A complex equipment fault diagnosis method based on a polynomial improved graph convolution network

Abstract

The application discloses a kind of complex equipment fault diagnosis methods based on polynomial improved graph convolution network.It includes the following steps: (1) the vibration signal of complex equipment operation is collected;(2) using cross-correlation coefficient, construct multi-objective fitness function, combine particle swarm optimization algorithm to optimize the selection of variational mode decomposition parameters;(3) according to the parameter obtained by optimization, the vibration signal is decomposed by variational mode, obtains several modal components and reconstructs to obtain denoising signal;(4) the signal after reconstruction is divided to construct graph;(5) the graph structure is input into the graph convolution model improved by Hermite polynomial to complete the diagnosis of fault.The application is used for the fault diagnosis of complex equipment, uses modal decomposition to denoise signal and improves the graph convolution model, improves the accuracy of diagnosis, and is suitable for the technical field of complex equipment fault diagnosis.

Description

Technical Field

[0001] This invention relates to fault diagnosis of complex equipment, and more particularly to a fault diagnosis method for complex equipment based on a polynomial improved graph convolutional network. Background Technology

[0002] As complex equipment is used for extended periods, components gradually degrade, leading to malfunctions and generating abnormal vibration signals that affect its normal operation. As complex systems, such equipment is susceptible to noise interference during operation. Therefore, vibration signals acquired by sensors often contain strong noise, making fault characteristics weak. Furthermore, complex equipment has multiple interconnected components, and vibration signals are influenced by these components. Thus, diagnosing complex equipment requires not only analyzing fault characteristics but also the interrelationships between vibration signals. Graph convolutional networks can represent one-dimensional vibration signals in a non-Euclidean space, enhancing the exploration of data relationships in higher-dimensional spaces and further improving the accuracy of fault diagnosis for complex equipment. Summary of the Invention

[0003] To address the problems in the background art, this invention proposes a fault diagnosis method for complex equipment based on a polynomial improved graph convolutional network, comprising the following steps:

[0004] 1) Use an accelerometer to collect vibration signals from the operation of complex equipment; the complex equipment includes, but is not limited to, elevators and escalators.

[0005] 2) Using cross-correlation coefficients, a multi-objective fitness function is constructed to update the particle swarm optimization algorithm, thereby obtaining the optimal parameters of variational mode decomposition;

[0006] 3) Based on the optimized parameters obtained in step 2), perform variational mode decomposition on the vibration signal acquired in step 1) to obtain several modal components and reconstruct the reconstructed signal, i.e., the denoised signal.

[0007] 4) Construct a graph by dividing the reconstructed signal;

[0008] 5) Input the graph structure constructed in step 4) into the graph convolution model improved by Hermitian polynomials to complete the fault diagnosis.

[0009] In step 2):

[0010] Variational mode decomposition can adaptively determine the center frequency and bandwidth of each subclass, thereby minimizing the sum of the bandwidths of each mode after decomposing the original signal. There are two key parameters in the variational mode decomposition process: the number of modes K and the penalty factor α. The particle swarm optimization algorithm continuously adjusts the position and velocity through information sharing between each particle to find the optimal solution. The optimal (K, α) can be found through the particle swarm optimization algorithm to perform variational mode decomposition.

[0011] In the particle swarm optimization (PSO) update process, the velocity update formula for each particle is:

[0012]

[0013] in, This represents the velocity of the i-th particle in the k-th iteration in the n-th dimension. Let represent the position of the i-th particle in the k-th iteration in the n-th dimension, γ be the inertia weight, l1 and l2 be the learning factors, and c1 and c2 ∈ [0,1]. Each particle finds its optimal position pb by tracking, and the optimal position gb of the group.

[0014] The particle position update formula is:

[0015]

[0016] in, This represents the position of the i-th particle in the (k+1)-th iteration in the n-th dimension;

[0017] To evaluate the quality of particle selection, a cross-correlation function is chosen as the fitness function. To comprehensively consider the independence of each mode during variational mode decomposition and the effect after decomposition and reconstruction, a multi-objective fitness function is constructed.

