Industrial boiler system set value optimization method based on agent-assisted multi-objective evolutionary algorithm

Abstract

The invention discloses an industrial boiler system set value optimization method based on an agent-assisted multi-objective evolutionary algorithm, aims to optimize the operation efficiency of an industrial boiler control system, and particularly aims to solve the problem of expensive high-dimensional multi-objective optimization of boiler combustion efficiency, nitrogen oxide emission concentration and power consumption. According to the method, an agent-assisted evolutionary algorithm for heterogeneous integration of a support vector machine (SVM) and a feed-forward neural network (FNN) is provided, data acquired by sensor equipment in an industrial boiler system is combined, and an agent model is constructed and trained for predicting the emission concentration of nitrogen oxide. Optimization is carried out on set values of a boiler control system such as steam flow and combustion temperature, convergence and diversity in the algorithm evolution process are evaluated by setting a double-file mechanism, and an optimization scheme is adjusted by utilizing a self-adaptive sampling strategy so as to cope with complex industrial environment changes. Experiments prove that the method has good performance in the aspect of industrial boiler operation control system set value optimization.

Description

Technical Field

[0001] The present invention belongs to the field of industrial boiler control system optimization. By introducing a heterogeneous integrated agent-assisted multi-objective evolutionary algorithm, the operating set values ​​of the industrial boiler system are accurately optimized using data modeling and optimization algorithms. The method comprehensively applies support vector machine (SVM) and feedforward neural network (FNN) to construct a heterogeneous agent model. By optimizing combustion efficiency and reducing nitrogen oxides (NO x ) emission concentration and reduce electricity consumption, achieving emission control and energy saving while ensuring boiler combustion efficiency. This technology improves the overall performance of the boiler system and provides an effective solution for the efficient and environmentally friendly operation of industrial boilers. Background Art

[0002] Industrial boilers are important equipment for energy conversion and industrial production. Factors such as combustion efficiency, pollutant emissions, and power consumption during their operation have a significant impact on the sustainability and economy of industrial production. In practical applications, how to optimize boiler combustion efficiency and reduce NO x Reducing the concentration of harmful gas emissions and electricity consumption at the same time constitutes a complex and expensive multi-objective optimization problem.

[0003] Traditional boiler control strategies mostly rely on fixed empirical parameters or control methods based on physical models, which are difficult to cope with the diverse needs of environmental conditions, fuel characteristics and load changes in actual operation. These needs correspond to multiple mutually restrictive goals, which may cause other goals (such as NOx) to be neglected when pursuing a certain goal (such as maximizing combustion efficiency). x emission concentration or energy consumption reduction). At the same time, modern NO x The detection equipment requires regular maintenance and calibration, and part of the detection process involves complex signal processing and analysis, which makes the detection difficult and costly. In addition, electricity consumption is the main source of energy consumption for system operation, and it has a complex nonlinear coupling relationship with combustion efficiency and emission targets. It is difficult for traditional methods to achieve a balanced optimization of these targets.

[0004] When dealing with expensive multi-objective optimization problems, researchers have proposed many methods and techniques. Among them, representative methods include multi-objective genetic algorithm (MOGA), multi-objective particle swarm optimization (MOPSO), etc. These methods maintain a population and use evolutionary strategies to continuously generate and optimize individuals to approach the true frontier solution set. However, due to the high computational cost of expensive multi-objective optimization problems, traditional optimization methods often face the challenge of high computational costs. It is often difficult to find the optimal solution within a reasonable time. In addition, each evaluation of the objective function consumes a lot of computing resources and time, so it is inefficient. Therefore, it is of great theoretical and practical significance to study how to improve the efficiency and feasibility of dealing with expensive multi-objective optimization problems.

