CN114186472B - Design method of multi-input multi-output urban solid waste incineration process model - Google Patents

Abstract

Aiming at the problem that a controlled object model is difficult to build in the urban solid waste incineration process, the invention designs a multi-input multi-output urban solid waste incineration process model design method; firstly, describing a core process flow of an urban solid waste incineration process and analyzing influencing factors of a model; then, a modeling strategy of a controlled object model is designed according to the control characteristics of the urban solid waste incineration process, and the strategy consists of a working condition identification module, a data preprocessing module, a characteristic reduction module, a controlled object model training module and a controlled object model testing module; finally, experiments show that the effectiveness of the controlled object model in the urban solid waste incineration process lays a foundation for researching an optimization control algorithm of the urban solid waste incineration process.

Description

A multi-input and multi-output model design method for municipal solid waste incineration process

Technical Field

Aiming at the problem that the internal mechanism of the municipal solid waste incineration process is complex and it is difficult to establish a controlled object model, the present invention designs a multi-input and multi-output controlled object model based on the Takagi-Sugeno type fuzzy neural network. The model consists of a working condition identification module, a data preprocessing module, a feature reduction module, a controlled object model training module and a controlled object model testing module. It solves the problems that the internal mechanism of the municipal solid waste incineration process is difficult to analyze, the multi-variable coupling is strong, and the internal rules are difficult to mine, and lays a model foundation for studying the optimization control of the municipal solid waste incineration process.

Background Art

The municipal solid waste incineration technology has outstanding advantages such as reduction, resource utilization and harmlessness, and has become one of the main technical means for treating municipal solid waste in the world. As of 2016, there were 303 solid waste incineration power plants in operation in mainland China, with a total processing capacity of 3.04×10 ⁵ t/day. Among them, there were 220 solid waste incineration power plants using mechanical grate furnaces, accounting for more than 72%. The grate furnace has become the main type of incinerator used for municipal solid waste incineration in China. The municipal solid waste incineration based on the grate furnace is a process with many uncertain characteristics such as strong nonlinearity, strong coupling and large time variation. The complex process inevitably involves many control problems. It is necessary to rely on advanced control technology to stabilize the solid waste incineration state and improve the operation efficiency. The establishment of an accurate controlled object model is the basis and necessary preparation for the implementation of control technology. Therefore, the object model design research of the municipal solid waste incineration process in this invention is of great significance.

Traditional controlled object models are usually constructed based on mechanism analysis, which are called mechanism models, also known as "white box models". Mechanism models are constructed based on principles such as material balance equations, energy balance equations, biological laws, and chemical kinetics. They establish relatively accurate mathematical models by deriving functional relationships between operating variables, state variables, and controlled variables. Mechanism models have the ability to intuitively reflect the internal laws and structural connections of the system. However, unlike traditional complex industrial processes, the raw materials used in the process of municipal solid waste incineration are solid waste, which is inherently complex and changeable. There are many factors that affect the composition of solid waste, including seasonal climate, the degree of classification of solid waste, the living standards, living habits, and environmental awareness of the people in the region. For strongly nonlinear industrial processes such as municipal solid waste incineration, models constructed based on mechanism analysis are not only difficult to analyze the properties and internal mechanisms of strongly nonlinear systems, but also difficult to apply to solid waste incineration processes under multiple working conditions. In recent years, with the rise of artificial intelligence, data-driven machine learning methods have provided a solution for modeling the control objects of municipal solid waste incineration processes.

Data-driven models are constructed by mining the mapping relationship between system input and output data, also known as black box models. Artificial neural networks are widely used in process analysis of complex industrial systems due to their good learning ability, computing ability and nonlinear approximation ability. They have important application value in the design of controlled object models with unknown internal mechanisms. Artificial neural networks have been increasingly used in the modeling of controlled objects in industrial processes and have become a current research hotspot.

The municipal solid waste incineration process is a typical multi-input and multi-output industrial process. Its solid waste calorific value is difficult to determine, the internal mechanism reaction is complex, multiple operating variables are seriously coupled with the controlled variables, and the system rules are difficult to mine. It has typical fuzzy characteristics. Fuzzy neural networks provide a good solution for complex industrial processes such as municipal solid waste incineration. As a fuzzy adaptive solution, fuzzy neural networks have both the nonlinear processing and analysis capabilities of fuzzy systems and the parameter learning and dynamic optimization capabilities of artificial neural networks. In recent years, they have been widely studied and have become an important branch of intelligent computing and neuroscience. It is a technology that is superior to the use of artificial neural networks and fuzzy systems alone.

