*3.2. Fault Simulation and Data Obtained*

Before the test operation, the standard of the experimental parameters needs to be determined first. After a number of optimization experiments on the shift section of the continuously variable transmission, it was found that when the oil pressure is 4 MPa and the flow rate is 5 L/min, the overall performance of the shift section is the best. Therefore, all of the following experiments were conducted under this parameter index.

Among the aforementioned fault modes, the T1 mode does not require special processing, and can directly collect oil pressure and flow data; the T2 mode can be simulated when the clutch is in the state of oil drain disconnection, by filling the joint gap between the clutch's main and driven shafts with sandpaper. At this time, the clutch piston was completely unable to extend and was forced to be stuck in place; the T3 mode can be simulated by installing seal rings with different degrees of wear on the rotary joint; T4 can be used to conduct simulation tests while reducing the opening of the governor valve. Additionally, because the characteristic component of the T4 mode is the gradual fault, the flow level can be controlled within the range of 0~4 L/min, while ensuring the interval of 1 L/min for the test. The T5 mode can be simulated by unscrewing the branch pipe joint.

The data to be measured in the test are the flow data of the clutch main oil circuit and the pressure data of the clutch branch oil circuit. Due to the strict proportional relationship between the observed value and the actual value of the original data, the original data can be directly identified without conversion. The data recording cycle of the data and programs obtained through the high-speed data acquisition system is 16 ms. The test was conducted 120 times in total, 24 times for each fault simulation test. In addition, we considered that the original data points of the flow and pressure of the hydraulic system were huge in the shifting process, so its characteristic attributes were calculated based on the following six statistics:

$$X\_f = \sqrt{\frac{1}{N\_f} \sum\_{i=1}^{N} x\_{fi}^2} \tag{1}$$

$$C\_f = \frac{\max\left( \left| \mathbf{x}\_{fi} \right| \right)}{X} \tag{2}$$

$$K\_f = \frac{\sum\_{i=1}^{N} x\_{fi}^4}{N\_f X^4} \tag{3}$$

$$I\_f = \frac{\max\left( \left| \mathbf{x}\_{fi} \right| \right)}{\frac{1}{N\_f} \sum\_{i=1}^{N} \left| \mathbf{x}\_{fi} \right|}\tag{4}$$

$$S\_f = \frac{X}{\frac{1}{N\_f} \sum\_{i=1}^{N} \left| \mathbf{x}\_{fi} \right|} \tag{5}$$

$$X\_p = \sqrt{\frac{1}{N\_p} \sum\_{i=1}^{N} \mathfrak{x}\_{pi}^2} \tag{6}$$

In the formula, *Xf*, *Cf*, *Kf*, *If* and *Sf* are flow statistics, respectively, representing the root mean square value of flow, peak factor, kurtosis factor, pulse factor and form factor during the transition period; *Xp* is the pressure statistic, which represents the root mean square pressure of the pressure during the transition; *xfi* and *xpi* represent the data of the *i*-th sampling point of flow and pressure, respectively, and *Nf* and *Np* represent the total number of data sampling points of flow and pressure, respectively. After the attribute calculation, a sample set of 120 fault data characteristic attributes was obtained. Randomly, we set 80 of them as training samples and 40 of them as test samples.

#### **4. BP Method for FAULT Diagnosis of HMCVT Shift Hydraulic System**

### *4.1. Fault Diagnosis of Shift Hydraulic System Based on BP Neural Network*

The BP neural network is mainly composed of an input layer. The output layer and hidden layer are composed of three parts, in which the number of input layers is determined by the eigenvalue of fault data and the number of output layers is determined by the fault diagnosis result. In the data collection, this paper collects the flow and pressure fault signals of the HMCVT hydraulic system as characteristic values, and takes the corresponding working state as output characteristics. The structure of the neural network is constructed according to the actual training results. Therefore, the number of neurons in the input layer of the neural network is set to six, the number of neurons in the output layer is one and the number of hidden layer neurons is as follows.

$$N = 2n + 1\tag{7}$$

$$N = \sqrt{n+m} + \alpha \tag{8}$$

$$N = \log\_2 n \tag{9}$$

In the formula, *N*—the number of neurons in the hidden layer; *n*—the number of neurons in the input layer; *m*—the number of neurons in the output layer; *α*—the constant from 1 to 10. After many neural network trainings, the number of neurons in the hidden layer of this paper was selected as 10. Its network structure is shown in Figure 3.

**Figure 3.** The topology of the three-layer neural network.

The BP neural network established in this paper comprises the following: one input layer, one hidden layer and one output layer. The BP neural network established in this paper comprises the following: one input layer, one hidden layer and one output layer, in which the number of neurons in the input layer is six, the number of neurons in the hidden layer is ten and the number of neurons in the output layer is one. The transfer function of the hidden layer uses the tansig function, and the output layer uses the purelin function. We inputted 40 groups of test samples into the unoptimized BP neural network model, and the resulting diagnosis results of the test samples are shown in Figure 4.

**Figure 4.** The effect of fault diagnosis of the unoptimized BP neural network test sample.

It can be seen from Figure 4 that the unoptimized BP neural network model has a good recognition ability for the normal mode (Fault Type 1), the clutch piston being stuck (Fault Type 2) and branch oil pipeline joint leakage (Fault Type 5).
