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

Abstract

The application provides a rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model, which comprises the following steps: establishing a finite element model of the rotating machinery, calculating dynamic response under a typical fault mode, obtaining corresponding characteristic parameters, and forming a fault sample set; establishing a similarity matrix according to the similarity coefficients of sample points in the fault sample set, and removing abnormal points based on the similarity matrix; performing cluster analysis on the sample points in the fault sample set after removing the abnormal points, and forming a multi-ellipsoid model under the typical fault mode; obtaining characteristic parameters under a to-be-inspected mode, establishing a corresponding ellipsoid model, calculating the coincidence degree of the ellipsoid model and the multi-ellipsoid model; establishing an identification framework based on the typical fault mode, combining probability fusion and maximum probability decision, and obtaining a diagnosis result of the to-be-inspected mode. The application establishes a rotating machinery fault diagnosis framework based on sample distribution characteristics and ellipsoid model, and improves the accuracy of fault diagnosis under dispersed data.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of machinery, and particularly relates to a rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model. BACKGROUND

[0002] Rotating machinery plays a vital role in industrial production and is a core component of the normal operation of many key equipment. However, in the long-term operation process, the rotating machinery is affected by complex working conditions such as high-load operation, vibration impact, temperature fluctuation, and environmental corrosion. These factors are prone to cause wear, fatigue, and even accidental failure of mechanical components, thereby leading to a decrease in production efficiency or damage to equipment, causing serious economic losses and safety hazards. Therefore, it is of great significance to carry out efficient and reliable fault diagnosis on rotating machinery to improve the stability of equipment operation, prolong the service life, and ensure production safety.

[0003] In engineering practice, due to differences in measurement methods and changes in service environments, the external load, boundary conditions, and other factors of rotating machinery are often affected by various uncertain factors, making the fault forms complex and diverse, and the measured data of various sensors inevitably present a large dispersion. The probability method is widely used in multi-sensor multi-source uncertainty modeling, but it usually requires sufficient experimental samples to establish a relatively 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, non-probabilistic methods such as interval models, ellipsoid models, and fuzzy theory can be used for uncertainty modeling. Among them, the ellipsoid model uses a regular boundary to describe the feasible region of variables, which can effectively handle the dispersion problem of small sample data with correlated variables.

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

[0005] In view of the above problems, the application 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] The rotating machinery fault diagnosis method based on sample distribution characteristics and an ellipsoid model provided by the embodiments of the application comprises:

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

[0008] Step two: calculate the similarity coefficients of all sample points in the fault sample set based on the absolute value reciprocal 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 three: perform cluster analysis on the sample points in the fault sample set after removing the abnormal points, obtain sample clusters of the sample points in each feature parameter under the typical fault mode, and establish a multi-ellipsoid model of the feature parameters under the typical fault mode according to the sample clusters;

[0010] Step four: select a plurality of feature parameters in the dynamic response under the to-be-detected mode to establish a to-be-detected sample set, establish an ellipsoid model of the feature parameters under the to-be-detected mode using the to-be-detected sample set, and calculate the coincidence degree of the ellipsoid model and the multi-ellipsoid model using the geometric measure method;

[0011] Step five: establish a recognition framework according to the typical fault mode, form a focal element set by performing an exhaustive combination of all typical fault modes under the recognition framework, normalize the coincidence 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 to-be-detected mode according to the maximum probability decision.

[0012] In some possible embodiments, the absolute value reciprocal method is used to calculate the similarity coefficients of all sample points in the fault sample set, 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, including:

[0013] The sample points in the fault sample set are normalized, and the similarity coefficients between the normalized sample points are obtained by the absolute value reciprocal method to form the similarity matrix;

[0014] The similarity matrix is sequentially squared until it no longer changes to obtain an equivalent matrix, and the diagonal elements of the equivalent matrix are all 1;

[0015] A plurality of continuous subintervals are uniformly divided on the interval [0, 1], and the distribution frequencies of the similarity coefficients in the equivalent matrix on all the subintervals are counted row by row;

[0016] It is judged whether the subinterval where each sample point is most concentrated is close to the lower bound of the interval, and if so, the sample point is an abnormal point;

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

[0018] In some possible embodiments, the coincidence degree is a ratio of a volume of an overlapping region of the ellipsoid model in the to-be-detected mode and the multi-ellipsoid model in the typical fault mode to a volume of the ellipsoid model.

