Lightweight learning stress prediction method and device based on adapter modulation, and medium

Abstract

The application discloses a lightweight learning stress prediction method based on adapter modulation, a device and a medium. The method comprises collecting ladle lining working condition data, and preprocessing to obtain characteristic tensor data; and the characteristic tensor data is input into a stress prediction model to obtain equivalent stress prediction results. The stress prediction model comprises a shared backbone network, an adapter modulation module and a prediction module. The shared backbone network is formed by stacking multiple KAN layers; the adapter modulation module is used for each KAN layer, and is differentiated and modulated through an adapter parameter group, thereby deriving K functionally differentiated sub-models in parallel in the shared backbone network; and the prediction module is used for aggregating the outputs of the K sub-models to generate a final equivalent stress prediction value. The application has the advantages of realizing efficient and interpretable stress prediction for different material layers and structure parameters, overcoming the problems of long modeling period, low prediction efficiency, poor interpretability, large parameter quantity, weak generalization ability and insufficient physical consistency in the prior art.

Description

Technical Field

[0001] This invention relates to the field of industrial structural stress prediction technology, specifically to a lightweight learning stress prediction method, device, and medium based on adapter modulation. Background Technology

[0002] The rapid development of artificial intelligence technology is propelling industrial intelligence into a new stage, with data-driven methods providing an innovative paradigm for solving complex problems in traditional manufacturing. As a typical process industry, the steel metallurgy industry relies on high-temperature ladle furnace linings subjected to extreme thermo-mechanical loads during cyclic service. Accurate prediction of the internal stress state of these linings is crucial for optimizing furnace lining structure, assessing lifespan, and enabling predictive maintenance. The stress distribution in ladle furnace linings is influenced by a combination of factors, including material properties (such as thermal conductivity and Young's modulus), geometric parameters (such as layer thickness and shell thickness), and service conditions (such as temperature gradient and load variations), exhibiting strong nonlinear characteristics. While traditional numerical simulation methods based on finite element analysis offer high physical clarity, they suffer from inherent limitations such as long modeling cycles, cumbersome preprocessing, and reliance on simplified physical assumptions, making it difficult to meet the dynamic demands of real-time diagnosis and rapid iterative design in digital production.

[0003] Currently, the application of machine learning and deep learning methods to prediction problems of such complex physical fields mainly includes the following categories:

[0004] (1) A single deep learning model is used, such as multilayer perceptron (MLP), Transformer and Kolmogorov-Arnold Networks (KAN). However, the fitting ability and generalization performance of a single model are limited, especially in complex scenarios such as steel ladle lining with strong coupling of multiple parameters, its prediction accuracy and stability are difficult to meet engineering requirements.

[0005] (2) Traditional ensemble learning methods, such as random forests, or ensemble multiple KAN models trained independently, are adopted. However, traditional ensemble learning methods require the independent training and storage of multiple sub-models, and the number of parameters and computational cost increases linearly with the number of sub-models. For example, ensemble 32 independent KAN models, and the total number of parameters will be 32 times that of a single model, resulting in high model deployment costs and slow inference speed, making it difficult to meet the real-time requirements of industrial scenarios.

[0006] (3) Physical information-driven AI models improve the physical consistency of predictions by introducing physical information such as material constitutive equations. However, these models are highly complex to design and are often limited by the expressive power of a single model architecture. Their generalization ability is still insufficient when dealing with unseen edge cases. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a lightweight learning stress prediction method, device and medium based on adapter modulation, which extracts deep interpretable nonlinear coupling features by explicit parameterization of B-spline basis functions of multiple KAN layers, and uses an adapter modulation mechanism to derive multiple functionally differentiated sub-models in parallel in the backbone network, so as to achieve high-efficiency and interpretable stress prediction for different material layers (working layer, permanent layer, insulation layer) and structural parameters. This overcomes the problems of long modeling cycle, low prediction efficiency, poor model interpretability, large number of integrated learning parameters, weak generalization ability and insufficient physical consistency in the prior art.

[0008] To address the aforementioned technical problems, the present invention provides a lightweight learning stress prediction method based on adapter modulation, comprising:

[0009] Data on the working conditions of the ladle furnace lining were collected and preprocessed to obtain characteristic tensor data;

[0010] The feature tensor data is input into the stress prediction model to obtain the equivalent stress prediction result.

