Rotating machine fault diagnosis method based on sample distribution characteristics and ellipsoid model

Abstract

The invention provides a rotating machine fault diagnosis method based on sample distribution characteristics and an ellipsoid model. The method comprises the following steps: establishing a finite element model of a rotating machine, calculating dynamic response in a typical fault mode, obtaining corresponding characteristic parameters, and forming a fault sample set; establishing a similarity matrix according to the similarity coefficients of the sample points in the fault sample set, and removing abnormal points based on the similarity matrix; performing clustering analysis on sample points in the fault sample set after the abnormal points are removed to form a multi-ellipsoid model in a typical fault mode; characteristic parameters in a to-be-detected mode are obtained, a corresponding ellipsoid model is established, and the overlap ratio of the ellipsoid model and the multi-ellipsoid model is calculated; and establishing an identification framework based on the typical fault mode, and obtaining a diagnosis result of the to-be-detected mode in combination with probability fusion and maximum probability decision. According to the invention, a rotating machinery fault diagnosis framework based on the sample distribution characteristics and the ellipsoid model is established, and the accuracy of fault diagnosis under dispersive data is improved.

Description

Technical Field

[0001] The invention belongs to the field of machinery, and in particular relates to a rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model. Background Art

[0002] Rotating machinery plays a vital role in industrial production and is a core component of the normal operation of many key equipment. However, during long-term operation, rotating machinery will be affected by complex working conditions, such as high-load operation, vibration shock, temperature fluctuations, and environmental corrosion. These factors can easily cause wear, fatigue, and even unexpected failures of mechanical parts, resulting in reduced production efficiency or equipment damage, causing serious economic losses and safety hazards. Therefore, carrying out efficient and reliable fault diagnosis for rotating machinery is of great significance to improving the stability of equipment operation, extending service life, and ensuring production safety.

[0003] In engineering practice, due to differences in measurement methods and changes in the service environment, the external loads and boundary conditions of rotating machinery are often affected by various uncertain factors, making their failure forms complex and diverse, and the measured data of various sensors inevitably show large dispersion. Probabilistic methods are widely used in multi-source uncertainty modeling of multiple sensors, but usually sufficient experimental samples are required to establish a more accurate probability density function, which limits the application of this method under the condition of small sample data. For the case of insufficient experimental samples, uncertainty modeling can be carried out through non-probabilistic methods such as interval models, ellipsoid models, and fuzzy theory. Among them, the ellipsoid model uses regular boundaries to describe the feasible domain of variables, which can effectively deal with the dispersion problem of small sample data with correlated variables.

[0004] However, the presence of abnormal points and class imbalance features in fault data affects the accuracy of ellipsoid modeling and reduces the accuracy of fault diagnosis results. Summary of the invention

[0005] In view of the above problems, the present invention provides a rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model, which is used to improve the accuracy of rotating machinery fault diagnosis results.

[0006] An embodiment of the present invention provides a rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model, which includes:

[0007] Step 1: discretizing the geometric model of the rotating machinery by using a finite element mesh to obtain a finite element model of the rotating machinery, and calculating the dynamic response of the finite element model under a typical fault mode to obtain a plurality of characteristic parameters in the dynamic response, and establishing a fault sample set according to all the characteristic parameters;

[0008] Step 2: Calculate similarity coefficients of all sample points in the fault sample set based on the inverse absolute value method, form a similarity matrix with all the similarity coefficients, and remove abnormal points in the fault sample set according to the statistical characteristics of the similarity matrix;

[0009] Step 3: performing cluster analysis on the sample points in the fault sample set after removing the abnormal points, obtaining sample clusters of the characteristic parameters of the sample points under the typical fault mode, and establishing a multi-ellipsoid model of the characteristic parameters under the typical fault mode based on the sample clusters;

[0010] Step 4: Select multiple characteristic parameters in the dynamic response under the test mode to establish a sample set to be tested, use the sample set to establish an ellipsoid model of the characteristic parameters under the test mode, and use a geometric measurement method to calculate the overlap between the ellipsoid model and the multi-ellipsoid model;

[0011] Step 5: Establish an identification framework based on the typical fault mode, form a focal element set by exhaustively combining all typical fault modes under the identification framework, normalize the overlap degree and use it as the basic probability assignment of each focal element in the focal element set, perform probability conversion on the basic probability assignment and obtain the diagnosis result of the mode to be tested based on the maximum probability decision.

