An industrial data modeling method based on fuzzy-migration random configuration network

Abstract

This invention provides an industrial data modeling method based on a fuzzy-transfer stochastic configuration network, belonging to the field of industrial process modeling. The method includes: acquiring historical datasets of industrial sensors in the source domain; obtaining the fuzzy layer parameters, enhancement layer parameters, output weights, and joint feature matrix of the source domain model by using a fuzzy stochastic configuration network model; acquiring sensor data in the target domain under new operating conditions; performing spatial mapping using a granular fuzzy domain adaptation strategy to obtain mapped fuzzy feature vectors; combining these with the frozen source domain model and employing a target domain transfer adaptation strategy to transfer the parameters of the frozen source domain model to the target domain, obtaining the target domain model; inputting real-time sensor data under the new operating conditions; and outputting predicted industrial data values ​​for future time periods. This invention solves the problems of existing industrial process modeling methods that struggle to simultaneously achieve strong nonlinear fitting capabilities, fuzzy uncertainty representation capabilities, and adaptability under small sample operating condition drift.

Description

Technical Field

[0001] This invention belongs to the field of industrial process modeling, and in particular relates to an industrial data modeling method based on fuzzy-transfer stochastic configuration networks. Background Technology

[0002] Many key parameters in industrial processes, such as furnace temperature in solid waste incineration and product concentration in chemical reactions, can be acquired in real time by sensors. However, these processes often exhibit significant lag characteristics. The current industrial measurement values ​​may no longer reflect the ongoing changes in operating conditions, making it difficult for feedback control based on current values ​​to adjust in a timely and accurate manner.

[0003] Data-driven modeling is currently an important technical approach for modeling key parameters in industrial processes to solve problems. However, existing traditional data-driven methods have inherent limitations: Partial Least Squares Regression (PLSR) is essentially a linear method, which is difficult to characterize the strong nonlinear features in industrial processes; Support Vector Regression (SVR) has computational complexity that increases too quickly with the sample size, making it unsuitable for massive or streaming data scenarios; Backpropagation Neural Networks rely on backpropagation for iterative training, which results in slow convergence, susceptibility to local optima, and unstable generalization performance.

[0004] To address the problem of decreased modeling accuracy caused by operating condition drift and scarcity of target domain label samples in non-stationary industrial processes, transfer learning and domain adaptation techniques have been introduced into the field of industrial process modeling. Although this method can achieve efficient transfer of mature knowledge from the source domain to small-sample scenarios in the target domain, it is only applicable to offline fuzzy models and is not combined with randomized networks. Therefore, it cannot be adapted to online streaming data scenarios in industry, does not integrate the rapid modeling advantages of randomized networks, and has limitations in nonlinear fitting capabilities. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides an industrial data modeling method based on fuzzy-transfer stochastic configuration networks, which solves the problems of existing industrial process modeling methods being unable to simultaneously achieve strong nonlinear fitting capabilities, fuzzy uncertainty representation capabilities, and adaptability under small sample operating condition drift.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: an industrial data modeling method based on fuzzy-transfer stochastic configuration networks, comprising the following steps: Obtain historical datasets of industrial sensors in the source domain, and obtain the fuzzy layer parameters, enhancement layer parameters, output weights, and source domain joint feature matrix of the frozen source domain model by fuzzy random configuration of the network model; Acquire target domain sensor data under new operating conditions, and based on the different manifestations between the target domain and the source domain, use a granular fuzzy domain adaptation strategy to spatially map the target domain sensor data to obtain the mapped fuzzy feature vector. Based on the mapped fuzzy feature vector and the frozen source domain model, a target domain transfer adaptation strategy is adopted to transfer the parameters of the frozen source domain model to the target domain, thereby obtaining the target domain model. Based on the target domain model, input real-time sensor data under the new operating conditions, and output predicted industrial data values ​​for future times.

[0007] Further: obtaining the fuzzy layer parameters, enhancement layer parameters, output weights, and joint feature matrix of the source domain model specifically includes: Obtain historical datasets of industrial sensors in the source domain, including input samples and their corresponding output values; Based on the historical dataset of industrial sensors in the source domain, several fuzzy rules and their corresponding cluster centers are determined by the fuzzy C-means clustering algorithm. The input samples are then clustered to obtain the membership degree of each input sample relative to each cluster center. The design matrix is ​​constructed based on the input samples and membership degrees, and the conclusion parameters of each fuzzy rule are obtained by solving the least squares method. The conclusion of the fuzzy rule is calculated based on the conclusion parameters of each fuzzy rule; Based on the membership degree of each input sample relative to each cluster center and the conclusions of the fuzzy rules, a fuzzy feature matrix is ​​constructed. Based on the fuzzy feature matrix, the weights and biases of the enhancement layer nodes are generated through a supervised random parameter configuration mechanism of the random configuration network, and the enhancement feature matrix is ​​calculated. Based on the fuzzy feature matrix and the enhanced feature matrix, the source domain joint feature matrix is ​​obtained by concatenation, and the output weights are calculated. Cluster centers and conclusion parameters are used as fuzzy layer parameters and frozen. Weights and biases of enhancement layer nodes are used as enhancement layer parameters and frozen. Source domain joint feature matrix and output weights are frozen.

[0008] Furthermore, the expression for the fuzzy feature matrix is ​​as follows:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] in, For the first The fuzzy feature matrix of each input sample. For the first The input sample relative to the first Membership degree of each cluster center For fuzzy rules and the total number of cluster centers, For the index of the input sample, For the first The first fuzzy rule The conclusion parameters for each input sample. For the first The first fuzzy rule The conclusion parameters for each input sample. , , All are the first The internal components of a fuzzy rule, The number of internal components within the feature dimension of the input sample. and All are the first The feature components of each input sample For the conclusion parameter vector, To design the matrix, the upper right corner It is the transpose symbol. The output value corresponding to the input sample. To design the transpose of the first row vector of the matrix, For the design matrix of the first Transpose of a row vector To input the total number of samples, For the first The input sample relative to the first Membership degree of each cluster center For the first Cluster centers, For the first Cluster centers, This is the fuzzification coefficient.

