Desulfurization optimization method based on multi-target control

Abstract

The invention relates to the technical field of desulfurization system control, and discloses a desulfurization optimization method based on multi-target control, which comprises the following steps: step 1, data acquisition and preprocessing; step 2, model training and optimization; step 3, performing multi-objective optimization; step 4, implementing a controller; 5, real-time monitoring and feedback are carried out; and 6, adjusting and updating the model. In the step of real-time monitoring and feedback, actual operation data are continuously monitored and compared with a model prediction result, errors are calculated, the mean square error MSE and the mean absolute error MAE of the errors are calculated, actions are taken when the errors exceed an acceptable range, the errors are monitored in real time, and the model weight is adjusted, so that the real-time monitoring and feedback of the real-time monitoring and feedback are realized. The model can continuously adapt to data changes, excessive dependence on training data is avoided, so that the risk of overfitting is reduced, and the beneficial effects of improving the stability of the model, preventing errors caused by model overfitting and establishing a feedback mechanism are achieved.

Description

Technical Field

[0001] The invention relates to the technical field of desulfurization system control, and in particular to a desulfurization optimization method based on multi-objective control. Background Art

[0002] The multi-objective optimization control in the process of wet flue gas desulfurization simultaneously solves the optimal values ​​of emission indicators and safety indicators, and introduces the obtained optimal set values ​​into the control system, so that the wet flue gas desulfurization system tracks and approaches the optimal set values ​​during operation, thereby achieving the operation optimization effect. The prior art publication number is CN 114740713 B, which is a multi-objective optimization control method for wet flue gas desulfurization process. Different neural network models and controllers are established according to different initial values, and a weighted multi-model adaptive controller for the desulfurization process is constructed to further improve the desulfurization efficiency of the desulfurization process and reduce the desulfurization cost.

[0003] Although the existing technology uses models to optimize the desulfurization process and LS-SVM is used for regression tasks, its performance depends on the selection of kernel functions and the tuning of parameters. The model overfits the training data and performs poorly on unseen data. In addition, as the operating conditions change, the model also needs to be updated regularly to maintain its accuracy, which leads to a gradual decrease in the accuracy of optimizing the desulfurization process as the model is used for a longer time. Summary of the invention

[0004] Technical issues solved:

[0005] In view of the shortcomings of the existing technology, the present invention provides a desulfurization optimization method based on multi-objective control, which has the advantages of improving the stability of the model to prevent errors caused by overfitting of the model, establishing a feedback mechanism, comparing the actual operation data with the model prediction results, adjusting the model parameters according to the errors or retraining the model, etc., thereby solving the problems of the above-mentioned technologies.

[0006] Technical solution:

[0007] To achieve the above object, the present invention provides the following technical solution: a desulfurization optimization method based on multi-objective control, comprising the following steps:

[0008] Step 1: Data collection and preprocessing: Continuously collect process variables and result data of the desulfurization process, and perform necessary preprocessing;

[0009] Step 2: Model training and optimization: Use LS-SVM to build a prediction model and select the optimal parameters through cross-validation;

[0010] Step 3: Multi-objective optimization: Apply multi-objective evolutionary algorithm to solve the optimization problem of desulfurization process and generate control strategy;

[0011] Step 4: Controller implementation: Construct a weighted multi-model adaptive controller to select the appropriate model for control according to the current working conditions;

[0012] Step 5: Real-time monitoring and feedback: Continuously monitor actual operation data, compare it with the model prediction results, and calculate the error;

[0013] Step 6: Model adjustment and update: When the error exceeds the set threshold, the model's adaptive adjustment or retraining process is triggered;

[0014] The preprocessing in step 1 includes data cleaning, normalization and feature extraction.

[0015] Preferably, the feature extraction calculation in step 1 is:

[0016] Data matrix: X∈R n×m ;

[0017] Mean Centering:

[0018] Covariance matrix:

[0019] Eigenvalue decomposition:

[0020] Before selection: k principal components = V k ;

[0021] Where X is the data matrix, n is the number of samples, m is the number of features, 1 n is a vector of all ones, μ is the mean vector, C is the covariance matrix, V is the eigenvector matrix, Λ is the eigenvalue matrix, and k is the number of principal components selected.

