Power system inertia prediction method based on adaptive wavelet KAN network

Abstract

The invention belongs to the field of power system modeling and artificial intelligence, and particularly provides a power system inertia prediction method based on an adaptive wavelet KAN network, and the method comprises the steps: constructing an adaptive wavelet KAN network structure, and carrying out the modeling of frequency response data of a power system after disturbance; a linear residual channel is embedded into the adaptive wavelet KAN network structure to form a dual-channel structure; automatically searching and adjusting the structure hyper-parameters of the adaptive wavelet KAN network by using a Bayesian optimization framework; constructing a multi-quantile output structure to realize confidence interval modeling of inertia prediction; designing a progressive pruning mechanism to cut redundant edge connections and wavelet channels; generating a corresponding visual neural network structure chart; an explicit activation function expression of each layer of the network is extracted, and an algebraic prediction formula capable of being directly deployed is generated; and outputting an inertia prediction result of the model and an explicit expression thereof. According to the prediction method, the prediction precision can be improved, and multi-scale disturbance signals can be effectively processed.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of power system modeling and artificial intelligence, and in particular, relates to a power system inertia prediction method based on an adaptive wavelet KAN network. BACKGROUND

[0002] The inertia of a power system is a key parameter for measuring the frequency stability and dynamic response capability of the system. In particular, in the context of a high proportion of renewable energy access leading to a continuous decrease in rotational inertia, accurately and real-time predicting the change in system inertia has become an important supporting technology for dispatching control and safety assessment. However, the current mainstream inertia evaluation methods still have obvious deficiencies: the methods based on equivalent models or identification algorithms rely on strong prior information of the system, and are difficult to adapt to the data incompleteness and diversity of disturbances in actual operation; while the deep learning methods based on pure data driving have improved the prediction accuracy, but generally have strong "black box" nature, complex structure, and cannot derive an explicit expression, which makes it difficult to meet the engineering needs for transparency and deployability of the prediction results.

[0003] In order to improve the explainability and structural controllability of the modeling process, in recent years, Kolmogorov-Arnold Networks (KAN) have been proposed. This structure is based on the Kolmogorov representation theorem, and replaces the setting of the unified activation function of the traditional neural network with a form of layer-by-layer mapping and single-variable function combination, so that each connection edge can learn an independent function transformation, and has advantages such as structural visibility, path traceability, and formula derivability. KAN has shown good modeling transparency in load prediction, time series modeling and other scenarios. However, the initial version of KAN mostly uses B-spline as the function base of the connection edge, which has problems such as complex interpolation calculation, low training efficiency, and limited function form, especially when dealing with inertia signals that contain trend, shock and mutation at the same time, the expression ability is still insufficient.

[0004] In order to enhance the modeling ability of KAN network for local disturbance and frequency domain features, existing research has attempted to embed fixed wavelet functions (such as Morlet, DOG, etc.) into KAN network to form a so-called "wavelet KAN" structure. This structure uses the good time-frequency locality and analytical form of wavelet functions to replace spline functions, improving the performance of the network in high-frequency disturbance modeling and edge feature learning. However, the existing wavelet KAN structure still has two significant limitations: (1) each edge only uses a single fixed wavelet function, which cannot adapt to the frequency response characteristics required by different edge connections; (2) the activation function parameters cannot be adaptively adjusted across channels, resulting in limited expression ability, and the coupled features between channels cannot be effectively fused. SUMMARY

[0005] The technical problem solved by the present application is to provide a power system inertia prediction method based on an adaptive wavelet KAN network, to improve prediction accuracy and effectively process multi-scale disturbance signals.

[0006] To solve the above technical problems, the technical solution adopted by the present application is: a power system inertia prediction method based on an adaptive wavelet KAN network, comprising the following steps: Step one, an adaptive wavelet KAN network structure is constructed to model the frequency response data after power system disturbance, and the edges between the layers of the adaptive wavelet KAN network structure adopt an activation function formed by a combination of multiple wavelet functions to perform nonlinear transformation on the input features; Step two, a linear residual channel is embedded in the adaptive wavelet KAN network structure to form a linear residual network structure, and the original input signal passes through the linear residual channel to retain the main trend information in a linear path, and then is superimposed with the output of the wavelet channel to form a double-channel structure; Step three, the structure hyperparameters of the adaptive wavelet KAN network are automatically searched and adjusted using a Bayesian optimization framework; Step four, the linear residual network structure constructed in step two is trained using a quantile regression mechanism based on the training data and the structure hyperparameters adjusted in step three, a multi-quantile point output structure is constructed to realize confidence interval modeling of inertia prediction; Step five, an incremental pruning mechanism is designed by combining L1 regularization and a sensitivity index constructed based on an approximate Hessian matrix to prune the network structure trained in step four, the pruning ratio is gradually increased in a multi-round cycle mode, and parameter fine-tuning and structure recovery are performed after each round to prune redundant edge connections and wavelet channels; Step six, based on the network structure and parameters pruned in step five, a corresponding visual neural network structure diagram is generated, and each connection edge in the visual neural network structure diagram is visually represented by its corresponding wavelet function; Step seven, based on the network structure pruned in step five, the wavelet activation function parameters on each edge are extracted, the explicit activation function expression of each layer of the network is extracted, and a directly deployable algebraic prediction formula is generated by combining a standardization inverse transformation mechanism; Step eight, based on the network structure pruned in step five, the inertia prediction result and the directly deployable algebraic prediction formula are output.

[0007] In the preferred scheme, in step one, the activation function adopted by the edges between the layers of the adaptive wavelet KAN network structure is expressed as: ; wherein, represents the Wavelet mother function; is an amplitude weight, is a translation parameter, is a scale parameter, all of which are learnable variables; the number of wavelet base functions is a positive integer, is an input variable.

[0008] In the preferred scheme, in step two, the linear residual channel is arranged in parallel in each wavelet KAN layer, specifically: The input vector is directly mapped to the linear term through a linear channel without wavelet transform , and the wavelet activation channel output is added element by element to obtain the total output of the layer: ; wherein, is a nonlinear output obtained based on the wavelet activation function matrix mapping; is a learnable linear mapping weight matrix. In the preferred scheme, in step three, the structural hyperparameters of the adaptive wavelet KAN network include but are not limited to the number of network hidden layers, the number of nodes in each layer, the initial learning rate, the L2 regularization term weight decay factor, and the training batch size.

[0009] In the preferred scheme, in step four, the quantile regression mechanism is used to train the linear residual network structure constructed based on step two, and a multi-quantile point output structure is constructed to realize the confidence interval modeling of the inertia prediction. After training, the median prediction value in the model output is taken as the inertia point estimate, and the prediction interval composed of the low-quantile point and the high-quantile point is output. Specifically, it includes: 1) For each input feature at each time, the network outputs multiple quantile points q corresponding prediction values , wherein , and the quantile point set includes but is not limited to: ; 2) The training target adopts a quantile loss function. For each real value and quantile prediction value , the loss is defined as: ; 3) The total loss of the quantile loss function is the weighted sum of the losses of all quantile points, and the expression is: ; wherein, is the loss weight coefficient corresponding to each quantile point.