[0016] Furthermore, the expression for the joint characteristic matrix of the source domain is as follows:

[0017]

[0018]

[0019] in, The joint characteristic matrix of the source domain, For fuzzy feature matrix, To enhance the feature matrix, To enhance the first layer The weight of each node, To enhance the first layer The bias of each node It is the Sigmoid activation function. The joint characteristic matrix of the source domain, To output weights, Output label vectors for the source domain. The regularization coefficient is . It is the identity matrix. To input the total number of samples, To represent the total number of fuzzy rules, This represents the total number of nodes in the enhancement layer. and All parameters are generated through a supervised random parameter configuration mechanism using a random configuration network.

[0020] The further beneficial effects are as follows: Fuzzy C-means clustering is used to divide the source domain industrial data, and membership degrees are used to describe the physical characteristics of overlapping working condition boundaries, making the fuzzy rules more consistent with the characteristics of fuzzy and difficult-to-divide working condition boundaries in industrial processes; the least squares method is combined to solve the conclusion parameters, ensuring the computational efficiency of fuzzy layer construction; a supervised random parameter configuration mechanism for randomly configured networks is introduced to generate the weights and biases of enhancement layer nodes, and inequality constraints ensure that newly added nodes effectively reduce training residuals, guaranteeing the model's general approximation capability, while avoiding the problems of slow convergence and easy getting trapped in local optima in traditional neural network backpropagation training; freezing the fuzzy layer parameters, enhancement layer parameters, source domain joint feature matrix, and output weights allows for knowledge transfer without retraining the entire network when migrating to the target domain, requiring only updating the output weights or adjusting the mapping parameters, thus reducing the modeling cost and data labeling requirements under new working conditions.

[0021] Furthermore: a granular fuzzy domain adaptation strategy is adopted to perform spatial mapping on the target domain sensor data, specifically including: input spatial mapping for changes in conditional distribution, output spatial mapping for changes in conclusion distribution, and joint mapping for changes in both conditions and conclusions; The expression for the input space mapping is as follows:

[0022]

[0023]

[0024]

[0025]

[0026] in, The mapped fuzzy feature vector, For the input sample, For target domain sensor data, For the first After mapping under the fuzzy rule, the input sample is relative to the mapped first... Membership degree of cluster centers For the first The conclusion parameters of the input sample after mapping by the fuzzy rules. For input space mapping, For the first The values ​​of the cluster centers after mapping the input space. For the first Cluster centers, For the first The conclusion parameter vector of the fuzzy rule. For the first The vector obtained by mapping the input samples in the target domain to the input space. For the first The first target domain input sample The values ​​of each feature component after being mapped through the input space For the first The first target domain input sample The values ​​of each feature component after being mapped through the input space This is the index of the Sigmoid basis function. The total number of Sigmoid basis functions. For the first The first feature component corresponding to the th feature component The weights of the sigmoid basis functions For the first The first target domain input sample The first feature component corresponding to the th feature component The output values ​​of the sigmoid basis functions For the first The first feature component corresponding to the th feature component The slope parameters of the sigmoid basis functions For the first The first target domain input sample Each feature component For the first The first feature component corresponding to the th feature component The center parameters of the Sigmoid basis functions The total number of labeled samples in the target domain. The index for the target domain sample. For the index of fuzzy rules, To represent the total number of fuzzy rules, For the first The output value corresponding to each target domain input sample; The input space mapping Optimization is achieved by minimizing a first objective function, the expression of which is as follows:

[0027] in, Let the first objective function be... The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner This is the transpose symbol.

[0028] Furthermore, the expression for the output space mapping is as follows:

[0029]

[0030]

[0031]

[0032]

[0033] in, The mapped fuzzy feature vector, For the input sample, For target domain sensor data, For the first The target domain input sample is relative to the first Membership degree of each cluster center For target domain sensor data, For the first Cluster centers, For output space mapping, For the first The conclusion parameters of the target domain input sample under a fuzzy rule. For the first The target domain input sample at the th th The values ​​of the conclusion parameters under the fuzzy rules after output space mapping. For the first The target domain input sample at the th th The values ​​of the conclusion parameters under the fuzzy rules after output space mapping. This is the index of the Sigmoid basis function. The total number of Sigmoid basis functions. For the first The first fuzzy rule corresponding to the The weights of the sigmoid basis functions For the first The target domain input sample at the th th The corresponding fuzzy rule under the first fuzzy rule The output values ​​of the sigmoid basis functions For the first The first fuzzy rule corresponding to the The slope parameters of the sigmoid basis functions For the first The first fuzzy rule corresponding to the The center parameters of the Sigmoid basis functions For the first The target domain input sample at the th th Conclusion parameters under fuzzy rules; The output space mapping Optimization is achieved by minimizing a second objective function, the expression of which is as follows:

[0034] Among them, among them, The value of the second objective function. The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner This is the transpose symbol.

[0035] Furthermore: the joint mapping specifically includes simultaneously using the input space mapping and output space mapping The joint mapping is optimized by minimizing a third objective function, the expression of which is as follows:

[0036] in, The value of the third objective function. The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner This is the transpose symbol.

[0037] The further beneficial effects mentioned above are as follows: This invention employs a granular fuzzy domain adaptation strategy to perform three spatial mappings: when the new working condition is an input change, the target domain data distribution is adjusted through input space mapping to adapt to the source domain fuzzy rules; when the new working condition is a change in conclusion parameters, the rule conclusion values ​​are adjusted through output space mapping to adapt to the target domain output characteristics; when both change, the input space and output space are adjusted simultaneously through joint mapping. All three mapping methods of the granular fuzzy domain adaptation strategy, without changing the frozen fuzzy rules in the source domain, effectively transfer knowledge from the source domain to the target domain by optimizing the nonlinear mapping parameters composed of Sigmoid basis functions. This approach can accommodate the adaptation needs of different drift types, reduce the computational overhead of the training model when transferring to the new working condition, maintain the interpretability of the source domain rules, and improve the prediction accuracy and generalization performance in small sample scenarios.

[0038] Furthermore: the target domain migration adaptation strategy includes: Retain the fuzzy layer parameters in the frozen source domain model and discard the enhancement layer parameters; Based on the target domain sensor data, the target domain fuzzy feature matrix is ​​calculated through the fuzzy layer; Using the target domain fuzzy feature matrix as input and the output value corresponding to the target domain sensor data as the target, the random configuration network algorithm is re-executed to train a new enhancement layer, resulting in new enhancement layer parameters and new output weights. The target domain model is obtained by combining the fuzzy layer parameters, the new enhancement layer parameters, and the new output weights.

