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<ul><li><p>Applied Energy 164 (2016) 6988</p><p>Contents lists available at ScienceDirect</p><p>Applied Energy</p><p>journal homepage: www.elsevier .com/locate /apenergy</p><p>Developing a whole building cooling energy forecasting modelfor on-line operation optimization using proactive system identification</p><p> 2015 Elsevier Ltd. All rights reserved.</p><p> Corresponding author. Tel.: +1 215 895 6941; fax: +1 215 895 1364.E-mail addresses: (X. Li), (J. Wen),</p><p> (E.-W. Bai).</p><p>Xiwang Li a,, Jin Wen a, Er-Wei Bai baDepartment of Civil, Architectural and Environmental Engineering, Drexel University, Philadelphia, PA 19104, USAbDepartment of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA 52242, USA</p><p>h i g h l i g h t s</p><p> Developed and verified a novel general methodology for building energy forecasting. Quantitatively evaluated energy system nonlinearity and system response time. Developed and adapted system identification model for building energy forecasting. Compared the proposed system identification model against four inverse models.</p><p>a r t i c l e i n f o</p><p>Article history:Received 19 October 2015Received in revised form 30 November 2015Accepted 1 December 2015</p><p>Keywords:Building energy modelingModel based optimizationSystem identificationSystem nonlinearitySystem response timeMonte Carlo simulation</p><p>a b s t r a c t</p><p>Optimal automatic operation of buildings and their subsystems in responding to signals from a smart gridis essential to reduce energy demand, and to improve the power resilience. In order to achieve such auto-matic operation, high fidelity and computationally efficiency whole building energy forecasting modelsare needed. Currently, data-driven (black box) models and hybrid (grey box) models are commonly usedin model based building control. However, typical black box models often require long training periodand are bounded to building operation conditions during the training period. On the other hand, creatinga grey box model often requires (a) long calculation time due to parameter optimization process; and (b)expert knowledge during the model development process. This paper attempts to quantitatively evaluatethe impacts of two significant system characteristics: system nonlinearity and response time, on theaccuracy of the model developed by a system identification process. A general methodology for buildingenergy forecasting model development is then developed. How to adapt the system identification processbased on these two characteristics is also studied. A set of comparison criteria are then proposed to eval-uate the energy forecasting models generated from the adapted system identification process againstother methods reported in the literature, including Resistance and Capacitance method, Support VectorRegression method, Artificial Neural Networks method, and N4SID subspace algorithm. Two commercialbuildings: a small and a medium commercial building, with varying chiller nonlinearity, are simulatedusing EnergyPlus in lieu of real buildings for model development and evaluation. The results from thisstudy show that the adapted system identification process is capable of significantly improve theperformance of the energy forecasting model, which is more accurate and more extendable under bothof the noise-free and noisy conditions than those models generated by other methods.</p><p> 2015 Elsevier Ltd. All rights reserved.</p><p>1. Introduction</p><p>Buildings are responsible for over 40% of the primary energyand 70% of the electricity consumption in the U.S. [1] More than25% of the U.S. electricity demand could be dispatchable if build-</p><p>ings can respond to the dispatch through advance operation strate-gies and smart grid infrastructure [2]. Recently, model basedpredictive control (MPC) has been proven to be a promising solu-tion for this active operation [3]. As the basis of MPC, high fidelityand computationally efficient building energy forecasting modelsare indispensable. How to develop an accurate, robust, and cost-effective building energy forecasting model is an urgent problemand therefore the objective of this study. The goals of this paperare twofold. One is to propose a system identification methodology</p><p>;domain=pdf</p></li><li><p>70 X. Li et al. / Applied Energy 164 (2016) 6988</p><p>that is able to adapt based on a buildings characteristics, to gener-ate a whole building cooling energy forecasting model. The otherone is to compare the performance of the proposed methodologywith other modeling methods reported in the literature.