Soft Sensing Method for Nitrogen Oxides in Municipal Solid Waste Incineration Process Based on Modular Neural Network

Abstract

The soft measurement method for nitrogen oxides in the urban solid waste incineration process based on a modular neural network belongs to the field of solid waste treatment. The real-time detection of the toxic gas - nitrogen oxides (NOx) generated in MSWI can effectively control the emission of NOx. In industrial sites, a high-precision instrument - the continuous emission monitoring system for flue gas is used to detect the NOx concentration in flue gas emissions. The measurement results are greatly affected by the environment, and the equipment maintenance cost is high. First of all, the fuzzy c-means algorithm is used for task decomposition, decomposing the task into different subtasks; secondly, for different subtasks, a radial basis function neural network is used to design soft measurement sub-models respectively, establishing the non-linear relationship between the characteristic variables and NOx; finally, the output of the sub-networks is integrated through a cascaded neural network. The effectiveness of the proposed method is verified by benchmark experiments and the actual data of a certain MSWI plant.

Description

Technical Field

[0001] The present invention belongs to the field of solid waste treatment. Background Art

[0002] In actual operation, the Continuous Emission Monitoring System (CEMS) is usually used to detect the NOx concentration in tail gas emissions. Most enterprises use imported equipment and entrust professional companies for maintenance. When the CEMS fails, there are characteristics such as the slow arrival speed of professional maintenance personnel, great difficulty and long time in troubleshooting faults. As a result, the data missing time is relatively long. Therefore, a new method for online measurement of NOx is of great significance for ensuring the economic, safe and efficient operation of MSWI plants. Soft sensing technology estimates the measured variable by establishing a mechanism model or a data-driven model, which is easy to implement and has been successfully applied to multiple industrial processes. At present, some scholars have applied soft sensing technology to NOx detection. The urban solid waste incineration process involves complex physical and chemical reactions. The NOx concentration is related to many process variables such as the composition of the waste entering the furnace, the temperature and air volume in the furnace. Moreover, the working conditions in the furnace are changeable during the incineration process, and it is difficult for a single neural network to establish an accurate soft sensing model.

[0003] The modular neural network simulates the "modular" structural characteristics and the "divide and conquer" functional characteristics of the brain network. It consists of multiple sub-networks, and each sub-network processes a sub-task in the global task, which can effectively improve the ability to handle complex tasks. In the solid waste incineration process, there are mainly three important sources of NOx in the tail gas emissions. One is prompt NOx, which is generated by the chemical reaction of organic and inorganic nitrogen-containing compounds contained in the solid waste itself with oxygen during incineration. The second is thermal NOx, which is generated by the oxidation of N2 in the primary air and secondary air at high temperature. The third is fuel NOx, which is generated by the cracking of the combustion-supporting fuel (such as gasoline) at high temperature. To inhibit the generation amount of pollutants, the Selective Non-Catalytic Reduction (SNCR) system is actually used as a denitrification device. By spraying urea, NOx is converted into N2. The flue gas containing a small amount of NOx passes through the reactor, the mixing gas and the bag filter to achieve the absorption and filtration of NOx and other pollutants. In the MSWI plant, the CEMS system is used to detect the concentration of NOx and other pollutant gases. The tail gas after meeting the emission standards is discharged into the atmosphere through the chimney. If the emission exceeds the standard, it will be fined according to the regulations. At present, the NOx concentration in the flue gas discharged from newly built MSWI plants complies with the content specified in Table 1. Therefore, the accurate detection of NOx is of great significance for controlling the generation of NOx and reducing industrial costs.

[0004] Table 1 NOx Concentration Limit in MSWI Plants

[0005] Summary of the Invention

[0006] A soft measurement method for NOx emission concentration in the MSWI process based on a modular neural network is proposed in this paper. First, the fuzzy C-means (FCM) algorithm is used to decompose the global task to reduce the task complexity. Then, according to the decomposed subtasks, a radial basis function (RBF) neural network is used to establish the corresponding sub-networks. Next, the sub-models are integrated by a fully connected cascade (FCC) neural network. Finally, the effectiveness of the proposed method is verified through benchmark experiments and real data from a certain MSWI power plant in China.