[0012] In some possible embodiments, similarity coefficients of all sample points in the fault sample set are calculated based on the inverse absolute value method, all the similarity coefficients are formed into a similarity matrix, and abnormal points in the fault sample set are removed according to statistical characteristics of the similarity matrix, including:

[0013] Normalizing the sample points in the fault sample set, and obtaining similarity coefficients between the normalized sample points by the inverse absolute value method to form the similarity matrix;

[0014] The similarity matrix is ​​successively squared until it does not change, to obtain an equivalent matrix, wherein the diagonal elements of the equivalent matrix are all 1;

[0015] The interval [0,1] is evenly divided into a plurality of continuous subintervals, and the distribution frequencies of the similarity coefficients in the equivalent matrix in all the subintervals are statistically analyzed row by row;

[0016] Determine whether the subinterval where each of the sample points is most concentrated is close to the lower bound of the interval, if so, the sample point is an outlier;

[0017] All the abnormal points in the sample fault set are removed.

[0018] In some possible embodiments, the overlap degree is the ratio of the volume of the overlapping area of ​​the ellipsoid model in the inspection mode and the multi-ellipsoid model in the typical failure mode to the volume of the ellipsoid model.

[0019] In some possible embodiments, calculating the degree of overlap between the ellipsoid model and the multi-ellipsoid model using a geometric measurement method includes:

[0020] Counting the distribution ranges of the ellipsoid model and the multi-ellipsoid model in the geometric space to determine the minimum cubic area that can cover the ellipsoid model and the multi-ellipsoid model;

[0021] Sampling is performed in the minimum cubic area, and the number of sample points falling into the overlapping area of ​​the ellipsoid model and the multi-ellipsoid model, as well as the number falling into the ellipsoid model, are calculated, and the ratio of the corresponding numbers is used as the overlap degree.

[0022] The rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model provided by the embodiment of the present invention has at least the following advantages:

[0023] (1) The method in the embodiment of the present invention fully considers the data dispersion caused by various uncertain factors in actual engineering, and the diagnosis result has more important guiding significance for rotating machinery fault diagnosis.

[0024] (2) Introducing outlier screening and cluster analysis when building the ellipsoid model can adaptively group sample data and improve the accuracy of the uncertainty quantification model.

[0025] (3) When calculating the basic probability assignment using the ellipsoid overlap, the distribution of the ellipsoid model is taken into account, and the volume ratio is converted into the sample quantity ratio, which is more convenient when calculating the basic probability assignment. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flow chart of a rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model in an embodiment of the present invention;

[0027] Figure 2 is a simplified flow chart of a rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model in an embodiment of the present invention;

[0028] Figure 3 It is a schematic diagram of the geometric model of the rotating machinery in an embodiment of the present invention.

[0029] Description of reference numerals:

[0030] 11-first support; 12-second support;

[0031] 21-first rotating shaft; 22-second rotating shaft;

[0032] 31-first rotor disk; 32-second rotating shaft disk;

[0033] 40-Coupling. DETAILED DESCRIPTION

[0034] In order to make the above-mentioned purposes, features and advantages of the embodiments of the present invention more understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0035] refer to Figure 1 and Figure 2 The embodiment of the present invention provides a rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model, comprising the following steps:

[0036] Step 1: Discretize the geometric model of the rotating machinery using the finite element mesh to obtain the finite element model of the rotating machinery, calculate the dynamic response of the finite element model under the typical fault mode, obtain multiple characteristic parameters in the dynamic response, and establish a fault sample set based on all the characteristic parameters.

