Industrial gearbox fault detection method based on robust single-class support matrix machine

Abstract

The present invention discloses an industrial gearbox fault detection method based on a robust single-classification support matrix machine, comprising the following steps: (1) collecting multi-source monitoring signals of the industrial gearbox under healthy status and different faults; (2) extracting the time domain and frequency domain features of each single-source signal collected in step (1), and constructing a two-dimensional fault feature matrix to maintain the spatial structural information between each signal source; (3) using the two-dimensional fault feature matrix in a normal state as input, training a robust single-classification support matrix machine model to construct an optimal detection model; (4) using the two-dimensional fault feature matrix in a fault state to verify the fault detection performance of the robust single-classification support matrix machine model in step (3), which can fully maintain the structural information between the multi-source features, can improve the fault detection performance of the model, and has good robustness to non-ideal data, especially noisy data and mislabeled data.

Description

Technical Field

[0001] The invention belongs to the field of industrial gearbox fault detection, and in particular relates to an industrial gearbox fault detection method based on a robust single-classification support matrix machine. Background Art

[0002] As a key transmission component, industrial gearboxes are widely used in complex electromechanical equipment such as wind turbines, aircraft engines, mining machinery, and high-speed railways. Once a gearbox fails, it may cause unplanned downtime for maintenance, reduce equipment efficiency, or even cause serious production safety accidents and even major casualties. Therefore, how to detect industrial gearbox failures in a timely and accurate manner is of great theoretical and engineering significance to ensure the safe and effective operation of equipment.

[0003] In actual engineering applications, industrial gearboxes mostly operate under normal conditions throughout their service life, so it is difficult to obtain sufficient fault samples, which means that the fault detection problem can actually be regarded as a typical single-classification problem. In recent years, one-class support vector machine (OCSVM) has been widely used in the field of fault detection due to its excellent generalization and small sample processing capabilities; however, when OCSVM processes multi-source signal industrial gearbox fault detection, there are still the following problems: (1) Each monitoring signal source has spatial attributes, and different signal sources have intrinsic connections. When OCSVM processes multi-source data, it needs to quantize the extracted features, which destroys the structural information between multi-source signals. (2) The multi-source monitoring data actually collected usually contains strong interference noise, and because it is impossible to accurately predict the time node of the fault, data mislabeling often occurs, which seriously affects the fault detection performance of OCSVM. Summary of the invention

[0004] In view of the above-mentioned technical deficiencies, the object of the present invention is to provide an industrial gearbox fault detection method based on a robust single-classification support matrix machine.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] The present invention provides an industrial gearbox fault detection method based on a robust single classification support matrix machine, comprising the following steps:

[0007] (1) Collect multi-source monitoring signals of the health status and different faults of industrial gearboxes;

[0008] (2) extracting the time domain and frequency domain features of each single source signal collected in step (1), and constructing a two-dimensional fault feature matrix to maintain the spatial structure information between each signal source;

[0009] (3) Taking the two-dimensional fault feature matrix under normal state as input, a robust single-classification support matrix machine model is trained to construct the optimal detection model;

[0010] (4) The fault detection performance of the robust single-classification support matrix machine model in step (3) is verified using a two-dimensional fault feature matrix under fault conditions.

[0011] Preferably, the signals collected in step (1) include vibration acceleration signals, rotation speed signals, and shaft runout signals.

[0012] Preferably, the step (2) specifically comprises the following steps:

[0013] (2.1) Extract the time domain and frequency domain features of each single source signal. The time domain features include mean, root mean square, root square amplitude, amplitude mean, maximum, minimum, peak-to-peak value, standard deviation, skewness, kurtosis, crest factor, clearance factor, waveform factor, and pulse factor, a total of 14 features; the frequency domain features include spectrum mean, spectrum standard deviation, center of gravity frequency, root mean square frequency, frequency mean, standard deviation frequency, frequency kurtosis, and frequency skewness, a total of 8 features;

[0014] (2.2) The 22 time domain and frequency domain features of each signal source extracted in step (2.1) are sequentially concatenated to construct a two-dimensional fault feature matrix:

[0015]

[0016] Where f i,j represents the jth sensitive feature of the ith signal source.