[0019] In some possible embodiments, the coincidence degree of the ellipsoid model and the multi-ellipsoid model is calculated by using a geometric measure method, comprising:

[0020] The distribution ranges of the ellipsoid model and the multi-ellipsoid model in a geometric space are counted, so as to determine a minimum cubic region capable of covering the ellipsoid model and the multi-ellipsoid model;

[0021] Sampling is performed in the minimum cubic region, the number of sampled sample points falling into the overlapping region of the ellipsoid model and the multi-ellipsoid model and the number of sample points falling into the ellipsoid model are calculated, and a ratio of the corresponding numbers is taken as the coincidence degree.

[0022] The method for diagnosing a rotating machine fault based on sample distribution characteristics and an ellipsoid model provided in the embodiments of the present application has at least the following advantages:

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

[0024] (2) Abnormal points are screened out and cluster analysis is introduced when the ellipsoid model is modeled, so that sample data can be adaptively grouped, and the accuracy of the uncertainty quantification model is improved.

[0025] (3) The distribution of the ellipsoid model is considered when the ellipsoid coincidence degree is used to calculate the basic probability assignment, and the volume ratio is converted into a sample quantity ratio, so that the calculation of the basic probability assignment is more convenient. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 A flowchart of the method for diagnosing a rotating machine fault based on sample distribution characteristics and an ellipsoid model in the embodiments of the present application is shown in FIG. 1.

[0027] Figure 2 A flowchart of the method for diagnosing a rotating machine fault based on sample distribution characteristics and an ellipsoid model in the embodiments of the present application is shown in FIG. 1.

[0028] Figure 3 A geometric model of a rotating machine in the embodiments of the present application is shown in FIG. 2.

[0029] REFERENCE SIGNS:

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

[0031] 21-First pivot; 22-Second pivot;

[0032] 31-First rotor disc; 32-Second shaft disc;

[0033] 40 - Coupling. Detailed Implementation

[0034] To make the above-mentioned objectives, features, and advantages of the embodiments of the present invention more readily understood, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] refer to Figure 1 and Figure 2 This invention provides a method for diagnosing rotating machinery faults based on sample distribution characteristics and an ellipsoidal model, comprising the following steps:

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

[0037] In this embodiment of the invention, rotating machinery exhibits N typical failure modes. The geometric model of the rotating machinery is discretized using a finite element mesh to obtain its finite element model. The N typical failure modes of the rotating machinery are then incorporated into this finite element model, and operating conditions are simulated under real service environments. Transient dynamic analysis is performed to obtain the dynamic response of the finite element model under the typical failure modes.

[0038] Let F represent a typical failure mode, and the j-th typical failure mode of the rotating machinery is called failure F. j (j=1,2,…,N). Rotating machinery may exhibit multiple dynamic responses under typical failure modes. M key dynamic responses are selected as characteristic parameters, forming 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. The fault F... j The i-th feature parameter is denoted as X i,j Then fault F j The feature parameter vector X j It can be represented 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), n independent finite element simulation experiments are performed to obtain n groups of sample points, which constitute a fault sample set. For the feature parameter X i,j , the fault sample set Γ i,j obtained in the foregoing n finite element simulation experiments can be expressed as:

[0041]

[0042] wherein, represents the kth group of sample points, represents the value of the feature parameter X i,j in the kth group of sample points.

[0043] In one possible example, the rotating machine is a single-span rotor system, and its geometric model is shown in Figure 3 . In the geometric model, the rotating machine includes a first support 11 and a second support 12 arranged oppositely, and a first rotating shaft 21, a second rotating shaft 22, a first rotor disc 31, a second rotor disc 32 and a coupling 40 arranged between the first support 11 and the second support 12.