[0037] In an embodiment of the present invention, there are N typical failure modes of the rotating machinery. The geometric model of the rotating machinery is discretized using a finite element mesh to obtain a finite element model thereof. The N typical failure modes of the rotating machinery are implanted into the finite element model, the working conditions are set to simulate the actual service environment, and a transient dynamic analysis is performed to obtain the dynamic response of the finite element model under the typical failure mode.

[0038] F represents the typical failure mode, and the jth typical failure mode of the rotating machinery is called failure F. j (j=1,2,…,N). Rotating machinery may have multiple dynamic responses under typical fault modes, from which M key dynamic responses are selected as characteristic parameters to form an M-dimensional characteristic parameter vector X=(X1,X2,…,X M ) T , where X i (i=1,2,…,M) represents the i-th characteristic parameter. j The i-th characteristic parameter is denoted as X i,j , then the fault F j The characteristic parameter vector X j It can be expressed as:

[0039] Xj =(X 1,j ,X 2,j ,…,X M,j ) T ,j=1,2,…,N;

[0040] For each fault F j (j=1,2,…,N), conduct n independent finite element simulation experiments, obtain n groups of sample points, and form a fault sample set. i,j , the fault sample set Γ obtained in the above n finite element simulation experiments i,j It can be expressed as:

[0041]

[0042] in, represents the kth group of sample points, Represents the characteristic parameter X in the kth group of sample points i,j The numerical value of .

[0043] In one possible example, the rotating machine is a single-span rotor system with a geometric model such as Figure 3 In the geometric model, the rotating machine includes a first support 11 and a second support 12 which are arranged opposite to each other, and a first rotating shaft 21, a second rotating shaft 22, a first rotor disk 31, a second rotor disk 32 and a coupling 40 which are arranged between the first support 11 and the second support 12.

[0044] One end of the first rotating shaft 21 is rotatably connected to the first support 11 , and the first rotating shaft 21 is also fixedly connected to the first rotor disk 31 so that the first rotor disk 31 and the first rotating shaft 21 move synchronously, and the other end of the first rotating shaft 21 is connected to the coupling 40 .

[0045] One end of the second rotating shaft 22 is rotatably connected to the second support 12, and a second rotor disk 32 is fixedly connected to the second rotating shaft 22 so that the second rotor disk 32 and the second rotating shaft 22 move synchronously, and the other end of the second rotating shaft 22 is connected to the coupling 40, so that the first rotating shaft 21 and the second rotating shaft 22 have the same rotation speed. The first rotating shaft 21 and the second rotating shaft 22 have the same structure and size, the first rotor disk 31 and the second rotor disk 32 have the same structure and size, and the first support 11 and the second support 12 have the same structure and size.

[0046] The geometric model of the above-mentioned rotating machinery is discretized using finite element meshes. Specifically, 1762 hexahedral units are used to mesh the geometric model of the rotating machinery. Fixed support boundary conditions are set on the bottom surfaces of the first support 11 and the second support 12 of the rotating machinery, binding contacts are set at the connections between the coupling and the first rotating shaft 21 and the second rotating shaft 22, friction contacts are set at the connections between the first rotating shaft 21 and the first support 11, the second rotating shaft 22 and the second support 12, and a fixed rotation speed is applied to the first rotating shaft 21, thereby obtaining a finite element model of the rotating machinery.

[0047] The above rotating machinery has three typical failure modes, namely loose support, misalignment and imbalance. The above three typical failure modes are implanted into the finite element model of the rotating machinery and transient dynamic analysis is performed. The connection between the second support 12 and the second rotating shaft 22 is selected as the observation point to obtain the dynamic response of the rotating machinery at the observation point under the typical failure mode.

