Machine Learning-Based Control Method for Waste Recycling and Silica Sol Production

Abstract

This invention discloses a machine learning-based method for controlling the production of silica sol from recycled waste residue. The method collects raw material parameters, process parameters, and product quality indicators from the waste residue to construct a time-series dataset. It then uses a prediction model to generate trend values ​​and residual prediction vectors. A dual-branch neural network is established to process the raw material and process parameters separately, and different learning rules are used to update the weights in the hidden layers. The residual prediction vector is input into the network connection layer to correct the channel weighting coefficients, obtaining updated predictions. The trend values ​​and updated predictions are weighted and fused to obtain a combined prediction value. Finally, constrained optimization is used to calculate the reaction temperature, pH, stirring rate, and additive concentration to achieve closed-loop control and data updates, thereby improving product quality stability and production efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of silica sol production control, and particularly relates to a waste residue recycling silica sol production control method based on machine learning. BACKGROUND

[0002] With the rapid development of industrial waste residue resource utilization and green chemical technology, the method of waste residue recycling to prepare silica sol has attracted widespread attention. As an important chemical material, the specific surface area, particle size distribution and gel time of silica sol directly affect the product performance and application effect. However, the composition of waste residue raw materials fluctuates greatly, the process conditions are complex and significantly interact, which brings challenges to the stable control of the production process. Traditional silica sol production control methods mostly rely on empirical formulas, single statistical models or simple process optimization strategies. These methods are often difficult to cope with complex multivariate coupling and dynamic changing production environment in actual production.

[0003] In the prior art, the following problems exist: the traditional modeling method cannot effectively separate long-term trends and short-term fluctuations, which easily leads to a decrease in the prediction accuracy of quality indicators. Existing models usually process or simply combine raw material parameters and process parameters separately, lack effective cross-channel correlation modeling capability, and are difficult to mine the potential relationship between multi-source data. When raw material fluctuations or process disturbances occur in the production process, the traditional method updates slowly and the structure is not timely adjusted, so that the prediction model is difficult to quickly adapt to the new data distribution. The existing optimization method is mostly static or single-objective optimization, and lacks dynamic optimization capability considering multiple variables such as reaction temperature, pH, stirring rate, and dosing agent concentration and their constraint conditions.

[0004] Therefore, how to provide a waste residue recycling silica sol production control method based on machine learning is a problem that those skilled in the art need to solve. SUMMARY

[0005] One object of the present application is to provide a waste residue recycling silica sol production control method based on machine learning. The present application makes full use of trend and residual decomposition modeling, double-branch neural network cross-channel coupling, adaptive weight update and constraint multi-parameter optimization, and has the advantages of high prediction accuracy, strong adaptability and good production control stability.

[0006] The waste residue recycling silica sol production control method based on machine learning according to the embodiments of the present application comprises the following steps:

[0007] S1, collecting waste residue raw material parameters, process control parameters and silica sol product quality indicators to construct a time series data set;

[0008] S2, constructing an N-BEATS model based on the time series data set to generate a trend prediction value and a residual prediction vector of the silica sol product quality indicators.

[0009] S3, constructing a Cross-Stitch double-branch neural network structure to output a prediction vector;

[0010] S4, inputting the residual prediction vector generated by the N-BEATS model into a Cross-Stitch connection layer of the Cross-Stitch double-branch neural network structure, correcting the weighting coefficient of the channel connection, and updating the prediction vector based on the corrected connection structure;

[0011] S5, linearly combining the trend prediction value generated by the N-BEATS model and the updated prediction vector output by the Cross-Stitch double-branch neural network structure to generate a combined prediction value of the target quality index;

[0012] S6, inputting the combined prediction value into a control parameter optimization structure to calculate the optimal reaction temperature, pH value, stirring rate and dosing agent concentration, inputting the calculation results into a control system, and updating the process feedback data to the time series data set.

[0013] Optionally, the S1 specifically comprises:

[0014] S11, collecting the waste residue raw material parameters at a uniform time interval;

[0015] S12, synchronously collecting the process control parameters at the corresponding time;

[0016] S13, collecting the quality index of the silica sol product at the same time stamp as the raw material parameters and process parameters;

[0017] S14, aligning the raw material parameter sequence , the process parameter sequence and the quality index sequence one by one according to the time stamp , constructing a sequence triple set indexed by time, defined as a time series data set .

[0018] Optionally, the S2 specifically comprises:

[0019] S21, based on the constructed time series data set, splicing the raw material parameters and the process parameters into a combined vector according to the feature order to form an input sequence arranged by time;

[0020] S22, setting the time window length, and extracting the historical data segment corresponding to the current time step as input by using a sliding window method and sending it into the N-BEATS model;

[0021] S23, the N-BEATS model comprises The residual structure units are sequentially connected in order of numbering, and each residual structure unit comprises:

[0022] The pre-encoding network: the input tensor is unfolded into a one-dimensional vector in time sequence, sequentially passes through a first fully connected layer and a nonlinear activation layer, and then passes through a second fully connected layer to output an intermediate vector as the input of the three branch paths;

[0023] The trend prediction branch: receives the intermediate vector, and obtains a feature vector through a first linear transformation layer; the feature vector and a group of channel weight vectors are multiplied element by element to perform channel reconstruction; the reconstructed vector is input into a second linear transformation layer to be mapped into a dimension equal to the number of target prediction indicators to obtain a trend prediction vector;

[0024] The residual prediction branch: receives the intermediate vector, and first performs normalization processing; sequentially inputs into a first fully connected layer and a nonlinear activation layer, and then inputs into a second fully connected layer; the output is mapped into a dimension equal to the number of target prediction indicators to obtain a residual prediction vector;

[0025] The reconstruction update branch: receives the intermediate vector, and obtains a one-dimensional vector through a linear layer; is reshaped into a matrix form with the same time steps and feature dimensions as the input tensor to serve as a reconstruction tensor; the input tensor of the next unit is obtained by subtracting the reconstruction tensor of the current unit from the input tensor of the current unit;

[0026] S24, sequentially adding the trend prediction vectors output by all residual structure units to obtain the trend prediction result of the current time step; sequentially adding all residual prediction vectors to obtain the residual prediction result of the current time step;

[0027] S25, weighting and combining the trend prediction result and the residual prediction result according to a preset weight to obtain a final prediction output.