[0005] The inventors found that the existing industrial boiler control strategies are generally difficult to achieve an effective balance between multiple objectives such as improving combustion efficiency, reducing pollutant emissions and reducing energy consumption. The control method based on physical models cannot cope with real-time changes in operating conditions. Although the model based on machine learning has good prediction capabilities, it has the limitations of high computational complexity and poor real-time performance when dealing with high-dimensional multi-objective optimization problems in the industrial field and industrial scenarios involving expensive physical testing. Therefore, for the complex multi-objective optimization problems of industrial boilers, there is an urgent need for an optimization method that can take into account various optimization objectives and has high efficiency and flexibility. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes an industrial boiler system set value optimization method based on an agent-assisted multi-objective evolutionary algorithm. The main purpose of the present invention is to use the industrial boiler system operation data to build an agent model to optimize the boiler operation parameters (such as fuel flow, oxygen concentration, air flow, etc.). By building a heterogeneous agent model integrating support vector machine (SVM) and feedforward neural network (FNN), the limitations of the traditional single agent model in prediction accuracy and response speed are replaced, and the actual detection times are reduced through historical data and model prediction; in the optimization process, an adaptive sampling strategy is incorporated to dynamically adjust the sampling data according to the real-time changes in the industrial boiler operating conditions to ensure that the model can quickly respond to fluctuations in the system environment, so as to better adapt to the complex and changeable industrial environment.

[0007] The method for optimizing the setpoint of an industrial boiler system based on an agent-assisted multi-objective evolutionary algorithm comprises the following steps:

[0008] Step 1: First, initialize the population and set parameters. Collect steam temperature, boiler pressure, combustion temperature, fan air flow, NO x Real-time operation data such as concentration and power consumption are collected to build the initial data set and perform data preprocessing operations.

[0009] Step 2: Select the data that affects NO x The concentration-related parameters are constructed to build a heterogeneous proxy model integrating SVM and FNN to obtain NO x Concentration, model training and fitness evaluation.

[0010] Step 3: Target three main optimization objectives of industrial boilers, namely boiler combustion efficiency, NO x The objective functions are constructed for emission concentration and electricity consumption respectively.

[0011] Step 4. Establish a dual-file mechanism to evaluate the convergence and diversity of the algorithm, use the evolutionary algorithm to optimize the optimization problem of industrial boilers and update the archive, update the solution set in the dual archive according to the prediction results, and continue to adjust the model according to the feedback during the optimization process.

[0012] Step 5. The algorithm uses an adaptive sampling strategy to generate new solutions during the evolution process, and combines the dual-file evaluation to obtain the final Pareto solution set. The optimization effect of the algorithm is verified based on the performance evaluation indicators.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] Aiming at the multi-objective optimization problem in the operation of industrial boilers, this paper proposes an optimization algorithm based on heterogeneous integrated model to overcome the limitations of traditional single agent model in dealing with high-dimensional complex working conditions. SVM is good at dealing with linear relationships and efficient generalization ability when dealing with a small amount of sample data, and is particularly suitable for some linearly separable input data in boiler systems, such as fan air volume and NO x The relationship between combustion temperature, boiler pressure and emission concentration. The FNN model is more suitable for describing the complex relationship between combustion temperature, boiler pressure and pollutant emission concentration due to its strong nonlinear fitting ability. Therefore, by integrating the high generalization ability of SVM and the nonlinear fitting ability of FNN, the shortcomings of a single model in processing complex industrial data can be made up to achieve accurate modeling of industrial boiler operation data, thereby optimizing combustion efficiency and reducing NO x It can provide effective decision-making on emission concentration and power consumption. At the same time, a dual-file management mechanism is designed for the algorithm, combining adaptive sampling standards with diversity and convergence indicators to cope with the variability of industrial boiler operating conditions, optimize the optimization process, and improve the optimization efficiency and convergence of the algorithm.

[0015] Through heterogeneous models and information sharing mechanisms, the present invention is suitable for practical applications such as industrial boiler combustion control, energy consumption optimization and emission management, and has certain reference significance for data analysis and optimization problem decision-making in the industrial field. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 : Schematic diagram of heterogeneous integration agent-assisted model construction.

[0017] Figure 2 : Overall flow chart of agent-assisted multi-objective evolutionary algorithm. DETAILED DESCRIPTION

[0018] The algorithm operation steps of the present invention are described in detail below. This algorithm case is implemented under the premise of the technical solution of the present invention, and a detailed implementation method and specific operation process are given, but the protection scope of the present invention is not limited to the following implementation case.

