# Application of Improved MFDFA and D-S Evidence Theory in Fault Diagnosis
## 4 Test Analysis
### D-S Fusion Fault Diagnosis  
As per the above discussion, in order to select a reasonable basic trust distribution function to realize the fault diagnosis of a multi-sensor centrifugal pump using D-S evidence theory, each group of sensor data is subjected to BP neural network fault identification. The data from the four sensors are collected and sorted into 120 groups for each of the four operating conditions. Subsequently, the \(\Delta f\), \(\alpha_{0}\), \(\Delta\alpha\), \(\alpha_{\min}\), and \(\alpha_{\max}\) of each group of sensor signals are extracted by the improved MFDFA method to form a feature vector, of which 60 feature vectors are randomly selected as the training data for the neural network's 3-layer structure, while the remaining 60 are used as diagnostic data. According to the number of feature parameters, the quantity of output conditions, and the empirical formula of the implicit layer [21], the number of nodes of the input, output, and implicit layers are taken as 5, 4, and 11, respectively. Thus, the network structure is constructed as \(5\times 11\times 4\), resulting in the diagnosis results of each group of sensors as shown in Table 1.  
As can be seen from Table 1, of the normal and faulty data of each group of sensors to be diagnosed by BP neural network fault recognition, the centrifugal pump vibration sensor for the normal state reached a recognition rate of 100%, while that for the severe cavitation state was 84.17%, while the highest and lowest recognition rates of the torque, motor, and oscillation sensors corresponded to the working conditions, though they were more different in the case of the centrifugal pump vibration sensor. The lowest recognition rate of the oscillation sensor was 83.33% for slight cavitation, which can show the improved MFDFA method extracted feature parameters combined with the BP neural network can better classify the different working conditions of centrifugal pump. Figure 7: Characteristic parameters of 4 centrifugal pump fault state under (**a**) pump vibration signal, (**b**) torque signal, (**c**) motor vibration signal, (**d**) swing signal. To further improve the accuracy of fault diagnosis, multi-sensor fusion diagnosis supplemented with D-S evidence theory was carried out. Another 60 feature vectors were selected and input to the BP neural network. The neural network had already been trained to obtain the basic trust assignment function for each condition. Then, the network's local and global trustworthiness were obtained according to Table 1 (as shown in Table 2), and the data in Table 2 were used as \(a\) priori information to reassign the basic trust assignment function for each condition according to Equation (16), and the Dempster combination rule [20] was adopted for the fusion, and the fault diagnosis results of fusion of multiple sensors and each single sensor as per D-S evidence theory were obtained according to the principle of maximum affiliation [22]. Displayed in Figure 8 is the basic trust distribution function for each working condition based on the D-S evidence fusion multi-sensor and single-sensor approach for the data to be diagnosed. Here, it can be seen that compared to diagnoses derived from single sensor data, the value of basic trust distribution function obtained by a multi-sensor system under different working conditions fluctuates more smoothly and has better stability. Moreover, when the real working conditions are determined according to the principle of maximum affiliation, the incidence of misjudgment is lower, with a correct rate of diagnosis reaching 92.5%. Compared to the diagnostic rates of single sensor systems derived from the centrifugal pump vibration, torque, motor vibration, and oscillation sensors, the accuracy increased by 3.33%, 2.08%, 2.50%, and 7.50%, respectively.