[0017] Preferably, the (3) specifically includes the following steps:

[0018] (3.1) Assume that the single-class sample set consisting of the two-dimensional fault feature matrix under normal conditions is Then the objective function of the robust single-class support matrix machine can be expressed as:

[0019]

[0020] sttr(W T X i )≥β-ζ i

[0021] 0≤ζ i , i=1,…,n

[0022] in: and β are the regression matrix and bias of the classification hyperplane respectively; in the objective function, Used to control the complexity of the model and avoid overfitting problems; nuclear norm ||W||* Used to mine the inherent topological structure information of matrix data; i is a slack variable used to improve the generalization of the model; μ and τ are regularization parameters of the model; in order to improve the robustness of the robust single-class support matrix machine, an adaptive weight generation strategy is designed, which can adaptively generate a weight for each sample X according to the prior distribution of the data. i Assign different weights

[0023]

[0024] Where Ψ(X i ) indicates X i With sample center The assembly matrix distance between min , max and ave They are Ψ(X i )’s minimum, maximum and mean values; ι is a very small positive integer; Ψ(X i ) can be expressed as:

[0025]

[0026] Where q>0 is the norm coefficient of the distance measure;

[0027] (3.2) Design a solver based on the alternating direction multiplier method:

[0028] According to the alternating direction multiplier method, an auxiliary variable Q is introduced into the objective function of the robust single-class support matrix machine and rewritten as:

[0029] min F(W, β)+G(Q)

[0030] stQ-W=0

[0031] in:

[0032]

[0033] Construct the Lagrangian function of a robust single-class support matrix machine:

[0034]

[0035] in is the Lagrange multiplier matrix, ε represents the iteration step size; the above formula can be decomposed into three sub-problems about (W, β), Q and A, and each sub-problem can be optimized by alternating iterations; for the kth iteration, the overall iterative process of the robust single-class support matrix machine is as follows:

[0036]

[0037] Considering (W, β) and A as constants, we can get the sub-optimization problem about Q:

[0038]

[0039] The above formula is equivalent to:

[0040]

[0041] Solving the above equation by the singular value contraction algorithm, the iterative formula for Q can be expressed as:

[0042]

[0043] In the formula represents the singular value contraction operator;

[0044] Treating Q and A as constants, we get the subproblem about (W, β):

[0045] Next, construct the Lagrangian function of the above formula:

[0046]

[0047] Where α i and γ i is the Lagrange multiplier; by solving the above formula, we get the iterative formula about (W, β):

[0048]

[0049] In the formula After obtaining the structural parameters of the robust single-class support matrix machine through iterative optimization, its final decision function is expressed as:

[0050] f(X)=sign[tr(W T X)-β]

[0051] Preferably, the regularization parameters μ and τ of the model are set by a 5-fold cross-validation method, where the candidate set of μ is {2 -5 ,2 -4 ,…,2 5}, the candidate set of τ is {10 -4 ,10 -3 ,…,10 2}.

[0052] The beneficial effects of the present invention are:

[0053] (1) Different from the traditional vectorized feature representation, the present invention constructs a two-dimensional fault feature matrix by extracting time domain and frequency domain sensitive parameters of multi-source monitoring signals. The use of this matrixed feature representation can fully preserve the structural information between multi-source features.

[0054] (2) The robust single-class support matrix machine provided by the present invention can directly use matrix-form features as model input, avoiding feature vectorization, thereby making full use of the topological structure between two-dimensional feature matrices and improving the fault detection performance of the model.

[0055] (3) The robust single-class support matrix machine of the present invention adopts an adaptive weight generation strategy and has good robustness to non-ideal data, especially noisy data and mislabeled data. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0057] Figure 1 It is the overall flow chart of the present invention;

[0058] Figure 2 is a diagram of fault detection results under different training samples of the present invention;

[0059] Figure 3 is a diagram of fault detection results under different noise intensities of the present invention;

[0060] Figure 4 This is a diagram of fault detection results under different mislabeling ratios of the present invention. DETAILED DESCRIPTION

[0061] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] like Figure 1 As shown, this embodiment provides an industrial gearbox fault detection method based on a robust single-class support matrix machine, which specifically includes the following steps:

[0063] Step S1: Collect multi-source monitoring signals of the health status and different faults of the industrial gearbox; this embodiment uses the multi-source monitoring data of the QPZZ-Ⅱ industrial gearbox fault analysis experimental platform for verification and analysis; in the experiment, a total of 8 signal source data were collected, including 5 vibration acceleration signals, 2 shaft displacement signals and 1 speed signal; during the collection process, the sampling frequency was set to 5120Hz, and the data length of each signal source was 1024;

[0064] Step S2: extract the time domain and frequency domain features of each single source signal, and construct a two-dimensional fault feature matrix to maintain the spatial structure information between each signal source; for each sample, the extracted two-dimensional fault feature matrix has a dimension of 8×22, specifically including:

[0065] Step S2.1: extract the time domain and frequency domain features of each single source signal, wherein the time domain features include mean, root mean square, root square amplitude, amplitude mean, maximum, minimum, peak-to-peak value, standard deviation, skewness, kurtosis, crest factor, clearance factor, waveform factor, and pulse factor, a total of 14; the frequency domain features include spectrum mean, spectrum standard deviation, centroid frequency, root mean square frequency, frequency mean, standard deviation frequency, frequency kurtosis, and frequency skewness, a total of 8;

[0066] Step S2.2: construct a two-dimensional fault feature matrix to maintain the spatial structure information between each signal source;

[0067] The 22 extracted time domain and frequency domain features of each signal source are spliced ​​in sequence to construct a two-dimensional fault feature matrix:

[0068]

[0069] Where f i,j Represents the jth sensitive feature of the i-th signal source; Different from the traditional vectorized feature representation, this two-dimensional matrix feature representation can fully preserve the structural information of each signal source;

[0070] Step S3: Taking the two-dimensional fault feature matrix in the normal state as input, training the robust single-classification support matrix machine model to construct the optimal detection model, specifically including:

[0071] Step S3.1: The basic principle of the robust single-class support vector machine is to obtain an optimal classification hyperplane to separate the coordinate origin and the single-class matrix data set with the maximum interval; assuming that the single-class sample set composed of the two-dimensional fault feature matrix under normal conditions is Then the objective function of the robust single-class support matrix machine can be expressed as:

[0072]

[0073] sttr(WT X i )≥β-ζ i

[0074] 0≤ζ i , i=1,…,n

[0075] in and β are the regression matrix and bias of the classification hyperplane respectively; in the objective function, Used to control the complexity of the model and avoid overfitting problems; nuclear norm ||W|| * Used to mine the inherent topological structure information of matrix data; i is a slack variable used to improve the generalization of the model; μ and τ are regularization parameters of the model; in addition, in order to improve the robustness of the robust single-class support matrix machine, an adaptive weight generation strategy is designed; this strategy can adaptively generate a weight for each sample X according to the prior distribution of the data. i Assign different weights

[0076]

[0077] Where Ψ(X i ) indicates X i With sample center The assembly matrix distance between min , max and ave They are Ψ(X i )'s minimum, maximum and mean values; ι is a very small positive integer and is set to 0.0001 in this embodiment; Ψ(X i ) can be expressed as:

[0078]

[0079] Where q>0 is the norm coefficient of the distance measure;

[0080] Step S3.2: Solve the robust single-class support matrix machine model:

[0081] Since there is a nuclear norm in the objective function of the robust single-class support matrix machine, it is difficult to directly obtain the global optimal solution of the model. Therefore, a solver based on the alternating direction multiplier method is designed. According to the alternating direction multiplier method, an auxiliary variable Q can be introduced into the objective function of the robust single-class support matrix machine and rewritten as:

[0082] min F(W, β)+G(Q)

[0083] stQ-W=0

[0084] in:

[0085]

[0086] Next, construct the Lagrangian function of the robust single-class support matrix machine:

[0087]

[0088] in is the Lagrange multiplier matrix, ε represents the iteration step size, which is 1.1 by default in this embodiment; the above formula can be decomposed into three sub-problems about (W, β), Q and A, and each sub-problem can be optimized by alternating iterations; for the kth iteration, the overall iteration process of the robust single-class support matrix machine is as follows:

[0089]

[0090] In summary, the core of solving the robust single-class support matrix machine is the sub-problem about Q and (W, β);

[0091] First, consider (W, β) and A as constants, and obtain the sub-optimization problem about Q:

[0092]

[0093] The above formula is equivalent to:

[0094]

[0095] Solving the above equation by the singular value contraction algorithm, the iterative formula for Q can be expressed as:

[0096]

[0097] In the formula represents the singular value contraction operator;

[0098] Then, considering Q and A as constants, we get the subproblem about (W, β):

[0099]

[0100] Next, construct the Lagrangian function of the above formula:

[0101]

[0102] Where α i and γ i is the Lagrange multiplier; by solving the above formula, we can get the iterative formula about (W, β):

[0103]

[0104] In the formula After obtaining the structural parameters of the robust single-class support matrix machine through iterative optimization, its final decision function can be expressed as:

[0105] f(X)=sign[tr(W T X)-β]

[0106] If the decision function is equal to 1, it means that X is a normal sample of the gearbox; otherwise, X is a faulty sample of the gearbox.

[0107] Step S4: using a two-dimensional fault feature matrix under a fault state to verify the fault detection performance of the robust single-class support matrix machine model; constructing a robust single-class support matrix machine model.