[0048] F represents the typical failure mode, and the jth typical failure mode of the rotating machinery is called failure F. j (j=1,2,3). Rotating machinery can have multiple dynamic responses under typical fault modes, from which three key dynamic responses are selected as characteristic parameters. The characteristic parameters include acceleration mean μ, acceleration variance σ 2 The acceleration frequency is twice f p ″ eak , forming a 3D feature parameter vector X = (μ, σ 2 ,f p ″ eak ) T . The fault F j The i-th characteristic parameter is denoted as X i,j , then the fault F j The characteristic parameter vector X j It can be expressed as:

[0049] X j =(X 1,j ,X 2,j ,X 3,j ) T ,j=1,2,3;

[0050] For each fault F j (j=1,2,3), 80 independent finite element simulation experiments are carried out to obtain 80 groups of sample points to form a fault sample set. i,j , the fault sample set Γ obtained through the above 80 finite element simulation experiments i,j It can be expressed as:

[0051]

[0052] in, represents the kth group of sample points, Represents the characteristic parameter X in the kth group of sample points i,j The numerical value of .

[0053] Step 2: Calculate the similarity coefficients of all sample points in the fault sample set based on the inverse absolute value method, form a similarity matrix with all similarity coefficients, and remove abnormal points in the fault sample set according to the statistical characteristics of the similarity matrix.

[0054] For the above fault sample set Γ i,j The n sample points in are normalized, and the similarity coefficient between the normalized sample points is calculated using the reciprocal absolute value method, that is, the similarity between the normalized sample points is obtained, specifically:

[0055]

[0056] Among them, the similarity coefficient ρ rs is the fault sample set Γ i,j The rth sample point in and the sth sample point The similarity between and The sample points and About the characteristic parameter X i,j The value of c is used to adjust ρ rs to a constant in the interval [0,1].

[0057] Furthermore, the similarity coefficient ρ between all n sample points in the aforementioned fault sample set is calculated rs , all similarity coefficients ρ rs Assemble into fuzzy similarity matrix R = (ρ rs ) n×n The fuzzy similarity matrix R is squared successively until it no longer changes, and the fuzzy equivalent matrix is ​​obtained. The fuzzy equivalence matrix Describes the similarity of all sample points, where Represents the updated similarity coefficient (for the convenience of expression, ρ is no longer distinguished in the future rs and collectively referred to as similarity coefficient). Fuzzy equivalence matrix The diagonal elements are all 1, and all similarity coefficients in each row It is used to characterize the similarity between the sample point corresponding to this row and the other sample points.

[0058] Then, a series of continuous subintervals are uniformly divided on the interval [0,1], and the fuzzy equivalence matrix Similarity coefficient The distribution frequency in all sub-intervals is counted row by row, and the results of n frequency row by row statistics are regarded as the similarity distribution of n sample points with the rest of the sample points. Find the sub-interval with the most concentrated similarity distribution of each sample point. If the sub-interval is closer to the lower bound of the interval [0,1] (that is, closer to 0), it is considered that the similarity between the sample point and most of the other sample points is low, and the sample point is regarded as an outlier. The above outlier determination process is performed n times in total to find all the outliers and remove them from the fault sample set.

[0059] In a possible example, based on the above example (the example given in step 1), the above fault sample set Γ i,j The 80 sample points in are normalized, and the similarity coefficient of the normalized sample points is calculated using the reciprocal absolute value method, which is:

[0060]

[0061] Among them, the similarity coefficient ρ rs is the fault sample set Γ i,j The rth sample point in and the sth sample point The similarity between and The sample points and About the characteristic parameter X i,j The value of c is used to adjust ρ rs to a constant in the interval [0,1].

[0062] Furthermore, the similarity coefficient ρ between all 80 sample points in the aforementioned fault sample set is calculated rs , all similarity coefficients ρ rs Assemble into fuzzy similarity matrix R = (ρ rs ) 80×80 The fuzzy similarity matrix R is squared successively until it no longer changes, and the fuzzy equivalent matrix is ​​obtained. The fuzzy equivalence matrix Describes the similarity of all sample points, where Represents the updated similarity coefficient (for the convenience of expression, ρ is no longer distinguished in the future rs and collectively referred to as similarity coefficient). Fuzzy equivalence matrix The diagonal elements are all 1, and all similarity coefficients in each row It is used to characterize the similarity between the sample point corresponding to this row and the other sample points.

