# A New Engine Fault Diagnosis Method Based on Multi-Sensor Data Fusion
## 1 Introduction  
Engine fault diagnosis, one of the aspects of fault diagnosis [1; 2], which is useful for engine design [3; 4], can make the maintenance personnel quickly grasp the engine fault type and make the corresponding maintenance measures. At present, there are many methods for fault diagnosis. For example, the methods based on expert systems [5; 6; 7], which utilize the experience accumulated by domain experts in long-term practice. In these kinds of methods, a computer program is designed to simulate the reasoning and decision-making process of human experts to diagnose faults. Other fault diagnosis methods, such as machine learning [8; 9] and signal processing [10; 11; 12], where there is a comparison of frequency analysis and SVM (support vector machine) classifiers in [11; 12], are also widely used in practical applications [13; 14]. There are also fault diagnosis methods in multi-sensor networks. As another efficient method to fault diagnosis, the residual-based unsupervised fault diagnosis method addresses uncertainty in the form of error bars around the soft computing models extracted from data [15; 16; 17]. Multi-sensor data fusion fault diagnosis [18; 19], which is widely used in sensor design [20; 21], as a data-driven approach, has been paid more and more attention. The advantages of multi-sensor data fusion for fault diagnosis can be concluded as follows:  
* Compared with single source data, multi-source information fusion or multi-sensor information fusion can improve the accuracy and promptness of fault diagnosis. * Multi-sensor data fusion method has the ability to deal with the uncertainty of data in fault diagnosis so as to enhance the credibility of diagnostic results. A number of theories have been developed on multi-sensor data fusion, such as the Dempster-Shafer (D-S) evidence theory [22; 23; 24; 25; 26], fuzzy set theory [27], rough sets theory [28; 29], Z numbers [30; 31], and Dnumbers [32; 33; 34; 35]. The D-S evidence theory, first proposed by [PERSON] [22] and then developed by [PERSON] [23], is able to deal with uncertain information without a prior probability. It has been applied to wide areas, such as decision making [36; 37; 38], pattern recognition [39; 40; 41] and risk assessment [42; 43; 44; 45]. In the D-S evidence theory, mass function (or basic probability assignment (BPA)), belief function and plausibility function are defined to express uncertain information. Many methods can be used to integrate multi-source information [46; 47; 48], while [PERSON]'s combination rule, which is effective at addressing uncertainty information, can be used to fuse multi-source information in uncertain environments to make a decision. Much research have been carried out in fault diagnosis based on multi-sensor data fusion [31; 49; 50; 51; 52]. Generally, the overall process of fault diagnosis based on multi-sensor data fusion is as follows. Firstly, prior to diagnosis, fault models are established using features extracted from known faulty equipment. Secondly, test models are established using the extracted features from a machine to be detected. Thirdly, BPAs are obtained by computing the BPA determination algorithm using the obtained fault models and test models. Finally, final BPA is obtained by using a combination rule to fuse all of the obtained BPAs. Decision making is carried out through the obtained final BPA. In this process, the key issues are the reasonable establishment of models and the reasonable determination of BPA. However, in previous studies, they are not well solved, especially considering the uncertainty. For example, in [31], the authors take ordinates of intersection points of functions as BPA, while it is not enough to express the uncertain information in fault models due to inadequate consideration on model variance information.