[0028] Optionally, the S3 specifically comprises:

[0029] S31, constructing a Cross-Stitch double-branch neural network structure: a first neural network branch receives a sequence of waste residue material parameters arranged in time sequence; a second neural network branch receives a sequence of process control parameters arranged in time sequence;

[0030] S32, the feature processing path of the first neural network branch:

[0031] The input vector is processed by a one-dimensional time domain convolution layer, and the time dimension is kept unchanged by zero padding; the convolution kernel weight initialization method is Xavier initialization or He initialization; a batch normalization layer and a nonlinear activation layer are arranged after the convolution layer, and the activation function is ReLU;

[0032] The convolution output is processed by a multi-head channel decomposition module, which includes h parallel branches; the channel division method is equal division or frequency band clustering-based; each branch after decomposition is provided with Layer Normalization or Batch Normalization;

[0033] Each branch is sequentially connected with a linear transformation layer and a nonlinear activation layer, the linear transformation layer is a full connection structure or a one-dimensional point-by-point convolution structure, and the activation function is ReLU or GELU;

[0034] The output of each branch is spliced into a current hidden layer output vector in the channel dimension;

[0035] S33, the feature processing path of the second neural network branch: the input vector is converted to the frequency domain by a fast Fourier transform module; segment filtering and amplitude normalization are performed in the frequency domain; inverse Fourier transform is used to restore to the time domain; after linear transformation layer and nonlinear activation layer processing, the current hidden layer output vector is obtained;

[0036] S34, Hebbian weight update of the first neural network branch:

[0037] The product of the input vector and the output vector is calculated for each connection, multiplied by the first learning rate, and added to the corresponding weight value;

[0038] The feature correlation coefficient of the same position output channel and the current channel of the second neural network branch is calculated, and the weight value is increased when the correlation coefficient is positive, and the weight value is reduced when the correlation coefficient is negative;

[0039] The updated weight matrix replaces the original matrix;

[0040] S35, Oja weight update of the second neural network branch:

[0041] Hebbian accumulation update is performed on the input vector and the output vector for each connection;

[0042] The product of the output component square and the weight value is subtracted from the updated weight value;

[0043] The correlation coefficient of each column weight vector and the same column vector of the first neural network branch is calculated, and when the correlation coefficient exceeds the set threshold, the projection component in the first branch direction is deducted from the column vector, and the column vector is normalized;

[0044] S36, Cross-Stitch connection layer processing:

[0045] The feature correlation coefficient of the current hidden layer output channel of the two branches is calculated and sorted;

[0046] Select the channel greater than or equal to the p quantile of the channel correlation coefficient distribution as the reserved channel, and set the weight of the remaining channels to zero;

[0047] Calculate the rate of change of the gradient between the previous batch and the current batch in the reserved channels, and multiply the channel weights below the threshold g by the scaling factor k2.

[0048] Normalize the coefficient matrix row by row so that the sum of the weights in each row equals 1;

[0049] The two branch output channels are weighted and combined according to the coefficient matrix, and used as the input of the next hidden layer.

[0050] S37. In the final Cross-Stitch connection layer, the outputs of the two branches are weighted and combined into a prediction vector. The dimension of the prediction vector is consistent with the number of quality indicators of the silica sol product.

[0051] Optionally, the multi-channel decomposition module performs a fast Fourier transform on the convolution result according to the channel dimension, dividing the spectrum into several frequency bands, the range of each frequency band being determined according to the energy distribution criterion; based on the energy distribution vector of each channel in each frequency band, a clustering algorithm is used to group the channels, with each group corresponding to a branch channel.

[0052] Optionally, S4 specifically includes:

[0053] S41, at time step Read the residual prediction vector from the N-BEATS model output. From the hierarchical structure of the Cross-Stitch dual-branch neural network Reading the coefficient matrix From the first neural network branch at the layer Read vectors from the output From the second neural network branch at the layer Read vectors from the output And align them according to channel order to form a channel dataset;

[0054] S42, For each channel Extracting the coefficient matrix Central and Channel The corresponding two rows and two columns form the channel submatrix. Extract vectors and Central Channel The components form the channel vector The channel submatrix and channel vector are linearly combined to generate a reconstruction vector, which is then combined with the residual prediction vector. The squared error is calculated by comparing the element positions to obtain the initial error value;

[0055] S43. Perform the finite difference update algorithm: preserve the channel submatrix. With the remaining elements unchanged, the target element is increased by a fixed increment and the reconstructed vector and squared error are recalculated. The initial error is subtracted from the new error and divided by the fixed increment to obtain the gradient approximation. The gradient approximation is multiplied by the preset learning step size and then directly subtracted from the target element value. The updated new element value is written into the channel submatrix.

[0056] S44. Implement the correlation coefficient threshold strategy: calculate the channel vector. With residual prediction vector The Pearson correlation coefficient; when the correlation coefficient is lower than a preset threshold, the channel submatrix will be... All element values ​​are set to zero; when the correlation coefficient is not lower than the preset threshold, the element values ​​updated by finite difference are retained;

[0057] S45. Update the coefficient matrix. Normalize by row so that the sum of the elements in each row is 1, and set an upper limit for the sum of the elements in each column. When the sum of the column exceeds the upper limit, reduce all elements in the column proportionally to no more than the upper limit.

[0058] S46. Using the updated coefficient matrix Output vectors for the first branch of the neural network respectively With the output vector of the second neural network branch A weighted combination is performed along the channel dimension to generate the input vector for the next layer. and The time steps are then passed sequentially through the dual-branch network until the output layer is reached. Update the prediction vector; and finally update the coefficient matrix. It is stored in the corresponding Cross-Stitch connection layer.

