A method for predicting magnetic core loss of an electrical element based on a soft-gating hybrid expert model

Abstract

The application relates to an electrical element magnetic core loss prediction method based on a soft gate mixed expert model, and the method adaptively adjusts expert weights, so that the model is more flexible and has strong adaptability when facing different types of data; diversified expert model combinations can complement respective advantages, improve overall robustness and generalization capability, and reduce the risk of overfitting; in addition, modular design makes the model easy to extend and maintain, and the model can be enhanced in interpretability by analyzing the output weight of the gating network; furthermore, automatic parameter adjustment and end-to-end training through an intelligent optimization algorithm further improve the performance of the model; finally, the soft gate mixed expert model can effectively process nonlinear and complex relationships, utilize the powerful nonlinear modeling capability of MLP to capture complex patterns in data, and improve calculation efficiency through parallel computing and dynamic resource allocation. These advantages make the soft gate mixed expert model have higher accuracy and reliability when processing complex tasks such as magnetic core loss prediction.

Description

TECHNICAL FIELD

[0001] The application relates to a magnetic core loss prediction method for an electrical element, in particular to a magnetic core loss prediction method for an electrical element based on a soft-gated hybrid expert model. TECHNICAL BACKGROUND

[0002] With the steady advancement of the modernization process in China, power electronics technology, as the core technology of electric energy conversion, has developed rapidly. Electric energy conversion or power conversion technology based on power electronics has become an important part of modern electric energy systems and has a wide range of applications in large intelligent equipment power supplies, electric vehicles, rail transit and smart grids. With the advancement of semiconductor technology, power converters are developing towards high frequency, high power density and high performance. Magnetic elements play a key role in power converters, and their loss accounts for a large proportion of the total power loss. Therefore, optimizing the performance of magnetic elements is crucial to improving the efficiency of the entire system.

[0003] Magnetic elements are usually composed of windings and magnetic cores, and the loss mainly includes two categories of magnetic core loss and winding loss. For winding loss, common methods include electromagnetic field finite element simulation, direct measurement under specific excitation waveform conditions, and measurement based on alternating current power, etc. In contrast, magnetic core loss is the energy loss generated by magnetic materials under the action of alternating magnetic field, which is affected by many factors such as operating frequency, magnetic flux density, excitation waveform, temperature and magnetic core material, making the calculation and modeling of magnetic core loss complex and challenging.

[0004] Existing magnetic core loss models can be roughly divided into two categories: one is a separation model that decomposes the magnetic core loss into hysteresis loss, eddy current loss and residual loss, and estimates the total magnetic core loss by calculating these components independently; the other is an empirical calculation model, which is mainly fitted based on a large amount of experimental data, among which the most widely used method is the Steinmetz Equation (SE) based method. However, the traditional Steinmetz equation is only applicable to the case of sinusoidal excitation. In order to adapt to the wider excitation waveform requirements, Rudy Severns proposed a modified Steinmetz equation (MSE), which can handle the problem of magnetic core loss under non-sinusoidal waveform conditions. In addition, Venkatachalam et al. also proposed an improved scheme considering the rate of change of magnetic flux density and double peak characteristics, further improving the prediction accuracy.

[0005] In recent years, with the development of big data and artificial intelligence technology, the global trend of industrial automation, intelligence and digitization is becoming increasingly apparent. In this context, the use of advanced data analysis techniques and machine learning algorithms to establish more accurate data-driven core loss analysis and prediction models has become a research hotspot. This approach not only helps to deepen the understanding of core loss mechanisms, but also provides reliable prediction results under different operating conditions, thereby guiding the research and application of new high-efficiency magnetic materials and promoting the continuous progress of power electronics technology. By combining traditional physical models with modern data science technology, researchers aim to develop a new generation of core loss evaluation tools that can accurately reflect actual operating conditions and meet the needs of engineering design. SUMMARY

[0006] The purpose of the present application is to propose a soft-gated hybrid expert model-based electrical element core loss prediction method. The present application enhances the model's explainability by analyzing the output weights of the gating network. The performance of the model is further improved through intelligent optimization algorithms for automatic parameter tuning and end-to-end training. The powerful non-linear modeling capabilities of MLP are used to capture complex patterns in the data, and parallel computing and dynamic resource allocation are used to improve computational efficiency. These advantages make the soft-gated hybrid expert model more accurate and reliable in handling complex tasks such as core loss prediction.