[0022] Preferably, the regression calculation of LS-SVM in step 2 is:

[0023]

[0024] Where: y(x) is the model's prediction of the input x; K(x,x i ) is the kernel function. Common kernel functions include: Linear kernel function: Polynomial kernel function: Gaussian kernel function:

[0025] Preferably, the LS-SVM optimization problem is calculated as:

[0026]

[0027] Where: w is the weight vector, which represents the weight parameter of the model, used to map the input features to the hyperplane in the high-dimensional space; b is the bias term, which represents the intercept or offset of the model, used to adjust the position of the hyperplane; ξ i is a slack variable, representing the error term of the i-th sample, used to handle the nonlinear separable case; when ξ i When >0, it means that the i-th sample is not within the boundary of ±1; γ is a regularization parameter, which is used to control the complexity of the model and the influence of the error term. A larger γ value means a larger penalty for the error term and a lower model complexity; a smaller γ value means a smaller penalty for the error term and a higher model complexity.

[0028] The constraints are: i (w T φ(x i )+b)=1-ξ i ,i=1,2,…,n;

[0029] Where: y i is the true label of the i-th sample. In the regression task, y i Usually a continuous value; φ(x i ) is the mapping of the i-th sample in the high-dimensional feature space, b is the bias term, which is the same as b in the optimization problem; ξ i is a slack variable, which is different from ξ in the optimization problem. i Same; i is the sample index, ranging from 1 to n, indicating the i-th sample.

[0030] Preferably, the detailed steps in step three are:

[0031] S1. Define the objective function: There are m objective functions f1(x), f2(x), …, fm(x), where x is a decision variable vector;

[0032] S2. Define constraints:

[0033] There are p inequality constraints and q equality constraints:

[0034] Inequality constraints: gi(x)≤0, i=1,2,…,p;

[0035] Equality constraints: hj(x) = 0, j = 1, 2, ..., q;

[0036] S3, Initialize the population: Generate an initial population P0, containing N solutions x1, x2, …, xN;

[0037] S4. Evaluate the population: Calculate the objective function value and constraint value for each solution:

[0038] Objective function value: f1(xi),f2(xi),…,fm(xi);

[0039] Constraint values: gi(xi) and hj(xi)

[0040] S5. Find non-dominated solutions: Use the fast non-dominated sorting algorithm to divide the population into non-dominated layers: F1, F2, …, Fk;

[0041] S6. Calculate crowding distance: For each non-dominated layer Fi, calculate the crowding distance di(xi) of each solution;

[0042] S7, selection operation: select N solutions from the non-dominated layer F1, F2, ..., Fk to form the next generation population Pt+1;

[0043] S8, crossover and mutation: perform crossover and mutation operations on the selected solution to generate a new population Qt+1;

[0044] S9, merge populations: merge the new population Qt+1 and the current population Pt+1 to form a temporary population Rt+1;

[0045] S10, find non-dominated solutions: perform fast non-dominated sorting on the temporary population Rt+1 to form a new non-dominated layer;

[0046] S11. Calculate crowding distance: For the new non-dominated layer, calculate the crowding distance of each solution;

[0047] S12, selection operation: select N solutions from the new non-dominated layer to form the next generation population Pt+1;

[0048] S13, termination condition: repeat steps 4 to 12 until the termination condition is met: the maximum number of iterations.

[0049] Preferably, the objective function in step 3 is calculated as: k (x)fork=1,2,…,m.

[0050] Preferably, the controller implementation in step 4 includes defining a model set:

[0051] There are M different models M1, M2, …, MM, each model is represented as:

[0052]

[0053] Where: y i (k) is the output of the ith model at time k; y(k) is the output of the actual system.

[0054] Preferably, the appropriate model is selected in step 4 to calculate:

[0055] Use recursive least squares method to update weights, the update formula is:

[0056]

[0057] w(k)=w(k-1)+P(k)z(k)[y(k)-z T (k)w(k-1)]

[0058] Where: P(k) is the gain matrix; λ is the forgetting factor, 0<λ≤1.