[0039] The target domain migration adaptation strategy also includes: Based on the target domain sensor data, the joint feature matrix of the original space is calculated by freezing the fuzzy layer parameters and enhancement layer parameters in the source domain model in the original feature space. The original spatial joint feature matrix is ​​used as the target domain feature, and the source domain joint feature matrix and source domain output weights in the frozen source domain model are used as source domain knowledge constraints to construct an optimization objective function; the optimization objective includes both source domain fitting error terms and target domain fitting error terms. The partial derivatives of the objective function are taken and set to zero to obtain the output weights in the objective domain. By fixing the output weights of the target domain, a granular fuzzy domain adaptation strategy is used to spatially map the sensor data in the target domain to obtain the optimal mapping. The target domain model is obtained by combining the fuzzy layer parameters, enhancement layer parameters, optimal mapping, and target domain output weights in the frozen source domain model.

[0040] The target domain migration adaptation strategy also includes: By fixing the fuzzy layer parameters, enhancement layer parameters, and source domain output weights in the frozen source domain model, a granular fuzzy domain adaptation strategy is used to spatially map the target domain sensor data to obtain the optimal mapping. Based on the optimal mapping, the joint feature matrix after mapping is calculated using sensor data in the target domain. The mapped joint feature matrix is ​​used as the target domain feature, and the source domain joint feature matrix and source domain output weights in the frozen source domain model are used as source domain knowledge constraints. The target domain output weights are calculated through the closed-form solution of knowledge transfer. The target domain model is obtained by combining the fuzzy layer parameters, enhancement layer parameters, optimal mapping, and target domain output weights in the frozen source domain model.

[0041] The further beneficial effects mentioned above are as follows: This invention proposes three optional transfer adaptation strategies for different degrees of operational condition drift: When the nonlinear characteristics of the source domain and the target domain differ significantly, the fuzzy layer is retained and the enhancement layer is reconstructed, ensuring the accuracy of nonlinear fitting under the new operational condition while reusing operational condition segmentation knowledge; when the target domain has very few labeled samples and a fast response is required, the closed-form solution is prioritized for transferring output weights, and then the feature distribution is fine-tuned through mapping, balancing efficiency and accuracy; when the distributions of the source domain and the target domain are significantly offset, the feature space is aligned through mapping, and then the output weights are transferred in the mapped space, ensuring that the transfer direction is consistent with the physical logic. The three transfer adaptation strategies share the same frozen source domain model, requiring only a small amount of target domain sensor data to complete the transfer adaptation without retraining, reducing the modeling cost and data labeling requirements under new operational conditions, while maintaining the interpretability of fuzzy rules and the fast learning advantage of randomly configured networks, providing differentiated solutions for operational condition drift in different industrial scenarios.

[0042] The beneficial effects of this invention are: During training, this invention first uses fuzzy C-means clustering to determine fuzzy rules, and then generates enhanced nodes through random network configuration. This enables the source domain frozen model to handle the uncertainty of industrial data and fit nonlinear relationships. In subsequent transfer processing, the fuzzy features of the source domain can be directly reused for extraction.

[0043] This invention calculates the joint feature matrix of the source domain together with the labeled data of the target domain, and updates all output weights of the blur layer and the enhancement layer at once. Only a small number of labeled samples in the target domain are needed to complete the weight transfer task. At the same time, the weights of the source domain are used to constrain the update of the target domain weights, reducing the risk of overfitting in the case of small samples.

[0044] This invention employs a granular fuzzy domain adaptation strategy. Based on the type of distribution difference between the source and target domains—that is, different input spaces, different output spaces, or both—a differential evolution algorithm is used to optimize the nonlinear mapping parameters composed of Sigmoid basis functions. The fuzzy rules of the source domain are fully preserved; only the input or output space of the target domain is adjusted through mapping, making the mapped fuzzy features and enhanced features more suitable for the target domain data. The granular fuzzy domain adaptation strategy is responsible for adjusting the data distribution of the target domain to match the fuzzy rules of the source domain, while the knowledge transfer closed-form solution is responsible for updating the model's output weights to adapt to the output characteristics of the target domain. Both work synergistically to improve prediction accuracy and generalization stability under new conditions. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of an industrial data modeling method based on fuzzy-transfer stochastic configuration networks. Detailed Implementation

[0046] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0047] Example 1 like Figure 1 The diagram shows a flowchart of an industrial data modeling method based on fuzzy-transfer stochastic configuration networks, including the following steps: Obtain historical datasets of industrial sensors in the source domain, and obtain the fuzzy layer parameters, enhancement layer parameters, output weights, and source domain joint feature matrix of the frozen source domain model by fuzzy random configuration of the network model; Acquire target domain sensor data under new operating conditions, and based on the different manifestations between the target domain and the source domain, use a granular fuzzy domain adaptation strategy to spatially map the target domain sensor data to obtain the mapped fuzzy feature vector. Based on the mapped fuzzy feature vector and the frozen source domain model, a target domain transfer adaptation strategy is adopted to transfer the parameters of the frozen source domain model to the target domain, thereby obtaining the target domain model. Based on the target domain model, input real-time sensor data under the new operating conditions, and output predicted industrial data values ​​for future times.