[0011] The stress prediction model is trained based on sample feature tensor data and the corresponding equivalent stress labels of the sample feature tensor data; the stress prediction model includes:

[0012] A shared backbone network, comprising a backbone network formed by stacking multiple KAN layers and a shared KAN layer, is used to progressively compress feature dimensions and extract nonlinear coupling features from input data;

[0013] The adapter modulation module includes adapter parameter groups that are independently set for K parallel sub-models. The adapter modulation module is used to perform differential modulation through the adapter parameter groups at each KAN layer of the backbone network, thereby deriving K functionally differentiated sub-models in parallel in the backbone network.

[0014] The prediction module is used to aggregate the output data of K sub-models to generate the final equivalent stress prediction value.

[0015] In a preferred embodiment, the mapping relationship of any of the KAN layers is implemented using the following calculation method:

[0016] ;

[0017] in, For input features, The dimension of the input feature. For output features, The dimension of the output feature. For learnable B-spline functions, These are the weights of the linear terms.

[0018] In a preferred embodiment, the learnable B-spline function is specifically parameterized in the following manner:

[0019] ;

[0020] in, The number of grid intervals, Let the order be the spline order. For K-order B-spline basis functions, These are the learnable spline coefficients.

[0021] In a preferred embodiment, the adapter parameter set includes an input adapter parameter set, an output adapter parameter set, and a bias adapter parameter set. The adapter modulation module is used to perform differential modulation on the features input to the KAN layer at each KAN layer of the backbone network through the corresponding input adapter parameter set, and to perform differential modulation on the features output from the KAN layer through the corresponding output adapter parameter set and bias adapter parameter set.

[0022] In a preferred embodiment, the adapter modulation module modulates the first... The sub-model in the first The forward transformation process of the KAN layer is implemented using the following calculation method:

[0023] ;

[0024] in, For the first Sub-model Features output by the KAN layer For the first Sub-model Features output by the KAN layer For element-wise multiplication, For the first Mapping of the KAN layer For the first Sub-model The input adapter parameter group of the KAN layer For the first Sub-model KAN layer output adapter parameter group For the first Sub-model The bias adapter parameter group for the KAN layer.

[0025] In a preferred embodiment, the ladle furnace lining operating condition data is in element-node form, including spatial coordinates in the global coordinate system, normal stress components in three orthogonal directions, and node temperature;

[0026] The preprocessing to obtain feature tensor data specifically includes the following steps:

[0027] The standardization of the ladle furnace lining operating data is achieved using the following calculation method:

[0028] ,

[0029] in, This is data on the operating conditions of the ladle furnace lining. The mean of the data. The standard deviation of the data;

[0030] The standardized data is expanded into 3D feature tensors adapted to K sub-models using the Kronecker product. The specific calculation method is as follows:

[0031] ;

[0032] in, For Kronecker product operation, It is a column vector whose elements are all 1s.

[0033] In a preferred embodiment, the backbone network in the first After the KAN layer performs tensor flattening on the input features, it performs parallel computation through the corresponding input adapter parameter set. The computation result is then reshaped and mapped to the corresponding KAN layer. The mapped result is then reshaped and performed in parallel computation through the corresponding output adapter parameter set and bias adapter parameter set. Finally, the computation result is tensor flattened and input to the first KAN layer. KAN layer.

[0034] In a preferred embodiment, the sample feature tensor data is obtained by orthogonal experimental design, covering ladle furnace structural layer parameters, material property parameters and steel shell parameters, and solved by finite element analysis method;

[0035] The structural layer parameters include the working layer thickness parameters, the permanent layer thickness parameters, and the insulation layer thickness parameters;

[0036] The material properties include thermal conductivity and Young's modulus;

[0037] The steel shell parameters include the steel shell thickness;

[0038] Set the equivalent stress results obtained from finite element analysis as the labels for the corresponding sample feature tensor data.

[0039] The present invention also provides a computer device including a memory and a processor, the memory storing a computer program configured to be executed by the processor, the computer program including instructions for performing the methods as described in any of the preceding claims.

[0040] The present invention also provides a computer-readable storage medium having a computer program / instruction stored thereon, characterized in that, when the computer program / instruction is executed by a processor, it implements the lightweight learning stress prediction method based on adapter modulation as described in any of the preceding claims.

