Industrial operation data filling and repairing method, device and equipment based on dynamic graph learning and medium

Abstract

The application discloses an industrial operation data filling and repairing method and device based on dynamic graph learning, equipment and medium, and relates to the technical field of data processing. The method comprises the following steps: a non-convex low-rank regularization term is constructed by introducing a truncated SCAD penalty function to protect the main signal energy; a dynamic graph total variation regularization term is constructed by using a graph attention neural network to capture the dynamic spatial correlation between variables evolving over time; an adaptive graph wavelet shrinkage mechanism is combined to distinguish the sudden change signals and random noise in the multi-scale frequency domain; and finally, an alternating direction multiplier method is used for iterative solution. The non-convex low-rank regularization term of the data is accurately reserved, the dynamic correlation of the industrial data is adapted, the effective sudden change and noise are distinguished, and the precision and adaptability of the data filling and repairing are improved.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method, apparatus, equipment, and medium for filling and repairing industrial operation data based on dynamic graph learning. Background Technology

[0002] Currently, industrial data imputation and repair mostly adopts the traditional low-rank matrix completion method, which uses the nuclear norm to constrain the low-rank characteristics of the data to fill missing values; at the same time, it combines static graph models to constrain the spatial correlation of the data to help improve the repair accuracy; for noise processing, wavelet shrinkage method with global threshold is used for noise reduction.

[0003] Traditional low-rank matrix completion uses a nuclear norm that penalizes all singular values ​​of the data with equal intensity, which can easily lead to excessive compression of the effective non-convex low-rank regularization terms of the data; static graph models cannot adapt to the dynamic relationship of industrial data with production status, and it is difficult to accurately capture the real-time local features of the data; wavelet shrinkage methods with global thresholds cannot distinguish between abrupt signals that conform to physical laws and random noise in industrial data, which can easily cause loss of effective information or noise residue.

[0004] Therefore, how to achieve high-precision data filling and repair in the case of missing industrial operation data, taking into full account the low-rank characteristics of the data and the dynamic spatial correlation that changes over time, has become an urgent problem to be solved. Summary of the Invention

[0005] The main objective of this application is to provide a method, apparatus, equipment, and medium for filling and repairing industrial operation data based on dynamic graph learning, aiming to solve the technical problem of how to improve the accuracy of data filling and repair.

[0006] To achieve the above objectives, this application proposes a method for filling and repairing industrial operation data based on dynamic graph learning, comprising:

[0007] Acquire data to be recovered from industrial processes;

[0008] A joint optimization model is constructed based on the data to be recovered. The joint optimization model includes a non-convex low-rank regularization term module, a dynamic graph learning module, and an adaptive graph wavelet shrinkage module. The non-convex low-rank regularization term module obtains the non-convex low-rank regularization term using a truncated SCAD penalty function. The dynamic graph learning module constructs a dynamic Laplacian matrix based on the non-convex low-rank regularization term using a graph attention neural network. The adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix to construct an adaptive graph wavelet shrinkage regularization term.

[0009] The joint optimization model was iteratively solved using the alternating direction multiplier method to obtain the fully repaired industrial operation data.

[0010] In one embodiment, the step of obtaining the non-convex low-rank regularization term using the truncated SCAD penalty function in the non-convex low-rank regularization term module includes:

[0011] Based on the data to be recovered and the corresponding observation index set, determine the data fidelity item corresponding to the data to be recovered;

[0012] Define a truncated SCAD penalty function, which includes a penalty intensity parameter and a preset constant, specifically expressed as follows:

[0013]

[0014] in This indicates the SCAD penalty function to be truncated. For the penalty intensity parameter, This represents a preset constant. Represents singular values;

[0015] Singular value decomposition is performed on the data to be recovered to separate the first r main singular values ​​and the smaller singular values ​​after the (r+1)th singular value.

[0016] No penalty is imposed on the first r major singular values; the numerical values ​​of the major singular values ​​are retained.

[0017] Substituting the smaller singular value into the truncated SCAD penalty function for calculation, a non-convex low-rank regularization term is obtained.

[0018] Combining the data fidelity term and the non-convex low-rank regularization term yields the non-convex low-rank regularization term, specifically expressed as follows:

[0019]

[0020] in This represents a non-convex low-rank regularization term. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, This represents a matrix of observed industrial operation data, i.e., data to be recovered, with dimensions of [missing information]. , This refers to the data fidelity item, which represents the data that needs to be recovered. At the observation location and the data to be recovered The degree of closeness Represents the observation operator. Represents the observation index set, Represents the regularization parameter. express The A singular value, This indicates that a penalty is imposed on the singular values ​​from the (r+1)th to the smallest dimension, where no penalty is imposed on the first r singular values. This indicates the preset number of principal components, and represents the rank of the main low-level non-convex low-rank regularization terms retained in the data. express The maximum possible rank depends on the number of rows. Number of columns The smaller value.

[0021] In one embodiment, the step of the dynamic graph learning module constructing a dynamic Laplacian matrix based on the non-convex low-rank regularization term using a graph attention neural network includes:

[0022] The non-convex low-rank regularization term is input into the graph attention neural network to dynamically calculate the attention coefficients between data nodes.

[0023] Generate an adjacency matrix and a corresponding degree matrix based on the attention coefficients;

[0024] The dynamic Laplace matrix is ​​obtained by calculating the difference between the degree matrix and the adjacency matrix.

[0025] In one embodiment, the adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix, and the step of constructing the adaptive graph wavelet shrinkage regularization term includes:

[0026] A kernel function is defined on the spectral domain corresponding to the dynamic Laplacian matrix, and several different scaling parameters are introduced;

[0027] Based on the kernel function and the multiple scaling parameters, multiple spectral wavelet transform matrices of different scales are generated;

[0028] The data to be recovered is mapped to the spectral wavelet domain by the multiple spectral wavelet transform matrices to obtain the decomposed wavelet coefficients at each scale.

[0029] Using the L1 norm to apply sparsity constraints to the wavelet coefficients at each scale after decomposition, an adaptive graph wavelet shrinkage regularization term is constructed, specifically expressed as:

[0030]

[0031] in This represents the adaptive graph wavelet shrinkage regularization term. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, Indicates the first The wavelet transform matrix of the spectral graph at each scale is generated by the dynamic Laplacian matrix. Denotes the wavelet regularization parameters. This indicates the range from the 1st to the 2nd. Calculate the L1 norm of all wavelet coefficient matrices at each scale and sum them. Indicates the total number of scales.

[0032] In one embodiment, the step of iteratively solving the joint optimization model using the alternating direction multiplier method to obtain the fully repaired industrial operation data includes:

[0033] Based on the structure of the joint optimization model, a first auxiliary variable, a second auxiliary variable, and a third auxiliary variable are introduced, wherein the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable correspond to the data to be recovered, the product of the dynamic Laplacian matrix and the data to be recovered, and the product of the wavelet transform matrix of the spectrum at each scale and the data to be recovered, respectively.

[0034] An augmented Lagrangian function is constructed by combining the first auxiliary variable, the second auxiliary variable, the third auxiliary variable, the non-convex low-rank regularization term, the dynamic Laplacian matrix, and the adaptive graph wavelet shrinkage regularization term.

[0035] By fixing the first auxiliary variable, the second auxiliary variable, the third auxiliary variable, and the Lagrange multipliers of the augmented Lagrange function, a subproblem concerning the data to be recovered is solved. The updated data value is obtained through numerical calculation, as specifically expressed by the following formula:

[0036]

[0037] in, Indicates the updated data value. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, This represents a matrix of observed industrial operation data, i.e., data to be recovered, with dimensions of [missing information]. , This refers to the data fidelity item, which represents the data that needs to be recovered. At the observation location and the data to be recovered The degree of closeness Represents the observation operator. Represents the observation index set, Indicates the first penalty parameter. Indicates the first auxiliary variable. Represents the first Lagrange multiplier. Indicates the second penalty parameter. Let Laplacian matrix be the dynamically generated matrix in the k-th iteration. Indicates the second auxiliary variable. Indicates the second Lagrange multiplier. This represents the third penalty parameter. Indicates the third auxiliary variable. Indicates the third Lagrange multiplier. Indicates the total number of scales. In the k-th iteration, the th... The spectral wavelet transform matrix at each scale, wherein the Lagrange multipliers include a first Lagrange multiplier, a second Lagrange multiplier, and a third Lagrange multiplier, which correspond to the data to be recovered, the product of the dynamic Laplacian matrix and the data to be recovered, and the product of the spectral wavelet transform matrix at each scale and the data to be recovered, respectively.

