Axial plunger pump fault diagnosis method of space-time DQN model

Abstract

The invention provides an axial plunger pump fault diagnosis method based on a space-time DQN model. The axial plunger pump fault diagnosis method comprises the following steps that a pressure signal sequence of key measuring points of an axial plunger pump is collected through a pressure sensor; performing time-frequency domain conversion on the one-dimensional pressure signal by using continuous wavelet transform to obtain a multi-scale time-frequency characteristic matrix and finish standardization processing; obtaining a time sequence representation vector and a space representation vector; and splicing and fusing the two types of representations in feature dimensions to form state representations, inputting the state representations into a Q network of a DQN model to output action values of various fault types, adaptively adjusting a risk penalty weight and a discount factor to construct a Bellman-based target equation, updating network parameters through Huber loss, and outputting a diagnosis result. According to the method, the time-frequency coupling characteristic of the pressure signal of the plunger pump and the dynamic uncertainty of the operation environment are considered, the time-space correlation information can be effectively captured, the diagnosis precision is high, the stability is high, the algorithm operation is efficient, and the method has good engineering practical value.

Description

Technical Field

[0001] This invention relates to the fields of mechanical engineering and information processing technology, specifically to a method for diagnosing axial piston pump faults using a spatiotemporal DQN model. Background Technology

[0002] In the operation of hydraulic transmission systems, axial piston pumps are critical power components. Failures (such as wear of the distribution pair, piston pair, slipper wear, cavitation, and leakage) can easily lead to abnormal pressure pulsations, decreased efficiency, increased temperature rise, and even system shutdown, resulting in equipment downtime and economic losses. Therefore, accurate fault diagnosis of the axial piston pump's operating status and subsequent condition-based maintenance are of great significance for improving equipment safety and reliability.

[0003] When axial piston pumps operate under complex conditions, the pressure signals they collect are often time-varying. Existing fault diagnosis methods, including those based on mechanistic models and those based on data-driven methods such as traditional classifier methods, convolutional neural networks, or recurrent neural networks, are often affected by sample size, changes in operating conditions, and model parameters, making it difficult to meet the needs of engineering diagnostic applications. Summary of the Invention

[0004] To overcome the aforementioned problem of insufficient diagnostic accuracy, especially for fault diagnosis under time-varying signal conditions of axial piston pumps, this invention proposes a spatiotemporal DQN model-based fault diagnosis method for axial piston pumps, which can achieve accurate diagnosis of axial piston pumps and provide a theoretical basis for fault diagnosis of axial piston pumps.

[0005] In one aspect of the present invention, a method for diagnosing axial piston pump faults using a spatiotemporal DQN model is proposed. According to an embodiment of the present invention, the method includes the following steps:

[0006] Step 1: Set up signal acquisition points on the axial piston pump equipment and collect pressure sequence data at each point through pressure sensors;

[0007] Step 2: Perform continuous wavelet transform on the pressure time-domain signal at each measuring point to obtain the multi-scale time-frequency features of the pressure signal; combine the multi-scale time-frequency features of the pressure signal with the original pressure time-domain signal to form a nodal feature tensor;

[0008] Step 3: Using a two-scale one-dimensional convolutional neural network with temporal branches, extract temporal features from the node feature tensors to obtain the temporal representation vector;

[0009] Step 4: Extract node association features from the node feature tensor using dynamic graph convolution and gated recurrent unit network. By constructing a dynamic adjacency matrix and performing sparsification and normalization, node association and spatial dependency are captured to obtain the spatial representation vector.

[0010] Step 5: Concatenate the temporal representation vector and the spatial representation vector to form a state, input it into the Q-network to obtain the action value Q(s,a), use ε (exploration rate) - greedily select action a, and store the experience replay sample (s, a, r, s', d) in the experience replay, where s is the current state; a is the action; r is the reward; s' is the next state; and d is the termination.

[0011] Step 6: Sample samples from the experience replay, construct the Bellman objective equation by adaptively adjusting the risk penalty weights and discount factors based on uncertainty estimation and adjacency change intensity, and update the Q network using Huber loss;

[0012] Step 7: Output the confusion matrix, fault category clustering diagram, identification accuracy, recall rate, and F1 score of the axial piston pump fault categories to complete the intelligent diagnosis of axial piston pump faults.

[0013] In addition, the axial piston pump fault diagnosis method based on a spatiotemporal DQN model according to the above embodiments of the present invention may also have the following additional technical features:

[0014] In some embodiments of the present invention, step 2 specifically includes the following steps:

[0015] Step 2.1: Collect pressure sequence data at each measuring point of the axial piston pump using a pressure sensor, as shown below:

[0016] ,

[0017] In the formula, x m [l] represents the pressure measurement value at the m-th measuring point at sampling time l, N is the number of measuring points, and L is the length of a single sequence;

[0018] Step 2.2: Let the scale set of the continuous wavelet transformation be W, and the mother wavelet be the Ricker wavelet. Then, the m-th measurement point at scale w... k The continuous wavelet coefficients under ∈W are expressed as:

[0019] ,

[0020] In the formula, c m,k [l] represents the wavelet coefficients; W = {w1, w2, …, w K} is the scale set; ψ wk (·) represents Ricker mother wavelet scale w k The generated wavelet function, x m [i] represents the original measurement value of the m-th measurement point at sampling time i; i is the time index of the convolution summation; k is the scale number; K is the total number of scales;

[0021] Step 2.3: Assemble the wavelet coefficients of the same measurement point at each scale to obtain the multi-scale representation matrix of the measurement point, denoted as:

[0022] ,

[0023] In the formula, C m Let w be the multi-scale representation matrix of the m-th measurement point, where the k-th row is the scale w. k The coefficient sequence under c m,K [l] represents the Kth scale w K The wavelet coefficients at time l;

[0024] Step 2.4: Fuse the original signal with the multi-scale wavelet coefficients in the feature dimension to construct node feature vectors and form a state tensor. Define the node feature vector of the m-th measurement point at time l as:

[0025] .

