CN108398939B - Fault diagnosis method based on DS evidence theory - Google Patents

Abstract

The invention provides a fault diagnosis method based on an evidence theory, and relates to the field of fault diagnosis. The method comprises the steps of establishing a triangular fuzzy model for each fault, establishing a triangular fuzzy model for data to be tested, generating a basic probability distribution function according to the overlapping degree between the model to be tested and the fault model, and fusing the basic probability distribution function generated under each fault by using an evidence theory combination rule to realize fault diagnosis. The invention realizes fault diagnosis by combining the evidence theory and the triangular fuzzy number, and has the advantage of simple calculation; the basic probability distribution function generation method provided by the invention can well realize the processing of fuzzy information; the fault diagnosis method provided by the invention can realize the fault diagnosis of the motor rotor.

Description

Fault diagnosis method based on DS evidence theory

Technical Field

The invention relates to the field of fault diagnosis, in particular to a method for realizing fault diagnosis based on DS evidence theory.

Background

The fault diagnosis technology is an engineering science closely combined with actual production and is a product of modern production development. With the application of modern science and technology to equipment, the structure of the equipment is more and more complex, the function is more and more perfect, the automation degree is higher and higher, and various faults can occur to the equipment due to the influence of many unavoidable factors, so that the preset function is reduced or lost, and even serious or even catastrophic accidents can be caused.

The failure diagnosis technology is to grasp the operation state of the equipment during operation of the equipment or without detaching the equipment, and to determine whether the state of the object to be diagnosed is in an abnormal state or a failure state by analyzing and processing useful information obtained by testing the object to be diagnosed.

The information fusion technology is an information comprehensive processing technology which utilizes multi-source information in a synergistic mode to obtain more objective and more essential knowledge about objects or targets, and is one of key technologies of intelligent scientific research. Among many fusion models and methods, the D-S evidence theory algorithm is one of the most effective algorithms. Evidence theory broadens the Basic event space in probability theory into a power set of Basic events, also called recognition framework, on which a Basic probability assignment function (BPA) is built. In addition, the evidence theory also provides a Dempster combination rule which can realize evidence fusion without prior information. In particular, when BPA is only assigned on a single subset proposition of the recognition framework, BPA is transformed into probabilities in probability theory, and the fusion result of the combination rules is the same as Bayes' formula in probability theory. From this point of view, DS evidence theory can more effectively represent and process uncertain information than probability theory, and these characteristics make it widely used in the field of information fusion. Due to the fact that DS evidence theory has excellent performance in the aspect of uncertain knowledge representation, the theory and application of DS evidence theory are rapidly developed in recent years, and the DS evidence theory plays an important role in the aspects of multi-sensor information fusion, medical diagnosis, military command and target identification.

Evidence theory has many advantages, and the uncertain information appearing in the sensor signal of the equipment can be better processed when the evidence theory is applied to fault diagnosis.

Disclosure of Invention

In order to realize fault diagnosis, the invention provides a fault diagnosis method based on DS evidence theory. The fault diagnosis realized by the method can better process uncertain information in equipment sensor signals and accurately diagnose the motor rotor fault.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

the method comprises the following steps: inputting fault sample data D of n faults and k characteristics_ij(i ═ 1,2, …, n, j ═ 1,2, …, k), the fault features are features that can be used for fault classification, the fault sample data are measured values of fault features, a triangular fuzzy number model is built for each feature of each fault, and the identification framework is Θ ═ { F ═ F₁,F₂,...,F_nThe triangular ambiguity number is a set of ambiguities over a given domain of discourse U, meaning that for any x ∈ U, there is a number μ (x) ∈ [0,1 ∈]Correspondingly, μ (x) is called the membership degree of x to U, μ is called the membership function of x, and the method for establishing the triangular fuzzy number model comprises the following steps:

will fail F_i(i ═ 1,2, …, n) sample data D for feature j_ijMinimum value minD of_ijMean aveD_ijAnd maximum value maxD_ijRespectively as fault F_iThe minimum value, the mean value and the maximum value of the feature j triangular fuzzy number model are determined as the fault F_iThe triangular fuzzy number of feature j is

Step two: inputting k kinds of characteristic sample data T to be tested of equipment to be tested_jAnd generating a triangular fuzzy number model, wherein the equipment to be tested is a motor rotor, and the method for establishing the triangular fuzzy number model comprises the following steps:

the characteristic j is sampled by the sample data T to be tested_jMinimum value minT of_jMean aveT_jAnd maximum value maxT_jRespectively as the minimum value, the average value and the maximum value of the triangular fuzzy number model of the characteristic j to be measured, and then the triangular fuzzy number of the characteristic j to be measured is