[0038] By fixing the data update value and the Lagrange multiplier, the subproblems of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable are solved in sequence to obtain the update values ​​of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable, respectively.

[0039] Based on the deviations between the updated data value and the updated values ​​of the first, second, and third auxiliary variables, the corresponding Lagrange multipliers are updated respectively to obtain the updated multipliers, as expressed by the following formula:

[0040]

[0041]

[0042]

[0043] in This represents the updated first Lagrange multiplier. This indicates the updated value of the first auxiliary variable. This represents the updated second Lagrange multiplier. This indicates the updated value of the second auxiliary variable. This represents the updated third Lagrange multiplier. This indicates the updated value of the third auxiliary variable;

[0044] The complete and repaired industrial operation data is obtained when the updated data value, the updated value of the first auxiliary variable, the updated value of the second auxiliary variable, and the updated value of the third auxiliary variable meet the preset convergence conditions.

[0045] In one embodiment, the step of fixing the data update value and the Lagrange multiplier, and sequentially solving the subproblems of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable to obtain the update values ​​of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable, respectively, includes:

[0046] With the data update value, second auxiliary variable, third auxiliary variable, first Lagrange multiplier, second Lagrange multiplier, and third Lagrange multiplier fixed, an optimization problem is constructed for the first auxiliary variable subproblem, which includes a truncated SCAD penalty term, a preset first regularization parameter, and a term related to the data update value and the first Lagrange multiplier.

[0047] Solve the first auxiliary variable subproblem to obtain the updated value of the first auxiliary variable;

[0048] With the data update value, first auxiliary variable, third auxiliary variable, first Lagrange multiplier, second Lagrange multiplier, and third Lagrange multiplier fixed, an optimization problem is constructed for the second auxiliary variable subproblem, which includes an L1 norm term, a preset second regularization parameter, a dynamic Laplacian matrix product term corresponding to the data update value, and a related term of the second Lagrange multiplier.

[0049] Solve the subproblem of the second auxiliary variable to obtain the updated value of the second auxiliary variable;

[0050] With the data update value, first auxiliary variable, second auxiliary variable, first Lagrange multiplier, second Lagrange multiplier, and third Lagrange multiplier fixed, an optimization problem is constructed for the subproblem of the third auxiliary variable, which includes an L1 norm term, a preset third regularization parameter, a product term of wavelet transform matrices of the spectral graphs at each scale corresponding to the data update value, and a related term of the third Lagrange multiplier.

[0051] Solve the subproblem of the third auxiliary variable to obtain the updated value of the third auxiliary variable.

[0052] In one embodiment, the step of obtaining the fully repaired industrial operation data until the updated data value, the updated value of the first auxiliary variable, the updated value of the second auxiliary variable, and the updated value of the third auxiliary variable satisfy a preset convergence condition includes:

[0053] Calculate the first deviation between the updated data value and the previous data value;

[0054] Calculate the second, third, and fourth deviation values ​​of the updated values ​​of the first, second, and third auxiliary variables and their corresponding auxiliary variables from the previous round;

[0055] When the first deviation value, the second deviation value, the third deviation value, and the fourth deviation value are all less than the preset convergence threshold, the iteration stops, and the current data update value is taken as the fully repaired industrial operation data.

[0056] Furthermore, to achieve the above objectives, this application also proposes an industrial operation data filling and repair device based on dynamic graph learning, the industrial operation data filling and repair device based on dynamic graph learning comprising:

[0057] The acquisition module is used to acquire the data to be recovered in the industrial process and the corresponding observation index set;

[0058] The model building module is used to build a joint optimization model based on the data to be recovered. The joint optimization model includes a non-convex low-rank regularization term module, a dynamic graph learning module, and an adaptive graph wavelet shrinkage module. The non-convex low-rank regularization term module obtains the non-convex low-rank regularization term using a truncated SCAD penalty function. The dynamic graph learning module constructs a dynamic Laplacian matrix through a graph attention neural network. The adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix to construct an adaptive graph wavelet shrinkage regularization term.

[0059] The results module is used to iteratively solve the joint optimization model using the alternating direction multiplier method to obtain the fully repaired industrial operation data.

[0060] In addition, to achieve the above objectives, this application also proposes a storage medium, which is a computer-readable medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the industrial operation data filling and repair method based on dynamic graph learning as described above.

[0061] In addition, to achieve the above objectives, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the industrial operation data filling and repair method based on dynamic graph learning as described above.

[0062] This application constructs a non-convex low-rank regularization term by introducing a truncated SCAD penalty function to protect the main signal energy. It utilizes a graph attention neural network to construct a dynamic graph total variational regularization term to capture the dynamic spatial correlation between variables evolving over time. Furthermore, it combines an adaptive graph wavelet contraction mechanism to distinguish abrupt signals from random noise in the multi-scale frequency domain. Finally, it employs an alternating direction multiplier method for iterative solution. This approach achieves accurate preservation of the non-convex low-rank regularization term, adapts to the dynamic correlation of industrial data, distinguishes between effective abrupt changes and noise, and improves the accuracy and adaptability of data incomplete repair. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a flowchart illustrating the first embodiment of the industrial operation data filling and repair method based on dynamic graph learning in this application.

[0065] Figure 2 This is a flowchart illustrating the second embodiment of the industrial operation data filling and repair method based on dynamic graph learning in this application.

[0066] Figure 3 This is a schematic diagram of the module structure of the industrial operation data filling and repair device based on dynamic graph learning, which is the first embodiment of the industrial operation data filling and repair method based on dynamic graph learning of this application.

[0067] Figure 4 This is a schematic diagram of the equipment structure of the hardware operating environment involved in the industrial operation data filling and repair method based on dynamic graph learning in the embodiments of this application.

[0068] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0069] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0070] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0071] Currently, industrial data imputation and repair mostly adopts the traditional low-rank matrix completion method, which uses the nuclear norm to constrain the low-rank characteristics of the data to fill missing values; at the same time, it combines static graph models to constrain the spatial correlation of the data to help improve the repair accuracy; for noise processing, wavelet shrinkage method with global threshold is used for noise reduction.

[0072] Traditional low-rank matrix completion methods, using kernel norms, penalize all singular values ​​of the data with equal intensity, easily leading to excessive compression of effective non-convex low-rank regularization terms. Static graph models cannot adapt to the dynamic relationships of industrial data as production status changes, making it difficult to accurately capture real-time local features. Wavelet shrinkage methods with global thresholds cannot distinguish between physically consistent abrupt changes and random noise in industrial data, easily resulting in the loss of effective information or residual noise. Therefore, this application proposes a dynamic graph learning-based method for industrial operation data completion and repair to improve the accuracy of data completion and repair.

[0073] Based on the above, this application also provides a method for filling and repairing industrial operation data based on dynamic graph learning, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the industrial operation data filling and repair method based on dynamic graph learning in this application.

[0074] In this embodiment, the industrial operation data filling and repair method based on dynamic graph learning includes steps S10~S30:

[0075] Step S10: Obtain the data to be recovered in the industrial process.

[0076] It should be noted that the data to be restored refers to data collected by sensors and other sensing devices during industrial processes that has been missing, abnormal, or contaminated by noise due to equipment failure, transmission interference, or other factors, and needs to be filled and repaired to restore its integrity and accuracy.

