A mechanical equipment moving component fault diagnosis method based on SVM-DS fusion prediction

Abstract

The application discloses a kind of mechanical equipment moving parts fault diagnosis method based on SVM-DS fusion prediction, including in the data acquisition process of mechanical equipment moving parts, vibration data is carried out noise reduction processing, then feature extraction is carried out, the feature sensitive to fault data is obtained, and feature matrix is generated;Periodic fault diagnosis is carried out to the extracted feature by SVM algorithm, and the prediction probability of different events in the identification framework is obtained;Periodic prediction result is fused based on DS evidence theory weighting, and the fusion probability and conflict coefficient of different events are obtained;According to conflict coefficient, the obtained fusion probability is corrected;The corrected fusion probability is normalized, and the event corresponding to the maximum normalized fusion probability is the final diagnostic result.The application corrects the prediction probability under different conflict scenarios, so that the influence factor of non-associated measuring points is attenuated, the reference value of analysis result is improved, and the applicability of the algorithm is enhanced.

Description

Technical Field

[0001] This invention relates to the field of multidimensional data fusion algorithm technology, specifically to a fault diagnosis method for moving parts of mechanical equipment based on SVM-DS fusion prediction. Background Technology

[0002] Mechanical equipment plays a crucial role in industrial production and operation. However, due to prolonged operation, mechanical wear, and improper use, the moving parts of mechanical equipment may malfunction. These malfunctions can lead to equipment downtime and production interruptions, as well as equipment damage, safety hazards, and personal injury. Therefore, conducting research on fault diagnosis of moving parts in mechanical equipment has significant practical importance.

[0003] Existing common methods for diagnosing mechanical equipment faults include empirical methods, expert systems, data mining, and machine learning. However, when using machine learning and data mining for fault diagnosis, several factors need to be considered, such as data noise, feature selection, and the possibility of multiple fault points. First, the performance of machine learning and data mining is affected by data quality. Noise, missing values, or outliers in the data can lead to inaccurate or unreliable predictions. Second, fault diagnosis involves a large number of features and parameters. Each feature requires corresponding data collection and preprocessing. Too many features may contain information irrelevant to the target task, increasing both computational cost and time. Selecting too many or unnecessary features will increase the burden of data collection and preprocessing. Furthermore, machine learning and data mining need to consider model complexity. Overly simple models can lead to underfitting, meaning the model lacks sufficient parameters to capture the basic structure of the training data. Conversely, overly complex models can lead to overfitting, where the model learns noise and randomness from the training data, thus losing its ability to generalize to new data. Finally, there is the generalization ability of the fault diagnosis model. The generalization ability of the fault diagnosis model is an important indicator that will directly affect the practicality and reliability of the fault diagnosis system. The real environment is very complex and changeable. If the generalization ability of the model is weak, when encountering new data that has not been seen in actual applications, the model's ability to process the data will decrease, and may even lead to wrong decisions. Wrong decisions may cause property damage or even a series of safety accidents. Summary of the Invention

[0004] The technical problem to be solved by this invention is to propose a fault diagnosis method for moving parts of mechanical equipment based on SVM-DS fusion prediction. Addressing the paradoxical problem in the prediction results of different fault diagnosis and analysis methods for moving parts of mechanical equipment, this invention fuses the prediction results obtained from different diagnostic methods in a weighted manner, corrects the prediction probabilities under different conflict scenarios, attenuates the influence factors of non-associated measurement points, reduces the conflict coefficient of the prediction results, improves the reference value of the analysis results, and enhances the applicability of the algorithm.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] The present invention proposes a fault diagnosis method for moving parts of mechanical equipment based on SVM-DS fusion prediction, comprising the following steps:

[0007] S1. During the data acquisition process of moving parts of mechanical equipment, noise reduction processing is performed on the vibration data, a set number of vibration data sample points are extracted for feature extraction, and features sensitive to fault data are obtained to generate a feature matrix.

[0008] S2. The extracted features are periodically diagnosed using the SVM algorithm to obtain the predicted probability of different events in the identification framework.

[0009] S3. Based on the predicted probabilities from step S2, the prediction results of the periodicity are weighted and fused according to the DS evidence theory to obtain the fusion probabilities and conflict coefficients of different events.

[0010] S4. Correct the obtained fusion probability based on the conflict coefficient in step S3.

[0011] S5. Normalize the corrected fusion probability to obtain the normalized fusion probability of each event of the moving parts of the mechanical equipment. The event corresponding to the highest normalized fusion probability is the final diagnosis result.

[0012] Furthermore, in step S1, feature extraction includes the following sub-steps:

[0013] S101. During the data acquisition process of moving parts of mechanical equipment, vibration data may be affected by noise interference. To reduce the impact of noise on subsequent fault analysis, a wavelet thresholding algorithm is used to denoise the vibration data. The original signal is symmetrically extended and convolved with the filter tap coefficients to decompose it into low-frequency components (i.e., useful components) and high-frequency components (i.e., noise components). The specific formula is as follows:

[0014]

[0015] Each decomposition of a one-dimensional signal contains both useful and noise components. In practice, the same signal can be decomposed multiple times to filter out as much noise as possible. The number of filter coefficients equals the number of input sample points, and there is a one-to-one correspondence between filter coefficients and sample points.

[0016] Where k represents a discrete time point, H(n) represents the tap coefficients of the low-pass filter, G(n) represents the tap coefficients of the high-pass filter, and A j+1 (n) represents the nth low-frequency component obtained by convolving it with the tap coefficients at the (j+1)th decomposition, D j+1 (n) represents the nth high-frequency component obtained by convolving with the tap coefficients at the (j+1)th decomposition.