[0041] The lightweight learning stress prediction method based on adapter modulation of the present invention has the following advantages compared with the prior art:

[0042] (1) The lightweight learning stress prediction method based on adapter modulation of the present invention includes the following steps: collecting ladle furnace lining working condition data and preprocessing to obtain feature tensor data. Through standardized preprocessing, the dimensional influence between different physical quantities (such as temperature, stress components, coordinates) is eliminated, enabling the stress prediction model to learn multi-parameter coupling relationships more stably. This provides a unified and standardized data input format for subsequent efficient feature extraction and sub-model modulation, ensuring the consistency and convergence speed of stress prediction model training. The feature tensor data is input into the stress prediction model to obtain equivalent stress prediction results, realizing end-to-end mapping from complex multi-physics input to equivalent stress output. This avoids the cumbersome manual modeling and assumption simplification process in the traditional finite element method, significantly improving prediction efficiency. Compared with the complex solution calculation process required by the traditional finite element analysis method, it can meet the real-time requirements of rapid iterative design in industrial scenarios.

[0043] The stress prediction model is trained based on sample feature tensor data and the corresponding equivalent stress labels. The model comprises a shared backbone network, an adapter modulation module, and a prediction module. The shared backbone network consists of a backbone network formed by stacking multiple KAN layers and shared KAN layers, used to progressively compress feature dimensions from the input data and extract nonlinear coupling features. On one hand, the KAN layers, built based on the Kolmogorov-Arnold theorem, possess inherent interpretability: their activation functions are explicitly parameterized by B-spline basis functions, clearly revealing the nonlinear mapping relationship between input features (such as temperature and thickness) and stress output, overcoming the "black box" problem of traditional deep learning models (such as MLP and Transformer). On the other hand, the stacked structure compresses feature dimensions layer by layer, achieving efficient feature abstraction and nonlinear coupling modeling while retaining key information, thus improving the modeling capability for complex thermo-mechanical coupling mechanisms.

[0044] The adapter modulation module includes adapter parameter sets independently configured for K parallel sub-models. On one hand, by introducing lightweight adapter parameter sets (R / S / B) into the backbone network, it achieves differentiated modulation of the input / output of the K sub-models, deriving a group of functionally complementary sub-models without requiring independent training of multiple complete models. On the other hand, compared with traditional integrated independent KAN models, this mechanism significantly reduces the number of parameters, greatly reducing deployment and inference costs. The adapter modulation module is used to perform differentiated modulation through adapter parameter sets at each KAN layer of the backbone network, thereby deriving K functionally differentiated sub-models in parallel within the backbone network. Firstly, through layer-by-layer input / output scaling and bias modulation, the model can achieve fine-grained differentiated learning of sub-models at different feature abstraction levels, enabling different sub-models to focus on local features under different working conditions, material layers, or stress states. Secondly, this layer-by-layer modulation mechanism enhances the model's adaptability to edge cases (such as extreme temperatures and special geometric parameters), significantly improving generalization performance.

[0045] The prediction module is used to aggregate the output data of K sub-models to generate the final equivalent stress prediction value. By fusing the prediction results of multiple sub-models, the bias and variance of a single model are effectively reduced, and the stability and accuracy of the overall prediction are improved.

[0046] (2) The lightweight learning stress prediction method based on adapter modulation of the present invention uses element-node as the data unit for ladle furnace lining operating data, including spatial coordinates in the global coordinate system, normal stress components in three orthogonal directions, and node temperature. Using "element-node" as the unit enables the stress prediction model to predict stress distribution at the node level, rather than an average output across the entire structure. This fine-grained modeling capability improves the identification of local stress concentration areas (such as the boundary between the working layer and the permanent layer). The standardized data is expanded into 3D feature tensors adapted to K sub-models using Kronecker products. On one hand, Kronecker products expand the original 2D input tensor into a 3D tensor, allowing the K sub-models to propagate forward in parallel within a unified tensor space, rather than through serial loop computation. This simultaneously processes batch data (B) and multiple sub-models (K), achieving dual parallelism of "batch processing × multiple sub-models." During training, gradients can be simultaneously backpropagated to the adapter parameters of all sub-models and the shared backbone network, achieving true end-to-end joint optimization and avoiding the cumbersome process of independently training multiple models in traditional ensemble learning. On the other hand, based on PyTorch's tensor sharing mechanism, this expansion operation achieves "logical expansion, physical sharing" at the memory level. The expanded 3D tensor does not actually copy the data; instead, it shares underlying memory through stride settings, reducing memory overhead and saving approximately K times the memory resources. For example, when K=32, memory usage drops from the theoretical 32 times to almost 1 time, which is significant in industrial deployment scenarios.