[0077] Specifically, a sensor network deployed in the industrial field collects real-time equipment operating status data, including multi-dimensional process parameters such as temperature, pressure, flow rate, and vibration, and records the data acquisition timestamps and sensor identification information to form a raw data stream. Next, the raw data stream is preprocessed to identify and mark the locations of missing values ​​caused by sensor failure, communication interruption, or electromagnetic interference. An observation index set is constructed to identify the distribution of valid and missing data points, resulting in a data matrix to be recovered. Finally, the data matrix to be recovered and its corresponding observation index set are subjected to subsequent steps to provide a data foundation for building a joint optimization model. This is done to ensure that the subsequent data repair process can accurately distinguish between known observations and the missing values ​​to be estimated, thereby ensuring that the repair results both conform to the constraints of the accuracy of the observed data and effectively restore the inherent structural characteristics of the missing parts.

[0078] Step S20: Construct a joint optimization model based on the data to be recovered.

[0079] It should be noted that the joint optimization model includes a non-convex low-rank regularization module, a dynamic graph learning module, and an adaptive graph wavelet shrinking module. The non-convex low-rank regularization module uses a truncated SCAD penalty function to obtain the non-convex low-rank regularization term. The truncated SCAD penalty function is a non-convex compromise penalty function that applies different intensities of penalty to singular values ​​of the data through a piecewise function form, maintaining a constant penalty when the singular values ​​are large. The dynamic graph learning module constructs a dynamic Laplacian matrix based on the non-convex low-rank regularization term using a graph attention neural network. A graph attention neural network is a graph neural network based on an attention mechanism that can accurately capture the correlation strength between nodes by calculating the attention coefficients between nodes. The adaptive graph wavelet shrinking module performs multi-scale wavelet transform and sparsity constraints based on the dynamic Laplacian matrix. Multi-scale wavelet transform refers to decomposing data into signal components of different scales, i.e., a decomposition process from low-frequency trends to high-frequency details, which can comprehensively capture the features of data in different frequency ranges. Sparse constraints are a type of constraint that limits the number of non-zero elements in data coefficients, making the data exhibit sparse characteristics in a specific domain. This can effectively eliminate redundant information and noise in the data while retaining key and effective signals.

[0080] Furthermore, the steps of obtaining the non-convex low-rank regularization term using the truncated SCAD penalty function in the non-convex low-rank regularization term module include: determining the data fidelity term corresponding to the data to be recovered based on the data to be recovered and the corresponding observation index set;

[0081] Define a truncated SCAD penalty function, which includes a penalty intensity parameter and a preset constant, specifically expressed as follows:

[0082]

[0083] in This indicates the SCAD penalty function to be truncated. For the penalty intensity parameter, This represents a preset constant, typically set to 3.7. Represents singular values;

[0084] Perform singular value decomposition on the data to be recovered, separating the first r principal singular values ​​and the smaller singular values ​​after the (r+1)th singular value;

[0085] No penalty is imposed on the first r principal singular values; the numerical values ​​of the principal singular values ​​are retained.

[0086] Substituting smaller singular values ​​into the truncated SCAD penalty function yields a non-convex low-rank regularization term.

[0087] Combining the data fidelity term and the non-convex low-rank regularization term, we obtain the non-convex low-rank regularization term, which is specifically expressed as follows:

[0088]

[0089] in This represents a non-convex low-rank regularization term. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, This represents a matrix of observed industrial operation data, i.e., data to be recovered, with dimensions of [missing information]. , This refers to the data fidelity item, which represents the data that needs to be recovered. At the observation location and the data to be recovered The degree of closeness Represents the observation operator. Represents the observation index set, Represents the regularization parameter. express The A singular value, This indicates that a penalty is imposed on the singular values ​​from the (r+1)th to the smallest dimension, where no penalty is imposed on the first r singular values. This indicates the preset number of principal components, and represents the rank of the main low-level non-convex low-rank regularization terms retained in the data. express The maximum possible rank depends on the number of rows. Number of columns The smaller value.

[0090] Specifically, data fidelity terms are determined based on the data to be recovered and the corresponding observation index set. This involves calculating the difference between the complete data matrix to be solved and the observation data matrix at the observation location, and taking half the square of the Frobenius norm of this difference to constrain the recovered data to maintain consistency with the original observation values ​​at known observation points. Secondly, a truncated SCAD penalty function is defined, with a penalty intensity parameter controlling the penalty strength and a preset constant controlling the function shape. This function is divided into three piecewise expressions based on the size of the singular values. Singular value decomposition is performed on the data to be recovered, separating the first r principal singular values ​​and the (r+1)th and subsequent smaller singular values. The penalty function applies a linear penalty to singular values ​​less than or equal to the penalty intensity parameter, a quadratic penalty to singular values ​​between the penalty intensity parameter and the product of the penalty intensity parameter and the preset constant, and a constant penalty to singular values ​​greater than the product of the penalty intensity parameter and the preset constant. This is done to avoid excessive contraction of larger singular values, thereby protecting the main signal energy. Then, singular value decomposition is performed on the data to be recovered, separating the principal singular values ​​before the preset number of principal components and the smaller singular values ​​after the preset number of principal components. The principal singular values ​​are not penalized to preserve the main low-convection low-rank regularization term information of the data. The smaller singular values ​​are substituted into the truncated SCAD penalty function for calculation to suppress noise and minor components. The data fidelity term is combined with the sum of the singular values ​​after the truncated SCAD penalty to obtain the non-convex low-rank regularization term. This is done because industrial data has low-rank characteristics and the main energy is concentrated in the first few large singular values. By protecting the principal singular values ​​through the truncation strategy and applying non-convex penalties to the minor singular values, the true non-convex low-rank regularization term of the data can be more accurately approximated, avoiding the excessive shrinkage problem caused by the traditional kernel norm.

[0091] Secondly, the steps of the dynamic graph learning module in constructing a dynamic Laplacian matrix based on the non-convex low-rank regularization term through a graph attention neural network include: inputting the non-convex low-rank regularization term into the graph attention neural network, dynamically calculating the attention coefficients between data nodes; generating an adjacency matrix and the corresponding degree matrix based on the attention coefficients; and calculating the dynamic Laplacian matrix based on the difference between the degree matrix and the adjacency matrix.

[0092] It should be noted that a data node refers to each independent information unit in the data to be recovered, corresponding to the parameter data collected by a single sensor at a specific time step in industrial production. The attention coefficient is a numerical value used to quantify the degree of correlation between data nodes; its magnitude reflects the importance of information interaction between two nodes. The adjacency matrix is ​​a matrix used to describe the connection relationships between data nodes; the values ​​of the matrix elements directly correspond to whether a correlation exists between nodes and the strength of that correlation. The degree matrix is ​​a diagonal matrix whose diagonal elements represent the number of correlations (i.e., node degrees) between corresponding data nodes, with all other elements being zero. Its value is derived from the correlation information of the corresponding nodes in the adjacency matrix.

[0093] Specifically, a non-convex low-rank regularization term is input into the graph attention neural network. The correlation between variables is dynamically captured by calculating attention coefficients between data nodes. Specifically, the feature vector of each node is concatenated with the feature vectors of its neighboring nodes. After mapping through a learnable weight matrix and passing through an activation function and nonlinear transformation, the attention weights between node pairs are obtained. This is done to enable the network to adaptively focus on neighboring nodes that have a greater impact on the current node, thereby dynamically reflecting the complex relationships between variables evolving over time in the industrial process. Secondly, an adjacency matrix is ​​generated based on the attention coefficients. Specifically, the normalized attention coefficients are used as matrix elements to construct a real symmetric matrix describing the connection strength and topological relationships between nodes. A degree matrix is ​​then calculated based on the adjacency matrix. The degree matrix is ​​a diagonal matrix with diagonal elements representing the sum of the connection weights of corresponding nodes. This is done to quantify the centrality and influence of each node in the graph structure. Finally, the dynamic Laplacian matrix is ​​obtained by calculating the difference between the degree matrix and the adjacency matrix. This is done because the Laplacian matrix can effectively characterize the structural characteristics of the graph and the smooth relationship between nodes. Furthermore, since both the adjacency matrix and the degree matrix are dynamically calculated based on the current data, the Laplacian matrix can be adjusted in real time as industrial conditions evolve, thereby providing dynamic graph structure support that fits the current system state for subsequent spatial smoothing constraints and frequency domain analysis.

