## 1 Introduction  
The high-speed, high-temperature heat-airflow test system (HHHTS) is a ground support equipment used to simulate high-speed heat flow field in aerospace field. Placing the key components of supersonic aircraft and aeroengine in the test section of the test system can simulate their heating conditions in the high-speed heat flow field and test their thermal performance. Placing temperature sensors in the test section of the test system can realize their static and dynamic calibration and evaluate their performance. Therefore, the HHHTS plays an important role in the development of aerospace equipment, such as supersonic aircraft and aeroengines, and improving its test performance is conducive to improving the quality of related aerospace equipment [1, 2]. The distribution uniformity of the temperature field and the control performance of gas temperature are important indicators for measuring the overall performance of the HHHTS. Therefore, it is an important research topic to ensure the rapidity, stability, and accuracy of gas temperature control, as well as the uniformity of temperature field distribution in the actual work process [3]. In order to achieve high performance control of gas temperature in the test section of the HHHTS, a precise lumped parameter model that can describe the gas temperature performance of the test system must be established first. This is because the accurately lumped parameter model of gas temperature is the basic guarantee for the realizing precise control of gas temperature in the test section of the HHHTS. For achieving the goal of the accurate control of gas temperature, the error of the mathematical model of gas temperature should not exceed 5%. According to the structure and operating principle of the HHHTS, the temperature field of the system is formed by the burning of aviation kerosene in the combustor with high-speed air flow. However, combustion of aviation kerosene is a complex chemical reaction process, and its mechanism has not been fully studied, which makes it difficult to obtain a precise lumped parameter model of gas temperature via the traditional first principle modeling method [4]. Therefore, it is urgent to find an effective method for obtaining a precise lumped parameter model of gas temperature for the HHHTS and lay a foundation for gas temperature control. At present, there are three common modeling methods, namely first principle modeling, system identification modeling, and grey box modeling [5]. First principle modeling has the advantages of clear physical meaning and can easily obtain the characteristics of the actual physical system. However, it can only be used to establish an accurate mathematical model of a relatively simple physical system (a system with simple structure and known principle), and it is difficult to obtain an accurate model of a complex physical system (a system with complex structure, unknown principle, or incomplete known knowledge) [6]. The advantage of the system identification method is that it does not need to know the principle of the dynamic process, but only needs to use the input and output data of the system and can continuously update the parameters of the model online and in real time. However, for the modeling problem of complex large-scale systems, because the information contained in the input and output data is relatively single, the accuracy of the model will decline, and the adaptability to new samples will deteriorate [7]. Grey box modeling is a new modeling method combining the advantages of first principle modeling and system identification modeling. The first principle provides a priori knowledge for grey box modeling, while system identification simplifies the modeling process. Therefore, grey box modeling has the advantages of the above two modeling methods and has high modeling efficiency and accuracy.