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Description
Calibrated simulation is the process of using a building simulation program for an existing building and "tuning" or calibrating the various inputs to the program so that predictions match closely with observed energy use. Historically, the calibration process has been an art form that inevitably relies on user knowledge, past experience, statistical expertise, engineering judgment, and an abundance of trial and error. Unfortunately, despite widespread interest in the professional community, no consensus guidelines have been published on how to perform a calibration using detailed simulation programs. This research project was initiated with the intention to cull the best tools, techniques, approaches, and procedures from the existing body of research and develop a coherent and systematic calibration methodology that includes both parameter estimation and the determination of the uncertainty in the calibrated simulation. A general methodology of calibrating detailed simulation programs to performance data is proposed, which we deem to be methodical, rational, robust, and computationally efficient while being flexible enough to satisfy different users with different personal preferences and biases.
The methodology involves various concepts and approaches borrowed from allied scientific disciplines that are also reviewed in this paper. The methodology essentially consists of five parts: (1) identify a building energy program that has the ability to simulate the types of building elements and systems present and set up the simulation input file to be as realistic as possible; (2) depending on the building type, heuristically define a set of influential parameters and schedules that have simple and clear correspondence to specific and easy-to-identify inputs to the simulation program, along with their best-guess estimates and their range of variation; (3) perform a coarse grid search wherein the heuristically defined influential parameters are subject to a Monte Carlo simulation involving thousands of simulation trials from which a small set of promising parameter vector solutions can be identified by filtering, the strong and weak parameters can be identified, and narrower bounds of variability of the strong parameters can be defined; (4) perform a guided grid search to further refine the promising parameter vector solutions; and (5) use this small set of solutions (as opposed to a single calibrated solution) to make predictions about intended changes to the building and its systems, and determine the prediction uncertainty of the entire calibration process. A companion paper (Reddy et al. 2007) will present the results of applying this calibration methodology to two synthetic office buildings and one actual office building.
INTRODUCTION AND OBJECTIVE
Calibrated simulation as applied to building energy simulation computer programs is the process of "tuning" or calibrating the various inputs to the program so that observed energy use matches closely with that predicted by the simulation program. Though several practitioners perform calibrated simulations, most do so based on certain procedures they have developed over years of experience. There seems to be a lack of homogeneity among these procedures and, more importantly, a lack of proper appreciation of the procedures followed by calibration professionals as a whole. Thus, historically, calibration has been an art form that inevitably relies on user knowledge, past experience, statistical expertise, engineering judgment, and an abundance of trial and error. To date, no consensus guidelines have been published on how to assess the comparison of the results from a building energy simulation program against measured data from an actual building. ASHRAE initiated a research project (RP-1051) intended to cull the best tools, techniques, approaches, and procedures from the existing body of research and develop a coherent and systematic calibration methodology that includes both parameter estimation and determination of the uncertainty in the calibrated simulation (Reddy et al. 2006). The objectives of this research also involved studying the extent to which an accurate calibration fit to the billing data subsequently allows accurate prediction of energy use under operational and/or equipment changes to the existing building and developing a procedure following which the associated prediction uncertainty can be specified.
A previous paper (Reddy 2006) provided a literature review of calibrated simulation techniques, describing their uses, strengths, weaknesses, procedures, tools, and pertinent issues related to model fitting uncertainty. This paper will present a general methodology of calibrating detailed building energy simulation programs, along with guidelines, tips, and recommendations that will allow practitioners to use their preferred procedures (if they so deem) in a more consistent and scientific manner within a well-structured overall framework. Though the methodology is applicable to any building energy simulation program, the scope of RP-1051 was restricted to the DOE-2 program, which is a widely used public domain fixed schematic hourly simulation program (Winkelmann et al. 1993), and to the widely prevalent case where year-long utility billing data are the only performance data available for calibration. Moreover, it was presumed that the level and accuracy of knowledge about the building geometry, scheduling, and various system equipment would be consistent with a "detailed investment grade" audit, involving equipment nameplate information as well as some limited on-site measurements (clamp-on meters, etc.) performed during different times of the day (morning, afternoon, night) as well as over different days of the week in order to better understand variability in some of the simulation inputs. Finally, it was determined that the scope of the research was most pertinent to medium and large commercial buildings with relatively complex HVAC & R equipment that can be modeled by the simulation program to be calibrated. It is only in such buildings that the cost of performing calibrated simulations would be justified. Energy-saving measures in small buildings are relatively easy to identify, and neither the audit budget nor the monitoring and verification (M & V) budget may be large enough to allow performing calibration simulation.
