Heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network

Abstract

The invention discloses a heavy duty gas turbine intelligent modeling method based on an EffiCANet and a KAN network, and belongs to the technical field of heavy duty gas turbine intelligent modeling, and the method comprises the following steps: S1, determining an input variable and an output variable; s2, historical operation data of the heavy duty gas turbine are collected according to the result of S1, and noise reduction is conducted on the data through variational mode decomposition after preprocessing is conducted; s3, constructing a heavy duty gas turbine model based on EffiCANet and a KAN network, initializing network parameters, inputting the data set processed in S2 into the model for training, and calculating total loss; and S4, based on the total loss, adopting an alpha evolutionary algorithm to optimize EffiCANet network hyper-parameters, stopping after the objective function value converges, obtaining the optimal hyper-parameters, and completing model construction. According to the method provided by the invention, the interpretability and generalization ability of the model are enhanced while the model is ensured to meet the actual operation data mapping relationship of the variables, and the alpha evolutionary algorithm is adopted to optimize the network hyper-parameters, so that the accuracy of the model is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent modeling of heavy-duty gas turbines, and in particular to an intelligent modeling method for heavy-duty gas turbines based on EffiCANet and KAN networks. Background Technique

[0002] With the increasing attention of the national energy development strategy to energy and environmental issues, clean and renewable energy such as solar energy, wind energy, and tidal energy has gradually become a trend in the power generation field. Gas-steam combined cycle power generation is a clean and efficient thermal power generation method. Using natural gas as fuel, electrical energy for users is generated through the efficient and organic cooperation between the gas turbine system and the steam turbine system. During the power generation process, less polluting gases such as sulfur oxides and nitrogen oxides are emitted, thus effectively promoting the realization of the clean and low-carbon goal. As one of the key components of the combined cycle unit, the operating stability and efficiency of the heavy-duty gas turbine play a crucial role in the entire power generation process. Therefore, how to achieve the safe and stable operation of the heavy-duty gas turbine system is an urgent problem to be solved currently.

[0003] In the prior art, the control system is often designed based on a model that accurately reflects the process characteristics of the controlled object. An accurate model of the controlled object is a prerequisite for the efficient and stable operation of the heavy-duty gas turbine system. However, this system has the characteristics of strong coupling, nonlinearity, and being easily affected by external disturbances. Traditional data-driven modeling methods are difficult to describe the internal physical laws of the system, resulting in a low accuracy of the established model. For this reason, the present invention provides an intelligent modeling method for heavy-duty gas turbines based on EffiCANet and KAN networks. Summary of the Invention

[0004] The purpose of the present invention is to provide an intelligent modeling method for heavy-duty gas turbines based on EffiCANet and KAN networks to solve the problems in the background technique.

[0005] To achieve the above purpose, the present invention provides an intelligent modeling method for heavy-duty gas turbines based on EffiCANet and KAN networks, including the following steps:

[0006] S1. Based on the operating characteristics of the heavy-duty gas turbine, use the Spearman correlation coefficient to perform a correlation analysis on the variables to determine the input variables and output variables;

[0007] S2. According to the results of S1, collect the historical operating data of the heavy-duty gas turbine, perform preprocessing, and then use variational mode decomposition to denoise the data of the input variables;

[0008] S3. Construct a heavy-duty gas turbine model based on EffiCANet and KAN networks, initialize the network parameters, input the data set processed in S2 into the model for training, and calculate the total loss;

[0009] S4. Based on the total loss obtained in S3, the hyperparameters of the EffiCANet network are optimized using the alpha evolution algorithm. Stop when the objective function value converges to obtain the optimal hyperparameters of the network and complete the model construction.

[0010] Preferably, in S1, the calculation formula of the Spearman correlation coefficient is:

[0011]

[0012] where R(x i ) and R(y i ) are the values of two variables, are the average values of variable x and variable y respectively, and n is the number of samples.