[0026] In some embodiments of the present invention, step 3 specifically includes the following steps:

[0027] Step 3.1: The temporal branch adopts a dual-scale one-dimensional convolutional network, which consists of two parallel convolutional branches with different convolutional kernels and a feature fusion module. Each branch sequentially includes one-dimensional convolution, batch normalization, activation and pooling to extract features at different time scales. The fusion module outputs a fixed-dimensional temporal representation vector through feature concatenation, 1×1 linear mapping and global pooling.

[0028] Step 3.2: Input sequence construction and dimensionality transformation, converting the node feature vectors obtained in Step 2 into state tensors: ,

[0029] In the formula, T is the time window length, p is the starting point of the sliding window, N is the number of measurement points, and F is the node feature dimension. For any measurement point m ∈ {1, 2, …, N}, its corresponding node feature matrix is ​​defined as:

[0030] ,

[0031] In the formula, (U m ) t,f Represents matrix U m The element value at time index t and the f-th feature dimension;

[0032] To satisfy the input format of one-dimensional convolution, we transpose it to obtain:

[0033] ,

[0034] In the formula, This can be represented as a one-dimensional convolutional input with the feature dimension being the channel and the time dimension being the sequence length.

[0035] Step 3.3: Extract features at different time scales using dual-scale parallel convolutional branches. Let the kernel size of the short-scale branch be k. s The long-term branched convolution kernel size is k l ,but:

[0036] (i) Short-time scale branch Z m,s The calculation process is as follows:

[0037] ,

[0038] In the formula, Pool represents pooling; The table represents nonlinear activation functions; BN represents batch normalization. This is represented as a convolution kernel with length k. s One-dimensional convolution;

[0039] (ii) Long-term scale branch Z m,l The calculation process is as follows:

[0040] ,

[0041] In the formula, This is represented as a convolution kernel with length k. l One-dimensional convolution;

[0042] Step 3.4: Feature Fusion and Temporal Representation Vector Generation:

[0043] (i) Concatenate the features output from the two branches along the channel dimension to obtain the fused feature Z. m express:

[0044] ,

[0045] (ii) For the fusion feature Z m Performing a 1×1 convolutional linear mapping to complete cross-channel information fusion yields:

[0046] ,

[0047] In the formula, θ f To fuse convolutional layer parameters, a f For bias; G m This is the fused temporal feature map;

[0048] (iii) To obtain a fixed-dimensional temporal representation, G m Global average pooling is performed to obtain the measurement-level time vector t. m :

[0049] ;

[0050] (iv) Aggregate the time-series vectors at all measurement points to obtain the time-series representation vector h. t :

[0051] ,

[0052] In the formula, h t This is the temporal representation vector output by the temporal branch, which is used for subsequent fusion with the representation output by the spatial branch.

[0053] In some embodiments of the present invention, step 4 specifically includes the following steps:

[0054] Step 4.1: Construct and sparsely normalize the adjacency matrix to represent node associations, extract high-order spatial features using graph convolution, and capture the spatiotemporal dependencies of spatial associations as they evolve over time using gated recurrent units.

[0055] Step 4.2: Complete the construction of the time step node representation. Let the state tensor obtained in Step 2 be X. For any time step t∈{1,2,…,T}, define the node feature matrix at that time as:

[0056] ,

[0057] In the formula, S t The characteristic matrix of the measurement point nodes at time t, (S t ) m,f Let matrix S t The element values ​​at the m measurement points and the f-th feature dimension;

[0058] S t The node embedding representation obtained by performing a linear mapping is as follows:

[0059] ,

[0060] In the formula, The linear mapping weight matrix, For bias vectors, For node embedding representation, d is the embedding dimension;

[0061] Step 4.3: Construction and normalization of the dynamic adjacency matrix:

[0062] (i) H is embedded in the node t The node association score matrix at the basic construction time t is defined as:

[0063] ,

[0064] In the formula, This is the node relevance score matrix;

[0065] (ii) Normalize the relevance score matrix to obtain the dynamic adjacency matrix, specifically:

[0066] ,

[0067] In the formula, Softmax(·) represents the Softmax normalization operation performed on the matrix row by row. Let be the dynamic adjacency matrix at time t;

[0068] Step 4.4: Sparsification and Self-Loop Compensation of the Adjacency Matrix

[0069] (i) To improve model efficiency and suppress noise, the dynamic adjacency matrix A is... t Top-k sparsity processing is performed, retaining the connections corresponding to the top k largest weights in each row to obtain a sparse adjacency matrix. It is represented as:

[0070] ,

[0071] In the formula, ⊙ represents element-wise multiplication; M t ∈{0,1} N×N For a sparse mask matrix, if the j-th node belongs to the Top-k set in the i-th row, then (M t ) i,j =1, otherwise 0;

[0072] (ii) Perform self-loop compensation on the sparse adjacency matrix to obtain:

[0073] ,

[0074] In the formula, I N It is an N-order identity matrix. This is the adjacency matrix after self-loop compensation;

[0075] (iii) To After performing row normalization, we obtain the final adjacency matrix used for graph convolution propagation:

[0076] ,

[0077] In the formula, D t It is a degree matrix;

[0078] Step 4.5: Graph convolution extracts high-order spatial association features. Two layers of graph convolution are used to perform adjacency propagation and linear transformation on the node embeddings to extract high-order spatial association features, specifically:

[0079] ,

[0080] In the formula, Γ1 and Γ2 are graph convolution weight matrices, η1 and η2 are bias vectors, σ(·) is a nonlinear activation function, and H t,1 H represents the node hidden feature matrix obtained after passing through the first layer of graph convolution in spacetime t. t,2 This indicates that the node hidden feature matrix is ​​obtained after passing through the second layer of graph convolution in spacetime t;

[0081] To obtain the spatial feature vector at time t, the node dimensions are aggregated to obtain:

[0082] ,

[0083] In the formula, g t Let H be the graph-level spatial eigenvector at time t. t,2 This indicates that the node hidden feature matrix is ​​obtained after passing through the second layer of graph convolution in spacetime t;

[0084] Step 4.6: The gated recurrent unit captures spatial dependencies and assembles the spatial feature vectors of each time step into a sequence G=[g1,g2,…,g…]. T The input gated recurrent unit (GRU) is used to model the evolution of spatial correlation over time, resulting in a spatial representation vector, expressed as:

[0085] ,

[0086] In the formula, h s Let r be a spatial representation vector. t The output sequence of GRU is used to fuse with the temporal representation vector from step 3 and input into the Q-network of DQN.