[0010] In the preferred scheme, the step five specifically comprises: 1) In the pruning stage, first construct the amplitude weight of wavelet activation function connected by each edge is the sensitivity index of the target , the expression is: ; Wherein, is the loss function, represents the layer, the edge on the kind of wavelet function amplitude weight; 2) The pruning process is carried out in an iterative manner, and the round of pruning rate is calculated as follows: ; Wherein, , is the basic pruning rate; is the total number of pruning rounds; is the current pruning round; 3) In each round of pruning, according to the Hessian sensitivity Size, the least important edge connection and the corresponding wavelet channel in the current proportion are shielded out; 4) After each round of pruning, the network structure accuracy is restored by adding Regularization term fine-tuning mechanism, the loss function is updated as: ; Wherein, is the original quantile loss function, is the regularization strength hyperparameter.

[0011] In the preferred scheme, in the step five, every fixed round in the fine-tuning process calculates Index on the validation set and judges whether to update the current network structure, the saving standard is: if the current network structure pruning rate is higher, and No less than the original network structure, update and save the current network structure; if the pruning rate of the original network structure and the current network structure is the same, prefer to keep The higher network structure.

[0012] In a preferred solution, in step six, the visualized neural network structure diagram adopts a bottom-up hierarchical representation, strictly following the architecture of the KAN network, with the input layer, hidden layer and output layer arranged in sequence, and directional edges connected between each layer, the number of edges corresponding one-to-one to the non-zero wavelet channels retained after training, and the activation function represented by each connection edge visually coded by the included wavelet type, wherein if three wavelets are fused on a connection edge, the edge is connected with a solid line; if only two wavelets are fused, the edge is connected with a dashed line; if only one wavelet is included, the edge is connected with a dotted dashed line; if the weights of the three wavelets on the connection edge are all set to zero, the connection edge is completely deleted.

[0013] In a preferred solution, in step seven, the following operations are included: 1) For each retained connection edge, extract the set of wavelet activation function parameters after training , and generate the explicit activation function form of the edge according to the fusion structure: ; wherein represents the number of wavelet functions participating in weighted fusion on the th layer and the th connection edge, represents the translation parameter of the corresponding wavelet , represents the scale parameter of the corresponding wavelet ; 2) Each output node is formed by weighted superposition of all input nodes from the previous layer after wavelet activation function mapping, with a residual connection added, i.e. ; wherein is the linear weight parameter of the residual channel; The overall formula function of the network generated without inverse normalization is the composite combination of all hierarchical mappings: ; wherein is the overall mapping function matrix of the th layer; represents the function composition operator, i.e. substituting the calculation result of each layer into the next layer ; 3) After inverse normalization conversion, the final derived algebraic prediction formula expression that can be directly deployed is: ; wherein , are the mean and standard deviation of the target variable training set, respectively, It is the prediction formula expression after inverse standard transformation, that is, the final output is a directly deployable algebraic prediction formula.

[0014] In the preferred embodiment, in step eight, partial derivative analysis is performed on the input variables based on the algebraic prediction formula to construct a global interpretability index system. The global interpretability index system includes global variable importance assessment, variable time-series sensitivity trajectory analysis, variable directional trend analysis, and second-order interaction analysis between variables. Global variable importance assessment: Calculate the importance of each input variable based on an algebraic prediction formula. The expectation of the square of the absolute value of the partial derivative is used as a sensitivity index to reflect the average sensitivity of the variable to the output result in the entire input space. Variable time-series sensitivity trajectory analysis: Calculating the value of each input variable based on algebraic prediction formulas. Construct a two-dimensional sensitivity matrix by taking the absolute values ​​of the first-order partial derivatives at all time points in the validation set. Each row of the matrix represents the trajectory of a variable over the entire time series. Variable directional trend analysis: Based on algebraic prediction formulas, calculate the directional trend of each input variable. The partial derivatives of the variable are as follows: a positive partial derivative indicates that the variable promotes the increase of the predicted value of inertia, a negative partial derivative indicates that it has a suppressive effect, and a partial derivative close to zero indicates that the variable has a weak or insensitive effect on the predicted result at that moment. Second-order interaction analysis between variables: Calculating input variables based on algebraic prediction formulas. and The second-order mixed partial derivatives between them, through the input variables and The second-order mixed partial derivatives determine the synergistic coupling relationship and nonlinear interaction characteristics between variables.

[0015] The present invention provides a power system inertia prediction method based on an adaptive wavelet KAN network, which has the following advantages: 1. In step one of this invention, based on the original Kolmogorov-Arnold network (KAN) structure, a learnable linear combination of wavelet functions is introduced to form the adaptive activation function for each connection edge, realizing a wavelet activation structure that is "heterogeneous across edges and adjustable in the frequency domain". This network not only retains the good algebraic expression ability and path visualization characteristics of the KAN structure, but also utilizes the time-frequency locality of wavelet functions to effectively improve the model's joint modeling ability for multi-scale disturbance features (such as trend changes, high-frequency oscillations, transient changes, etc.) in power system inertial signals. Compared with the traditional B-spline KAN, the proposed structure has significant advantages in interpretability, training efficiency, parameter compression, and multi-frequency feature adaptability, and is particularly suitable for power grid signal modeling tasks under complex dynamic features.

[0016] 2. In step two of this invention, a linear residual path is introduced in parallel in each KAN layer to achieve the fusion of linear preservation of the original input and nonlinear wavelet response, thereby improving the ability to capture the main trend changes of the inertial signal. Compared with the pure wavelet nonlinear channel, the dual-channel structure enhances the model's robust expression of long-term trends while maintaining high-frequency response capability.

[0017] 3. In step three of this invention, a multi-quantile joint training mechanism is introduced to achieve end-to-end modeling of the inertia prediction interval. This method does not rely on the distribution assumption of the prediction error and supports the output of multiple confidence interval boundaries, including 0.1, 0.5, and 0.9, thereby improving the risk control capability and explanatory power of the prediction model in actual scheduling decisions.

[0018] 4. In step four of this invention, the present invention adopts a Bayesian optimization strategy based on the expected improvement criterion to automatically adjust the network structure and training parameters; finally, a single-layer dual-node simplified network architecture that balances accuracy and structural complexity is formed, which not only ensures prediction performance, but also facilitates structural visualization and formula derivation, and has good engineering deployment feasibility.

[0019] 5. In step five of this invention, the present invention designs a pruning mechanism based on approximate Hessian sensitivity, and combines L1 regularization to fine-tune the network structure round by round to optimize the network structure, which significantly improves the sparsity and running efficiency of the model. Compared with the node pruning method in the original KAN, the "masking connection edge weights" mechanism adopted can more effectively control the accuracy loss and achieve visual path preservation.

[0020] 6. In step six of this invention, the present invention constructs a neural network structure graph. Each connection edge in the graph is visually encoded according to its corresponding wavelet type, and is distinguished by different line types according to the number of wavelet combinations, effectively realizing the modeling and display of "readable structure, traceable path, and visual function"; providing visual support for subsequent feature link analysis and visual interpretation.