[0017] S102. Perform threshold selection on the high-frequency components generated during decomposition, and use the obtained low-frequency and high-frequency components to reconstruct the original signal. The specific formula is as follows:

[0018] R j (n)=H(n)*A j+1 (n)+G(n)*D j+1 (n);

[0019] Among them, R j (n) represents the reconstructed signal.

[0020] S103. Different features have varying degrees of sensitivity to data. Here, seven feature factors that are relatively sensitive to normal and fault data are selected, including margin factor, mean, standard deviation, skewness, energy, kurtosis, and root mean square. The vibration sample is then represented as:

[0021] D i =[d i-1 ,d i-2 ,…d i-V ];

[0022] Where P represents the number of vibration data sample points; D i d represents the i-th vibration sample; i-V Let V represent the V sample points in the i-th group, and T represents the number of characteristic factor groups.

[0023] Now, taking the i-th vibration sample as an example, feature extraction is performed. We assume the maximum value of the i-th vibration sample is max. i The minimum value is min i Each feature factor is calculated as follows:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] Among them, margin i Denotes the margin factor of the i-th group, means i std represents the mean of the i-th group. i skew represents the standard deviation of the i-th group. i Energy represents the skewness of the i-th group. i Let krtos represent the energy of the i-th group. i RMS represents the kurtosis of the i-th group. i Let d represent the root mean square of the i-th group. l This represents the value corresponding to the l-th sample in the i-th group.

[0032] The characteristic factors of each group are denoted as:

[0033] FM i =[margin] i means i std i skew i energy i krtos i rms i ];

[0034] Among them, FM i This represents the characteristic factor calculated from the i-th vibration sample group.

[0035] S104. After feature extraction, T sets of feature factors are obtained, resulting in a T×7 feature matrix. The expression for the feature matrix is ​​as follows:

[0036]

[0037] Among them, FM T×7 It is a T×7 feature matrix, where each row is a set of feature factors.

[0038] Furthermore, in step S2, the SVM algorithm is used to diagnose faults in the moving parts of the mechanical equipment using vibration data. The essence of the SVM algorithm is to find two hyperplanes: a positive hyperplane to determine the boundaries of the positive component and a negative hyperplane to determine the boundaries of the negative component. To divide a set of data into two classes, it is essentially about finding the maximum distance between the two hyperplanes. Obtaining the predicted probability includes the following sub-steps:

[0039] S201, Simplify each set of characteristic factors as (F t ,L t ), where F t =FM t L represents the t-th characteristic factor; t Let L be a scalar, representing the label corresponding to the t-th feature factor. t =1 indicates that the t-th characteristic factor belongs to the positive example component, L t = -1 indicates that the t-th characteristic factor belongs to the negative example component.

[0040] S202. Represent the positive and negative hyperplanes using two linear functions, with the specific expressions as follows:

[0041]

[0042] Where W is a 7×1 column vector representing the slope of the hyperplane; F t It is a 7×1 column vector, corresponding to each set of feature factors; F represents t , where b represents the transpose of ; b represents an undetermined constant.

[0043] S203, The maximum distance between two hyperplanes is expressed as:

[0044]

[0045] Where, d max W represents the maximum distance, and ||W|| represents the modulus of the hyperplane slope. L represents the characteristic plane corresponding to the t-th group of characteristic factors. t It is the label corresponding to the t-th feature factor.

[0046] The decisive factor is W; by substituting a support vector, the numerator... Since it is a constant, the formula for the maximum distance simplifies to:

[0047]

[0048] The final optimization problem is:

[0049]

[0050] in, This indicates a constraint.

[0051] S204. The classifier's discrimination rate is not 100% accurate and may make some erroneous operations, such as ignoring positive components. Therefore, it is necessary to control the error within a small range. This can be addressed by introducing a penalty factor. The optimization problem can be rewritten as:

[0052]

[0053] Where c represents the penalty factor; the larger c is, the stronger the penalty for misclassification, and the more accurate the model classification, but the more prone it is to overfitting. When c approaches positive infinity, it becomes a hard-margin optimization; ε t ε represents the slack variable adjusted for the t-th eigenfactor group, and signifies the tolerance for outliers. Outliers are points that belong neither to the positive nor negative components. Each eigenfactor group corresponds to one slack variable; t It must be greater than 0, and it must be used in conjunction with c. The larger c is, the smaller the slack variable should be, and the lower the tolerance for outliers.

[0054] S205. Solve the extreme value problem under constraints using the Lagrange multiplier method. The specific formula is as follows:

[0055]

[0056] Among them, L p ε represents the label corresponding to the p-th feature factor. p λ represents the slack variable used to adjust the p-th group of characteristic factors. p Let F represent the Lagrange multiplier of the p-th constraint. p This represents the characteristic factor of the p-th group. F represents p The transpose of .

[0057] S206. Because the objective function and inequality constraints of the original optimization problem are both convex functions, and the inequality constraints are strictly feasible, therefore, there exists... Make and This is the solution to the primal problem. The SMO algorithm is used to solve the dual problem, yielding the slope of the decision hyperplane. The specific formula is as follows:

[0058]

[0059] in, Let represent the optimal solution to the dual problem. This represents the t-th element in the optimal solution vector.