[0047] (3) The lightweight learning stress prediction method based on adapter modulation of the present invention uses orthogonal experimental design for the sample feature tensor data, covering the structural layer parameters, material property parameters, and steel shell parameters of the ladle furnace, and is solved by finite element analysis. On the one hand, the orthogonal experimental design is used to cover the largest parameter space with the fewest number of experiments; on the other hand, it ensures that each level of each parameter appears equally in the dataset, avoiding oversampling or undersampling of certain parameter combinations. This allows the trained model to learn the stress response law under different parameter configurations in a balanced way, without bias due to uneven data distribution, and significantly improves the generalization ability of the model. The constructed sample feature tensor data realizes a dedicated dataset for the thermo-mechanical coupling of the ladle furnace, providing a standardized benchmark testing platform for subsequent research and solving the core problem of "lack of dedicated high-quality dataset" pointed out in the background technology. The equivalent stress structure calculated by finite element analysis is set as the label of the corresponding sample feature tensor data. On the one hand, although finite element analysis itself has limitations such as long modeling cycles and reliance on assumptions, the physical accuracy of its calculation results has been widely verified by the engineering community. Using it as a label for supervised learning is equivalent to distilling the "domain knowledge" of the finite element method into the data-driven model, achieving "the accuracy of finite element and the speed of data-driven learning". On the other hand, a standardized process of "orthogonal experimental design → finite element calculation → data post-processing → model training" has been established, which is easy to extend to new parameter ranges or new material types. New data can be generated by following the same process to incrementally update or retrain the model, which has good scalability. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the technical process of an embodiment of the lightweight learning stress prediction method based on adapter modulation of the present invention.

[0049] Figure 2 This is a schematic diagram of the stress prediction model of an embodiment of the lightweight learning stress prediction method based on adapter modulation of the present invention.

[0050] Figure 3 This is a schematic diagram of the adapter modulation principle of the iKAN layer in an embodiment of the lightweight learning stress prediction method based on adapter modulation of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0052] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0053] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, an integral connection, or a detachable connection; they can refer to the internal connection of two components; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0054] Example

[0055] The lightweight learning stress prediction method based on adapter modulation in this embodiment, such as Figure 1 As shown, it includes:

[0056] Step S1. Collect ladle furnace lining operating condition data and preprocess it to obtain feature tensor data. Through standardized preprocessing, the dimensional influence between different physical quantities (such as temperature, stress components, and coordinates) is eliminated, enabling the stress prediction model to learn multi-parameter coupling relationships more stably. This provides a unified and standardized data input format for subsequent efficient feature extraction and sub-model modulation, ensuring the consistency and convergence speed of stress prediction model training.

[0057] Ladle Furnace Lining Operating Data The data unit is an element-node. In this embodiment, The value is set to 7, including spatial coordinates (X, Y, Z) in the global coordinate system, normal stress components in three orthogonal directions (S11, S22, S33), and nodal temperatures. Using "element-node" units, the stress prediction model can predict stress distribution at the node level, rather than an average output across the entire structure. This fine-grained modeling capability improves the identification of local stress concentration areas (such as the boundary between the working layer and the permanent layer). The ladle furnace lining operating data is preprocessed to obtain feature tensor data, specifically including the following steps:

[0058] Step S11. Standardize the ladle furnace lining operating data, specifically using the following calculation method:

[0059] ,

[0060] in, This is data on the operating conditions of the ladle furnace lining. The mean of the data. This represents the standard deviation of the data.