According to the above analysis, the present invention designs a multi-input multi-output controlled object model based on Takagi-Sugeno type fuzzy neural network for the characteristics of the municipal solid waste incineration process. First, the operating conditions of municipal solid waste incineration are identified and data preprocessed according to the incineration mechanism and expert experience; then, the key operating quantities and controlled quantities that can reflect the system state are extracted; then, multiple post-part sub-networks are constructed, and the local and overall parameters of the network are optimized using the gradient descent algorithm to ensure the convergence accuracy of the model and the synchronization of the output; finally, the effectiveness of the controlled object model is verified through the process data of a solid waste incineration plant in Beijing.

Summary of the invention

The present invention obtains a multi-input multi-output controlled object model based on Takagi-Sugeno type fuzzy neural network, which consists of a working condition identification module, a data preprocessing module, a feature reduction module, a controlled object model training module and a controlled object model testing module, realizes accurate prediction of key controlled variables, solves the problem that the controlled object model of the municipal solid waste incineration process is difficult to establish, and lays a foundation for studying the optimization control of municipal solid waste incineration;

The present invention adopts the following technical solutions and implementation steps:

A multi-input and multi-output municipal solid waste incineration process model design method comprises the following steps:

1. A multi-input and multi-output municipal solid waste incineration process model design method, characterized by comprising the following steps:

(1) Working condition identification module: This module constructs an expert evaluation mechanism for working condition identification based on primary wind pressure, divides the working conditions according to the primary wind pressure setting value, and then constructs corresponding controlled object models for different working conditions;

(2) Data preprocessing module: This module preprocesses the collected data by eliminating abnormal data and normalizing the data. The calculation steps are as follows:

① Abnormal data elimination: First, the normal distribution of the data is tested by drawing a quantile diagram, and then the abnormal data is eliminated by the 3σ criterion. The key controlled variables at time 1 to T are collected: main steam flow, furnace temperature and flue gas oxygen content, which are defined as Y _s (t), where s = 1, 2, ..., q, q is 3, t = 1, 2, ..., T, and the residual error ε _s (t) corresponding to Y _s (t) is calculated as:

Calculate the standard deviation _σs of the data set as:

When the residual error ε _s (t) corresponding to Y _s (t) meets the following conditions:

|ε _s (t)|＞3σ _s (3)

Then perform a elimination operation on this Y _s (t), and set T = T-1;

② Data normalization: Extract the key operating variables of the municipal solid waste incineration process: drying grate air flow (left 1, right 1, left 2, right 2), combustion 1 grate air flow (left 1, right 1, left 2, right 2), combustion 2 grate air flow (left 1, right 1, left 2, right 2), burnout grate air flow (left, right), secondary air flow, drying grate speed (left inner, right inner, left outer, right outer), combustion 1 grate speed (left inner, right inner, left outer, right outer), combustion 2 grate speed (left inner, right inner, left outer, right outer) and burnout grate speed (left inner, right inner), define them as _Xi (t), where i = 1, 2, ..., N, N is 29, t = 1, 2, ..., T, normalize the collected data _Xi (t) and _Ys (t), and the calculation formula is as follows:

Wherein, _Xi (t) represents the normalized value of data _Xi (t), _ys (t) represents the normalized value of data _Ys (t), _Xi represents all the data of the i-th parameter in the collection time period, and _Ys represents all the data of the s-th parameter in the collection time period;

(3) Feature reduction module: Calculate the Pearson correlation coefficient between the above key operating variables x _i (t) and the key controlled variables y _s (t). The Pearson correlation coefficient is defined as ρ _ds , and its calculation method is:

According to the calculation results, the absolute values of ρ _ds are sorted, and the top 3 operating variables are selected and recorded as x _i (t), where i = 1, 2, ..., n, and n is 3;

(4) Multi-input multi-output Takagi-Sugeno type fuzzy neural network training module: The model structure designed in this module consists of two parts: the antecedent network and the consequent network. The antecedent network includes five layers, namely the input layer, the membership function layer, the rule layer, the consequent layer and the output layer. The consequent network includes three layers, namely the input layer, the rule layer and the consequent layer. The mathematical description is as follows:

① Input layer: This layer has n neurons, n is 3, and its function is to transmit the input value. When the tth sample enters, the output of the input layer is:

x _i (t), i = 1, 2, ..., n (7)

② Membership function layer: This layer has a total of n×m neurons, m is 12, and the output of each node represents the membership value of the corresponding input quantity. The membership function is:

Where c _ij (t) and δ _ij (t) are the center and width of the membership function, respectively. The initial value is a random real number uniformly distributed in the range [0,2] generated by the rand random function.