[0007] The present invention proposes a soft measurement model for NOx emission concentration based on a modular neural network. This model consists of four parts: data preprocessing, task decomposition, sub-module construction, and output integration. First, the original process data is collected from the MSWI power plant, denoted as X; after normalization, outlier removal, and feature selection, the data set Q is obtained, where Q ∈ R N×P ; then the FCM algorithm is used to decompose the data set Q into C groups of data clusters with different operating conditions, denoted by representing the data clusters under the first, second, and Cth operating conditions after clustering, where C represents the number of operating conditions, that is, the number of data clusters; then, corresponding RBF sub-modules are constructed for each operating condition, denoted by RBF_1, RBF_2,..., RBF_C respectively, to establish the non-linear mapping relationship between the input process variables and NOx under different operating conditions "divide and conquer". Finally, the outputs of multiple simultaneously activated sub-models are integrated by a FCC neural network, and a comprehensive evaluation of the outputs of each sub-model is performed to obtain the final output, where Y train and Y test respectively represent

[0008] In the MSWI process, in order to eliminate the influence of the dimension between process variables, accelerate the solution speed of the sub-network, and improve the training accuracy, the Z-score standardization method is adopted in this paper, as shown in Equation (1).

[0009]

[0010] where, x nor_m represents the standardized data of the mth process variable affecting the NOx emission concentration, x m represents the mth process variable in the collected original data set, μ m and σ mRepresent the mean and standard deviation of the m-th process variable respectively.

[0011] Since CEMS is vulnerable to the complex environment in the incinerator, the collected NOx concentration data often contains outliers. These outliers are either much higher than the limit values given in Table 1 or much lower than the normal values, which brings troubles to subsequent data analysis. Therefore, the Rajda criterion

[17] is used in this paper to eliminate the outliers in the original data by the method of being higher than three times the standard deviation of the NOx concentration data, as shown in Equation (2).

[0012] |y o -m NOx |≥3σ NOx (2)

[0013] Among them, y o represents the NOx concentration data corresponding to the o-th original data sample in the sample, μ NOx and σ NOx represent the mean and standard deviation of the NOx concentration data respectively. The NOx data y o satisfying Equation (2) is regarded as an outlier, and then the o-th sample should be removed from the data set. Then the preprocessed data set is denoted as S, so S = [s1, s2,..., s N T , s1, s2,..., s N represent the 1st, 2nd, and N-th samples obtained after removing the outliers respectively, and N represents the sample size after removing the outliers.

[0014] The reaction process in MSWI is complex. After selecting process variables based on prior and mechanistic knowledge, there are many process variables, and the variables are interrelated and coupled with each other. In order to improve the calculation efficiency and accuracy of the soft measurement model, the mRMR algorithm based on mutual information (MI) is used in this paper

[18] to select potential variables. As the name implies, this algorithm aims to maximize the correlation between process variables and NOx concentration and minimize the redundancy between process variables. In this paper, feature selection is performed on the data set S obtained after preprocessing, and the relationship between process variables in each data set S is measured by MI. The definition of MI is shown in Equation (3).

[0015]

[0016] Among them, I represents the degree of association between the i-th process variable s i and the j-th process variable s j , and p(s i ) and p(s j ) are the probabilities of s i and s j respectively.The probability density function, p(s i , s j ) is the joint probability density function of the i-th process variable s i and the j-th process variable s j . Therefore, maximizing the correlation between the i-th process variable and the NOx concentration in the process can be expressed as

[0017]

[0018] where D represents the degree of association between each process variable in the data set S and the NOx concentration, s i and s NOx are the i-th process variable and the NOx concentration variable respectively, and S is the data set after normalization of the process variables and removal of NOx outliers. Similarly, minimizing the redundancy between process variables can be expressed as

[0019]

[0020] where R represents the degree of association between process variables. Combining equations (4) and (5), the evaluation criterion Φ of the mRMR algorithm is

[0021] maxΦ(D, R), Φ = D - R (6)

[0022] The data set after feature selection is represented as Q ∈ R N×F , N represents the sample size, and F represents the number of selected process variables.