[0061] Step S12. The standardized data is expanded into three-dimensional feature tensors adapted to K sub-models using the Kronecker product. The specific calculation method is as follows:

[0062] ;

[0063] in, For Kronecker product operation, This is a column vector with all elements equal to 1. On one hand, the original two-dimensional input tensor is expanded into a three-dimensional tensor through the Kronecker product, enabling K sub-models to propagate forward in parallel within a unified tensor space, rather than being computed sequentially in a loop. This simultaneously processes batch data (B) and multiple sub-models (K), achieving dual parallelism of "batch processing × multiple sub-models." During training, gradients can be simultaneously propagated back to the adapter parameters of all sub-models and the shared backbone network, achieving true end-to-end joint optimization and avoiding the cumbersome process of independently training multiple models in traditional ensemble learning. On the other hand, based on PyTorch's tensor sharing mechanism, this expansion operation achieves "logical expansion, physical sharing" at the memory level. The expanded three-dimensional tensor does not actually copy the data, but shares the underlying memory through stride settings, reducing memory overhead and saving approximately K times the memory resources. When K=32, the total number of parameters is only 15936, while the number of parameters of 32 independent KAN models is 322560. The memory usage is reduced from 32 times the theoretical value to almost half, which is of great significance in industrial deployment scenarios.

[0064] Step S2. Input the feature tensor data into the stress prediction model to obtain the equivalent stress prediction results. This achieves an end-to-end mapping from complex multiphysics input to equivalent stress output, avoiding the cumbersome manual modeling and assumption simplification process in traditional finite element methods, significantly improving prediction efficiency. Compared to the complex solution calculation process required by traditional finite element analysis methods, it can meet the real-time requirements of rapid iterative design in industrial scenarios.

[0065] The stress prediction model is trained based on sample feature tensor data and corresponding equivalent stress labels. The sample feature tensor data employs an orthogonal experimental design, covering ladle furnace structural layer parameters, material property parameters, and steel shell parameters, and is solved using finite element analysis. On the one hand, the orthogonal experimental design covers the largest parameter space with the fewest experiments; on the other hand, it ensures that each level of each parameter appears equally in the dataset, avoiding oversampling or undersampling of certain parameter combinations. This allows the trained model to learn the stress response characteristics under different parameter configurations in a balanced manner, without bias due to uneven data distribution, significantly improving the model's generalization ability. The constructed sample feature tensor data realizes a dedicated dataset for ladle furnace thermo-mechanical coupling, providing a standardized benchmark testing platform for subsequent research and solving the core problem of "lack of dedicated high-quality datasets" pointed out in the background section.

[0066] The structural layer parameters include the working layer thickness, the permanent layer thickness, and the insulation layer thickness. The ladle furnace lining consists of three layers of materials with different functions: a working layer, a permanent layer, and an insulation layer. Each layer exhibits significantly different response mechanisms under thermo-mechanical loads. The working layer directly contacts the high-temperature molten steel and bears the most severe thermal shock; the permanent layer provides support and mainly bears mechanical loads; the insulation layer primarily affects the temperature gradient distribution. On the one hand, considering the thickness parameters of these three layers simultaneously allows the stress prediction model to learn the differentiated stress evolution laws of different functional layers; on the other hand, it improves physical consistency. Independent modeling of the three layer thicknesses enables the stress prediction model to distinguish the response differences of different material layers under tensile / compressive stress states. In this embodiment, the working layer thickness, permanent layer thickness, and insulation layer thickness parameters are set to 30-270 mm. Material property parameters include thermal conductivity and Young's modulus. Thermal conductivity determines the rate of heat transfer in the furnace lining, directly affecting the temperature gradient distribution; Young's modulus reflects the material's resistance to deformation, determining the magnitude of stress generated at a given strain. These two parameters serve as a bridge connecting the "thermal field" and the "force field," and are the core physical quantities for thermo-mechanical coupling modeling. Using them as features allows the stress prediction model to autonomously learn the physical laws governing thermo-mechanical coupling from the data. In this embodiment, the thermal conductivity is set to 1.5–10.5 W·m. -1 ·K -1The Young's modulus was set to 5-115 GPa. Steel shell parameters included thickness. As the outermost constraint structure of the furnace lining, the thickness of the steel shell directly affected the overall stiffness and deformation capacity. A thicker steel shell would restrict the thermal expansion of the furnace lining, potentially leading to higher compressive stress; a thinner steel shell would provide weaker constraint but could result in excessive deformation. Incorporating the steel shell thickness into the modeling allowed the stress prediction model to fully consider the coupled response of the "furnace lining-steel shell" system. In this embodiment, the steel shell thickness parameters included 15mm, 20mm, 23mm, 26mm, 30mm, and 35mm. The equivalent stress results obtained from the finite element analysis were set as labels for the corresponding sample characteristic tensor data. On the one hand, although finite element analysis itself has limitations such as long modeling cycles and reliance on assumptions, the physical accuracy of its calculation results has been widely verified by the engineering community. Using it as a label for supervised learning is equivalent to distilling the "domain knowledge" of the finite element method into the data-driven model, achieving "the accuracy of finite element and the speed of data-driven learning". On the other hand, a standardized process of "orthogonal experimental design → finite element calculation → data post-processing → model training" has been established, which is easy to extend to new parameter ranges or new material types. New data can be generated by following the same process to incrementally update or retrain the model, which has good scalability.