[0059] Optionally, S5 specifically includes:

[0060] S51, at time step Read the trend prediction vector generated by the N-BEATS model Updated prediction vectors from the output of the Cross-Stitch two-branch neural network structure The channel set is obtained by aligning the channel numbers with the target quality indicators in order and by dimension. ;

[0061] S52, for channel Construct a two-dimensional time window matrix, with the first row storing the intervals sequentially. within The sequence values, the second row stores the ranges sequentially. within Sequence values, window length It is a preset positive integer;

[0062] S53, Channel Singular value decomposition is performed on the two-dimensional time window matrix to extract the first left singular vector as the principal direction vector; the angle between the principal direction vector and the unit vector of the first coordinate axis is calculated to obtain the channel similarity angle. ;

[0063] S54, according to Generate channel weight pairs :when Less than the threshold When the trend weight is equal to the square of the cosine of the included angle, the updated weight is one minus the trend weight; when In the range When the trend weight is equal to the update weight, the trend weight is taken as equal to the update weight. Greater than or equal to the threshold At that time, the trend weight is taken as a fixed lower limit value, and the update weight is taken as one minus the fixed lower limit value;

[0064] S55. Perform column vector sum-of-squares normalization on the weights of all channels: calculate separately. and The sum of squares and the square root are used to obtain the normalization factor. Each channel weight is then divided by its corresponding normalization factor to ensure that the sum of squares of both columns of weights equals 1. For single-channel weight pairs... Simultaneously constrained within the open interval ;

[0065] S56, in the passage Calculate the combined components and generate the combined prediction vector. According to the channel number sequence Concatenate into a combined prediction vector ;

[0066] S57, to Perform channel de-biasing operation: in the window Calculate the median for each channel separately, and then calculate the median from the channel dimension. Subtract the corresponding median from the middle; input the debiased result into the linear mapping layer, the parameters of which are fixed matrices;

[0067] S58. Record in time-series storage as well as , With window statistics.

[0068] Optionally, S6 specifically includes:

[0069] S61, at time step Read the combined prediction vector Read the target set vector Read the control parameter vector and sampling period length of the previous batch; map the target quality index channel to the control parameter channel according to the preset mapping table;

[0070] S62. Calculate the channel sensitivity coefficient: In the most recent Within each time step, the absolute value of the linear regression coefficient is calculated for the measured value and the change in control parameter for each quality indicator channel.

[0071] S63. Construct the objective function:

[0072] The first part is the sum of squared prediction errors, categorized by channel. and Subtract the two, multiply by the sensitivity coefficient of the corresponding channel, square the result, and sum them up.

[0073] The second part is the sum of squares of the control parameter changes. The current candidate control parameter is subtracted from the previous batch of control parameters by channel, multiplied by a fixed control weight, squared, and then accumulated.

[0074] Adding the two parts together yields the numerical value of the objective function;

[0075] S64. Set control parameter constraints;

[0076] S65. The gradient of the objective function with respect to each control parameter is approximated using the finite difference method: a fixed small value is added to each single control parameter in turn, the objective function is recalculated, and the difference between the original objective function and the fixed small value is divided to obtain the approximate gradient value; the above process is repeated for all control parameters to obtain the gradient vector.

[0077] S66. Update control parameters using the projected gradient descent method: Subtract the product of the gradient and the preset step size from the current control parameter vector in the gradient direction to obtain the update vector; project the update vector channel by channel to the constraint interval, and detect the rate of change constraint during the projection process. If the rate exceeds the upper limit, reduce the change amount of the corresponding channel proportionally.

[0078] S67. Repeat gradient calculation and parameter update until the upper limit of the number of iterations is reached, or the change of the control parameter in two consecutive updates is lower than the minimum change threshold; take the parameter vector obtained in the final iteration as the optimal control parameter.

[0079] The beneficial effects of this invention are as follows: By employing the N-BEATS model of trend and residual decomposition in time series forecasting, and combining it with a Cross-Stitch dual-branch neural network, the waste residue raw material parameters and process control parameters are input into different branches respectively. Within each branch, Hebbian and Oja learning rules are used to update the weights, achieving independent learning and cross-channel coupling of the two types of features. This structure can better utilize the correlation between multi-source data, maintaining high prediction accuracy for silica sol quality indicators even under fluctuations in raw materials and processes.

[0080] This invention introduces the residual prediction vector into the Cross-Stitch connection layer, uses the finite difference method to correct the channel weighting coefficients, and applies constraints such as correlation coefficient thresholds and column and upper limits, so that the network can automatically adjust the coupling strength between branches when the prediction deviation is large, thereby improving the model's adaptability to new data distributions and abnormal fluctuations.

[0081] This invention uses the SVD-angle method to weight and fuse trend prediction values ​​and updated prediction vectors, which can dynamically adjust the weights according to the correlation between the two prediction results, thereby obtaining more stable combined prediction values ​​at different production stages. Attached Figure Description

[0082] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0083] Figure 1 This is a flowchart of the waste residue recycling silica sol production control method proposed in this invention. Detailed Implementation

[0084] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0085] refer to Figure 1 A machine learning-based method for controlling the production of recycled silica sol from waste residue includes the following steps:

[0086] S1. Collect waste residue raw material parameters, process control parameters, and silica sol product quality indicators to construct a time series dataset;

[0087] S2. Construct an N-BEATS model based on the time series dataset to generate trend prediction values ​​and residual vectors for the quality indicators of silica sol products;

[0088] S3. Construct a Cross-Stitch dual-branch neural network structure. The first neural network branch inputs the waste residue raw material parameters and updates the connection weights in each hidden layer using the Hebbian learning rule. The second neural network branch inputs the process control parameters and updates the connection weights in each hidden layer using the Oja learning rule. A Cross-Stitch connection layer is set between the two neural network branches to establish channel connections and output the prediction vector.

[0089] S4. Input the residual vector generated by the N-BEATS model into the Cross-Stitch connection layer of the Cross-Stitch dual-branch neural network structure, correct the weighting coefficients of the channel connections, and update the prediction vector based on the corrected connection structure.

[0090] S5. Linearly combine the trend prediction value generated by the N-BEATS model with the update prediction vector output by the Cross-Stitch dual-branch neural network structure to generate a combined prediction value of the target quality index.

[0091] S6. Input the combined predicted values ​​into the control parameter optimization structure, calculate the optimal reaction temperature, pH value, stirring rate and additive concentration, input the calculation results into the control system, and update the process feedback data to the time series dataset.

[0092] In this embodiment, S1 specifically includes:

[0093] S11. Hourly data collection of waste residue raw material parameters is performed at uniform time intervals. These parameters include silicon dioxide content (SiO2), aluminum oxide content (Al2O3), and raw material particle size (D). 50 And the moisture content W of the raw materials, the collected results are categorized by timestamp. Numbering, forming a raw material parameter sequence ;

[0094] S12. Synchronously acquire the process control parameters at the corresponding time points. The process control parameters include reaction temperature T, solution pH value, stirring rate v, and additive concentration C, forming a process parameter sequence. ;

[0095] S13. Collect quality indicators of the silica sol product at the same timestamp as the raw material parameters and process parameters. The quality indicators include specific surface area S, particle size distribution range P, and gelation time τ, forming a quality indicator sequence. ;

[0096] S14, Sequence of raw material parameters Process parameter sequence With quality indicator series By timestamp Align each pair sequentially to construct a set of time-indexed sequence triples, which is defined as a time series dataset. .