[0087] In some embodiments of the present invention, step 5 specifically includes the following steps:

[0088] Step 5.1: The temporal representation vector output by the fusion of dual-branch features is as follows: The spatial representation vector output by the spatial branch is The two are then concatenated and fused along their feature dimensions to obtain the fused state representation vector:

[0089] ;

[0090] Step 5.2: The Q-network outputs an action value vector, defining the fault category action set as:

[0091] ,

[0092] In the formula, a represents the action, and J represents the number of actions;

[0093] The Q-function of a deep Q-network approximates Qθ (·), whose input is the fused state representation vector s, and whose output is the action value vector for action space A, expressed as:

[0094] ,

[0095] In the formula, θ represents the Q-network parameters; action a j ∈ A corresponds to the fault category of the axial piston pump;

[0096] Step 5.3: Based on the action value vector, an ε-greedy strategy is used to select actions. Action a is randomly selected from the action space A with probability ε; the action with the maximum action value is selected with probability 1-ε, as follows:

[0097] ,

[0098] In the formula, a* represents the final selected action, and the interaction sample is stored in the experience replay for subsequent Bellman updates.

[0099] In some embodiments of the present invention, step 6 includes the following steps:

[0100] Step 6.1: Uncertainty estimation and adjacent change intensity calculation, specifically including:

[0101] (i) In the DQN update, to obtain the uncertainty of the action value of the next state s', random deactivation inference is introduced into the Q network and M forward computations are performed to obtain the j-th output as Q. (j) If (s',a), then the mean and standard deviation of the action value are respectively:

[0102] ,

[0103] In the formula, μ(s',a) is the mean value, and σ(s',a) is the measure of value uncertainty;

[0104] (ii) Using the normalized adjacency matrix generated in step 4, the adjacency change intensity is defined as follows:

[0105] ,

[0106] In the formula, △t represents the degree of dynamic change in the node association structure;

[0107] Step 6.2: The adjusted score is obtained by fusing the upper bound of uncertainty with the intensity of adjacent changes. The upper bound of uncertainty is...

[0108] ,

[0109] The fusion adjustment amount is constructed as follows:

[0110] ,

[0111] In the formula, w0 and w1 are the fusion weight parameters;

[0112] The risk penalty weights and discount factors are adaptively determined as follows:

[0113] ,

[0114] In the formula, β0 and γ0 are initial parameters, and β min With β max Risk penalty weight β t The lower and upper limits of γ min With γ max Discount factor γ t The lower and upper limits of k β With k γ The adjustment coefficient is clip(·), and clip(·) is the interval clipping function.

[0115] Step 6.3: Dynamic Bayesian Time Bellman Objective Construction, using the Double-DQN method to determine the next state action, defined as:

[0116] ,

[0117] In the formula, a* represents the optimal action that maximizes the action value function in state s'; θ is the parameter of the online Q-network; s' is the next state; a represents the action; A is the action set; a∈A means that action a takes a value from action set A;

[0118] And by introducing a value estimate in the form of lower confidence bound (LCB), we obtain:

[0119] ,

[0120] In the formula, LCB(s') is the value estimate based on the lower confidence bound at the next state s'; μ is the mean estimate; s' is the next state; β t The exploration coefficient is adjusted with time step t;

[0121] Therefore, the objective value of the constructed dynamic Bayesian spatiotemporal Bellman update is:

[0122] ,

[0123] In the formula, r represents the instant reward. Let be the discount factor at time t;

[0124] Step 6.4: Huber loss optimization and fault classification output, specifically including:

[0125] (i) Using the target value y and the current estimated Qo The bias is used to construct the Huber loss function:

[0126] ,

[0127] ,

[0128] In the formula, θ represents the online Q-network parameters, and k is the Huber threshold. yt is the TD error at time step t; yt is the target Q value at time step t; θ is the parameter of the online Q network; k is the Huber loss threshold;

[0129] (ii) Minimize L(θ) using gradient descent to update the Q network parameters, and select the action as follows during online inference:

[0130] ,

[0131] In the formula, The optimal action selected by the online Q-network in the current state s;

[0132] The corresponding fault category is the fault diagnosis classification result of the axial piston pump.

[0133] Compared with the prior art, the beneficial effects of the present invention are:

[0134] Step 2 of this invention performs continuous wavelet multi-scale analysis on the pressure signal to reveal transient information such as shocks and sudden changes, as well as variations in different frequency bands. Step 3 employs dual-scale one-dimensional convolution to extract temporal features in parallel, capturing both short-term fluctuations and preserving trends over longer periods. Step 4 constructs a dynamically updated sparse adjacency matrix, uses graph convolution to extract the correlation between measurement points, and employs a GRU to characterize its changes over time. Step 5 fuses the temporal and spatial features as state input to a DQN, which is used to output the fault category. Step 6 integrates uncertainty and adjacency change intensity in the target value calculation and uses Huber loss for training to reduce the impact of abnormal errors on parameter updates. Through the above process, more stable training results and more reliable diagnostic results can be obtained under complex working conditions, improving the accuracy and robustness of axial piston pump fault identification. Attached Figure Description

[0135] Figure 1 This is a flowchart of an axial piston pump fault diagnosis method based on a spatiotemporal DQN model in an embodiment of the present invention.