[0021] 7. In step seven of this invention, the network structure and wavelet parameters are combined to generate explicit algebraic expressions layer by layer, and an input-output normalization inverse transform mechanism is used to convert the complex neural network into a directly deployable formula form. This method has higher transparency, control stability, and compatibility with edge devices compared to traditional deep networks. 8. In step eight of this invention, a systematic interpretability analysis mechanism is proposed, which supports: (1) evaluating the global importance of variables based on the DGSM index; (2) analyzing the direction of the promoting or inhibiting effect of variables on the output using partial derivative symbols; (3) constructing a waterfall plot of partial derivatives showing the change of variable importance over time, thereby achieving dynamic identification and rolling scheduling support for inertia influence factors; and (4) estimating the interaction strength between variables based on the expectation of the second derivative. Compared with traditional neural network interpretability methods (such as SHAP, LIME, etc.), this mechanism does not require an approximate surrogate model or sampling perturbation process, and has a closed-loop full-chain analysis, supporting causal chain reasoning. It can correspond one-to-one between the multi-layer paths between input variables and output indicators and the specific forms of activation functions, significantly improving the credibility of modeling. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 Here are schematic diagrams of three types of wavelets; Figure 2 Diagram of the adaptive wavelet KAN network structure; Figure 3 The structure of the pruned adaptive wavelet KAN network is shown in the figure. Figure 4 The image shows the prediction results of the adaptive wavelet KAN. Figure 5 Ablation experiment diagram for adaptive wavelet and linear residual connection; Figure 6 A partial diagram for deriving the formula; Figure 7 A comparison of directly plotting mathematical formulas and plotting neural network output values; Figure 8 A waterfall plot showing the change in the importance of each variable over time, generated using the absolute value of partial derivatives method; Figure 9 A heatmap showing the change of the direction of action of each variable over time, generated using the partial derivative method; Figure 10 A bar chart showing the global importance ranking of variables using the DGSM method; Figure 11 A heatmap of the interaction intensity between variables generated using the cross-second derivative expectation analysis method. Detailed Implementation

[0023] 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 for illustrative purposes only and are not intended to limit the invention.

[0024] The following is combined Figures 1-11Explain the entire plan.

[0025] Example 1: A power system inertia prediction method based on adaptive wavelet KAN network, such as Figures 1-2 As shown, it includes the following steps: Step 1: Construct an adaptive wavelet KAN network structure to model the frequency response data of the power system after disturbance. The edges between each layer of the adaptive wavelet KAN network structure use activation functions formed by a combination of multiple wavelet functions to perform nonlinear transformation on the input features.

[0026] An adaptive wavelet Kolmogorov-Arnold network structure is used to model the frequency response data of a power system after disturbance. This network is an improvement on the Kolmogorov-Arnold network (KAN). The core idea of ​​KAN is to replace the uniform linear mapping and activation function structure in the traditional fully connected neural network with each connection edge... Each of these features possesses an independent one-dimensional learnable nonlinear function, achieving stronger expressive power and higher interpretability. The KAN network is built upon the Kolmogorov-Arnold representation theorem, which states that any continuous function... It can be represented as a combination of a set of single-variable functions, that is: ; in: and It is a single-variable function. For the first input variable Each component.

[0027] The KAN network uses this theorem to represent the output of each layer as a linear superposition of function mappings of the inputs of the previous layer. Specifically, for the A layer, whose input is a vector. The output is a vector. Then each output component of this layer The calculation method is as follows: ; in: It is a learnable one-dimensional nonlinear function; each input variable After undergoing an independent function transformation, the signal is transmitted to all downstream output nodes; unlike the "uniform activation function" of traditional fully connected neural networks, the function on each edge (connection) in a KAN is independently adjustable. This design is called a KAN layer, and stacking these KAN layers creates a KAN network. Assume the network has... If the layer (excluding the input layer) has a global mapping function, then its global mapping function is... This can be expressed as: ; The mapping of each layer By the above definition of the summation structure: ; In the original KAN, the activation function Typically, learnable spline functions (such as cubic B-splines) are used for construction. However, in this invention, learnable univariate wavelet functions are used to replace the fixed activation functions in traditional KAN networks, achieving the representation capability of multi-layer neural structures. Specifically, this includes: (1) The structure supports each connecting edge The combined weights and parameters of multiple wavelet mother functions are independently learned to construct a learnable activation mechanism based on multi-wavelet linear fusion. Specifically, the activation function on each connection edge... Expressed as: ; in: Indicates the first One wavelet mother function; As amplitude weight, For translation parameters, The scale parameters are all learnable variables; the number of wavelet basis functions... It can be a positive integer, which can be selected according to the task settings; For input variables.

[0028] (2) The wavelet mother function includes, but is not limited to, the following three standard forms, the images of which are shown below. Figure 1 As shown: ①DOG wavelet (first-order Gaussian derivative): ; This wavelet is most sensitive to first-order changes in the signal and is good at fitting trends.

[0029] ②Mexican Hat wavelet (second-order Gaussian derivative): ; This wavelet has good analytical ability for medium-scale oscillatory structures and is good at fitting periods.

[0030] ③Morlet wavelet (modulated Gaussian wave): ; in For the preset frequency, it is generally taken as This wavelet can effectively analyze high-frequency fluctuations and is adept at fitting oscillations.

[0031] (3) The single-layer structure of the adaptive wavelet KAN adopts a fully connected form, and its structure is as follows:Figure 2 As shown, let the first... Layer input is The output is Then we have: ; Each of them Indicates from the input node To the output node Wavelet activation function on the connection edge.

[0032] (4) The overall mapping function of the multilayer network is: ; in, For the above-mentioned first The overall mapping function matrix of the layer.

[0033] (5) The structure allows each edge to independently learn the wavelet combination and its parameter configuration, forming a heterogeneous wavelet channel to improve the model’s ability to express different frequency domain features, especially suitable for the mixed features of trend, oscillation and sudden change that exist simultaneously in the inertial signal of the power system.

[0034] This structure has the following advantages: ① Possesses multi-resolution modeling capability: Based on the time-frequency locality characteristics of wavelet functions, it can simultaneously analyze high-frequency short-term disturbances and low-frequency long-term trends in inertial signals, achieving joint modeling; ②Simple structural parameters and efficient training: Compared with the original KAN with B-spline activation, the wavelet activation function does not require the definition of interpolation nodes and grid control points, which reduces hyperparameter dependence and significantly reduces model complexity and training time; ③ Adaptive mechanism supporting multi-wavelet fusion: Through end-to-end training, the network can automatically combine wavelet functions such as DOG, Mexican Hat, and Morlet on different edges, effectively improving the model's expressive and generalization capabilities, while enhancing its robust modeling ability for inertia dynamics under different behavior patterns.

