CN113869359A

CN113869359A - Modular neural network-based prediction method for nitrogen oxides in urban solid waste incineration process

Info

Publication number: CN113869359A
Application number: CN202110948598.7A
Authority: CN
Inventors: 乔俊飞; 段滈杉; 蒙西; 汤健
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2021-08-18
Filing date: 2021-08-18
Publication date: 2021-12-31
Anticipated expiration: 2041-08-18
Also published as: CN113869359B

Abstract

A modular neural network-based prediction method for nitrogen oxides in an urban solid waste incineration process belongs to the field of solid waste treatment, and tail gas emission control is a main problem in an MSWI process. The accurate prediction of the NOx concentration has important significance for improving the SNCR denitration efficiency and reducing the NOx emission. In the invention, a modular neural network-based NOx prediction method is developed. Firstly, dividing time series data by adopting an exponential smoothing prediction method, and dividing the data into subsets with different distribution characteristics; secondly, aiming at different subsets, establishing corresponding sub-networks by adopting radial basis functions to realize the prediction of NOx; and finally, measuring the matching degree of the test sample and each subset by adopting a measurement method based on Euclidean distance, thereby selecting a proper sub-network for testing. The effectiveness of the proposed method is verified based on the actual industrial data of a certain MSWI plant.

Description

Modular neural network-based prediction method for nitrogen oxides in urban solid waste incineration process

Technical Field

The invention belongs to the field of urban solid waste incineration.

Background

With the increase of population and the acceleration of urbanization process, the yield of Municipal Solid Waste (MSW) is increased year by year, and the MSW clearing volume in China reaches about 2.42 hundred million tons as late as 2019^[1]. In recent 20 years, the MSW incineration (MSWI) power generation technology has rapidly developed in China due to the advantages of reduction, reclamation and harmlessness, and becomes one of the main modes of MSW disposal in China. However, pollution emission control remains a major problem for MSWI processes, such as nitrogen oxides (NOx, mainly including NO and NO)₂). The MSWI has a very complex operation process, and if the MSWI is improperly controlled, the emission of nitrogen oxides exceeds the standard, so that secondary pollution is brought to the environment. At present, in MSWI plants, Selective non-catalytic reduction (SNCR) denitration technology is adopted to further reduce NOx emission, and urea diluent is sprayed into flue gas in a hearth, so that NOx in the flue gas and urea are subjected to chemical reaction to convert NOx into N₂The denitration efficiency depends on the amount of sprayed urea diluent, and if the amount of sprayed urea diluent is small, the SNCR denitration efficiency is affected, so that the concentration of NOx is increased, and the pollutant emission exceeds the standard; if too much urea diluent is injected, excess urea can cause ammonia slip and unreacted NH₃Discharged out of the boiler, not only pollutes the atmosphere, but also can be mixed with SO in the flue gas₃And the acidic gases form ammonium salts, corroding and plugging downstream equipment. Obviously, timely and accurate urea diluent spraying can realize low emission of NOx, low ammonia leakage and low by-product.

The SNCR control system adjusts the spraying amount of the urea diluent according to the emission of NOx in tail gas, the MSWI measures the concentration of the NOx by adopting a Continuous flue gas emission monitoring system (CEMS), but the measurement result of the CEMS has larger hysteresis due to the characteristics of an SNCR reaction mechanism and longer transmission distance of flue gas, so that the denitration efficiency of the SNCR control system is reduced. Therefore, accurate prediction of the NOx concentration is the key to ensure reliable control of the SNCR system and to improve the denitration efficiency.

Currently, some researchers have focused on using soft-measurement methods to achieve prediction of NOx concentration. Li and the like^[2]In order to solve time-varying characteristics and nonlinearity in NOx prediction, a soft measurement method of local weighted regression based on moving window partial least squares is provided to realize the prediction of NOx; due to the good nonlinear mapping capability of LSSVM, an adaptive LSSVM is also applied to the real-time prediction of NOx^[3][4]. Although these methods achieve good predictive results, they rely on a single model. The MSWI process has the characteristics of high nonlinearity, dynamics, system uncertainty and the like, is influenced by time-varying characteristics, and industrial time series data follow different distributions under different operating conditions, so that a single global model is difficult to accurately describe local characteristics of a complex process.