[0097] In this embodiment, S2 specifically includes:

[0098] S21. Based on the constructed time series dataset, the dataset consists of waste residue raw material parameters, process control parameters and silica sol product quality indicators aligned by timestamps. The raw material parameters and process parameters are concatenated into a combined vector according to the feature order to form an input sequence arranged by time.

[0099] S22. Set the time window length, use a sliding window method to extract historical data segments corresponding to the current time step as input, and feed them into the N-BEATS model;

[0100] S23, the N-BEATS model is composed of It consists of residual structural units connected sequentially in numerical order, and each residual structural unit includes:

[0101] Pre-encoding network: The input tensor is unfolded into a one-dimensional vector in time sequence, and then passed through the first fully connected layer and the non-linear activation layer, and then through the second fully connected layer. The output intermediate vector is used as the input of the three branch paths.

[0102] Trend prediction branch: Receives the intermediate vector, passes it through the first linear transformation layer to obtain the feature vector; multiplies the feature vector with a set of channel weight vectors element by element to achieve channel reconstruction; sends the reconstructed vector into the second linear transformation layer, maps it to a dimension equal to the number of target prediction indicators, and obtains the trend prediction vector.

[0103] Residual prediction branch: Receives the intermediate vector, performs normalization processing first; feeds it sequentially into the first fully connected layer and the nonlinear activation layer, then into the second fully connected layer; maps the output to a dimension equal to the number of target prediction indicators to obtain the residual prediction vector;

[0104] Deconstruction update branch: Receives the intermediate vector, transforms it through a linear layer to obtain a one-dimensional vector; reshapes it into a matrix form with the same time steps and feature dimensions as the input tensor, as the deconstruction tensor; subtracts the current unit's deconstruction tensor from the current unit's input tensor to obtain the input tensor of the next unit;

[0105] S24. Add the trend prediction vectors output by all residual structural units in sequence to obtain the trend prediction result for the current time step; add the residual prediction vectors in sequence to obtain the residual prediction result for the current time step.

[0106] S25. The trend prediction results and residual prediction results are weighted and combined according to preset weights to obtain the final prediction output, which is used for subsequent process parameter optimization and closed-loop control.

[0107] In this embodiment, S3 specifically includes:

[0108] S31. Construct a Cross-Stitch dual-branch neural network structure: The first neural network branch receives the sequence of waste residue raw material parameters arranged in chronological order, including the SiO2 content, Al2O3 content, and particle size D at each time step. 50 The first branch of the neural network receives the sequence of process control parameters arranged in chronological order, with the reaction temperature T, pH value, stirring rate v, and additive concentration C at each time step forming the input vector.

[0109] S32, Feature processing path of the first neural network branch:

[0110] The input vector is processed by a one-dimensional temporal convolutional layer. The kernel size of the convolutional layer is an odd number of 3 to 7, and the stride is 1 to 3. Zero padding is used to keep the temporal dimension unchanged. The kernel weights are initialized using Xavier initialization or He initialization. After the convolutional layer, a batch normalization layer and a non-linear activation layer are set, and the activation function is ReLU.

[0111] The convolutional output is processed by a multi-channel decomposition module, which includes h parallel branches, where h ranges from 4 to 8; the channel partitioning method is equal division or based on frequency band clustering; each branch after decomposition is configured with LayerNormalization or BatchNormalization.

[0112] Each branch is connected sequentially to a linear transformation layer and a nonlinear activation layer. The linear transformation layer is a fully connected structure or a one-dimensional pointwise convolutional structure, and the activation function is ReLU or GELU.

[0113] The outputs of each branch are concatenated along the channel dimension to form the current hidden layer output vector;

[0114] S33, Feature processing path of the second neural network branch: The input vector is transformed to the frequency domain by the fast Fourier transform module; piecewise filtering and amplitude normalization are performed in the frequency domain; the inverse Fourier transform is used to restore it to the time domain; after processing by the linear transform layer and the nonlinear activation layer, the output vector of the current hidden layer is obtained;

[0115] S34, Hebbian weight update of the first neural network branch:

[0116] The input vector and the output vector are concatenated one by one, and the product is calculated. The product is then multiplied by the first learning rate and added to the corresponding weight.

[0117] Calculate the feature correlation coefficient between the output channel at the same position of the second neural network branch and the current channel. Increase the weight when the correlation coefficient is positive and decrease the weight when the correlation coefficient is negative.

[0118] The updated weight matrix replaces the original matrix;

[0119] S35, Oja weight update of the second neural network branch:

[0120] Perform Hebbian cumulative update by concatenating the input and output vectors one by one;

[0121] Subtract the product of the square of the output component and the weight from the updated weight;

[0122] Calculate the correlation coefficient between each column weight vector and the column vector of the first neural network branch. When the correlation coefficient exceeds a set threshold, subtract the projection component in the direction of the first branch from the column vector and normalize the column vector.

[0123] S36, Cross-Stitch connection layer processing:

[0124] Calculate and sort the feature correlation coefficients of the current hidden layer output channels of the two branches;

[0125] Channels with correlation coefficients greater than or equal to the p-th quantile of the channel correlation coefficient distribution are selected as retained channels, and the weights of the remaining channels are reset to zero.

[0126] Calculate the rate of change of the gradient between the previous batch and the current batch in the reserved channels, and multiply the channel weights below the threshold g by the scaling factor k2.

[0127] Normalize the coefficient matrix row by row so that the sum of the weights in each row equals 1;

[0128] The two branch output channels are weighted and combined according to the coefficient matrix, and used as the input of the next hidden layer.

[0129] S37. Perform the above steps sequentially until the last layer. In the final Cross-Stitch connection layer, the outputs of the two branches are weighted and combined into a prediction vector. The dimension of the prediction vector is consistent with the number of quality indicators of the silica sol product.

[0130] In this embodiment, the frequency band clustering strategy of the multi-channel decomposition module includes: performing a fast Fourier transform on the convolution result according to the channel dimension to divide the spectrum into several frequency band intervals, the range of each frequency band interval being determined according to the energy distribution criterion; and using a clustering algorithm to group the channels based on the energy distribution vector of each channel in each frequency band, with each group corresponding to a branch channel.

[0131] The segmented filtering after the fast Fourier transform includes low-pass, high-pass, or band-pass filtering, and the cutoff frequency of the filter is determined by the boundary of the frequency band.