[0019] Step 1: Collect the industrial boiler operation data (including steam temperature, boiler pressure, combustion temperature, fan air flow, NO x The population information is preprocessed (e.g., concentration, power consumption, and fuel supply), and the corresponding algorithm’s population initialization process performs feature selection and normalization on the population information.

[0020] In the process of population initialization, in order to effectively reduce the data dimension and improve the population evolution performance, data feature selection is performed in the data preprocessing stage. The appropriate number of features is selected by calculating the information gain of the features. Corresponding to the initialization of population information, the information entropy of the given data set is first calculated and expressed as Entropy. The calculation formula is as follows:

[0021] Where D0 represents the initial data set, which contains n samples, b is the number of categories in the data set D0, and p a is the probability of each category a appearing in the data set.

[0022] Then the information gain of each feature is calculated according to the information entropy. The information gain is represented by IG, and the IG calculation formula is as follows:

[0023] A represents a feature, which is used to partition the data set. Values(A) represents the value set of feature A, that is, all possible values ​​of feature A. It represents the subset obtained by dividing the data set D0 according to the value v of feature A, where v is one of the values ​​of feature A. |D0| represents the number of samples in the data set D0, that is, the total number of samples in the data set. Represents the number of samples in the subset, that is, the subset The number of samples.

[0024] The information gain is calculated for each feature of the data set, and the number of feature variables is adjusted according to the complexity of the industrial process to be solved. Finally, the features selected in order of information gain are primary fan air volume, secondary fan air volume, fuel supply, fuel injection rate and air valve opening.

[0025] After that, the data is normalized and scaled linearly to the specified minimum and maximum range according to the minimum-maximum scaling principle. For a given data set, the minimum value is d min , the maximum value is d max , the normalized data set is defined as D, and the formula is expressed as:

[0026] Among them, d is the original data, d max and d min is the maximum and minimum value in the data set, norm min and norm max are the minimum and maximum boundary values ​​of the normalized data range.

[0027] Step 2: Construction of heterogeneous integrated agent model. By combining two different types of models, SVM and FNN, we can describe NO x The relationship between concentration and the operating variable is used as the fitness function in the optimization process of the proxy model evaluation algorithm. The overall construction process of the heterogeneous integrated proxy-assisted model is as follows Figure 1 shown.

[0028] In the process of constructing the SVM model, five parameters after data processing are selected: primary fan air volume, secondary fan air volume, fuel supply, fuel injection rate and air valve opening as input features for SVM model construction. In order to prevent the data from being affected by factors such as noise and improve the robustness of the model, the insensitive loss function used in the training process is Hinge Loss, which is defined as follows:

[0029] L(y S ,f S (x))=max(0,1-y S ·f S (x)) (4) where y S is the true category label of the sample, x is the input data point, and f S (x) is the predicted value of the model.

[0030] The kernel function in the model building process will be used to perform nonlinear mapping on the data during training and prediction. The kernel function is selected as the Gaussian kernel function, and the formula is expressed as follows:

[0031] K(x a ,x b ) = exp(-γ||x a -x b || 2 ) (5) In the formula, x a and x b Represents the eigenvector of two data points. γ is the parameter of the Gaussian kernel function, which controls the smoothness of the function. In order to match the width of the Gaussian kernel with the data dimension, its value is set to 0.2.

[0032] During the training process of the neural network model, the neurons in the input layer are defined as: primary fan air volume, secondary fan air volume, fuel supply, fuel injection rate and air valve opening, and the neurons in the output layer are NO x Concentration, the nonlinear activation function between the input layer and the hidden layer is the Sigmoid function, the input is an arbitrary value, the output is (0,1), and the expression is shown in (11).

[0033]

[0034] The mathematical expectation of the mean square error is used as the objective function to test the performance of the neural network. The mean square error at the lth iteration is:

[0035] Where m is the total number of iterations of network training, t(l) is the expected output at the lth iteration, and y(l) is the actual output at the lth iteration.