[0136] Figure 2 This is a node feature construction diagram of the spatiotemporal DQN model in an embodiment of the present invention;

[0137] Figure 3This is a temporal branching result diagram of the spatiotemporal DQN model in an embodiment of the present invention;

[0138] Figure 4 This is a diagram showing the spatial branching results of the spatiotemporal DQN model in an embodiment of the present invention.

[0139] Figure 5 This is the action value map of the spatiotemporal DQN model Q-network in this embodiment of the invention;

[0140] Figure 6 This is a training error diagram of the spatiotemporal DQN model in an embodiment of the present invention;

[0141] Figure 7 This is a confusion matrix diagram for axial piston pump fault diagnosis in an embodiment of the present invention;

[0142] Figure 8 This is a clustering diagram of axial piston pump failure categories in an embodiment of the present invention;

[0143] Figure 9 The identification accuracy, recall rate, and F1-score of the axial piston pump fault diagnosis in this embodiment of the invention are given. Detailed Implementation

[0144] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0145] like Figure 1 As shown in the figure, the axial piston pump fault diagnosis method based on a spatiotemporal DQN model described in this embodiment specifically includes the following steps:

[0146] Step 1: Set up signal acquisition points on the axial piston pump equipment and collect pressure sequence data at each point through pressure sensors.

[0147] Specifically, this embodiment uses an axial piston pump test bench, and arranges two pressure signal acquisition points at key locations on the pump body (oil inlet and oil outlet). The original pressure sequence data of the pump under different operating conditions is collected by pressure sensors, and the collected sequence is truncated by sliding window to construct a sample sequence of length T.

[0148] Step 2: Perform continuous wavelet transform on the pressure time-domain signal at each measuring point to obtain the multi-scale time-frequency features of the pressure signal; combine the multi-scale time-frequency features of the pressure signal with the original pressure time-domain signal to form a nodal feature tensor.

[0149] Step 2.1: Collect pressure sequence data at each measuring point of the axial piston pump using a pressure sensor, as shown below:

[0150] ,

[0151] In the formula, x m [l] represents the pressure measurement value at the m-th measuring point at sampling time l, N is the number of measuring points, and L is the length of a single sequence;

[0152] Step 2.2: Let the scale set of the continuous wavelet transformation be W, and the mother wavelet be the Ricker wavelet. Then, the m-th measurement point at scale w... k The continuous wavelet coefficients under ∈W are expressed as:

[0153] ,

[0154] In the formula, c m,k [l] represents the wavelet coefficients; W = {w1, w2, …, w K} is the scale set; ψ wk (·) represents Ricker mother wavelet scale w k The generated wavelet function, x m [i] represents the original measurement value of the m-th measurement point at sampling time i; i is the time index of the convolution summation; k is the scale number; K is the total number of scales;

[0155] Step 2.3: Assemble the wavelet coefficients of the same measurement point at each scale to obtain the multi-scale representation matrix of the measurement point, denoted as:

[0156] ,

[0157] In the formula, C m Let w be the multi-scale representation matrix of the m-th measurement point, where the k-th row is the scale w. k The coefficient sequence under c m,K [l] represents the Kth scale w K The wavelet coefficients at time l;

[0158] Step 2.4: Fuse the original signal with the multi-scale wavelet coefficients in the feature dimension to construct the node feature vector, as shown in the example below. Figure 2 As shown, the left figure is the curve of the pressure sequence changing with the sampling point index, and the right figure is the multi-scale time-frequency coefficient heatmap obtained by continuous wavelet transform of the sequence. A state tensor is formed, and the nodal feature vector of the m-th measurement point at time l is defined as:

[0159] .

[0160] Step 3: Utilize a two-scale one-dimensional convolutional neural network with temporal branches to extract temporal features from the node feature tensors, obtaining a temporal representation vector. Specifically, the short-scale convolutional branch is used to capture local mutations and short-term oscillation patterns, while the long-scale convolutional branch is used to characterize trend information over longer time windows. The temporal representation vector is obtained through feature fusion and global pooling. An example of the temporal branch extraction result is shown below. Figure 3 As shown, the distribution of the time-series representation vector output by the time-series branch along the feature dimension.

[0161] Step 3.1: The temporal branch adopts a dual-scale one-dimensional convolutional network, which consists of two parallel convolutional branches with different convolutional kernels and a feature fusion module. Each branch sequentially includes one-dimensional convolution, batch normalization, activation and pooling to extract features at different time scales. The fusion module outputs a fixed-dimensional temporal representation vector through feature concatenation, 1×1 linear mapping and global pooling.

[0162] Step 3.2: Input sequence construction and dimensionality transformation, converting the node feature vectors obtained in Step 2 into state tensors: ,

[0163] In the formula, T is the time window length, p is the starting point of the sliding window, N is the number of measurement points, and F is the node feature dimension. For any measurement point m ∈ {1, 2, …, N}, its corresponding node feature matrix is ​​defined as:

[0164] ,

[0165] In the formula, (U m ) t,f Represents matrix U m The element value at time index t and the f-th feature dimension;

[0166] To satisfy the input format of one-dimensional convolution, we transpose it to obtain:

[0167] ,

[0168] In the formula, This can be represented as a one-dimensional convolutional input with the feature dimension being the channel and the time dimension being the sequence length.

[0169] Step 3.3: Extract features at different time scales using dual-scale parallel convolutional branches. Let the kernel size of the short-scale branch be k. s The long-term branched convolution kernel size is k l ,but:

[0170] (i) Short-time scale branch Z m,s The calculation process is as follows:

[0171] ,

[0172] In the formula, Pool represents pooling; The table represents nonlinear activation functions; BN represents batch normalization. This is represented as a convolution kernel with length k. s One-dimensional convolution;

[0173] (ii) Long-term scale branch Z m,l The calculation process is as follows:

[0174] ,

[0175] In the formula, This is represented as a convolution kernel with length k. l One-dimensional convolution;

[0176] Step 3.4: Feature Fusion and Temporal Representation Vector Generation:

[0177] (i) Concatenate the features output from the two branches along the channel dimension to obtain the fused feature Z. m express:

[0178] ,

[0179] (ii) For the fusion feature Z m Performing a 1×1 convolutional linear mapping to complete cross-channel information fusion yields:

[0180] ,

[0181] In the formula, θ f To fuse convolutional layer parameters, a f For bias; G m This is the fused temporal feature map;

[0182] (iii) To obtain a fixed-dimensional temporal representation, G m Global average pooling is performed to obtain the measurement-level time vector t. m :

[0183] ;

[0184] (iv) Aggregate the time-series vectors at all measurement points to obtain the time-series representation vector h. t :

[0185] ,

[0186] In the formula, h t This is the temporal representation vector output by the temporal branch, which is used for subsequent fusion with the representation output by the spatial branch.