[0048] In complex industrial scenarios, such as municipal solid waste incineration, the composition of waste fluctuates greatly and the combustion process is delayed. To ensure complete dioxin decomposition, the furnace temperature must be maintained above 850°C with minimal fluctuations. Simply relying on the current readings of temperature sensors is insufficient to predict impending temperature drops. Traditional data-driven modeling methods, such as partial least squares regression and other linear models, struggle to characterize the strongly nonlinear thermodynamics of the incineration process. While backpropagation neural networks possess nonlinear fitting capabilities, their iterative training is slow to converge and prone to getting trapped in local optima. Although fuzzy stochastic configuration networks combine the advantages of fuzzy inference and randomized learning, they are only suitable for offline modeling. When the type of waste fuel changes or the incineration conditions shift, a large number of labeled samples under the new conditions need to be collected to retrain the entire network, which cannot meet the rapid adaptation requirements of online predictive control in solid waste incineration plants. To address the challenges of balancing strong nonlinearity, fuzzy uncertainty, and small-sample modeling under varying operating conditions in complex industrial scenarios, this invention provides an industrial data modeling method based on a fuzzy-transfer stochastic configuration network (F-SCN). A F-SCN model is trained on historical industrial sensor data from existing operating conditions using a TS fuzzy model, freezing its internal parameters. When a new operating condition (target domain) emerges with only a few labeled samples, two methods are employed for transfer: adjusting the distribution of fuzzy features using the granular fuzzy domain adaptation strategy GFRDA; and updating the output weights using the knowledge transfer KT-OSCN closed-loop solution. This invention integrates the structure of the fuzzy stochastic configuration network, the mapping strategy of granular fuzzy domain adaptation, and the weight transfer mechanism of the knowledge transfer closed-loop solution. By freezing model knowledge in the source domain and synergistically combining spatial mapping and closed-loop solution weight transfer in the target domain, it achieves rapid and high-precision modeling even with very few labeled samples.

[0049] In a specific embodiment of the present invention, a historical dataset of industrial sensors in the source domain is obtained. Through a fuzzy randomized network model, the fuzzy layer parameters, enhancement layer parameters, output weights, and source domain joint feature matrix of the frozen source domain model are obtained. The source domain training of the present invention aims to obtain a fuzzy randomized network (F-SCN) model with fixed parameters, comprising a fuzzy layer, enhancement layer, and output weights. Specifically, this includes obtaining the fuzzy layer parameters, enhancement layer parameters, output weights, and source domain joint feature matrix of the frozen source domain model. Obtain the historical dataset of source domain industrial sensors, including input samples and their corresponding output values; extract sensor time-series data under normal operating conditions from the historical database of the industrial field distributed control system to obtain the historical dataset of source domain industrial sensors. ,in For the input sample, To input the total number of samples, As the characteristic latitude, The corresponding output value; Based on historical data from industrial sensors in the source domain, several fuzzy rules and corresponding cluster centers were determined using the fuzzy C-means clustering algorithm. The input samples were then clustered to obtain the membership degree of each input sample relative to each cluster center. Compared to conventional clustering algorithms, the fuzzy C-means clustering algorithm allows a data point to belong to multiple clusters simultaneously with different membership degrees. This characteristic aligns with the fuzzy boundary and gradual state changes inherent in industrial processes. The fuzzy C-means clustering algorithm can describe, for example, the gradual transition region between stable combustion and slow temperature decrease in industrial solid waste incineration, where there is no clear boundary. Specifically, the gradual characteristics of industrial data are described through membership degrees. First, based on the characteristics and type of industrial data, several fuzzy rules and corresponding cluster centers are determined. A fuzzy rule is used to obtain the corresponding... Cluster centers ,in For the first The cluster centers of the rule are calculated. Input Samples Compared to the first The expression for the membership degree of a fuzzy rule is as follows:

[0050] in, This is the fuzzification coefficient, usually set to 2, which controls the degree of fuzziness in the membership degree. A larger value indicates a more uniform distribution of membership degrees among different clusters for each input sample.

[0051] The conclusion of the TS fuzzy model is a linear function of the input variables. ,in For the first The conclusion parameters of a fuzzy rule determine the local linear mapping relationship between the input and output under that fuzzy rule. To solve for the optimal conclusion parameters from the source domain data, it is necessary to integrate information from all samples and all rules into a unified design matrix. Each fuzzy rule contains a condition, which is derived from the prototype. A description, and a conclusion, which is determined by the input variables. linear functions The coefficients determine that when the input to the TS fuzzy model is When, output Represented as The design matrix is ​​constructed based on the input samples and membership degrees, and the conclusion parameters of each fuzzy rule are obtained by solving the least squares method. The conclusion parameters of each fuzzy rule are then used to calculate the fuzzy rule conclusions. Finally, based on the membership degrees of each input sample relative to each cluster center and the fuzzy rule conclusions, a fuzzy feature matrix is ​​constructed by multiplication. The expression for the fuzzy feature matrix is ​​as follows:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] in, For the first The fuzzy feature matrix of each input sample. For the first The input sample relative to the first Membership degree of each cluster center For fuzzy rules and the total number of cluster centers, For the index of the input sample, For the first The first fuzzy rule The conclusion parameters for each input sample. For the first The first fuzzy rule The conclusion parameters for each input sample. , , All are the first The internal components of a fuzzy rule The feature dimension of the input sample. and All are the first The feature components of each input sample For the conclusion parameter vector, To design the matrix, the upper right corner It is the transpose symbol. The output value corresponding to the input sample. To design the transpose of the first row vector of the matrix, For the design matrix of the first Transpose of a row vector To input the total number of samples, For the first The input sample relative to the first Membership degree of each cluster center For the first Cluster centers, For the first Cluster centers, This is the fuzzification coefficient.

[0059] In complex industrial scenarios, relying solely on fuzzy feature matrices Such linear functions are difficult to fully fit the nonlinearity of complex industrial processes. Therefore, this invention introduces a Randomized Network (SCN) as an enhancement layer to supplement the extraction of nonlinear residual information from fuzzy features. The core advantage of SCN lies in its supervised random parameter configuration mechanism: when randomly generating the input weights and biases of the enhancement layer nodes, inequality constraints ensure that newly added nodes can minimize the residuals of the current model. This invention utilizes its supervised random parameter configuration mechanism to ensure that the residuals of the current model are minimized as the number of nodes increases. With the addition of [unclear], the Fuzzy Randomized Network (F-SCN) model can quickly converge to the target accuracy, while avoiding the problems of slow backpropagation training and easy getting trapped in local optima in traditional neural networks; ultimately, the enhancement layers have [unclear]. With nodes, the output of the enhancement layer is:

[0060] in, To enhance the first layer The weight of each node, To enhance the first layer The bias of each node. The Sigmoid activation function is used; this invention is based on the fuzzy feature matrix. The weights and biases of the enhancement layer nodes are generated through a supervised random parameter configuration mechanism of the random network, and the enhancement feature matrix is ​​calculated. ;in, and All parameters are generated through a supervised random parameter configuration mechanism using a random configuration network.