[0067] In this embodiment, a high-fidelity dataset of 160 fully parameterized cases was generated using Abaqus simulation. Using "element-node" as the data unit, key physical quantities were extracted, including: normal stress components in three orthogonal directions (S11, S22, S33), nodal temperature, and spatial coordinates (X, Y, Z) in the global coordinate system. All data was stored in CSV format, with file naming following... <odbname> _ <stepname> _t <timeinseconds>The s_combined.csv file is formatted and stored in separate subfolders under the Temp&S / main directory, categorized by simulated cases, ensuring data traceability and ease of batch processing. The dataset is randomly divided into training, validation, and test sets in a 7:1.5:1.5 ratio.

[0068] Stress prediction models, such as Figure 2 As shown, it includes a shared backbone network, an adapter modulation module, and a prediction module. During training, the loss function includes the mean squared error loss function (MSE), the L1 loss function, or a hybrid MSE+L1 loss function. In this embodiment, the loss function is the mean squared error (MSE), specifically calculated using the following method:

[0069] ;

[0070] Where N is the total number of training samples. This is the predicted output for the i-th sample. Let be the label corresponding to the i-th sample. In this embodiment, the Adam optimizer is used, with a learning rate set to 1e-4 and a training step count of 200.

[0071] The shared backbone network consists of a backbone network formed by stacking multiple KAN layers and a shared KAN layer, used to progressively compress feature dimensions from input data and extract nonlinear coupling features. On the one hand, the KAN layer, built based on the Kolmogorov-Arnold theorem, has inherent interpretability: its activation function is explicitly parameterized by B-spline basis functions, which can clearly reveal the nonlinear mapping relationship between input features (such as temperature and thickness) and stress output, overcoming the "black box" problem of traditional deep learning models (such as MLP and Transformer). On the other hand, the stacked structure compresses feature dimensions layer by layer, achieving efficient feature abstraction and nonlinear coupling modeling while retaining key information, thus improving the ability to model complex thermo-mechanical coupling mechanisms.

[0072] The mapping relationship of any KAN layer is calculated using the following method:

[0073] ;

[0074] in, For input features, The dimension of the input feature. For output features, The dimension of the output feature. For learnable B-spline functions, These are the weights of the linear terms.

[0075] Learnable B-spline functions are parameterized in the following way:

[0076] ;

[0077] in, The number of grid intervals, Let the order be the spline order. For K-order B-spline basis functions, These are learnable spline coefficients. In this embodiment, the number of grid intervals... Set to 5, spline order Set it to 5.

[0078] The K-order B-spline basis function is calculated using a recursive formula and the following method:

[0079] ;

[0080] ;

[0081] Where K is the spline order, and m is the basis function of the m-th segment. Let the order be the spline order. For the m-th node, For the (m+1)th node, For the (m+K)th node, It is the (m+K+1)th node.

[0082] In this embodiment, the shared backbone network employs a backbone network with two stacked KAN layers and a shared KAN layer. The backbone network consists of the 1st KAN layer and the 2nd KAN layer. The 1st KAN layer receives the input feature dimension. The first KAN layer has a feature dimension of 7 (including normal stress components in three orthogonal directions (S11, S22, S33), nodal temperature, and spatial coordinates in the global coordinate system (X, Y, Z)), with an output data dimension of 32 and a spline basis function of 5. The second KAN layer has an input feature dimension of 32 and an output data dimension of 16, while maintaining the spline basis function of 5. The shared KAN layer has an input feature dimension of 16 and an output data dimension of 5. The value is 1, representing the stress prediction result of the generated single sub-model.