[0035] Step 2: Embed a linear residual channel into the adaptive wavelet KAN network structure to form a linear residual network structure. The original input signal passes through the linear residual channel to retain the main trend information in a linear path, and then is superimposed with the output of the wavelet channel to form a dual-channel structure.

[0036] input vector It can be directly mapped to a linear term through a linear channel without wavelet transform. and the output of the wavelet activation channel. Add the elements together to get the total output of this layer: ; in: This is a nonlinear output obtained based on wavelet activation function matrix mapping; The weight matrix is ​​a learnable linear mapping; the structure is consistent with the idea of ​​residual networks, but the residual path is a complete linear mapping rather than an identity mapping.

[0037] By introducing this linear channel, the model can directly model the trend component in the inertia signal while maintaining the nonlinear wavelet representation capability, thereby improving the fitting accuracy and training stability of steady-state inertia level changes.

[0038] Step 3: Use the Bayesian optimization framework to automatically search and adjust the structural hyperparameters of the adaptive wavelet KAN network.

[0039] Specifically, it includes: (1) The optimization process is based on the Bayesian optimization framework Optuna, which uses the Expected Improvement (EI) criterion or the Gaussian Process surrogate model for performance estimation and sampling strategy guidance.

[0040] (2) The search space covers multiple structures and training hyperparameters, including but not limited to: the number of hidden layers in the network. Number of nodes per layer Initial learning rate L2 regularization term weight decay factor Training batch size per round .

[0041] (3) In the optimization process, an early stopping mechanism and a dynamic learning rate scheduler are introduced to accelerate convergence and avoid overfitting.

[0042] (4) In structural parameters (such as...) and In the final selection of the network architecture, although Optuna can provide structural suggestions that are optimal in performance on the validation set, this method introduces artificial interpretability constraints while ensuring prediction performance, and finally adopts a simplified network architecture with a single hidden layer and 2 nodes per layer.

[0043] (5) This structural design ensures modeling accuracy while optimizing the engineering adaptability of subsequent interpretability analysis and embedded deployment, and has good practical application value.

[0044] Step 4: Using the training data and the structural hyperparameters adjusted in Step 3, the linear residual network structure built in Step 2 is trained using a quantile regression mechanism to construct a multi-quantile output structure, thereby realizing the confidence interval modeling of inertia prediction.

[0045] Specifically, it includes: (1) Input features at each time step The network simultaneously outputs predicted values ​​corresponding to multiple quantiles. ,in quantile set Including but not limited to: ; (2) The network training objective adopts the quantile loss function, for each true value... Compared with quantile predicted values Its loss is defined as: ; (3) Quantile loss function total loss Loss at all quantiles The weighted summation is expressed as: ; in, The loss weighting coefficients for each quantile can be the mean or adjusted according to the risk level.

[0046] (4) After training, the model can output the median prediction (e.g., ) as an inertia point estimate, and output the low quantile points (e.g. ) and high quantiles (such as The prediction interval is formed by: ; This interval provides an estimate of the uncertainty of model predictions without requiring assumptions about the error distribution, and has good engineering applicability.

[0047] Step 5: Combining L1 regularization and a sensitivity index based on an approximate Hessian matrix, a progressive pruning mechanism is designed to prune the network structure trained in Step 4. The pruning ratio is gradually increased through multiple rounds of iteration, and parameter fine-tuning and structure restoration are performed after each round to remove redundant edge connections and wavelet channels.

[0048] Specifically, it includes: (1) In the pruning stage, first construct the amplitude weights of the wavelet activation functions connected by each edge. Sensitivity indicators for the target: ; in, For loss function, Indicates the first Layer, First The first edge Amplitude weights for wavelet functions.

[0049] The aforementioned sensitivity is essentially an unbiased estimate of the main diagonal terms of the FIM (Fisher Information Matrix), constituting a conservative approximation of the main diagonal elements of the Hessian matrix, and possesses a generally accepted basis for pruning robustness.

[0050] (2) The derivative calculation process is based entirely on the automatic differentiation function of the PyTorch framework, constructing the second derivative information of the parameters with respect to the loss function element by element, without the need to explicitly solve the full Hessian matrix, thus ensuring pruning efficiency and scalability. (3) The pruning mechanism adopts a connection edge weight masking strategy instead of the node deletion method in the traditional KAN method, that is, only the importance index is masked. Wavelet channel weights below a certain threshold are reset to zero while preserving the original structural topology, thus significantly reducing the risk of accuracy loss; the pruning process is performed iteratively, with the first pruning step... Rotation pruning rate The calculation is as follows: ; in, The base pruning rate (e.g., 0.1), This represents the total number of pruning rounds. This represents the current pruning round. In each pruning round, the least important edge connections and their corresponding wavelet channels are masked based on Hessian sensitivity. This strategy is more granular than the "node-level pruning" in the original KAN paper, effectively controlling the decline in prediction performance while maintaining the gradual improvement in the interpretability of the structure.

[0051] (4) After each round of pruning, add The fine-tuning mechanism of the regularization term restores model accuracy, and the loss function is updated as follows: ; in, It is the original quantile loss function. This is the hyperparameter for regularization intensity.

[0052] (5) During the fine-tuning process, calculations are performed on the validation set every fixed number of rounds (e.g., 10 rounds). The metrics are used to determine whether to update the current optimal model structure. The criteria for saving include: If the current model has a higher pruning rate, and If the result is not lower than the original model, then update and save. If the pruning rates are the same, priority should be given to retaining them. A more advanced model.

[0053] (6) The mechanism ultimately achieves the gradual reduction of redundant edges and channels, improving model performance while maintaining structural simplicity, and enhancing its prediction accuracy, symbolic differentiability, interpretability and embedded deployment efficiency.

[0054] Step 6: Based on the network structure and parameters pruned in Step 5, generate the corresponding visualized neural network structure diagram. Each connection edge in the visualized neural network structure diagram is represented by its corresponding wavelet function.

[0055] Specifically, it includes: (1) The visualization structure diagram adopts a bottom-up hierarchical representation method, strictly follows the architecture of the KAN network, with the input layer, hidden layer and output layer arranged in sequence, and each layer is connected by directional edges. The number of edges corresponds one-to-one with the non-zero wavelet channels retained after training. (2) The activation function on each connecting edge is represented by a purple box, and its wavelet activation combination function response curve pattern is marked inside. The wavelet fusion form of the edge can be seen intuitively through the pattern. (3) In the figure, the activation function represented by each connecting edge is visually encoded according to the types of wavelets it contains. If a connecting edge fuses three wavelets (DOG, Mexican Hat, Morlet), it is connected by a solid line; if it fuses only two of the wavelets, it is connected by a dashed line; if it contains only one wavelet, it is connected by a dotted dashed line; if the weights of all three wavelets on the connecting edge are set to zero, the connecting edge is completely deleted. This linear encoding method is used to intuitively distinguish the complexity of wavelet fusion and its ability to model the diversity of local responses. (4) The structure map not only has structural readability and path traceability, but also supports consistency verification with the explicit derived formula of the model, ensuring a one-to-one correspondence between the structure map and the function expression, providing system schedulers with an intuitive and structurally transparent analysis tool.