[0094] Furthermore, the adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix. The steps for constructing the adaptive graph wavelet shrinkage regularization term include: defining a kernel function on the spectral domain corresponding to the dynamic Laplacian matrix and introducing multiple different scaling parameters.

[0095] Based on the kernel function and the multiple scaling parameters, multiple spectral wavelet transform matrices of different scales are generated;

[0096] The data to be recovered is mapped to the spectral wavelet domain by the multiple spectral wavelet transform matrices to obtain the decomposed wavelet coefficients at each scale.

[0097] Using the L1 norm to apply sparsity constraints to the wavelet coefficients at each scale after decomposition, an adaptive graph wavelet shrinkage regularization term is constructed, specifically expressed as:

[0098]

[0099] in This represents the adaptive graph wavelet shrinkage regularization term. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, Indicates the first The wavelet transform matrix of the spectral graph at each scale is generated by the dynamic Laplacian matrix. Denotes the wavelet regularization parameters. This indicates the range from the 1st to the 2nd. Calculate the L1 norm of all wavelet coefficient matrices at each scale and sum them. Indicates the total number of scales.

[0100] It should be noted that the spectral domain refers to the mathematical space constructed based on spectral decomposition using the dynamic Laplacian matrix. It is the fundamental space for spectral wavelet transform, enabling the conversion of nodal-domain features of data into spectral-domain features for analysis. The kernel function, defined in the spectral domain, is a mapping function used to generate the basis functions for the spectral wavelet transform. Its role is to map the eigenvalues ​​of the dynamic Laplacian matrix to wavelet bases with localization properties, supporting multi-scale signal decomposition. Scaling parameters are used to adjust the scale of the spectral wavelet basis functions. Different scaling parameters correspond to wavelet bases in different frequency ranges, and multiple scaling parameters can achieve multi-scale coverage of the data. The spectral wavelet transform matrix is ​​a matrix constructed based on the kernel function and scaling parameters. Essentially, it is a bandpass filter in the spectral domain, capable of mapping the data matrix from the nodal domain to the spectral wavelet domain, achieving multi-scale signal decomposition. The spectral wavelet domain is the space where the signal after the spectral wavelet transform resides. Data in this space is presented in the form of wavelet coefficients, with wavelet coefficients at different scales corresponding to different frequency feature components of the data. Wavelet coefficients are coefficients obtained after data undergoes spectral wavelet transform. They are a specific representation of the data in the spectral wavelet domain. Wavelet coefficients at different scales correspond to the low-frequency trend and high-frequency details of the data, respectively.

[0101] Specifically, a kernel function is defined in the spectral domain corresponding to the dynamic Laplacian matrix. This kernel function characterizes the signal attenuation in the frequency domain, and multiple scaling parameters are introduced to control the frequency bandwidth. Each scaling parameter corresponds to a specific frequency resolution. This is done to construct a multi-scale analysis framework in the spectral domain, enabling the simultaneous capture of low-frequency trend components and high-frequency detail components in the data. Secondly, based on the kernel function and multiple scaling parameters, multiple spectral wavelet transform matrices at different scales are generated by applying the kernel function to the eigenvalues ​​of the dynamic Laplacian matrix. Each transform matrix corresponds to a specific frequency band, serving as a bandpass filter in the spectral domain. This is done to ensure that the wavelet basis functions can be adjusted in real time as the correlation between industrial process variables evolves, guaranteeing that the frequency domain analysis always reflects the current system state. Then, the data to be recovered is mapped to the spectral wavelet domain using multiple spectral wavelet transform matrices. Matrix multiplication is performed between the transform matrix at each scale and the data to be recovered to obtain the decomposed wavelet coefficients at each scale. These wavelet coefficients contain multi-resolution information from coarse to fine scales. This is done to transform the time-domain signal into a graph frequency domain representation with clear physical meaning, facilitating the subsequent distinction between abrupt signals conforming to physical laws and random noise. Finally, sparsity constraints are applied to the decomposed wavelet coefficients at each scale using the first norm. Specifically, the absolute values ​​of all elements in the wavelet coefficient matrix at each scale are calculated, and the results at each scale are then weighted and summed to construct an adaptive graph wavelet shrinkage regularization term. This is because real industrial signals typically exhibit sparsity in the graph wavelet domain, meaning energy is concentrated in a few large-amplitude coefficients. Sparsity constraints adaptively shrink coefficients with smaller amplitudes, representing random noise, to zero during the optimization process, while retaining large-amplitude coefficients representing real abrupt signals, thereby achieving refined spatiotemporal denoising and restoration at multiple scales.

[0102] Step S30: The joint optimization model is iteratively solved using the alternating direction multiplier method to obtain the fully repaired industrial operation data.

[0103] It should be noted that the alternating direction multiplier method is a numerical iterative algorithm for solving large-scale optimization problems. Its core is to decompose a complex joint optimization problem into multiple simpler subproblems by alternately optimizing multiple variables, solving them one by one, while using multiplier terms to ensure the consistency of solutions to each subproblem. The joint optimization model refers to a mathematical model that integrates data fidelity terms, non-convex low-rank regularization terms, and adaptive graph wavelet shrinkage regularization terms. Its goal is to obtain a complete and accurate industrial operation data matrix while satisfying various constraints. Completely restored industrial operation data refers to industrial operation data that, after iterative solving using the joint optimization model, has missing values ​​filled, noise removed, and its true structure and characteristics restored, accurately reflecting the actual state of the industrial production process.

[0104] Specifically, three auxiliary variables are introduced into the joint optimization model, corresponding to the data to be recovered itself, the product of the dynamic Laplacian matrix and the data to be recovered, and the product of the spectral wavelet transform matrix and the data to be recovered, respectively. An augmented Lagrangian function is constructed based on the three auxiliary variables to decompose the joint optimization problem into multiple sub-problems. Some variables are alternately fixed, and the sub-problems about the data to be recovered and the three auxiliary variables are solved in sequence, while the Lagrangian multipliers are updated. The above iterative process is repeated until the change in variables is less than the preset convergence threshold, and the fully repaired industrial operation data is output.

[0105] This embodiment introduces a truncated SCAD penalty function to construct a non-convex low-rank regularization term to protect the main signal energy. It utilizes a graph attention neural network to construct a dynamic graph total variational regularization term to capture the dynamic spatial correlation between variables evolving over time. Furthermore, it combines an adaptive graph wavelet contraction mechanism to distinguish abrupt signals from random noise in the multi-scale frequency domain. Finally, it uses the alternating direction multiplier method for iterative solution. This approach achieves accurate preservation of the non-convex low-rank regularization term, adapts to the dynamic correlation of industrial data, distinguishes between valid abrupt changes and noise, and improves the accuracy and adaptability of data incomplete repair.

[0106] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in Embodiment 1 above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 2 The industrial operation data filling and repair method based on dynamic graph learning, step S30, further includes steps S201 to S206:

[0107] Step S201: Based on the structure of the joint optimization model, introduce the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable.

[0108] It should be noted that the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable correspond to the data to be recovered, the product of the dynamic Laplacian matrix and the data to be recovered, and the product of the wavelet transform matrix of the spectrum at each scale and the data to be recovered, respectively.