③ Rule layer: This layer has m neurons and uses fuzzy multiplication operators as fuzzy logic rules. The output of the rule layer is:

后件参数是由后件网络计算得出的，后件网络输入层传入n+1个变量，其中第0个节点的输入为常数，即x₀(t)＝1，将 后件参数传回前件网络的后件层中，其计算过程如下：④ Consequence layer: This layer has a total of m×q neurons, q is 3, and each node performs the linear summation of TS-type fuzzy rules. The function of this layer is to calculate the consequent parameters of the output corresponding to each rule

The subsequent parameters are calculated by the subsequent network. The input layer of the subsequent network passes n+1 variables, where the input of the 0th node is a constant, that is, x ₀ (t) = 1. The subsequent parameters are passed back to the subsequent layer of the antecedent network. The calculation process is as follows:

为模糊系统的参数，其初始值设为0.3，x₀(t),x₁(t),…, x_n(t)为输入变量；In the formula,

are the parameters of the fuzzy system, whose initial value is set to 0.3, and x ₀ (t), x ₁ (t),…, x _n (t) are the input variables;

⑤ Output layer: This layer has q output nodes, each of which performs weighted summation on the input parameters. The calculation formula is as follows:

⑥Model parameter learning: Use the gradient descent algorithm to adjust the network parameters. First, define the error calculation method as follows:

是第t个输入样本对应的 第s个计算输出，e_s(t)为两者之间的误差，依据误差对网络的中心、宽度和模糊系统参数 更新算法定义如下：Where _ys (t) is the sth actual output corresponding to the tth input sample,

is the sth calculated output corresponding to the tth input sample, _es (t) is the error between the two, and the center, width and fuzzy system parameter update algorithm of the network are defined as follows based on the error:

分 别为第t-1个样本输入时网络隶属函数层的中心、宽度和模糊系统的参数，完成本次参数 更新后，输入训练样本数据x_i(t+1)，重复步骤①～⑥，直至所有训练样本全部输入，训练 样本数为总样本数T的80％，之后对模型进行迭代训练，，直至迭代次数达到最大迭代值It_max，It_max为500；Where η is the online learning rate, the value range of η is [0.01, 0, 05], c _ij (t-1), δ _ij (t-1) and

are the center, width and fuzzy system parameters of the network membership function layer when the t-1th sample is input. After completing this parameter update, input the training sample data x _i (t+1), and repeat steps ① to ⑥ until all training samples are input. The number of training samples is 80% of the total number of samples T. Then, the model is iteratively trained until the number of iterations reaches the maximum iteration value It _max , _which is 500.

(5) After the model training is completed, the multi-input and multi-output model of the municipal solid waste incineration process is built. At this time, the primary air flow rate, secondary air flow rate and grate speed are input into the model, and the model outputs the main steam flow rate, furnace temperature and flue gas oxygen content.

The creativity of the present invention is mainly reflected in:

(1) The present invention solves the problems that the internal mechanism of the municipal solid waste incineration process is difficult to analyze, the multivariable coupling is strong, and the internal rules are difficult to explore, and lays a model foundation for studying the optimization control of the municipal solid waste incineration process;

(2) The present invention designs a modeling strategy with multi-condition identification and feature simplification based on the process characteristics of domestic municipal solid waste incineration, and the model has good robustness and applicability;

(3) The controlled object model established by the present invention has multi-output learning capability, and uses the complementary information between multiple tasks to accurately fit multiple controlled quantities at the same time, and to update the network parameters online;

(4) The method for modeling the controlled object of the municipal solid waste incineration process based on the multi-input multi-output controlled object model of the Takagi-Sugeno type fuzzy neural network proposed in the present invention has strong learning ability, high modeling accuracy, and has wide application value;

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a process flow chart of the municipal solid waste incineration process of the present invention.