[0007] The purpose of the present application is achieved through the following technical solutions:

[0008] A soft-gated hybrid expert model-based electrical element core loss prediction method, comprising the following steps:

[0009] 1. Obtain a core loss dataset;

[0010] 2. Perform feature engineering on the dataset, extract features, and then perform skew correction on continuous features and one-hot encoding on discrete features;

[0011] 3. Perform feature selection on the current features, use the XGBoost and SHAP combined method to evaluate the influence of each feature on core loss, and then remove features with low importance;

[0012] 4. Establish an expert model, select several well-performing base models as experts, such as Extra-tree, Ridge regression, LASSO regression, CatBoost, LightGBM, etc., and establish their ensemble model as one of the experts. These models should have complementarity, i.e., they can capture different features and patterns of data in different aspects.

[0013] 5. Train the ensemble of experts, train each selected expert model independently using a dataset, and each model should be tuned for hyperparameters to achieve the best performance by using an intelligent optimization algorithm.

[0014] 6. Design the gating network, usually a multi-layer perceptron (MLP) is used as the gating network, which is responsible for computing the weights for each expert model given the input data. The output layer of the MLP usually has as many nodes as the number of experts, and the output values of these nodes are normalized (e.g. by the softmax function) to obtain a valid set of weights. The gating network needs to be trained to learn how to assign appropriate weights to each expert for a given data sample.

[0015] 7. Combine the expert models, use the gating network to determine the weights for each expert model given the input data. Then, weight the prediction results of each expert model by the weights given by the gating network and obtain the final prediction result by averaging.

[0016] The magnetic core loss prediction method based on the soft gating hybrid expert model according to the above disclosure of the application can further have the following additional technical features:

[0017] According to an embodiment of the application, in S1, the variables affecting the magnetic core loss are: temperature, material type, 1024 sampling point values in a period, excitation waveform, frequency, wherein the material type has 4 types, the excitation waveform has 3 types, which are sine wave, triangle wave and trapezoidal wave, the 1024 sampling points are obtained by sampling at the same interval in a period of time, the temperature takes 4 values: 25, 50, 70, 90, unit: Celsius degree;

[0018] According to an embodiment of the application, in S2, feature extraction is performed on the existing dataset, and statistical features, gradient features, gradient mutation points, spectral features and part of the PCA principal component analysis features are extracted respectively.

[0019] According to an embodiment of the application, in S4, Extra-tree, Ridge regression, LASSO regression, CatBoost and LightGBM are used respectively.

[0020] Extra-Tree is an ensemble learning method that makes predictions by building multiple decision trees. For regression tasks, the predicted value is the average of all tree predictions, and the formula is:

[0021]

[0022] where T is the number of trees, f t (x) is the prediction value of the tth tree for input x.

[0023] The prediction formula for Ridge regression is the same as for ordinary linear regression, but with an L2 regularization term introduced during training to prevent overfitting. The formula is:

[0024]

[0025] where β0 is the intercept term and β j are the coefficients for the features x j , which are obtained by minimizing an objective function during training.

[0026] The prediction formula for LASSO regression is also the same as for ordinary linear regression, but the coefficient estimates are constrained by an L1 regularization term. The formula is:

[0027]

[0028] Here, β j are again obtained by minimizing an objective function during training, but this time the objective function includes an L1 regularization term.

[0029] CatBoost uses gradient boosting decision trees for prediction. Each tree outputs a prediction value, and the final prediction is the sum of all tree prediction values. The formula is:

[0030]

[0031] where N is the number of trees, w_i is the weight of the i-th tree, and f_i(x) is the prediction value of the i-th tree for input x.

[0032] LightGBM is also a gradient boosting decision tree model, and its prediction formula is similar to CatBoost, where the final prediction is obtained by summing up the prediction values of all trees.

[0033]

[0034] In LightGBM, f_i(x) and f_i(x,c) represent the prediction value of the i-th tree for input x and the probability or score of predicting class c, respectively.

[0035] In addition, there are ensemble learning methods that use LightGBM as the base learner and other algorithms as the sub-learners. Suppose we have M primary models h_1, h_2, …, h_M, each of which has a prediction value for sample x. We can combine these prediction values into a vector z(x)

[0036] z(x) = [h1(x), h2(x), …, h M (x)]

[0037] This vector z(x) is the input feature of the secondary model. The secondary model can be any regression model, such as linear regression, logistic regression, random forest, etc.