[0056] Step 7: Based on the network structure pruned in Step 5, extract the wavelet activation function parameters on each edge, extract the explicit activation function expressions of each layer of the network, and combine them with the standardized inverse transform mechanism to generate an algebraic prediction formula that can be directly deployed.

[0057] Specifically, it includes: (1) For each preserved connection edge, extract its set of wavelet activation function parameters after training. The explicit activation function form for this edge is generated based on the fusion structure: ; in, Indicates the first Layer, number The number of wavelet functions participating in weighted fusion on each connecting edge. Indicates the first The amplitude weights of each wavelet function Indicates the corresponding wavelet Translation parameters, Indicates the corresponding wavelet The scale parameter.

[0058] (2) Each output node is formed by weighted superposition of all input nodes from the previous layer after wavelet activation function mapping, and residual connections are added, i.e.: ; in represents the linear weighting parameter of the residual channel.

[0059] The resulting overall network formula function, without inverse normalization, is a composite combination of all level mappings: ; in, For the first The overall mapping function matrix of the layer; This represents the function composition operator, that is, each level of the compound operator. The calculation results are substituted into the next layer. middle.

[0060] (3) The final output node, since it is trained using the quantile loss function, defaults to selecting the median. The output of the corresponding node serves as the point estimate, which facilitates the expression of formulas and simplifies deployment.

[0061] (4) After inverse standardization, the final directly deployable algebraic prediction formula is: ; in, , These are the mean and standard deviation of the training set for the target variable, respectively. It is the prediction formula expression after inverse standard transformation, that is, the final output is a directly deployable algebraic prediction formula.

[0062] (5) The formula derivation mechanism automatically generates a layer-by-layer explicit expression chain by traversing the network graph structure and trained parameters, and has the following characteristics: Each layer of the structure has an explicit algebraic representation, supporting symbolic computation and path analysis; With neural network structure Figure 1 One-to-one correspondence ensures consistency between diagrams and symbols; It can be deployed to embedded modules or edge nodes in power grid control systems without running a full neural network inference engine.

[0063] Step 8: Based on the network structure pruned in Step 5, output the inertia prediction results and the directly deployable algebraic prediction formula.

[0064] Meanwhile, partial derivative analysis of input variables can be performed based on algebraic prediction formulas to construct a global interpretability index system. The global interpretability index system includes global variable importance assessment, variable time-series sensitivity trajectory analysis, variable directional trend analysis, and second-order interaction analysis between variables.

[0065] (1) Global Variable Importance Assessment (DGSM method): Based on algebraic prediction formulas, the importance of each input variable is calculated. The expectation of the square of the absolute value of the partial derivative is used as a sensitivity index to reflect the average sensitivity of the variable to the output result in the entire input space.

[0066] For the derived output prediction function ,in Represents an input variable vector, and calculates each input variable. The expectation of the square of the absolute value of the partial derivative is used as a sensitivity index and is defined as: ; in: Output variables for the model The first-order partial derivative; Represents the set of validation samples; This represents the mean operation on the sample set. The above indicators reflect the average sensitivity of variables to the output across the entire input space, and the contribution strength of each variable to the model output is displayed by sorting them using a bar chart.

[0067] (2) Variable time-series sensitivity trajectory analysis (partial derivative absolute value method): Based on algebraic prediction formula, calculate the time-series sensitivity trajectory of each input variable. Construct a two-dimensional sensitivity matrix by taking the absolute values ​​of the first-order partial derivatives at all time points in the validation set. Each row of the matrix represents the trajectory of a variable over the entire time series.

[0068] Based on each input variable Construct a two-dimensional sensitivity matrix by taking the absolute values ​​of the first-order partial derivatives at all time points on the validation set: ; in: For the first Model prediction output at each time point; Indicates the first Input variables in time The sensitivity matrix represents the local importance intensity of a variable; each row of the matrix represents the trajectory of a variable's change over the entire time series. The sensitivity matrix is ​​visualized as a 3D waterfall plot, which is used to analyze the time-varying patterns of the variable's impact on inertia prediction results, identify the sensitive periods and lag response intervals of key variables during disturbance response, and is suitable for applications such as rolling optimization of scheduling indicators and selection of time window features.

[0069] (3) Variable directional trend analysis (partial derivative method): Based on algebraic prediction formulas, calculate the directional trend of each input variable. The partial derivatives of the variable are as follows: a positive partial derivative indicates that the variable promotes the increase of the predicted value of inertia, a negative partial derivative indicates that it has a suppressive effect, and a partial derivative close to zero indicates that the variable has a weak influence on the prediction result at that moment or is not sensitive to changes.

[0070] For each variable Preserving the original sign (positive or negative) of its partial derivatives, a two-dimensional heatmap of the variable-time is plotted, with colors representing the magnitude and direction of the partial derivative values ​​for identification: 1) A positive partial derivative indicates that the variable contributes to an increase in the predicted inertia value; 2) A negative partial derivative indicates its inhibitory effect; 3) Partial derivatives close to zero indicate that the variable has a weak impact on the prediction result at that moment or is not sensitive to changes.

[0071] This trend chart uses color coding to express the dynamic adjustment direction of variables over time, and is used to schedule causal chain inference.

[0072] (4) Second-order interaction analysis between variables (cross-second derivative expectation analysis method): Based on algebraic prediction formula, the input variables are calculated. and The second-order mixed partial derivatives between variables are used to identify the cooperative coupling relationship and nonlinear interaction characteristics between variables: if the derivative is significantly non-zero in the input space, it indicates that the variables... and The responses in the model are not independent, and their combined changes have a significant nonlinear synergistic effect on the output.

[0073] Based on prediction function Calculate input variables and The second-order mixed partial derivatives between: ; in: express about and The mixed second-order partial derivatives between them are calculated; the absolute values ​​are taken and averaged over the validation samples to characterize the overall effect of the interaction strength; the resulting interaction matrix is ​​a symmetric matrix, with the main diagonal elements denoted as . (Without analyzing self-interactions), and normalized to Intervals. This matrix, displayed as a heatmap, helps identify the cooperative coupling relationships and nonlinear interaction characteristics between variables.

[0074] All four types of indicators are automatically generated by formula-level symbolic differentiation. The calculation process relies entirely on the mathematical formulas derived from the model, without the need for additional proxy models or black-box tools. This ensures that the interpretability analysis results are completely consistent with the original model's prediction path, possessing logical traceability and path traceability. It is suitable for key scenarios such as power grid dispatch optimization, variable screening, and causal analysis.

[0075] Example 2: To verify the effectiveness of the method proposed in this invention, measured data from the power systems of the four Nordic countries (Eastern Denmark, Finland, Norway, and Sweden) were selected as the research object, covering typical grid operation scenarios with multi-energy complementarity and high proportion of renewable energy access.

