Elsevier

Energy and Buildings

Volume 47, April 2012, Pages 292-301
Energy and Buildings

A methodology for meta-model based optimization in building energy models

https://doi.org/10.1016/j.enbuild.2011.12.001Get rights and content

Abstract

As building energy models become more accurate and numerically efficient, model-based optimization of building design and operation is becoming more practical. The state-of-the-art typically couples an optimizer with a building energy model which tends to be time consuming and often leads to suboptimal results because of the mathematical properties of the energy model. To mitigate this issue, we present an approach that begins by sampling the parameter space of the building model around its baseline. An analytical meta-model is then fit to this data and optimization can be performed using different optimization cost functions or optimization algorithms with very little computational effort. Uncertainty and sensitivity analysis is also performed to identify the most influential parameters for the optimization. A case study is explored using an EnergyPlus model of an existing building which contains over 1000 parameters. When using a cost function that penalizes thermal comfort and energy, 45% annual energy reduction is achieved while simultaneously increasing thermal comfort by a factor of two. We compare the optimization using the meta-model approach with an approach using the EnergyPlus model integrated with the optimizer on a smaller problem using only seven optimization parameters illustrating good performance.

Highlights

▸ An analytic fit is derived for building energy models for optimization and analysis. ▸ Efficient deterministic parameter sampling is used to create the fit (meta-model). ▸ Uncertainty and sensitivity (UA/SA) analysis is performed on the analytic model. ▸ SA is performed to determine which parameters are best for optimization. ▸ The new methodology is compared to traditional optimization using EnergyPlus.

Introduction

Currently, model-based analysis of buildings is predominately used for code compliance such as LEED certification, and some minor scenario studies in architectural and engineering firms, or in the research or academic community in a more detailed context. As building energy models become more advanced, accurate, and easy to use, model-based building design is becoming more widespread. In order to be useful in an industrial context, the design cycle iteration time for a building design and operation scenario (DOS1) must be very fast. This cycle includes not only simulation time, but analysis of its results and action based on these results.

One form of analysis that is currently performed with building energy models is optimization, which investigates how the DOS of a building influences key measurables of the building (e.g. thermal comfort, energy consumption, life cycle costs) and seeks a DOS that meets some optimal combination of these (often weights are used to indicate different levels of importance of each variable in the cost function). In the building energy modeling literature, there are examples of this procedure using methods ranging from finding this optimal in a detailed but ad hoc way (e.g. [1], [2]) to advanced numerical methods that automatically find the optimum which are reviewed below.

Numerical optimization of energy models first arose in the 1970s and continues to be an active research area. The anatomy of the optimization process typically includes an optimizer and a function which it is trying to optimize. This function is usually an energy model, that once given a certain building DOS, a cost or objective value is produced through numerical simulation (usually for an entire year of typical weather and environmental conditions). Software environments for optimizing building energy models exist for this purpose that are either specific to an energy simulator [3], or more generic [4]. The goal of the optimizer is to intelligently determine new DOSs (based on previous attempts), in such a way that the final DOS has converged to an optimal value.

In the building energy modeling community, derivative-free (DF) optimization routines [5], which do not require gradient information from the simulation model are typically used. The reason that these methods are used is because derivative information, if obtained numerically from the model, is often not accurate because a continuous or differentiable objective function does not exist (see [6], [7], [8]). This often results in the optimizer converging to local optimal points, for example in [9] where many optimal design alternatives were found in the optimization process. There are many specific types of DF methods and in the building energy community, two types: genetic algorithms and pattern search are often employed in the buildings community and are discussed below.

Genetic algorithms (GA) are a class of mathematical optimization approaches that imitate natural biological evolution in which the process of inheritance, mutation, selection, and crossover is utilized to determine the best solution. The likelihood of converging to a suboptimal solution (local minima) is reduced in this method because the search considers a population of solutions and not a descent along a gradient. Examples of the use of GA-based optimization in building energy modeling include [10] which seeks an optimal building envelope design based on life cycle costs, or [9] that studied a case where building form (12 orientations), materials (16 choices) and HVAC operation (6 load control steps) were optimized. Similarly, Wright et al. [11] used a GA-based optimizer to optimize energy cost and occupant comfort by varying 63 control variables (for a single day). A simple model of a single zone with an HVAC system operating open loop using only outside air was used for this example.