[0018] Using cross-correlation coefficients, a multi-objective fitness function is constructed as follows:

[0019] R all =λR signal +(1-λ)(1-R avg )

[0020] The reconstructed signal is obtained by pre-defining the number of mode decompositions K and the penalty factor α, and then performing mode decomposition reconstruction, where R represents the cross-correlation coefficient calculation. signal The cross-correlation coefficient between the reconstructed signal and the acquired vibration signal is represented by λ∈[0,1], which is a weighting factor used to balance the signal reconstruction effect and modal independence. The calculated R... all As the fitness value in the particle update process, the optimal position of the particle is updated and adjusted to obtain a new modal decomposition quantity K and a penalty factor α. The optimal modal decomposition quantity K and penalty factor α are continuously adjusted in the adaptation process. The optimal modal decomposition quantity K and penalty factor α are decomposed, and the components are added together to reconstruct the denoised signal.

[0021] In step 2):

[0022] There are two key parameters in variational mode decomposition: the number of mode decompositions K and the penalty factor α. The optimal (K, α) is found through particle swarm optimization to perform variational mode decomposition. Specifically:

[0023] The variational mode decomposition yields K modal components {IMF1, IMF2, ..., IMF}. K} Calculate the normalized cross-correlation coefficient between each pair of modal components. The cross-correlation coefficient between the i-th mode and the j-th mode is:

[0024]

[0025] Take all non-diagonal R ij R is obtained by calculating the average of the absolute values ​​of (i≠j). avg :

[0026]

[0027] Among them, R avg The smaller the value, the higher the independence of the modal components; according to the optimization R... all The target is obtained by particle swarm optimization (K, α), and the original vibration signal is subjected to variational mode decomposition and reconstruction by adding the decomposed components to obtain the cross-correlation coefficient R between the reconstructed signal and the acquired vibration signal. signal Finally, R is obtained. all As the fitness function value in the particle swarm optimization algorithm update process.

[0028] Step 4) specifically involves:

[0029] The reconstructed signal is divided and used to construct a graph.

[0030] The reconstructed signal data is divided into subsamples by setting the window size, with each subsample being a node:

[0031]

[0032] Where window is the length of the partition window, Input is the input signal, and s i ,l i This represents each segmented subsample and its corresponding label;

[0033] For each node, select its neighboring nodes. If the current node is node_1, then select the neighboring nodes. i And if a graph consists of 2k+1 nodes, then the set of nodes surrounding the current node is [node i-k ,…,node i ,…,node i+k ] Calculate the distance from each node to the current node to form a set of adjacent nodes;

[0034] The weights between nodes are calculated using a Gaussian function and used as the features of the edges.

[0035]

[0036] edge ij Let σ represent the edge between node i and node j, and let dis represent the bandwidth parameter of the Gaussian kernel. ij Represents the distance between node i and node j, (x i ,y i ),(x j ,y j ) represents the two-dimensional coordinates of a node. The distances between any two nodes are calculated to form an edge set, thus forming a graph structure with the node set and the edge set.

[0037] Step 5) specifically involves:

[0038] The graph structure is input into the graph convolution model improved by Hermitian polynomials to obtain the final fault diagnosis result. The graph convolution kernel in the graph convolution model is approximated by Hermitian polynomials.

[0039] The denoised signal from step 3) is represented as follows:

[0040] x = [x1, x2, ..., x] n ]

[0041] Where n is the number of subsamples formed by window partitioning;

[0042] The graph structure is represented as follows:

[0043] G = (N, E, W)

[0044] Where N is the node set, E is the edge set, W is the weighted adjacency matrix, L is the Laplacian matrix L = WD, and D is the degree matrix, obtained by normalizing L. Then L is obtained by eigenvalue decomposition as the feature matrix U = [u1, u2, ..., u]. n ] and the eigenvalue matrix Λ=diag([λ1,λ2,...,λ n ]);

[0045] According to the convolution theorem, the convolution operation between two partitioned nodes is equal to the product of their Fourier transforms in the frequency domain:

[0046]

[0047] Where, x x x y For nodes in the denoised signal x, * G Represented as a convolution operation, U T x yDefined as convolution kernel g θ Then x x * G x y =Ug θ U T x x ;

[0048] Choose to use Hermitian polynomials for the convolution kernel g. θ Approximating, the convolution kernel is represented as:

[0049]

[0050] in, This represents the convolution kernel after polynomial approximation. I represents the identity matrix. This represents a K-order Hermitian polynomial, where K is an artificially defined order of the Hermitian polynomial. Let K be the coefficients of a K-order polynomial, where the expression for the Hermitian polynomial is:

[0051]

[0052] Where n is the degree of differentiation, the recurrence relation for the Kth order Hermitian polynomial is:

[0053]

[0054] The graph convolution kernel is obtained by approximation using a K-order Hermitian polynomial. This kernel is then used to analyze the graph structure. Finally, after processing by pooling and softmax layers, the fault diagnosis result is output. The diagnosis result output is as follows:

[0055]

[0056] Where W is the weight coefficient, b is the bias parameter, and Mean() is the average pooling.