[0187] Step 4: Extract node association features using dynamic graph convolution and gated recurrent unit networks. This is achieved by constructing a dynamic adjacency matrix and performing Top-k sparsity, self-loop compensation, and normalization to capture node associations and spatiotemporal dependencies. Dynamic graph convolution is used to extract higher-order spatial association features, while gated recurrent unit networks characterize the spatiotemporal evolution of spatial associations over time. An example of the spatial branch extraction results is shown below. Figure 4 As shown, the spatial representation vector output by the spatial branch has values ​​distributed across each dimension.

[0188] Step 4.1: The dynamic graph convolution and gated recurrent unit network includes four steps: dynamic adjacency matrix construction, adjacency matrix sparsification and normalization, graph convolution feature extraction, and gated recurrent unit temporal modeling. The adjacency matrix is ​​constructed and sparsely normalized to represent node associations, graph convolution extracts high-order spatial features, and gated recurrent units capture the spatiotemporal dependencies of spatial associations as they evolve over time.

[0189] Step 4.2: Complete the construction of the time step node representation. Let the state tensor obtained in Step 2 be X. For any time step t∈{1,2,…,T}, define the node feature matrix at that time as:

[0190] ,

[0191] In the formula, S t The characteristic matrix of the measurement point nodes at time t, (S t ) m,f Let matrix S t The element values ​​at the m measurement points and the f-th feature dimension;

[0192] S t The node embedding representation obtained by performing a linear mapping is as follows:

[0193] ,

[0194] In the formula, The linear mapping weight matrix, For bias vectors, For node embedding representation, d is the embedding dimension;

[0195] Step 4.3: Construction and normalization of the dynamic adjacency matrix:

[0196] (i) H is embedded in the node t The node association score matrix at the basic construction time t is defined as:

[0197] ,

[0198] In the formula, This is the node relevance score matrix;

[0199] (ii) Normalize the relevance score matrix to obtain the dynamic adjacency matrix, specifically:

[0200] ,

[0201] In the formula, Softmax(·) represents the Softmax normalization operation performed on the matrix row by row. Let be the dynamic adjacency matrix at time t;

[0202] Step 4.4: Sparsification and Self-Loop Compensation of the Adjacency Matrix

[0203] (i) To improve model efficiency and suppress noise, the dynamic adjacency matrix A is... t Top-k sparsity processing is performed, retaining the connections corresponding to the top k largest weights in each row to obtain a sparse adjacency matrix. It is represented as:

[0204] ,

[0205] In the formula, ⊙ represents element-wise multiplication; M t ∈{0,1} N×N For a sparse mask matrix, if the j-th node belongs to the Top-k set in the i-th row, then (M t ) i,j =1, otherwise 0;

[0206] (ii) Perform self-loop compensation on the sparse adjacency matrix to obtain:

[0207] ,

[0208] In the formula, I N It is an N-order identity matrix. This is the adjacency matrix after self-loop compensation;

[0209] (iii) To After performing row normalization, we obtain the final adjacency matrix used for graph convolution propagation:

[0210] ,

[0211] In the formula, D t It is a degree matrix;

[0212] Step 4.5: Graph convolution extracts high-order spatial association features. Two layers of graph convolution are used to perform adjacency propagation and linear transformation on the node embeddings to extract high-order spatial association features, specifically:

[0213] ,

[0214] In the formula, Γ1 and Γ2 are graph convolution weight matrices, η1 and η2 are bias vectors, σ(·) is a nonlinear activation function, and H t,1 H represents the node hidden feature matrix obtained after passing through the first layer of graph convolution in spacetime t. t,2 This indicates that the node hidden feature matrix is ​​obtained after passing through the second layer of graph convolution in spacetime t;

[0215] To obtain the spatial feature vector at time t, the node dimensions are aggregated to obtain:

[0216] ,

[0217] In the formula, g t Let H be the graph-level spatial eigenvector at time t. t,2 This indicates that the node hidden feature matrix is ​​obtained after passing through the second layer of graph convolution in spacetime t;

[0218] Step 4.6: The gated recurrent unit captures spatial dependencies and assembles the spatial feature vectors of each time step into a sequence G=[g1,g2,…,g…]. T The input gated recurrent unit (GRU) is used to model the evolution of spatial correlation over time, resulting in a spatial representation vector, expressed as:

[0219] ,

[0220] In the formula, h s Let r be a spatial representation vector. t The output sequence of GRU is used to fuse with the temporal representation vector from step 3 and input into the Q-network of DQN.

[0221] Step 5: Concatenate and fuse the temporal representation vector output by the temporal branch with the spatial representation vector output by the spatial branch to form state s. t The input to the Q-network of the DQN model yields Q(s,a). An ε-greedy action a is selected, and a reward r is obtained based on the action's execution result. t The next state s' is set, and (s, a, r, s', d) is stored in the experience replay, where s is the current state; a is the action; r is the reward; s' is the next state; and d is the termination condition. For example... Figure 5 As shown in the bar chart, the action values ​​Q(s,a) of the four types of actions are compared. The normal action has the highest value, indicating that the model is more inclined to select the normal action.