[0036] According to the gradient descent method, the neural weight adjustment is calculated. The weight between the kth neuron in the output layer and the jth neuron in the hidden layer is defined as w jk , the adjustment amount at the lth iteration is Δw jk (l), and the weight between the i-th neuron in the hidden layer and the j-th neuron in the input layer is defined as w ij , the adjustment amount at the lth iteration is Δw ij (l), the specific calculation formulas are as follows:

[0037] Δw jk (l) = -αδ k y j (l) (8)

[0038] Δw ij (l) = -αδ j y i (l) (9) where α is the learning rate during neural network training, and its value range is [10 -3,10 -2 ]. k is the error propagation coefficient between the kth neuron in the output layer and the jth neuron in the hidden layer, δ j is the error propagation coefficient between the i-th neuron in the hidden layer and the j-th neuron in the input layer, y j (l) is the output of the hidden layer neuron at the lth iteration, y i (l) is the output of the input layer neuron at the lth iteration.

[0039] Error propagation coefficient δ k The specific expression at the lth iteration is as follows:

[0040]

[0041] Where F(w(l)) represents the mean square error function at the lth iteration, x k (l) and y k (l) are the input and output values ​​of the kth neuron in the output layer after the lth iteration, t k (l), y k (l) are the expected output value and actual output value in the lth iteration, respectively, f′ k (x k (l)) is the derivative operation of the action function of the kth neuron.

[0042] At the same time, the error propagation coefficient δ j The specific expression at the lth iteration is as follows:

[0043]

[0044] Among them, x j (l) and y j (l) are the input and output of the jth neuron in the hidden layer at the lth iteration, p is the number of neurons, and f j ′(x j (l)) represents the derivation operation of the action function of the jth neuron.

[0045] The above models were trained by cross-validation, and the two models SVM and FNN updated the RMSE of their respective test groups after each training was completed.

[0046] SVM and FNN predict the input data respectively and generate their own NO xEmission concentration estimation output. For the output of the heterogeneous model, the output weight is allocated according to the RMSE ratio between the two models to share population parameter information. Specifically, based on the mean square error (RMSE) of the two models, the weights of the two outputs are dynamically adjusted according to formulas (12) and (13). The basis for weight allocation is that the smaller the RMSE of each model, the greater the weight of its prediction result in the final output. This allocation strategy ensures that when the data changes or the system state fluctuates, the system can automatically tend to the model with better performance. The ratio is used to represent the weight of the neural network model output. The output of the heterogeneous model is defined as O H , the formula is as follows:

[0047]

[0048] O H =ratio×O F +(1-ratio)×O S (13) Among them, R S , R F Respectively represent the RMSE size of the two models SVM and FNN, O F , O S Represent the output values ​​of the two models respectively.

[0049] Step 3: Design boiler combustion efficiency, nitrogen oxides (NO x )Emission concentration and electricity consumption design optimization objectives.

[0050] Set the optimization targets f1(t), f2(t) and f3(t) of the industrial boiler control system, where f1(t) represents the boiler combustion efficiency, i.e., the boiler energy utilization rate η = S e / F e , S e is the steam thermal energy, F e is the total energy generated by fuel combustion. Specifically, the combustion efficiency calculation formula is:

[0051] Among them, S r and Q r Represent steam flow and fuel consumption, h s With h r Respectively represent the steam enthalpy and feed water enthalpy, H v Indicates the calorific value of fuel.

[0052] f2(t) represents NO x The heterogeneous agent model is used as the objective function to describe and solve the problem. The input is the operating value of the industrial boiler operation system, and the output value is the NO x Emissions of OH .

[0053] f3(t) represents the power consumption of the equipment during operation. The fan is the part with the largest power consumption in the boiler system. Usually, the fan speed is adjusted to control the combustion process. The corresponding power consumption C e The calculation formula is as follows:

[0054] C e =E×t e (15) Where E represents the power consumption of the fan per unit time, t e Represents the fan operating time.

[0055] The final multi-objective optimization problem model was determined to be min{-f1(t),f2(t),f3(t)}.