[0013] Preferably, in S1, the input variables are the opening degree of the inlet guide vane of the compressor and the fuel quantity; the output variables are the rotor speed, the exhaust temperature, the exhaust pressure, and the output power.

[0014] Preferably, in S2, the preprocessing process is as follows:

[0015] 1) Process the missing values and outliers in the data;

[0016] 2) Perform min-max normalization on the state variables with different orders of magnitude in the collected data. The specific formula is:

[0017]

[0018] where x * is the normalized data, x is the original data, x min is the minimum value of the original data of the processed feature variable, and x max is the maximum value of the original data of the processed feature variable.

[0019] Preferably, in S2, the noise reduction process is as follows:

[0020] 1) Through variational optimization, the original signal is decomposed into k modal components with finite bandwidths having center frequencies, and at the same time, the sum of the bandwidths of each modal component is minimized. The constraint condition is that the original signal is equal to the sum of all modal components. The formula is expressed as:

[0021]

[0022] where k is the number of center frequencies, j is the imaginary unit, ω k is the center frequency, u k is the modal component, and δ(t) is the Dirac function. is the time derivative operator, t is the time variable, and f is the original signal to be denoised;

[0023] 2) The quadratic penalty parameter and the Lagrange multiplier are introduced, and the constraint condition is converted into an unconstrained Lagrangian optimization problem, which is expressed as:

[0024]

[0025] where α is the quadratic penalty parameter, λ is the Lagrange multiplier, and f(t) is the original signal;

[0026] 3) By alternately updating the modal components, the center frequencies, and the Lagrange multiplier, the objective function is gradually optimized, and finally each modal component and the corresponding center frequency are obtained.

[0027] Preferably, the specific steps of S3 are as follows:

[0028] S31. The data processed in S2 is input into the EffiCANet network in the form of a matrix [B, M, H], where B represents the batch size, M represents the number of feature variables, and H represents the window length; each sliding window data x ∈ R M×H increases the dimension through a non-squeezing operation x ∈ R M×1×H , and the sequence is divided into N patches through a convolutional layer with a kernel size of P and a stride of S, and each input channel is mapped to D output channels to obtain x emb ∈ R M×D×N ;

[0029] where

[0030] S32. The short-term and long-term features in the multivariate time series are extracted through the temporal large kernel decomposition convolutional module, and the depth-wise intelligent convolution is used to extract the short-term dependence relationship, which is expressed as:

[0031] x short = DWConv(x emb );

[0032] The depth-wise dilated convolution is used to extract the long-term dependence relationship, which is expressed as:

[0033] x long = DWDConv(x emb );

[0034] The two elements are added to obtain:

[0035] x combined = x short + x long ;

[0036] S33. Model the dependencies between variables through the variable group convolution module, pad the time dimension so that the time dimension is divisible by the window size, and implement convolution between multiple time windows, expressed as:

[0037]

[0038] Among them, N pad1 is the necessary padding length, T is the time dimension, and W is the window size;

[0039] Then adopt the head and tail padding strategy to obtain the dynamic pattern, expressed as:

[0040]

[0041] Among them, N left_pad2 is the padding length on the left side of the time dimension, N right_pad2 is the padding length on the right side of the time dimension; perform one-dimensional group convolution on each tensor in the channel dimension, expressed as:

[0042] Y padded1 = Conv(X padded1 );

[0043] Y padded2 = Conv(X padded2 );

[0044] Among them, padded1 represents standard padding, padded2 represents head and tail padding, Conv is convolution, X padded1 is the input data after standard padding, X padded2 is the input data after head and tail padding, Y padded1 is the data after standard padding and convolution, Y padded2 is the data after head and tail padding and convolution;

[0045] After merging the above results, perform convolution processing to refine and extract the interaction between time and variables, and obtain the convolution output, expressed as:

[0046] Y = Conv(Y padded1 + Y padded2 );

[0047] Among them, Y is the convolution output.