[0023] To prevent overfitting, the data is divided into three parts with a division ratio of 2:1:1, represented by Q1, Q2, and Q3 respectively. The sizes of these three sub-data sets are N1, N2, and N3 respectively. Then Q = Q1 ∪ Q2 ∪ Q3, N = N1 + N2 + N3, and N represents the size of the data set before division. First, use Q1 for task decomposition to obtain subsets of process variables under different operating conditions; then train corresponding RBF sub-network models for each subset under each condition to establish the mapping relationship between the process variables and NOx under each operating condition; then use Q2 to test the sub-models established under each operating condition, and at the same time use the test output of the sub-models to train the FCC neural network to achieve output integration under different conditions, comprehensively considering the prediction ability of the sub-models under different operating conditions; finally, use Q3 to test the RBF sub-model and the FCC neural network to complete the test of the entire soft sensor model for NOx emission concentration.

[0024] Task decomposition is the prerequisite for achieving modular design. Through task decomposition, process data is classified and divided into different subsets. In MSWI, the NOx concentration emission characteristics are greatly affected by the composition of the waste entering the furnace, the air volume, and the temperature, and the relevant influencing variables also have different distribution characteristics. Therefore, the FCM algorithm is used in this paper to cluster the influencing variables of the NOx concentration.

[0025] Then the sample set to be clustered is Q1, and is used to represent the first, second, and N1th samples in the set. The FCM algorithm obtains the membership degree of each sample point to all cluster centers by optimizing the objective function. The objective function of the FCM algorithm is defined as:

[0026]

[0027] where U is the membership matrix composed of u cn , V represents the cluster center of the data cluster under each operating condition, C represents the number of data clusters, that is, the number of operating conditions, c represents any one of the data clusters in the Cth data cluster, that is, any one of the operating conditions. Since the operating conditions of the NOx concentration soft measurement can be divided into 3 types, C is selected as 3 in the task decomposition process of this paper. N1 represents the number of process variable samples, and u cn represents the membership degree of the nth sample in Q1 to the cth operating condition, and u cn ∈(0,1). r represents the weighting exponent. For simplicity of calculation, most researchers take the value of r as 2. Therefore, the value of r is selected as 2 in this paper. v c represents the cth cluster center point, and q n represents the nth sample in the sample set Q1 to be clustered. The sum of the membership degrees of each sample point under each operating condition is 1. Therefore, the constraint condition satisfied by Equation (7) is:

[0028]

[0029] To find the minimum value of the objective function, the Lagrange multiplier λ is introduced to construct the Lagrangian function:

[0030]

[0031] Equation (9) is differentiated with respect to u cn , v c and λ respectively, and the equation is set to 0 to obtain:

[0032]

[0033] Combining Equations (10)(11)(12), the calculation of the membership degree value and the cluster center of each operating condition is:

[0034]

[0035] Among them, u cn represents the membership value that the nth sample belongs to the cth operating condition, and v c represents the clustering center of the data cluster of the cth operating condition. Since the process variables affecting the change of NOx concentration, such as primary air, secondary air, furnace temperature, and the amount of urea injected by the SNCR system, etc., show different distribution changes under different operating conditions, the FCM algorithm clusters the process variables under the same operating condition according to the similarity of their distribution in the feature space, so as to obtain data clusters with different operating condition distributions in the MSWI process. According to equations (13) and (14), the fuzzy membership matrix U of the input process variables with respect to each operating condition data cluster can be obtained:

[0036]