[0060] There exists at least one p such that Therefore, the optimal solution for the undetermined variables can be obtained. The specific formula is as follows:

[0061]

[0062] The final solution yields the decision hyperplane. The classification decision function is then:

[0063]

[0064] Where f(F) represents the classification decision result.

[0065] S207. During prediction, for each set of input feature factors, the decision function outputs a decision result, which takes the value 1 or -1, representing a predicted event. Assuming B sets of input feature factors, B decision results can be obtained, where the number of times the decision result is 1 is B1, and the number of times the decision result is -1 is B2. Therefore, the prediction probability of the decision result being 1 is... The prediction probability of a decision outcome of -1 is

[0066] Furthermore, in step S3, the SVM prediction results from multiple cycles are fused and judged. A single moving part of mechanical equipment may have multiple faults, and these faults may have causal relationships or accompanying relationships. The purpose of fusion judgment is to take into account the correlation between other faults and the current fault. Obtaining the fusion probability and conflict coefficient includes the following sub-steps:

[0067] S301. Construct a recognition framework for different moving parts. In DS evidence theory, the sample space composed of all propositions is defined as the recognition framework, denoted as Θ. This is a set of mutually exclusive propositions that constitute a complete set, representing all possible answers to a given question.

[0068] Not every detection will result in a failure; a non-failure is merely a predicted scenario. For consistency, regardless of whether a failure occurs, the prediction result and the threshold judgment result are collectively referred to as an "event"; let θ1, θ2, ... θ Y To predict all possible events, the expression is:

[0069] Θ = {θ1, θ2, ... θ} Y};

[0070] Where, θ Y Let Y represent the Y-th event in the recognition frame, and Θ represent the recognition frame for a certain moving part.

[0071] Since different events within the same recognition framework are mutually exclusive, they must satisfy... Each moving part has its own recognition frame, and the recognition frame Θ for different measurement points r The specific formula is as follows:

[0072] Θ r ={θ r1 ,θ r2 ,…θ rY}, 1≤r≤Y;

[0073] Where Y represents the number of events involved in this prediction, and θ rY For the r-th moving part, identify the Y-th event corresponding to the frame, Θ r The identification frame represents the r-th moving part.

[0074] S302. To prevent events with low correlation from affecting the fusion prediction results of the current event, and to ensure the effective use of information, this method is improved compared to direct application to DS fusion by weighting the predicted probabilities in step S2. The predicted probabilities of evidence that are far from other evidence (with large deviations) will be attenuated, while those of evidence that are closer will be amplified. The specific formula is as follows:

[0075] m(A s ) = X h m′(A s );

[0076] Where, m′(A s ) represents the predicted probability of the s-th event before weighting, m(A) s X represents the predicted probability of the s-th event after weighting. h These are the weighting coefficients under different conditions.

[0077] The total probability of 1 is divided into three intervals, with the dividing points α1 and α2. The weighting coefficients for each interval are β1, β2, and β3, respectively. These weighting coefficients are positive integers, satisfying 0 < β1 < β2 < β3. It is important to note that the weighting coefficients should not be too large to avoid excessive amplification. The higher the predicted probability, the more significant the amplification effect. Under normal circumstances, all weighting coefficients X... h When the value is 1, it represents the original DS evidence theory. Specifically:

[0078] (1) If 0 <P x <0.4, weighting coefficient X h =1;

[0079] (2) If 0.4 ≤ P x <0.7, weighting coefficient X h =2;

[0080] (3) If 0.7 ≤ P x <1, weighting coefficient X h =3.

[0081] S303. Based on Dempster's synthesis rule, the predicted probabilities of the same object in each period are fused to obtain the fused probability and conflict coefficient. The specific formula is as follows:

[0082]

[0083] Where A represents an event that may occur during the operation of the moving part; A s M(A) represents the s-th event within a certain frame; s ) represents the fusion probability of the s-th event after initial fusion; K represents the conflict coefficient, which describes the magnitude of conflict between evidence from different periods. The larger K is, the greater the conflict between evidence from different periods; Q represents the number of periods; m ρ (A s ) represents the predicted probability of the s-th event within the frame of a certain moving part in the ρ-th period; m τ (A s ) represents the predicted probability of the s-th event within the frame of a certain moving part in the τ-th cycle; m ρ (A ∈ ) represents the predicted probability of the ∈ i-th event within the frame of a certain moving part in the ρ-th period. This indicates the position of a moving part within the frame during the τth period. The predicted probability of an event.

[0084] Furthermore, in step S4, the correction of the fusion probability includes the following:

[0085] The conflict coefficient K represents the credibility of this fusion, which may affect the final diagnostic results of the moving parts of the mechanical equipment. To achieve the desired effect, the fusion probability is appropriately optimized after the initial fusion. When the conflict coefficient is greater than 0.6, it indicates that the credibility of this fusion is low, and the fusion probability in this case is determined by the average prediction probability before fusion. When the conflict coefficient is less than or equal to 0.6, it indicates that the credibility of this fusion is high, and the fusion probability in this case is determined by the fusion probability output by the DS evidence theory, specifically expressed as:

[0086]

[0087] Among them, M ′ (A s M(A) represents the fusion probability of the s-th event after correction within the current moving part frame. s ) represents the fusion probability of the s-th event within the current moving part frame that has not yet been corrected, q(A)s ) represents the average predicted probability of the s-th event within the current moving part frame in different periods.