[0061] After obtaining the fuzzy feature matrix With enhanced feature matrix Then, based on the fuzzy feature matrix and the enhanced feature matrix, the source domain joint feature matrix is ​​obtained by concatenation, and the output weights are calculated; at this point, the output of the source domain freezing model can be expressed as: Among them, the joint feature matrix of the source domain The expression is subscript Represents source domain data, output weights The expression is ,in, It is an identity matrix.

[0062] After completing the construction and training of the fuzzy randomized network (F-SCN) model, the cluster centers and conclusion parameters are used as fuzzy layer parameters and frozen. The weights and biases of the enhancement layer nodes are used as enhancement layer parameters and frozen. The source domain joint feature matrix and output weights are also frozen. In the subsequent knowledge transfer process for new working conditions, the frozen parameters will remain unchanged.

[0063] In a specific embodiment of the present invention, when a new operating condition, i.e., the target domain, appears, the fuzzy rules of the frozen source domain are no longer fully applicable. Training a new model directly from scratch would require a large amount of labeled data in the target domain and waste the knowledge already accumulated in the source domain. The present invention only requires acquiring a small amount of labeled data in the target domain, obtaining sensor data in the target domain under the new operating condition, and, based on the different manifestations between the target domain and the source domain, using a granular fuzzy domain adaptation strategy to spatially map the sensor data in the target domain, obtaining the mapped fuzzy feature vector. The core idea of ​​the granular fuzzy domain adaptation strategy GFRDA is to maintain the fuzzy rules frozen in the source domain without altering them. By constructing a nonlinear mapping, the data input to the fuzzy rules (input space) or the conclusion values ​​generated by the rules (output space) are adjusted, enabling the originally mismatched source domain rules to more effectively describe the target domain data and adapt to new working conditions. Based on the specific manifestation of the difference between the source and target domains—namely, changes in condition distribution, changes in conclusion distribution, or both—this invention divides the mapping into three forms, including: Input space mapping for conditions with varying distributions: The input distributions of the source and target domains differ, such as changes in the statistical properties of industrial process variables, but the mapping relationship between inputs and outputs, i.e., the conclusion parameters, remains unchanged. For example, a change in the waste feed rate causes a shift in the overall distribution of furnace temperature, but the fundamental pattern of temperature variation with each input variable does not change.

[0064] Output space mapping for changes in the conclusion distribution: The input distribution is basically the same, but the conclusion parameters change, that is, the mapping relationship between input and output has shifted. For example, the furnace heat exchange efficiency decreases due to ash accumulation, resulting in different output temperature responses under the same input conditions.

[0065] Joint mappings are used when both the conditions and the conclusion change: both the input distribution and the conclusion parameters change. For example, if the fuel type is changed and equipment aging occurs simultaneously, the two changes are superimposed.

[0066] In one embodiment of the present invention, when the input distributions of the source domain and the target domain are different, but the conclusion parameters are the same, an input space mapping for conditional distribution changes is employed. A nonlinear mapping consisting of a weighted sum of P sigmoid basis functions is constructed. Input the target domain Mapped to Therefore, the first The mapping of each feature component is as follows:

[0067]

[0068] in, For the first The first target domain input sample The values ​​of each feature component after being mapped through the input space This is the index of the Sigmoid basis function. The total number of Sigmoid basis functions. For the first The first feature component corresponding to the th feature component The weights of the sigmoid basis functions For the first The first target domain input sample The first feature component corresponding to the th feature component The output values ​​of the sigmoid basis functions For the first The first feature component corresponding to the th feature component The slope parameters of the sigmoid basis functions For the first The first target domain input sample Each feature component For the first The first feature component corresponding to the th feature component The center parameters of the Sigmoid basis functions; The first variable representing the output variable The weights of the sigmoid functions satisfy... , , , These are the parameters that need to be mapped and optimized. At the same time, in order to ensure that the output range is consistent with the original data, the value range of the Sigmoid function is 0-1. If no restriction is imposed, the maximum value can be any number, or it can be very small. The mapped value may far exceed the normal range of the source domain input. The distance when calculating the membership degree will become meaningless. When searching for parameters, if the weights are not constrained, the objective function will become unstable due to scale changes.

[0069] All input features are mapped during the mapping process. After transformation, it becomes Represented in matrix form as follows:

[0070] Optimization yields the final mapping result. Input space mapping Optimization is achieved by minimizing the first objective function, which is expressed as follows:

[0071] in, Let the first objective function be... The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner The sign is transpose. The first term is the root mean square error, which measures the prediction accuracy of the mapped model on labeled samples in the target domain; the second term... For regularization terms, It is a vector composed of all weight parameters. This is the regularization coefficient, used to prevent overfitting due to excessively large mapping parameters. After optimization, it is used... Replace the original target domain Calculate the membership degree and conclusion value; the mapped fuzzy feature vector is:

[0072] In one embodiment of the present invention, when the input distribution is basically the same but the conclusion parameters change, an output space mapping for the change in the conclusion distribution is used. A mapping is constructed using... A nonlinear mapping consisting of a weighted sum of Sigmoid basis functions , fuzzy rule conclusions of the target domain Mapped to , No. The mapping of the rule conclusion values ​​is as follows:

[0073]

[0074] in, For the slope parameter, Center parameter, Let these be the weight parameters. The weight parameters satisfy... , and These are the parameters that need to be mapped and optimized. To ensure the output range is consistent with the original data, the Sigmoid function's range is 0-1. Without restrictions, the maximum value can be arbitrarily large or very small. The mapped values ​​may far exceed the normal range of the source domain input, making the distance calculation for membership meaningless. If the weights are not constrained during parameter search, the objective function will become unstable due to scaling changes.