[0044] Wherein, one end of the first rotating shaft 21 is rotationally connected with the first support 11, and the first rotating shaft 21 is further fixedly connected with the first rotor disc 31, so that the first rotor disc 31 and the first rotating shaft 21 move synchronously, and the other end of the first rotating shaft 21 is connected with the coupling 40.

[0045] One end of the second rotating shaft 22 is rotationally connected with the second support 12, and the second rotating shaft 22 is further fixedly connected with the second rotor disc 32, so that the second rotor disc 32 and the second rotating shaft 22 move synchronously, and the other end of the second rotating shaft 22 is connected with the coupling 40, so that the rotating speeds of the first rotating shaft 21 and the second rotating shaft 22 are the same. The first rotating shaft 21 and the second rotating shaft 22 are the same in structure and size, the first rotor disc 31 and the second rotor disc 32 are the same in structure and size, and the first support 11 and the second support 12 are the same in structure and size.

[0046] The geometric model of the rotating machine is discretized by using finite element meshes. Specifically, the geometric model of the rotating machine is meshed by using 1762 hexahedral elements. A fixed support boundary condition is set on the bottom surface of the first support 11 and the second support 12, a bonded contact is set at the connection between the coupling and the first rotating shaft 21 and the second rotating shaft 22, a frictional contact is set at the connection between the first rotating shaft 21 and the first support 11 and the connection between the second rotating shaft 22 and the second support 12, and a fixed rotational speed is applied to the first rotating shaft 21, so as to obtain a finite element model of the rotating machine.

[0047] The rotating machine has three typical fault modes, which are support loosening, misalignment and imbalance.

[0048] Let F represent the typical fault mode, and the jth typical fault mode of the rotating machine be referred to as fault F j (j = 1, 2, 3). The rotating machine can have multiple dynamic responses under the typical fault mode, and three key dynamic responses are selected as characteristic parameters. The characteristic parameters include the mean value μ of acceleration, the variance σ 2 and the acceleration double frequency f p . eak , forming a 3-dimensional characteristic parameter vector X = (μ, σ 2 , f p . eak ) T The ith characteristic parameter of fault F j is denoted as X i,j , and the characteristic parameter vector X j under fault F j 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 performed to obtain 80 groups of sample points, which form a fault sample set. For the characteristic parameter X i,j , the fault sample set Γ i,j obtained by the aforementioned 80 finite element simulation experiments can be expressed as:

[0051]

[0052] in, Represents the k-th sample point. X represents the feature parameter X in the k-th sample point. i,j The value.

[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 from all similarity coefficients, and remove outliers from the fault sample set based on the statistical characteristics of the similarity matrix.

[0054] For the aforementioned fault sample set Γ i,j The n sample points in the dataset are normalized, and the similarity coefficient between the normalized sample points is calculated using the inverse absolute value method, which yields the similarity between the normalized sample points. Specifically:

[0055]

[0056] Wherein, the similarity coefficient ρ rs For the fault sample set Γ i,j The r-th sample point and the s-th sample point Similarity between them and Sample points and Regarding the characteristic parameter X i,j The value of ρ, c is the value of ρ. rs The value of the constant is a constant in the interval [0,1].

[0057] Furthermore, the similarity coefficient ρ among all n sample points in the aforementioned fault sample set is calculated. rs All similarity coefficients ρ rs Assemble into a fuzzy similarity matrix R = (ρ rs ) n×n By successively squaring the fuzzy similarity matrix R until it no longer changes, the fuzzy equivalence matrix is ​​obtained. The fuzzy equivalence matrix The similarity of all sample points is described, where, This represents the updated similarity coefficient (ρ will not be distinguished hereafter for ease of description). rs and Collectively referred to as similarity coefficients). Fuzzy equivalence matrix. The diagonal elements are all 1s, and the similarity coefficients of each row are... It is used to characterize the similarity between the sample point corresponding to the row and the other sample points.