</p><p>Although there are a large number of studies regarding buildingenergy forecasting using different methods, they all can be catego-rized as white box, black box and the grey box models. All thesethree types of models have their own limitations in applicationto real field building control. For example, black box models, suchas autoregressive exogenous (ARX), Artificial Neural Networks(ANN), Support Vector Machine for Regression (SVR), and N4SIDstate space model have been applied in building energy forecastingand control studies [411]. These data-driven models, however,often require long training period and the model extensibility islimited to the training data. In this study, model extensibility isdefined as the forecasting accuracy of a model, when it is subjectto weather and operation conditions that are different from thoseduring the model training period. This is an important model prop-erty because building systems are often nonlinear systems. Amodel that is trained using one range of operating/weather condi-tions often is not usable for a different operating/weather condi-tion. Grey box models, such as Resistance and Capacitance (RC)network and lumped parameters models, are popular models inbuilding control and operation studies [3]. They are widely usedin MPC for buildings such as those to estimate the cooling energyconsumption [1214], to utilize the building passive thermal massstorage [1517], or to utilize active thermal storage devices [18,19]and the energy generation systems [20,21] to reduce energy con-sumption or energy cost. Even though different advance parameterdetermination methods have been implemented to identify theparameters of the grey box models [12,13], the parameter determi-nation process is often computational demanding. In [14], theauthors developed a method for parameters and variable selectionusing Singular value decomposition and solving the RC equation infrequency domain. Developing the structure of a gray box model,however, often requires expert knowledge, and the parameterdetermination process is also time consuming. Therefore, whenapplying these modeling approaches in the real field, each of theseapproaches has its own barriers such as training data availability/quality, implementation time, and implementation cost (whenexpert knowledge is required).</p><p>In order to solve technique gaps from these methods, somestudies started to combine different methods to improve the modelperformance. Lee and Tong [22] presented a hybrid grey modelwith genetic programming for energy consumption forecasting.Fux et al. [23] combined RC model with Kalman filter to improvethe model accuracy and robustness. L et al. [24] developed a com-bined RC and autoregressive-integrated-moving-average (ARIMA)model for heterogeneous building energy forecasting. These meth-ods tried to reduce the efforts in the grey-box modeling, but theinherited limitations from the grey box models are still there. Itis also difficult to develop a general model structure for differentbuildings, and it requires high engineering effort in implementingit into real model predictive controllers. On the other hand, datadriven models have also been combined with Kalman filter[25,26] to improve the data driven model performance by bringingin the real measurements. Similarly, the inherited drawbacks ofdata driven models still cannot be solved there.</p><p>As results, a novel generalmethodology for building energy fore-castingmodel development has been proposed and validated in thisstudy to solve the limitations of the existing methods. Differentfrom the above described modeling approaches, which collects sys-tem data in a passive manner, system identification (SID) is a pro-cess of developing or improving a mathematical representation ofa physical system using data that is collected from a designedoperation or experiment, in an active manner. Although system</p><p>identification techniques have been widely used in other engineer-ing applications, there are only limited applications in the buildingenergymodeling field. In an earlier study by the authors [27], a sys-tem identificationmethodology, using frequency response functionwith an active system excitation, is proposed and tested for build-ing energy forecasting. The method is demonstrated to be able todevelop accurate and computationally efficient energy forecastingmodel for a small commercial building. However, when the pro-posed SID process is applied to develop an energy forecastingmodelfor a medium commercial building, the model accuracy is not satis-factory. It is suspected that a building systems nonlinearity andresponse time affect the SID models accuracy since frequencyresponse function method is better used for more linear systems[28]. Therefore, this study focuses on investigating such impactsand how to adapt the SID process systematically based on asystems nonlinearity and response time. The goal is to develop asystematic SID methodology which can be scaled for buildings withvarying nonlinearity and response time.