[0222] Step 5.1: The temporal representation vector output by the fusion of dual-branch features is as follows: The spatial representation vector output by the spatial branch is The two are then concatenated and fused along their feature dimensions to obtain the fused state representation vector:

[0223] ;

[0224] Step 5.2: The Q-network outputs an action value vector, defining the fault category action set as:

[0225] ,

[0226] In the formula, a represents the action, and J represents the number of actions;

[0227] The Q-function of a deep Q-network approximates Q θ (·), whose input is the fused state representation vector s, and whose output is the action value vector for action space A, expressed as:

[0228] ,

[0229] In the formula, θ represents the Q-network parameters; action a j ∈ A corresponds to the fault category of the axial piston pump;

[0230] Step 5.3: Based on the action value vector, an ε-greedy strategy is used to select actions. Action a is randomly selected from the action space A with probability ε; the action with the maximum action value is selected with probability 1-ε, as follows:

[0231] ,

[0232] In the formula, a* represents the final selected action, and the interaction sample is stored in the experience replay for subsequent Bellman updates.

[0233] Step 6: Sample interaction samples from the experience replay, estimate the uncertainty of the next state action value, and adaptively adjust the risk penalty weight and discount factor based on the change intensity of the dynamic adjacency matrix in adjacent time steps; on this basis, construct the target Q value according to the Bellman equation, update the Q network parameters using Huber loss, and use the updated Q network output as the final fault category as the diagnostic result. Figure 6 As shown, the Huber loss decreases rapidly with the number of training steps and gradually stabilizes, indicating that the model training process converges.

[0234] Step 6.1: Uncertainty estimation and adjacent change intensity calculation, specifically including:

[0235] (i) In the DQN update, to obtain the uncertainty of the action value of the next state s', random deactivation inference is introduced into the Q network and M forward computations are performed to obtain the j-th output as Q. (j) If (s',a), then the mean and standard deviation of the action value are respectively:

[0236] ,

[0237] In the formula, μ(s',a) is the mean value, and σ(s',a) is the measure of value uncertainty;

[0238] (ii) Using the normalized adjacency matrix generated in step 4, the adjacency change intensity is defined as follows:

[0239] ,

[0240] In the formula, △t represents the degree of dynamic change in the node association structure;

[0241] Step 6.2: The adjusted score is obtained by fusing the upper bound of uncertainty with the intensity of adjacent changes. The upper bound of uncertainty is...

[0242] ,

[0243] The fusion adjustment amount is constructed as follows:

[0244] ,

[0245] In the formula, w0 and w1 are the fusion weight parameters;

[0246] The risk penalty weights and discount factors are adaptively determined as follows:

[0247] ,

[0248] In the formula, β0 and γ0 are initial parameters, and β min With β max Risk penalty weight β t The lower and upper limits of γ min With γ max Discount factor γ t The lower and upper limits of k β With k γ The adjustment coefficient is clip(·), and clip(·) is the interval clipping function.

[0249] Step 6.3: Dynamic Bayesian Time Bellman Objective Construction, using the Double-DQN method to determine the next state action, defined as:

[0250] ,

[0251] In the formula, a* represents the optimal action that maximizes the action value function in state s'; θ is the parameter of the online Q-network; s' is the next state; a represents the action; A is the action set; a∈A means that action a takes a value from action set A;

[0252] And by introducing a value estimate in the form of lower confidence bound (LCB), we obtain:

[0253] ,

[0254] In the formula, LCB(s') is the value estimate based on the lower confidence bound at the next state s'; μ is the mean estimate; s' is the next state; β t The exploration coefficient is adjusted with time step t;

[0255] Therefore, the objective value of the constructed dynamic Bayesian spatiotemporal Bellman update is:

[0256] ,

[0257] In the formula, r represents the instant reward. Let be the discount factor at time t;

[0258] Step 6.4: Huber loss optimization and fault classification output, specifically including:

[0259] (i) Using the target value y and the current estimated Q o The bias is used to construct the Huber loss function:

[0260] ,

[0261] ,

[0262] In the formula, θ represents the online Q-network parameters, k is the Huber threshold, and ;

[0263] (ii) Minimize L(θ) using gradient descent to update the Q network parameters, and select the action as follows during online inference:

[0264] ,

[0265] In the formula, yt is the TD error at time step t; yt is the target Q value at time step t; θ is the parameter of the online Q network; k is the Huber loss threshold. The optimal action selected by the online Q-network in the current state s;

[0266] The corresponding fault category is the fault diagnosis classification result of the axial piston pump.

[0267] Step 7: Output the confusion matrix, fault category clustering diagram, identification accuracy, recall rate, and F1 score of the axial piston pump fault categories to complete the intelligent fault diagnosis of the axial piston pump. Results are as follows: Figure 7-9 As shown. Figure 8 The four types of samples showed clear clustering and separation in the three-dimensional feature space. Figure 7 The confusion matrix indicates that the overall accuracy of the classification results is high, with only a small number of faults being misclassified as normal. Figure 9The comparison of recognition accuracy, recall rate and F1-score for four types of working conditions is shown. The overall index is between 0.96 and 1.00. Among them, moderate wear has the lowest accuracy, while severe wear has the highest accuracy but a slightly lower recall rate.

[0268] The above description is merely an example and illustration of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the structure of the present invention or exceed the scope defined in the claims, all of which should fall within the protection scope of the present invention.