[0048] S34. Adopt the global time variable attention module to selectively enhance the feature learning of the time dimension and variable dimension in the multivariate time series. Given the input tensor Y ∈ R M×D×N , capture the global time dependencies and variable dependencies, and combine the time weights and variable weights with the convolution output as the output Y out ; Combine Y out with the input xemb Combine them as the input for the next module;

[0049] S35. Obtain the predicted value through the prediction layer Calculate the predicted value and the label value Y label Calculate the mean squared error between them, and use the mean squared error as the data loss term MSE in the total loss function u ;

[0050] S36. Fit the non - linear equation inside the heavy - duty gas turbine system, expressed as:

[0051]

[0052] Obtain the derivative of the output result of the EffiCANet network with respect to the input through automatic differentiation Use the KAN network to obtain Calculate and Calculate the mean squared error between them as the physical loss term MSE in the total loss function f ;

[0053] S37. Calculate the total loss to guide the update of the EffiCANet network parameters. The total loss is expressed as:

[0054] MSE = MSE u + MSE f ,

[0055] where MSE represents the total loss, MSE u represents the data loss term; MSE f represents the physical loss term.

[0056] Preferably, the specific steps of S34 are as follows:

[0057] 1) Capture the global time - dependence relationship: Reshape the input tensor into Y temp ∈R (N×D)×M , apply global average pooling along the variable dimension, and then process this representation using a fully - connected network. This process is expressed as:

[0058] T pool = AvgPool(Y temp ) ∈ R (N×D) ;

[0059] T atten = σ(W 2 · ReLU(W 1 · T pool ));

[0060] where T attenis the time weight, AvgPool is the global average pooling, and T pool is the time-centered representation of the input tensor, and W 1 and W 2 are the weight matrices, σ is the sigmoid activation function, and ReLU is the rectified linear unit activation function;

[0061] 2) Capture the dependencies between variables: Reshape the input tensor into Y var ∈R (M×D)×N , apply global average pooling along the time dimension, and then process this representation using a fully connected network. This process is expressed as:

[0062] V pool = AvgPool(Y var ) ∈ R (M×D) ;

[0063] V atten = σ(W 4 · ReLU(W 3 · V pool ));

[0064] where V atten is the variable weight, V pool is the variable-centered representation of the input tensor, and W 3 and W 4 are the weight matrices;

[0065] 3) Combine the time and variable weights with the convolutional output as the output, expressed as: Y out = σ(T atten ⊙ V atten ⊙ Y);

[0066] where Y out represents the output, and ⊙ represents the Hadamard product.

[0067] 4) Further refine the feature representation by combining Y out with x emb as the input to the next module.

[0068] Preferably, the specific steps of S4 are as follows:

[0069] S41. Consider the initial hyperparameters of the EffiCANet network as candidate solution individuals and initialize the candidate solution individuals, expressed as:

[0070] X i = lb + (ub - lb) · rand(0, 1, [1, D dim ), i = 1, 2, …, N pop ;

[0071] where Xi Denote the \(i\)-th candidate solution individual, where \(lb\) and \(ub\) represent the lower and upper bounds of the hyperparameters respectively, \(rand\) represents the random number generator, \(D\) dim represents the dimension of the candidate solution, and \(N\) pop represents the total number of candidate solutions;

[0072] S42. Determine the optimal candidate solution based on the fitness function, expressed as:

[0073] \(f(X\) i ) = MSE u '(X i );

[0074] where is a \(D\) dim -dimensional vector; \(MSE\) u '(X i ) represents the optimal data loss obtained by training the network based on the candidate solution \(X\) i ;

[0075] S43. Update the value of the candidate solution, expressed as:

[0076]

[0077] where E i represents the \(i\)-th evolved solution, \(t\) represents the current iteration number, \(P\) represents the starting position of the evolution, \(\beta\) represents the decay factor, \(\Delta r\) i represents the \(i\)-th random step size, \(\theta\) represents the control parameter, \(W\) i and \(L\) i represent the sampled solutions, and \(f(W\) i ) \(\leq f(E\) i ) \(\leq f(L\) i );

[0078] S44. Perform boundary constraint on the candidate solution, and the specific formula is:

[0079]

[0080] where \(E\) i,j is the \(i\)-th evolved solution of the \(j\)-th candidate solution individual;

[0081] S45. Judge whether the objective function value converges. If it converges, obtain the optimal hyperparameters of the EffiCANet network; otherwise, return to step S43.