[0037] Among them, C represents the number of operating conditions, N1 represents the size of the samples to be clustered, and the membership matrix shows the similarity degree of each sample vector affecting NOx concentration with the distribution of each operating condition data cluster. The higher the similarity, the larger the membership value u cn . Then the probability that the process variable belongs to the cth operating condition is higher, and the sum of the membership degrees of the same sample vector under each operating condition is 1, as shown in equation (8). In order to accurately define the operating condition category to which the sample vector belongs, the membership threshold t is used in this paper to perform "soft partitioning" on the data, as shown in equation (16). When u cn >t, the corresponding sample q n belongs to the cth category. If the value of t is too large, a small number of sample vectors form their own categories, and the functional significance of the sub-models established under each operating condition is enhanced, resulting in a decrease in the generalization ability of this module for some critical points, that is, sample vectors on the edge of the operating condition; if the value of t is too small, the difference between operating conditions is too small, and the functional significance of each sub-model is reduced, which violates the original intention of "divide and conquer". In order to balance the two problems, this paper compares the influence of different t values on the module performance by the trial-and-error method, and finally determines that the value of t is 0.36.

[0038] {cluster(q n ) = c | u cn >t} (16)

[0039] Among them, cluster(·) is used to judge the operating condition category to which the sample q n belongs. After the task decomposition, the influencing variables of NOx emission concentration can be clustered into C operating conditions.

[0040]

[0041] Among them, FCM(·) represents the adopted FCM algorithm, t represents the membership threshold, and Q1 represents the dataset to be clustered. represents the data clusters under the first, second, and Cth operating conditions obtained after clustering. Then

[0042] After obtaining the data clusters under C operating conditions through clustering, a modular neural network is used to process different subsets "divide and conquer". Since the RBF network has a simple structure and can approximate any nonlinear function, the newrb function in matlab2014a is used in this paper to construct the nonlinear mapping relationship between the process variables and NOx under different MSWI operating conditions. This function uses the predetermined accuracy and the number of hidden layer nodes as the training stop mechanism.

[0043] The RBF network consists of three parts: the input layer, the hidden layer, and the output layer. The input layer transmits the process data that affects NOx into the network. For the data cluster under the cth operating condition use and to represent the first, second, and Pth process variables under the nth training sample respectively. These process variables are used as the input of the RBF network; the hidden layer completes the nonlinear transformation from the input space to the hidden space through H basis functions to achieve the high-dimensional mapping of MSWI process variables. Denote the number of nodes in the hidden layer as H; the output layer performs a linear weighted combination in the new space to obtain the NOx test result. For any sample under the kernel function of the RBF neural network can be expressed by the following formula

[0044]

[0045] Among them, represents the nth process variable under the cth class of MWSI operating conditions, θ h and σ h are the center and width of the hth radial basis function respectively. represents for this sample, the output of the hth hidden layer node. Then the actual output value of the NOx emission concentration is expressed as

[0046]

[0047] Among them, w0 is the bias. wh(h = 1, ..., H) are the connection weights between the hidden layer and the output layer. The least squares algorithm is used to optimize the parameters in the newrb function, and the mean square error (MSE) is used as the model performance index, as shown in Equation (20).

[0048]

[0049] Among them is the true value of the NOx concentration corresponding to the nth training sample, and N c is the number of samples of the process variables under the same operating condition of the cth category. To ensure the calculation time and efficiency, MSE is preset to 0.001 in this paper, and the maximum number of nodes H in the hidden layer max is 40. Then the value of H can be determined according to the preset MSE and H max When the RBF network reaches MSE or H max , the number of nodes in the hidden layer will no longer increase.

[0050] When a certain process variable activates multiple sub-models simultaneously, it indicates that this process variable complies with the operating conditions of multiple MSWIs, and it is necessary to comprehensively evaluate the ability of each sub-model to measure the NOx concentration. Since each sub-model has the characteristic of "divide and conquer", their respective functions have significant differences, and there is a non-linear mapping relationship between the NOx concentration test results and the true values. To better integrate the outputs of the sub-models, the FCC neural network is used for integration in this paper. The training of the FCC network is completed by the second part of the dataset Q2. Suppose there are nun groups of process variables activating multiple RBF sub-modules in the dataset Q2, and the number of activated modules is denoted as mod (mod < C).