[0088] Furthermore, in step S5, obtaining the final diagnostic result includes the following:

[0089] The identification framework for a moving part contains multiple events, such as normal events, bearing damage events, and bearing loosening events. After DS evidence fusion and correction, each event corresponds to a fusion probability. Let Ψ be the set of fusion probabilities for all events in a moving part, and its specific expression is:

[0090] Ψ={M ′ (A1),M ′ (A2),…,M ′ (A s )};

[0091] Here, Ψ represents the fusion probability set of different events of the current moving part.

[0092] The sum of the fusion probabilities of all events after correction is not 1. Therefore, a normalization process is performed, using the following formula:

[0093]

[0094] Where, ψ s Let A represent the normalized fusion probability of the s-th event. v Let M represent the v-th event in the current motion recognition framework. ′ (A v ) represents the fusion probability corresponding to the v-th event in the current motion recognition framework.

[0095] After normalization, the event with the highest normalization fusion probability within the same identification framework becomes the final fault diagnosis prediction result. If the prediction result is a normal event, it indicates that the moving parts have no faults and are operating normally; if the prediction result is a bearing damage event, it indicates that the moving parts are abnormal, and the cause of the abnormality is bearing damage.

[0096] Furthermore, the present invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the aforementioned method for fault diagnosis of moving parts of mechanical equipment based on SVM-DS fusion prediction.

[0097] Furthermore, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the aforementioned method for fault diagnosis of moving parts of mechanical equipment based on SVM-DS fusion prediction.

[0098] The present invention adopts the above technical solution, and its significant technical effects compared with the prior art are as follows:

[0099] This invention combines machine learning with multidimensional data fusion, making adjustments based on this foundation. It then integrates information from multiple dimensions, including sensor data, log data, and device status data, to gain a more comprehensive understanding of the system's operational status and abnormal behavior, enabling more accurate fault diagnosis. Furthermore, it allows for the establishment of fault prediction models to identify potential fault risks in advance and implement corresponding preventative measures. In addition, through multidimensional data fusion, the correlations between different data sources can be used to fill in missing data and mitigate impacts, identifying key features for fault identification and isolation, thus enabling faster fault diagnosis. Attached Figure Description

[0100] Figure 1 This is a flowchart illustrating the overall implementation of the present invention.

[0101] Figure 2 These are the results before and after noise reduction using the wavelet threshold algorithm in this embodiment of the invention.

[0102] Figure 3 This is a graph showing the relationship between the conflict coefficient and different fusion methods in an embodiment of the present invention.

[0103] Figure 4 This is a comparison chart of prediction results before and after DS improvement in an embodiment of the present invention. Detailed Implementation

[0104] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0105] like Figure 1 As shown, this invention presents a fault diagnosis method for moving parts of mechanical equipment based on SVM-DS fusion prediction. This method uses vibration data from mechanical equipment to diagnose faults in its moving parts. The specific steps are as follows:

[0106] S1. During the data acquisition process of moving parts of mechanical equipment, noise reduction processing is performed on the vibration data. 2048 vibration data sample points are extracted for feature extraction to obtain features sensitive to fault data, and a feature matrix is ​​generated. The specific content is as follows:

[0107] S101. During the data acquisition process of moving parts of mechanical equipment, wavelet thresholding algorithm is used to denoise the vibration data. The original signal is symmetrically extended and convolved with the filter tap coefficients to decompose it into low-frequency and high-frequency components. The specific formula is as follows:

[0108]

[0109] Where k represents a discrete time point, H(n) represents the tap coefficients of the low-pass filter, G(n) represents the tap coefficients of the high-pass filter, and A j+1 (n) represents the nth low-frequency component obtained by convolving it with the tap coefficients at the (j+1)th decomposition, D j+1 (n) represents the nth high-frequency component obtained by convolving with the tap coefficients at the (j+1)th decomposition.

[0110] In this embodiment, the input original vibration data is A1(n) = [12.10, 12.18, 12.12…12.07], the low-pass filter tap coefficients are H(n) = [-0.0106, 0.0329, 0.0308,…, 0.2304], and the high-pass filter tap coefficients are G(n) = [-0.2304, 0.7148, -0.6309,…, -0.0280]. It should be noted that the dimension of the input original vibration data needs to be consistent with the tap coefficients.

[0111] The useful component A2(n) obtained after the first layer decomposition is [17.0831,17.2517,17.2350,…17.1134], and the noise component D2(n) is [-0.1201,-0.2993,0.0747,…,0.0176].

[0112] S102. Perform threshold selection on the high-frequency components generated during decomposition, and use the obtained low-frequency and high-frequency components to reconstruct the original signal. The specific formula is as follows:

[0113] R j (n)=H(n)*A j+1 (n)+G(n)*D j+1 (n);

[0114] Among them, R j (n) represents the reconstructed signal.

[0115] In this embodiment, R1(n) = [12.2077, 12.1794, 12.1451, ..., 12.0895].

[0116] Figure 2The simulation comparison charts before and after noise reduction of vibration data are shown. The number of decomposition layers is 1, and the number of input points is 1024. The upper part is the original data line graph, and the lower part is the line graph after wavelet threshold decomposition and reconstruction. The simulation results show that compared with the data before noise reduction, the reconstructed data has reduced a lot of spikes, which basically achieves the expected purpose.

[0117] S103. Different features have varying degrees of sensitivity to data. Here, seven feature factors that are relatively sensitive to normal and fault data are selected, including margin factor, mean, standard deviation, skewness, energy, kurtosis, and root mean square. The vibration sample is then represented as:

[0118] D i =[d i-1 ,d i-2 ,…d i-V ];

[0119] Where P represents the number of vibration data sample points; D i d represents the i-th vibration sample; i-V Let V represent the V sample points in the i-th group, and T represents the number of characteristic factor groups.