[0109] Specifically, based on the structure of the joint optimization model, a first auxiliary variable is introduced. This first auxiliary variable is set as a matrix with the same dimension as the data to be recovered, and an equality constraint relationship is established between the first auxiliary variable and the data to be recovered. This is done to separate the non-convex low-rank regularization term from the original objective function, allowing it to be independently processed for singular value thresholding, thereby avoiding complex non-convex optimization operations directly on the main optimization variable. Secondly, a second auxiliary variable is introduced. This second auxiliary variable is set as a substitute variable for the product of the dynamic Laplacian matrix and the data to be recovered, and an equality constraint relationship is established between the second auxiliary variable and the product. This is because the product of the dynamic Laplacian matrix and the data to be recovered involves complex graph structure operations. By introducing an auxiliary variable, the total variational regularization term of the dynamic graph can be transformed into a first norm constraint on the auxiliary variable, thereby efficiently solving the spatial smoothing problem using soft thresholding operations. Then, a third auxiliary variable is introduced, which is set as a set of substitute variables for the product of the spectral wavelet transform matrix and the data to be recovered at each scale. Each scale corresponds to a sub-auxiliary variable, and an equality constraint relationship is established between each sub-auxiliary variable and the product of the spectral wavelet transform matrix and the data to be recovered at the corresponding scale. This is done because multi-scale spectral wavelet transform involves matrix operations in multiple different frequency bands. By introducing auxiliary variables, the adaptive graph wavelet shrinkage regularization term at each scale can be decoupled into an independent sparse constraint subproblem, which is convenient for parallel processing and efficient optimization.

[0110] In step S202, the augmented Lagrangian function is constructed by combining the first auxiliary variable, the second auxiliary variable, the third auxiliary variable, the non-convex low-rank regularization term, the dynamic Laplacian matrix, and the adaptive graph wavelet shrinkage regularization term.

[0111] Specifically, the data fidelity term is used as a fundamental term of the augmented Lagrange function. This involves calculating half the square of the Frobenius norm of the complete data matrix to be solved and the observed data matrix at the observation location. This ensures that the restored data remains consistent with the original observations at known observation points, maintaining data authenticity. Secondly, the non-convex low-rank regularization term is transformed into a penalty term for the first auxiliary variable. Specifically, this is the truncated smooth shear absolute deviation penalty function value of the first auxiliary variable, along with a first and second quadratic penalty term for the difference between the first auxiliary variable and the data to be restored, and the inner product term of the corresponding first Lagrange multiplier and the difference. This decouples the non-convex low-rank constraint into an independent subproblem, facilitating efficient solution through singular value thresholding. Then, the dynamic graph total variational regularization term is transformed into a constraint term about the second auxiliary variable. Specifically, this involves multiplying the first norm of the second auxiliary variable by a preset first weighting coefficient, and adding a second quadratic penalty term for the difference between the second auxiliary variable and the product of the dynamic Laplacian matrix and the data to be recovered, along with an inner product term of the corresponding second Lagrange multiplier and the difference. This is done to transform the spatial smoothness constraint into a sparse optimization problem for the auxiliary variable, using soft thresholding contraction to achieve local smoothness constraints. Next, the adaptive graph wavelet contraction regularization term is transformed into a multi-scale constraint term about the third auxiliary variable. Specifically, this involves summing the first norm of each scale sub-auxiliary variable multiplied by a preset second weighting coefficient, and adding a third quadratic penalty term for the difference between the sub-auxiliary variable and the product of the corresponding spectral wavelet transform matrix and the data to be recovered, along with an inner product term of the corresponding third Lagrange multiplier and the difference, for each scale. This is done to decouple the multi-scale frequency domain analysis into sparse constraint sub-problems independent of each scale, achieving refined noise suppression and signal preservation. Finally, all the above terms are linearly combined to construct the complete augmented Lagrangian function. The weights of each quadratic penalty term are controlled by the first, second, and third penalty parameters. This is done to form a unified optimization framework, so that the alternating direction multiplier method can gradually approach the optimal solution that satisfies all constraints by iteratively updating each variable and multiplier.

[0112] Step S203: Fix the first auxiliary variable, the second auxiliary variable, the third auxiliary variable and the Lagrange multipliers of the augmented Lagrange function, solve the subproblem about the data to be recovered, and obtain the updated data value through numerical calculation methods.

[0113] It should be noted that the specific formula is expressed as follows:

[0114]

[0115] in, Indicates the updated data value. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, This represents a matrix of observed industrial operation data, i.e., data to be recovered, with dimensions of [missing information]. , This refers to the data fidelity item, which represents the data that needs to be recovered. At the observation location and the data to be recovered The degree of closeness Represents the observation operator. Represents the observation index set, Indicates the first penalty parameter. Indicates the first auxiliary variable. Represents the first Lagrange multiplier. Indicates the second penalty parameter. Let Laplacian matrix be the dynamically generated matrix in the k-th iteration. Indicates the second auxiliary variable. Indicates the second Lagrange multiplier. This represents the third penalty parameter. Indicates the third auxiliary variable. Indicates the third Lagrange multiplier. Indicates the total number of scales. In the k-th iteration, the th... The spectral wavelet transform matrix at each scale includes a first Lagrange multiplier, a second Lagrange multiplier, and a third Lagrange multiplier, which correspond to the data to be recovered, the product of the dynamic Laplacian matrix and the data to be recovered, and the product of the spectral wavelet transform matrix at each scale and the data to be recovered, respectively.

[0116] Specifically, by fixing the first auxiliary variable, the second auxiliary variable, the third auxiliary variable, and the Lagrange multipliers of the augmented Lagrange function, the terms in the augmented Lagrange function that are only related to the data to be recovered are retained, while the constant terms that are not related to the fixed variables are ignored, and the objective function of the subproblem about the data to be recovered is obtained. This is done in order to simplify the complex multivariate optimization problem into a quadratic optimization problem that is only about the data matrix, so as to facilitate efficient solution. Secondly, the objective function of the subproblem is differentiated with respect to the data to be recovered. Specifically, the gradients of the data fidelity term, the first and second quadratic penalty terms, the second and third quadratic penalty terms, and the third quadratic penalty term are calculated respectively. The gradient of the data fidelity term is the projection of the difference between the data to be recovered and the observed data at the observation location. The gradient of the first and second quadratic penalty terms is the difference between the data to be recovered and the combined value of the first auxiliary variable and the first Lagrange multiplier multiplied by the first penalty parameter. The gradient of the second quadratic penalty term is the product of the transpose of the dynamic Laplace matrix and the data to be recovered, minus the difference between the second auxiliary variable and the combined value of the second Lagrange multiplier multiplier, and then multiplied by the preset second penalty parameter. The gradient of the third quadratic penalty term is the sum of the transpose of the wavelet transform matrix of the spectrum at each scale, the product of the wavelet transform matrix of the spectrum at the corresponding scale and the data to be recovered, minus the difference between the combined value of the third auxiliary variable and the third Lagrange multiplier multiplier at the corresponding scale, and then multiplied by the preset third penalty parameter. This is done to obtain the optimality condition of the objective function and establish a system of linear equations about the data to be recovered. Then, the gradient terms are merged and rearranged to construct a linear matrix equation for the data to be recovered. The left side of the equation contains a linear combination of the quadratic terms of the identity matrix, the dynamic Laplacian matrix, and the quadratic terms of the wavelet transform matrices of the spectrograms at each scale. The right side contains the sum of the observed data projection terms, the combination of the first auxiliary variable and the first Lagrange multiplier, the combination of the dynamic Laplacian matrix and the second auxiliary variable and the second Lagrange multiplier, and the sum of the combination of the wavelet transform matrices of the spectrograms at each scale and the combination of the third auxiliary variable and the third Lagrange multiplier at the corresponding scale. This is done to transform the complex gradient conditions into a standard linear algebra problem. Finally, the linear matrix equation is solved using numerical methods. Specifically, the large-scale sparse linear system is solved iteratively using the conjugate gradient method or the preprocessed conjugate gradient method, or the analytical solution of the small-scale system is directly calculated by matrix inversion to obtain the updated data values. This is because the linear equation system usually has the characteristics of being large-scale, sparse, and symmetric positive definite, making it suitable for solving using efficient numerical linear algebra methods. This ensures computational accuracy while controlling computational complexity, enabling rapid updates of the data matrix.

