prioritization of which properties should be explored first. These subjects will be partially addressed in publications for previously conducted work, whereas the following subjects may be addressed in future work. The Autotune process is simulation-engine agnostic and is being designed to ease its general application; it is currently being tested as a calibration procedure for DOE's Weatherization Assistance Program's National Energy Audit Tool (NEAT) used to weatherize one million homes as part of the American Recovery and Reinvestment Act (ARRA). More importantly, the Autotune project (New et al. 2012) is designed to be domain-agnostic as a way of bridging the gap between the virtual world and the real one in holding software accountable and automating the process of empirical science.

ACKNOWLEDGMENTS

This work was funded by field work proposal CEBT105 under the Department of Energy Building Technology Activity Number BT0201000. We would like to thank Amir Roth for his support and review of this project. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. Our work has been enabled and supported by data analysis and visualization experts at the RDAV (Remote Data Analysis and Visualization) Center of the University of Tennessee, Knoxville (NSF grant no. ARRA-NSF-OCI-0906324 and NSF-OCI 1136246). Oak Ridge National Laboratory is managed by UT-Battelle, LLC, forthe U.S. Dept. of Energy under contract DEAC05-00OR22725. This manuscript has been authored by UT-Battelle, LLC, under Contract Number DEAC05 00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

DISCUSSION

Ron Judkoff, Chief Architectural Engineer, NREL, Golden, CO: Regarding "metrics," the presenter only mentioned "goodness of fit" or "fitness" as a metric. It is possible to have a good fit for the wrong reasons. The NREL methodology for testing calibration procedures uses three metrics, "goodness of fit," accuracy of retrofit savings predictions, and how well the calibration method identified the "truth" input parameters.

Joshua New: We have collected metrics that show per-variable accuracy of 15% when monthly data is available and 8% with hourly data that is outside the scope of this current ASHRAE publication (is in review), but these metrics which quantify the extent to which Autotune matches "the real building" was shared in DOE Building Technology Office peer review: www1.eere.energy.gov/buildings/technologies/pdfs/emrg tech03_new_040213.pdf.

The key is that there is a set of metrics which quantify the physical realism of a tuning process, which corresponds to metric #3 from the commenter's list of methods. We shared results in the paper for metric #1, and metric #2 was notapplicable since there was no retrofit to the building used in this study.

Stephen Long, Manager, Southern California Edison, Rosemead, CA: Can this approach be applied to other modelling approaches than Energy Plus?

Joshua New: Yes. Autotune was designed to be simulation engine agnostic from the beginning and can apply to any computer program which meets the 4 following criteria:

1) Takes input

2) Provides output

3) Can be run in a tractable amount of time, and

4) Has "real world" data to compare against.

This was necessary due to foreseen changes in EnergyPlus (separate story). The primary items that need to be changed to accommodate a new simulation engine is to convert the file input/output mechanisms for the simulation engine and have a running engine on a platform that runs Autotune. As an example, we converted the Office of Weatherization and Intergovernmental Programs' (OWIP) National Energy Audit Tool (NEAT), which uses a variable-degree-day method, to use Autotune in about a man-month.

While the NEAT conversion hasn't been made public, the general approach, technical details, and methods for Autotune are well-documented in 29 related publications since April 2012 (attached with links to preprint PDFs). It is ok to share my contact information if they are interested in following-up directly.

REFERENCES

ASHRAE. 2002. ASHRAE Guideline 14, Measurement of Energy and Demand Savings. Atlanta: ASHRAE.

ASHRAE. 2013. ASHRAE Handbook--Fundamentals, Chapter 26, "Heat, Air, and Moisture Control in Building Assemblies--Material Properties." Atlanta: ASHRAE.

Back, T., F. Hoffmeister, and H.-P. Schwefel. 1991. A survey of evolution strategies. In R. K. Belew and L. B. Booker, editors, Proceedings of the 4th International Conference on Genetic Algorithms, pp. 2-9.