[0057] The beneficial effects of this invention are:

[0058] Compared with existing technologies, this invention can effectively reduce the impact of noise on vibration analysis. It optimizes the parameters in variational mode decomposition by using particle swarm optimization algorithm and mines deep features in fault vibration signals by Hermitian polynomial-improved graph convolution, effectively optimizing the fault diagnosis effect. It is highly innovative and practical. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of a fault simulated in an embodiment of the present invention.

[0060] Figure 2 The method flowchart provided by the present invention

[0061] Figure 3 A schematic diagram of VMD decomposition of elevator vibration signal.

[0062] Figure 4 Schematic diagram for fault diagnosis of graph convolutional networks

[0063] Figure 5 Figure 1 shows the results of fault diagnosis for a convolutional network. Specific Implementation

[0064] The above embodiments are not limited to the technical solutions of the embodiments themselves, and the embodiments can be combined with each other to form new embodiments. The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the technical solutions of the present invention.

[0065] The analysis process and results of this invention are explained using a high-speed elevator as a specific example. Seven different damage states, including normal operating conditions, were constructed by simulating faults in a high-speed elevator. Specific fault categories are as follows: Figure 1 As shown in the figure. 1-1 is a high-speed elevator simulation test bench, 1-2 is guide rail misalignment, 1-3 is guide rail step, and 1-4 is guide wheel wear in the guide shoes. The guide wheel wear in 1-4 is simulated by placing the upper left guide shoe, upper right guide shoe, lower right guide shoe, and lower right and lower right guide shoes to simulate different spatial locations of the failure. Therefore, there are 4 different states of guide wheel wear, and a total of 7 different damage states.

[0066] The detailed analysis process of a fault diagnosis method for complex equipment based on polynomial improved graph convolutional networks is as follows: Figure 2 As shown. The steps include: (1) collecting vibration signals of complex equipment operation; (2) using cross-correlation values ​​to construct a multi-objective fitness function, and combining particle swarm optimization algorithm to optimize the selection of variational mode decomposition parameters; (3) performing variational mode decomposition on the vibration signal according to the optimized parameters, obtaining several mode components and reconstructing a denoised signal; (4) dividing the reconstructed signal to construct a graph; (5) inputting the graph structure into the graph convolution model improved by Hermitian polynomials to complete the fault diagnosis.

[0067] The aforementioned method for fault diagnosis of complex equipment based on a polynomial improved graph convolutional network is characterized in that step 2 uses cross-correlation coefficients to construct a multi-objective fitness function and combines it with particle swarm optimization (PSO) to optimize the selection of variational mode decomposition (VMD) parameters. VMD can adaptively determine the center frequency and bandwidth of each subclass, thereby minimizing the sum of bandwidths of each mode after decomposing the original signal. Two key parameters in the VMD process are the number of modes K and the penalty factor α. The PSO algorithm continuously adjusts the position and velocity through information sharing among particles to find the optimal solution. Through PSO optimization, the optimal (K, α) can be found for VMD. During the PSO update process, each particle updates its velocity.

[0068]

[0069] in This represents the velocity of the i-th particle in the k-th iteration in the n-th dimension. Let represent the position in the k-th iteration, γ be the inertia weight, l1 and l2 be the learning factors, and c1 and c2 ∈ [0,1]. Each particle finds its optimal position pb through tracking, and the optimal position gb of the group is the same. The particle position update formula is:

[0070]

[0071] To evaluate the quality of particle selection, a cross-correlation function is chosen as the fitness function. To comprehensively consider the independence of each mode during variational mode decomposition and the effect after decomposition and reconstruction, a multi-objective fitness function is constructed.

[0072] R all =λR signal +(1-λ)(1-R avg (3)

[0073] Where R signal This represents the maximum normalized cross-correlation between the denoised signal and the original signal, where λ∈[0,1] is a weighting factor used to balance the denoising effect and modal independence. Variational mode decomposition yields K modal components {IMF1, IMF2, ..., IMF...}. K First, calculate the normalized cross-correlation value between each pair of modal components. The cross-correlation value between the i-th mode and the j-th mode is:

[0074]

[0075] Take all non-diagonal R ij R is obtained by calculating the average of the absolute values ​​of (i≠j). avg :

[0076]

[0077] R avg A smaller value indicates a higher degree of independence of the modal components. According to the optimization R... avg The target signal is obtained by particle swarm optimization (K, α), and the signal is decomposed and reconstructed. The cross-correlation value R between the reconstructed signal and the denoised signal is then calculated. signal Finally, through comprehensive optimization, R is obtained. all .

