# Multi-Model Identification of HVAC System
## 1 Introduction  
Nowadays, heat, ventilation, and air conditioning (HVAC) systems are essential for indoor air quality, thereby on occupants' health and comfortability. Due to nonlinearity and uncertainty, it is inaccurate to identify this process using conventional and first-principle models. Hence, during the last decade, many papers have been published on identifying this system using data-driven methods [1, 2, 3, 4]. However, these data are commonly sampled from one operation region, so they are not general enough to predict the system behavior in other operating conditions. Although varying operation condition is common in an HVAC system, traditional identification approaches are usually calculated for a single operating mode--under stationary conditions. One possible solution is to utilize a multi-model approach to deal with the problem of multi-mode and nonlinear process operations. The multi-model approach's main idea is to represent the nonlinear system with a combination of (weighted) linear models. The main challenges of this approach are determining the sufficient number of models, local model weights, as well as the operation points in which the linear models should be constructed. These challenges are more cumbersome when no information about the system operation is available, so the operation point and clustering should be done just by using routine operating data. One possible approach is to separate nonstationary data into several stationary ones to overcome the problem of multi-model operations. In this way, each stationary operation mode can be interpreted as a single steady-state operation. Then, the linear approach can be conducted for each stationary portion of data. This task requires executing clustering and identification, each of which has its cost function. Implementing these two tasks separately cannot guarantee global optimality. For instance, let us assume that we have obtained an optimal solution for clustering data into different operating modes. That optimal solution might not lead to an optimal solution for the identification of models. A hybrid approach is required to incorporate individual cost functions of dynamic clusteringand model identification to form a single cost function to resolve this problem. This can be accomplished using a support vectors-based identification method, which is introduced in this paper. To identify models for each labeled group of data (cluster), support vector (SV) regression is applied, aiming to maximize the distance between models and decrease the mean square of the overall residuals. As mentioned, optimality in individual steps of clustering and regression does not necessarily lead to overall optimality, which is due to their different objectives. This paper aims to align the goals of these two steps to predict variables. To this end, the SV method is extended to handling clustering and regression analysis simultaneously. In this way, we are able to ensure the optimality of prediction. After deciding and identifying the local linear models, the question is how to construct the global model using the local linear models. One possible way to build a global model is assigning weights to each local model. The weights are commonly calculated using distances between local models. In [5], [PERSON] et al. suggested using the gap metric, which measures the distance between two linear models, as a guideline for selecting local models. The distance should not be larger than a prescribed threshold level. The advantage of the method is no detailed information about the nonlinear model of the system is required. Furthermore, by this approach, the number of local models can also be determined. To decide the operation point for the construction of local models, the measure of nonlinearity approach [6; 7] can be utilized. The idea behind this approach is constructing the local linear models on operating points near which the system is most nonlinear to cover the nonlinearity of the system.