[0058] Subsequently, a series of continuous subintervals are uniformly divided on the interval [0,1], and this fuzzy equivalence matrix is ​​then processed. similarity coefficient The frequency distribution across all sub-intervals is statistically analyzed row by row. The results of the n frequency analyses are considered as the similarity distribution between the n sample points and the remaining sample points. The sub-interval with the highest concentration of similarity distribution for each sample point is identified. If this sub-interval is closer to the lower bound of the interval [0,1] (i.e., closer to 0), it is considered to have low similarity with most other sample points, and thus is regarded as an outlier. This outlier identification process is executed n times to find all outliers, and these outliers are then removed from the faulty sample set.

[0059] In one possible example, based on the example described above (the example given in step one), the aforementioned fault sample set Γ is... i,j The 80 sample points were normalized, and the similarity coefficients of the normalized sample points were calculated using the inverse absolute value method, specifically:

[0060]

[0061] Wherein, the similarity coefficient ρ rs For the fault sample set Γ i,j The r-th sample point and the s-th sample point Similarity between them and Sample points and Regarding the characteristic parameter X i,j The value of ρ, c is the value of ρ. rs The value of the constant is a constant in the interval [0,1].

[0062] Furthermore, the similarity coefficient ρ among all 80 sample points in the aforementioned fault sample set is calculated. rs All similarity coefficients ρ rs Assemble into a fuzzy similarity matrix R = (ρ rs ) 80×80 By successively squaring the fuzzy similarity matrix R until it no longer changes, the fuzzy equivalence matrix is ​​obtained. The fuzzy equivalence matrix The similarity of all sample points is described, where, This represents the updated similarity coefficient (ρ will not be distinguished hereafter for ease of description). rs and Collectively referred to as similarity coefficients). Fuzzy equivalence matrix. The diagonal elements are all 1s, and the similarity coefficients of each row are... It is used to characterize the similarity between the sample point corresponding to the row and the other sample points.

[0063] Subsequently, the interval [0,1] is evenly divided into 5 consecutive subintervals Interv.p = (p, p+1] x 0.2p = 0, 1, …, 4, for the fuzzy equivalence matrix Similarity coefficient The distribution frequency on all sub-intervals is counted row by row, and the result of 80 times of frequency counting row by row is regarded as the similarity distribution of 80 sample points and the rest of the sample points. The most concentrated sub-interval of the similarity distribution of each sample point is found, and if the sub-interval is closer to the lower bound of the interval [0, 1] (i.e. closer to 0), it is regarded as the similarity between the sample point and the rest of the sample points being lower, so that the sample point is regarded as an abnormal point.

[0064] The above abnormal point determination process is performed a total of 80 times to find all abnormal points, and these abnormal points are removed from the fault sample set. For example, among the given 80 sample points, 4 abnormal points are identified and removed, and after removing the abnormal points, the sample points of the aforementioned fault sample set remain 76.

[0065] Step three: performing clustering analysis on the sample points in the fault sample set after removing the abnormal points to obtain sample clusters of each feature parameter of the sample points under the typical fault mode, and establishing a multi-ellipsoid model of the feature parameters under the typical fault mode according to the sample clusters.

[0066] The remaining multiple sample points in the fault sample set Γ i,j after removing the abnormal points are clustered and analyzed by using a Bayesian Gaussian Mixture Model (BGMM), and the optimal number of sample clusters n c is calculated, and then all sample points (regarded as a total sample cluster Λ j ) in the fault sample set after removing the abnormal points are divided into n c sample clusters, which is represented as:

[0067]

[0068] Among them, represents the hth sample cluster under the fault F j .

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

[0070]

[0071] Among them, Ω h,j (h = 1, 2, …, n c ) represents the ellipsoid model established according to the sample cluster (i.e. the hth ellipsoid model under the fault F j ), and X h,j represents the feature vector corresponding to the ellipsoid model Ω h,j . G h,j and ω h,j denote the center, the characteristic matrix and the size factor of the ellipsoid model Ω h,j , respectively.

[0072] Further, taking the union of all ellipsoid models under the fault F j , a multi-ellipsoid model Ω j is synthesized, which is expressed as:

[0073]

[0074] wherein ∪ denotes the union operation.