[0076] The dataset used was provided by the Nordic Transmission System Operator (TSO), spanning from January 2020 to August 2024, with a time resolution of 1 hour. Each sample record corresponds to the grid operation status at a specific point in time. To comprehensively reflect the dynamic changes in system inertia, 18 basic input variables were selected, including meteorological information, renewable power generation, load level, interconnection channel flow, and frequency regulation capability. Specifically, these variables include: relative humidity at 2 meters, real-time regional load, total shortwave downward irradiance, interconnection flow, photovoltaic power, diffuse irradiance, direct irradiance, nuclear power, wind speed at 50 meters, temperature at 2 meters, hydropower, coal-fired power, total precipitation, wind speed at 10 meters, reserve capacity, wind power, wind direction angle, and the target variable, inertia constant.

[0077] To capture the daily periodicity and weekly rhythm effects in the temporal variation of inertia, four time feature dimensions are further derived based on timestamp information: current minutes, hours, day of week, and month, which ultimately constitute a complete 22-dimensional input feature vector.

[0078] In the data processing workflow, the dataset is standardized to avoid biases in the modeling results caused by inconsistent units. Data from July 28, 2023 to August 9, 2023 is extracted using a Boolean mask as the test set, and the remaining data is used for training. Relevant prediction evaluation metrics are calculated using the partitioned test dataset to assess the model's performance.

[0079] In this example analysis, the main parameters of the model are shown in Table 1 below, and the optimizer type is AdamW.

[0080]

[0081] To further improve the sparsity and inference efficiency of the model, a sensitivity pruning mechanism based on the Hessian main diagonal approximation, as described in step five, was introduced in the experiment. This was combined with an L1 regularization fine-tuning strategy to mask redundant edges. The resulting pruned neural network structure diagram is shown below. Figure 3 As shown, it can significantly reduce network complexity while improving prediction accuracy.

[0082] After training the model using the above data, the final prediction result is shown in the figure below. Figure 4 As shown in Table 2, the performance evaluation of the 0.5 quantile output was conducted using the R² coefficient of determination, mean square error (MAE), root mean square error (RMSE), and mean absolute error (MAPE) as the main metrics. The results were also compared with mainstream deep learning models. The results show that the adaptive wavelet KAN model outperforms the comparison models on multiple metrics, especially demonstrating stronger inertial response capture capability and interval prediction reliability in oscillating conditions and abrupt change periods.

[0083]

[0084] As shown in the table above, this method, through the quantile mechanism, not only provides high-precision point prediction capabilities but also constructs interval output results with risk identification, confidence assessment, and decision support capabilities, laying a predictive foundation for building a robust inertia scheduling mechanism for uncertain disturbances. In contrast, while BiLSTM, Transformer, and TCN have certain capabilities in time series modeling, they generally suffer from problems such as delayed response to high-frequency disturbances and fuzzy capture of the main trend, exhibiting an error range with MAE higher than 0.15 and MAPE exceeding 3%. Traditional XGBoost, although possessing strong point prediction capabilities, has a closed structure and lacks an interpretability mechanism, failing to meet the interpretability requirements of scheduling auxiliary systems. The VAE model, due to reconstruction errors dominating the training process, exhibits severe prediction distortion, with an R² of only 0.32 and significantly large errors.

[0085] Furthermore, after introducing the unique and effective pruning mechanism proposed in this invention, the model not only did not experience a performance decline, but also achieved slight improvements across all metrics. In particular, the coefficient of determination (R²) increased by approximately 0.33 percentage points, while RMSE and MAPE decreased by approximately 8% and 11%, respectively. This performance gain is not accidental; it is attributed to the pruning strategy effectively eliminating redundant paths and noisy connections in the modeling process, improving the model's generalization ability, and mitigating overfitting tendencies. Simultaneously, due to the lighter model, interpretability is further enhanced, breaking the previous general understanding that lightweight models and high performance are mutually exclusive.

[0086] To verify the effectiveness of the linear residual connection and adaptive fusion wavelet used in this invention, ablation experiments were also conducted. The following three types of sub-models were constructed, and the model compared is the unpruned adaptive wavelet KAN model: 1) Baseline model: Original wavelet KAN structure, using a fixed single wavelet (DOG) as the activation function, and removing residual channels; 2) Variant 1: Only linear residual connections are added, while the fixed wavelet structure is retained; 3) Variant 2: Only enable the adaptive wavelet mechanism, without using linear residual connections.

[0087] The prediction results of the three are as follows Figure 5 As shown in Table 3, the comparison results of the evaluation indicators are as follows.

[0088]

[0089] As can be seen from the data above, both linear residual connectivity and adaptive wavelet mechanism bring significant performance improvements without any other modifications: 1) Using linear residual connections alone, even without changing the activation structure, can still reduce MAE from 0.1703 to 0.1246, a reduction of more than 1 percentage point in MAPE. This indicates that the mechanism has a significant effect on modeling the main trend of inertia and weakening non-stationary disturbances, and is a key structure for stabilizing the prediction path.

[0090] 2) The adaptive wavelet mechanism improves the dynamic response capability of the activation function layer, enabling the network to automatically adjust the feature extraction method according to the input perturbation. When used alone, it can improve R² to 0.9596, which is significantly better than the fixed wavelet structure, verifying the necessity of intelligent wavelet structure.

[0091] When used together, the effects are further amplified, with the R² of the full structure model increasing to 0.9779 and the MAE decreasing to 0.1093, forming a unified optimal solution that combines prediction accuracy, response sensitivity, and interpretability.

[0092] This experiment fully demonstrates that for power system inertia prediction scenarios, residual connectivity helps preserve physical trend information, while the adaptive wavelet mechanism improves the disturbance response matching capability. Together, they construct a modeling paradigm that combines interpretability and prediction accuracy.

[0093] Figure 6 The method described in step seven, after model training is complete, automatically extracts and reconstructs the explicit function expressions of each layer of the network based on the adaptive wavelet KAN network structure and edge connection parameters, generating a partial screenshot of a directly deployable algebraic prediction formula. The formula derivation mechanism automatically generates layer-by-layer explicit expression chains by traversing the network graph structure and trained parameters, possessing the following characteristics: 1) Each layer of the structure has an explicit algebraic representation, supporting symbolic computation and path analysis; 2) With neural network structure Figure 1 One-to-one correspondence ensures consistency between diagrams and symbols; 3) It can be deployed to embedded modules or edge nodes of the power grid control system without running a full neural network inference engine.

[0094] Figure 7 The comparison between plotting the mathematical formula and plotting the neural network output values ​​shows that they are completely identical. This verifies that the formula is entirely the mathematical expression of the neural network. This means that field engineers and researchers in power systems can directly use the raw data to apply the formula for efficient and reliable field prediction and analysis.

[0095] Figure 8 , 9 Steps 10 and 11 are constructed by performing partial derivative analysis on the input variables based on the formula described in step eight after the model training is completed and the explicit prediction formula is derived, thereby building a global interpretability index system.