FIG. 2 is a control flow chart of the municipal solid waste incineration process of the present invention.

FIG. 3 is a method for constructing a controlled object model of a municipal solid waste incineration process based on data drive according to the present invention.

FIG. 4 is a multi-input multi-output model based on Takagi-Sugeno type fuzzy neural network of the present invention.

FIG. 5 is a diagram showing the RMSE variation during the model training process of the present invention.

FIG. 6 is a diagram showing the model training sample fitting effect of the present invention.

FIG. 7 is a diagram showing the model test sample fitting effect of the present invention.

FIG. 8 is a diagram showing the fitting effect of the furnace temperature training sample of the present invention.

FIG. 9 is a diagram showing the fitting effect of the smoke oxygen content training sample of the present invention.

FIG. 10 is a diagram showing the fitting effect of the main steam flow test sample of the present invention.

FIG. 11 is a diagram showing the fitting effect of the furnace temperature test sample of the present invention.

FIG. 12 is a diagram showing the fitting effect of the smoke oxygen content test sample of the present invention.

FIG. 13 is a test error diagram of a main steam flow test sample of the present invention.

FIG. 14 is a test error diagram of a furnace temperature test sample of the present invention.

FIG. 15 is a test error diagram of a flue gas oxygen content test sample of the present invention.

DETAILED DESCRIPTION

The present invention obtains a multi-input multi-output controlled object model based on Takagi-Sugeno type fuzzy neural network, which consists of a working condition identification module, a data preprocessing module, a feature reduction module, a controlled object model training module and a controlled object model testing module, realizes accurate prediction of key controlled variables, solves the problem that the controlled object model of the municipal solid waste incineration process is difficult to establish, and lays a foundation for studying the optimization control of municipal solid waste incineration;

This experiment collected process data from a certain city solid waste incineration power plant with a sampling frequency of 1s/time, and a total of 2×10 ⁵ sets of data were collected as experimental samples;

A multi-input and multi-output municipal solid waste incineration process model design method comprises the following steps:

(1) Working condition identification module: This module constructs an expert evaluation mechanism for working condition identification based on primary wind pressure, divides the working conditions according to the primary wind pressure setting value, and then constructs corresponding controlled object models for different working conditions;

(2) Data preprocessing module: This module preprocesses the collected data by eliminating abnormal data and normalizing the data. The calculation steps are as follows:

① Abnormal data elimination: First, the normal distribution of the data is tested by drawing a quantile diagram, and then the abnormal data is eliminated by the 3σ criterion. The key controlled variables at time 1 to T are collected: main steam flow, furnace temperature and flue gas oxygen content, which are defined as Y _s (t), where s = 1, 2, ..., q, q is 3, t = 1, 2, ..., T, and the residual error ε _s (t) corresponding to Y _s (t) is calculated as:

Calculate the standard deviation _σs of the data set as:

When the residual error ε _s (t) corresponding to Y _s (t) meets the following conditions:

|ε _s (t)|＞3σ _s (3)

Then perform a elimination operation on this Y _s (t), and set T = T-1;

② Data normalization: Extract the key operating variables of the municipal solid waste incineration process: drying grate air flow (left 1, right 1, left 2, right 2), combustion 1 grate air flow (left 1, right 1, left 2, right 2), combustion 2 grate air flow (left 1, right 1, left 2, right 2), burnout grate air flow (left, right), secondary air flow, drying grate speed (left inner, right inner, left outer, right outer), combustion 1 grate speed (left inner, right inner, left outer, right outer), combustion 2 grate speed (left inner, right inner, left outer, right outer) and burnout grate speed (left inner, right inner), define them as _Xi (t), where i = 1, 2, ..., N, N is 29, t = 1, 2, ..., T, normalize the collected data _Xi (t) and _Ys (t), and the calculation formula is as follows:

Wherein, _Xi (t) represents the normalized value of data _Xi (t), _ys (t) represents the normalized value of data _Ys (t), _Xi represents all the data of the i-th parameter in the collection time period, and _Ys represents all the data of the s-th parameter in the collection time period;

(3) Feature reduction module: Calculate the Pearson correlation coefficient between the above key operating variables x _i (t) and the key controlled variables y _s (t). The Pearson correlation coefficient is defined as ρ _ds , and its calculation method is:

According to the calculation results, the absolute values of ρ _ds are sorted, and the top 3 operating variables are selected and recorded as x _i (t), where i = 1, 2, ..., n, and n is 3;

(4) Multi-input multi-output Takagi-Sugeno type fuzzy neural network training module: The model structure designed in this module consists of two parts: the antecedent network and the consequent network. The antecedent network includes five layers, namely the input layer, the membership function layer, the rule layer, the consequent layer and the output layer. The consequent network includes three layers, namely the input layer, the rule layer and the consequent layer. The mathematical description is as follows:

① Input layer: This layer has n neurons, n is 3, and its function is to transmit the input value. When the tth sample enters, the output of the input layer is:

x _i (t), i = 1, 2, ..., n (7)

② Membership function layer: This layer has a total of n×m neurons, m is 12, and the output of each node represents the membership value of the corresponding input quantity. The membership function is:

Where c _ij (t) and δ _ij (t) are the center and width of the membership function, respectively. The initial value is a random real number uniformly distributed in the range [0,2] generated by the rand random function.

③ Rule layer: This layer has m neurons and uses fuzzy multiplication operators as fuzzy logic rules. The output of the rule layer is:

后件参数是由后件网络计算得出的，后件网络输入层传入n+1个变量，其中第0个节点的输入为常数，即x₀(t)＝1，将 后件参数传回前件网络的后件层中，其计算过程如下：④ Consequence layer: This layer has a total of m×q neurons, q is 3, and each node performs the linear summation of TS-type fuzzy rules. The function of this layer is to calculate the consequent parameters of the output corresponding to each rule

The subsequent parameters are calculated by the subsequent network. The input layer of the subsequent network passes n+1 variables, where the input of the 0th node is a constant, that is, x ₀ (t) = 1. The subsequent parameters are passed back to the subsequent layer of the antecedent network. The calculation process is as follows:

为模糊系统的参数，其初始值设为0.3，x₀(t),x₁(t),…, x_n(t)为输入变量；In the formula,

are the parameters of the fuzzy system, whose initial value is set to 0.3, and x ₀ (t), x ₁ (t),…, x _n (t) are the input variables;

⑤ Output layer: This layer has q output nodes, each of which performs weighted summation on the input parameters. The calculation formula is as follows:

⑥Model parameter learning: Use the gradient descent algorithm to adjust the network parameters. First, define the error calculation method as follows:

是第t个输入样本对应的 第s个计算输出，e_s(t)为两者之间的误差，依据误差对网络的中心、宽度和模糊系统参数 更新算法定义如下：Where _ys (t) is the sth actual output corresponding to the tth input sample,

is the sth calculated output corresponding to the tth input sample, _es (t) is the error between the two, and the center, width and fuzzy system parameter update algorithm of the network are defined as follows based on the error:

分 别为第t-1个样本输入时网络隶属函数层的中心、宽度和模糊系统的参数，完成本次参数 更新后，输入训练样本数据x_i(t+1)，重复步骤①～⑥，直至所有训练样本全部输入，训练 样本数为总样本数T的80％，之后对模型进行迭代训练，，直至迭代次数达到最大迭代值It_max，It_max为500；Where η is the online learning rate, the value range of η is [0.01, 0, 05], c _ij (t-1), δ _ij (t-1) and

are the center, width and fuzzy system parameters of the network membership function layer when the t-1th sample is input. After completing this parameter update, input the training sample data x _i (t+1), and repeat steps ① to ⑥ until all training samples are input. The number of training samples is 80% of the total number of samples T. Then, the model is iteratively trained until the number of iterations reaches the maximum iteration value It _max , _which is 500.

(5) After the model training is completed, the multi-input and multi-output model of the municipal solid waste incineration process is built. At this time, the primary air flow rate, secondary air flow rate and grate speed are input into the model, and the model outputs the main steam flow rate, furnace temperature and flue gas oxygen content.

FIG. 1 is a process flow chart of the municipal solid waste incineration process of the present invention.

FIG. 2 is a control flow chart of the municipal solid waste incineration process of the present invention.

FIG. 3 is a structural diagram of a multi-input multi-output model based on a Takagi-Sugeno type fuzzy neural network of the present invention.

FIG. 4 is a diagram showing the RMSE variation of the main steam flow rate training process of the present invention.

FIG. 5 is a diagram showing the RMSE variation of the furnace temperature training process of the present invention.