[0132] The amplitude normalization includes scaling the amplitude proportionally according to the statistical amplitude of the frequency band;

[0133] The p-quantile is a threshold selected based on the distribution of channel feature correlation coefficients, and the correlation coefficients are calculated from the feature correlation coefficients of the corresponding channels within multiple consecutive time steps.

[0134] In this embodiment, S4 specifically includes:

[0135] S41, at time step Read the residual vector from the N-BEATS model output. From the hierarchical structure of the Cross-Stitch dual-branch neural network Reading the coefficient matrix From the first neural network branch at the layer Read vectors from the output From the second neural network branch at the layer Read vectors from the output And align them according to channel order to form a channel dataset;

[0136] S42, For each channel Extracting the coefficient matrix Central and Channel The corresponding two rows and two columns form the channel submatrix. Extract vectors and Central Channel The components form the channel vector The channel submatrix and channel vector are linearly combined to generate a reconstructed vector, which is then combined with the residual vector. The squared error is calculated by comparing the element positions to obtain the initial error value;

[0137] S43. Perform the finite difference update algorithm: preserve the channel submatrix. With the remaining elements unchanged, the target element is increased by a fixed increment and the reconstructed vector and squared error are recalculated. The initial error is subtracted from the new error and divided by the fixed increment to obtain the gradient approximation. The gradient approximation is multiplied by the preset learning step size and then directly subtracted from the target element value. The updated new element value is written into the channel submatrix.

[0138] S44. Implement the correlation coefficient threshold strategy: calculate the channel vector. With residual vector The Pearson correlation coefficient; when the correlation coefficient is lower than a preset threshold, the channel submatrix will be... All element values ​​are set to zero; when the correlation coefficient is not lower than the preset threshold, the element values ​​updated by finite difference are retained;

[0139] S45. Update the coefficient matrix. Normalize by row so that the sum of the elements in each row is 1, and set an upper limit for the sum of the elements in each column. When the sum of the column exceeds the upper limit, reduce all elements in the column proportionally to no more than the upper limit.

[0140] S46. Using the updated coefficient matrix Output vectors for the first branch of the neural network respectively With the output vector of the second neural network branch A weighted combination is performed along the channel dimension to generate the input vector for the next layer. and The time steps are then passed sequentially through the dual-branch network until the output layer is reached. Update the prediction vector; and finally update the coefficient matrix. It is stored in the corresponding Cross-Stitch connection layer.

[0141] In this embodiment, S5 specifically includes:

[0142] S51, at time step Read the trend prediction vector generated by the N-BEATS model Updated prediction vectors from the output of the Cross-Stitch two-branch neural network structure The channel set is obtained by aligning the channel numbers with the target quality indicators in order and by dimension. ;

[0143] S52, for channel Construct a two-dimensional time window matrix, with the first row storing the intervals sequentially. within The sequence values, the second row stores the ranges sequentially. within Sequence values, window length It is a preset positive integer;

[0144] S53, Channel Singular value decomposition is performed on the two-dimensional time window matrix to extract the first left singular vector as the principal direction vector; the angle between the principal direction vector and the unit vector of the first coordinate axis is calculated to obtain the channel similarity angle. The included angle is calculated using the inverse cosine function, and the unit of angle is radians.

[0145] S54, according to Generate channel weight pairs :when Less than the threshold When the trend weight is equal to the square of the cosine of the included angle, the updated weight is one minus the trend weight; when In the range When the trend weight is equal to the update weight, the trend weight is taken as equal to the update weight. Greater than or equal to the threshold At that time, the trend weight is taken as a fixed lower limit value, and the update weight is taken as one minus a fixed lower limit value, with a threshold value. and For preset constants and satisfying ;

[0146] S55. Perform column vector sum-of-squares normalization on the weights of all channels: calculate separately. and The sum of squares and the square root are used to obtain the normalization factor. Each channel weight is then divided by its corresponding normalization factor to ensure that the sum of squares of both columns of weights equals 1. For single-channel weight pairs... Simultaneously constrained within the open interval ;

[0147] S56, in the passage Calculate the combined components and generate the combined prediction vector. According to the channel number sequence Concatenate into a combined prediction vector ;

[0148] S57, to Perform channel de-biasing operation: in the window Calculate the median for each channel separately, and then calculate the median from the channel dimension. Subtract the corresponding median from the middle; input the debiased result into the linear mapping layer, the parameters of which are fixed matrices;

[0149] S58. Record in time-series storage as well as , With window statistics.

[0150] In this embodiment, S6 specifically includes:

[0151] S61, at time step Read the combined prediction vector Read the target set vector Read the control parameter vector from the previous batch. And the sampling period length; the target quality index channels and control parameter channels are mapped one-to-one according to the preset mapping table;

[0152] S62. Calculate the channel sensitivity coefficient: In the most recent Within each time step, the absolute value of the linear regression coefficient is calculated for the measured value and the change in control parameter for each quality indicator channel. This absolute value is then normalized and used as the sensitivity coefficient vector for the current time step. ;

[0153] S63. Construct the objective function:

[0154] The first part is the sum of squared prediction errors, categorized by channel. and Subtract the two, multiply by the sensitivity coefficient of the corresponding channel, square the result, and sum them up.

[0155] The second part is the sum of squares of the control parameter changes. The current candidate control parameter is subtracted from the previous batch of control parameters by channel, multiplied by a fixed control weight, squared, and then accumulated.

[0156] Adding the two parts together yields the numerical value of the objective function;

[0157] S64. Set control parameter constraints: temperature is limited between the lower and upper temperature limits, pH value is limited between the lower and upper pH limits, stirring rate is limited between the minimum and maximum rates, and additive concentration is limited between the minimum and maximum concentrations; set the maximum allowable variation and the maximum allowable rate of change per unit time for each control parameter.

[0158] S65. The gradient of the objective function with respect to each control parameter is approximated using the finite difference method: a fixed small value is added to each single control parameter in turn, the objective function is recalculated, and the difference between the original objective function and the original objective function is divided by the small value to obtain the approximate gradient value; this process is repeated for all control parameters to obtain the gradient vector.

[0159] S66. Update control parameters using the projected gradient descent method: Subtract the product of the gradient and the preset step size from the current control parameter vector in the gradient direction to obtain the update vector; project the update vector channel by channel to the constraint interval, and detect the rate of change constraint during the projection process. If the rate exceeds the upper limit, reduce the change amount of the corresponding channel proportionally.