[0056] Step 4: Establish a dual-file evaluation mechanism, use the agent-assisted multi-objective evolutionary algorithm to optimize the optimization problem of industrial boilers and update the solution set in the dual files in real time.

[0057] According to the algorithm convergence and diversity indicators, a dual-archive mechanism for evaluating algorithm convergence and diversity is established, and the population Population is placed in the initial convergence archive (CA) and archived in the diversity archive (DA) at the same time.

[0058] The dual-file management mechanism is designed based on the algorithm convergence and diversity indicators. CA measures the file quality by calculating the sum of the squares of the objective function value differences between the solution set and the true optimal solution. The evaluation formula is as follows:

[0059] Among them, P CA represents the solution set contained in the convergence archive CA, |P CA | represents the size of the solution set, x t 、x y P CA The solution in, P* represents the true optimal solution set, o represents the number of objective functions, that is, o = 3, F u (x t ) is the value of the solution on the u-th objective function, is the true optimal value on target u.

[0060] The uniformity of the solution set distribution and the differences between the solutions are set as indicators to measure the diversity evaluation archive DA. The crowding distance of the uniformity of the solution set distribution is expressed as D c Represented by , and the difference of solution set is represented by Δd, then the specific formula is as follows:

[0061]

[0062] Among them, P DA represents the solution set contained in the diversity archive, |P DA | represents the size of the solution set, x g 、x f 、x t All P DA The solution in d(x f ,x g ) represents the solution x g With solution x f The Euclidean distance between u is the set of objective functions, F u (next(x t ))、F u (prev(x t )) are the solutions to x t The values ​​of the previous and next solutions on the u-th target after sorting, are the maximum and minimum values ​​of the u-th objective in the solution set, respectively.

[0063] Finally, the evaluation formula of the diversity assessment archive DA is:

[0064] DA=w d ×D c +(1-w)×Δd (19) Among them, w d is the weight coefficient, through w d To balance the importance of crowding distance evaluation and difference evaluation to obtain the final evaluation result. When there is no special preference for the problem to be solved, take w d =0.5 for comprehensive evaluation.

[0065] The population size of the agent-assisted evolutionary algorithm is set to N = 100, the maximum number of evaluations MaxFE = 300, the maximum capacity of the population individuals is MaxPop = 120, and the number of evolution generations g max =5, mutation rate p mu = 0.05. The initial fitness evaluation is performed according to the objective functions f1(t), f2(t), and f3(t), and the population information is archived in the CA and DA files, and then the population evolution stage is entered.

[0066] The heterogeneous surrogate model is used to predict the objective function value of the offspring solution, that is, the output value of the heterogeneous model is used as the fitness value of the offspring solution during the population evolution process, and then when the evolutionary generation g is reached max Then update the archive.

[0067] In the population update process, two groups of parent solutions are first randomly selected from CA and DA, named P1 and P2 respectively, and the number of each group is N / 2. Then, the dominance relationship between P1 and P2 is calculated, and non-dominated sorting is performed according to the Pareto dominance relationship.

[0068] Then, N / 2 more parents are selected from DA and combined with the CA parent population to form a new parent population. The selected parent solutions are crossovered to generate some new child solutions. At the same time, the parent solutions in DA are mutated to generate another part of child solutions.

[0069] The two parts of the offspring solutions generated by the crossover and mutation operations are merged to form a new offspring population, which will be evaluated and evolved using the proxy model later.

[0070] Step 5: Generate new solutions using adaptive sampling strategies to improve population quality to adapt to changes in the operating state of industrial boilers. max =5, the adaptive sampling strategy is triggered to generate a new solution and update the archive. In the adaptive sampling process, according to the general setting standard, the sampling ratio is set to 10%, that is, 10% of individuals are randomly selected from the current population, and the calculation formula for the number of samples is: S=10%Pop (20)

[0071] Among them, S represents the number of samples, Pop represents the total number of the current population, and when Pop is 100, the corresponding number of adaptive sampling individuals is 10.