[0082] Therefore, an intelligent modeling method for heavy-duty gas turbines based on EffiCANet and KAN networks according to the present invention selects the input and output variables of the neural network through Spearman correlation analysis based on the actual operation data of a certain heavy-duty gas turbine; uses variational mode decomposition to denoise the data and reduce the model error from the data source; adopts the EffiCANet network to extract the features between the input data time and variables, establishes the mapping relationship between the input and output variables, and uses the prediction error as the data loss term; uses the KAN network to fit the internal nonlinear equation of the heavy-duty gas turbine, and uses the prediction error as the physical loss term; guides the network to update parameters based on the data loss and physical loss; optimizes the hyperparameters of the EffiCANet network through the alpha evolutionary algorithm to improve the accuracy of the model.

[0083] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 is a flowchart of the modeling method according to an embodiment of the present invention;

[0085] Figure 2 is a structural diagram of the modeling method according to an embodiment of the present invention;

[0086] Figure 3 is a simplified structural diagram of the heavy-duty gas turbine system according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0087] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0088] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0089] Embodiment

[0090] As Figures 1-3 shown, the present invention provides an intelligent modeling method for heavy-duty gas turbines based on EffiCANet and KAN networks, including the following steps:

[0091] S1. The model of a heavy-duty gas turbine mainly includes three key components: a compressor, a combustion chamber, and a turbine. The external gas is compressed step by step by the compressor to form high-pressure gas, which then enters the combustion chamber to mix with the injected fuel and burn, generating high-temperature and high-pressure gas. The gas flows through the turbine to expand and do work, driving the turbine to drive the generator to rotate at high speed and generate electrical energy. Fully considering the operating characteristics of the heavy-duty gas turbine, the Spearman correlation coefficient is used to analyze the correlation of variables, and the input variables are determined to be the guide vane opening of the compressor inlet and the fuel quantity; the output variables are the rotor speed, exhaust temperature, exhaust pressure, and output power.

[0092] The calculation formula of the Spearman correlation coefficient is:

[0093]

[0094] Among them, R(x i ) and R(y i ) are the values of two variables, are the average values of variable x and variable y respectively, and n is the number of samples.

[0095] S2. According to the results of S1, collect the historical operation data of the heavy-duty gas turbine, preprocess the missing values and outliers in the data, and then use the Min-Max normalization method to normalize the data set. The specific formula is:

[0096]

[0097] Among them, x * is the normalized data, x is the original data, x min is the minimum value of the original data of the processed characteristic variable, and x max is the maximum value of the original data of the processed characteristic variable. Denoise the data of the input variables using variational mode decomposition. The denoising process is as follows:

[0098] 1) Through variational optimization, variational mode decomposition decomposes the original signal into k modal components with center frequencies and finite bandwidths, and at the same time minimizes the sum of the bandwidths of each modal component. Taking the sum of all modal components equal to the original signal as a constraint condition, the formula is expressed as:

[0099]

[0100] Among them, k is the number of center frequencies, j is the imaginary unit, ω k is the center frequency, u k is the modal component, δ(t) is the Dirac function, is the time derivative operator, t is the time variable, and f is the original signal to be denoised;

[0101] 2) To solve this constrained optimization problem, a quadratic penalty parameter and Lagrange multipliers are introduced to transform the constraint conditions into an unconstrained Lagrangian optimization problem, which is expressed as:

[0102]

[0103] where α is the quadratic penalty parameter, λ is the Lagrange multiplier, and f(t) is the original signal;

[0104] 3) By alternately updating the modal components, center frequencies, and Lagrange multipliers, the objective function is gradually optimized, and finally each modal component and the corresponding center frequency are obtained.