[0160] S67. Repeat gradient calculation and parameter update until the upper limit of the number of iterations is reached, or the change in the control parameter between two consecutive updates is less than the minimum change threshold; take the parameter vector obtained from the final iteration. As the optimal control parameter;

[0161] S68. Optimal reaction temperature Write the target value register of the reactor temperature control loop to set the optimal pH value. Write the setpoint register of the acid-base dosing device to the optimal stirring rate. Write the setting register of the stirring inverter controller to set the optimal dosing concentration. Write the set value register of the dosing pump control module and record the issuance timestamp and batch number;

[0162] S69. Run the process under optimal control parameters, and collect actual temperature, actual pH, actual stirring rate, actual additive concentration, and online quality detection results within the sampling window. Align these results with timestamps and channel numbers to form a data set containing... Record entries for predicted and measured quality indicators are written into the time series dataset.

[0163] Example 1: To verify the feasibility of this invention, it was applied to a chemical plant with an annual production capacity of 20,000 tons of silica sol. The plant uses industrial waste as its main raw material, including fly ash from coal-fired power plants and metallurgical waste. The raw material composition fluctuates greatly, especially the silica and alumina content. Previously, the plant relied on experience and a single statistical regression model to predict key quality indicators such as specific surface area, particle size distribution, and gelation time, and manually adjusted the reaction temperature, pH, stirring rate, and additive concentration accordingly. However, this approach has significant shortcomings: low prediction accuracy, the model cannot quickly adapt to raw material fluctuations, control optimization is lagging, ultimately leading to poor product quality stability, with the pass rate even falling below 90% in some months, and high adjustment frequency and low efficiency during the production process.

[0164] In this scenario, the method of the present invention is deployed into the factory's production monitoring system, directly interfacing with the existing data acquisition equipment and control system. Before all waste residue raw materials enter the reaction system, the raw material laboratory obtains the silica content, alumina content, and raw material particle size D through online and offline testing methods. 50 The system records the moisture content of the raw materials and transmits this data to the data server in the form of minute-level timestamps. At the same time, the control system in the production workshop records process parameters such as reaction temperature, solution pH value, stirring rate, and additive concentration, and aligns them with the product quality test results (specific surface area S, particle size distribution range P, gel time τ) at the same time point to form a standardized time series dataset.

[0165] In practical applications, this invention first trains time-series data using the N-BEATS model to generate trend prediction values ​​and residual prediction vectors for product quality indicators. Trend prediction captures long-term trends, while residual prediction vectors reflect short-term disturbances and unpredictable components. Subsequently, the system constructs a Cross-Stitch dual-branch neural network. One branch inputs waste material parameters, using the Hebbian learning rule to update the connection weights of each hidden layer, enhancing the weights of highly correlated features. The other branch inputs process control parameters, using the Oja learning rule to update the connection weights, ensuring parameter stability and orthogonality. The Cross-Stitch connection layer establishes channel-level coupling between the two feature paths. During prediction, the N-BEATS residual prediction vector is input into this layer, and the channel weighting coefficients are corrected using the finite difference method. Simultaneously, constraints are imposed on correlation coefficient thresholds and column sum upper limits, enabling the model to quickly adjust the feature fusion strategy in response to raw material fluctuations or process disturbances.

[0166] During the prediction phase, the system fuses the trend prediction value with the updated prediction vector using the SVD-angle weighted method. The fusion weights are dynamically adjusted based on the angle between the two sets of predictions to obtain a more robust combined prediction value. This combined prediction value is then input into the projection gradient optimization module, which considers boundary and rate variation constraints of reaction temperature, pH value, stirring rate, and additive concentration. This module calculates the optimal control parameters under the current production conditions and sends them to the control system for real-time adjustment. New data generated during production is written back into the time-series dataset for continuous model training and optimization, thus forming a prediction-optimization-feedback closed-loop control system.

[0167] To verify the effectiveness of this invention in actual production, the factory conducted a comparative experiment over a three-month production cycle. For the first month of the experiment, the factory used traditional statistical modeling and manual adjustments; for the last two months, the control method of this invention was fully applied. Key indicators compared included quality pass rate, quality indicator prediction error, response time for process parameter adjustments, batch-to-batch fluctuations in indicators, and production energy consumption. The following are the actual collected and compiled data results: Table 1 compares the effectiveness of the traditional method and the method of this invention.

[0168]

[0169] As shown in the table, the product quality pass rate increased to 97.8% in the second month after application of the method of this invention, and further increased to 98.3% in the third month. The prediction errors of specific surface area, particle size distribution, and gelation time were all reduced by more than 60% compared with traditional methods, indicating a significant improvement in prediction accuracy. The response time for adjusting process parameters was shortened from an average of 28 minutes using traditional methods to less than 10 minutes, greatly improving adjustment efficiency. The standard deviation of specific surface area between batches decreased significantly, indicating more stable product quality; at the same time, the overall energy consumption per unit product decreased by about 6.5%, reflecting the positive effect of optimized control on energy management.

[0170] In actual operation, the plant's technicians reported that the production process, which previously required experience-based judgment and frequent adjustments, can now be adjusted in one go using the optimal control parameters automatically calculated by the system, and the predicted results are stable across different raw material batches. For example, in a production run in mid-March, the silica content of the waste residue raw material plummeted from 67% to 62%. Under traditional methods, it would have required two to three consecutive days of process adjustments to stabilize the quality. However, after detecting the change in raw materials, the system of this invention immediately adjusted the pH value and stirring rate control scheme through residual-driven Cross-Stitch weight correction, ensuring that the specific surface area and particle size distribution indicators of the day's production remained within the standard range, and no batches of substandard products occurred.

[0171] Another typical case occurred on a production line in late February. At that time, the reaction temperature was difficult to stabilize due to changes in external temperature, and traditional manual adjustments often lagged behind. After monitoring the temperature fluctuation trend in real time, the system of this invention determined that the current prediction reliability was low by using SVD-angle weighted fusion prediction results. The system automatically increased the step size of temperature adjustment and simultaneously reduced the concentration of the additive, ultimately controlling the gel time fluctuation of this batch of products within ±1.5 minutes, a significant improvement compared to the ±4 minutes of traditional control.

[0172] In summary, this embodiment demonstrates that the method of the present invention can continuously provide high-precision quality index prediction and rapid optimization control under conditions of waste residue composition fluctuations, process disturbances, and changes in the external environment. It significantly improves the quality stability, control response speed, and energy utilization efficiency of silica sol production, reduces the need for manual intervention, and provides a feasible, efficient, and economical solution for waste residue resource utilization and high-quality silica sol production.