[0075] All original conclusions are mapped and transformed Represented in matrix form as follows:

[0076] in, For the first The target domain input sample at the th th The values ​​of the conclusion parameters under the fuzzy rules after output space mapping. For the first The target domain input sample at the th th The final result is obtained by optimizing the values ​​of the conclusion parameters under the fuzzy rules after output space mapping. Output space mapping Optimization is achieved by minimizing a second objective function, the expression of which is as follows:

[0077] After mapping, the complete mapping is obtained. The fuzzy feature vector Each component is The expression for the mapped fuzzy feature vector is as follows:

[0078] In one embodiment of the present invention, when the input distribution and conclusion parameters of both the target domain and the source domain change, input space mapping is employed simultaneously. and output space mapping The mapping parameters are jointly optimized by minimizing a third objective function, the expression of which is as follows:

[0079] in, The value of the third objective function. The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner Using the transpose symbol, after optimization, the complete mapping is obtained. In this invention, the first, second, and third objective functions all adopt a structure of root mean square error (RMSE) plus a regularization term. The first objective function corresponds to input space mapping optimization, adjusting only the input distribution; the second objective function corresponds to output space mapping optimization, adjusting only the conclusion distribution; and the third objective function corresponds to joint mapping optimization, adjusting both the input and conclusion distributions. The three objective functions share the same RMSE-regularization structure, ensuring logical consistency in model optimization under different drift types.

[0080] The parameter optimization for all three mapping methods in this invention is achieved using the L-SHADE differential evolution algorithm, and the optimal parameters are denoted as follows: The optimal mapping is denoted as This invention selects a matching mapping method based on the specific manifestation of operational drift, achieving optimal transfer performance with minimal parameter adjustments. Input mapping adjusts only the input distribution, output mapping adjusts only the conclusion distribution, and joint mapping adjusts both simultaneously, avoiding the overfitting risk associated with blindly adjusting all parameters. Furthermore, the nonlinear mapping constructed from a weighted sum of Sigmoid basis functions combines flexibility and controllability. The superposition of multiple Sigmoid basis functions can approximate arbitrarily complex nonlinear transformations. Weight constraints and regularization terms effectively control the degrees of freedom of the mapping, ensuring stable optimization even with a small number of target domain labeled samples. Moreover, this invention's strategy of fully preserving the source domain fuzzy rules and adjusting the target domain data distribution only through mapping maintains the interpretability of the source domain rules. Users can understand the physical meaning of each fuzzy rule, and interpretability is not lost due to model parameter retraining.

[0081] In a specific embodiment of the present invention, based on the mapped fuzzy feature vector and the frozen source domain model, a target domain migration adaptation strategy is adopted to migrate the parameters of the frozen source domain model to the target domain to obtain the target domain model; according to the characteristics of actual working condition changes, the present invention provides three optional migration adaptation strategies.

[0082] Variant 1: Independent Reconstruction of Enhancement Layer in Target Domain This strategy is adopted when the nonlinear characteristics of the source and target domains differ significantly and the source domain enhancement layer completely fails; specifically, it includes: Preserve the fuzzy layer parameters, i.e., cluster centers, in the frozen source domain model. and conclusion parameters Discard the enhancement layer parameters, i.e., the weight matrix. and bias vector ; Based on the sensor data in the target domain, the fuzzy feature matrix of the target domain is calculated through the fuzzy layer. ; fuzzy feature matrix of the target domain As input, the output value corresponding to the sensor data in the target domain. As a goal, the randomized network algorithm is re-executed to train a new enhancement layer, resulting in new enhancement layer parameters and new output weights. The new enhancement layer parameters include a new weight matrix. and the new bias vector ; The target domain model is obtained by combining the blur layer parameters, the new enhancement layer parameters, and the new output weights. When using the target domain model for prediction, new samples in the target domain are processed. First, calculate the fuzzy feature vector. Recalculate the enhancement layer output Finally, it outputs the predicted industrial data values ​​for future times. .

[0083] Variant 2: Transfer output weights first, then optimize by mapping. This strategy is adopted when the source domain enhancement layer still has some applicability and a fast response is required; specifically, it includes: Based on the target domain sensor data, the fuzzy layer parameters and enhancement layer parameters in the source domain model are frozen in the original feature space, i.e., the cluster centers. Conclusion parameters Weight matrix and bias vector The unmapped fuzzy feature matrix is ​​calculated. and unmapped enhanced feature matrix And construct the original spatial joint feature matrix. ; Joint feature matrix of the original space As a feature of the target domain, the joint feature matrix of the source domain in the frozen source domain model will be used. Source domain output weights As a source domain knowledge constraint, an optimization objective function is constructed; the optimization objective simultaneously includes both source domain fitting error terms and target domain fitting error terms; the expression of the optimization objective function is as follows:

[0084] in, The joint characteristic matrix of the source domain, Output to the source domain. For the joint feature matrix of the target domain, Output for the target domain. and These are all regularization coefficients, and the first term of the optimization objective function. The second term is an L2 regularization term to prevent excessively large weights. The third term is the source domain fitting error term, which constrains the new weights to prevent forgetting old knowledge; The error term is fitted to the target domain to make the new weights suitable for the new working condition data.

[0085] For optimizing the objective function about Taking the partial derivative and setting it to zero yields the target domain output weights, expressed as follows:

[0086] in, and All are regularization coefficients. The identity matrix is ​​used; the target domain output weights are calculated using the formula. The closed-form solution, which utilizes the source domain data, is obtained. Perform constraints and target domain new data pair The adaptation adjustment only requires a small number of target domain label samples to calculate the transferred output weights in one step; Fixed target domain output weights A granular fuzzy domain adaptation strategy is employed to spatially map the sensor data in the target domain. Specifically, based on the type of operating condition difference, input spatial mapping, output spatial mapping, or joint mapping is selected to obtain the optimal mapping. ; The fuzzy layer parameters, enhancement layer parameters, optimal mapping, and target domain output weights in the frozen source domain model are combined to obtain the target domain model. When using the target domain model for prediction, for new samples in the target domain... First apply the optimal mapping Calculate the joint eigenvector Then use the data obtained from the original space Predictive output of industrial data forecasts for future times .