[0051] Among them, respectively represent the measurement of the NOx concentration by the 1st and the modth modules in the activated sub-modules. The number of sub-modules activated by the process variable under different operating conditions is equal to the number of input nodes of the FCC neural network. Therefore, the number of input nodes of the FCC network is mod, b represents the bias of the network, and its input can be set to +1, ρ represents the input weight, that is, ρ = [ρ 11 , ρ 12 , ..., ρ 1F ; ...; ρ mod,1 , ρ mod,2 , ..., ρ mod,F ; ρ b,1 , ..., ρ b,f , ..., ρ b,F , ρ 11 , ρ 12 , ..., ρ 1FDenote the weights between the first input node and each network node; ρ mod,1 , ρ mod,2 ,..., ρ mod,F Denote the weights between the mod-th input node and each network node; ρ b,1 ,..., ρ b,f ,..., ρ b,F Denote the biases of the first, f-th, and F-th nodes; W represents the internal weights between network nodes, i.e., W = [w 12 , w 13 ,..., w 1F ; w 23 ,..., w 2F ;...; w F-1,F , then ψ = [ρ, W], and ψ is used to represent all weights. Denote the integrated output of the module's different NOx concentration prediction capabilities for the same process variable (the n-th process variable) under multiple operating conditions, y n represents the true value of NOx corresponding to this sample, F represents the number of network nodes. Considering the depth of the FCC network itself, the larger the F value, the more complex the network structure. Considering that the NOx measurement results under different operating conditions have certain similarities and the number of samples input into the FCC network is limited, after multiple experiments, this paper selects F as 4. Select tanh(·) as the activation function for the first F - 1 neurons, and tanh(·) is expressed as

[0052]

[0053] where net f represents the input of the f-th node in the network. The last neuron F linearly sums all the inputs to obtain the final output. Then the integrated output of the FCC network for the NOx prediction value is

[0054]

[0055] where f(·) represents the non-linear mapping between the sub-module output and the NOx prediction value of the FCC network.

[0056] The effects of the present invention are mainly manifested in: (1) The proposed modular neural network captures the internal distribution characteristics of input variables through task decomposition, establishes a NOx emission concentration measurement model under different operating conditions, and finally integrates the output results of each module through the FCC neural network, realizing the soft measurement of the NOx concentration in the MSWI process tail gas; (2) Different from the traditional weighted integration method, the FCC neural network is used in this paper to integrate the outputs of sub-modules, and a small number of neurons are used to reflect the non-linear relationship between the NOx true value and the NO measurement value of the sub-module, improving the accuracy of the soft measurement model. Description of the Drawings

[0057] Figure 1 is the data segmentation diagram of the present invention

[0058] Figure 2 is the topological structure diagram of the RBF neural network of the present invention

[0059] Figure 3 is the topological structure diagram of the FCC neural network of the present invention

[0060] Figure 4 is the fitting training and test result diagram of the sinE function of the present invention

[0061] Figure 5 is the fitting test error curve of the sinE function of the present invention

[0062] Figure 6 is the soft measurement result of the NOx concentration in the MSWI of the present invention

[0063] Figure 7 is the test error of the soft measurement model of the present invention Detailed Embodiments

[0064] The simulation experiments in this paper are divided into two parts. First, the performance of the modular neural network model is verified by using the benchmark experiment (sinE function fitting), and then the actual data of the MSWI plant is used to conduct industrial experiments on this model. By comparing with the existing methods, the effectiveness of the proposed algorithm is demonstrated.

[0065] Combining the mRMR algorithm selection results with the solid waste incineration mechanism, 20 features are finally determined in this paper, as shown in Table 2.

[0066] Table 2 Feature Selection Results

[0067]

[0068]

[0069] After feature selection by the mRMR algorithm, combined with the mechanism of solid waste incineration, the NOx emissions are considered from two parts: generation and elimination. From the analysis of the generation process, it is mainly related to temperature and air volume. From the consideration of the elimination process, it is mainly related to the injection amount of urea in the SNCR system and the adsorption amount of activated carbon in the flue gas purification system. After the above analysis, 20 final features are obtained.