[0063] Then, the interval [0,1] is evenly divided into 5 consecutive subintervals Intervp =(p,p+1]×0.2p=0,1,…,4, for this fuzzy equivalent matrix Similarity coefficient The distribution frequency in all sub-intervals is counted row by row, and the results of 80 frequency counts are regarded as the similarity distribution of 80 sample points with the rest of the sample points. Find the sub-interval with the most concentrated similarity distribution of each sample point. If the sub-interval is closer to the lower bound of the interval [0,1] (that is, closer to 0), it is considered that the similarity between the sample point and most of the other sample points is low, and the sample point is regarded as an outlier.

[0064] The above abnormal point determination process is performed 80 times in total to find all abnormal points and remove them from the fault sample set. For example, among the given 80 sample points, 4 abnormal points are identified and screened out. After the abnormal points are screened out, there are 76 sample points remaining in the above fault sample set.

[0065] Step 3: Perform cluster analysis on the sample points in the fault sample set after removing abnormal points, obtain sample clusters of various characteristic parameters of the sample points under typical fault modes, and establish a multi-ellipsoid model of the characteristic parameters under typical fault modes based on the sample clusters.

[0066] The Bayesian Gaussian mixture model (BGMM) is used to analyze the fault sample set Γ after removing abnormal points. i,j Perform cluster analysis on the remaining sample points and calculate the optimal number of sample clusters n c , and then all the sample points in the fault sample set after removing the abnormal points (considered as a total sample cluster Λ j ) is divided into n c Sample clusters are expressed as:

[0067]

[0068] in, Indicates fault F j The next h-th sample cluster.

[0069] Then, an ellipsoid model is established for each sample point in each sample cluster. In the embodiment of the present invention, the ellipsoid model is calculated by the following formula:

[0070]

[0071] Among them, Ω h,j (h=1,2,…,n c ) indicates that the sample cluster The ellipsoid model (i.e. fault F j hth ellipsoid model), X h,j Represents the ellipsoid model Ω h,j The corresponding feature vector. G h,j and ω h,j Represent the ellipsoid model Ω h,j The center, characteristic matrix and size factor of .

[0072] Furthermore, for the fault F j All ellipsoid models under the above formula are combined into a multi-ellipsoid model Ω j , expressed as:

[0073]

[0074] Among them, ∪ represents the union operation.

[0075] In a possible example, based on the above example (the example given in step 2), the Bayesian-Gaussian mixture model is used to perform cluster analysis on the fault sample set after removing the abnormal points. Under the three fault modes of loose support, misalignment, and imbalance, the optimal number of sample clusters corresponding to the fault sample set is 2, 3, and 3 respectively, and then all sample points in each fault sample set after removing the abnormal points (considered as an overall sample cluster Λ j ) is divided into several sample clusters, expressed as:

[0076]

[0077] in, Indicates fault F j The next h-th sample cluster.

[0078] Subsequently, an ellipsoid model is established for the sample points in each sample cluster, and the information of the established ellipsoid model is shown in Tables 1 to 3 (in order to ensure the consistency of dimensions, the values ​​of the sample points are subsequently expressed in scientific notation when establishing the ellipsoid model, and only the coefficient part is retained).

[0079] Table 1 Ellipsoid model established under bearing loosening failure mode F1

[0080]

[0081] Table 2 Ellipsoid model established under misalignment failure mode F2

[0082]

[0083]

[0084] Table 3 Ellipsoid model established under unbalanced fault mode F3

[0085]

[0086] Furthermore, all ellipsoid models under each fault are combined into a multi-ellipsoid model Ω j , expressed as:

[0087] Ω1={Ω 1,1 ∪Ω 2,1};

[0088] Ω2={Ω 1,2 ∪Ω 2,2 ∪Ω 3,2};

[0089] Ω3={Ω 1,3 ∪Ω 2,3 ∪Ω 3,3};

[0090] Among them, ∪ represents the union operation.

[0091] Step 4: Select multiple characteristic parameters in the dynamic response under the test mode to establish a test sample set, use the test sample set to establish an ellipsoid model of the characteristic parameters under the test mode, and use the geometric measurement method to calculate the overlap between the ellipsoid model and the multi-ellipsoid model.