</p><p>This study firstly proposes a method to quantitativelydetermine a systems nonlinearity and response time, and theirimpacts on the SID model development. Based on such character-istics (nonlinearity and response time), a methodology is thendeveloped to adapt the SID modeling process. A comparison studyis also conducted to evaluate the performance of the adapted SIDmodel, developed based on a buildings nonlinearity and responsetime, against literature-reported RC model, SVR model, ANN modeland N4SID model. Four criteria, namely, energy forecasting accu-racy, calculation speed, extendibility and uncertainty are used forthe model performance comparison. Again, forecasting extendibil-ity concerns the model forecasting accuracy when the weatherand/or operating conditions are different from those during thetraining period. Forecasting uncertainty concerns the model fore-casting performance when training and forecasting data containsnoise. Two commercial building, a small and a medium commer-cial building, with varying chiller nonlinearity, are simulated usingEnergyPlus in lieu of real buildings for model development andcomparison. In the following sections, the methodology for systemcharacteristics test and SID model development is introducedfirstly in Section 2, the EnergyPlus modeling and data generationprocess are discussed in Section 3, the system characteristic testresults and SID model adaptation results are summarized in Sec-tions 4 and 5, and then the comparison study is presented inSection 6.</p><p>2. Methodology</p><p>In this section, the test method used to determine a systemsnonlinearity and response time is first introduced. How to adaptthe SID model development based on the nonlinearity andresponse time are then discussed.</p><p>2.1. Building energy system characteristics test method</p><p>2.1.1. System nonlinearity testIt is believed that a systems nonlinearity is one of the most</p><p>important characteristics for a systems model development, espe-cially for nonparametric methods [29]. In this study, a magnitudesquared coherence based method for system nonlinearity test[29] is adopted. This method is based on the cross-spectral densityof the inputs and outputs:</p><p>Cxy Sxy 2SxxSyy</p><p>1</p><p>where the magnitude squared coherence (Cxy) estimate the powertransfer between input and output to estimate the causality</p></li><li><p>X. Li et al. / Applied Energy 164 (2016) 6988 71</p><p>between system input and output. Sxy is the cross power spectraldensity between system inputs (x), such as outdoor air temperature,and system output (y), such as building energy consumption. Sxxand Syy are the auto power spectral density of x and y, respectively.They can be estimated from the Fourier transformation of theauto-correlation of the inputs (Rxx) and outputs (Ryy), and thecross-correlation between inputs and outputs (Rxy). The equationsfor the transformation are presented as Eqs. (2)(4):</p><p>Sxy 1NXNs1</p><p>Rxysej2pksl 2</p><p>Sxx 1NXNs1</p><p>Rxxsej2pksl 3</p><p>Syy 1NXNs1</p><p>Ryysej2pksl 4</p><p>where l is sampling window length of the spectral density analysis.N is the number of sampling windows. The purpose of the Fouriertransformation is to convert the signal into frequency domain tocapture the system dynamics. Rxy is calculated in (Eq. (5)), Rxx andRyy are calculated in Eq. (6).</p><p>Rxy s 1lXl1i1</p><p>u i yT i s 5</p><p>Rxxs 1l sXlss1</p><p>xjxTj s 6</p><p>During an auto-correlation process, the similarity between anobservation and the same variable with a time lag is analyzed todiscover similar patterns in a signal. Cross-correlation is a measureof similarity between one signal and another signal with lag time.For example, cross-correlation can be used to examine the similar-ity between temperature setpoint and cooling energy consump-tion. The power spectral density describes how the power of asignal is distributed over different frequencies. The cross power</p><p>Fig. 1. Data sampling window and excitation injection during a</p><p>spectral density can be calculated from the Fourier transformationof the cross-correlation between two signals, and the auto powerspectral density can be calculated from Fourier transformation ofthe auto-correlation of one signal.</p><p>In this nonlinearity evaluation process, the analysis time period(e.g. one day) will be divided into multiple moving Welchs over-lapped l-long (e.g. 6 h) segments. The nonlinearity evaluation pro-cess (Eqs. (2)(4)) will be conducted in each segment. Theoverlapping portion in this study is chosen as 50%. That meansthe 6-h sampling window will move forward for 3 h at each time.The sampling window and excitation injection are illustrated inFig. 1. The excitation signals will be injected into the system ateach excitation injection time. The injection interval is predeter-mined and will be updated based on the system response time testresults. The details about system response time test will be intro-duced in Section 2.1.2. During the nonlinearity evaluation, the non-linearity index (Cxy), frequency response (Suu and Syu in Fig. 2), andMarkov parameters (G(t) in Fig. 2) will be evaluated at each mea-surement time step for each...</p></li></ul>


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