The RP-1051 research was also meant to benefit software developers in that it would specify additional capabilities to existing building energy simulation programs, which would allow calibration to be performed by practitioners with relative ease and with higher consistency. A companion paper (Reddy et al. 2007) will present the results of applying the calibration methodology to both synthetic and actual case study buildings. The appendices in this paper include literature reviews of several concepts, issues, and procedures related to the building design process that were deemed pertinent enough to the calibration process that they would be of interest to calibration professionals.
Review of Allied Science and Engineering Literature on Calibration
Model calibration and validation have been addressed in several books and journal articles in allied areas of engineering and science, such as environmental, structural, hydrological, epidemiological, and structural engineering. The problem, which has been well known in these fields for several decades, is similar to the problem of calibrating detailed building energy simulation programs, which is aptly stated by Hornberger and Spear (1981): "most simulation models will be complex, with many parameters, state-variables and non-linear relations. Under the best circumstances, such models have many degrees of freedom and, with judicious fiddling, can be made to produce virtually any desired behavior, often with both plausible structure and parameter values." This process is also referred to in the scientific community as GIGOing (garbage in--garbage out), where a false sense of confidence can result since precise outputs are obtained by arbitrarily restricting the input space (Saltelli 2002). A brief review of some salient background notions is given below.
First, we distinguish between two types of models: (1) single models, which can be mechanistic differential equations or even empirical correlations, or (2) linked complex models, which require simulation programs with relatively long run times. The literature abounds with calibration and parameter estimation studies pertinent to the first type of model, while those dealing with the second type are relatively few. This research is intended to deal primarily with the latter that include calibration of simulation models. Given the limited monitored data available, one can at best identify only some of the numerous input parameters on which a simulation program is based. Hence, a first important step is to perform a sensitivity analysis in order to identify the influential system or model parameters (scientists often view this in terms of uncertainty, i.e., which are the main contributors to model output uncertainty).
There is a wide range of such analytical methods presented in a book edited by Saltelli et al. (2000) and a very large number of technical papers. In such methods, the analyst is often faced with the difficult task of selecting the one method most appropriate for a particular application. Broadly speaking, sensitivity analysis methods can be viewed as mathematical, statistical, or graphical. A workshop on sensitivity analysis was hosted in 2001, where selected experts were invited to write and present white papers reviewing the application of sensitivity and/or uncertainty analysis to complex engineering and/or environmental systems (Frey 2002; Frey and Patil 2002; Saltelli 2002).
A report by Iman and Helton (1985) compares different sensitivity analysis methods as applied to complex engineering systems and summarizes current knowledge in this area. Of all the techniques, three have been found to be promising: (1) response surface replacement of the computer model where fractional factorial design is used to generate the response surface--this method is optimal if the models are linear; (2) differential analysis, which is intended to provide information with respect to small perturbations about a point--however, this approach is not suited for complex models with large uncertainties; (3) Latin hypercube sampling, which was deemed very suitable overall to the current research. A short introduction to this method follows.
Experimental design methods, such as [2.sup.k] or [3.sup.k] factorial designs, have been in existence for several decades, well before the computer era. However, these methods have not been identified as promising since they only provide one-way sensitivity (i.e., the effect on the system response when only one parameter is varied at a time) rather than the multi-response sensitivity sought. When the number of input parameters is large, along with large uncertainty in the input parameters, and when the input parameters are interdependent and nonlinear, Monte Carlo (MC) methods (though computationally more demanding) are simpler to implement and require a much lower level of mathematics while providing adequate robustness.
In general, theoretical mathematicians deduce conclusions from postulates, while experimental mathematicians infer conclusions from observations (Hammersley and Handscomb 1964). MC methods, of which there are several types, as discussed below, comprise that branch of experimental mathematics that rely on experiments, using random numbers to infer the response of a system. Two types of problems can be handled by MC methods--probabilistic and deterministic--according to whether or not they are directly concerned with the behavior and outcome of random processes. For example, MC methods can be used to infer sampling distributions (e.g., mean, interquartile ranges). They can also be used as a numerical method of solving engineering problems using random sampling wherein certain... |
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