Back, T., U. Hammel, and H.-P. Schwefel. 1997. Evolutionary computation: Comments on the history and current state. IEEE Transactions on Evolutionary Computation 1(1):3-17.

Biswas, K., A. Gehl, R. Jackson, P. Boudreaux, and J. Christian. 2012. Comparison of Two High-Performance Energy Efficient Homes: Annual Performance Report, December 1, 2010-November 30, 2011. Oak Ridge National Laboratory report ORNL/TM-2011/539. http:// info.ornl.gov/sites/publications/files.Pub34163.pdf

Briggs, R.S., R.G. Lucas, and Z.T. Taylor. 2003. Climate classification for building energy codes and standards: Part 1--Development process and Part 2--Zone definitions, maps, and comparisons. ASHRAE Transactions 109(1):109-30.

DeJong, K.A., and W. Spears. 1993. On the state of evolutionary computation. In Stephanie Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, CA, pp. 618-623.

DeJong, K. A. 2006. Evolutionary Computation: A Unified Approach. Cambridge, MA: MIT Press.

Deru, M., K. Field, D. Studer, K. Benne, B. Griffith, P. Torcellini, B. Liu, M. Halverson, D. Winiarski, and M. Rosenberg. 2011. U.S. Department of Energy commercial reference building models of the national building stock. Technical Report NREL/TP-5500-46861, National Renewable Energy Laboratory, U.S. Department of Energy, Washington, D.C.

DOE. 2008. Energy efficiency trends in residential and commercial buildings, Figure 18. U.S. Department of Energy, Washington, D.C. http://apps1.eere.energy.gov/ buildings/publications/pdfs/corporate/ bt_stateindustry.pdf.

DOE. 2011. Buildings Energy Data Book. U.S. Department of Energy, Washington, D.C. http://buildingsdatabook.eren.doe.gov.

DOE. 2012a. Buildings Energy Data Book. Average annual energy expenditures per household, by year ($2010). U.S. Department of Energy, Washington, D.C. http:// buildingsdatabook.eren.doe.gov/docs/xls_pdf/2.3.9.pdf.

DOE. 2012b. Buildings Energy Data Book. Residential sector energy consumption, Table 2.1.5. U.S. Department of Energy, Washington, D.C. http://buildingsdatabook.eren.doe.gov/TableView.aspx?table=2.1.5.

DOE. 2012c. Buildings Energy Data Book. 2010 residential energy end-use expenditure splits by fuel type ($2010 billion), Table 2.3.5. U.S. Department of Energy, Washington, D.C. http://buildingsdatabook.eren.doe.gov/ TableView.aspx?table=2.3.5.

DOE. 2012d. Building energy software tools directory. Department of energy tools 2012. U.S. Department of Energy, Washington, D.C. http://apps1.eere.energy.gov/ buildings/tools_directory/subjects_sub.cfm.

DOE. 2012e. Getting started with EnergyPlus: Basic concepts manual. U.S. Department of Energy, Washington, D.C. http://energyplus.gov.

DOE. 2012f. OpenStudio: Commercial buildings research and software development. National Renewable Energy Laboratory, U.S. Department of Energy, Washington, D.C. http://openstudio.nrel.gov.

Earth Advantage Institute. 2009. Energy performance score 2008 pilot: Findings and recommendations report. Report prepared for EnergyTrust of Oregon. Earth Advantage Institute, Portland, OR and Conservation Services Group, Westborough, MA.

EIA. 2012. Frequently asked questions. http://www.eia.gov/ tools/faqs/faq.cfm?id=97&t=3. U.S. Energy Information Administration, Washington, D.C.

Eiben, A.E. and J.E. Smith. 2007. Introduction to Evolutionary Computing. New York: Springer.

Fogel, D.B. 1994. An introduction to simulated evolutionary optimization. IEEE Transactions on Neural Networks 5(1):3-14.