[0173] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for controlling production of a silica sol from waste residue based on machine learning, characterized by, The method comprises the following steps: S1, collecting waste residue raw material parameters, process control parameters and silica sol product quality indicators to construct a time series data set; S2, constructing an N-BEATS model based on the time series data set to generate trend prediction values and residual prediction vectors of the silica sol product quality indicators; S3, constructing a Cross-Stitch double-branch neural network structure to output the prediction vectors; S4, inputting the residual prediction vectors generated by the N-BEATS model into the Cross-Stitch connection layer of the Cross-Stitch double-branch neural network structure to correct the weighting coefficients of the channel connection, and updating the prediction vectors based on the corrected connection structure; S41, at a time step reading a residual prediction vector from an output of the N-BEATS model reading a coefficient matrix from a level of the Cross-Stitch dual-branch neural network structure reading a vector from an output of the first neural network branch at a level reading a vector from an output of the second neural network branch at a level and aligning the vectors in a channel order to form a channel dataset;​​​ S42, for each channel , extract the coefficient matrix , in which the two rows and two columns corresponding to the channel form a channel sub-matrix , extract the vector , and , in which the components of the channel form a channel vector , linearly combine the channel sub-matrix and the channel vector to generate a reconstruction vector, and compare it with the residual prediction vector Calculate the square error by comparing the element positions to get the initial error value; S43, execute a finite difference update algorithm: keep the channel sub-matrix The remaining elements remain unchanged, the target element is increased by a fixed increment, and the reconstruction vector and the square error are recalculated; the new error is subtracted from the initial error and divided by the fixed increment to obtain the gradient approximation value, the gradient approximation value is multiplied by the preset learning step length, and the new element value obtained by directly deducting from the target element value is written into the channel sub-matrix; S44, execute correlation coefficient threshold strategy: calculate channel vector with the Pearson correlation coefficient of the residual prediction vector ; When the correlation coefficient is lower than a preset threshold, the channel submatrix will be... All element values ​​are set to zero; When the correlation coefficient is not less than the preset threshold, the element value updated by the finite difference is retained; S45. Update the coefficient matrix. Normalize by row so that the sum of the elements in each row is 1, and set an upper limit for the sum of the elements in each column. When the sum of the column exceeds the upper limit, reduce all elements in the column proportionally to no more than the upper limit. S46, utilize the updated coefficient matrix respectively to the first neural network branch output vector and the second neural network branch output vector perform weighted combination in the channel dimension to generate the input vector of the next layer and and sequentially pass in the double-branch network until the output layer to obtain the updated prediction vector of the time step ; store the final updated coefficient matrix in the corresponding Cross-Stitch connection layer; S5, linearly combining the trend prediction values generated by the N-BEATS model and the updated prediction vectors output by the Cross-Stitch double-branch neural network structure to generate combined prediction values of the target quality indicators; S6, inputting the combined prediction values into a control parameter optimization structure to calculate the optimal reaction temperature, pH value, stirring rate and dosing agent concentration, inputting the calculation results into a control system, and updating process feedback data to the time series data set.

2. The machine learning-based production control method of silica sol from waste residue recycling according to claim 1, characterized by, The S1 specifically comprises: S11, collecting waste residue raw material parameters at a uniform time interval; S12, synchronously collecting process control parameters at the corresponding time; S13, collecting quality indicators of silica sol products at the same time stamp as the raw material parameters and process parameters; S14, aligning the raw material parameter sequence , the process parameter sequence with the quality indicator sequence by timestamp one by one, constructing a time-indexed sequence triplet set, defined as a time series dataset .

3. The machine learning-based production control method of silica sol from waste residue recycling according to claim 1, characterized by, The S2 specifically comprises: S21, based on the constructed time series data set, splicing the raw material parameters and process parameters into a combined vector in a feature order to form an input sequence arranged by time; S22, setting a time window length, extracting a historical data segment corresponding to the current time step as an input by using a sliding window method, and feeding the input into the N-BEATS model; S23, the N-BEATS model is composed of one or more residual structure units connected in turn in number order, each residual structure unit comprising: The pre-encoding network: the input tensor is unfolded into a one-dimensional vector in time order, sequentially passes through a first fully connected layer and a nonlinear activation layer, and then passes through a second fully connected layer to output an intermediate vector as the input of the three branch paths; The trend prediction branch: receiving the intermediate vector, obtaining a feature vector through a first linear transformation layer; multiplying the feature vector and a group of channel weight vectors element by element according to the position to reconstruct the channels; feeding the reconstructed vector into a second linear transformation layer to map it to a dimension equal to the number of target prediction indicators to obtain a trend prediction vector; The residual prediction branch: receiving the intermediate vector, first performing normalization processing; sequentially feeding into a first fully connected layer and a nonlinear activation layer, and then feeding into a second fully connected layer; mapping the output to a dimension equal to the number of target prediction indicators to obtain a residual prediction vector; The anti-construct update branch: receiving the intermediate vector, transforming it into a one-dimensional vector through a linear layer; reshaping it into a matrix form with the same time step and feature dimension as the input tensor to serve as an anti-constructed tensor; subtracting the anti-constructed tensor of the current unit from the input tensor of the current unit to obtain the input tensor of the next unit; S24, add the trend prediction vectors output by all residual structure units in sequence to obtain a trend prediction result of the current time step; add all residual prediction vectors in sequence to obtain a residual prediction result of the current time step; S25, combine the trend prediction result and the residual prediction result according to a preset weight to obtain a final prediction output.