[0078] The result obtained by optimizing the parameters using the particle swarm optimization algorithm is as follows: Figure 3 As shown, after iteration, the key parameters of variational mode decomposition (K, α) = (7, 106) are finally obtained. Therefore, the signal is decomposed and reconstructed according to the selected parameters. The specific analysis process of the signal being decomposed and graph constructed and then input into a graph convolutional neural network for diagnosis is as follows: Figure 4 As shown.

[0079] Step 4 is characterized in that the reconstructed signal is divided into a graph and the signal data is divided into subsamples by setting the window size.

[0080]

[0081] Where window is the length of the partition window, Input is the input signal, and s i ,l i This represents each partitioned subsample and its corresponding label. For each node, select its neighboring nodes; if the current node is a node... i If we consider a graph with 5 nodes, then the set of nodes surrounding the current node is [node i-2 ,node i-1 ,node i ,node i+1 ,node i+2 ] Calculate the distance from each node to the current node to form a set of adjacent nodes.

[0082]

[0083] pass The weights between nodes are calculated as the features of the edges.

[0084] The method for fault diagnosis of complex equipment based on polynomial-improved graph convolutional networks is characterized in that step 5 inputs the graph structure into the graph convolutional model improved by Hermitian polynomials, and the convolutional kernel is approximated by Hermitian polynomials. The denoised signal can be represented as:

[0085] x = [x 1， x2,...,x T(8)

[0086] An undirected graph can be represented as G = (N, E, W), where N is the set of nodes, E is the set of edges, W is the weighted adjacency matrix, L is the Laplacian matrix L = WD, and D is the degree matrix. The result is obtained by normalizing L. Then, through eigenvalue decomposition, the characteristic matrix U = [u1, u2, ..., u] can be obtained. n ] and the eigenvalue matrix Λ=diag([λ1,λ2,...,λ n According to the convolution theorem, the convolution of two signals is equal to the product of their Fourier transforms in the frequency domain:

[0087]

[0088] Will U T x y Represented as convolution kernel g θ Then x x * G x y =Ug θ U T x x .

[0089] Choose to use Hermitian polynomials for the convolution kernel g. θ Approximating, the convolution kernel can be represented as:

[0090]

[0091] I is the identity matrix, where the expression for the Hermitian polynomial is:

[0092]

[0093] The Hermitian polynomial, through a k-th order approximate convolution kernel, has the following recurrence relation:

[0094]

[0095] Approximating with a k-th order Hermitian polynomial, the convolution output is:

[0096]

[0097] The diagnostic results of the graph convolutional network model improved by Hermitian polynomials for seven different damage states of high-speed elevators are as follows: Figure 5 As shown in the table below, the experimental results were compared with other methods under the same conditions:

[0098]

[0099] It can be seen that the fault diagnosis method for complex equipment based on polynomial improved graph convolutional network proposed in this paper has obvious advantages and can improve the accuracy of fault diagnosis.