[0038] The final prediction result is:

[0039]

[0040] According to an embodiment of the present application, the single-objective algorithm used for optimizing each model is Tree-structured Parzen Estimator (TPE), which is a hyperparameter optimization algorithm based on Bayesian optimization. It guides the search process by constructing two probability density functions, effectively finding the optimal combination of hyperparameters. The main idea of TPE algorithm is to divide the search space into "good" and "bad" two parts, and try to sample new hyperparameter combinations in the "good" area.

[0041] The single objective of TPE optimization is the Root Mean Squared Error (RMSE), which is the square root of the average of the squares of the differences between the predicted value and the actual value. Its formula is as follows:

[0042]

[0043] n is the number of samples. y_i is the actual observation value of the i-th sample. \hat{y}_i is the predicted value of the i-th sample.

[0044] According to an embodiment of the present application, S7, we use a gating network to dynamically assign weights to each expert model, so as to achieve optimal prediction of input data. The gating network is usually a multi-layer perceptron (MLP), whose input is the same as the expert model, and the number of nodes in the output layer is equal to the number of expert models. The output of each node is normalized to a weight value between 0 and 1 through the Softmax function, representing the importance of the corresponding expert model under the current input. The gating network is trained together with the expert models, optimizing the parameters by minimizing the overall prediction error, ensuring that the gating network can learn how to reasonably allocate the weights of the expert models for different types of input data.

[0045] In the prediction phase, for each new input, the gating network first calculates the weight of each expert model, and then applies these weights to the prediction results of each expert model to obtain the final prediction output through weighted averaging. This process not only improves the flexibility of the model, but also enhances the robustness and generalization ability of the system, because different expert models can play their respective advantages under different input modes. In this way, the hybrid expert model can more accurately adapt to various complex data distributions and provide more reliable prediction results.

[0046] The advantages and positive effects of the present application are:

[0047] Compared with the existing integrated stacking technology, the present application can adaptively adjust the expert weight, making the model more flexible and adaptive when facing different types of data. Secondly, the diversified combination of expert models can complement each other's advantages, improve the overall robustness and generalization ability, and reduce the risk of overfitting. In addition, the modular design makes the model easy to extend and maintain, and can enhance the model's explainability by analyzing the output weight of the gating network. Furthermore, through intelligent optimization algorithm automatic tuning and end-to-end training, the performance of the model is further improved. Finally, the soft-gating hybrid expert model can effectively handle nonlinear and complex relationships, using the powerful nonlinear modeling capability of MLP to capture complex patterns in the data, and improving computational efficiency through parallel computing and dynamic resource allocation. These advantages make the soft-gating hybrid expert model perform better in handling complex tasks such as magnetic core loss prediction in terms of accuracy and reliability. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 is the step diagram of the technical scheme of the present application;

[0049] Figure 2 is the feature evaluation comparison chart of the present application;

[0050] Figure 3 is the structure chart of the soft-gating hybrid expert model of the present application; DETAILED DESCRIPTION

[0051] The specific embodiments of the present application will be further described in detail below with reference to the drawings, and the purpose is to help the technical personnel in the field to have a more complete, accurate and in-depth understanding of the inventive concept and technical scheme of the present application, and to facilitate its implementation. In order to make the technical scheme of the present application more clear, the present application is explained and described by the following embodiments:

[0052] A magnetic core loss prediction method based on a soft-gating hybrid expert model, the method can be seen Figure 1 , comprising the following steps:

[0053] 1. Obtain a magnetic core loss data set;

[0054] 2. Perform feature engineering on the data set, extract features, and then perform skew correction on continuous features and one-hot encoding on discrete features;

[0055] 3. Perform feature selection on the current features, use the XGBoost combined with SHAP method to evaluate the influence degree of each feature on the magnetic core loss, and then remove the features with low importance, which can be seen Figure 2 ;

[0056] 4. Establishing expert models, selecting several well-performing base models as experts, such as Extra-tree, Ridge regression, LASSO regression, CatBoost, LightGBM, etc., and establishing their ensemble models as one of the experts. These models should have complementarity, i.e., they can capture different features and patterns of data in different aspects.