[0117] Step S204: Fix the data update value and Lagrange multipliers, and solve the subproblems of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable in sequence to obtain the update values ​​of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable, respectively.

[0118] Furthermore, with fixed data update values, second auxiliary variables, third auxiliary variables, first Lagrange multipliers, second Lagrange multipliers, and third Lagrange multipliers, an optimization problem is constructed for the first auxiliary variable subproblem, which includes a truncated SCAD penalty term, a preset first regularization parameter, and a term related to the data update value and the first Lagrange multiplier.

[0119] Solve the subproblem of the first auxiliary variable to obtain the updated value of the first auxiliary variable. The specific formula is as follows:

[0120]

[0121] in, This indicates the updated value of the first auxiliary variable. This represents the first auxiliary variable currently being updated. This represents the first regularization parameter. This indicates the SCAD penalty function to be truncated. Indicates the first penalty parameter. Indicates the updated data value. Represents the first Lagrange multiplier. Describe the Frobenius norm. This represents the relevant terms of the first Lagrange multiplier. This represents the function that takes the first minimum value.

[0122] Given fixed data update values, a first auxiliary variable, a third auxiliary variable, a first Lagrange multiplier, a second Lagrange multiplier, and a third Lagrange multiplier, for the subproblem of the second auxiliary variable, construct an optimization problem that includes an L1 norm term, a preset second regularization parameter, a dynamic Laplacian matrix product term corresponding to the data update value, and a related term of the second Lagrange multiplier.

[0123] Solve the subproblem of the second auxiliary variable to obtain the updated value of the second auxiliary variable. The specific formula is as follows:

[0124]

[0125] in This indicates the updated value of the second auxiliary variable. This represents the second regularization parameter. This represents the second auxiliary variable currently being updated. Indicates the second penalty parameter. Indicates the updated data value. Indicates the second Lagrange multiplier. Describe the Frobenius norm. This represents the relevant terms of the second Lagrange multiplier. This represents the function that takes the second minimum value. Let represent the dynamic Laplacian matrix generated in the k-th iteration. Represents the L1 norm;

[0126] Given fixed data update values, a first auxiliary variable, a second auxiliary variable, a first Lagrange multiplier, a second Lagrange multiplier, and a third Lagrange multiplier, an optimization problem is constructed for the subproblem of the third auxiliary variable. This problem includes an L1 norm term, a preset third regularization parameter, a product term of the wavelet transform matrix of the spectral graph at each scale corresponding to the data update value, and a related term of the third Lagrange multiplier.

[0127] Solving the subproblem of the third auxiliary variable yields the updated value of the third auxiliary variable, as shown in the following formula:

[0128]

[0129] in This indicates the updated value of the third auxiliary variable. This represents the third regularization parameter. This represents the third auxiliary variable currently being updated. This represents the third penalty parameter. Indicates the updated data value. Indicates the third Lagrange multiplier. Describe the Frobenius norm. This represents the relevant term of the third Lagrange multiplier. This represents the third minimum value function. Indicates the total number of scales. In the k-th iteration, the th... Spectral wavelet transform matrix at each scale This represents the L1 norm.

[0130] Step S205: Based on the deviations between the updated data values ​​and the updated values ​​of the first, second, and third auxiliary variables, update the corresponding Lagrange multipliers respectively to obtain the updated multipliers.

[0131] It should be noted that the specific formula is expressed as follows:

[0132]

[0133]

[0134]

[0135] in This represents the updated first Lagrange multiplier. This indicates the updated value of the first auxiliary variable. This represents the updated second Lagrange multiplier. This indicates the updated value of the second auxiliary variable. This represents the updated third Lagrange multiplier. This indicates the updated value of the third auxiliary variable.

[0136] Step S206 continues until the updated data values, the first auxiliary variable update value, the second auxiliary variable update value, and the third auxiliary variable update value meet the preset convergence conditions, thus obtaining the fully repaired industrial operation data.

[0137] It should be noted that the calculation process involves calculating the first deviation value between the updated data value and the previous data value; calculating the second, third, and fourth deviation values ​​between the updated values ​​of the first, second, and third auxiliary variables and their corresponding auxiliary variables from the previous round; and stopping the iteration when all four deviation values ​​are less than a preset convergence threshold, and using the current updated data value as the fully repaired industrial operation data.

[0138] Specifically, the first deviation between the updated data value and the previous data value is calculated by taking the Frobenius norm of the difference between the updated data value and the previous data value, or by taking the maximum absolute value of each element of the difference. This is done to quantify the degree of change of the data matrix between two adjacent iterations and to determine whether the main optimization variable tends to stabilize. Secondly, the second deviation between the updated value of the first auxiliary variable and the previous first auxiliary variable is calculated by taking the Frobenius norm of the difference between the two. The third deviation between the updated value of the second auxiliary variable and the previous second auxiliary variable is calculated by taking the first norm or Frobenius norm of the difference between the two. The fourth deviation between the updated value of the third auxiliary variable and the previous third auxiliary variable is calculated by taking the Frobenius norm of the difference for each scale sub-auxiliary variable and then summing or taking the maximum value. This is done to comprehensively monitor the convergence state of all auxiliary variables, ensuring that the constraints are satisfied and the solutions to each subproblem tend to be consistent. Then, the first, second, third, and fourth deviation values ​​are compared with preset convergence thresholds. These thresholds are set based on data accuracy requirements and computational resource limitations to establish an objective iteration termination criterion, avoiding premature stopping leading to insufficient solution quality or premature stopping resulting in wasted computational resources. Finally, when all four deviation values ​​are less than the preset convergence thresholds, the alternating direction multiplier method is considered to have reached convergence, the iteration process is stopped, and the current updated data value is output as the fully repaired industrial operation data. This ensures that the final output repaired data simultaneously satisfies data fidelity, low-rank structure, spatial smoothness, and multi-scale sparsity constraints, achieving high-precision and robust industrial operation data filling and repair.

[0139] This embodiment decouples the joint optimization model by introducing first, second, and third auxiliary variables, constructs an augmented Lagrangian function, and iteratively solves it using the alternating direction multiplier method. The data update subproblem is solved using numerical computation with fixed auxiliary variables, and each auxiliary variable subproblem is solved sequentially with fixed data update values. The Lagrangian multipliers are updated according to the deviation until the convergence condition is met. This method protects the main signal energy by truncating and smoothing the absolute deviation penalty, captures dynamic spatial correlations using a graph attention neural network, and distinguishes between physical mutations and random noise using multi-scale spectral wavelet transform. It effectively solves the technical defects of traditional methods, such as over-compressing the global structure, ignoring dynamic correlations, and difficulty in fine-grained denoising, achieving high-precision and robust data restoration in complex industrial environments.

[0140] Based on the first embodiment of this application, this application also provides an industrial operation data filling and repair device based on dynamic graph learning. Please refer to... Figure 3 The device includes:

[0141] The acquisition module 10 is used to acquire the data to be recovered in the industrial process and the corresponding observation index set.

[0142] The model building module 20 is used to build a joint optimization model based on the data to be recovered. The joint optimization model includes a non-convex low-rank regularization term module, a dynamic graph learning module, and an adaptive graph wavelet shrinkage module. The non-convex low-rank regularization term module obtains the non-convex low-rank regularization term by using the truncated SCAD penalty function. The dynamic graph learning module constructs a dynamic Laplacian matrix through a graph attention neural network. The adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix to construct an adaptive graph wavelet shrinkage regularization term.

[0143] Result module 30 is used to iteratively solve the joint optimization model using the alternating direction multiplier method to obtain the fully repaired industrial operation data.