[0105] S3. Construct a heavy gas turbine model based on the EffiCANet and KAN networks. The EffiCANet network is responsible for fitting the actual operating data, and the corresponding error loss is used as the data loss term of the total loss function. The KAN network is responsible for fitting the internal nonlinear equations of the system, and the corresponding error loss is used as the physical loss term of the total loss function. Initialize the network parameters, input the dataset processed in S2 into the model for training, and calculate the total loss. The specific steps are as follows:

[0106] S31. Input the data processed in S2 into the EffiCANet network in the form of a matrix [B, M, H], where B represents the batch size, M represents the number of feature variables, and H represents the window length; for each sliding window data x ∈ R M×H Increase the dimension through a non-squeezing operation x ∈ R M×1×H , ensuring that each variable can be processed independently. Divide the sequence into patches through a convolutional layer with a kernel size of P and a stride of S, and map each input channel to D output channels to obtain x emb ∈ R M×D×N ;

[0107] S32. Extract the short-term and long-term features in the multivariate time series through the temporal large kernel decomposition convolutional module, and use depth-wise intelligent convolution to extract short-term dependencies, which is expressed as:

[0108] x short = DWConv(x emb );

[0109] Use depth-wise dilated convolution to extract long-term dependencies, which is expressed as:

[0110] x long = DWDConv(x emb );

[0111] Add the two elements to get:

[0112] x combined = xshort +x long ;

[0113] S33. Model the dependencies between variables through the variable group convolution module, pad the time dimension so that the time dimension is divisible by the window size, and implement convolution between multiple time windows, expressed as:

[0114]

[0115] where N pad1 is the necessary padding length, T is the time dimension, and W is the window size;

[0116] Then, adopt the head and tail padding strategy to obtain various dynamic patterns, expressed as:

[0117]

[0118] where N left_pad2 is the padding length on the left side of the time dimension, and N right_pad2 is the padding length on the right side of the time dimension;

[0119] Perform one-dimensional group convolution on each tensor in the channel dimension, expressed as:

[0120] X padded1 = Conv(X padded1 );

[0121] Y padded2 = Conv(X padded2 );

[0122] where padded1 represents standard padding, padded2 represents head and tail padding, Conv is convolution, X padded1 is the input data after standard padding, X padded2 is the input data after head and tail padding, Y padded1 is the data after standard padding and convolution, and Y padded2 is the data after head and tail padding and convolution;

[0123] After merging the above results, perform convolution processing to further refine and extract the interaction between time and variables, and obtain the convolution output, expressed as:

[0124] Y = Conv(T padded1 + Y padded2 );

[0125] where Y is the convolution output.

[0126] S34. Adopt the global time variable attention module to selectively enhance the feature learning of the time dimension and variable dimension in the multivariate time series. Given the input tensor Y ∈ R M×D×N, capture the global time dependencies and dependencies between variables, and combine the time weights and variable weights with the convolution output as the output Y out ; Combine Y out with the input x emb as the input to the next module; specifically:

[0127] 1) Capture the global time dependencies: Reshape the input tensor into Y temp ∈ R (N×D)×M , apply global average pooling along the variable dimension, and then process this representation using a fully connected network. This process is expressed as:

[0128] T pool = AvgPool(Y temp ) ∈ R (N×D) ;

[0129] T atten = σ(W 2 · ReLU(W 1 · T pool ));

[0130] Where, T atten is the time weight, AvgPool is the global average pooling, T pool is the time-centered representation of the input tensor, W 1 and W 2 are weight matrices, σ is the sigmoid activation function, and ReLU is the rectified linear unit activation function;

[0131] 2) Capture the dependencies between variables: Reshape the input tensor into Y var ∈ R (M×D)×N , apply global average pooling along the time dimension, and then process this representation using a fully connected network. This process is expressed as:

[0132] V pool = AvgPool(Y var ) ∈ R (M×D) ;

[0133] V atten = σ(W 4 · ReLU(W 3 · V pool ));

[0134] Where, V atten is the variable weight, V pool is the variable-centered representation of the input tensor, W 3 and W 4 are weight matrices;

[0135] 3) Combine the time and variable weights with the convolution output as the output, expressed as: Yout = σ(T atten ⊙ V atten ⊙ Y);

[0136] Where Y out represents the output, and ⊙ represents the Hadamard product.