Claims

1. A method for diagnosing axial piston pump faults using a spatiotemporal DQN model, characterized in that, Includes the following steps: Step 1: Set up signal acquisition points on the axial piston pump equipment and collect pressure sequence data at each point through pressure sensors; Step 2: Perform continuous wavelet transform on the pressure time-domain signal at each measuring point to obtain the multi-scale time-frequency features of the pressure signal; combine the multi-scale time-frequency features of the pressure signal with the original pressure time-domain signal to form a nodal feature tensor; Step 3: Using a two-scale one-dimensional convolutional neural network with temporal branches, extract temporal features from the node feature tensors to obtain the temporal representation vector; Step 4: Extract node association features from the node feature tensor using dynamic graph convolution and gated recurrent unit network. By constructing a dynamic adjacency matrix and performing sparsification and normalization, node association and spatial dependency are captured to obtain the spatial representation vector. Step 5: Concatenate the temporal representation vector and the spatial representation vector to form a state, input it into the Q network to obtain the action value Q(s,a), use ε-greedy selection of action a, and store the experience replay sample (s, a, r, s', d) into the experience replay, where s is the current state, a is the action, r is the reward, s' is the next state, and d is the termination. Step 6: Sample samples from the experience replay, construct the Bellman objective equation by adaptively adjusting the risk penalty weights and discount factors based on uncertainty estimation and adjacency change intensity, and update the Q network using Huber loss; Step 7: Output the confusion matrix, fault category clustering diagram, identification accuracy, recall rate, and F1 score of the axial piston pump fault categories to complete the intelligent diagnosis of axial piston pump faults.

2. The method for axial piston pump fault diagnosis using a spatiotemporal DQN model according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Collect pressure sequence data at each measuring point of the axial piston pump using a pressure sensor, as shown below: ， In the formula, x m [l] represents the pressure measurement value at the m-th measuring point at sampling time l, N is the number of measuring points, and L is the length of a single sequence; Step 2.2: Let the scale set of the continuous wavelet transformation be W, and the mother wavelet be the Ricker wavelet. Then, the m-th measurement point at scale w... k The continuous wavelet coefficients under ∈W are expressed as: ， In the formula, c m,k [l] represents the wavelet coefficients; W = {w1, w2, …, w K } is the scale set; ψ wk (·) represents Ricker mother wavelet scale w k The generated wavelet function, x m [i] represents the original measurement value of the m-th measurement point at sampling time i; i is the time index of the convolution summation; k is the scale number; K is the total number of scales; Step 2.3: Assemble the wavelet coefficients of the same measurement point at each scale to obtain the multi-scale representation matrix of the measurement point, denoted as: ， In the formula, C m Let w be the multi-scale representation matrix of the m-th measurement point, where the k-th row is the scale w. k The coefficient sequence under c m,K [l] represents the Kth scale w K The wavelet coefficients at time l; Step 2.4: Fuse the original signal with the multi-scale wavelet coefficients in the feature dimension to construct node feature vectors and form a state tensor. Define the node feature vector of the m-th measurement point at time l as: 。 3. The method for axial piston pump fault diagnosis using a spatiotemporal DQN model according to claim 2, characterized in that, Step 3 specifically includes the following steps: Step 3.1: The temporal branch adopts a dual-scale one-dimensional convolutional network, which consists of two parallel convolutional branches with different convolutional kernels and a feature fusion module. Each branch sequentially includes one-dimensional convolution, batch normalization, activation and pooling to extract features at different time scales. The fusion module outputs a fixed-dimensional temporal representation vector through feature concatenation, 1×1 linear mapping and global pooling. Step 3.2: Input sequence construction and dimensionality transformation, converting the node feature vectors obtained in Step 2 into state tensors: , In the formula, T is the time window length, p is the starting point of the sliding window, N is the number of measurement points, and F is the node feature dimension. For any measurement point m ∈ {1, 2, …, N}, its corresponding node feature matrix is ​​defined as: ， In the formula, (U m ) t,f Represents matrix U m The element value at time index t and the f-th feature dimension; To satisfy the input format of one-dimensional convolution, we transpose it to obtain: ， In the formula, This can be represented as a one-dimensional convolutional input with the feature dimension being the channel and the time dimension being the sequence length; Step 3.3: Extract features at different time scales using dual-scale parallel convolutional branches. Let the kernel size of the short-scale branch be k. s The long-term branched convolution kernel size is k l ,but: (i) Short-time scale branch Z m,s The calculation process is as follows: ， In the formula, Pool represents pooling; The table represents nonlinear activation functions; BN represents batch normalization. This is represented as a convolution kernel with length k. s One-dimensional convolution; (ii) Long-term scale branch Z m,l The calculation process is as follows: ， In the formula, This is represented as a convolution kernel with length k. l One-dimensional convolution; Step 3.4: Feature Fusion and Temporal Representation Vector Generation: (i) Concatenate the features output from the two branches along the channel dimension to obtain the fused feature Z. m express: ， (ii) For the fusion feature Z m Performing a 1×1 convolutional linear mapping to complete cross-channel information fusion yields: ， In the formula, θ f To fuse convolutional layer parameters, a f For bias; G m This is the fused temporal feature map; (iii) To obtain a fixed-dimensional temporal representation, G m Global average pooling is performed to obtain the measurement-level time vector t. m : ； (iv) Aggregate the time-series vectors at all measurement points to obtain the time-series representation vector h. t : ， In the formula, h t This is the temporal representation vector output by the temporal branch, which is used for subsequent fusion with the representation output by the spatial branch.