[0083] The adapter modulation module, comprising adapter parameter sets independently configured for K parallel sub-models, enables differentiated modulation of the inputs / outputs of these K sub-models. This allows for the generation of a group of functionally complementary sub-models without the need for independently training multiple complete models. Furthermore, compared to traditional integrated independent KAN models, this mechanism significantly reduces the number of parameters, substantially lowering deployment and inference costs. The adapter modulation module performs differentiated modulation at each KAN layer of the backbone network using adapter parameter sets, thereby generating K functionally differentiated sub-models in parallel within the backbone network. On one hand, through layer-by-layer input / output scaling and bias modulation, the model can achieve fine-grained differentiated learning of sub-models at different feature abstraction levels, enabling different sub-models to focus on local features under different operating conditions, material layers, or stress states. On the other hand, this layer-by-layer modulation mechanism enhances the model's adaptability to edge cases (such as extreme temperatures and special geometric parameters), significantly improving generalization performance.

[0084] Adapter parameter group, such as Figure 3 As shown, the system includes an input adapter parameter set, an output adapter parameter set, and a bias adapter parameter set. The adapter modulation module is used to perform differential modulation on the features input to each KAN layer in the backbone network using the corresponding input adapter parameter set, and to perform differential modulation on the features output from each KAN layer using the corresponding output adapter parameter set and bias adapter parameter set. The adapter modulation module modulates the features input to each KAN layer using the corresponding input adapter parameter set and bias adapter parameter set. The sub-model in the first The forward transformation process of the KAN layer is implemented using the following calculation method:

[0085] ;

[0086] in, For the first Sub-model Features output by the KAN layer For the first Sub-model Features output by the KAN layer For element-wise multiplication, For the first Mapping of the KAN layer For the first Sub-model The input adapter parameter group of the KAN layer For the first Sub-model KAN layer output adapter parameter group For the first Sub-model The bias adapter parameter group of the KAN layer. In this embodiment, the first... Sub-model KAN layer input adapter parameter group , stored in (nn.parameterList), with dimensions of ;No. Sub-model KAN layer output adapter parameter group , stored in (nn.parameterList), with dimensions of ;No. Sub-model KAN layer bias adapter parameter group , stored in (nn.parameterList), dimensions and Consistent.

[0087] In this embodiment, the input adapter parameter set of the first KAN layer from Sampling, reflecting the initial diversity; the remaining KAN layers and Initialize to 1, Initialize to 0 to ensure consistent behavior of sub-models in the early stages of training, allowing them to gradually differentiate during training. The first sub-model in the backbone network... After the KAN layer performs tensor flattening on the input features, it performs parallel computation through the corresponding input adapter parameter set. The computation result is then reshaped and mapped to the corresponding KAN layer. The mapped result is then reshaped and performed in parallel computation through the corresponding output adapter parameter set and bias adapter parameter set. Finally, the computation result is tensor flattened and input to the first KAN layer. KAN layer.

[0088] The prediction module aggregates the output data of K sub-models to generate the final equivalent stress prediction value. By fusing the prediction results of multiple sub-models, it effectively reduces the bias and variance of a single model, improving the overall prediction stability and accuracy. In this embodiment, K is set to 32. Initial features (7→32 dimensions) are extracted through the first KAN layer. The adapter modulation module performs differential modulation on the input / output of the 32 sub-models, generating 32 sets of differential features. After differential modulation through the second KAN layer (32→16 dimensions) and the corresponding adapter modulation module, and after differential modulation through the shared KAN layer (16→1 dimension) and the corresponding adapter modulation module, the prediction values ​​of the 32 sub-models are obtained. The prediction module aggregates the outputs of the 32 sub-models using an arithmetic mean to obtain the final equivalent stress prediction value.

[0089] This embodiment also provides a computer device including a memory and a processor. The memory stores a computer program configured to be executed by the processor. The computer program includes instructions for performing the methods described in any of the preceding embodiments.

[0090] This embodiment also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the lightweight learning stress prediction method based on adapter modulation as described in any of the preceding embodiments.

