# Application of Improved MFDFA and D-S Evidence Theory in Fault Diagnosis
## 1 Introduction  
The traditional technique of fault diagnosis consists of acquiring single sensor data and obtaining the corresponding features using the signal feature extraction method for fault pattern identification. However, traditional signal feature extraction method presents with certain limitations, and the fault information contained in a single sensor is incomplete, thereby this approach is incapable of fully reflecting the fault status of the specific object being tested [1, 2, 3]. To address this problem, scholars have proposed solutions from improving the accuracy of fault signal feature extraction and using data fusion techniques. For example, [PERSON] [4] applied MFDFA, as proposed by [PERSON] [5], to the acoustic signal, and extracted the multiple fractal spectral feature parameters as the eigenvalues, which finally allowed for the fault diagnosis to be realized. In addition, [PERSON] [6] used SVM and information fusion technology to diagnose the fault by a single signal. With the improvement of monitoring technology, the research of fault diagnosis tends to use multi-sensor data, and D-S theory is more and more widely used [7]. For example, [PERSON] [8] integrated the empirical modal decomposition of fault vibration signals from different position sensors to obtain energy values as fault eigenvalues and used the D-S evidence theory to achieve integrated diagnostic results. Further, [PERSON] [9] and [PERSON] [10] obtained the fault features of multiple sensor signals through different feature extraction methods and applied the D-Sevidence theory to consolidate the information, effectively resulting in the improvement of the diagnosis rate. [PERSON] [11] used the improved MFDFA to analyze the random part of the power load data to obtain the information of the probability distribution and reveal the information contained in these data, which further shows that the MFDFA has a good effect on processing nonlinear non-stationary data and has a wide range of applications. [PERSON] [12] and [PERSON] [13], for the MFDFA's flaws, assuming that the signal local trend term is in polynomial form, but the actual signal local trend is not all polynomial form, improved this via the introduction of moving average method and in other ways, instead of polynomial fitting for local trend removal, but such methods lack adaptability to signals. Therefore, inspired by various studies, this paper offers an improved MFDFA [14] and combines BP neural network [15] output with D-S evidence theory [7] to propose a new method of fault diagnosis. Among them, in order to overcome the defects of MFDFA, the automatic determination of EMD trend term method is introduced and the least squares method is fitted instead of polynomial fitting, so that it can well describe the structural characteristics and local scale behavior of the fault signal and quantitatively reflect the characteristics of the fault signal, while D-S evidence theory [16], as a decision-level information fusion method of data fusion technology, can effectively synthesize the information of multiple sensors and overcome the uncertainty and limitations of single sensors. It provides a new way to solve the uncertainty of equipment failure in complex systems. Therefore, this paper takes the centrifugal pump as the research object, the proposed method is applied by using the improved MFDFA method to extract the multifractal spectral parameters of the signals from centrifugal pump vibration, torque, motor vibration, and oscillation sensors and form them into feature vectors \(\Delta f\), \(\alpha_{0}\), \(\Delta\alpha\), \(\alpha_{\min}\), and \(\alpha_{\max}\). This is then input to the BP neural network and combined with D-S evidence theory for the decision level fusion of the multi-sensor data. The final fault diagnosis results of the centrifugal pump are subsequently obtained according to the established diagnostic rules. Therefore, this method can provide a practical reference for the accuracy of fault diagnosis in the field of signal analysis of complex power systems.