[0059] Preferably, the model prediction output in step 5 is calculated as:

[0060]

[0061] Where: w i (k) is the weight of the i-th model, y i (k) is the predicted output of the ith model.

[0062] Preferably, in step 6, whether the error exceeds the threshold is determined as follows:

[0063] |e(k)|>∈ th

[0064] The current error e(k) = 0.12, set the threshold ∈ th =0.1, then |0.12|>0.1, triggering model adjustment.

[0065] Compared with the prior art, the present invention provides a desulfurization optimization method based on multi-objective control, which has the following beneficial effects:

[0066] 1. The present invention continuously monitors the actual operation data in the real-time monitoring and feedback steps, compares it with the model prediction results, calculates the error, calculates the mean square error (MSE) and the mean absolute error (MAE) of the error, and takes action when the error exceeds an acceptable range. By monitoring the error in real time and adjusting the model weights, the model can continuously adapt to changes in data and avoid over-reliance on training data, thereby reducing the risk of overfitting. When the model performs poorly, the model is retrained to learn the latest data features to avoid overfitting due to changes in data distribution. A feedback mechanism is established to enable the model to self-adjust according to actual performance. This continuous learning process helps to improve the stability and generalization ability of the model, thereby achieving the beneficial effects of improving the stability of the model, preventing errors caused by overfitting of the model, and establishing a feedback mechanism.

[0067] 2. The present invention continuously collects actual operation data and compares it with the model prediction results through a real-time monitoring and feedback mechanism, and calculates the error to evaluate the model performance. When the error exceeds the set threshold, the dynamic adjustment of the model parameters is triggered, and the gradient descent method or the least squares method is used to optimize the model to make it better fit the current data. If the error continues to exceed the threshold, the model is retrained and the model parameters are updated using the latest data to ensure that it adapts to system changes. This process not only improves the stability of the model, but also effectively prevents the overfitting problem through dynamic adjustment and retraining, so that the model maintains a high prediction accuracy and generalization ability in practical applications, and achieves the beneficial effect of comparing the actual operation data with the model prediction results, adjusting the model parameters according to the error, or retraining the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a schematic diagram of the structure of the present invention; DETAILED DESCRIPTION

[0069] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] See also Figure 1 A desulfurization optimization method based on multi-objective control comprises the following steps:

[0071] Step 1: Data collection and preprocessing: Continuously collect process variables and result data of the desulfurization process, and perform necessary preprocessing;

[0072] Step 2: Model training and optimization: Use LS-SVM to build a prediction model and select the optimal parameters through cross-validation;

[0073] Step 3: Multi-objective optimization: Apply multi-objective evolutionary algorithm to solve the optimization problem of desulfurization process and generate control strategy;

[0074] Step 4: Controller implementation: Construct a weighted multi-model adaptive controller to select the appropriate model for control according to the current working conditions;

[0075] Step 5: Real-time monitoring and feedback: Continuously monitor actual operation data, compare it with the model prediction results, and calculate the error;

[0076] Step 6: Model adjustment and update: When the error exceeds the set threshold, the model's adaptive adjustment or retraining process is triggered.

[0077] 1. Comparison of actual operation data and model prediction results

[0078] (1) Collecting actual operation data

[0079] During the actual system operation, the output data is collected, which is the real response of the system.

[0080] (2) Calculation model prediction results

[0081] Computes the predicted output of the model using the current model parameters and input data.

[0082] (3) Comparison of actual data with predicted results

[0083] Compare the actual operating data with the model prediction results and calculate the error.

[0084] 2. Adjust model parameters based on errors

[0085] (1) Setting the error threshold

[0086] In order to determine whether the model needs to be adjusted, an error threshold is set. If the error exceeds the threshold, the adjustment process is triggered.

[0087] (2) Error threshold judgment

[0088] Determine whether the current error exceeds the threshold.

[0089] (3) Adjust model parameters

[0090] When the error exceeds the threshold, the model parameters are adjusted using the following method:

[0091] (a) Gradient descent method

[0092] By calculating the gradient of the error, the model parameters are adjusted.

[0093] (b) Least Squares Method

[0094] If the error is large, retrain the model parameters and use the least squares optimization method.