[0087] Variant 3: First map the optimization, then transfer the output weights Fix the fuzzy layer parameters, enhancement layer parameters, and source domain output weights (i.e., cluster centers) in the frozen source domain model. Conclusion parameters Weight matrix Bias vector Source domain output weights A granular fuzzy domain adaptation strategy is employed to spatially map sensor data in the target domain. Based on the type of operating condition difference, input spatial mapping, output spatial mapping, or joint mapping is selected to obtain the optimal mapping. ; According to the optimal mapping The joint feature matrix after mapping is calculated using sensor data from the target domain. ; The mapped joint feature matrix As a feature of the target domain, the joint feature matrix of the source domain in the frozen source domain model will be used. Source domain output weights As a source domain knowledge constraint, the target domain output weight is calculated through a closed-form solution of knowledge transfer. Its expression is as follows:

[0088] in, and All are regularization coefficients. This closed-form solution updates the output weights of both the direct-connection part of the fuzzy layer and the enhancement part simultaneously. The fuzzy layer parameters, enhancement layer parameters, optimal mapping, and target domain output weights in the frozen source domain model are combined to obtain the target domain model. When using the target domain model for prediction, for new samples in the target domain... First apply the optimal mapping Calculate the joint eigenvector Then use the data obtained from the original space Predictive output of industrial data forecasts for future times .

[0089] In real-world industrial scenarios, operating condition drift manifests in various ways. This invention provides three variants to address this: Variant 1 is used when the enhancement layer completely fails; Variant 2 is used when only rapid adjustment of output weights is needed; and Variant 3 is used when data distribution alignment must be ensured before weight migration. All three variants share the same frozen source domain model, requiring only a small number of target domain label samples for adaptation. Specifically, the granular fuzzy domain adaptation strategy adjusts the data distribution to match the source domain rules, while the knowledge transfer closed-form solution updates the output weights to adapt to the target domain output characteristics. These two strategies work synergistically to improve prediction accuracy and generalization stability under new operating conditions.

[0090] The beneficial effects of this invention are as follows: During training, this invention first uses fuzzy C-means clustering to determine fuzzy rules, and then generates enhanced nodes through random network configuration. This enables the source domain frozen model to handle the uncertainty of industrial data and fit nonlinear relationships. In subsequent transfer processing, the fuzzy features of the source domain can be directly reused for extraction.

[0091] This invention calculates the joint feature matrix of the source domain together with the labeled data of the target domain, and updates all output weights of the blur layer and the enhancement layer at once. Only a small number of labeled samples in the target domain are needed to complete the weight transfer task. At the same time, the weights of the source domain are used to constrain the update of the target domain weights, reducing the risk of overfitting in the case of small samples.

[0092] This invention employs a granular fuzzy domain adaptation strategy. Based on the type of distribution difference between the source and target domains—that is, different input spaces, different output spaces, or both—a differential evolution algorithm is used to optimize the nonlinear mapping parameters composed of Sigmoid basis functions. The fuzzy rules of the source domain are fully preserved; only the input or output space of the target domain is adjusted through mapping, making the mapped fuzzy features and enhanced features more suitable for the target domain data. The granular fuzzy domain adaptation strategy is responsible for adjusting the data distribution of the target domain to match the fuzzy rules of the source domain, while the knowledge transfer closed-form solution is responsible for updating the model's output weights to adapt to the output characteristics of the target domain. Both work synergistically to improve prediction accuracy and generalization stability under new conditions.

Claims

1. An industrial data modeling method based on fuzzy-transfer stochastic configuration networks, characterized in that, Includes the following steps: Obtain historical datasets of industrial sensors in the source domain, and obtain the fuzzy layer parameters, enhancement layer parameters, output weights, and source domain joint feature matrix of the frozen source domain model by fuzzy random configuration of the network model; Acquire target domain sensor data under new operating conditions, and based on the different manifestations between the target domain and the source domain, use a granular fuzzy domain adaptation strategy to spatially map the target domain sensor data to obtain the mapped fuzzy feature vector. Based on the mapped fuzzy feature vector and the frozen source domain model, a target domain transfer adaptation strategy is adopted to transfer the parameters of the frozen source domain model to the target domain, thereby obtaining the target domain model. Based on the target domain model, input real-time sensor data under the new operating conditions, and output predicted industrial data values ​​for future times.

2. The industrial data modeling method based on the blur-migration random configuration network according to claim 1, wherein, The process of obtaining the fuzzy layer parameters, enhancement layer parameters, output weights, and joint feature matrix of the source domain model specifically includes: Obtain historical datasets of industrial sensors in the source domain, including input samples and their corresponding output values; Based on the historical dataset of industrial sensors in the source domain, several fuzzy rules and their corresponding cluster centers are determined by the fuzzy C-means clustering algorithm. The input samples are then clustered to obtain the membership degree of each input sample relative to each cluster center. The design matrix is ​​constructed based on the input samples and membership degrees, and the conclusion parameters of each fuzzy rule are obtained by solving the least squares method. The conclusion of the fuzzy rule is calculated based on the conclusion parameters of each fuzzy rule; Based on the membership degree of each input sample relative to each cluster center and the conclusions of the fuzzy rules, a fuzzy feature matrix is ​​constructed. Based on the fuzzy feature matrix, the weights and biases of the enhancement layer nodes are generated through a supervised random parameter configuration mechanism of the random configuration network, and the enhancement feature matrix is ​​calculated. Based on the fuzzy feature matrix and the enhanced feature matrix, the source domain joint feature matrix is ​​obtained by concatenation, and the output weights are calculated. Cluster centers and conclusion parameters are used as fuzzy layer parameters and frozen. Weights and biases of enhancement layer nodes are used as enhancement layer parameters and frozen. Source domain joint feature matrix and output weights are frozen.

3. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 2, characterized in that, The expression for the fuzzy feature matrix is ​​as follows: in, For the first The fuzzy feature matrix of each input sample. For the first The input sample relative to the first Membership degree of each cluster center For fuzzy rules and the total number of cluster centers, For the index of the input sample, For the first The first fuzzy rule The conclusion parameters for each input sample. For the first The first fuzzy rule The conclusion parameters for each input sample. , , All are the first The internal components of a fuzzy rule The feature dimension of the input sample. and All are the first The feature components of each input sample For the conclusion parameter vector, To design the matrix, the upper right corner It is the transpose symbol. The output value corresponding to the input sample. To design the transpose of the first row vector of the matrix, For the design matrix of the first Transpose of a row vector To input the total number of samples, For the first The input sample relative to the first Membership degree of each cluster center For the first Cluster centers, For the first Cluster centers, This is the fuzzification coefficient.

4. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 3, characterized in that, The expression for the joint characteristic matrix of the source domain is as follows: in, The joint characteristic matrix of the source domain, with subscripts... Represents source domain data, For fuzzy feature matrix, To enhance the feature matrix, To enhance the first layer The weight of each node, To enhance the first layer The bias of each node It is the Sigmoid activation function. The joint characteristic matrix of the source domain, To output weights, Output label vectors for the source domain. The regularization coefficient is . It is the identity matrix. To input the total number of samples, To represent the total number of fuzzy rules, This represents the total number of nodes in the enhancement layer. and All parameters are generated through a supervised random parameter configuration mechanism using a random configuration network.

5. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 1, characterized in that, The spatial mapping of target domain sensor data using a granular fuzzy domain adaptation strategy specifically includes: input spatial mapping for changes in conditional distribution, output spatial mapping for changes in conclusion distribution, and joint mapping for changes in both conditions and conclusions. The expression for the input space mapping is as follows: in, The mapped fuzzy feature vector, For the input sample, For target domain sensor data, For the first After mapping under the fuzzy rule, the input sample is relative to the mapped first... Membership degree of cluster centers For the first The conclusion parameters of the input sample after mapping by the fuzzy rules. For input space mapping, For the first The values ​​of the cluster centers after mapping the input space. For the first Cluster centers, For the first The conclusion parameter vector of the fuzzy rule. For the first The vector obtained by mapping the input samples in the target domain to the input space. For the first The first target domain input sample The values ​​of each feature component after being mapped through the input space For the first The first target domain input sample The values ​​of each feature component after being mapped through the input space This is the index of the Sigmoid basis function. The total number of Sigmoid basis functions. For the first The first feature component corresponding to the th feature component The weights of the sigmoid basis functions For the first The first target domain input sample The first feature component corresponding to the th feature component The output values ​​of the sigmoid basis functions For the first The first feature component corresponding to the th feature component The slope parameters of the sigmoid basis functions For the first The first target domain input sample Each feature component For the first The first feature component corresponding to the th feature component The center parameters of the Sigmoid basis functions The total number of labeled samples in the target domain. The index for the target domain sample. For the index of fuzzy rules, To represent the total number of fuzzy rules, For the first The output value corresponding to each target domain input sample; The input space mapping Optimization is achieved by minimizing a first objective function, the expression of which is as follows: in, Let the first objective function be... The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner This is the transpose symbol.

6. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 5, characterized in that, The expression for the output space mapping is as follows: in, The mapped fuzzy feature vector, For the input sample, For target domain sensor data, For the first The target domain input sample is relative to the first Membership degree of each cluster center For target domain sensor data, For the first Cluster centers, For output space mapping, For the first The conclusion parameters of the target domain input sample under a fuzzy rule. For the first The target domain input sample at the th th The values ​​of the conclusion parameters under the fuzzy rules after output space mapping. For the first The target domain input sample at the th th The values ​​of the conclusion parameters under the fuzzy rules after output space mapping. This is the index of the Sigmoid basis function. The total number of Sigmoid basis functions. For the first The first fuzzy rule corresponding to the The weights of the sigmoid basis functions For the first The target domain input sample at the th th The corresponding fuzzy rule under the first fuzzy rule The output values ​​of the sigmoid basis functions For the first The first fuzzy rule corresponding to the The slope parameters of the sigmoid basis functions For the first The first fuzzy rule corresponding to the The center parameters of the Sigmoid basis functions For the first The target domain input sample at the th th Conclusion parameters under fuzzy rules; The output space mapping Optimization is achieved by minimizing a second objective function, the expression of which is as follows: in, The value of the second objective function. The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner This is the transpose symbol.

7. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 6, characterized in that, The joint mapping specifically includes using input space mapping simultaneously. and output space mapping The joint mapping is optimized by minimizing a third objective function, the expression of which is as follows: in, The value of the third objective function. The regularization coefficient is . The vector consisting of all mapping parameters to be optimized, top right corner This is the transpose symbol.

8. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 1, characterized in that, The target domain migration adaptation strategy includes: Retain the fuzzy layer parameters in the frozen source domain model and discard the enhancement layer parameters; Based on the target domain sensor data, the target domain fuzzy feature matrix is ​​calculated through the fuzzy layer; Using the target domain fuzzy feature matrix as input and the output value corresponding to the target domain sensor data as the target, the random configuration network algorithm is re-executed to train a new enhancement layer, resulting in new enhancement layer parameters and new output weights. The target domain model is obtained by combining the fuzzy layer parameters, the new enhancement layer parameters, and the new output weights.

9. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 1, characterized in that, The target domain migration adaptation strategy also includes: Based on the target domain sensor data, the joint feature matrix of the original space is calculated by freezing the fuzzy layer parameters and enhancement layer parameters in the source domain model in the original feature space. The original spatial joint feature matrix is ​​used as the target domain feature, and the source domain joint feature matrix and source domain output weights in the frozen source domain model are used as source domain knowledge constraints to construct an optimization objective function; the optimization objective includes both source domain fitting error terms and target domain fitting error terms. The partial derivatives of the objective function are taken and set to zero to obtain the output weights in the objective domain. By fixing the output weights of the target domain, a granular fuzzy domain adaptation strategy is used to spatially map the sensor data in the target domain to obtain the optimal mapping. The target domain model is obtained by combining the fuzzy layer parameters, enhancement layer parameters, optimal mapping, and target domain output weights in the frozen source domain model.

10. The industrial data modeling method based on fuzzy-transfer stochastic configuration network according to claim 1, characterized in that, The target domain migration adaptation strategy also includes: By fixing the fuzzy layer parameters, enhancement layer parameters, and source domain output weights in the frozen source domain model, a granular fuzzy domain adaptation strategy is used to spatially map the target domain sensor data to obtain the optimal mapping. Based on the optimal mapping, the joint feature matrix after mapping is calculated using sensor data in the target domain. The mapped joint feature matrix is ​​used as the target domain feature, and the source domain joint feature matrix and source domain output weights in the frozen source domain model are used as source domain knowledge constraints. The target domain output weights are calculated through the closed-form solution of knowledge transfer. The target domain model is obtained by combining the fuzzy layer parameters, enhancement layer parameters, optimal mapping, and target domain output weights in the frozen source domain model.

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