The modularized neural network starts from a simulated human brain information processing mechanism, decomposes a complex task into a plurality of simpler subtasks through a divide-and-conquer strategy, establishes a corresponding sub-network model based on each subtask, and improves the precision of the model. To improve the accuracy of model prediction in time-varying processes, Hoori et al^[5]Clustering data using K-d tree algorithm, constructing multi-column RBF neural network for power load prediction, and similarly, Wang et al^[6]And a density-based clustering algorithm is adopted to carry out task decomposition on the data, and an LSTM sub-network prediction model is established, so that the power load prediction precision is improved. Compared with a single model, the modularized neural network reduces the complexity of tasks through task decomposition, establishes a local network model based on subtasks and improves the prediction precision of the model.

In summary, the MSWI process-oriented NOx prediction method based on the modular neural network is provided, and comprises four parts, namely firstly, carrying out normalization preprocessing on data to eliminate the influence of dimensions among different variables; then, dividing time sequence data by adopting an exponential smoothing prediction-based method, and dividing original data into subsets with different working condition distributions; then, aiming at each subset, establishing a corresponding sub-network model by using an RBF neural network to realize the prediction of NOx concentration; finally, in order to improve the prediction precision of the test sample, a sample matching method based on Euclidean distance is adopted to determine the type of the test sample, the prediction of the test sample is completed, and the effectiveness of the method is verified based on the actual industrial data of certain MSWI factory in Beijing.

Disclosure of Invention

The study object of this document is the MSWI factory in Beijing. The process flow of the MSWI plant is shown in figure 1.

The process comprises 5 subsystems, namely a solid waste storage and transportation system, a solid waste incineration system, a waste heat boiler system, a steam power generation system and a flue gas treatment system. Firstly, collecting solid waste by a special transport vehicle, and then transporting the collected solid waste to a solid waste pool for composting and fermentation; then, solid waste is put into a hopper by a manually operated grab bucket, enters a hearth through a feeder, and passes through a drying grate, a combustion grate 1, a combustion grate 2 and a burn-out grate to realize full combustion; then the waste heat boiler system and the steam power generation system use the heat generated in the process for steam power generation; finally, toxic substances and particles in the flue gas are purified in the flue gas treatment system.

The mechanism of NOx formation and elimination is shown in FIG. 2. In the actual MSWI process, there are two main sources of NOx, respectively: n in air₂And nitrogen-containing organic matters in the solid waste. When the temperature is about 1800K, N in the air₂Is oxidized into NOx at high temperature, and moreover, nitrogen-containing organic matters (mainly comprising CHi) in the solid waste are extremely easy to react with N₂NOx is generated. In order to eliminate NOx produced during combustion, MSWI plants use SNCR processes for denitration. The SNCR control system sprays dilute solution of urea into the hearth, the urea is decomposed into NH3 at high temperature, and NOx is converted into N through chemical reaction₂So as to achieve the aim of denitration. In the denitration process, the injection amount of the urea diluent is a key influence on the denitration efficiency, if the injection amount is too small, the emission amount of NOx is increased, and if the injection amount is too large, excessive urea can cause ammonia to escape and corrode a flue gas sampling device, so that the NOx concentration needs to be predicted to ensure the denitration efficiency of SNCR, and the NOx emission is reduced.

Due to the influence of a plurality of process variables such as the composition of garbage entering a furnace, the temperature, the air volume and the like, the MSWI process has strong time-varying characteristics and uncertainty, and NOx has different distribution characteristics under different working conditions, aiming at the characteristics, a modular neural network method is constructed to predict the NOx concentration under different working conditions, and a modeling strategy is shown in figure 3.