Fogel, D.B. 2000. What is evolutionary computation? IEEE Spectrum 37(2):26-32.

Fogel, L.J., A.J. Owens, and M.J. Walsh. 1966. Artificial Intelligence through Simulated Evolution. New York: Wiley.

Forrest, S. 1993. Genetic algorithms: Principles of natural selection applied to computation. Science 60:872-78.

Goldberg, D.E. 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley.

Holland, J.H. 1975. Adaptation in Natural and Artificial Systems. Ann Arbor, MI: University of Michigan Press.

ICC/ASHRAE. 2009. 2009 International Energy Conservation Code and ANSI/ASHRAE/IESNA Standard 90.12007 Energy Standard for Buildings Except Low-Rise Residential Buildings. Washington, D.C.: International Code Council and Atlanta: ASHRAE.

Michalewicz, Z., and D.B. Fogel. 2004. How to Solve It: Modern Heuristics. New York: Springer.

New, J.R., J. Sanyal, M. Bhandari, and S. Shrestha. 2012. Autotune E+ building energy models. Proceedings of the 5th National SimBuild of IBPSA-USA, Aug. 1-3. http://www.ibpsa.us/simbuild2012/Papers/ SB12_TS05a_1_New.pdf.

Reddy, T.A., I. Maor, S. Jian, and C. Panjapornporn. 2006. Procedures for reconciling computer-calculated results with measured energy data. ASHRAE Research Project RP-1051, ASHRAE, Atlanta, GA.

Roberts, D., N. Merket, B. Polly, M. Heahey, S. Casey, and J. Robertson. 2012. Assessment of the U.S. Department of Energy Scoring Tool. National Renewable Energy Laboratory, Washington, D.C.

Russell, S., and P. Norvig. 2002. Artificial Intelligence: A Modern Approach. Prentice Hall, 2nd edition.

Spears, W.M., K.A. DeJong, T. Back, D.B. Fogel, and H. de Garis. 1993. An overview of evolutionary computation. In Proceedings of the 1993 European Conference on Machine Learning.

Vose, M.D. 1999. The Simple Genetic Algorithm: Foundations and Theory. Cambridge, MA: MIT Press.

ZEBRAlliance. 2012. An alliance maximizing cost-effective energy efficiency in buildings. ZEBRAlliance, Oak Ridge, TN. http://www.zebralliance.org.

DISCUSSION

Ron Judkoff, Chief Architectural Engineer, NREL, Golden, CO: Regarding "metrics," the presenter only mentioned "goodness of fit" or "fitness" as a metric. It is possible to have a good fit for the wrong reasons. The NREL methodology for testing calibration procedures uses three metrics, "goodness of fit," accuracy of retrofit savings predictions, and how well the calibration method identified the "truth" input parameters.

Joshua New:We have collected metrics that show per-variable accuracy of 15% when monthly data is available and 8% with hourly data that is outside the scope of this current ASHRAE publication (is in review), but these metrics which quantify the extent to which Autotune matches "the real building" was shared in DOE Building Technology Office peer review: www1.eere.energy.gov/buildings/technologies/pdfs/emrg tech03_new_040213.pdf.

The key is that there is a set of metrics which quantify the physical realism of a tuning process, which corresponds to metric #3 from the commenter's list of methods. We shared results in the paper for metric #1, and metric #2 was not applicable since there was no retrofit to the building used in this study.

Stephen Long, Manager, Southern California Edison, Rosemead, CA: Can this approach be applied to other modelling approaches than Energy Plus?

Joshua New: Yes. Autotune was designed to be simulation engine agnostic from the beginning and can apply to any computer program which meets the 4 following criteria:

1) Takes input

2) Provides output

3) Can be run in a tractable amount of time, and

4) Has "real world" data to compare against.