4. The machine learning-based production control method of silica sol from waste residue recycling according to claim 1, characterized by, The S3 specifically comprises: S31, constructing a Cross-Stitch double-branch neural network structure: a first neural network branch receives a time-sequentially arranged slag raw material parameter sequence; a second neural network branch receives a time-sequentially arranged process control parameter sequence; S32, a feature processing path of the first neural network branch: The input vector is processed by a one-dimensional time domain convolution layer, and the time dimension is kept unchanged by zero padding; the convolution kernel weight initialization method is Xavier initialization or He initialization; a batch normalization layer and a nonlinear activation layer are arranged after the convolution layer, and the activation function is ReLU; The convolution output is processed by a multi-head channel decomposition module, which comprises h parallel branches; the channel division method is equal division or frequency band clustering based division; LayerNormalization or BatchNormalization is arranged in each branch after decomposition; Each branch is sequentially connected with a linear transformation layer and a nonlinear activation layer, the linear transformation layer is a full connection structure or a one-dimensional point-by-point convolution structure, and the activation function is ReLU or GELU; The outputs of each branch are spliced into a current hidden layer output vector according to the channel dimension; S33, a feature processing path of the second neural network branch: the input vector is converted to the frequency domain by a fast Fourier transform module; segment filtering and amplitude normalization are performed in the frequency domain; inverse Fourier transform is used to restore to the time domain; a current hidden layer output vector is obtained after linear transformation layer and nonlinear activation layer processing; S34, Hebbian weight update of the first neural network branch: The product of the input vector and the output vector is calculated for each connection, multiplied by the first learning rate, and added to the corresponding weight value; The feature correlation coefficient of the output channel of the second neural network branch and the current channel is calculated, the weight value is increased when the correlation coefficient is positive, and the weight value is reduced when the correlation coefficient is negative; The updated weight matrix replaces the original matrix; S35, Oja weight update of the second neural network branch: Hebbian accumulation update is performed on the input vector and the output vector for each connection; The product of the output component square and the weight value is subtracted from the updated weight value; The correlation coefficient of each column weight vector and the column vector of the first neural network branch is calculated, and when the correlation coefficient exceeds a set threshold, the projection component in the first branch direction is deducted from the column vector, and the column vector is normalized; S36, Cross-Stitch connection layer processing: The feature correlation coefficient of the current hidden layer output channel of the two branches is calculated and sorted; Select the channel equal to or greater than the p quantile of the channel correlation coefficient distribution as the reserved channel, and set the weight of the remaining channels to zero; The change rate of the gradient of the previous batch and the current batch is calculated in the reserved channel, and the weight of the channel below the threshold g is multiplied by the proportion coefficient k2; The coefficient matrix is normalized row by row, so that the weight sum of each row is equal to 1; The two branch output channels are weighted and combined according to the coefficient matrix as the input of the next hidden layer; S37, the two branch outputs are weighted and combined as a prediction vector by a final Cross-Stitch connection layer, and the dimension of the prediction vector is consistent with the number of silica sol product quality indicators.

5. The machine learning-based production control method of silica sol from waste residue recycling according to claim 4, characterized by, The multi-head channel decomposition module: performs fast Fourier transform on the convolution result according to the channel dimension, divides the frequency spectrum into several frequency band intervals, and determines the range of each frequency band interval according to the energy distribution criterion; based on the energy distribution vector of each channel in each frequency band, the channels are grouped by using a clustering algorithm, and each group corresponds to a branch channel.

6. The machine learning-based production control method of silica sol from waste residue recycling according to claim 1, wherein, The S5 specifically includes: S51、In time step reading the trend prediction vector generated by the N-BEATS model the update prediction vector output by the Cross-Stitch double-branch neural network structure , aligning the order and dimension according to the target quality index channel number, obtaining a channel set ; S52, for the channel A two-dimensional time window matrix is constructed, the first row sequentially stores interval sequence values, the second row sequentially stores interval sequence values, the window length is a preset positive integer;​​ S53, to the channel perform singular value decomposition on the two-dimensional time window matrix of the channel, extract a first left singular vector as a principal direction vector; calculate an included angle by taking the dot product of the principal direction vector and a first coordinate axis unit vector, to obtain a channel similarity angle ; S54, according to Generate channel weight pairs :when Less than the threshold When the trend weight is equal to the square of the cosine of the included angle, the updated weight is one minus the trend weight; when In the range When the trend weight is equal to the update weight, the trend weight is taken as equal to the update weight. Greater than or equal to the threshold At that time, the trend weight is taken as a fixed lower limit value, and the update weight is taken as one minus the fixed lower limit value; S55. Perform column vector sum-of-squares normalization on the weights of all channels: calculate separately. and The sum of squares and the square root are used to obtain the normalization factor. Each channel weight is then divided by its corresponding normalization factor to ensure that the sum of squares of both columns of weights equals 1. For single-channel weight pairs... Simultaneously constrained within the open interval ; S56, in the channel computing the combined components and generating a combined prediction vector , in the order of channel numbers splicing into a combined prediction vector ; S57, to Perform channel de-biasing operation: in the window Calculate the median for each channel separately, and then calculate the median from the channel dimension. Subtract the corresponding median from the middle; input the debiased result into the linear mapping layer, the parameters of which are fixed matrices; S58. Record in time series store and , with window statistics.

7. The machine learning-based production control method of silica sol from waste residue recycling according to claim 1, wherein, The S6 specifically includes: S61、in time step reading a combined prediction vector , reading a target setting vector , reading a last batch control parameter vector and a sampling period length; mapping the target quality indicator channel and the control parameter channel one by one according to a preset mapping table; S62, calculate the split-channel sensitivity coefficient: in the last Calculate the absolute value of the linear regression coefficient of the measured value of each quality indicator channel and the control parameter change amount respectively within the last time step. S63, constructing a target function: The first part is the sum of square of prediction error, which is subtracted by the original signal, multiplied by the sensitivity coefficient of the corresponding channel, and then squared and accumulated by channel. And Subtracting the original signal, multiplying by the sensitivity coefficient of the corresponding channel, and then squaring and accumulating. The second part is the sum of squares of control parameter changes, which is obtained by subtracting the current candidate control parameter from the last batch of control parameters, multiplying by a fixed control weight, squaring and accumulating; The target function value is obtained by adding the two parts; S64, setting control parameter constraints; S65, using finite difference method to approximate calculate the gradient of the target function to each control parameter: adding a fixed small value to a single control parameter in turn, recalculating the target function, and obtaining the gradient approximation value by dividing the difference value of the original target function by the fixed small value; repeat the above process to obtain the gradient vector for all control parameters; S66, updating the control parameters by using the projection gradient descent method: subtracting the product of the gradient and a preset step size from the current control parameter vector in the gradient direction to obtain an update vector; projecting the update vector to the constraint interval channel by channel, and detecting the change rate constraint in the projection process, and reducing the change amount of the corresponding channel in proportion when the upper limit of the rate is exceeded; S67, repeat the gradient calculation and parameter update until the upper limit of the iteration number is reached, or the change amplitude of the control parameters obtained by two consecutive updates is lower than the minimum change threshold; take the parameter vector obtained by the final iteration as the optimal control parameter.

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