[0144] The industrial operation data filling and repair device based on dynamic graph learning provided in this application, employing the industrial operation data filling and repair method based on dynamic graph learning in the above embodiments, can solve the technical problem of how to improve the accuracy of data filling and repair. Compared with the prior art, the beneficial effects of the industrial operation data filling and repair device based on dynamic graph learning provided in this application are the same as the beneficial effects of the industrial operation data filling and repair method based on dynamic graph learning provided in the above embodiments, and other technical features in the industrial operation data filling and repair device based on dynamic graph learning are the same as the features disclosed in the methods of the above embodiments, and will not be repeated here.

[0145] This application provides an industrial operation data filling and repair device based on dynamic graph learning. The industrial operation data filling and repair device based on dynamic graph learning includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the industrial operation data filling and repair method based on dynamic graph learning in the above embodiment 1.

[0146] The following is for reference. Figure 4 This document illustrates a structural schematic diagram of an industrial operation data filling and repair device based on dynamic graph learning, suitable for implementing embodiments of this application. The industrial operation data filling and repair device based on dynamic graph learning in the embodiments of this application may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 4 The industrial operation data filling and repair device based on dynamic graph learning shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0147] like Figure 4As shown, the industrial operation data filling and repair device based on dynamic graph learning may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage device 1003 into a random access memory (RAM) 1004. The RAM 1004 also stores various programs and data required for the operation of the industrial operation data filling and repair device based on dynamic graph learning. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following can be connected to I / O interface 1006: input devices 1007 including, for example, touchscreens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. Communication device 1009 allows the dynamic graph learning-based industrial operation data filling and repair equipment to wirelessly or wiredly communicate with other devices to exchange data. Although various dynamic graph learning-based industrial operation data filling and repair equipment are shown in the figures, it should be understood that implementation or possession of all shown is not required. More or fewer may be implemented alternatively.

[0148] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0149] The industrial operation data filling and repair device based on dynamic graph learning provided in this application, employing the industrial operation data filling and repair method based on dynamic graph learning in the above embodiments, can solve the technical problem of how to improve the accuracy of data filling and repair. Compared with the prior art, the beneficial effects of the industrial operation data filling and repair device based on dynamic graph learning provided in this application are the same as the beneficial effects of the industrial operation data filling and repair method based on dynamic graph learning provided in the above embodiments, and other technical features in this industrial operation data filling and repair device based on dynamic graph learning are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0150] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0151] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0152] This application provides a computer-readable medium having computer-readable program instructions (i.e., a computer program) stored thereon, the computer-readable program instructions being used to execute the industrial operation data filling and repair method based on dynamic graph learning in the above embodiments.

[0153] The computer-readable medium provided in this application may be, for example, a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor devices, or any combination thereof. More specific examples of computer-readable media may include, but are not limited to: electrical connections with one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable medium may be any tangible medium containing or storing a program that can be executed by instructions, used by a device, or used in conjunction with it. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0154] The aforementioned computer-readable medium may be included in an industrial operation data filling and repair device based on dynamic graph learning; or it may exist independently and not assembled into an industrial operation data filling and repair device based on dynamic graph learning.

[0155] The aforementioned computer-readable medium carries one or more programs that, when executed by the dynamic graph learning-based industrial operation data filling and repair device, enable the dynamic graph learning-based industrial operation data filling and repair device to write computer program code for performing the operations of this application in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—and conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0156] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and computer program products according to various embodiments of this application. In this regard, all blocks in the flowcharts or block diagrams may represent a module, segment, or portion of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that all blocks in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using dedicated hardware-based implementations that perform the specified functions or operations, or using a combination of dedicated hardware and computer instructions.

[0157] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0158] The readable medium provided in this application is a computer-readable medium, which stores computer-readable program instructions (i.e., a computer program) for executing the above-described industrial operation data filling and repair method based on dynamic graph learning, and can solve the technical problem of how to improve the accuracy of data filling and repair. Compared with the prior art, the beneficial effects of the computer-readable medium provided in this application are the same as the beneficial effects of the industrial operation data filling and repair method based on dynamic graph learning provided in the above embodiments, and will not be repeated here.

[0159] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method for filling and repairing industrial operation data based on dynamic graph learning.

[0160] The computer program product provided in this application can solve the technical problem of how to improve the accuracy of data filling and repair. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the industrial operation data filling and repair method based on dynamic graph learning provided in the above embodiments, and will not be repeated here.

[0161] The above description is only a part of the embodiments of this application and does not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. A method for filling and repairing industrial operation data based on dynamic graph learning, characterized in that, The method includes: Acquire data to be recovered from an industrial process, including data such as temperature, pressure, flow rate, and vibration. A joint optimization model is constructed based on the data to be recovered. The joint optimization model includes a non-convex low-rank regularization term module, a dynamic graph learning module, and an adaptive graph wavelet shrinkage module. The non-convex low-rank regularization term module obtains the non-convex low-rank regularization term using a truncated SCAD penalty function. The dynamic graph learning module constructs a dynamic Laplacian matrix based on the non-convex low-rank regularization term using a graph attention neural network. The adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix to construct an adaptive graph wavelet shrinkage regularization term. The joint optimization model is iteratively solved using the alternating direction multiplier method to obtain the fully repaired industrial operation data; The steps for obtaining the non-convex low-rank regularization term using the truncated SCAD penalty function in the non-convex low-rank regularization term module include: Based on the data to be recovered and the corresponding observation index set, determine the data fidelity item corresponding to the data to be recovered; Define a truncated SCAD penalty function, which includes a penalty intensity parameter and a preset constant, specifically expressed as follows: in This indicates the SCAD penalty function to be truncated. For the penalty intensity parameter, This represents a preset constant. Represents singular values; Singular value decomposition is performed on the data to be recovered to separate the first r main singular values ​​and the smaller singular values ​​after the (r+1)th singular value. No penalty is imposed on the first r major singular values; the numerical values ​​of the major singular values ​​are retained. Substituting the smaller singular value into the truncated SCAD penalty function for calculation, a non-convex low-rank regularization term is obtained. Combining the data fidelity term and the non-convex low-rank regularization term yields the non-convex low-rank regularization term, specifically expressed as follows: in This represents a non-convex low-rank regularization term. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, This represents a matrix of observed industrial operation data, i.e., data to be recovered, with dimensions of [missing information]. , This refers to the data fidelity item, which represents the data that needs to be recovered. At the observation location and the data to be recovered The degree of closeness, Represents the observation operator. Represents the observation index set, Represents the regularization parameter. express The A singular value, This indicates that a penalty is imposed on the singular values ​​from the (r+1)th to the smallest dimension, where no penalty is imposed on the first r singular values. This indicates the preset number of principal components, and represents the rank of the main low-level non-convex low-rank regularization terms retained in the data. express The maximum possible rank depends on the number of rows. Number of columns The smaller value.

2. The method as described in claim 1, characterized in that, The steps of the dynamic graph learning module in constructing a dynamic Laplacian matrix based on the non-convex low-rank regularization term using a graph attention neural network include: The non-convex low-rank regularization term is input into the graph attention neural network to dynamically calculate the attention coefficients between data nodes. Generate an adjacency matrix and a corresponding degree matrix based on the attention coefficients; The dynamic Laplace matrix is ​​obtained by calculating the difference between the degree matrix and the adjacency matrix.

3. The method as described in claim 1, characterized in that, The adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix, and the steps for constructing the adaptive graph wavelet shrinkage regularization term include: A kernel function is defined on the spectral domain corresponding to the dynamic Laplacian matrix, and several different scaling parameters are introduced; Based on the kernel function and the multiple scaling parameters, multiple spectral wavelet transform matrices of different scales are generated; The data to be recovered is mapped to the spectral wavelet domain by the multiple spectral wavelet transform matrices to obtain the decomposed wavelet coefficients at each scale. Using the L1 norm to apply sparsity constraints to the wavelet coefficients at each scale after decomposition, an adaptive graph wavelet shrinkage regularization term is constructed, specifically expressed as: in This represents the adaptive graph wavelet shrinkage regularization term. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, Indicates the first The wavelet transform matrix of the spectral graph at each scale is generated by the dynamic Laplace matrix. Denotes the wavelet regularization parameters. This indicates the range from the 1st to the 2nd. Calculate the L1 norm of all wavelet coefficient matrices at each scale and sum them. Indicates the total number of scales.