This was necessary due to foreseen changes in Energy-Plus (separate story). The primary items that need to be changed to accommodate a new simulation engine is to convert the file input/output mechanisms for the simulation engine and have a running engine on a platform that runsAutotune. As an example, we converted the Office ofWeatherization and Intergovernmental Programs' (OWIP) National Energy Audit Tool (NEAT), which uses a variable-degree-day method, to use Autotune in about a man-month.

While the NEAT conversion hasn't been made public, the general approach, technical details, and methods for Autotune are well-documented in 29 related publications since April 2012 (attached with links to preprint PDFs). It is ok to share my contact information if they are interested in following-up directly.

(1.) The SAE was chosen as the primary metric, rather than RMSE for example, because of its ease of interpretation in terms of relative error or dollar savings.

Aaron Garrett, PhD

Joshua New

Member ASHRAE

Theodore Chandler

Aaron Garrett is an assistant professor and Theodore Chandler is an undergraduate student in the Department of Mathematical, Computing, and Information Sciences, Jacksonville State University, Jacksonville, AL. Joshua New is an R&D staff member of the Whole Building and Community Integration Group, Oak Ridge National Laboratory, Oak Ridge, TN.
Table 1. Correlations between Four-Day and Yearly Sum of
Absolute Errors of Electrical Use

Data   Trial 1   Trial 2   Trial 3   Trial 4
Used

100%   0.96033   0.94215   0.90148   0.95553
90%    0.86677   0.84380   0.65458   0.87881
80%    0.86830   0.85725   0.64437   0.89219
70%    0.87257   0.85605   0.62313   0.89435
60%    0.86708   0.84889   0.60779   0.89516
50%    0.87030   0.84888   0.55566   0.89711
40%    0.87743   0.84174   0.56627   0.90195
30%    0.87944   0.82078   0.60146   0.89731
20%    0.88406   0.82313   0.59878   0.88600
10%    0.87962   0.82348   0.39849   0.87144

Table 2. Final Population Statistics in
[DELTA]Kilowatt-hours ([DELTA]Megajoules) from Tuning
Refined Model

Trial      Four-Day Average   Four-Day Minimum

Refined    12.813 (46.1268)
1          10.595 (38.1420)   9.997 (35.9892)
2          10.748 (38.6928)   10.248 (36.8928)
3          10.686 (38.4696)   10.133 (36.4788)
4          10.914 (39.2904)   10.504 (37.8144)
5          10.849 (39.0564)   10.440 (37.5840)
6          11.083 (39.8988)   10.631 (38.2716)
7          10.720 (38.5920)   10.090 (36.3240)
8          10.548 (37.9728)   10.031 (36.1116)

Trial        Yearly Average        Yearly Minimum

Refined    1276.340 (4594.824)
1          1098.040 (3952.944)   1055.857 (3801.085)
2          1129.179 (4065.044)   1095.948 (3945.413)
3          1068.646 (3847.126)   1034.244 (3723.278)
4          1132.985 (4078.746)   1098.540 (3954.758)
5          1143.954 (4118.234)   1099.360 (3957.696)
6          1146.128 (4126.061)   1110.514 (3997.850)
7          1100.887 (3963.193)   1064.195 (3831.102)
8          1104.110 (3974.796)   1072.097 (3859.549)

Table 3. Final Population Statistics in
[DELTA]Kilowatt-hours ([DELTA]Megajoules) from Tuning
Primitive Model

Trial       Four-Day Average   Four-Day Minimum

Primitive   17.955 (64.7820)
Refined     12.813 (46.1268)
1           13.085 (47.1060)   12.564 (45.2304)
2           13.580 (48.8880)   12.863 (46.3068)
3           13.774 (49.5864)   12.875 (46.3500)
4           13.407 (48.2652)   12.788 (46.0368)
5           13.422 (48.3192)   12.892 (46.4112)
6           13.689 (49.2804)   12.877 (46.3572)
7           13.504 (48.6144)   12.815 (46.1340)
8           13.283 (47.8188)   12.724 (45.8064)