[0072] By adding partial solutions to the archive until the total number is less than or equal to the maximum number of individuals 120. Among them, when the number of individuals in the archive exceeds 120, the CA and DA evaluation formulas are used to calculate the newly sampled individuals, and the calculation results are equalized to take the individuals corresponding to the previous ones and retain them until the number of individuals is less than or equal to 120. After that, the original objective function is used for evaluation, which is the NO in the data collection stage. x The true value of emissions will complete the solution archive update of the above population evolution process.

[0073] When the maximum number of evaluations preset by the algorithm is 300, the population evolution process ends and the algorithm returns the final Pareto frontier solution set. Figure 2 shown.

[0074] The evaluation indicators Generational Distance (GD) and Spacing are selected as the core evaluation indicators to measure the performance of the algorithm. Among them, GD is used to measure the distance between the solution set and the true optimal frontier, emphasizing the convergence of the algorithm. The smaller the value, the closer the solution set is to the optimal frontier, and the better the convergence of the algorithm; Spacing is used to measure the uniformity between solutions, emphasizing the diversity of the algorithm. The smaller the value, the more uniform the distribution of solutions, and the better the diversity of the algorithm. At the same time, the experimental results of the algorithm in the DTLZ series of test problems are presented in Table 1. In the table, M = {3, 4, 6, 8, 10} corresponds to the target number of test problems, and the evaluation results include the mean and standard deviation. Finally, the numerical results of the two indicators GD and Spacing are within a small range, which can verify the effectiveness of the proposed algorithm. Table 1 Performance evaluation results of the algorithms on the DTLZ test set

Claims

1. An industrial boiler system set point optimization method based on agent-assisted multi-objective evolutionary algorithm, characterized in that: The following steps are involved: Step 1: Obtain real-time operation data through industrial boiler system sensors, build an initial data set and perform data preprocessing operations; Step 2: Build a heterogeneous surrogate model integrating SVM and FNN to describe NO x The relationship between emission concentration and system operating setpoints; Step 3: Design boiler combustion efficiency, NO according to industrial boiler operation system x Three optimization goals: emission concentration and electricity consumption; Step 4: Establish a dual-file evaluation mechanism, use a multi-objective evolutionary algorithm to optimize the optimization problem of industrial boilers and update the solution set in real time; Step 5: Incorporate an adaptive sampling strategy into the algorithm to generate new solutions and obtain the final Pareto solution set.

2. The method for optimizing the operating setpoints of an industrial boiler system based on an agent-assisted multi-objective evolutionary algorithm according to claim 1 is characterized in that: Step 1: Obtain operating data through the industrial boiler control system sensor, build an initial data set and perform data preprocessing; select the appropriate number of features by calculating the information gain of the features, corresponding to the population information in the algorithm initialization process, first calculate the information entropy of the given data set, and the information entropy is expressed by Entropy. The specific calculation formula is as follows: Among them, D0 represents the initial data set, b is the number of categories in the data set D0, and p a is the probability of each category a appearing in the data set; Then the information gain of each feature is calculated according to the information entropy. The information gain is represented by IG, and the IG calculation formula is as follows: Among them, A represents any feature, which is used to divide the data set; Values(A) represents the value set of feature A, that is, all possible values ​​of feature A; represents the subset obtained by dividing the data set D0 according to the value v of feature A, where v represents one of the values ​​of feature A; |D0| represents the number of samples in the data set D0, that is, the total number of samples in the data set D0; Representation Subset The number of samples in the subset The number of samples; The information gain is calculated for each feature of the data set, and the number of feature variables is adjusted according to the complexity of the industrial process to be solved. Finally, the features selected in order of information gain are primary fan air volume, secondary fan air volume, fuel supply, fuel injection rate and air valve opening. After that, the data is linearly scaled to the specified minimum and maximum ranges using the normalization method according to the minimum-maximum scaling principle, and the minimum value in the data set is set to d min , the maximum value is d max , the normalized data set is defined as D, and the formula is expressed as: Among them, d is the original data, d max and d min is the maximum and minimum value in the data set, norm min and norm max are the minimum and maximum boundary values ​​of the normalized data range.