[0075] In a possible example, on the basis of the above example (the example given in step two), the fault sample set after removing the abnormal points is subjected to cluster analysis by using the Bayesian Gaussian mixture model. Under the three fault modes of bearing loosening, misalignment and imbalance, the optimal sample cluster numbers of the corresponding fault sample sets are 2, 3 and 3, respectively. Then, all sample points in each fault sample set after removing the abnormal points (regarded as a total sample cluster Λ j ) are divided into a plurality of sample clusters, which is expressed as:

[0076]

[0077] wherein Λ j denotes the hth sample cluster under the fault F .

[0078] Subsequently, ellipsoid models are established for the sample points in each sample cluster, and the established ellipsoid model information is shown in Tables 1-3 (in order to ensure the consistency of the dimension, the numerical values of the sample points are expressed by using the scientific notation in the subsequent establishment of the ellipsoid models, and only the coefficient part is reserved).

[0079] Table 1: Ellipsoid model established under the bearing loosening fault mode F1

[0080]

[0081] Table 2: Ellipsoid model established under the misalignment fault mode F2

[0082]

[0083]

[0084] Table 3: Ellipsoid model established under the imbalance fault mode F3

[0085]

[0086] Further, all ellipsoid models under each fault are taken the union and combined into a multi-ellipsoid model Ω j , which is 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] Wherein, ∪ represents the union operation.

[0091] Step four: selecting a plurality of characteristic parameters in the dynamic response under the to-be-detected mode to establish a to-be-detected sample set, using the to-be-detected sample set to establish an ellipsoid model of the characteristic parameters under the to-be-detected mode, and using the geometric measure method to calculate the coincidence degree of the ellipsoid model and the multi-ellipsoid model.

[0092] U represents the to-be-detected mode, M dynamic parameters same as those in step one under the typical fault mode are selected to form an M-dimensional to-be-detected parameter vector X U =(X 1,U ,X 2,U ,…,X M,U ) T , the values of each component of the to-be-detected parameter vector under the to-be-detected mode U are calculated, and the corresponding to-be-detected sample set is established. Using the to-be-detected sample set, an ellipsoid model Ω U under the to-be-detected mode U is directly established, which is expressed as:

[0093]

[0094] Wherein, G U and ω U respectively represent the center, characteristic matrix and size factor of the ellipsoid model Ω U .

[0095] Further, the coincidence degree μ (F j ) of the ellipsoid model Ω U under the to-be-detected mode U and the multi-ellipsoid model Ω j under the typical fault F j is defined, which is expressed as:

[0096]

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

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

[0099]

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

[0101] In one possible example, on the basis of the above example (the example given in step three), use U to represent the to-be-inspected mode, select the same three dynamic parameters as in step one under the typical fault mode to form a three-dimensional to-be-inspected parameter vector X U =(μ,σ 2 ,f p ″ eak ) T , calculate the numerical value of each component of the to-be-inspected parameter vector under the to-be-inspected mode U, and establish the corresponding to-be-inspected sample set. Use the to-be-inspected sample set to directly establish the ellipsoid model Ω U under the to-be-inspected mode U, which is expressed as:

[0102]

[0103] The coincidence degree of the ellipsoid model under the to-be-inspected mode U with the multi-ellipsoid models under the three fault modes of bearing loosening, misalignment, and imbalance is shown in Table 4.

[0104] Table 4 Coincidence degree of ellipsoid model under to-be-inspected mode with multi-ellipsoid models under each fault mode

[0105]

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

[0107] Based on the N typical fault modes in step one, an identification framework is established, and the set of all typical fault modes constitutes the identification framework Θ = {F1, F2, ..., F...}. N The power set of the identification frame Θ constitutes the proposition set 2. Θ For proposition set 2 Θ Any nonempty proposition A = {F1, F2, ..., F} N′}, which is defined as the intersection of the multi-ellipsoidal models under all typical failure modes:

[0108] A = Ω1 ∩ Ω2 ∩ … ∩ Ω N′ ;

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

[0110] Furthermore, we define the ellipsoidal model Ω under the mode to be inspected U. U The degree of overlap of the intersection of multiple ellipsoidal models under the same proposition A is μ(A), expressed as:

[0111]

[0112] Among them, Vol(A∩Ω) U ) represents the ellipsoidal model Ω U The volume of the overlapping region with the geometric region corresponding to proposition A, Num(A∩Ω) U ) indicates falling into the ellipsoid model Ω U The number of sample points in the overlapping region of the geometric region corresponding to proposition A.