In FIG. 3, x^ori_1,x^ori_2,...,x^ori_NRespectively representing original process variables collected from a hearth under the influence of complex environmental changes in the hearth, wherein abnormal values are easy to appear in data collected by a sensor, and different variable dimensions are different, so that abnormal value elimination and normalization processing operation needs to be carried out on the original data, and after data preprocessing, the obtained data is represented as x¹,x²,...,x^NThen, the time series data is divided by adopting a method based on exponential smooth prediction, and the data is divided into K +1 sections which are respectively expressed as X₁,X₂,...,X_K+1(ii) a Then, aiming at each subset, establishing a corresponding sub-network by adopting an RBF neural network, and carrying out NOx prediction on data with different working condition distributions; finally, carrying out optimal working condition matching on the test sample on the test set according to the distance between the sample point and the center of each time sequence subset, and realizing the prediction of NOx on the test set;

the functions of the modules are respectively as follows:

(1) a data preprocessing module: and carrying out abnormal value elimination and normalization processing on the original process variable.

(2) A time sequence data segmentation module: dividing time series data by adopting an exponential smooth prediction-based method, and dividing the time series data into subsets with different distribution characteristics;

(3) a sub-network construction module: a sub-network model based on subset driving is established by adopting RBF, so that the accuracy of NOx prediction is improved;

(4) a test sample matching module: and determining the membership class of the sample by calculating the shortest Euclidean distance between the test sample and the central point of each subset, and selecting a corresponding sub-network model for prediction.

NOx values are collected by the CEMS and are influenced by the complex environment in the hearth, and the collected NO is caused by faults of the CEMS due to various reasons in the use processAbnormal values of the x value are generated, the abnormal values bring great interference to the analysis of the data, and the abnormal values need to be detected and eliminated. Using Rajda's criterion^[7]Namely, the method which is three times higher than the standard deviation of the data eliminates the abnormal value in the original data, as shown in formula (1):

wherein, mu^NOxAnd σ^NOxThe abnormal value satisfying the formula (1) is the mean and variance of NOx, respectively

And (5) removing from the data set. In order to eliminate dimensional differences between variables and improve the accuracy of the model, the Z-score method is used to normalize the original process variables as shown in equation (2):

wherein x is^mData, x, representing the normalized mth process variable affecting NOx emissions^ori_mRepresents the mth process variable, μ, in the collected data set^mAnd σ^mRespectively, mean and standard deviation of the mth process variable. The preprocessed data set is denoted X, X ═ X₁,x₂,...,x_N]＝[x¹,x²,...,x^M]^T,X∈R^N×MWhere N represents the sample size and M represents the number of process variables.

The MSWI process has the characteristics of high nonlinearity, dynamics, system uncertainty and the like, is influenced by time-varying characteristics, and industrial time series data follow different distributions under different operating conditions, so that a single global model is difficult to accurately describe local characteristics of a complex process. The method for exponential smooth prediction is simple in calculation, high in solving speed andthe accuracy of the division is high^[8]Therefore, the method of single-based exponential smooth prediction is adopted in the text to segment the NOx time series data. The single exponential smoothing method is shown in equation (3):

S_t＝a·y_t-1+(1-a)S_t-1 (3)

wherein S is_tAnd S_t-1Indicating the exponentially smoothed values at time t and t-1, respectively, y_t-1Is the true value at time t-1, a represents the exponential smoothing factor;

by iterative computation, equation (4) can be written as:

in order to obtain good prediction performance, two indexes, namely a smoothing factor a and a smoothing initial value S, need to be considered₀. The smoothing factor a reflects the difference between the smooth value and the real value, if the value of a is close to 1, the real value of the historical time has little influence on the smooth value of the t moment, and the accumulated error is increased therewith, otherwise, if the value of a is close to 0, the real value of the historical time has great influence on the smooth value of the t moment, and a good smoothing effect can be generated. Smoothed initial value S₀Determined by equation (5):

the time sequence segmentation method based on the exponential smoothing prediction is summarized as follows:

step 1: initializing a segmentation point set SegNum, an error vector Err, a total residual error TSE and a smooth initial value S₀The compression ratio p;

step 2: calculating a smoothed value S at time t_t；

Step 3: calculating the absolute prediction error, Err, at time t_t＝|y_t-S_t|；

Step 4: updating Err mean μ^ErrAnd standard deviation σ^Err；

Step 5: determination of Err_tIf Err is in the distribution interval of_tIn the interval [ mu ]^Err-p*σ^Err,μ^Err+p*σ^Err]Then y is determined_tSegNum (t) y as a division point_tAnd reinitializing S according to equation (5)_t(ii) a Otherwise, return to Step 2;

dividing the time sequence data to obtain K division points, and dividing the data set X into K +1 subsets according to the K division points, wherein the X subsets are respectively expressed as X₁,X₂,...,X_K+1；