4. The method for axial piston pump fault diagnosis using a spatiotemporal DQN model according to claim 3, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Construct and sparsely normalize the adjacency matrix to represent node associations, extract high-order spatial features using graph convolution, and capture the spatiotemporal dependencies of spatial associations as they evolve over time using gated recurrent units. Step 4.2: Complete the construction of the time step node representation. Let the state tensor obtained in Step 2 be X. For any time step t∈{1,2,…,T}, define the node feature matrix at that time as: ， In the formula, S t The characteristic matrix of the measurement point nodes at time t, (S t ) m,f Let matrix S t The element values ​​at the m measurement points and the f-th feature dimension; S t The node embedding representation obtained by performing a linear mapping is as follows: ， In the formula, The linear mapping weight matrix, For bias vectors, Let d be the embedding dimension of the node; Step 4.3: Construction and normalization of the dynamic adjacency matrix: (i) H is embedded in the node t The node association score matrix at the basic construction time t is defined as: ， In the formula, This is the node relevance score matrix; (ii) Normalize the relevance score matrix to obtain the dynamic adjacency matrix, specifically: ， In the formula, Softmax(·) represents the Softmax normalization operation performed on the matrix row by row. Let be the dynamic adjacency matrix at time t; Step 4.4: Sparsification and Self-Loop Compensation of the Adjacency Matrix (i) To improve model efficiency and suppress noise, the dynamic adjacency matrix A is... t Top-k sparsity processing is performed, retaining the connections corresponding to the top k largest weights in each row to obtain a sparse adjacency matrix. It is represented as: ， In the formula, ⊙ represents element-wise multiplication; M t ∈{0,1} N×N For a sparse mask matrix, if the j-th node belongs to the Top-k set in the i-th row, then (M t ) i,j =1, otherwise 0; (ii) Perform self-loop compensation on the sparse adjacency matrix to obtain: ， In the formula, I N It is an N-order identity matrix. This is the adjacency matrix after self-loop compensation; (iii) To After performing row normalization, we obtain the final adjacency matrix used for graph convolution propagation: ， In the formula, D t It is a degree matrix; Step 4.5: Graph convolution extracts high-order spatial association features. Two layers of graph convolution are used to perform adjacency propagation and linear transformation on the node embeddings to extract high-order spatial association features, specifically: ， In the formula, Γ1 and Γ2 are graph convolution weight matrices, η1 and η2 are bias vectors, σ(·) is a nonlinear activation function, and H t,1 H represents the node hidden feature matrix obtained after passing through the first layer of graph convolution in spacetime t. t,2 This indicates that the node hidden feature matrix is ​​obtained after passing through the second layer of graph convolution in spacetime t; To obtain the spatial feature vector at time t, the node dimensions are aggregated to obtain: ， In the formula, g t Let H be the graph-level spatial eigenvector at time t. t,2 This indicates that the node hidden feature matrix is ​​obtained after passing through the second layer of graph convolution in spacetime t; Step 4.6: The gated recurrent unit captures spatial dependencies and assembles the spatial feature vectors of each time step into a sequence G=[g1,g2,…,g…]. T The input gated recurrent unit (GRU) is used to model the evolution of spatial correlation over time, resulting in a spatial representation vector, expressed as: ， In the formula, h s Let r be a spatial representation vector. t The output sequence of GRU is used to fuse with the temporal representation vector from step 3 and input into the Q-network of DQN.

5. The method for axial piston pump fault diagnosis using a spatiotemporal DQN model according to claim 4, characterized in that, Step 5 specifically includes the following steps: Step 5.1: The temporal representation vector output by the fusion of dual-branch features is as follows: The spatial representation vector output by the spatial branch is The two are then concatenated and fused along their feature dimensions to obtain the fused state representation vector: ； Step 5.2: The Q-network outputs an action value vector, defining the fault category action set as: ， In the formula, a represents the action, and J represents the number of actions; The Q-function of a deep Q-network approximates Q θ (·), whose input is the fused state representation vector s, and whose output is the action value vector for action space A, expressed as: ， In the formula, θ represents the Q-network parameters; action a j ∈ A corresponds to the fault category of the axial piston pump; Step 5.3: Based on the action value vector, an ε-greedy strategy is used to select actions. Action a is randomly selected from the action space A with probability ε; the action with the maximum action value is selected with probability 1-ε, as follows: ， In the formula, a* represents the final selected action, and the interaction sample is stored in the experience replay for subsequent Bellman updates.

6. The method for axial piston pump fault diagnosis using a spatiotemporal DQN model according to claim 1, characterized in that, Step 6 includes the following steps: Step 6.1: Uncertainty estimation and adjacent change intensity calculation, specifically including: (i) In the DQN update, to obtain the uncertainty of the action value of the next state s', random deactivation inference is introduced into the Q network and M forward computations are performed to obtain the j-th output as Q. (j) If (s',a), then the mean and standard deviation of the action value are respectively: ， In the formula, μ(s',a) is the mean value, and σ(s',a) is the measure of value uncertainty; (ii) Using the normalized adjacency matrix generated in step 4, the adjacency change intensity is defined as follows: ， In the formula, △t represents the degree of dynamic change in the node association structure; Step 6.2: The adjusted score is obtained by fusing the upper bound of uncertainty with the intensity of adjacent changes. The upper bound of uncertainty is... ， The fusion adjustment amount is constructed as follows: ， In the formula, w0 and w1 are the fusion weight parameters; The risk penalty weights and discount factors are adaptively determined as follows: ， In the formula, β0 and γ0 are initial parameters, and β min With β max Risk penalty weight β t The lower and upper limits of γ min With γ max Discount factor γ t The lower and upper limits of k β With k γ The adjustment coefficient is clip(·), and clip(·) is the interval clipping function. Step 6.3: Dynamic Bayesian Time Bellman Objective Construction, using the Double-DQN method to determine the next state action, defined as: ， In the formula, a* represents the optimal action that maximizes the action value function in state s'; θ is the parameter of the online Q-network; s' is the next state; a represents the action; A is the action set; a∈A means that action a takes a value from action set A; And by introducing a value estimate in the form of lower confidence bound (LCB), we obtain: ， In the formula, LCB(s') is the value estimate based on the lower confidence bound at the next state s'; μ is the mean estimate; s' is the next state; β t The exploration coefficient is adjusted with time step t; Therefore, the objective value of the constructed dynamic Bayesian spatiotemporal Bellman update is: ， In the formula, r represents the instant reward. Let be the discount factor corresponding to time t; Step 6.4: Huber loss optimization and fault classification output, specifically including: (i) Using the target value y and the current estimated Q o The bias is used to construct the Huber loss function: ， ， In the formula, θ represents the online Q-network parameters, and k is the Huber threshold. yt is the TD error at time step t; yt is the target Q value at time step t; θ is the parameter of the online Q network; k is the Huber loss threshold; (ii) Minimize L(θ) using gradient descent to update the Q network parameters, and select the action as follows during online inference: ， In the formula, The optimal action selected by the online Q-network in the current state s; The corresponding fault category is the fault diagnosis classification result of the axial piston pump.

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