## 1 Introduction
established a fault hierarchy model for the data characteristics of a hydraulic system, and evaluated the health status through data mining and the fuzzy synthetic evaluation model [18]. The gray clustering method is a way to divide the indexes into different gray classes by a gray whitening weight function. [PERSON] [19] and [PERSON] [20] et al. determined the weights of each evaluation index of each component of the aircraft hydraulic system by expert experience, the entropy weight method and an extension of the analytic hierarchy process, and used the gray clustering method to evaluate the weights to obtain the health status level of each component and the whole system. To obtain sensitive feature quantities for health state evaluation, ref. [21] used wavelet packet decomposition and used the magnitude of the sensitive quantities to complete the hydraulic system health state evaluation. To overcome the effect of noise on data analysis, ref. [22] proposed a method of wavelet energy transfer rate to monitor the unit gearbox health status. Taken together, the signal processing-based evaluation method requires establishing a very accurate database of signal features or setting thresholds to classify data labels. The knowledge-based health evaluation method is an idea and method that makes full use of the experience and knowledge of experts to simulate problem solving by domain experts [23]. No mathematical model of the object under consideration is required for this method, so it is suitable for dealing with complex and large nonlinear systems. The main methods are expert systems based on knowledge, knowledge-based evolutionary methods such as artificial neural networks and Bayesian networks based on statistical knowledge, etc. The key to this type of method is network training and classification decisions [24; 25]. Based on the standard LeNet, an improved convolutional neural network (CNN) with a particle swarm optimization algorithm was constructed in ref. [26], where the model was used to train the acoustic signal of the hydraulic piston pump to analyze the health status. To tackle the difficulty of severe class imbalance in faulty samples, ref. [27] proposed the invariant temporal-spatial attention fusion network (ITSA-FN) to evaluate the bearing health status with imbalance conditions. In order to rapidly predict the important performance indicators of mechanical devices, ref. [28] proposed a prediction algorithm of comprehensively using a composite variable wavelet transform, deep auto-encoder and long short term memory (CWD-LSTM) hybrid neural network. In particular, it has a great advantage for time series. To implement the medical device health status evaluation, ref. [29] proposed a partial least squares regression (PLSR) algorithm combined with deep neural networks (DNNs). Briefly, the knowledge-based method involves massive amounts of data for network training. In addition, there is high accuracy with more different kinds of data, but it cannot explain the connection between the data and the system, i.e., the conclusion has uncertainty. Integrating the current state of the research, model-based methods have a deep theoretical foundation and strong implementability, and will remain the main direction of research in the field of health state evaluation technology in future development. Among them, the parameter estimation method is very suitable for hydraulic systems with strong nonlinearity. In this paper, the system variable parameters are used as indicators to evaluation the real health status of the system, and the system parameters are obtained by establishing a nonlinear mathematical model of the hydraulic system based on system identification. The simulation experiment was conducted using MATLAB simulation software. The fourth-order Runge-Kutta method was used to obtain the measurable data of the system, and the differential data of measurable data were obtained by a tracking-differentiator (T-D).