FIG. 6 is a diagram showing the RMSE variation of the flue gas oxygen content training process of the present invention.

FIG. 7 is a diagram showing the fitting effect of the main steam flow training sample of the present invention.

FIG. 8 is a diagram showing the fitting effect of the furnace temperature training sample of the present invention.

FIG. 9 is a diagram showing the fitting effect of the smoke oxygen content training sample of the present invention.

FIG. 10 is a diagram showing the fitting effect of the main steam flow test sample of the present invention.

FIG. 11 is a diagram showing the fitting effect of the furnace temperature test sample of the present invention.

FIG. 12 is a diagram showing the fitting effect of the smoke oxygen content test sample of the present invention.

FIG. 13 is a test error diagram of a main steam flow test sample of the present invention.

FIG. 14 is a test error diagram of a furnace temperature test sample of the present invention.

FIG. 15 is a test error diagram of a flue gas oxygen content test sample of the present invention.

The process flow of the municipal solid waste incineration process is shown in Figure 1; the control process of the municipal solid waste incineration process is shown in Figure 2; the multi-input multi-output model structure based on the Takagi-Sugeno type fuzzy neural network is shown in Figure 3; the training sample data is used as the input of the model, and the RMSE changes in the model training process are shown in Figures 4 to 6; Figure 4 is the RMSE change in the main steam flow training process, X-axis: training steps, Y-axis: training RMSE value; Figure 5 is the RMSE change in the furnace temperature training process, X-axis: training steps, Y-axis: training RMSE value; Figure 6 is the RMSE change in the flue gas oxygen content training process, X-axis: training steps, Y-axis: training RMSE value; the model training sample fitting effect is shown in Figures 7 to 9; Figure 7 is the main steam flow training sample fitting effect, X-axis: sample number, Y-axis: main steam flow, the unit is t/h, the black line is the predicted output, and the gray line is the actual output; Figure 8 is the furnace temperature training sample fitting effect, X-axis: sample number, Y axis: furnace temperature, unit is ℃, black line is predicted output, gray line is actual output; Figure 9 is the fitting effect of flue gas oxygen content training sample, X axis: sample number, Y axis: flue gas oxygen content, unit is %, black line is predicted output, gray line is actual output; take the test sample data as the trained model input, the model test sample fitting effect is shown in Figure 10 to Figure 12; Figure 10 is the main steam flow test sample fitting effect, X axis: sample number, Y axis: main steam flow, unit is t/h, black line is predicted output, gray line is actual output; Figure 11 is the furnace temperature test sample fitting effect, X axis: sample number, Y axis: furnace temperature, unit is ℃, black line is predicted output, gray line is actual output; Figure 12 is the flue gas oxygen content test sample fitting effect, X axis: sample number, Y axis: flue gas oxygen content, unit is %, black line is predicted output, gray line is actual output; model test sample test error is shown in Figure 13 to Figure 15 Figure 13 is the test error of the main steam flow test sample, X-axis: sample number, Y-axis: main steam flow, the unit is t/h; Figure 14 is the test error of the furnace temperature test sample, X-axis: sample number, Y-axis: furnace temperature, the unit is ℃; Figure 15 is the test error of the flue gas oxygen content test sample, X-axis: sample number, Y-axis: flue gas oxygen content, the unit is %; The results show the effectiveness of the model in modeling the controlled object of the municipal solid waste incineration process.

Claims (1)

1. A multi-input and multi-output municipal solid waste incineration process model design method, characterized by comprising the following steps: (1) Working condition identification module: The working conditions are divided according to the primary wind pressure setting value, and then the corresponding controlled object model is constructed for different working conditions; (2) Data preprocessing module: This module preprocesses the collected data by removing abnormal data and normalizing the data. The calculation steps are as follows: ① Abnormal data elimination: First, the normal distribution of the data is tested by drawing a quantile diagram, and then the abnormal data is eliminated by the 3σ criterion. The key controlled variables at time 1 to T are collected: main steam flow, furnace temperature and flue gas oxygen content, which are defined as Y _s (t), where s = 1, 2, ..., q, q is 3, t = 1, 2, ..., T, and the residual error ε _s (t) corresponding to Y _s (t) is calculated as:

Calculate the standard deviation _σs of the data set as:

When the residual error ε _s (t) corresponding to Y _s (t) meets the following conditions: |ε _s (t)|＞3σ _s (3) Then perform a elimination operation on this Y _s (t), and set T = T-1; ② Data normalization: Extract key operating variables of the municipal solid waste incineration process: drying section grate air flow includes: left 1, right 1, left 2, right 2; combustion section grate air flow includes: left 1, right 1, left 2, right 2; combustion section grate air flow includes: left 1, right 1, left 2, right 2; burnout section grate air flow includes left and right; secondary air flow; drying section grate speed includes: left inner, right inner, left outer, right outer; combustion section grate speed includes left inner, right inner, left outer, right outer; combustion section grate speed includes left inner, right inner, left outer, right outer; and burnout section grate speed includes left inner, right inner; define it as _Xi (t), where i = 1, 2, ..., N, N is 29, t = 1, 2, ..., T, normalize the collected data _Xi (t) and _Ys (t), and the calculation formula is as follows:

Wherein, _Xi (t) represents the normalized value of data _Xi (t), _ys (t) represents the normalized value of data _Ys (t), _Xi represents all the data of the i-th parameter in the collection time period, and _Ys represents all the data of the s-th parameter in the collection time period; (3) Feature reduction module: Calculate the Pearson correlation coefficient between the above key operating variables x _i (t) and the key controlled variables y _s (t). The Pearson correlation coefficient is defined as ρ _ds , and its calculation method is:

According to the calculation results, the absolute values of ρ _ds are sorted, and the top 3 operating variables are selected and recorded as x _i (t), where i = 1, 2, ..., n, and n is 3; (4) Multi-input multi-output Takagi-Sugeno type fuzzy neural network training module: The model structure designed in this module consists of two parts: the antecedent network and the consequent network. The antecedent network includes five layers, namely the input layer, the membership function layer, the rule layer, the consequent layer and the output layer. The consequent network includes three layers, namely the input layer, the rule layer and the consequent layer. The mathematical description is as follows: ① Input layer: This layer has n neurons, n is 3, and its function is to transmit the input value. When the tth sample enters, the output of the input layer is: x _i (t), i = 1, 2, ..., n (7) ② Membership function layer: This layer has a total of n×m neurons, m is 12, and the output of each node represents the membership value of the corresponding input quantity. The membership function is:

Where c _ij (t) and δ _ij (t) are the center and width of the membership function, respectively. The initial value is a random real number uniformly distributed in the range [0,2] generated by the rand random function. ③Rule layer: This layer has m neurons and uses fuzzy multiplication operators as fuzzy logic rules. The output of the rule layer is:

④ Consequence layer: This layer has a total of m×q neurons, q is 3, and each node performs the linear summation of TS-type fuzzy rules. The function of this layer is to calculate the consequent parameters of the output corresponding to each rule

The subsequent parameters are calculated by the subsequent network. The input layer of the subsequent network passes n+1 variables, where the input of the 0th node is a constant, that is, x ₀ (t) = 1. The subsequent parameters are passed back to the subsequent layer of the antecedent network. The calculation process is as follows:

In the formula,

are the parameters of the fuzzy system, whose initial value is set to 0.3, and x ₀ (t), x ₁ (t),…, x _n (t) are the input variables; ⑤ Output layer: This layer has q output nodes, each of which performs weighted summation on the input parameters. The calculation formula is as follows:

⑥Model parameter learning: Use the gradient descent algorithm to adjust the network parameters. First, define the error calculation method as follows:

In the formula, _ys (t) represents the normalized value of data _Ys (t),

is the sth calculated output corresponding to the tth input sample, _es (t) is the error between the two, and the center, width and fuzzy system parameter update algorithm of the network are defined as follows based on the error:

Where η is the online learning rate, the value range of η is [0.01, 0, 05], c _ij (t-1), δ _ij (t-1) and

are the center, width and fuzzy system parameters of the network membership function layer when the t-1th sample is input. After completing this parameter update, input the training sample data x _i (t+1), and repeat steps ① to ⑥ until all training samples are input. The number of training samples is 80% of the total number of samples T. Then, the model is iteratively trained until the number of iterations reaches the maximum iteration value It _max , _which is 500. (5) After the model training is completed, the multi-input and multi-output model of the municipal solid waste incineration process is built. At this time, the primary air flow rate, secondary air flow rate and grate speed are input into the model, and the model outputs the main steam flow rate, furnace temperature and flue gas oxygen content.

Images