[0120] Now, taking the i-th vibration sample as an example, feature extraction is performed. We assume the maximum value of the i-th vibration sample is max. i The minimum value is min i Each feature factor is calculated as follows:

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] Among them, margin i Denotes the margin factor of the i-th group, means i std represents the mean of the i-th group. i skew represents the standard deviation of the i-th group. i Energy represents the skewness of the i-th group. i Let krtos represent the energy of the i-th group. iRMS represents the kurtosis of the i-th group. i Let d represent the root mean square of the i-th group. l This represents the value corresponding to the l-th sample in the i-th group.

[0129] The characteristic factors of each group are denoted as:

[0130] FM i =[margin] i means i std i skew i energy i krtos i rms i ];

[0131] Among them, FM i This represents the characteristic factor calculated from the i-th vibration sample group.

[0132] S104. After feature extraction, T sets of feature factors are obtained, resulting in a T×7 feature matrix. The expression for the feature matrix is ​​as follows:

[0133]

[0134] Among them, FM T×7 It is a T×7 feature matrix, where each row is a set of feature factors.

[0135] In this embodiment, feature extraction is performed on R1(n) to obtain a set of feature factors FM1 = [0.0871, 12.0401, -0.2124, 0.2363, 74251.2982, 3.2112, 12.0425]. The calculation method for the feature factors of other groups is similar. The 2048 extracted vibration data are divided into 32 groups, with 128 vibration samples in each group, thus obtaining a 32×7 feature matrix FM. 32×7 .

[0136] S2. Using the SVM algorithm, perform three cycles of fault diagnosis on the extracted features to obtain the predicted probabilities of different events within the corresponding recognition framework. The specific details are as follows:

[0137] S201, Simplify each set of characteristic factors as (F t ,L t ), where F t =FM t L represents the t-th characteristic factor; t Let L be a scalar, representing the label corresponding to the t-th feature factor. t =1 indicates that the t-th characteristic factor belongs to the positive example component, L t= -1 indicates that the t-th characteristic factor belongs to the negative example component.

[0138] S202. Represent the positive and negative hyperplanes using two linear functions, with the specific expressions as follows:

[0139]

[0140] Where W is a 7×1 column vector representing the slope of the hyperplane; F t It is a 7×1 column vector, corresponding to each set of feature factors; F represents t , where b represents the transpose of ; b represents an undetermined constant.

[0141] S203, The maximum distance between two hyperplanes is expressed as:

[0142]

[0143] Where, d max W represents the maximum distance, and ||W|| represents the modulus of the hyperplane slope. L represents the characteristic plane corresponding to the t-th group of characteristic factors. t It is the label corresponding to the t-th feature factor.

[0144] The decisive factor is W; by substituting a support vector, the numerator... Since it is a constant, the formula for the maximum distance simplifies to:

[0145]

[0146] The final optimization problem is:

[0147]

[0148] in, This indicates a constraint.

[0149] S204. The classifier's discrimination rate is not 100% accurate and may make some erroneous operations, such as ignoring positive components. Therefore, it is necessary to control the error within a small range. This can be addressed by introducing a penalty factor. The optimization problem can be rewritten as:

[0150]

[0151] Where c represents the penalty factor; the larger c is, the stronger the penalty for misclassification, and the more accurate the model classification, but the more prone it is to overfitting. When c approaches positive infinity, it becomes a hard-margin optimization; ε tε represents the slack variable adjusted for the t-th eigenfactor group, and signifies the tolerance for outliers. Outliers are points that belong neither to the positive nor negative components. Each eigenfactor group corresponds to one slack variable; t It must be greater than 0, and it must be used in conjunction with c. The larger c is, the smaller the slack variable should be, and the lower the tolerance for outliers.

[0152] S205. Solve the extreme value problem under constraints using the Lagrange multiplier method. The specific formula is as follows:

[0153]

[0154] Among them, L p ε represents the label corresponding to the p-th feature factor. p λ represents the slack variable used to adjust the p-th group of characteristic factors. p Let F represent the Lagrange multiplier of the p-th constraint. p This represents the characteristic factor of the p-th group. F represents p The transpose of .

[0155] S206. Because the objective function and inequality constraints of the original optimization problem are both convex functions, and the inequality constraints are strictly feasible, therefore, there exists... Make and This is the solution to the primal problem. The SMO algorithm is used to solve the dual problem, yielding the slope of the decision hyperplane. The specific formula is as follows:

[0156]

[0157] in, Let represent the optimal solution to the dual problem. This represents the t-th element in the optimal solution vector.

[0158] There exists at least one p such that Therefore, the optimal solution for the undetermined variables can be obtained. The specific formula is as follows:

[0159]

[0160] The final solution yields the decision hyperplane. The classification decision function is then:

[0161]

[0162] Where f(F) represents the classification decision result.

[0163] In this embodiment, c = 100.