[0092] Let U represent the mode to be tested, select M dynamic parameters that are the same as those in the typical fault mode in step 1 to form an M-dimensional parameter vector X U =(X 1,U ,X 2,U ,…,X M,U ) T , calculate the values ​​of each component of the parameter vector to be tested under the test mode U, and establish the corresponding sample set to be tested. Use the sample set to be tested to directly establish the ellipsoid model Ω under the test mode U U , expressed as:

[0093]

[0094] in, G U and ω U Represent the ellipsoid model Ω U The center, characteristic matrix and size factor of .

[0095] Furthermore, the ellipsoid model Ω under the inspection mode U is defined as U Same as typical fault F j Multi-ellipsoid model Ω j The overlap degree μ(F j ), expressed as:

[0096]

[0097] Where ∩ represents the intersection operation, Vol(·) represents the volume of the geometric domain, and Vol(Ωj ∩Ω U ) represents the ellipsoid model Ω U and multi-ellipsoid model Ω j The volume of the overlapping area, Vol(Ω U ) represents the ellipsoid model Ω U The volume of the area.

[0098] Subsequently, the volume ratio of the calculated geometric model is converted into the number ratio of the calculated samples to reduce the computational complexity when solving the above-mentioned overlap. Specifically, the statistical ellipsoid model Ω U and multi-ellipsoid model Ω j In the distribution range of geometric space, the minimum cubic area that can completely cover all ellipsoid models is further determined. Random sampling is performed in this minimum cubic area, and the number of sample points falling in different geometric areas is regarded as the volume of the corresponding geometric area. At this time, the overlap degree μ(F j ) can be approximately expressed as:

[0099]

[0100] Among them, Num(·) represents the number of sample points falling into the geometric region, Num(Ω j ∩Ω U ) means falling into the ellipsoid model Ω U and multi-ellipsoid model Ω j The number of sample points in the overlapping area, Vol(Ω U ) means falling into the ellipsoid model Ω U The number of sample points in the region.

[0101] In a possible example, based on the above example (the example given in step 3), the mode to be tested is represented by U, and the same three dynamic parameters as those in the typical fault mode in step 1 are selected to form a three-dimensional parameter vector X to be tested. U =(μ,σ 2 ,f p ″ eak ) T , calculate the values ​​of each component of the parameter vector to be tested under the test mode U, and establish the corresponding sample set to be tested. Use the sample set to be tested to directly establish the ellipsoid model Ω under the test mode U U , expressed as:

[0102]

[0103] The degree of overlap between the ellipsoid model under the inspection mode U and the multi-ellipsoid model under the three fault modes of loose support, misalignment and imbalance is shown in Table 4.

[0104] Table 4 The overlap between the ellipsoid model under the inspection mode and the multi-ellipsoid model of each fault mode

[0105]

[0106] Step 5: Establish an identification framework based on typical fault modes, and exhaustively combine all typical fault modes under the identification framework to form a focal element set. Normalize the overlap degree and use it as the basic probability assignment of each focal element in the focal element set. Perform probability conversion on the basic probability assignment and obtain the diagnostic result of the mode to be tested based on the maximum probability decision.

[0107] According to the N typical fault modes in step 1, an identification framework is established, and the set of all typical fault modes constitutes an identification framework Θ={F1,F2,…,F N The power set of the identification framework Θ constitutes the proposition set 2 Θ , for the set of propositions 2 Θ Any non-empty proposition A={F1,F2,…,F N′}, which is defined as the intersection of multiple ellipsoid models for all typical failure modes:

[0108] A=Ω1∩Ω2∩…∩Ω N′ ;

[0109] Where N′ is the number of elements in proposition A.

[0110] Furthermore, the ellipsoid model Ω under the test mode U is defined as U The overlap degree of the intersection of multiple ellipsoid models under Proposition A is μ(A), which can be expressed as:

[0111]

[0112] Among them, Vol(A∩Ω U ) represents the ellipsoid model Ω U The volume of the overlapping area of ​​the geometric area corresponding to Proposition A, Num(A∩Ω U ) means falling into the ellipsoid model Ω U The number of sample points in the overlapping area of ​​the geometric area corresponding to Proposition A.

