1.2 Modeling Approaches in HVAC Field
1.2.2 Data-Driven Modeling Approach
Physics-based models provide good generalization capability but lack of accuracy compared with the data-driven ones. In addition, the calibrations of physics-based models are confronted with great challenge due to the identification of large number of parameters. Major methods used for data-driven modeling of HVAC systems include frequency-domain, data mining, fuzzy logic, and statistical method [46].
1.2.2.1 Frequency-Domain Models
Due to the heavy thermal inertia existing in the HVAC system, many processes such as dynamics of exit air temperature of air-cooling/heating coils are changing slowly with time delay. Such processes can be modeled using the first- and the second-order formula with dead time as follows [54,55]:
Gðsị ẳ Yðsị Uðsịẳ K
ssỵ1eLs ð1:1ị
Gðsị ẳYðsị
Uðsịẳ 1
as2 ỵbsỵceLs ð1:2ị where,Kis static gain;Lis apparent dead time of the process;sis time constant;a, b, andcare unknown coefficients.
Thefirst- and second-order models are developed for SISO systems and can be extended to MIMO systems. Thefirst-order process model has been employed for developing advanced PID autotuner of AHU and describing dynamics offlow meter [55] and cooling coils [56]. First- and second-order frequency-domain models with dead time have simple structure and a small number of parameters to be determined from the measured data. The identification techniques are often applied to identify these parameters.
1.2.2.2 Data Mining Models
The data mining and machine learning algorithms such as ANN and support vector machine (SVM) are often applied to complicated and nonlinear system like HVAC systems. The network is trained by a supervised learning algorithm, and the SVM-based approach projects the nonlinearly separable data into higher dimensional feature space through a mapping function in which it can be separated linearly.
The ANN method is often employed to estimate the performance of HVAC systems and components. For example, Hosoz and Ertunc [57] predicted the per- formance of an automobile air-conditioning system using ANN. They developed a multilayer feed-forward networks (MLFFN) for predicting the performance parameters such as compressor power, heat rejection rate in the condenser, refrigerant mass flow rate, compressor discharge temperature with reference to compressor speed, cooling capacity, and condensing temperature. Ertunc and Hosoz [58] compared the performance predictions of an evaporative condenser using ANN techniques. They predicted the condenser heat rejection rate, exit refrigerant temperature of condenser as well as dry- and wet-bulb temperatures of the leaving air stream with respect to the following parameters: inlet air temperature and humidity, airflow rate, refrigerantflow rate, waterflow rate, absolute pressure, and temperature of the refrigerant at the inlet of the condenser.
The SVM method has been applied to load prediction in building HVAC systems.
In the study by Ding et al. [59], the SVM was used to establish a load forecasting model based on measured data of cooling load over a period. The global optima of SVM penalty parameter, intensive loss function, and kernel function were found by using the ant colony optimization (ACO). To improve the load forecasting capacity, the SVM model was often combined with the other data analysis algorithms, e.g., hybrid SVM combined with autoregressive integrated moving average (ARIMA), hybrid SVM combined with kernel principal component analysis (KPCA), and hybrid SVM combined with particle swarm optimization (SAPSO) algorithm.
Unlike the ANN, the SVM is resistant to over-fitting the data and has better performance than simple ANN. SVMfinds the global optimum solution in the data
and provides the bestfit for the data. In order to build the models using data mining algorithms, large amount of training and testing data is needed. No physical interpretation of the developed model is possible and the performance degrades when conditions deviate from training and testing conditions. These algorithms are suitable for offline model development, and online implementation of these algo- rithms is often cumbersome [46].
1.2.2.3 Fuzzy Logic Models
The fuzzy logical model is developed based on the expert knowledge, and it is implemented through the if-then-else statements or rules which are written in the form of a table or database. Fuzzy logical model is developed usually for the control of HVAC system. For example, Becker et al. [60] designed a fuzzy controller for temperature and relative humidity in refrigeration system by considering their thermodynamic coupling. He et al. [61] established a multiple model predictive control (MMPC) strategy based on Takagi-Sugeno (T-S) fuzzy models for tem- perature control of air-handling unit (AHU) in HVAC systems. The overall HVAC control system was constructed by a hierarchical two-level structure. The higher level is a fuzzy partition based on AHU operating range to schedule the fuzzy weights of local models in lower level, while the lower level is composed of a set of T-S models based on the relation of manipulated inputs and system outputs cor- respond to the higher level. There are also other new fuzzy logical models com- bined with some data mining algorithms, such as artificial neural fuzzy interface system (ANFIS) model [62], gradient autotuned Takagi-Sugeno fuzzy forward model [63], and genetic algorithm-based adaptive fuzzy logic model [64]. Models developed with fuzzy logic require experiences and comprehensive knowledge about the objects as well as large amount offield data for training. However, these may not be readily available for many HVAC components and thus presents a difficulty in modeling these components using fuzzy logical method.
1.2.2.4 Statistical Models
The statistical models used in the HVAC fields mainly include autoregressive exogenous (ARX), autoregressive moving average exogenous (ARMAX), ARIMA, Box-Jenkins (BJ), and output error (OE). The mathematical expression for the generalized structure of statistical black box models in a simple input–output relationship is given below:
aðq1ịyðsị ẳb1ðq1ị
h1ðq1ịuðsị ỵ b2ðq1ị
h2ðq1ịwðsị ð1:3ị where a;b1;b2;h1;h2 are polynomials; q1 is back shift operator; uðsị;yðsị, and wðsịare input, output, and noise at the time points.
The model ARMAX is superior to ARX as it incorporates the time series of error in the model structure which is essential for capturing the dynamics of the error and better control performance. ARIMA is a generalization of ARMAX, modeling the stationary and non-stationary data into a single step, and consists of autoregressive, integrated, and moving average parts [46]. Mustafaraj et al. [65] investigated Box-Jenkins (BJ), autoregressive with external inputs (ARX), autoregressive moving average with external inputs (ARMAX), and OE models to identify the thermal behavior of an office room in a modern commercial building in London.
Their study manifested that these numerical models could all be potentially used for improving the performance of the thermal environment control system. Other examples of statistical model applications in HVAC areas include the following:
predicting the room temperature variations for both short-term and long-term periods with ARMAX method [45], and load forecasting in air-conditioned non-residential buildings with the ARX and the ARIMA method [66]. Since the processes in an HVAC system depend on their previous values, a time series regression model (i.e., ARX, ARMAX, and ARIMA) captures these correlations by including the process variables from the previous sampling times, which will result in a favorably accurate model of the process dynamics.