3. The method for optimizing the operating setpoints of an industrial boiler system based on an agent-assisted multi-objective evolutionary algorithm according to claim 1 is characterized in that: Step 2: Construct a heterogeneous proxy model integrating SVM and FNN to describe NO x The relationship between concentration and operating variables; the five parameters after data processing are selected as input features to build the SVM model, namely, primary fan air volume, secondary fan air volume, fuel supply, fuel injection rate and air valve opening, and the insensitive loss function Hinge Loss is used in the training process; L(y S ,f S (x))=max(0,1-y S ·f S (x)) (4) Among them, y S is the true category label of the sample, x is the input data, and f S (x) is the predicted value of the model; The kernel function is selected as the Gaussian kernel function, and the formula is expressed as: K(x a ,x b )=exp(-γ||x a -x b || 2 )(5) In the formula, x a and x b They represent the eigenvectors of two data points respectively. γ is the parameter of the Gaussian kernel function, which controls the smoothness of the function. In order to match the width of the Gaussian kernel with the data dimension, its value is set to 0.

2. In the training process of the neural network model, the neurons in the input layer are defined as: primary fan air volume, secondary fan air volume, fuel supply, fuel injection rate and air valve opening, and the neurons in the output layer are NO x Concentration, the nonlinear activation function between the input layer and the hidden layer is selected as the Sigmoid function, set it to g(x), and the expression is: The mathematical expectation of the mean square error is used as the objective function to test the performance of the neural network. The mean square error at the lth iteration is: Where m is the total number of iterations of network training, t(l) is the expected output at the lth iteration, and y(l) is the actual output at the lth iteration; According to the gradient descent method, the neural weight adjustment is calculated. The weight between the kth neuron in the output layer and the jth neuron in the hidden layer is defined as w jk , the adjustment amount at the lth iteration is Δw jk (l), and the weight between the i-th neuron in the hidden layer and the j-th neuron in the input layer is defined as w ij , the adjustment amount at the lth iteration is Δw ij (l), the error propagation coefficient between the two is defined as δ k , the specific calculation formulas are as follows: Δw jk (l)=-adh k y j (1) (8) Δw ij (l)=-adh j y i (l) (9) Among them, α is the learning rate during the neural network training process, and its value range is [10 -3 ,10 -2 ];δ k is the error propagation coefficient between the kth neuron in the output layer and the jth neuron in the hidden layer, δ j is the error propagation coefficient between the i-th neuron in the hidden layer and the j-th neuron in the input layer, y j (l) is the output of the hidden layer neuron at the lth iteration, y i (l) is the output of the input layer neuron at the lth iteration; At this time, the error propagation coefficient δ k The specific expression at the lth iteration is as follows: Where F(w(l)) represents the mean square error function at the lth iteration, x k (l) and y k (l) are the input and output values ​​of the kth neuron in the output layer after the lth iteration, t k (l), y k (l) are the expected output value and actual output value in the lth iteration, respectively, and f k ′(x k (l)) is the derivative operation of the action function of the kth neuron; At the same time, the error propagation coefficient δ j The specific expression at the lth iteration is as follows: Among them, x j (l) and y j (l) are the input and output of the jth neuron in the hidden layer at the lth iteration, p is the number of neurons, and f j ′(x j (l)) represents the derivation operation of the action function of the jth neuron; The above models were trained by cross-validation. The two models SVM and FNN updated their respective test group root mean square error (RMSE) after each training. SVM and FNN predict the input data respectively and generate their own NO x Emission concentration estimation output; for the output of the heterogeneous model, the weights of the two outputs are dynamically adjusted according to formulas (12) and (13), and the ratio is used to represent the weight of the neural network model output. The output of the heterogeneous model is defined as O H , the formula is as follows: EITHER H ratio×O F +(1-ratio)×O S (13) Among them, R S , R F Respectively represent the RMSE size of the two models SVM and FNN, O F , O S Respectively represent the output values ​​of the two models; The output value O of the heterogeneous model H It is used as the fitness value of the offspring solution during population evolution and performs subsequent operations.