[0057] 5. Training expert models, training each selected expert model independently using the data set, and each model should be optimized for hyperparameters through intelligent optimization algorithms to achieve the best performance.

[0058] 6. Designing a gating network, usually using a multi-layer perceptron (MLP) as the gating network, which is responsible for calculating the weight of each expert model according to the input data. The output layer of the MLP usually has the same number of nodes as the number of experts, and the output values of these nodes are normalized (e.g., through the softmax function) to obtain a set of valid weights. The gating network needs to be trained to learn how to assign appropriate weights to each expert for a given data sample.

[0059] 7. Combining expert models, using the gating network to determine the weight of each expert model according to the input data. Then, the prediction results of each expert model are weighted and averaged according to the weight given by the gating network to obtain the final prediction result.

[0060] The magnetic core loss prediction method based on the soft gating hybrid expert model according to the above disclosure of the present application can also have the following additional technical features:

[0061] According to an embodiment of the present application, in S1, the variables affecting the magnetic core loss are: temperature, material type, 1024 sampling point values in a period, excitation waveform, frequency, where the material type has 4 types, the excitation waveform has 3 types, which are sine wave, triangle wave and trapezoidal wave, the 1024 sampling points are obtained by sampling at the same interval within a period of time, the temperature takes 4 values: 25, 50, 70, 90, unit: Celsius;

[0062] According to an embodiment of the present application, in S2, feature extraction is performed on the existing data set, and statistical features, gradient features, gradient mutation points, spectral features and partial features of PCA principal component analysis are extracted respectively.

[0063] According to an embodiment of the present application, in S4, Extra-tree, Ridge regression, LASSO regression, CatBoost and LightGBM are used respectively;

[0064] Extra-Tree is an ensemble learning method that makes predictions by building multiple decision trees. For regression tasks, the predicted value is the average of all tree predictions, as shown in the following formula:

[0065]

[0066] Where T is the number of trees, f t (x) is the predicted value of the t-th tree for the input x.

[0067] The prediction formula of Ridge regression is the same as that of ordinary linear regression, except that the L2 regularization term is introduced during the training process to prevent overfitting. The formula is:

[0068]

[0069] Where β0 is the intercept term, β j is feature x j These coefficients are obtained by minimizing the objective function during the training process.

[0070] The prediction formula of LASSO regression is the same as that of ordinary linear regression, but its coefficient estimation is subject to L1 regularization constraints. The formula is:

[0071]

[0072] Here β j It is also obtained by minimizing the objective function including the L1 regularization term during training.

[0073] CatBoost uses gradient boosting decision trees to make predictions. Each tree outputs a prediction value, and the final prediction is the sum of all the tree predictions. The formula is:

[0074]

[0075] Where N is the number of trees, w_i is the weight of the i-th tree, and f_i(x) is the prediction of the i-th tree for input x.

[0076] LightGBM is also a gradient boosting decision tree model. Its prediction formula is similar to CatBoost, and the final prediction is obtained by accumulating the prediction values ​​of all trees.

[0077]

[0078] In LightGBM, f_i(x) and f_i(x,c) represent the predicted value of the i-th tree for the input x and the probability or score of the prediction being category c, respectively.

[0079] In addition, there is an ensemble learning method that uses LightGBM as the base learner and other algorithms as the sub-learners. Suppose we have M primary models h_1, h_2, …, h_M, each of which has a prediction value for a sample x. We can combine these prediction values into a vector z(x)

[0080] z(x) = [h1(x), h2(x), …, h M (x)]

[0081] This vector z(x) is the input feature of the secondary model. The secondary model can be any regression model, such as linear regression, logistic regression, random forest, etc.

[0082] The final prediction result is:

[0083]

[0084] According to an embodiment of the present application, the single-objective algorithm used for optimizing each model is Tree-structured Parzen Estimator (TPE), which is a hyperparameter optimization algorithm based on Bayesian optimization. It guides the search process by constructing two probability density functions, effectively finding the optimal combination of hyperparameters. The main idea of the TPE algorithm is to divide the search space into "good" and "bad" parts, and try to sample new hyperparameter combinations in the "good" area.

[0085] The single objective of TPE optimization is the Root Mean Squared Error (RMSE), which is the square root of the average of the squares of the differences between the predicted value and the actual value. Its formula is as follows:

[0086]

[0087] n is the number of samples. y_i is the actual observation value of the i-th sample. \widehat{y_i} is the predicted value of the i-th sample.