[0113] For the identification framework Θ={F1,F2,…,F N}, and all the basic propositions (i.e., fault F j ) to exhaustively combine, proposition set 2 Θ All non-empty elements in form the focal element set Ψ:

[0114]

[0115] Among them, h (h=1,2,…,2 N -1) represents the hth focal element, and For the convenience of description and calculation, no distinction will be made between focus elements and propositions in the following.

[0116] Using the summation and averaging method, we can h (h=1,2,…,2 N -1) is normalized:

[0117]

[0118] in, The normalized proposition Υ h The degree of overlap.

[0119] After normalization, the proposition set 2 Θ The overlap degree of all non-empty propositions in is directly used as the basic probability assignment of all focal elements in the focal element set Ψ, that is:

[0120]

[0121] Among them, m(Υ h ) represents the basic probability assignment of the focal element Υh.

[0122] Subsequently, the probability conversion method is used to convert the basic probability assignment m into a probability distribution P m Specifically, the basic probability assignment m(F i ) remains unchanged, and the basic probability assignment m(Υ) of the multi-subset proposition (i.e., the multi-subset focal element) is evenly distributed to the basic propositions it contains. The conversion formula is as follows:

[0123]

[0124] Among them, P m (F i ) indicates that the pending mode U belongs to fault F i probability.

[0125] Traversing the proposition set 2 Θ Among all the N basic propositions, use the maximum probability decision method to find the basic proposition with the highest probability. This basic proposition corresponds to the fault F with the highest probability. * :

[0126] P m (F * )=max{P m (F1),P m (F2),…,P m (F N )};

[0127] Among them, max represents the maximum value operation.

[0128] Finally, the fault F * As the fault diagnosis result of the detection mode U, that is, U = F * .

[0129] In a possible example, based on the above example (the example given in step 4), an identification framework is established according to the three typical fault modes in step 1, and the set of all typical fault modes constitutes the identification framework Θ = {F1, F2, F3}, and all basic propositions are combined to form a focal element set Ψ:

[0130] Ψ={Υ1, Υ2, …, Υ7};

[0131] Among them, h (h=1,2,…,7) represents the hth focal element, and For the convenience of description and calculation, no distinction will be made between focus elements and propositions in the following.

[0132] Using the summation and averaging method, we can h The overlap degree of (h=1,2,…,7) is normalized:

[0133]

[0134] in, The normalized proposition Υ h The degree of overlap.

[0135] After normalization, the proposition set 2 Θ The overlap degree of all non-empty propositions in ({F1}, {F2}, {F3}, {F1,F2}, {F1,F3}, {F2,F3} and {F1,F2,F3} in turn) is directly used as the basic probability assignment of all focal elements in the focal element set Ψ. The results are shown in Table 5.

[0136] Table 4 The overlap between the test pattern and the seven propositions and the basic probability assignment

[0137]

[0138] Subsequently, the probability conversion method is used to convert the basic probability assignment m into a probability distribution P m Specifically, the basic probability assignment m(F i ) remains unchanged, and the basic probability assignment m(Υ) of the multi-subset proposition (i.e., the multi-subset focal element) is evenly distributed to the basic propositions it contains. The conversion formula is as follows:

[0139]

[0140] Among them, P m (F i) indicates that the pending mode U belongs to fault F i The conversion results are shown in Table 5.

[0141] Table 5 Fault diagnosis results after probability conversion

[0142]

[0143] Traversing the proposition set 2 Θ Among all the three basic propositions, the maximum probability decision method is used to find the basic proposition with the highest probability, which corresponds to the fault F with the highest probability. * :

[0144] P m (F * )=max{P m (F1),P m (F2),P m (F3)};

[0145] Among them, max represents the maximum value operation.

[0146] Finally, fault F3 is used as the fault diagnosis result of the mode to be detected U, that is, the mode to be detected U is an unbalanced fault.

