## 1 Introduction  
In response to global warming and climate change, governments worldwide have implemented related policies and technical efforts that include the use of renewable energies and the increase in the energy efficiency to reduce energy consumption and greenhouse gas (GHG) emissions. In the United States in 2015, approximately 40% of the total consumed energy was used in commercial and residential buildings [1]. Approximately 41% of the energy consumed in the building sector was used for heating and cooling, and between 15% and 30% was wasted owing to poor maintenance or inadequate control [2]. To operate and maintain air conditioning systems efficiently, the energy efficiency should be maximized through optimal control and with fault diagnosis technology. Faults in air conditioning systems can be classified into hard and soft faults. Hard faults that lead to system halt can be easily detected and diagnosed. By contrast, soft faults such as refrigerant leakage and heat exchanger fouling are difficult to detect and diagnose before the faults reaches a severe degree; this can lead to energy loss and a damaged system. Refrigerant charge fault is the next most costly fault among the different types of heat pump faults, except for electrical fault; the former are mainly caused by refrigerant leakage [3]. The refrigerant charge amount is one of the main parameters that affect the performance and energy consumption of heat pumps [4; 5; 6; 7]. When the refrigerant charge exceeds 90% of the rated charge, the effect on the COP and cooling capacity is small. The refrigeration capacity and COP decrease if the initial charge of the system is low or if the charge decreases owing to leakage during operation. Even under an overcharge, the COP decreases owing to the increasing compression work; however, the performance of the air conditioner is more severely degraded under undercharging than under overcharging [8]. Refrigerant charge faults occur frequently owing to refrigerant leakage, equipment relocation, the installation of piping systems, and incorrect initial charging. Direct emission and performance degradation by refrigerant leakage will have an impact on global warming [9]. Accordingly, many research studies have been conducted to detect refrigerant charge faults [10; 11; 12; 13; 14; 15; 16]. Several researchers have predicted the refrigerant charge amount by monitoring air conditioning systems in real time [14; 15; 16]. For instance, [PERSON] et al. implemented a relatively inexpensive leak detection system with the degree of superheat and subcooling as detection parameters [14]. In addition, [PERSON] and [PERSON] tried to monitor continuously the refrigerant charge level by constructing a monitoring system with a virtual refrigerant charge sensor [14; 15; 16]. Since variable speed compressors are commonly adopted in high-efficiency air conditioners, researchers have studied the dynamic characteristics and modeling of refrigeration cycles for the stable control of systems equipped with variable speed compressors [17; 18; 19; 20; 21]. Accordingly, research studies of the detection of the refrigerant charge amount have been extended to VRF (Variable Refrigerant Flow) systems with complex physical structures such as variable speed compressors, electric expansion valve (EVs), and heat recovery devices [14; 18; 19; 20; 21; 22]. [PERSON] et al. proposed a relatively simple model that can be developed in a short time with a statistical method belonging to the category of history-based method [22]. These studies have been based on steady-state operating data. To develop a model for the prediction of the refrigerant charge amount, experimental data that reflect the characteristics of a system under steady-state conditions are required; the related experiments, which are conducted to increase the prediction performance of the model, are expensive and time-consuming.