[0095] 3. Retrain the model

[0096] If the error continues to exceed the threshold, it means that the current model may be overfit or no longer applicable, and the model needs to be retrained:

[0097] (1) New data training

[0098] Retrain the model using the latest actual running data and corresponding input data.

[0099] (2) Update model collection

[0100] The retrained model is added to the model ensemble and the weight vector is updated to ensure that the model ensemble can adapt to the current system status.

[0101] Specifically, the regression calculation of LS-SVM in step 2 is:

[0102]

[0103] Where: y(x) is the model's prediction of the input x; K(x,x i ) is the kernel function. Common kernel functions include: Linear kernel function: Polynomial kernel function: Gaussian kernel function:

[0104] Specifically, the LS-SVM optimization problem is calculated as:

[0105]

[0106] Where: w is the weight vector, which represents the weight parameter of the model, used to map the input features to the hyperplane in the high-dimensional space; b is the bias term, which represents the intercept or offset of the model, used to adjust the position of the hyperplane; ξ i is a slack variable, representing the error term of the i-th sample, used to handle the nonlinear separable case; when ξ i When >0, it means that the i-th sample is not within the boundary of ±1; γ is a regularization parameter, which is used to control the complexity of the model and the influence of the error term. A larger γ value means a larger penalty for the error term and a lower model complexity; a smaller γ value means a smaller penalty for the error term and a higher model complexity.

[0107] The constraints are: i (w T φ(x i )+b)=1-ξ i ,i=1,2,…,n;

[0108] Where: y i is the true label of the i-th sample. In the regression task, y i Usually a continuous value; φ(x i ) is the mapping of the i-th sample in the high-dimensional feature space, b is the bias term, which is the same as b in the optimization problem; ξ i is a slack variable, which is different from ξ in the optimization problem. i Same; i is the sample index, ranging from 1 to n, indicating the i-th sample.

[0109] Specifically, the detailed steps in step three are:

[0110] S1. Define the objective function: There are m objective functions f1(x), f2(x), …, fm(x), where x is a decision variable vector;

[0111] S2. Define constraints:

[0112] There are p inequality constraints and q equality constraints:

[0113] Inequality constraints: gi(x)≤0, i=1,2,…,p;

[0114] Equality constraints: hj(x) = 0, j = 1, 2, ..., q;

[0115] S3, Initialize the population: Generate an initial population P0, containing N solutions x1, x2, …, xN;

[0116] S4. Evaluate the population: Calculate the objective function value and constraint value for each solution:

[0117] Objective function value: f1(xi),f2(xi),…,fm(xi);

[0118] Constraint values: gi(xi) and hj(xi)

[0119] S5. Find non-dominated solutions: Use the fast non-dominated sorting algorithm to divide the population into non-dominated layers: F1, F2, …, Fk;

[0120] S6. Calculate crowding distance: For each non-dominated layer Fi, calculate the crowding distance di(xi) of each solution;

[0121] S7, selection operation: select N solutions from the non-dominated layer F1, F2, ..., Fk to form the next generation population Pt+1;

[0122] S8, crossover and mutation: perform crossover and mutation operations on the selected solution to generate a new population Qt+1;

[0123] S9, merge populations: merge the new population Qt+1 and the current population Pt+1 to form a temporary population Rt+1;

[0124] S10, find non-dominated solutions: perform fast non-dominated sorting on the temporary population Rt+1 to form a new non-dominated layer;

[0125] S11. Calculate crowding distance: For the new non-dominated layer, calculate the crowding distance of each solution;

[0126] S12, selection operation: select N solutions from the new non-dominated layer to form the next generation population Pt+1;

[0127] S13, termination condition: repeat steps 4 to 12 until the termination condition is met: the maximum number of iterations.

[0128] Specifically, the objective function in step 3 is calculated as: k (x)fork=1,2,…,m.

[0129] Specifically, the controller implementation in step 4 includes defining a model collection:

[0130] There are M different models M1, M2, …, MM, each model is represented as:

[0131]

[0132] Where: y i (k) is the output of the ith model at time k; y(k) is the output of the actual system.

[0133] Specifically, the appropriate model is selected in step 4 for calculation:

[0134] Use recursive least squares method to update weights, the update formula is:

[0135]

[0136] Where: P(k) is the gain matrix; λ is the forgetting factor, 0<λ≤1.

