Research on Multi-element Fusion of Equipment Fault Monitoring Based on Evidence Theory

: The multi-information fusion method of health monitoring based on evidence theory is used to study the problem of equipment fault diagnosis. The multi-information of fault monitoring is fused by the evidence theory and the reliability of the relevant evidence can be judged according to the ambiguity and uncertainty of the fault monitoring signal. Also it can determine the importance and reliability of the evidence from different sources. The data from multi-information fusion has higher reliability and accuracy which provides more reliable data for fault diagnosis.


Analysis of equipment fault monitoring performance signal
The data of equipment fault monitoring performance signal is essentially a kind of nonstationary time series data (signal) mixed with strong random noise, the data abnormity mainly shows as data point mutation (sporadic data abnormity, such as peak pulse) and data trend Mutation (large data abnormity) . The typical characteristics of time series data of equipment fault monitoring performance parameters are analyzed, and the data must be preprocessed before further processing or analyzing.

Identification and reconstruction of signal abrupt change based on modulus maximum curve of continuous wavelet transform
The wavelet basis function can be obtained by setting ( ) t ψ as a basic wavelet In the expression，* denotes conjugation. The inverse wavelet transform is given by the following theorem： Theorem 1 Aassume Then ) (t x can be inversed by its wavelet (3) is called the admissibility condition of wavelets, from which it can be inferred that the basic wavelets should at least satisfy 0 ( ) 0 ω Ψ ω = = . Because wavelet transform and inverse transform have many kinds of definition forms such as inner product, convolution and so on, and the methods used in numerical processing are different, so there are many kinds of realization algorithms. In this project, the continuous wavelet transform formula (2) and its Inverse Transform Formula (4) are transformed into frequency domain by discrete Fourier transform and inverse transform to avoid convolution computation in time domain, thus improving the operation speed.
The Fourier transform of   (4) is also treated as a signal, the inverse wavelet transform can be treated similarly, but here, scale by scale.The Fourier transform of ( ) ( , ) (8) It is obvious that both formulas (6) and (8) contain the basic form of inverse fourier transform, so the inverse discrete fourier transform can be used for numerical processing.
The wavelet transform modulus Maxima of the signal can identify the sudden change of the signal, which is based on the following two points: θ is a low-pass smooth function, the signal ( ) x t can obtain ( ) y t after ( ) t θ smoothing, and then take the derivative of ( ) y t , equivalent to the direct use derivatives of ( ) t θ for signal processing (such as convolution) .
2 ) Any low-pass smooth function ( ) t θ ， its derivatives must be bandpass functions ， the frequency characteristic is that there must be a zero In addition, Mallat and Hwang have shown that if the wavelet transform of a signal does not have a modulus maximum at a small scale, then the signal must be locally regular. It can be seen that the modulus maximum of wavelet transform is closely related to the abrupt change of signal. But this does not mean that the modulus Maxima of wavelet transform must correspond to the signal mutation, Mallat proves this point by a counter-example, and also puts forward the corresponding method to solve this problem, the Lipschitz Index, which describes the regularity of the curve, is used to further verify the detected "mutation", thus ensuring the feasibility of identifying the signal mutation with wavelet transform modulus Maxima. In summary, the rule of signal and white noise changing with wavelet transform scale is different and the rule of some special types of sudden change and normal signal changing with wavelet transform scale is also different. In the proper scale range of wavelet transform, the wavelet transform modulus of normal signal will increase with the increase of scale, however, the wavelet transform modulus such as white noise and spike pulse will decrease or even disappear as the scale of wavelet transform increases. Therefore, tracking the final direction of the modulus maximum of the signal wavelet transform from the large scale to the small scale, that is, searching the modulus maximum curve of the signal wavelet Transform, as long as the scale selection is appropriate, the final modulus maximum position may be the signal mutation point or the signal trend mutation point; the modulus maximum curve obtained by the search is the signal rather than the noise of the wavelet transform mode of the link. Therefore, all the wavelet transform corresponding to all the modulus maximum curves can be used to reconstruct the signal details and filter the noise, then, all the wavelet transform on other large scale without searching modulus maximum curve is used to recover the trend information of the signal, and the whole signal can be reconstructed by adding the two. It should be pointed out here that the starting scale of modulus maximum curve search is not the maximum scale of signal wavelet transform, because the wavelet function of larger scale has longer duration and the signal wavelet transform is smoother, the wavelet transform of larger scale is the reflection of the signal trend, and the existence of larger scale is only to improve the accuracy of signal reconstruction.
It can be seen that this method can detect the abrupt change of the signal and filter the singularity such as noise or spike pulse, so as to realize the signal reconstruction.

Multi-information fusion method based on evidence theory
The evidence theory uses the recognition framework U to represent the set of propositions of interest, which defines the basic probability assignment function ( BPAF ) over U In the formula, proposition A is a non-empty subset of U, and M(A) reflects the reliability of A.
If K is the BPAF derived from n independent evidences on the same recognition frame U, then the combination rule of Dempster is used to calculate the BPAF under the action of these independent evidences.
How to make a decision after using evidence theory is a problem closely related to its application. The common decision-making methods include decision-making based on trust function, decisionmaking based on assignment of basic probability and decision-making based on minimum risk. Because the computation is small, the decision method based on the basic probability assignment is adopted here. Let U be the identification frame. M is the basic probability assignment based on Dempster combination rule. assume A is the verdict.

Example analysis
Firstly, an Agent-oriented modeling method and a distributed fault monitoring model are used to build the system structure of the intelligent fault monitoring system, as shown in figure 1.  Four evidence bodies are used to analyze the fault monitoring capability of the fault monitoring system.The basic probability distribution of F 1 (fault A), F 2 (fault B) and F 3 (Fault C) in the fault space is obtained from the preliminary diagnosis analysis of four evidence bodies, as shown in Table  1. Since the evidence bodies E1 and E2 are in conflict with each other, the use of the rule of evidence composition will produce results contrary to the facts, the combination rule of evidence theory based on support degree of Focus Element can effectively avoid the influence of conflicting evidence on the combination result. The composite results for the four evidence bodies are shown in Table 2. As can be seen from Table 2, the new composition rule can reallocate conflicts according to the degree of Focus Element's support for conflicting evidences. In the previous example, the diagnosis was F 3 when there were only two conflicting sources of evidence, but with the addition of new evidence to support F 1 , the diagnosis became F 1 , this shows that the new combination rule can not only avoid conflict effectively, but also reflect the influence of new evidence body on the diagnosis result quickly, and has higher diagnosis efficiency.

Conclusion
The multi-information fusion algorithm of equipment fault health monitoring based on evidence theory is based on multi-information monitoring and using Dempster combination rule. Firstly, the attributes of health monitoring characteristic parameters are fused. Secondly, the time domain fusion of multiple monitoring cycles is carried out, and then the spatial domain fusion of multiple monitoring devices is carried out, and finally the fault source is identified. The multiinformation fusion method of equipment structure and moving parts health monitoring based on evidence theory can process abnormal data, and the filtering ratio of noise data and error information is over 90%, multi-information fusion fault source identification reliability ≥90% .