Step three: matching the triangular fuzzy number model to be detected under the characteristic j with the fault triangular fuzzy number model to generate a basic probability distribution function m_jThe basic probability distribution function is defined in evidence theory as for any one of the subsets A, m (A) E [0, 1] belonging to theta]And satisfyThen m is 2^ΘA basic probability distribution function of wherein 2^ΘIn order to identify the power set of the frame,

the basic probability distribution function m_jThe generation method comprises the following steps:

will be provided with

And

cross area ofThe ratio of the areas under the curve is taken as the corresponding single subset element { F_iThe confidence of } willIntersection area of multiple fault ambiguity numbers with feature j

The ratio of the areas under the curve is used as the reliability of the corresponding multi-subset element, and the single-subset element { F }_iMeans that in step one if and only if the subset A contains the ith (i e [1, N ] in the recognition frame theta]) The element is that the subset A in the step one contains more than two elements in the identification frame theta, the Sum of the generated credibility is recorded as Sum, if Sum is more than or equal to 1, the generated credibility is normalized, and the normalization method comprises the following steps:

if Sum<1, then m is_j{F₁,F₂,…,F_nIs updated to m_j{F₁,F₂,…,F_n}+1-Sum；

Step four: sequentially fusing the k generated BPA by using evidence theory combination rules to obtain m_FThe combination rule of the evidence theory is

Wherein the ratio of A to B,

m₁,m₂two groups to be fused BPA, m is m₁And m₂The fused BPA, K is m₁,m₂The collision factor of (a) is determined,

step five: fusing the m obtained in the fourth step by using a Pistic probability transformation method_FConverting into probability distribution P, wherein the conversion method comprises the following steps:wherein

Step six: diagnosing the equipment fault according to the obtained probability distribution P, if P ({ F)_iGet P ({ F) }) if the maximum probability in P is greater than 0.5_i}) the category corresponding to the maximum probability is taken as the equipment fault diagnosis result.

The method has the advantages that the evidence theory and the triangular fuzzy number are combined to realize fault diagnosis, and the method has the advantage of simple calculation; the invention uses triangular fuzzy number to model the fault characteristics, thus solving the problem of representation of fuzzy information; the basic probability distribution function generation method provided by the invention can well realize the processing of fuzzy information; the fault diagnosis method provided by the invention can realize the fault diagnosis of the motor rotor.

Drawings

FIG. 1 is a general flow chart of an implementation of the present invention.

FIG. 2 is a failure F₁Feature 1 sample data D₁₁。

FIG. 3 shows the data T to be measured for feature 1₁。

FIG. 4 shows a feature 1 to-be-tested triangular fuzzy model and a fault triangular fuzzy model.

Fig. 5 is an intersection region of two blur numbers.

Fig. 6 is an intersection region of three blur numbers.

Detailed Description

The invention is further illustrated with reference to the figures and examples. Given an example of a fault diagnosis for a rotor of an electric machine, experimental data are from [1]]。[1]In total, three faults are set, here F₁,F₂,F₃There are four signature data for each fault, each containing five sets of 40 observations each. And selecting four groups of feature data of each feature of each fault as training samples to generate a fault triangular fuzzy number model. Selection of failure F₃The remaining set of data for the four features, i.e., data not selected as training samples, is used asTest samples illustrating the implementation steps of the proposed fault diagnosis method.

The method comprises the following steps: inputting three-fault four-characteristic fault sample data D_ij(i ═ 1,2, …,3, j ═ 1,2, …,4), the fault features are features that can be used for fault classification, the fault sample data are measured values of fault features, a triangular fuzzy number model is built for each feature of each fault, and the identification framework is Θ ═ { F ═ F₁,F₂,F₃The triangular ambiguity number is a set of ambiguities over a given domain of discourse U, meaning that for any x ∈ U, there is a number μ (x) ∈ [0,1 ∈]Correspondingly, μ (x) is called the membership degree of x to U, μ is called the membership function of x, and the method for establishing the triangular fuzzy number model comprises the following steps:

we have a fault F₁Feature 1 triangle fuzzy number establishment exemplifies a method for establishing a fault triangle fuzzy number model, and a fault F₁Feature 1 feature data is shown in figure 2. Will fail F₁Feature 1 sample data D₁₁The minimum value 0.1518, the mean value 0.1614 and the maximum value 0.1820 of (A) are respectively taken as the fault F_iThe minimum value, the mean value and the maximum value of the feature j triangular fuzzy number model are determined as the fault F₁The triangular fuzzy number of feature 1 is