The pattern search (PS) method is another valuable DF optimization technique that searches along coordinates in an intelligent way to find the minimum of an objective function. This method has been used in [12] where the software GenOpt [4] was used to investigate how 10 parameters (9 parameters relating to the hydronic system, and 1 envelope parameter) influence energy consumption, capital cost, and comfort. Additionally, in [13] 30 design variables were optimized using pattern search (Hooke–Jeeves) through the simulation of the model approximately 5000–10,000 times. In this case, the model was a simple set of algebraic equations that did not take very long to simulate.

In a recent and very thorough study [14], both GA and PS based methods (with some modification) were compared on a large set of test functions as well as an EnergyPlus building energy model. The conclusion was that both methods find a similar objective function value (energy consumption), but with a different combination of parameter values. This highlights that it is not always the best practice to use only one optimizer on a problem that has multiple minima. This is especially relevant if the building model is complex and the number of optimization parameters is large.

In most of the cases listed above, the number of evaluations of the numerical simulation of the energy model is in the 1000s for a single cost function (another set of simulations would be needed if for instance the weights in the cost function were changed even slightly). As discussed in [10], the computational cost limits the ability to study large sets of optimization parameters. For instance, in [12], approximately 400 simulations were needed to find the optimal of 10 parameters, and this sequence was repeated 10 times for different water supply temperatures. In addition to this, in [14] the number of model simulations needed to find an optimum was approximately 3000, but 5 runs were performed to capture the influence of different initial conditions (seeds) of the optimizer, and in [7], 13 parameters were optimized taking on the order of 600 extensive EnergyPlus simulations. Because of this, time becomes an important issue and in many cases, a full model of a building (created in one of many simulation packages like eQUEST, EnergyPlus, or TRNSYS) is avoided and a simpler model is created (as in [15], [13], among others).

To alleviate some of the issues with optimization time, in this paper we present a method that begins by characterizing the building energy model by varying all of the input parameters of the model within a certain range around its baseline design. Once these simulations are complete, a meta-model (a ‘model of a model’) is fitted to the simulated data and an optimization algorithm is applied to either this model or a reduced form of it. This approach has been performed in other building energy studies to predict energy usage [16] and to perform sensitivity analysis [17]. The kernel method was also used in [18] where over a year's worth of building energy data was used to create an accurate model that is capable of predicting excursions that may be due to faulty conditions.

In the meta-model scenario, the optimization itself takes on the order of a minute on a typical desktop or notebook computer. Because of this, many cost functions, optimization algorithms, or subsets of optimization parameters can be investigated without performing additional and exhaustive simulations.

A schematic of this approach is presented in Fig. 1, and the following sections discuss in detail each step. Following this, we demonstrate this approach using an EnergyPlus model as a case study including the results for multiple optimization scenarios (different cost functions, different parameter sets, and different optimizers). Most of the steps in this flowchart were performed using the integrated Global Sensitivity and Uncertainty Management and Optimization software [19]. We compare the meta-model approach with the traditional full order model approach in one case where the number of parameters in the optimization set is small (7 optimization parameters), and illustrate that computation time is decreased while maintaining similar convergence properties.

Section snippets

Repeated sampling

The goal of the sampling is to expand the prediction of a building energy model from one single baseline DOS to many cases around it. This is done by varying the parameters of the model within a range around their baseline value. There are multiple ways to specifically define this variation, including the Monte Carlo method, which randomly selects these samples. Unfortunately, when doing this, the parameter space is sampled non-uniformly. To avoid this issue, we use a quasi-Monte Carlo

The building and model

As a proof of concept, we exercise the meta-model based optimization methodology on a specific EnergyPlus model of a full-scale building. The Atlantic Fleet Drill Hall (building 7230) at the Naval Station Great Lakes (Great Lakes, IL, USA) is a two-storey facility with a gymnasium-like drill deck as well as a section primarily comprised of offices. The total area of the building is approximately 6430 m2 (69 kft2).

The building is conditioned using four air handling units (AHUs) and has variable

Concluding remarks

In this paper we presented an approach to perform optimization of building energy models using a meta-model generated from sample design and operation scenarios of the building around its baseline. The advantage of this approach is that once the meta-model is generated, many different cost functions, choices of parameters, or optimization algorithms can be exercised without repeating time-intensive energy simulations. The numerical quality of the solution using this approach was compared to the

Acknowledgement

This work was performed under the contract W912HQ-09-C-0054 (Project Number: SI-1709) administered by SERDP technology program of the Department of Defense by Dr. Jim Galvin.

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