[0070] The expression of the sinE function is

[0071] y = 0.8 * sin(10x) * e -0.2x x ∈ (0, 1) (27)

[0072] The training data is 1500 groups, and the test data is 500 groups. The fitting effect obtained by using the modular neural network model proposed in the article on the training set and test set and the prediction error of the model on the test set are respectively as Figure 4 and Figure 5 shown.

[0073] The sinE function decreases oscillatingly with the increase of the variable x. Based on the FCM algorithm, the input variables are clustered into three categories, and three sub-modules are correspondingly constructed, where the membership threshold t is 0.36. Figure 4 Among them, the data that only activates a single RBF sub-network is represented by circles, and the data that activates two RBF sub-networks simultaneously is represented by stars. Figure 5 The test error curve shown indicates that the model can fit the benchmark function well.

[0074] In the article, industrial tests are carried out based on the actual data of a certain MSWI plant in Beijing in 2019. A total of 4000 groups of samples are selected, among which 2000 groups of data are used to train the RBF sub-network, 1000 groups of data are used to test the RBF sub-network and train the FCC integrated network, and the last 1000 groups are the test set. First, the input variables of the training set are preprocessed. After task decomposition, the data set is divided into three categories, and three sub-modules are correspondingly constructed. Finally, the NOx outputs of the sub-modules are integrated based on the FCC network. The results obtained on the test set and training set are as Figure 6 shown, and the test error is as Figure 7 shown.

[0075] The training mean square error of the NOx soft sensor model established based on the modular neural network is 20.0096, and the test mean square error is 18.0307. From Figure 6 and Figure 7 it can be seen that the output of the soft sensor model can fit the actual NOx concentration well. In addition, the article also compares this method with other methods, namely single RBF neural network and MNN based on weighted integration. The comparison results are shown in Table 3.

[0076] Table 3 Comparison of NOx prediction results in MSWI

[0077]

[0078] Compared with a single RBF neural network, the modular neural network demonstrates its higher test accuracy, reflecting the superiority of the modular neural network's "divide and conquer" approach. At the same time, the measurement accuracy of the soft sensor model based on the FCC output integration in this paper is higher than that of the MNN network based on weighted integration. This is because the FCC neural network can better capture the non-linear mapping relationship between data, comprehensively analyze the soft sensor capabilities of different MSWI operating conditions for the same sample, and reflect the effectiveness of the FCC neural network.