[0164] S207. During prediction, for each set of input feature factors, the decision function outputs a decision result, which takes the value 1 or -1, representing a predicted event. Assuming B sets of input feature factors, B decision results can be obtained, where the number of times the decision result is 1 is B1, and the number of times the decision result is -1 is B2. Therefore, the prediction probability of the decision result being 1 is... The prediction probability of a decision outcome of -1 is

[0165] In this embodiment, a set of feature factors [0.0871, 12.0401, -0.2124, 0.2363, 74251.2982, 3.2112, 12.0425] are input and substituted into... The result is 2090.22, because Therefore, the final result of the sign function is 1, indicating that the current set of input feature factors is a positive component. If the decision result obtained by inputting 10 sets of feature factors is [1,1,1,1,-1,1,1,1,-1,1], it means that the prediction probability of the positive component is 0.8, while the prediction probability of the negative component is 0.2. The positive and negative components can each represent a certain event, and in the current context, they can represent that an abnormal event may occur at a certain measurement point.

[0166] S3. Based on the predicted probabilities from step S2, and using the DS evidence theory to weightedly fuse the prediction results from three periods, the fusion probabilities and conflict coefficients for different events are obtained. The specific details are as follows:

[0167] S301. Construct a recognition framework for different moving parts. In DS evidence theory, the sample space composed of all propositions is defined as the recognition framework, denoted as Θ. This is a set of mutually exclusive propositions that constitute a complete set, representing all possible answers to a given question.

[0168] Not every detection will result in a failure; a non-failure is merely a predicted scenario. For consistency, regardless of whether a failure occurs, the prediction result and the threshold judgment result are collectively referred to as an "event"; let θ1, θ2, ... θ Y To predict all possible events, the expression is:

[0169] Θ = {θ1, θ2, ... θ} Y};

[0170] Where, θ Y Let Y represent the Y-th event in the recognition frame, and Θ represent the recognition frame for a certain moving part.

[0171] In this embodiment, the identification framework for the moving parts of the motor is Θ1 = {motor overheating, motor normal}, and the predicted probabilities of each event obtained from step S2 are m(motor overheating) = 0.8 and m(motor normal) = 0.2 respectively.

[0172] Since different events within the same recognition framework are mutually exclusive, they must satisfy... Each moving part has its own recognition frame, and the recognition frame Θ for different measurement points r The specific formula is as follows:

[0173] Θ r ={θ r1 ,θ r2 ,…θ rY}, 1≤r≤Y;

[0174] Where Y represents the number of events involved in this prediction, and θ rY For the r-th moving part, identify the Y-th event corresponding to the frame, Θ r The identification frame represents the r-th moving part.

[0175] S302. To prevent events with low correlation from affecting the fusion prediction results of the current event, and to ensure the effective use of information, this method is improved compared to direct application to DS fusion by weighting the predicted probabilities in step S2. The predicted probabilities of evidence that are far from other evidence (with large deviations) will be attenuated, while those of evidence that are closer will be amplified. The specific formula is as follows:

[0176] m(A s ) = X h m′(A s );

[0177] Where, m′(A s ) represents the predicted probability of the s-th event before weighting, m(A) s X represents the predicted probability of the s-th event after weighting. h These are the weighting coefficients under different conditions.

[0178] The total probability of 1 is divided into three intervals, with the dividing points α1 and α2. The weighting coefficients for each interval are β1, β2, and β3, respectively. These weighting coefficients are positive integers, satisfying 0 < β1 < β2 < β3. It is important to note that the weighting coefficients should not be too large to avoid excessive amplification. The higher the predicted probability, the more significant the amplification effect. Under normal circumstances, all weighting coefficients X... h When the value is 1, it represents the original DS evidence theory. Specifically:

[0179] (1) If 0 <P x<0.4, weighting coefficient X h =1;

[0180] (2) If 0.4 ≤ P x <0.7, weighting coefficient X h =2;

[0181] (3) If 0.7 ≤ P x <1, weighting coefficient X h =3.

[0182] m(motor overheating) = 0.8, corresponding weighting coefficient X h =3; m (motor normal) = 0.2, corresponding weighting coefficient X h =1.

[0183] S303. Based on Dempster's synthesis rule, the predicted probabilities of the same object in each period are fused to obtain the fused probability and conflict coefficient. The specific formula is as follows:

[0184]

[0185] Where A represents an event that may occur during the operation of the moving part; A s M(A) represents the s-th event within a certain frame; s ) represents the fusion probability of the s-th event after initial fusion; K represents the conflict coefficient, which describes the magnitude of conflict between evidence from different periods. The larger K is, the greater the conflict between evidence from different periods; Q represents the number of periods; m ρ (A s ) represents the predicted probability of the s-th event within the frame of a certain moving part in the ρ-th period; m τ (A s ) represents the predicted probability of the s-th event within the frame of a certain moving part in the τ-th cycle; m ρ (A ∈ ) represents the predicted probability of the ∈ i-th event within the frame of a certain moving part in the ρ-th period. This indicates the position of a moving part within the frame during the τth period. The predicted probability of an event.

[0186] In this embodiment, the prediction probabilities for the three input cycles are m1(motor overheating) = 0.8, m1(motor normal) = 0.2; m2(motor overheating) = 0.8, m2(motor normal) = 0.2; m3(motor overheating) = 0.3, m3(motor normal) = 0.7. The fusion probability and conflict coefficient for each fault at the motor measuring point are: M(motor overheating) = 0.5245, K = 0.7217; M(motor normal) = 0.3557, K = 0.7710.

[0187] Figure 3 This section describes the relationship between the conflict coefficient K and different fusion methods for a given event. It shows that the original DS evidence theory has a relatively high conflict coefficient, resulting in low confidence in the prediction results. After averaging or weighting the predicted probabilities, the conflict coefficient significantly decreases, improving the confidence of the prediction results.

