## 1 Introduction  
As a stable and efficient power source, diesel engine plays an important role in industry, agriculture and transportation. Since the advent of the world's first diesel engine, researchers have been committed to improving the performance of the diesel engine to meet more severe application conditions. The combustion condition in the cylinder is directly related to the power output and emission level of the diesel engine. In order to analyze and optimize the combustion process of the diesel engine, the most commonly used method is to measure the in-cylinder pressure. By analyzing the heat release rate according to the in-cylinder pressure, the variation characteristics of many parameters in the combustion process can be acquired. In the development and calibration stage of diesel engines, the cylinder pressure is a very valuable reference indicator, which is of great significance to improve power and economy, reduce noise and emissions and reduce failure probability for engines [1]. [PERSON] proposed that real-time closed-loop control of in-cylinder pressure is one of the effective methods to achieve efficient and clean combustion of diesel engines in the future [2], and the control of combustion phase and heat release is the key to ensure stable and efficient operation of engines. [PERSON] et al. proposed four real-time estimation methods of a compression ratio based on an in-cylinder pressure track, and used the estimation method to evaluate the simulation cycle and test cycle, which improved the stability of the variable compression ratio engine [3]. [PERSON] et al. proposed and verified a method for diagnosing noise sources by extracting appropriate components from in-cylinder pressure, which can accurately predict the noise level of diesel engines and identify noise-related combustion characteristic parameters [4]. [PERSON] et al. studied the relationship between the diesel engine combustion noise and the double-peak characteristics of the cylinder pressure rise rate, and the results showed that the second peak is the characteristic quantity of the combustion noise, and the combustion noise is a function of the diesel engine load [5]. [PERSON] et al. calculated CA50 (Phase of 50% heat release) according to the in-cylinder pressure, and analyzed the relationship between CA50 and NOx emission. The results showed that NOx emission and CA50 had a certain logarithmic function relationship [6]. [PERSON] et al. calculated various combustion characteristic parameters according to the cylinder pressure, and ECU adjusted the fuel injection parameters according to the combustion characteristic parameters, which significantly improved the combustion stability in the cylinder and the non-uniformity of each cylinder [7]. The above research proves the importance of cylinder pressure in the process of diesel engine performance optimization. However, the acquisition of cylinder pressure data currently relies on many physical tests, the test cost is high, and there are many uncertain factors in the test process, which is prone to measurement errors. Moreover, the test time is long, and the measurement results cannot meet the real-time requirements. Therefore, it is very important to develop a high-accuracy and fast-responding technology to predict the in-cylinder pressure of diesel engines. With the rapid development of data science and artificial intelligence, machine learning, as the core of artificial intelligence, has been widely used in finance, Internet, medicine, and other fields [8; 9; 10]. Machine learning refers to computers continuously refining and summarizing knowledge from data by simulating human learning behavior, thereby adjusting their structure to achieve or even surpass human intelligence. Compared with experimental measurement and physical calculation models, machine learning has advantages such as fast response, high accuracy, and strong generalization ability [11; 12].