[0137] 4) Further refine the feature representation, and combine Y out with x emb as the input of the next module.

[0138] S35. Obtain the predicted value through the prediction layer Calculate the predicted value and the label value Y label to obtain the mean squared error between them, and use the mean squared error as the data loss term MSE in the total loss function u ;

[0139] S36. Fit the non-linear equation inside the heavy gas turbine system, expressed as:

[0140]

[0141] Obtain the derivative of the output result of the EffiCANet network with respect to the input through automatic differentiation Use the KAN network to obtain Calculate and to obtain the mean squared error between them as the physical loss term MSE in the total loss function f ;

[0142] S37. Calculate the total loss to guide the update of the EffiCANet network parameters. The total loss is expressed as:

[0143] MSE = MSE u + MSE f .

[0144] S4. Based on the total loss obtained in S3, use the alpha evolution algorithm to optimize the hyperparameters of the EffiCANet network. Stop when the objective function value converges to obtain the optimal hyperparameters of the network and complete the model construction. The specific steps are as follows:

[0145] S41. Regard the initial hyperparameters of the EffiCANet network as candidate solution individuals, and initialize the candidate solution individuals, expressed as:

[0146] X i = lb + (ub - lb) · rand(0,1,[1,D dim ), i = 1,2,…,N pop ;

[0147] Where Xi Denote the \(i\)-th candidate solution individual, \(lb\) and \(ub\) represent the lower and upper bounds of the hyperparameters respectively, \(rand\) represents the random number generator, \(D\) dim represents the dimension of the candidate solution, \(N\) pop represents the total number of candidate solutions;

[0148] S42. Determine the optimal candidate solution based on the fitness function, expressed as:

[0149] \(f(X\) i ) = MSE u '(X i );

[0150] where, is a \(D\) dim -dimensional vector; \(MSE\) u '(X i ) represents the optimal data loss obtained by training the network based on the candidate solution \(X\) i ;

[0151] S43. Update the value of the candidate solution, expressed as:

[0152]

[0153] where, E i represents the \(\theta\)-th evolved solution, \(t\) represents the current iteration number, \(P\) represents the starting position of evolution, \(\beta\) represents the decay factor, \(\Delta r\) i represents the \(\theta\)-th random step size, \(\theta\) represents the control parameter, \(W\) i and \(L\) i represent the sampled solutions, \(f(W\) i ) \(\leq f(E\) i ) \(\leq f(L\) i );

[0154] S44. Perform boundary constraint on the candidate solution, and the specific formula is:

[0155]

[0156] where, \(E\) i,j is the \(\theta\)-th evolved solution of the \(j\)-th candidate solution individual;

[0157] S45. Judge whether the objective function value converges. If it converges, obtain the optimal hyperparameters of the EffiCANet network; otherwise, return to step S43.

[0158] Therefore, an intelligent modeling method for heavy-duty gas turbines based on EffiCANet and KAN networks of the present invention adopts a structure that integrates EffiCANet and KAN networks. The EffiCANet is used to analyze the actual operation data to obtain the mapping relationship between input and output variables. The KAN network is used to model the internal nonlinear equations of the heavy-duty gas turbine, adding physical constraints to the established mapping relationship to provide the generalization ability of the model. The alpha evolution algorithm is used to optimize the network hyperparameters to improve the accuracy of the model.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network, characterized in that: The following steps are involved: S1. Based on the operating characteristics of heavy-duty gas turbines, the Spearman correlation coefficient is used to perform correlation analysis on the variables to determine the input variables and output variables; S2, collecting historical operating data of heavy-duty gas turbines according to the results of S1, and using variational mode decomposition to reduce noise on the data of input variables after preprocessing; S3, build a heavy-duty gas turbine model based on EffiCANet and KAN network, initialize network parameters, input the data set processed by S2 into the model for training, and calculate the total loss; S4. Based on the total loss obtained in S3, the Alpha evolutionary algorithm is used to optimize the EffiCANet network hyperparameters. When the objective function value converges, the optimization is stopped to obtain the optimal hyperparameters of the network and complete the model construction.