Claims

1. A soft-sensing method for nitrogen oxides in municipal solid waste incineration process based on modular neural network is characterized by: It includes four parts: data preprocessing, task decomposition, sub-module construction and output integration; First, the original process data is collected from the MSWI power plant, denoted by X. After normalization, outlier removal and feature selection, the dataset Q is obtained. The sample size in Q is N and the number of process variables is P. Then, the FCM algorithm is used to decompose the dataset Q into C groups of data clusters with different operating conditions, denoted by represents the data clusters under the first, second and Cth operating conditions after clustering, where C represents the number of operating conditions, that is, the number of data clusters; then, for each operating condition, a corresponding RBF submodule is constructed, represented by RBF_1, RBF_2, …, RBF_C, respectively, and a nonlinear mapping relationship between the input process variables and NOx is established under different operating conditions; finally, the outputs of multiple simultaneously activated submodels are integrated using the FCC neural network, and the outputs of each submodel are comprehensively evaluated to obtain the final output, where Y train and Y test Respectively; Data preprocessing includes: The Z-score standardization method is used, as shown in formula (1); Among them, x nor_m represents the standardized data of the mth process variable affecting NOx emission concentration, x m Indicates the mth process variable in the original data set, μ m and σ m denote the mean and standard deviation of the mth process variable respectively; The Rajda criterion, which is three times higher than the standard deviation of the NOx concentration data, is used to eliminate outliers in the original data, as shown in formula (2); |y o -m NOx |≥3σ NOx (2) Among them, y o Indicates the NOx concentration data corresponding to the oth raw data sample in the sample, μ NOx and σ NOx Represent the mean and standard deviation of NOx concentration data respectively. The NOx data y that satisfies formula (2) o If it is regarded as an outlier, the oth sample should be removed from the data set. The preprocessed data set is represented by S, then S = [s1,s2,...,s N ] T ,s1,s2,...,s N They represent the first, second, and Nth samples after removing outliers, respectively, and N represents the sample size after removing outliers; Perform feature selection on the data set S obtained after preprocessing, and use MI to measure the relationship between process variables in each data set S. The definition of MI is shown in formula (3); Where I represents the i-th process variable s i and the jth process variable s j The correlation between them, p(s i ) and p(s j ) are s i and s j The probability density function, p(s i ,s j ) is the i-th process variable s i and the jth process variable s j The joint probability density function of , therefore, the correlation between the ith process variable and NOx concentration in the maximization process is expressed as Where D represents the correlation between each process variable and NOx concentration in the data set S, s i and s NOx are the i-th process variable and NOx concentration variable, respectively, and S is the data set after process variable normalization and NOx outlier removal. Similarly, minimizing the redundancy between process variables is expressed as Where R represents the degree of correlation between process variables. Combining Equation (4) and Equation (5) to obtain the evaluation criterion Φ of the mRMR algorithm is: maxΦ(D,R),Φ=DR (6) The dataset after feature selection is denoted as Q, and the sample size and the number of selected process variables are denoted by N and F respectively; The data Q is divided into three parts with a division ratio of 2:1:1, represented by Q1, Q2 and Q3 respectively. The sizes of these three sub-datasets are N1, N2 and N3 respectively. Then Q=Q1∪Q2∪Q3, N=N1+N2+N3, N represents the size of the data set before division. First, Q1 is used to perform task decomposition to obtain process variable subsets under different operating conditions; then the corresponding RBF subnetwork model is trained for the subset under each operating condition, and the mapping relationship between the process variables and NOx under each operating condition is established; then Q2 is used to test the submodels established under each operating condition, and the FCC neural network is trained on the test output of NOx using the submodel; finally, Q3 is used to test the RBF submodel and FCC neural network to complete the test of the entire NOx emission concentration soft measurement model.