[0188] S4. Based on the conflict coefficient in step S3, the obtained fusion probability is corrected, specifically as follows:

[0189] The conflict coefficient K represents the credibility of this fusion, which may affect the final diagnostic results of the moving parts of the mechanical equipment. To achieve the desired effect, the fusion probability is appropriately optimized after the initial fusion. When the conflict coefficient is greater than 0.6, it indicates that the credibility of this fusion is low, and the fusion probability in this case is determined by the average prediction probability before fusion. When the conflict coefficient is less than or equal to 0.6, it indicates that the credibility of this fusion is high, and the fusion probability in this case is determined by the fusion probability output by the DS evidence theory, specifically expressed as:

[0190]

[0191] Among them, M ′ (A s M(A) represents the fusion probability of the s-th event after correction within the current moving part frame. s ) represents the fusion probability of the s-th event within the current moving part frame that has not yet been corrected, q(A) s ) represents the average predicted probability of the s-th event within the current moving part frame in different periods.

[0192] S5. Normalize the corrected fusion probabilities to obtain the normalized fusion probabilities of each event of the moving parts of the mechanical equipment. The event corresponding to the highest normalized fusion probability is the final diagnostic result. The specific content is as follows:

[0193] The identification framework for a moving part contains multiple events, such as normal events, bearing damage events, and bearing loosening events. After DS evidence fusion and correction, each event corresponds to a fusion probability. Let Ψ be the set of fusion probabilities for all events in a moving part, and its specific expression is:

[0194] Ψ={M ′ (A1),M ′ (A2),…,M ′ (A s )};

[0195] Here, Ψ represents the fusion probability set of different events of the current moving part.

[0196] The sum of the fusion probabilities of all events after correction is not 1. Therefore, a normalization process is performed, using the following formula:

[0197]

[0198] Where, ψ s Let A represent the normalized fusion probability of the s-th event. v Let M represent the v-th event in the current motion recognition framework. ′ (A v ) represents the fusion probability corresponding to the v-th event in the current motion recognition framework.

[0199] Based on the results obtained in step S3, the fusion probabilities after correction for different events within the same recognition framework are obtained: M ′ (Motor overheating) = 0.75, (Motor normal) = 0.39. After normalization, the fusion probability M for different events can be obtained. ′ (Motor overheating) = 0.7679, M ′ (Motor normal) = 0.3421, at which point the diagnosis result is that the motor is overheating.

[0200] Figure 4 This section presents the fusion probability distribution of different events within the same framework before and after the DS improvement. Before the DS improvement, the fusion probabilities of the three events—normal drive end, inner drive ring fault, and outer drive ring fault—were almost identical, all around 0.2. In fact, the rolling element fault event might even act as a distractor, affecting the judgment of other events. However, after the DS improvement, the distractor rolling element fault was directly eliminated. The fusion probabilities of the remaining three events—normal drive end, inner drive ring fault, and outer drive ring fault—were 0.2, 0.77, and 0.05, respectively, showing a significant difference and providing a more intuitive understanding of which component was more likely to fail.

[0201] This invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. It should be noted that when the processor executes the computer program, it corresponds to the specific steps of the method provided in this invention, possessing the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in this invention.

[0202] This invention also proposes a computer-readable storage medium storing a computer program. It should be noted that when the computer program is executed by a processor, it corresponds to the specific steps of the method provided in this invention, possessing the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in this invention.