Claims

1. A method for fault diagnosis of complex equipment based on polynomial improved graph convolutional networks, characterized in that, Includes the following steps: 1) Collect vibration signals from complex equipment during operation using accelerometers; 2) Using cross-correlation coefficients, a multi-objective fitness function is constructed to update the particle swarm optimization algorithm, thereby obtaining the optimal parameters for variational mode decomposition; 3) Based on the optimized parameters obtained in step 2), perform variational mode decomposition on the vibration signal collected in step 1) to obtain several modal components and reconstruct the reconstructed signal, i.e., the denoised signal. 4) Construct a graph by dividing the reconstructed signal; 5) Input the graph structure constructed in step 4) into the graph convolution model improved by Hermitian polynomials to complete the fault diagnosis; In step 2): In the particle swarm optimization (PSO) update process, the velocity update formula for each particle is: in, This represents the velocity of the i-th particle in the k-th iteration in the n-th dimension. This represents the position of the i-th particle in the k-th iteration in the n-th dimension. For inertial weights, As a learning factor, Each particle finds its optimal position by tracking. The optimal position of the group ; The particle position update formula is: in, This indicates that the i-th particle is in the n-th dimension. Next iteration position; Using cross-correlation coefficients, a multi-objective fitness function is constructed as follows: By predefined modality decomposition quantity K and penalty factor The reconstructed signal is obtained by modal decomposition and reconstruction, where This indicates the calculation of the cross-correlation coefficient. This represents the cross-correlation coefficient between the reconstructed signal and the acquired vibration signal. The weighting factor is used to balance the signal reconstruction effect and modal independence. The calculated value is... The fitness value, used in the particle update process, is used to update and adjust the optimal position of the particles to obtain a new modality decomposition number K and a penalty factor. Thus, by continuously adjusting through adaptation, the optimal number of mode decompositions K and the penalty factor are obtained. Using the optimal mode decomposition number K and penalty factor The components are decomposed and reconstructed to obtain the denoised signal. In step 2): There are two key parameters in variational mode decomposition: the number of mode decompositions K and the penalty factor. The optimal (K, Variational mode decomposition is performed, specifically as follows: The variational mode decomposition is defined to obtain K modal components. Calculate the normalized cross-correlation coefficient between each pair of modal components. The cross-correlation coefficient between the i-th mode and the j-th mode is: Take all non-diagonal lines The absolute average value is calculated to obtain : in, The smaller the value, the higher the independence of the modal components; according to optimization The target is obtained by particle swarm optimization (K, The original vibration signal was subjected to variational mode decomposition and the decomposed components were added together to reconstruct the signal, thus obtaining the cross-correlation coefficient between the reconstructed signal and the acquired vibration signal. Finally, the comprehensive results are obtained As the fitness function value in the particle swarm optimization algorithm update process.

2. The method for fault diagnosis of complex equipment based on polynomial improved graph convolutional networks according to claim 1, characterized in that, Step 4) specifically refers to: The reconstructed signal is divided and used to construct a graph. The reconstructed signal data is divided into subsamples by setting the window size, with each subsample being a node: Where window represents the length of the partition window, and Input represents the input signal. This represents each segmented subsample and its corresponding label; For each node, select its neighboring nodes. If the current node is... And if a graph consists of 2k+1 nodes, then the set of nodes surrounding the current node is [ , ] Calculate the distance from each node to the current node to form a set of adjacent nodes; The weights between nodes are calculated using a Gaussian function and used as the features of the edges. This represents the edge between node i and node j. This represents the bandwidth parameter of the Gaussian kernel. This represents the distance between node i and node j. , The two-dimensional coordinates of the nodes are represented, and the distances between each pair of nodes are calculated to form an edge set, thus forming a graph structure with the node set and the edge set.

3. The method for fault diagnosis of complex equipment based on polynomial improved graph convolutional networks according to claim 1, characterized in that, Step 5) specifically involves: The graph structure is input into the graph convolution model improved by Hermitian polynomials to finally obtain the fault diagnosis result. The graph convolution kernel in the graph convolution model is approximated by Hermitian polynomials. The denoised signal from step 3) is represented as follows: Where n is the number of subsamples formed by window partitioning; The graph structure is represented as follows: Where N is the node set, E is the edge set, W is the weighted adjacency matrix, L is the Laplacian matrix L=WD, and D is the degree matrix, obtained by normalizing L. Then L obtains the characteristic matrix through eigenvalue decomposition. With eigenvalue matrix ; According to the convolution theorem, the convolution operation between two partitioned nodes is equal to the product of their Fourier transforms in the frequency domain: in, Let x be a node in the denoised signal. Represented as a convolution operation, Defined as convolution kernel ,but ; Choose to use Hermitian polynomials for the convolution kernel. Approximating, the convolution kernel is represented as: in, This represents the convolution kernel after polynomial approximation. , As a unit array, This represents a K-order Hermitian polynomial, where K is an artificially defined order of the Hermitian polynomial. Let K be the coefficients of a K-order polynomial, where the expression for the Hermitian polynomial is: Where n is the degree of differentiation, the recurrence relation for the Kth order Hermitian polynomial is: The graph convolution kernel is obtained by approximation using a K-order Hermitian polynomial. This kernel is then used to analyze the graph structure. Finally, after processing by pooling and softmax layers, the fault diagnosis result is output. The diagnosis result output is as follows: )+b) Where W is the weight coefficient, b is the bias parameter, and Mean() is the average pooling.

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