2. The method according to claim 1, wherein: The process data is classified into different subsets through task decomposition. In MSWI, the NOx concentration emission characteristics are greatly affected by the composition of the waste entering the furnace, the air volume and the temperature. Therefore, the FCM algorithm is used to cluster the influencing variables of NOx concentration. The sample set to be clustered is Q1, and Represents the first, second, and N1th samples in the set. The FCM algorithm obtains the membership of each sample point to all class centers by optimizing the objective function. The objective function of the FCM algorithm is defined as: Among them, U is composed of u cn The membership matrix is constructed, V represents the cluster center of the data cluster under each operating condition, C represents the number of data clusters, that is, the number of operating conditions, c represents any type of data in the C-th data cluster, that is, any operating condition. Since the operating conditions of the NOx concentration soft measurement are divided into three types, C is selected as 3 in the decomposition process, N1 represents the number of process variable samples, u cn Indicates the membership of the nth sample in Q1 to the cth operating condition and u cn ∈(0,1), r represents the weighted index, the value is 2, v c represents the cth cluster center, q n represents the nth sample in the sample to be clustered Q1; the sum of the membership degree of each sample point under each operating condition is 1, so the constraint condition satisfied by formula (7) is: In order to find the minimum value of the objective function, the Lagrange multiplier λ is introduced to construct the Lagrange function: Formula (9) respectively calculates u cn 、v c Taking the derivative of λ and setting the equation to 0 gives: Combining equations (10), (11), and (12), the membership value and the cluster center of each operating condition are calculated as follows: Among them, u cn Indicates that the nth sample belongs to the cth type of operating condition, v c represents the cluster center of the c-th operating condition data cluster. The FCM algorithm clusters the process variables under the same operating condition according to the similarity of their feature space distribution, thereby obtaining data clusters with different operating condition distributions in the MSWI process. According to Equations (13) and (14), the fuzzy membership matrix U of the input process variables relative to each operating condition data cluster is obtained: Where C represents the number of operating conditions, N1 represents the sample size to be clustered, and the membership matrix shows the similarity between each sample vector affecting NOx concentration and the distribution of each operating condition data cluster. The higher the similarity, the higher the membership value u cn The larger the value is, the higher the probability that the process variable belongs to the cth operating condition, and the sum of the membership of the same sample vector under each operating condition is 1, as shown in formula (8); In order to accurately define the operating condition category to which the sample vector belongs, the membership threshold t is used to take the value of t as 0.36; {cluster(q n )=c|u cn >t}(16) where cluster(·) is used to determine the sample q n The category of the operating condition to which it belongs; after task decomposition, the influencing variables of NOx emission concentration can be clustered into C operating conditions; Among them, FCM(·) represents the FCM algorithm used, t represents the membership threshold, Q1 represents the data set to be clustered, represents the data clusters under the first, second and Cth operating conditions obtained after clustering, then After obtaining C data clusters under different working conditions through clustering, the RBF network is used to "divide and conquer" the different subsets; The RBF network consists of three parts: input layer, hidden layer and output layer. The input layer transmits the process data affecting NOx to the network. The first part of the data set Q1 is obtained after task decomposition. hour, and They represent the first, second and Pth process variables under the nth training sample respectively, and these process variables are used as the input of the RBF network; the hidden layer is constructed through H basis functions Complete the nonlinear transformation from input space to hidden space, realize the high-dimensional mapping of MSWI process variables, and record the number of nodes in the hidden layer as H; the output layer performs linear weighted combination in the new space to obtain the NOx test results; Any sample under The kernel function of the RBF neural network can be expressed as follows: in, represents the nth process variable under the cth type MWSI operating condition, θ h and σ h are the center and width of the h-th radial basis function, Indicates that For this sample, the output of the hth hidden layer node is the actual output value of NOx emission concentration Expressed as Among them, w0 is the deviation, w h (h=1,...,H) is the connection weight between the hidden layer and the output layer. The least squares algorithm is used in the newrb function to optimize the parameters. (Mean square error, MSE) is used as the model performance indicator, as shown in formula (20); in is the true value of NOx concentration corresponding to the nth training sample, N c is the number of samples of process variables belonging to the cth type of operating conditions; set MSE to 0.001, and the maximum number of hidden layer nodes H max is 40, then the value of H is determined based on the pre-set MSE and H max When the RBF network reaches MSE or H max When , the number of hidden layer nodes no longer increases; The training of the FCC network is completed by the second part of the data set Q2. Assume that there are nun sets of process variables in the data set Q2 to activate multiple RBF submodules, and the number of activated modules is recorded as mod (mod <C), The number of input nodes of the FCC network is mod, b represents the bias of the network, and its input can be set to +1, and ρ represents the input weight, that is, ρ = [ρ 11 ,ρ 12 ,...,ρ 1F ;...;ρ mod,1 ,ρ mod,2 ,...,ρ mod,F ; ρ b,1 ,...,ρ b,f ,...,ρ b,F ],ρ 11 ,ρ 12 ,...,ρ 1F Represents the weight between the first input node and each network node; ρ mod,1 ,ρ mod,2 ,...,ρ mod,F represents the weight between the mod-th input node and each network node; ρ b,1 ,...,ρ b,f ,...,ρ b,F represents the bias of the 1st, fth, and Fth nodes; W represents the internal weight between network nodes, that is, W = [w 12 ,w 13 ,...,w 1F ;w 23 ,...,w 2F ;...;w F-1,F ], then ψ=[ρ,W], and ψ is used to represent all weights; It represents the integrated output of the modules’ prediction capabilities for different NOx concentrations of the same process variable, i.e., the nth process variable, under multiple operating conditions. n represents the true value of NOx corresponding to the sample, F represents the number of network nodes, and F is 4; We choose tanh(·) as the activation function for the first F-1 neurons. Tanh(·) is expressed as Among them, net f Represents the input of the fth node in the network. The last neuron F performs linear summation on each input to obtain the final output. The integrated output of the FCC network for the NOx prediction value is for where f(·) represents the nonlinear mapping between the submodule output and the FCC network’s NOx prediction value.

Images