[0088] According to an embodiment of the present application, the single-objective algorithm used for optimizing each model is Tree-structured Parzen Estimator (TPE), which is a hyperparameter optimization algorithm based on Bayesian optimization. It guides the search process by constructing two probability density functions, effectively finding the optimal combination of hyperparameters. The main idea of the TPE algorithm is to divide the search space into "good" and "bad" parts, and try to sample new hyperparameter combinations in the "good" area.

[0085] TPE optimization is a single objective of the Root Mean Squared Error (RMSE), which is the square root of the average of the squares of the differences between the predicted value and the actual value. Its formula is as follows:

[0086]

[0087] n is the number of samples. y_i is the actual observation value of the i-th sample. \widehat{y_i} is the predicted value of the i-th sample.

[0088] According to an embodiment of the present application, the single-objective algorithm used for optimizing each model is Tree-structured Parzen Estimator (TPE), which is a hyperparameter optimization algorithm based on Bayesian optimization. It guides the search process by constructing two probability density functions, effectively finding the optimal combination of hyperparameters. The main idea of the TPE algorithm is to divide the search space into "good" and "bad" parts, and try to sample new hyperparameter combinations in the "good" area.

[0085] TPE optimization is a single objective of the Root Mean Squared Error (RMSE), which is the square root of the average of the squares of the differences between the predicted value and the actual value. Its formula is as follows:

[0086]

[0087] n is the number of samples. y_i is the actual observation value of the i-th sample. \widehat{y_i} is the predicted value of the i-th sample.

[0088] According to an embodiment of the present application, the single-objective algorithm used for optimizing each model is Tree-structured Parzen Estimator (TPE), which is a hyperparameter optimization algorithm based on Bayesian optimization. It guides the search process by constructing two probability density functions, effectively finding the optimal combination of hyperparameters. The main idea of the TPE algorithm is to divide the search space into "good" and "bad" parts, and try to sample new hyperparameter combinations in the "good" area.Figure 3 .

[0089] In the prediction phase, for each new input, the gating network first calculates the weights for each expert model, and then applies these weights to the prediction results of individual expert models to obtain the final prediction output through weighted averaging. This process not only improves the flexibility of the model, but also enhances the robustness and generalization ability of the system, as different expert models can take advantage of different input patterns. In this way, the hybrid expert model can more accurately adapt to various complex data distributions and provide more reliable prediction results.

[0090] Although the present application is described in detail with reference to the preferred embodiments, the present application is not limited to this. Any modification or replacement of the embodiments of the present application made by those skilled in the art without departing from the spirit and essence of the present application shall be within the scope of the present application. Any modification or replacement made by those skilled in the art within the technical scope disclosed by the present application shall be within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A method for predicting core loss of electrical components based on a soft-gated hybrid expert model, characterized by: The method obtains the prediction results of each expert model by weighting according to the weight provided by the gating network, including the following steps: 1) Obtain a core loss dataset; 2) Perform feature engineering on the dataset to extract features, perform skewness correction on continuous features, and perform one-hot encoding on discrete features; 3) Perform feature screening on the current features, use a combination of XGBoost and SHAP to evaluate the impact of each feature on core loss, and then remove features with low importance; 4) Establish an expert model. Select several basic models with good performance as experts, including Extra-tree, Ridge regression, LASSO regression, CatBoost, and LightGBM. In addition, establish an integrated model of these models as one of the experts. These models should be complementary, that is, they can capture different characteristics and patterns of the data in different aspects. 5) Train the expert model. Each selected expert model should be trained independently using the dataset, and each model should have its hyperparameters tuned by an intelligent optimization algorithm to achieve optimal performance. 6) Design a gating network, using a multilayer perceptron (MLP) as the gating network. This network is responsible for calculating the weights of each expert model based on the input data. The output layer of the MLP will have the same number of nodes as the number of experts, and the output values ​​of these nodes will be normalized to obtain a set of valid weights. The gating network needs to be trained to learn how to assign appropriate weights to each expert for a given data sample. 7) Combine the expert models and use the gating network to determine the weight of each expert model based on the input data; then, the prediction results of each expert model are weighted averaged according to the weight given by the gating network to obtain the final prediction result; In step 5, the single-objective algorithm used to optimize each model is TPE, a hyperparameter optimization algorithm based on Bayesian optimization. It constructs two probability density functions to guide the search process, thereby effectively finding the optimal hyperparameter combination. The idea of ​​the TPE algorithm is to divide the search space into "good" and "bad" parts and try to sample new hyperparameter combinations in the "good" area. The single objective of TPE optimization is the root mean square error (RMSE). RMSE is the square root of the average of the squares of the differences between the predicted value and the actual value. The formula is as follows: n is the sample size; y i is the actual observation value of the i-th sample; is the predicted value of the i-th sample.