4. The method for optimizing the operating setpoints of an industrial boiler system based on an agent-assisted multi-objective evolutionary algorithm according to claim 1 is characterized in that: Step 3: Based on the combustion efficiency, NO x The objective functions are designed separately for emission concentration and electricity consumption; Set the optimization targets f1(t), f2(t) and f3(t) of the industrial boiler control system, where f1(t) represents the boiler combustion efficiency, i.e., the boiler energy utilization rate η = S e / F e , S e is the steam thermal energy, F e is the total energy generated by fuel combustion. Specifically, the combustion efficiency calculation formula is: Among them, S r and Q r Represent steam flow and fuel consumption, h s With h r Respectively represent the steam enthalpy and feed water enthalpy, H v Indicates the calorific value of fuel; f2(t) represents NO x The heterogeneous agent model is used as the objective function to describe and solve the problem. The input is the operating value of the industrial boiler operation system, and the output value is the NO x Emissions of O H ; f3(t) represents the power consumption of the equipment during operation. The fan is the part with the largest power consumption in the boiler system. Usually, the fan speed is adjusted to control the combustion process. The corresponding power consumption C e The calculation formula is as follows: C e =E×t e (15) Where E represents the power consumption of the fan per unit time, t e Represents the fan running time; Finally, the multi-objective optimization problem model is determined as 5. The method for optimizing the operating setpoints of an industrial boiler system based on an agent-assisted multi-objective evolutionary algorithm according to claim 1 is characterized in that the steps 4. Establish a dual-archive evaluation mechanism, place the processed data in the initial convergence archive CA archive, and simultaneously place it in the diversity archive DA archive; CA measures the quality of archives by calculating the sum of squares of the objective function value differences between the solution set and the true optimal solution. The evaluation formula is as follows: Among them, P CA represents the solution set contained in the convergence archive CA, |P CA | represents the size of the solution set, x t 、x y P CA The solution in, P* represents the true optimal solution set, o represents the number of objective functions, that is, o = 3, F u (x t ) is the value of the solution on the u-th objective function, is the true optimal value on target u; In addition, the uniformity of the solution set and the differences between the solutions are set as indicators to measure the diversity evaluation archive DA. The crowding distance of the uniformity of the solution set distribution is expressed as D C Represented by , and the difference of solution set is represented by Δd, then the specific formula is as follows: Among them, P DA represents the solution set contained in the diversity archive, |P DA | represents the size of the solution set, x g 、x f 、x t All P DA The solution in d(x f ,x g ) represents the solution x g With solution x f The Euclidean distance between u is the set of objective functions, F u (next(x t ))、F u (prev(x t )) are the solutions for x t The values ​​of the previous and next solutions on the u-th target after sorting, are the maximum and minimum values ​​of the u-th target in the solution set respectively; The evaluation formula of the diversity evaluation archive DA is: AND = w d ×D C +(1-w d )×Δd(19) Among them, w d is the weight coefficient, take w d =0.5 for comprehensive evaluation.

6. The method for optimizing the operating setpoints of an industrial boiler system based on an agent-assisted multi-objective evolutionary algorithm according to claim 1 is characterized in that: Step 5 introduces an adaptive sampling strategy into the algorithm. When the population evolution generation reaches the set evolution generation g max =5, the adaptive sampling strategy is triggered; In the adaptive sampling process, the sampling ratio is set to 10% according to the general setting standard, that is, 10% of individuals are randomly selected from the current population, and the calculation formula for the sampling quantity is: S=10%Pop (20) Among them, S represents the number of samples, Pop represents the current population total; By adding partial solutions to the archive until the total number is less than or equal to the maximum number of individuals 120; when the number of individuals in the archive exceeds 120, the CA and DA evaluation formulas are used to calculate the newly sampled individuals, and the calculation results are equalized to take the individuals corresponding to the previous ones and retain them until the number of individuals is less than or equal to 120, and then the original objective function is used for evaluation, which is the NO in the data collection stage. x The true value of the emission will complete the solution archive update of the above population evolution process; Continue to iterate until the preset maximum number of fitness function evaluations, 300, is reached.

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