## 1 Introduction
### Background of Thermal Models for HVAC System of Office Buildings  
As defined by ANSI/ASHRAE 55: Thermal Environmental Conditions for Human Occupancy [2] and ISO7730: Ergonomics of the thermal environment--Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria [3], thermal comfort is the condition of mind that expresses satisfaction with the thermal environment and is assessed by subjective evaluation. Therefore, thermal comfort is the combined result of physical environment and psychological activities. In the course of thermal comfort theory, static thermal comfort and adaptive thermal comfort have become two main categories. In terms of static thermal comfort, predicted mean vote (PMV) developed by [PERSON] [4] is the most widely accepted thermal model where seven variables are accepted to be the indicators of thermal comfort, which are indoor air temperature, indoor relative humidity, indoor air velocity, mean radiant temperature, clothing insulation, metabolic rate and the external work (normally 0). However, PMV was derived from a strictly controlled climate chamber where the thermal environment is static and is different from the real office environment. Moreover, since PMV predicts the average vote of a large group of people based on the seven-point thermal sensation scale, instead of individual thermal comfort, it only describes the overall thermal sensation of multiple occupants in a shared thermal environment. In order to overcome the disadvantages of static thermal comfort, adaptive thermal comfort aims to provide insights in increasing opportunities for personal and responsive control, thermal comfort enhancement, energy consumption reduction and climatically responsive and environmentally responsible building design [5]. One of the milestone projects of adaptive thermal comfort is the ASHRAE RP-884, which collected a total of 22,000 sets of data from the real office environments across the world. This project has been widely used to investigate various adaptive thermal models, which have been integrated into personalized HVAC controls. With RP884 dataset, [PERSON] et al. [6] proposed a method for learning personalized thermal preference profiles by formulating a combined classification and inference problem with 5-cluster models. Moreover, the thermal preference of a new user is inferred by mixture of sub-models for each cluster where clusters are used to group occupants with similar thermal preferences. However, instead of predicting 7-point thermal sensation described in ASHRAE 55, the paper predicts thermal preferences with three classes, namely \"want cooler\", \"want warmer\" and \"no change\". [PERSON] et al. [7] proposed a personalized thermal model using a Bayesian network to learn individual thermal comfort by predicting thermal sensation of occupants within a specific area, such as San Francisco with ASHRAE RP-884 dataset. However, the results were not promising that the highest accuracy of the model was only 30%. In addition to ASHRAE RP884 dataset, other data-driven studies have also been conducted for the development of adaptive thermal model comfort model. For instance, a unified framework was presented by [PERSON] et al. [8] for personal comfort models and challenges were discussed for the application of personal comfort models in the real world. In the framework, instead of survey, the feedback regarding thermal preferences was collected with the interactions between personal a comfort system (PCS) and occupants. Moreover, machine learning algorithms were proposed for the development of personal comfort models. Thermoregulation is a dynamic equilibrium with the environment where body regulates its internal core temperature in terms of heat generation and heat exchange with the environment [9]. In detail, if the ambient temperature is below skin temperature, heat is dissipated from the body by radiation and convection.