[0113] For the identification frame Θ={F1,F2,…,F… N}, and all the basic propositions (i.e., fault F) j Exhaustive combination is performed, resulting in a set of 2 propositions. Θ All non-empty elements form the focal element set Ψ:

[0114]

[0115] Among them, Υ h (h = 1, 2, ..., 2) N -1) represents the h-th focal element. and For ease of description and calculation, the focus element and proposition will not be distinguished thereafter.

[0116] Using the method of summation and averaging, we can apply it to proposition Y. h (h = 1, 2, ..., 2) N The overlap of -1) is normalized:

[0117]

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

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

[0120]

[0121] Wherein, m(Υ) h ) represents the basic probability assignment of Υh.

[0122] Subsequently, the basic probability assignment m is transformed into a probability distribution P using the probability transformation method. m Specifically, the basic probability assignment m(F) of the basic propositions (i.e., the focal elements of the monomial) is maintained. i Without changing the basic probability assignment m(Υ) of a multi-subset proposition (i.e., a multi-subset focal element), the basic probability assignment m(Υ) is evenly distributed among the basic propositions it contains. The transformation formula is as follows:

[0123]

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

[0125] Traversing the set of propositions 2 Θ Given all 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] Here, max represents the operation of finding the maximum value.

[0128] Finally, the fault F * is diagnosed as the to-be-detected mode U, i.e. U=F * .

[0129] In one possible example, on the basis of the above example (the example given in step four), an identification framework is established according to the three typical fault modes in step one, and the set of all typical fault modes constitutes the identification framework Θ={F1, F2, F3}, and all basic proposition combinations form the set of focal elements Ψ:

[0130] Ψ={Υ1, Υ2, …, Υ7};

[0131] wherein Υ h (h=1, 2, …, 7) represents the hthfocal element, and For ease of description and calculation, the focal elements and propositions are not distinguished in the following.

[0132] The coincidence degree of the proposition Υ h (h=1, 2, …, 7) is normalized by using the sum-averaging method:

[0133]

[0134] wherein is the coincidence degree of the normalized proposition Υ h .

[0135] The coincidence degrees of all non-empty propositions (in turn, {F1}, {F2}, {F3}, {F1, F2}, {F1, F3}, {F2, F3} and {F1, F2, F3}) in the normalized proposition set 2 Θ are directly taken as the basic probability assignments of all focal elements in the focal element set Ψ, and the results are shown in Table 5.

[0136] Table 4 Coincidence degrees of to-be-detected modes with seven propositions and basic probability assignments

[0137]

[0138] Subsequently, the basic probability assignment m is converted into a probability distribution P m by using a probability conversion method. Specifically, the basic probability assignment m(F i ) of a basic proposition (i.e. a single-subset focal element) is kept unchanged, and the basic probability assignment m(Υ) of a multi-subset proposition (i.e. a multi-subset focal element) is evenly distributed to the basic propositions contained therein, and the conversion formula is as follows:

[0139]

[0140] wherein P m (F irepresents the probability that the to-be-tested mode U belongs to the fault F i The conversion result is shown in Table 5.

[0141] Table 5 Fault diagnosis result after probability conversion

[0142]

[0143] Traverse all 3 basic propositions in the proposition set 2, find the basic proposition with the maximum probability by using the maximum probability decision method, and the basic proposition corresponds to the fault F Θ with the maximum probability. *

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

[0145] Wherein, max represents the maximum value operation.

[0146] Finally, the fault F3 is taken as the fault diagnosis result of the to-be-tested mode U, that is, the to-be-tested mode U is an unbalance fault.