[0147] In summary, the rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model in the embodiment of the present invention, by extracting characteristic parameters through the establishment of a finite element model, forms a fault sample set, and removes abnormal points based on the similarity matrix, effectively improving the quality of sample data; establishing a multi-ellipsoid model of typical fault modes through cluster analysis, accurately describing the distribution characteristics of different fault modes; using the geometric measurement method to calculate the overlap between the mode to be tested and the typical fault mode, providing a quantitative basis for fault identification; combining the identification framework, basic probability assignment and probability conversion method, the diagnosis results of different fault modes are integrated. The embodiment of the present invention establishes a rotating machinery fault diagnosis framework based on sample distribution characteristics and ellipsoid model, which improves the accuracy of fault diagnosis under dispersed data.

[0148] The various embodiments or implementation methods in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts between the various embodiments can be referenced to each other.

[0149] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiments or examples are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model, characterized in that: include: Step 1: discretizing the geometric model of the rotating machinery by using a finite element mesh to obtain a finite element model of the rotating machinery, and calculating the dynamic response of the finite element model under a typical fault mode to obtain a plurality of characteristic parameters in the dynamic response, and establishing a fault sample set according to all the characteristic parameters; Step 2: Calculate similarity coefficients of all sample points in the fault sample set based on the inverse absolute value method, form a similarity matrix with all the similarity coefficients, and remove abnormal points in the fault sample set according to the statistical characteristics of the similarity matrix; Step 3: performing cluster analysis on the sample points in the fault sample set after removing the abnormal points, obtaining sample clusters of the characteristic parameters of the sample points under the typical fault mode, and establishing a multi-ellipsoid model of the characteristic parameters under the typical fault mode based on the sample clusters; Step 4: Select multiple characteristic parameters in the dynamic response under the test mode to establish a sample set to be tested, use the sample set to establish an ellipsoid model of the characteristic parameters under the test mode, and use a geometric measurement method to calculate the overlap between the ellipsoid model and the multi-ellipsoid model; Step 5: Establish an identification framework based on the typical fault mode, form a focal element set by exhaustively combining all typical fault modes under the identification framework, normalize the overlap degree and use it as the basic probability assignment of each focal element in the focal element set, perform probability conversion on the basic probability assignment and obtain the diagnosis result of the mode to be tested based on the maximum probability decision.

2. The rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model according to claim 1 is characterized in that: Calculating similarity coefficients of all sample points in the fault sample set based on the inverse absolute value method, forming a similarity matrix with all the similarity coefficients, and removing abnormal points in the fault sample set according to statistical characteristics of the similarity matrix, including: Normalizing the sample points in the fault sample set, and obtaining similarity coefficients between the normalized sample points by the inverse absolute value method to form the similarity matrix; The similarity matrix is ​​successively squared until it does not change, to obtain an equivalent matrix, wherein the diagonal elements of the equivalent matrix are all 1; The interval [0,1] is evenly divided into a plurality of continuous subintervals, and the distribution frequencies of the similarity coefficients in the equivalent matrix in all the subintervals are statistically analyzed row by row; Determine whether the sub-interval where each of the sample points is most concentrated is close to the lower bound of the interval, if so, the sample point is an outlier; All the abnormal points in the sample fault set are removed.

3. The rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model according to claim 1 is characterized in that: The overlap degree is the ratio of the volume of the overlapping area of ​​the ellipsoid model in the inspection mode and the multi-ellipsoid model in the typical failure mode to the volume of the ellipsoid model.

4. The rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model according to claim 3 is characterized in that: Calculating the degree of overlap between the ellipsoid model and the multi-ellipsoid model using a geometric measurement method includes: Counting the distribution ranges of the ellipsoid model and the multi-ellipsoid model in the geometric space to determine the minimum cubic area that can cover the ellipsoid model and the multi-ellipsoid model; Sampling is performed in the minimum cubic area, and the number of sample points falling into the overlapping area of ​​the ellipsoid model and the multi-ellipsoid model, as well as the number falling into the ellipsoid model, are calculated, and the ratio of the corresponding numbers is used as the overlap degree.

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