Step two: inputting sample data T with 4 characteristics to be tested of equipment to be tested_j(j ═ 1,2, …,4), generating a triangular fuzzy number model, wherein the method for establishing the triangular fuzzy number model comprises the following steps:

the method for establishing the fuzzy number model of the triangle to be detected is described by taking the establishment of the fuzzy number of the triangle to be detected with the characteristic 1 as an example, and the characteristic data of the triangle to be detected is shown in figure 3. Sample data T to be tested of the feature 1₁The minimum value 0.3207, the mean value 0.3387 and the maximum value 0.3476 of the feature 1 to be tested are respectively used as the minimum value, the mean value and the maximum value of the triangular fuzzy number model of the feature 1 to be tested, and then the triangular fuzzy number of the feature 1 to be tested is the minimum value, the mean value and the maximum value

Step three: treat under the characteristic jMatching the triangle measuring fuzzy number model with the fault triangle fuzzy number model to generate a basic probability distribution function m_jThe basic probability distribution function is defined in evidence theory as for any one of the subsets A, m (A) E [0, 1] belonging to theta]And satisfy

Then m is 2^ΘA basic probability distribution function of wherein 2^ΘIn order to identify the power set of the frame,

the basic probability distribution function m_jThe generation method comprises the following steps:

will be provided with

And

cross area of

The ratio of the areas under the curve is taken as the corresponding single subset element { F_iThe confidence of } will

Intersection area of multiple fault ambiguity numbers with feature j

The ratio of the areas under the curve is used as the reliability of the corresponding multi-subset element, and the single-subset element { F }_iMeans that in step one if and only if the subset A contains the ith (i e [1, N ] in the recognition frame theta]) The element is that the subset A in the step one contains more than two elements in the identification frame theta, the Sum of the generated credibility is recorded as Sum, if Sum is more than or equal to 1, the generated credibility is normalized, and the normalization method comprises the following steps:

if Sum<1, then m is_j{F₁,F₂,…,F_nIs updated to m_j{F₁,F₂,…,F_n}+1-Sum；

Let us take m₁Production as an example illustrates the BPA production process:

(1) computingArea under the curve S ═ (0.3476-0.3207) × 1/2 ═ 0.0135;

(2)m₁({F₁})，m₁({F₂})，m₁({F₃}):

computing

And

cross area of

Then

Computing

And

cross area of

Then

ComputingAndcross area ofThen

(3)m₁({F₁,F₂})，m₁({F₁,F₃})，m₁({F₂,F₃})，m₁({F₁,F₂,F₃}):

computing

And

cross area of

Then

Computing

And

cross area of

Then

Computing

And

cross area of

Then

Computing

And

cross area of

Then

(4) Since the Sum of the degrees of reliability Sum generated as described above is 0.2848, m is updated₁({F₁,F₂,F₃})＝0+1-Sum＝0.7152。

M can be generated by the same method₂,m₃,m₄The results are as follows:

m₂({F₁})＝0.0867，m₂({F₂})＝0.2094，m₂({F₃})＝0.3216，m₂({F₁,F₂})＝0.0365，m₂({F₁,F₃})＝0.0547，m₂({F₂,F₃})＝0.1694，m₂({F₁,F₂,F₃})＝0.1217；

m₃({F₁})＝0，m₃({F₂})＝0，m₃({F₃})＝0.4482，m₃({F₁,F₂})＝0，m₃({F₁,F₃})＝0，m₃({F₂,F₃})＝0，m₃({F₁,F₂,F₃})＝0.5518；

m₄({F₁})＝0，m₄({F₂})＝0，m₄({F₃})＝0.9745，m₄({F₁,F₂})＝0，m₄({F₁,F₃})＝0，m₄({F₂,F₃})＝0，m₄({F₁,F₂,F₃})＝0.0255；

step four: sequentially fusing the 4 generated BPA by using evidence theory combination rules to obtain m_FThe combination rule of the evidence theory is

Wherein the ratio of A to B,

m₁,m₂two groups to be fused BPA, m is m₁And m₂The fused BPA, K is m₁,m₂The collision factor of (a) is determined,

the fusion result is: m is_F({F₁})＝0.0013，m_F({F₂})＝0.0031，m_F({F₃})＝0.9898，m_F({F₁,F₂})＝0.0006，m_F({F₁,F₃})＝0.0008，m_F({F₂,F₃})＝0.0026，m_F({F₁,F₂,F₃})＝0.0018；