[0091] In summary, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.< / timeinseconds> < / stepname> < / odbname>

Claims

1. A lightweight learning stress prediction method based on adapter modulation, characterized in that, include: Data on the working conditions of the ladle furnace lining were collected and preprocessed to obtain characteristic tensor data; The feature tensor data is input into the stress prediction model to obtain the equivalent stress prediction result. The stress prediction model is trained based on sample feature tensor data and the corresponding equivalent stress labels of the sample feature tensor data; the stress prediction model includes: A shared backbone network, comprising a backbone network formed by stacking multiple KAN layers and a shared KAN layer, is used to progressively compress feature dimensions and extract nonlinear coupling features from input data; The adapter modulation module includes adapter parameter groups that are independently set for K parallel sub-models. The adapter modulation module is used to perform differential modulation through the adapter parameter groups at each KAN layer of the backbone network, thereby deriving K functionally differentiated sub-models in parallel in the backbone network. The prediction module is used to aggregate the output data of K sub-models to generate the final equivalent stress prediction value.

2. The lightweight learning stress prediction method based on adapter modulation according to claim 1, characterized in that, The mapping relationship of any of the KAN layers is calculated using the following method: ； in, For input features, The dimension of the input feature. For output features, The dimension of the output feature. For learnable B-spline functions, These are the weights of the linear terms.

3. The lightweight learning stress prediction method based on adapter modulation according to claim 2, characterized in that, The learnable B-spline function is parameterized in the following manner: ； in, The number of grid intervals, Let the order be the spline order. For K-order B-spline basis functions, These are the learnable spline coefficients.

4. The lightweight learning stress prediction method based on adapter modulation according to any one of claims 1-3, characterized in that: The adapter parameter set includes an input adapter parameter set, an output adapter parameter set, and a bias adapter parameter set. The adapter modulation module is used to perform differential modulation on the features input to the KAN layer at each KAN layer of the backbone network through the corresponding input adapter parameter set, and to perform differential modulation on the features output from the KAN layer through the corresponding output adapter parameter set and bias adapter parameter set.

5. The lightweight learning stress prediction method based on adapter modulation according to claim 4, characterized in that, The adapter modulation module for the first The sub-model in the first The forward transformation process of the KAN layer is implemented using the following calculation method: ； in, For the first Sub-model Features output by the KAN layer For the first Sub-model Features output by the KAN layer For element-wise multiplication, For the first Mapping of the KAN layer For the first Sub-model The input adapter parameter group of the KAN layer For the first Sub-model KAN layer output adapter parameter group For the first Sub-model The bias adapter parameter group for the KAN layer.

6. The lightweight learning stress prediction method based on adapter modulation according to any one of claims 1-3 or 5, characterized in that: The ladle furnace lining operating condition data uses element-node as the data unit, including spatial coordinates in the global coordinate system, normal stress components in three orthogonal directions, and node temperature; The preprocessing to obtain feature tensor data specifically includes the following steps: The standardization of the ladle furnace lining operating data is achieved using the following calculation method: ， in, This is data on the operating conditions of the ladle furnace lining. The mean of the data. The standard deviation of the data; The standardized data is expanded into 3D feature tensors adapted to K sub-models using the Kronecker product. The specific calculation method is as follows: ； in, For Kronecker product operation, It is a column vector whose elements are all 1s.

7. The lightweight learning stress prediction method based on adapter modulation according to claim 6, characterized in that: The backbone network in the first After the KAN layer performs tensor flattening on the input features, it performs parallel computation through the corresponding input adapter parameter set. The computation result is then reshaped and mapped to the corresponding KAN layer. The mapped result is then reshaped and performed in parallel computation through the corresponding output adapter parameter set and bias adapter parameter set. Finally, the computation result is tensor flattened and input to the first KAN layer. KAN layer.

8. The lightweight learning stress prediction method based on adapter modulation according to any one of claims 1-3, 5 or 7, characterized in that: The sample feature tensor data were obtained by orthogonal experimental design, covering ladle furnace structural layer parameters, material property parameters and steel shell parameters, and were solved by finite element analysis method. The structural layer parameters include the working layer thickness parameters, the permanent layer thickness parameters, and the insulation layer thickness parameters; The material properties include thermal conductivity and Young's modulus; The steel shell parameters include the steel shell thickness parameter; Set the equivalent stress results obtained from finite element analysis as the labels for the corresponding sample feature tensor data.

9. A computer device, characterized in that, It includes a memory and a processor, the memory storing a computer program configured to be executed by the processor, the computer program including instructions for performing the method of any one of claims 1-8.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the lightweight learning stress prediction method based on adapter modulation as described in any one of claims 1-8.

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