[0137] Specifically, the model prediction output in step 5 is calculated as:

[0138]

[0139] Where: w i (k) is the weight of the i-th model, y i (k) is the predicted output of the ith model.

[0140] Specifically, in step 6, whether the error exceeds the threshold is determined as follows:

[0141] |e(k)|>∈ th

[0142] The current error e(k) = 0.12, set the threshold ∈ th =0.1, then |0.12|>0.1, triggering model adjustment.

[0143] In the real-time monitoring and feedback step, the actual operation data is continuously monitored and compared with the model prediction results to calculate the error. The prediction accuracy of the model is quantified by calculating the mean square error (MSE) and mean absolute error (MAE). These indicators help evaluate the performance of the model and take action when the error exceeds the acceptable range.

[0144] Error calculation: Quantify the prediction error of the model by calculating the difference between the actual output and the predicted output.

[0145] Performance evaluation: Use metrics such as MSE and MAE to evaluate the overall performance of the model and identify cases where performance has degraded.

[0146] Real-time adjustment: Through real-time feedback control, the control input is adjusted according to the error, so that the system can respond quickly to changes and improve stability.

[0147] When the error exceeds the set threshold, the model's adaptive adjustment or retraining process is triggered. This step is designed to dynamically adapt to changes in the system and prevent the model from overfitting.

[0148] Error threshold trigger: Set an error threshold. When the error exceeds this threshold, it indicates that the model may no longer be suitable for the current system state and needs to be adjusted.

[0149] Weight adjustment: Use optimization algorithms such as gradient descent to adjust model weights based on error feedback so that the model can better fit the current data.

[0150] Retrain the model: If the error continues to exceed the threshold, it means that the current model may be overfit or no longer applicable, and the model needs to be retrained to obtain better generalization ability.

[0151] Dynamic adjustment: By monitoring errors in real time and adjusting model weights, the model can continuously adapt to changes in data, avoid over-reliance on training data, and thus reduce the risk of overfitting.

[0152] Retraining: When the model performs poorly, retrain the model to make it learn the latest data features to avoid overfitting due to changes in data distribution.

[0153] Feedback mechanism: Establish a feedback mechanism so that the model can adjust itself according to actual performance. This continuous learning process helps improve the stability and generalization ability of the model.

[0154] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and alterations may be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A desulfurization optimization method based on multi-objective control, characterized in that: The following steps are involved: Step 1: Data collection and preprocessing: Continuously collect process variables and result data of the desulfurization process, and perform necessary preprocessing; Step 2: Model training and optimization: Use LS-SVM to build a prediction model and select the optimal parameters through cross-validation; Step 3: Multi-objective optimization: Apply multi-objective evolutionary algorithm to solve the optimization problem of desulfurization process and generate control strategy; Step 4: Controller implementation: Construct a weighted multi-model adaptive controller to select the appropriate model for control according to the current working conditions; Step 5: Real-time monitoring and feedback: Continuously monitor actual operation data, compare it with the model prediction results, and calculate the error; Step 6: Model adjustment and update: When the error exceeds the set threshold, the model's adaptive adjustment or retraining process is triggered; The preprocessing in step 1 includes data cleaning, normalization and feature extraction.

2. A desulfurization optimization method based on multi-objective control according to claim 1, characterized in that: The feature extraction calculation in step 1 is: Data matrix: X∈R n×m ; Mean Centering: Covariance matrix: Eigenvalue decomposition: Before selection: k principal components = V k ; Where X is the data matrix, n is the number of samples, m is the number of features, 1 n is a vector of all ones, μ is the mean vector, C is the covariance matrix, V is the eigenvector matrix, Λ is the eigenvalue matrix, and k is the number of principal components selected.