[0147] In conclusion, the rotating machinery fault diagnosis method based on sample distribution characteristics and ellipsoid model in the embodiment of the application extracts the characteristic parameters by establishing a finite element model, forms a fault sample set, removes abnormal points based on a similarity matrix, and effectively improves the quality of sample data; the multi-ellipsoid model of the typical fault mode is established by cluster analysis, and the distribution characteristics of different fault modes are accurately described; the coincidence degree of the to-be-tested mode and the typical fault mode is calculated by using the geometric measure method, and a quantitative basis is provided for fault identification; the diagnosis results of different fault modes are fused by combining the identification framework, basic probability assignment and probability conversion method. The rotating machinery fault diagnosis framework based on sample distribution characteristics and ellipsoid model is established in the embodiment of the application, and the precision of fault diagnosis under dispersed data is improved.

[0148] Each embodiment or implementation in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts between each embodiment can be referred to each other.

[0149] ​In the description of the present specification, the description referring to the terms "one embodiment", "some embodiments", "exemplary embodiment", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the exemplary description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in one or more embodiments or examples.

[0150] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for diagnosing a rotating machine fault based on sample distribution characteristics and an ellipsoid model, characterized in that, The method comprises the following steps: Step 1: discretize the geometric model of the rotating machinery by using a finite element mesh to obtain a finite element model of the rotating machinery, and calculate 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 establish a fault sample set according to all the characteristic parameters; Step 2: calculate the similarity coefficients of all sample points in the fault sample set based on an absolute value reciprocal method, form a similarity matrix from all the similarity coefficients, and remove abnormal points in the fault sample set according to the statistical characteristics of the similarity matrix; Step 3: perform cluster analysis on the sample points in the fault sample set after removing the abnormal points to obtain sample clusters of the sample points under each characteristic parameter in the typical fault mode, and establish a multi-ellipsoid model of the characteristic parameters under the typical fault mode according to the sample clusters; Step 4: select a plurality of characteristic parameters in the dynamic response under a to-be-detected mode to establish a to-be-detected sample set, establish an ellipsoid model of the characteristic parameters under the to-be-detected mode by using the to-be-detected sample set, and calculate the coincidence degree of the ellipsoid model and the multi-ellipsoid model by using a geometric measure method; Step 5: establish an identification framework according to the typical fault mode, form a focus element set by performing an exhaustive combination of all typical fault modes under the identification framework, normalize the coincidence degree and take it as a basic probability assignment of each focus element in the focus element set, perform probability conversion on the basic probability assignment, and obtain a diagnostic result of the to-be-detected mode according to a maximum probability decision.

2. The method according to claim 1, wherein, The method for calculating the similarity coefficients of all sample points in the fault sample set based on the absolute value reciprocal method, forming a similarity matrix from all the similarity coefficients, and removing abnormal points in the fault sample set according to the statistical characteristics of the similarity matrix comprises the following steps: Perform normalization processing on the sample points in the fault sample set, and obtain the similarity coefficients between the normalized sample points by using the absolute value reciprocal method to form the similarity matrix; Perform successive squaring on the similarity matrix until no change occurs to obtain an equivalent matrix, and the diagonal elements of the equivalent matrix are all 1; Uniformly divide a plurality of continuous subintervals on the interval [0, 1], and perform row-by-row statistics on the distribution frequencies of the similarity coefficients in the equivalent matrix in all the subintervals; Determine whether the subinterval in which each sample point is most concentrated is close to the lower bound of the interval, and if so, the sample point is an abnormal point; Remove all the abnormal points in the fault sample set.

3. The method according to claim 1, wherein, The coincidence degree is the ratio of the volume of the overlapping region of the ellipsoid model under the to-be-detected mode and the multi-ellipsoid model under the typical fault mode to the volume of the ellipsoid model.

4. The method according to claim 3, characterized in that, The method for calculating the coincidence degree of the ellipsoid model and the multi-ellipsoid model by using the geometric measure method comprises the following steps: Statistically determine the distribution ranges of the ellipsoid model and the multi-ellipsoid model in a geometric space to determine a minimum cubic region capable of covering the ellipsoid model and the multi-ellipsoid model; Sampling in the minimum cubical region, calculating the number of the sampled sample points falling into the overlapping region of the ellipsoid model and the multi-ellipsoid model and the number of the ellipsoid model, and taking the ratio of the corresponding numbers as the coincidence degree.

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