2. The method for predicting core loss of electrical components based on a soft-gated hybrid expert model according to claim 1, characterized in that: In step 1, the variables affecting the core loss are: temperature, material type, 1024 sampling point values ​​within a cycle, excitation waveform, and frequency. There are four material types and three excitation waveform types, namely, sine wave, triangle wave, and trapezoidal wave. The 1024 sampling points are obtained by sampling at the same interval within a cycle time. The temperature takes four values: 25, 50, 70, and 90, in degrees Celsius.

3. The method for predicting core loss of electrical components based on a soft-gated hybrid expert model according to claim 1, characterized in that: In step 2, feature extraction is performed on the existing data set, and statistical features, gradient features, gradient mutation points, spectrum features and partial features of PCA principal component analysis are extracted respectively.

4. The method for predicting core loss of electrical components based on a soft-gated hybrid expert model according to claim 1, wherein: In step 4, Extra-tree, Ridge regression, LASSO regression, CatBoost and LightGBM are used respectively; Extra-Tree is an ensemble learning method that makes predictions by building multiple decision trees; For regression tasks, the predicted value is the average of all tree predictions, and the formula is: Where T is the number of trees, f t (x) is the predicted value of the t-th tree for the input x; The prediction formula of Ridge regression is the same as that of ordinary linear regression, except that the L2 regularization term is introduced during training to prevent overfitting; The formula is: Where β0 is the intercept term, β j is feature x j The coefficients of , which are obtained by minimizing the objective function during the training process; The prediction formula of LASSO regression is also the same as that of ordinary linear regression, but its coefficient estimation is subject to L1 regularization constraints; The formula is: Here β j It is also obtained by minimizing the objective function containing the L1 regularization term during training; CatBoost uses gradient boosted decision trees to make predictions; each tree outputs a prediction value, and the final prediction is the sum of all the tree predictions. The formula is: Where N is the number of trees, w i is the weight of the i-th tree, f i (x) is the predicted value of the i-th tree for input x; LightGBM is also a gradient boosting decision tree model. Its prediction formula is similar to CatBoost, and the final prediction is obtained by accumulating the prediction values ​​of all trees. In LightGBM, f i (x) represents the predicted value of the i-th tree for input x; In addition, there is an ensemble learning method that uses LightGBM as a base learner and other algorithms as sub-learners; suppose there are M primary models h_1,h_2,...,h_M, each model has a prediction value for sample x; these prediction values ​​are combined into a vector z(x) z(x)=[h1(x),h2(x),…,h M (x)] This vector z(x) is the input feature of the secondary model; the secondary model is a regression model; The final prediction results are:

5. The method for predicting core loss of electrical components based on a soft-gated hybrid expert model according to claim 1, characterized in that: In step 7, a gating network is used to dynamically assign weights to each expert model, thereby achieving optimal prediction of the input data. The gating network is a multi-layer perceptron (MLP), whose input is the same as the expert model, and the number of nodes in the output layer is equal to the number of expert models. The output of each node is normalized to a weight value between 0 and 1 using a Softmax function, indicating the importance of the corresponding expert model under the current input. The gating network is trained together with the expert model, and the parameters are optimized by minimizing the overall prediction error, ensuring that the gating network can learn how to reasonably assign weights to the expert models for different types of input data. During the prediction phase, for each new input, the gating network first calculates the weights of each expert model, then applies these weights to the prediction results of each expert model, and obtains the final prediction output through weighted averaging. This process not only improves the flexibility of the model, but also enhances the robustness and generalization ability of the system, because different expert models play their respective advantages under different input modes. In this way, the hybrid expert model can more accurately adapt to various complex data distributions and provide more reliable prediction results.

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