Step five: fusing the m obtained in the fourth step by using a Pistic probability transformation method_FConverting into probability distribution P, wherein the conversion method comprises the following steps:

wherein

Step six: diagnosing the equipment fault according to the obtained probability distribution P, if P ({ F)_iGet P ({ F) }) if the maximum probability in P is greater than 0.5_i}) the category corresponding to the maximum probability is used as the equipment fault diagnosis result;

the maximum probability in probability distribution P is P ({ F)₃}) and P ({ F)₃})>0.5, so the equipment failure is diagnosed as F₃Consistent with the true fault type.

Reference to the literature

[1] Wencheng forest, xu dawn shore, multisource uncertain information fusion theory and applications [ M ] scientific press, 2012.

Claims (1)

1. A fault diagnosis method based on DS evidence theory is characterized by comprising the following steps:

the method comprises the following steps: inputting fault sample data D of n faults and k characteristics_ij(i ═ 1,2, …, n, j ═ 1,2, …, k), the fault features are features that can be used for fault classification, the fault sample data are measured values of fault features, a triangular fuzzy number model is built for each feature of each fault, and the identification framework is Θ ═ { F ═ F₁,F₂,...,F_nThe triangular ambiguity number is a set of ambiguities over a given domain of discourse U, meaning that for any x ∈ U, there is a number μ (x) ∈ [0,1 ∈]Correspondingly, μ (x) is called the membership degree of x to U, μ is called the membership function of x, and the method for establishing the triangular fuzzy number model comprises the following steps:

will fail F_i(i ═ 1,2, …, n) sample data D for feature j_ijMinimum value minD of_ijMean aveD_ijAnd maximum valuemaxD_ijRespectively as fault F_iThe minimum value, the mean value and the maximum value of the feature j triangular fuzzy number model are determined as the fault F_iThe triangular fuzzy number of feature j is

Step two: inputting k kinds of characteristic sample data T to be tested of equipment to be tested_jAnd generating a triangular fuzzy number model, wherein the equipment to be tested is a motor rotor, and the method for establishing the triangular fuzzy number model comprises the following steps:

the characteristic j is sampled by the sample data T to be tested_jMinimum value minT of_jMean aveT_jAnd maximum value maxT_jRespectively as the minimum value, the average value and the maximum value of the triangular fuzzy number model of the characteristic j to be measured, and then the triangular fuzzy number of the characteristic j to be measured is

Step three: matching the triangular fuzzy number model to be detected under the characteristic j with the fault triangular fuzzy number model to generate a basic probability distribution function m_jThe basic probability distribution function is defined in evidence theory as for any one of the subsets A, m (A) E [0, 1] belonging to theta]And satisfy

Then m is 2^ΘA basic probability distribution function of wherein 2^ΘIn order to identify the power set of the frame,

the basic probability distribution function m_jThe generation method comprises the following steps:

will be provided with

And

cross area of

The ratio of the areas under the curve is taken as the corresponding single subset element { F_iThe confidence of } will

Intersection area of multiple fault ambiguity numbers with feature j

The ratio of the areas under the curve is used as the reliability of the corresponding multi-subset element, and the single-subset element { F }_iMeans that in step one if and only if the subset A contains the ith (i e [1, N ] in the recognition frame theta]) The element is that the subset A in the step one contains more than two elements in the identification frame theta, the Sum of the generated credibility is recorded as Sum, if Sum is more than or equal to 1, the generated credibility is normalized, and the normalization method comprises the following steps:

if Sum<1, then m is_j{F₁,F₂,…,F_nIs updated to m_j{F₁,F₂,…,F_n}+1-Sum；

Step four: sequentially fusing the k generated BPA by using evidence theory combination rules to obtain m_FThe combination rule of the evidence theory is

Wherein the ratio of A to B,

m₁,m₂two groups to be fused BPA, m is m₁And m₂The fused BPA, K is m₁,m₂The collision factor of (a) is determined,

step five: fusing the m obtained in the fourth step by using a Pistic probability transformation method_FConverting into probability distribution P, wherein the conversion method comprises the following steps:wherein

Step six: diagnosing the equipment fault according to the obtained probability distribution P, if P ({ F)_iGet P ({ F) }) if the maximum probability in P is greater than 0.5_i}) the category corresponding to the maximum probability is taken as the equipment fault diagnosis result.

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