4. The method as described in claim 1, characterized in that, The step of iteratively solving the joint optimization model using the alternating direction multiplier method to obtain the fully repaired industrial operation data includes: Based on the structure of the joint optimization model, a first auxiliary variable, a second auxiliary variable, and a third auxiliary variable are introduced, wherein the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable correspond to the data to be recovered, the product of the dynamic Laplacian matrix and the data to be recovered, and the product of the wavelet transform matrix of the spectrum at each scale and the data to be recovered, respectively. An augmented Lagrangian function is constructed by combining the first auxiliary variable, the second auxiliary variable, the third auxiliary variable, the non-convex low-rank regularization term, the dynamic Laplacian matrix, and the adaptive graph wavelet shrinkage regularization term. By fixing the first auxiliary variable, the second auxiliary variable, the third auxiliary variable, and the Lagrange multipliers of the augmented Lagrange function, a subproblem concerning the data to be recovered is solved. The updated data value is obtained through numerical calculation, as specifically expressed by the following formula: in, Indicates the updated data value. This represents the complete industrial operation data matrix to be solved, i.e., the data that needs to be recovered, with dimensions of [missing information]. , For the number of sensors, For time step, This represents a matrix of observed industrial operation data, i.e., data to be recovered, with dimensions of [missing information]. , This refers to the data fidelity item, which represents the data that needs to be recovered. At the observation location and the data to be recovered The degree of closeness, Represents the observation operator. Represents the observation index set, Indicates the first penalty parameter. Indicates the first auxiliary variable. Represents the first Lagrange multiplier. This represents the second penalty parameter. Let Laplacian matrix be the dynamically generated matrix in the k-th iteration. Indicates the second auxiliary variable. Indicates the second Lagrange multiplier. This represents the third penalty parameter. Indicates the third auxiliary variable. Indicates the third Lagrange multiplier. Indicates the total number of scales. In the k-th iteration, the first... The spectral wavelet transform matrix at each scale, wherein the Lagrange multipliers include a first Lagrange multiplier, a second Lagrange multiplier, and a third Lagrange multiplier, which correspond to the data to be recovered, the product of the dynamic Laplacian matrix and the data to be recovered, and the product of the spectral wavelet transform matrix at each scale and the data to be recovered, respectively. By fixing the data update value and the Lagrange multiplier, the subproblems of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable are solved in sequence to obtain the update values ​​of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable, respectively. Based on the deviations between the updated data value and the updated values ​​of the first, second, and third auxiliary variables, the corresponding Lagrange multipliers are updated respectively to obtain the updated multipliers, as expressed by the following formula: in This represents the updated first Lagrange multiplier. This indicates the updated value of the first auxiliary variable. This represents the updated second Lagrange multiplier. This indicates the updated value of the second auxiliary variable. This represents the updated third Lagrange multiplier. This indicates the updated value of the third auxiliary variable; The complete and repaired industrial operation data is obtained when the updated data value, the updated value of the first auxiliary variable, the updated value of the second auxiliary variable, and the updated value of the third auxiliary variable meet the preset convergence conditions.

5. The method as described in claim 4, characterized in that, The steps of fixing the data update value and the Lagrange multiplier, and sequentially solving the subproblems of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable to obtain the update values ​​of the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable, respectively, include: With the data update value, second auxiliary variable, third auxiliary variable, first Lagrange multiplier, second Lagrange multiplier, and third Lagrange multiplier fixed, an optimization problem is constructed for the first auxiliary variable subproblem, which includes a truncated SCAD penalty term, a preset first regularization parameter, and a term related to the data update value and the first Lagrange multiplier. Solve the first auxiliary variable subproblem to obtain the updated value of the first auxiliary variable; With the data update value, first auxiliary variable, third auxiliary variable, first Lagrange multiplier, second Lagrange multiplier, and third Lagrange multiplier fixed, an optimization problem is constructed for the second auxiliary variable subproblem, which includes an L1 norm term, a preset second regularization parameter, a dynamic Laplacian matrix product term corresponding to the data update value, and a related term of the second Lagrange multiplier. Solve the subproblem of the second auxiliary variable to obtain the updated value of the second auxiliary variable; With the data update value, first auxiliary variable, second auxiliary variable, first Lagrange multiplier, second Lagrange multiplier, and third Lagrange multiplier fixed, an optimization problem is constructed for the subproblem of the third auxiliary variable, which includes an L1 norm term, a preset third regularization parameter, a product term of wavelet transform matrices of the spectral graphs at each scale corresponding to the data update value, and a related term of the third Lagrange multiplier. Solve the subproblem of the third auxiliary variable to obtain the updated value of the third auxiliary variable.

6. The method as described in claim 4, characterized in that, The step of obtaining the fully repaired industrial operation data until the updated data value, the updated value of the first auxiliary variable, the updated value of the second auxiliary variable, and the updated value of the third auxiliary variable satisfy the preset convergence condition includes: Calculate the first deviation between the updated data value and the previous data value; Calculate the second, third, and fourth deviation values ​​of the updated values ​​of the first, second, and third auxiliary variables and their corresponding auxiliary variables from the previous round; When the first deviation value, the second deviation value, the third deviation value, and the fourth deviation value are all less than the preset convergence threshold, the iteration stops, and the current data update value is taken as the fully repaired industrial operation data.

7. An industrial operation data filling and repair device based on dynamic graph learning, characterized in that, The apparatus is applied to the industrial operation data filling and repair method based on dynamic graph learning as described in any one of claims 1-6, and the apparatus comprises: The acquisition module is used to acquire data to be recovered in the industrial process, including temperature, pressure, flow rate, and vibration. The model building module is used to construct a joint optimization model based on the data to be recovered. The joint optimization model includes a non-convex low-rank regularization term module, a dynamic graph learning module, and an adaptive graph wavelet shrinkage module. The non-convex low-rank regularization term module obtains the non-convex low-rank regularization term using a truncated SCAD penalty function. The dynamic graph learning module constructs a dynamic Laplacian matrix through a graph attention neural network. The adaptive graph wavelet shrinkage module performs multi-scale wavelet transform and sparse constraints based on the dynamic Laplacian matrix to construct an adaptive graph wavelet shrinkage regularization term. The module is also used to construct an adaptive graph wavelet shrinkage regularization term based on the data to be recovered and the corresponding... The observation index set determines the data fidelity term corresponding to the data to be recovered; a truncated SCAD penalty function is defined, which includes a penalty strength parameter and a preset constant; singular value decomposition is performed on the data to be recovered to separate the first r principal singular values ​​and the (r+1)th and subsequent smaller singular values; no penalty is applied to the first r principal singular values, and the values ​​of the principal singular values ​​are retained; the smaller singular values ​​are substituted into the truncated SCAD penalty function for calculation to obtain a non-convex low-rank regularization term; the data fidelity term and the non-convex low-rank regularization term are combined to obtain a non-convex low-rank regularization term. The results module is used to iteratively solve the joint optimization model using the alternating direction multiplier method to obtain the fully repaired industrial operation data.

8. An industrial operation data filling and repair device based on dynamic graph learning, characterized in that, The device includes: a memory, a processor, and an industrial operation data filling and repair program based on dynamic graph learning stored on the memory and running on the processor, the industrial operation data filling and repair program based on dynamic graph learning configured to implement the steps of the industrial operation data filling and repair method based on dynamic graph learning as described in any one of claims 1-6.

9. A storage medium, characterized in that, The storage medium stores an industrial operation data filling and repair program based on dynamic graph learning. When the industrial operation data filling and repair program based on dynamic graph learning is executed by the processor, it implements the steps of the industrial operation data filling and repair method based on dynamic graph learning as described in any one of claims 1-6.

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