2. The heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network according to claim 1 is characterized in that: In S1, the Spearman correlation coefficient calculation formula is: Among them, R(x i )、R(y i ) are the values ​​of the two variables, are the means of variables x and y respectively, and n is the number of samples.

3. The heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network according to claim 1 is characterized in that: In S1, the input variables are the compressor inlet guide vane opening and the fuel quantity; the output variables are the rotor speed, exhaust temperature, exhaust pressure, and output power.

4. The heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network according to claim 1 is characterized in that: In S2, the preprocessing process is: 1) Process missing values ​​and outliers in the data; 2) Perform maximum and minimum normalization on the state variables of different orders of magnitude in the collected data. The specific formula is: Among them, x * is the normalized data, x is the original data, and x min is the minimum value of the original data of the feature variable, x max is the maximum value of the original data of the processed feature variable.

5. The heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network according to claim 1 is characterized in that: In S2, the noise reduction process is as follows: 1) Through variational optimization, the original signal is decomposed into k modal components with limited bandwidth and center frequency, and the sum of the bandwidths of each modal component is minimized. The constraint condition is that the original signal is equal to the sum of all modal components. The formula is expressed as: Where k is the number of center frequencies, j is the imaginary unit, ω k is the center frequency, u k is the modal component, δ(t) is the Dirac function, is the time derivative operator, t is the time variable, and f is the original signal to be denoised; 2) The quadratic penalty parameter and Lagrange multiplier are introduced to transform the constraints into an unconstrained Lagrangian optimization problem, which can be expressed as: Among them, α is the quadratic penalty parameter, λ is the Lagrange multiplier, and f(t) is the original signal; 3) By alternately updating the modal components, center frequencies, and Lagrange multipliers, the objective function is gradually optimized, and finally each modal component and the corresponding center frequency are obtained.

6. The heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network according to claim 1 is characterized in that: The specific steps of S3 are as follows: S31, input the data processed by S2 into the EffiCANet network in the form of a matrix [B, M, H], where B represents the batch size, M represents the number of feature variables, and H represents the window length; each sliding window data x∈R M×H Increase the dimension x∈R by a non-squeezing operation M×1×H , the sequence is divided into N patches through a convolutional layer with a kernel size of P and a stride of S, and each input channel is mapped to D output channels, resulting in x emb ∈R M×D×N ; in, S32, extract short-term and long-term features from multivariate time series through the time series large kernel decomposition convolution module, use deep intelligent convolution to extract short-term dependencies, use deep extended convolution to extract long-term dependencies, and add the two elements; S33, the dependency relationship between variables is modeled through the inter-variable group convolution module, and the time dimension is filled so that the time dimension can be divided by the window size, and convolution between multiple time windows is realized, which is expressed as: Among them, N pad1 is the necessary padding length, T is the time dimension, and W is the window size; Then the head and tail filling strategy is adopted to obtain the dynamic mode, which is expressed as: Among them, N left_pad2 The left padding length of the time dimension, N right_pad2 Fill the right side of the time dimension with length; Perform a one-dimensional group convolution on each tensor in the channel dimension, expressed as: Y padded1 =Conv(X padded1 ); Y padded2 =Conv(X padded2 ); Among them, padded1 means standard padding, padded2 means head and tail padding, Conv means convolution, X padded1 is the input data after standard filling, X padded2 is the input data after padding at the beginning and end, Y padded1 is the data after standard padding and convolution, Y padded2 The data is padded at the beginning and end and convolved; The results are combined and then convolved to obtain the convolution output, which is expressed as: And=Conv(And padded1 +Y padded2 ); Among them, Y is the convolution output; S34, adopt the global time variable attention module to selectively enhance the feature learning of time dimension and variable dimension in multivariate time series. Given the input tensor YeR M×D×N , capturing global temporal dependencies and inter-variable dependencies, combining temporal weights and variable weights with the convolution output as the output Y out ; Y out With input x emb Combined as input for the next module; S35. Get the predicted value through the prediction layer Calculate predicted values With label value Y label The mean square error between them is used as the data loss term in the total loss function; S36. Fitting the nonlinear equation inside the heavy-duty gas turbine system is expressed as: The derivative of the output of the EffiCANet network with respect to the input is obtained by automatic differentiation Using KAN network to obtain calculate and The mean square error between them is used as the physical loss term in the total loss function; S37. Calculate the total loss to guide the EffiCANet network parameter update. The total loss is expressed as: MSE=MSE u +MSE f ; Among them, MSE represents the total loss, MSE u Represents data loss term; MSE f Represents the physical loss term.