3. A desulfurization optimization method based on multi-objective control according to claim 2, characterized in that: The regression calculation of LS-SVM in step 2 is: Where: y(x) is the model's prediction of the input x; K(x,x i ) is the kernel function. Common kernel functions include: Linear kernel function: Polynomial kernel function: Gaussian kernel function:

4. The desulfurization optimization method based on multi-objective control according to claim 3 is characterized in that: The LS-SVM optimization problem is calculated as: Where: w is the weight vector, which represents the weight parameter of the model, used to map the input features to the hyperplane in the high-dimensional space; b is the bias term, which represents the intercept or offset of the model, used to adjust the position of the hyperplane; ξ i is a slack variable, representing the error term of the i-th sample, used to handle the nonlinear separable case; when ξ i When >0, it means that the i-th sample is not within the boundary of ±1; γ is a regularization parameter, which is used to control the complexity of the model and the influence of the error term. A larger γ value means a larger penalty for the error term and a lower model complexity; a smaller γ value means a smaller penalty for the error term and a higher model complexity. The constraints are: i (w T φ(x i )+b)=1-ξ i ,i=1,2,…,n; Where: y i is the true label of the i-th sample. In the regression task, y i Usually a continuous value; φ(x i ) is the mapping of the i-th sample in the high-dimensional feature space, b is the bias term, which is the same as b in the optimization problem; ξ i is a slack variable, which is different from ξ in the optimization problem. i Same; i is the sample index, ranging from 1 to n, indicating the i-th sample.

5. The desulfurization optimization method based on multi-objective control according to claim 1 is characterized in that: The detailed steps in step three are: S1. Define the objective function: There are m objective functions f1(x), f2(x), …, fm(x), where x is a decision variable vector; S2. Define constraints: There are p inequality constraints and q equality constraints: Inequality constraints: gi(x)≤0, i=1,2,…,p; Equality constraints: hj(x) = 0, j = 1, 2, ..., q; S3, Initialize the population: Generate an initial population P0, containing N solutions x1, x2, …, xN; S4. Evaluate the population: Calculate the objective function value and constraint value for each solution: Objective function value: f1(xi),f2(xi),…,fm(xi); Constraint values: gi(xi) and hj(xi) S5. Find non-dominated solutions: Use the fast non-dominated sorting algorithm to divide the population into non-dominated layers: F1, F2, …, Fk; S6. Calculate crowding distance: For each non-dominated layer Fi, calculate the crowding distance di(xi) of each solution; S7, selection operation: select N solutions from the non-dominated layer F1, F2, ..., Fk to form the next generation population Pt+1; S8, crossover and mutation: perform crossover and mutation operations on the selected solution to generate a new population Qt+1; S9, merge populations: merge the new population Qt+1 and the current population Pt+1 to form a temporary population Rt+1; S10, find non-dominated solutions: perform fast non-dominated sorting on the temporary population Rt+1 to form a new non-dominated layer; S11. Calculate crowding distance: For the new non-dominated layer, calculate the crowding distance of each solution; S12, selection operation: select N solutions from the new non-dominated layer to form the next generation population Pt+1; S13, termination condition: repeat steps 4 to 12 until the termination condition is met: the maximum number of iterations.

6. The desulfurization optimization method based on multi-objective control according to claim 5 is characterized in that: The objective function of step 3 is calculated as: k (x)fork=1,2,…,m.

7. The desulfurization optimization method based on multi-objective control according to claim 1 is characterized in that: The controller implementation in step 4 includes defining a model set: There are M different models M1, M2, …, MM, each model is represented as: Where: y i (k) is the output of the ith model at time k; y(k) is the output of the actual system.

8. The desulfurization optimization method based on multi-objective control according to claim 7 is characterized in that: In step 4, the appropriate model is selected and calculated as: Use recursive least squares method to update weights, the update formula is: w(k)=w(k-1)+P(k)z(k)[y(k)-z T (k)w(k-1)] Where: P(k) is the gain matrix; λ is the forgetting factor, 0<λ≤1.

9. The desulfurization optimization method based on multi-objective control according to claim 1, characterized in that: The model prediction output calculation in step 5 is: Where: w i (k) is the weight of the i-th model, y i (k) is the predicted output of the ith model.

10. The desulfurization optimization method based on multi-objective control according to claim 1, characterized in that: In step 6, whether the error exceeds the threshold is determined as follows: |e(k)|>∈ th The current error e(k) = 0.12, set the threshold ∈ th =0.1, then |0.12|>0.1, triggering model adjustment.

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