[0108] Figure 2 : is the fault diagnosis result diagram of this embodiment under different training samples; it can be seen from the figure that the fault detection accuracy of this embodiment continues to increase with the increase of the number of samples; when the number of training samples is only 25, the fault diagnosis accuracy of the present invention reaches 99.12%, which shows that the present invention has good fault detection performance under small sample conditions.

[0109] In order to illustrate that this embodiment still has good fault detection performance under strong background noise, different degrees of Gaussian white noise are added to the original signal. The experimental results are as follows: Figure 3 As shown; it can be seen from the figure that the fault detection accuracy of this embodiment is above 90% under -2dB-6dB noise, which shows that the present invention has good noise robustness.

[0110] In addition, certain fault data is added to the gearbox health data to reflect the robustness of the present invention to mislabeled data. The fault detection results of this embodiment under different mislabel ratios are as follows: Figure 4 As shown; it can be seen from the figure that even if the proportion of mislabeling reaches 20%, the fault detection accuracy of the present invention still reaches 90.48%, which shows that this embodiment has good anti-interference ability for mislabeled data.

[0111] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. An industrial gearbox fault detection method based on a robust single-class support matrix machine is characterized by: The following steps are involved: (1) Collect multi-source monitoring signals of the health status and different faults of industrial gearboxes; (2) extracting the time domain and frequency domain features of each single source signal collected in step (1), and constructing a two-dimensional fault feature matrix to maintain the spatial structure information between each signal source; (3) Taking the two-dimensional fault feature matrix under normal state as input, training the robust single-classification support matrix machine model to construct the optimal detection model; specifically, the following steps are included: (3.1) Assume that the single-class sample set consisting of the two-dimensional fault feature matrix under normal conditions is , then the objective function of the robust single-class support matrix machine can be expressed as: in: and are the regression matrix and bias of the classification hyperplane respectively; in the objective function, Used to control the complexity of the model and avoid overfitting problems; nuclear norm Used to mine the inherent topological structure information of matrix data; is a slack variable used to improve the generalization of the model; and is the regularization parameter of the model; in order to improve the robustness of the robust single-class support matrix machine, an adaptive weight generation strategy is designed, which can adaptively generate weights for each sample according to the prior distribution of the data. Assign different weights : in express With sample center The assembly matrix distance between , and They are The minimum, maximum and mean of ; is a very small positive integer; The specific calculation formula can be expressed as: in is the norm coefficient of the distance measure; (3.2) Design a solver based on the alternating direction multiplier method: According to the alternating direction multiplier method, an auxiliary variable is introduced into the objective function of the robust single-class support matrix machine. , and rewrite it as: in: Construct the Lagrangian function of a robust single-class support matrix machine: in is the Lagrange multiplier matrix, Represents the iteration step; the above formula can be decomposed into , and There are three sub-problems, and each sub-problem can be optimized through alternating iterations; for the k The overall iterative process of the robust single-class support matrix machine is as follows: Will and Assuming it as a constant, we can get The sub-optimization problem is: The above formula is equivalent to: Solve the above equation by using the singular value contraction algorithm, then The iteration formula can be expressed as: In the formula represents the singular value contraction operator; Will and Assuming it as a constant, we can get Sub-questions: Next, construct the Lagrangian function of the above formula: In the formula and is the Lagrange multiplier; by solving the above formula, we can get The iteration formula is: In the formula ; After obtaining the structural parameters of the robust single-class support matrix machine through iterative optimization, its final decision function is expressed as: ; Regularization parameter of the model and It is set by the 5-fold cross validation method, where The candidate set is , The candidate set is ; (4) The fault detection performance of the robust single-classification support matrix machine model in step (3) is verified using the two-dimensional fault feature matrix under fault conditions.

2. The industrial gearbox fault detection method based on robust single-class support matrix machine according to claim 1 is characterized in that: The signals collected in step (1) include vibration acceleration signals, rotation speed signals, and shaft runout signals.

3. The industrial gearbox fault detection method based on robust single-class support matrix machine according to claim 1 is characterized in that: The step (2) specifically includes the following steps: (2.1) Extract the time domain and frequency domain features of each single source signal. The time domain features include mean, root mean square, root square amplitude, amplitude mean, maximum, minimum, peak-to-peak value, standard deviation, skewness, kurtosis, crest factor, clearance factor, waveform factor, and pulse factor, a total of 14 features; the frequency domain features include spectrum mean, spectrum standard deviation, center of gravity frequency, root mean square frequency, frequency mean, standard deviation frequency, frequency kurtosis, and frequency skewness, a total of 8 features; (2.2) The 22 time domain and frequency domain features of each signal source extracted in step (2.1) are sequentially concatenated to construct a two-dimensional fault feature matrix: In the formula Indicates i The signal source j A sensitive feature.

Images