7. A heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network according to claim 6, characterized in that The specific steps of S34 are: 1) Capture global temporal dependencies: Reshape the input tensor into Y temp ∈R (N×D)×M , global average pooling is applied along the variable dimension, and then a fully connected network is used to process the representation, which is expressed as: T pool =AvgPool(Y temp )∈R (N×D) ; T atten =σ(W2·ReLU(W1·T pool )); Among them, T atten is the time weight, AvgPool is the global average pool, T pool is the time-centric representation of the input tensor, W1 and W2 are weight matrices, σ is the S-type activation function, and ReLU is the rectified linear unit activation function; 2) Capture dependencies between variables: Reshape the input tensor into Y var ∈R (M×D)×N , global average pooling is applied along the time dimension, and then a fully connected network is used to process the representation, which is expressed as: V pool =AvgPool(Y var )∈R (M×D) ; V atten =σ(W4·ReLU(W3·V pool )): Among them, V atten is the variable weight, V pool is the variable-centric representation of the input tensor, W3 and W4 are weight matrices; 3) Combine the time and variable weights with the convolution output as the output, expressed as: Y out =σ(T atten ⊙V atten ⊙Y); Among them, Y out represents output, ⊙ represents Hadamard product; 4) Further refine the feature representation and convert Y out With x emb Combined as input for the next module.

8. The heavy-duty gas turbine intelligent modeling method based on EffiCANet and KAN network according to claim 1 is characterized in that: The specific steps of S4 are: S41. The initial hyperparameters of the EffiCANet network are regarded as candidate solution individuals, and the candidate solution individuals are initialized, which is expressed as: X i =lb+(ub-lb)·rand(0,1,[1,D dim ]),i=1,2,…,N pop ; Among them, X i represents the i-th candidate solution individual, lb and ub represent the lower and upper bounds of the hyperparameters respectively, rand represents the random number generator, and D dim represents the dimension of candidate solutions, N pop represents the total number of candidate solutions; S42, determining the optimal candidate solution based on the fitness function, expressed as: f(X i )=MSE u ′(X i ); in, It is a D dim dimensional vector; MSE u ′(x i ) represents the candidate solution X i The optimal data loss obtained by training the network; S43, update the value of the candidate solution, expressed as: in, E i represents the i-th evolution solution, t represents the current iteration number, P represents the starting position of the evolution, β represents the attenuation factor, Δr i represents the i-th random step, θ represents the control parameter, W i and L i represents the sampling solution, f(W i )≤f(E i )≤f(L i ); S44. Apply boundary constraints to candidate solutions. The specific formula is: Among them, E i，j is the i-th evolutionary solution of the j-th candidate solution individual; S45. Determine whether the objective function value converges. If so, obtain the optimal hyperparameters of the EffiCANet network; otherwise, return to step S43.

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