[0203] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for fault diagnosis of moving parts of mechanical equipment based on SVM-DS fusion prediction, characterized in that, include: S1. During the data acquisition process of moving parts of mechanical equipment, the vibration data is denoised, a set number of vibration data sample points are extracted for feature extraction, and features sensitive to fault data are obtained to generate a feature matrix. Specifically: S101. The vibration data is denoised using a wavelet thresholding algorithm. The original signal is symmetrically extended and convolved with the filter tap coefficients to decompose it into low-frequency and high-frequency components. The specific formula is as follows: ； in, Representing discrete time points, This represents the tap coefficients of the low-pass filter. This represents the tap coefficients of the high-pass filter. Indicates the first The first decomposition is obtained by convolving with the tap coefficients. A low-frequency component Indicates the first The first decomposition is obtained by convolving with the tap coefficients. One high-frequency component; S102. Perform threshold selection on the high-frequency components, and reconstruct the original signal using the obtained low-frequency and high-frequency components. The specific formula is as follows: ； in, Signals indicating reconstruction; S103. Select a set number of feature factors that are sensitive to fault data, then the vibration sample is represented as: ； in, This indicates the number of vibration data sample points; Indicates the first Group vibration samples; Indicates the first group 100 sample points, and , Indicates the number of groups of characteristic factors; Setting the first The maximum value of the group of vibration samples is The minimum value is The calculation method for each feature factor includes the following formula, specifically: ； ； ； ； ； ； ； in, Indicates the first The group's margin factor Indicates the first group mean Indicates the first The standard deviation of the group Indicates the first skewness of the group Indicates the first The energy of the group Indicates the first The ravine of the group, Indicates the first The root mean square of the group Indicates the first Group 1 The values ​​corresponding to each sample; The characteristic factors of each group are represented by the following formula, specifically: ； in, Indicates the first Characteristic factors calculated from a group of vibration samples; S104. After feature extraction is complete, obtain... Group characteristic factors, thus obtaining The characteristic matrix of is expressed by the following formula: ； in, for The feature matrix, where each row is a set of feature factors; Indicates the number of characteristic factors; S2. Perform periodic fault diagnosis on the extracted features using the SVM algorithm to obtain the predicted probability of different events in the corresponding recognition framework; S3. Based on the predicted probabilities from step S2, and using the weighted fusion of periodic prediction results according to DS evidence theory, the fusion probabilities and conflict coefficients for different events are obtained; specifically: S301. The prediction result and the threshold judgment result are collectively referred to as events. The expression for all events that occur in the recognition framework is: ； in, Indicating the first in the recognition framework Such events, A frame for identifying a moving part; Different events within the same recognition framework must satisfy the following: ( For different measurement points, the identification framework The specific formula is as follows: ； in, This indicates the number of events involved in this prediction. For the first The first moving part recognition framework corresponds to the first Such events, Representing the A framework for recognizing individual moving parts; S302. Weight the predicted probabilities from step S2. The specific formula is as follows: ； in, Indicates the first before weighting The predicted probability of an event. Indicates the weighted number of... The predicted probability of an event. These are the weighting coefficients under different conditions; The total probability of 1 is divided into three intervals, and the dividing points of the three intervals are: and The weighting coefficients for different intervals are respectively The weighting coefficients are positive integers, satisfying The specific details are as follows: (1) If < Weighting coefficients = ; (2) If < Weighting coefficients = ; (3) If <1, weighting coefficient = ; S303. Based on Dempster's synthesis rule, the predicted probabilities of the same object in each period are fused to obtain the fused probability and conflict coefficient. The specific formula is as follows: ； in, This indicates events that occur during the operation of moving parts. Indicates the first within a certain frame One event, Indicates the first stage after initial fusion The fusion probability of events, Indicates the conflict coefficient. Indicates the number of periods. Indicates the first Within a certain moving part frame in a given cycle, the first... The predicted probability of an event. Representing the Within a certain moving part frame in a certain cycle, the first... The predicted probability of an event. Indicates the first Within a certain moving part frame during the cycle, the first The predicted probability of an event. Indicates the first Within a certain moving part frame during the cycle, the first The predicted probability of an event; S4. Based on the conflict coefficient in step S3, the obtained fusion probability is corrected; specifically: When the conflict coefficient is greater than a preset threshold, the fusion probability is determined by the average prediction probability before fusion; when the conflict coefficient is less than or equal to the preset threshold, the fusion probability is determined by the fusion probability output by the DS evidence theory, specifically expressed as follows: ； in, Indicates the corrected first [number]th [unit] within the current moving part frame. The fusion probability of events, This indicates the first uncorrected part within the current moving component frame. The fusion probability of events, Indicates the number of the moving parts within the current frame. The average predicted probability of an event over different periods; S5. Normalize the corrected fusion probability to obtain the normalized fusion probability of each event of the moving parts of the mechanical equipment. The event corresponding to the highest normalized fusion probability is the final diagnosis result.

2. The method for fault diagnosis of moving parts of mechanical equipment based on SVM-DS fusion prediction according to claim 1, characterized in that, Step S2, obtaining the predicted probability includes the following sub-steps: S201, Simplify each group of characteristic factors as follows: ),in, Indicates the first Group characteristic factors; Indicates the first The labels corresponding to the group feature factors; S202. Represent the positive and negative hyperplanes using two linear functions, with the specific expressions as follows: ； in, yes The column vectors represent the slopes of the hyperplane; yes The column vectors correspond to each set of feature factors; Transpose of; Indicates an undetermined constant; S203, The maximum distance between two hyperplanes is expressed as: ； in, Indicates the maximum distance. The modulus of the slope of the hyperplane is represented. Indicates the first The feature plane corresponding to the group feature factors It is the first The labels corresponding to the group feature factors; The formula for the maximum distance simplifies to: ； The final optimization problem is: ； in, Indicates constraints; S204. Introducing a penalty factor to control error, the optimization problem becomes: ； in, Indicates the penalty factor. Indicates adjustment of the first Slack variables of group characteristic factors; S205. Solve the extreme value problem under constraints using the Lagrange multiplier method. The specific formula is as follows: ； in, Indicates the first The labels corresponding to the group feature factors Indicates adjustment of the first Relaxation variables of group characteristic factors Indicates the first Lagrange multipliers for each constraint condition Indicates the first Group characteristic factors express Transpose of; S206. Solve the dual problem using the SMO algorithm to obtain the slope of the decision hyperplane. The specific formula is as follows: ； in, Let represent the optimal solution to the dual problem. Represents the first element in the optimal solution vector. One element; There exists a Make Thus, the optimal solution for the undetermined variables is obtained. The specific formula is as follows: ； The final solution yields the decision hyperplane. Then the classification decision function is: ； in, Indicates the classification decision result; S207, Input Group feature factors, decision function output There are several decision outcomes, where decision outcome a1 occurs the most times. The predicted probability of decision result a1 is: .

3. The method for fault diagnosis of moving parts of mechanical equipment based on SVM-DS fusion prediction according to claim 1, characterized in that, In step S5, the final diagnostic result includes the following: Let the set of event fusion probabilities in a certain moving part be defined as follows: The specific expression is: ； in, This represents the fused probability set of different events for the currently moving component; The sum of the fusion probabilities of all events after correction is not 1. Therefore, a normalization process is performed, using the following formula: ； in, Indicates the first The normalized fusion probability of each event. Indicates the first in the current motion recognition framework Such events, Indicates the first in the current motion recognition framework The fusion probability corresponding to each event.

4. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium storing a computer program, characterized in that, The computer program is executed by the processor to perform the method of any one of claims 1 to 3.

Images