[0096] Figure 8 This is a waterfall plot showing the change in the importance of each input variable to the output y over time, obtained using partial derivative absolute value analysis. The plot visually illustrates how the local importance (or sensitivity) of each input variable to the inertia prediction dynamically changes over time. It is clear from the plot that the vast majority of variables have a very weak impact (close to zero) for most of the time, while wind power, hydropower, and nuclear power exhibit significant and dynamically changing "peaks." This indicates that the model assumes that the change in system inertia is mainly dominated by the output of these key power sources, but their influence is not constant; rather, it exhibits different dominant roles on different dates and at different times (especially during periods of significant inertia fluctuation).

[0097] Figure 9 This is a heatmap showing the directional impact of variables on the output y, obtained using partial derivative analysis. Red represents positive derivatives, and blue represents negative derivatives. The graph shows that the direction of the variable impacts closely matches the actual situation of the Nordic power system. The graph indicates that wind power has a significant negative effect on inertia for most of the time period, consistent with the reality that asynchronous wind power integration and replacement of synchronous generator output leads to a decrease in inertia. Hydropower and nuclear power, on the other hand, consistently show a positive effect, reflecting their supporting role in the system's inertia as the main synchronous power sources in the Nordic region. The impacts of variables such as regional load and wind speed are relatively mild but directional. Meteorological variables (such as temperature, humidity, and irradiance) have virtually no significant impact, consistent with the expectation that they have a small effect on physical inertia. This demonstrates that the model possesses strong physical consistency and explanatory power.

[0098] Figure 10This analysis utilizes the Derivative Expectation Method (DSGM) for global variable importance analysis. The figure ranks the importance of all input variables from a global and average perspective, clearly demonstrating the overall impact of each input variable on the inertia prediction model output. The results highly align with the actual structure of the Nordic power system. The top-ranked variables are wind power, hydropower, and nuclear power, which together account for the majority of the model's explanatory power. Wind power is the most important, reflecting its significant output in the Nordic system. However, due to asynchronous connection and lack of physical inertia, higher wind power output reduces the required synchronous inertia source, leading to a decrease in overall inertia levels. Therefore, the model is extremely sensitive to changes in wind power. Hydropower ranks second, clearly demonstrating that the Nordic countries (especially Norway and Sweden) rely on hydropower as the primary source of synchronous inertia support, and its output level has a direct and decisive impact on system inertia. Nuclear power, as a stable synchronous power source, plays a crucial role in supporting basic inertia in Finland and Sweden; its importance is slightly lower than hydropower but still significant.

[0099] Furthermore, wind speed (especially at a height of 50 meters) also carries a certain weight in the model as a meteorological driver of wind power output, reflecting the indirect impact of wind speed on wind power. While regional load contributes less to the model than the main energy variables, its positive relationship indicates that the system often requires more synchronous generator output during peak load periods, thereby increasing system inertia. In contrast, variables such as photovoltaic power and irradiance contribute almost nothing to the output, consistent with the reality of limited solar resources and a very low proportion of photovoltaic power in the Nordic region.

[0100] Figure 11 This is a heatmap of the interaction strength between variables, obtained after analysis and normalization using the Hessian-based Interaction Score. This heatmap reveals deeper information learned by the model—the nonlinear interactions between variables. The redder the color in the graph, the stronger the synergistic interaction effect between the two variables. The graph shows that the interaction strength between wind power and hydropower is the highest, indicating that the model highly relies on the relative changes of these two variables to determine the system's inertia level. This aligns closely with the structure of the Nordic power system: wind power, as an asynchronous source, plays a negative role in inertia, while hydropower is the main provider of synchronous inertia, and its regulation capability directly determines the system's inertia support capability. In contrast, while other variables may have some influence on first-order sensitivity (such as wind speed and load), they do not exhibit significant coupling strength at the interaction level with other variables. This indicates that the model's inertia modeling mechanism is based on wind-hydropower synergy, with other variables acting more as independent influencing factors than as interacting coupling terms. This structure not only helps improve the model's interpretability but also implies that the model has good sparsity and generalization ability.

[0101] Among other interaction terms, some interaction exists between wind power and wind speed, indicating that the model can identify the indirect impact of wind speed changes on wind power output and consequently on inertia. Real-time regional load also interacts with hydropower and wind power, demonstrating the model's dynamic response capability to grid operation status and resource allocation matching. For example, during high-load periods, hydropower typically undertakes the main output, and the load and hydropower synergy determine the synchronous generator output level. Furthermore, some meteorological variables such as humidity and temperature also show a certain degree of interaction with hydropower output, possibly reflecting the indirect impact of hydrological conditions on hydropower dispatching capabilities.

[0102] Overall, the heatmap validates the model's ability to capture the physical interactions between key energy variables, particularly within the context of the synchronous inertia-supported mechanism in Northern Europe, primarily based on hydropower, where the interaction structure exhibits high real-world consistency. It also suggests that variables such as photovoltaics, irradiance, and their combinations have extremely weak influence in the current system and can be simplified in the modeling process. These interaction analysis results provide strong support for model compression, feature construction, and interpretation enhancement.

[0103] The four types of indicators are all automatically generated by formula-level symbolic differentiation. The calculation process relies entirely on the mathematical formulas derived from the model, without the need for additional proxy models or black-box tools. This ensures that the interpretability analysis results are completely consistent with the original model's prediction path, possessing logical traceability and path traceability. It is suitable for key scenarios such as power grid dispatch optimization, variable selection, and causal analysis. This interpretability framework enables the model not only to be used for prediction but also for decision support, feature diagnosis, and tracing the source of system control mechanisms. It provides a new means for renewable energy penetration, load disturbance identification, and dispatch optimization in power systems, establishing a verifiable, traceable, and understandable model interpretation system in the field of inertia prediction, filling the gap in practical modeling of existing interpretability research. At the same time, the derivative analysis method proposed in this invention is extremely efficient, requiring only one formula analysis and differentiation to achieve accurate analysis of global and local sensitivities, fully meeting the real-time calculation needs of power systems. It is particularly suitable for promotion and application in actual power grids with a high proportion of renewable energy and strict requirements for computational efficiency.

[0104] Those skilled in the art will readily understand that the above description is merely 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 scope of protection of the present invention.

Claims

1. A method for predicting the inertia of a power system based on an adaptive wavelet KAN network, characterized in that, Includes the following steps: Step 1: Construct an adaptive wavelet KAN network structure to model the frequency response data of the power system after disturbance. The edges between each layer of the adaptive wavelet KAN network structure adopt activation functions formed by a combination of multiple wavelet functions to perform nonlinear transformation on the input features. Step 2: Embed a linear residual channel into the adaptive wavelet KAN network structure to form a linear residual network structure. The original input signal passes through the linear residual channel to retain the main trend information in a linear path, and then is superimposed with the output of the wavelet channel to form a dual-channel structure. Step 3: Use the Bayesian optimization framework to automatically search and adjust the structural hyperparameters of the adaptive wavelet KAN network; Step 4: Using the training data and the structural hyperparameters adjusted in Step 3, the linear residual network structure built in Step 2 is trained using a quantile regression mechanism to construct a multi-quantile output structure in order to model the confidence interval for inertia prediction. Step 5: Combining L1 regularization and a sensitivity index based on an approximate Hessian matrix, a progressive pruning mechanism is designed to prune the network structure trained in Step 4. The pruning ratio is gradually increased in a multi-round loop, and parameter fine-tuning and structure restoration are performed after each round to remove redundant edge connections and wavelet channels. Step 6: Based on the network structure and parameters pruned in Step 5, generate the corresponding visualized neural network structure diagram. Each connection edge in the visualized neural network structure diagram is visualized using its corresponding wavelet function. Step 7: Based on the network structure pruned in Step 5, extract the wavelet activation function parameters on each edge, extract the explicit activation function expressions of each layer of the network, and combine the standardized inverse transform mechanism to generate an algebraic prediction formula that can be directly deployed. Step 8: Based on the network structure pruned in Step 5, output the inertia prediction results and the directly deployable algebraic prediction formula.

2. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 1, characterized in that, In step one, the activation function used for the edges between layers of the adaptive wavelet KAN network structure is... Expressed as: ； in, Indicates the first One wavelet mother function; As amplitude weight, For translation parameters, The scale parameters are all learnable variables; the number of wavelet basis functions It is a positive integer. For input variables.

3. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 1, characterized in that, In step two, the linear residual channels are connected in parallel in each wavelet KAN layer, specifically as follows: input vector It can be directly mapped to a linear term through a linear channel without wavelet transform. and the output of the wavelet activation channel. Add the elements together to get the total output of this layer: ； in, This is a nonlinear output obtained based on wavelet activation function matrix mapping; It is a learnable linear mapping weight matrix.

4. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 1, characterized in that, In step three, the structural hyperparameters of the adaptive wavelet KAN network include, but are not limited to, the number of hidden layers, the number of nodes per layer, the initial learning rate, the L2 regularization term weight decay factor, and the training batch size.

5. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 1, characterized in that, In step four, a quantile regression mechanism is used to train the linear residual network structure built in step two, constructing a multi-quantile output structure to model the confidence interval for inertia prediction. After training, the model outputs the median prediction value as the inertia point estimate and outputs the prediction interval composed of the low quantile and the high quantile, specifically including: 1) Input features at each time step The network outputs multiple quantiles simultaneously. q Corresponding predicted value ,in quantile set Including but not limited to: ； 2) The training objective uses a quantile loss function, for each true value... Compared with quantile predicted values Its loss is defined as: ； 3) Quantile loss function total loss Loss at all quantiles The weighted summation is expressed as: ； in, represents the loss weight coefficient corresponding to each quantile.

6. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 1, characterized in that, Step five specifically includes: 1) During the pruning stage, first construct the amplitude weights of the wavelet activation functions connected by each edge. Sensitivity index for the target The expression is: ； in, For loss function, Indicates the first Layer, First The first edge Amplitude weights for wavelet functions; 2) The pruning process is carried out iteratively, the first... Rotation pruning rate The calculation is as follows: ； in, The basic pruning rate; This represents the total number of pruning rounds; This is the current pruning cycle; 3) In each round of pruning, based on Hessian sensitivity... The size sorting eliminates the least important edge connections and corresponding wavelet channels in the current ratio; 4) After each round of pruning, add The fine-tuning mechanism of the regularization term restores the accuracy of the network structure, and the loss function is updated as follows: ； in, It is the original quantile loss function. This is the hyperparameter for regularization intensity.

7. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 6, characterized in that, In step five, during the fine-tuning process, calculations are performed on the validation set at fixed intervals. The system uses metrics to determine whether to update the current network structure, saving it based on the following criteria: if the current network structure has a higher pruning rate, and... If the current network structure is not lower than the original network structure, then update and save the current network structure; if the pruning rates of the original network structure and the current network structure are the same, then retain the original network structure first. A more sophisticated network structure.

8. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 1, characterized in that, In step six, the visualized neural network structure diagram adopts a bottom-up hierarchical representation, strictly following the architecture of the KAN network. The input layer, hidden layer, and output layer are arranged sequentially, and each layer is connected by directional edges. The number of edges corresponds one-to-one with the non-zero wavelet channels retained after training. The activation function represented by each connection edge is visualized and encoded according to the types of wavelets it contains. If a connection edge integrates three wavelets, it is connected with a solid line; if it integrates only two wavelets, it is connected with a dashed line; if it contains only one wavelet, it is connected with a dotted dashed line; if the weights of all three wavelets on the connection edge are set to zero, the connection edge is completely deleted.

9. The power system inertia prediction method based on adaptive wavelet KAN network according to claim 1, characterized in that, Step seven includes the following operations: 1) For each preserved connection edge, extract its trained wavelet activation function parameter set. The explicit activation function form for this edge is generated based on the fusion structure: ； in, Indicates the first Layer, First The number of wavelet functions participating in weighted fusion on each connecting edge. Indicates the corresponding wavelet Translation parameters, Indicates the corresponding wavelet Scale parameters; 2) Each output node is formed by weighted superposition of all input nodes from the previous layer after wavelet activation function mapping, with residual connections added, i.e.: ； in, The linear weighting parameters for the residual channel; The resulting overall network formula function, without inverse normalization, is a composite combination of all level mappings: ； in, For the first The overall mapping function matrix of the layer; This represents the function composition operator, that is, each level of the function composition operator. The calculation results are substituted into the next layer. middle; 3) After inverse standardization, the final derived, directly deployable algebraic prediction formula is: ； in, , These are the mean and standard deviation of the training set for the target variable, respectively. It is the prediction formula expression after inverse standard transformation, that is, the final output is a directly deployable algebraic prediction formula.

10. A power system inertia prediction method based on an adaptive wavelet KAN network according to claim 1, characterized in that, In step eight, partial derivative analysis of the input variables is performed based on the algebraic prediction formula to construct a global interpretability index system. The global interpretability index system includes global variable importance assessment, variable time-series sensitivity trajectory analysis, variable directional trend analysis, and second-order interaction analysis between variables. Global variable importance assessment: Calculate the importance of each input variable based on an algebraic prediction formula. The expectation of the square of the absolute value of the partial derivative is used as a sensitivity index to reflect the average sensitivity of the variable to the output result in the entire input space. Variable time-series sensitivity trajectory analysis: Calculating the value of each input variable based on algebraic prediction formulas. Construct a two-dimensional sensitivity matrix by taking the absolute values ​​of the first-order partial derivatives at all time points in the validation set. Each row of the matrix represents the trajectory of a variable over the entire time series. Variable directional trend analysis: Based on algebraic prediction formulas, calculate the directional trend of each input variable. The partial derivatives of the variable are as follows: a positive partial derivative indicates that the variable promotes the increase of the predicted value of inertia, a negative partial derivative indicates that it has a suppressive effect, and a partial derivative close to zero indicates that the variable has a weak or insensitive effect on the predicted result at that moment. Second-order interaction analysis between variables: Calculating input variables based on algebraic prediction formulas. and The second-order mixed partial derivatives between them, through the input variables and The second-order mixed partial derivatives determine the synergistic coupling relationship and nonlinear interaction characteristics between variables.

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