Trial          Yearly Average         Yearly Minimum

Primitive   1623.364 (5844.1100)
Refined     1276.340 (4594.8240)
1           1423.893 (5126.0148)   1395.917 (5025.3012)
2           1439.713 (5182.9668)   1415.510 (5095.8684)
3           1471.857 (5298.6852)   1437.560 (5175.2160)
4           1444.796 (5201.2656)   1415.741 (5096.6676)
5           1447.312 (5210.3232)   1416.477 (5099.3172)
6           1445.754 (5204.7144)   1420.612 (5114.2032)
7           1451.337 (5224.8132)   1421.126 (5116.0536)
8           1428.582 (5142.8952)   1398.754 (5035.5144)

Table 4. Modifications between Primitive and
Refined Models

Components       Primitive        Refined Model
                   Model

Building           Full           Full Exterior
solar            Exterior       with Reflections
distribution

Surface            TARP         Ceiling Diffuser
convection
algorithm:
inside

Surface            DOE-2         Simple Combined
convection
algorithm:
outside

Schedule          Simple,     Complex, independent
                pre-defined     schedule for each
                 schedule         major system

Air gap          Does not          Included as
material           exist      construction material

Construction                   Additional wall and
                                  modified roof
                                  construction

Zone inside        TARP              Default
convection
algorithm

Zone outside       DOE-2             Default
convection
algorithm

Lights          Unspecified       Specified for
(interior and                       each zone
exterior)

Zone            0.01515 per     0.00758 per zone
infiltration       zone
flow
coefficient

HVAC                               Significant
control/                        differences from
thermostat                          primitive

Table 5. Final Full-Year Population Statistics
in [DELTA]Kilowatt-Hours ([DELTA]Megajoules)
from Tuning Models

Trial                       Refined

              Average                Minimum

1       1079.026 (3884.4936)   1043.687 (3757.2732)
2       1070.660 (3854.3760)   1035.439 (3727.5804)
3       1051.714 (3786.1704)   1014.915 (3653.6940)
4       1061.497 (3821.3892)   1035.180 (3726.6480)
5       1043.299 (3755.8764)   1014.629 (3652.6644)
6       1071.961 (3859.0596)   1035.432 (3727.5552)
7       1058.082 (3809.0952)   1026.530 (3695.5080)
8       1036.930 (3732.9480)   1008.939 (3632.1804)

Trial                       Primitive

              Average                Minimum

1       1417.083 (5101.4988)   1388.076 (4997.0736)
2       1431.135 (5152.0860)   1397.486 (5030.9496)
3       1405.782 (5060.8152)   1386.083 (4989.8988)
4       1440.669 (5186.4084)   1394.712 (5020.9632)
5       1419.470 (5110.0920)   1391.053 (5007.7908)
6       1420.174 (5112.6264)   1389.923 (5003.7228)
7       1443.183 (5195.4588)   1417.371 (5102.5356)
8       1404.181 (5055.0516)   1376.801 (4956.4836)

Table 6. Summary of [DELTA]Kilowatt-Hours
([DELTA]Megajoules) for Different Approaches

Model        Baseline       Tuning        Tuning
                          Abbreviated     Serial

Refined      1276.340      1078.842      1026.844
            (4594.8240)   (3883.8312)   (3696.6384)
Primitive    1623.364      1415.213      1392.688
            (5844.1104)   (5094.7668)   (5013.6768)

Table 7. Summary of CV(RMSE) of Monthly
Electrical Use for Different Approaches

Model       Baseline     Tuning      Tuning
                       Abbreviated   Serial

Refined      33.7%        31.7%      30.5%
Primitive    62.5%        52.3%      51.4%
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Author:Garrett, Aaron; New, Joshua; Chandler, Theodore
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jul 1, 2013
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