After K +1 subsets are obtained by time-sequential segmentation, the different subsets are processed "divide-by-divide" using a modular neural network. Because the RBF network has a simple structure and can approach any nonlinear function, a corresponding RBF neural network is established for each subset, and the RBF neural network consists of three parts, namely an input layer, a hidden layer and an output layer as shown in FIG. 4; the input layer transmits potential auxiliary variables affecting NOx into the network in a first subset X of segments₁For example, the input of the neural network is

These variables represent the first segment subset X, respectively₁The 1 st, 2 nd, as well as the M auxiliary variables under the nth training sample; the hidden layer comprises H hidden layer nodes, each node selects a Gaussian kernel function as a basis function, and the basis functions are respectively used

And (3) representing that the nonlinear mapping from the input space to the hidden layer space is completed, and the calculation of the Gaussian kernel function is shown as the formula (7):

wherein x_1,nRepresents a subset X₁The nth sample in (1), c_hAnd σ_hRespectively representing the center and width of the h-th hidden node,

and representing the output of the h hidden layer node, the output of the RBF neural network for predicting the NOx concentration is as follows:

wherein, w₀Indicates a deviation, w_h(H ═ 1, …, H) represents the weight between the hidden node and the output node;

parameter c of the network_h，σ_h，w_hUsing a second-order LM algorithm^[9]Training adjustment is carried out until the desired precision is achieved, and the updating rule of the algorithm is as follows:

Δ_n+1＝Δ_n-(Q_n+μ_nI)^-1g_n (9)

where Δ is all the parameters to be trained of the network, including center c, width σ and weight w, i.e., Δ ═ c₁,...,c_H,σ₁,...,σ_H,w₀,w₁,...,w_H]Q is the Hessian matrix, μ_nIs step size, I is identity matrix, g represents gradient vector;

the Hessian matrix Q is obtained by summing Hessian submatrices:

wherein N is₁Is a subset X₁Number of samples j contained in_nIs a jacobian component, represented by equation (11):

the gradient vector g is obtained by summing the gradient sub-vectors:

wherein

Predicted value indicating NOx concentration

And expected value

The difference of (a):

the Root Mean Square Error (RMSE) is used as a model performance index, and is shown as a formula (17):

in order to select a proper sub-network to accurately evaluate a test sample, a membership class k of the test sample needs to be determined, Euclidean distance is selected as a basis for measuring the similarity of the sample, namely, the Euclidean distance between the test sample and the center of each sub-set is calculated, the class corresponding to the center of the sub-set with the shortest distance to the test sample is determined as the class of the current test sample, and the test result is tested by the corresponding sub-network;

the center point of the subset should satisfy the following condition: the sum of the distances to the point, except the center point, of all the other points is minimal, i.e. the

A point x satisfying the formulas (18) and (19)_c1As subset X₁Center point of (1), same principle, x_c2,...,x_c(K+1)Is a subset X₂,...,X_K+1A center point of (a);

determining the membership class of the test sample by selecting the central point closest to the test sample:

cluster(x_test)＝min dist(x_test,x_ck),k＝1,2,...,K+1 (20)

the k value satisfying the formula (20) was taken as a test sample x_testIs of a membership class of x_testBy the sub-network RBF_kGiven, as shown in equation (21):

wherein, c_k，σ_k，w_kAs a subnetwork RBF_kParameters obtained after training.

Drawings

FIG. 1A process flow of a certain MSWI factory in China

FIG. 2NOx formation and elimination mechanism

FIG. 3 NOx prediction framework based on modular neural networks

FIG. 4RBF neural network topology structure diagram

FIG. 5 NOx time series data partitioning results based on exponential smoothing prediction

FIG. 6 sub-network 1 training results

FIG. 7 sub-network 2 training results

FIG. 8 sub-network 3 training results

FIG. 9 training Performance of a Modular neural network

FIG. 10 test sample matching results

FIG. 11 Modular neural network test results

FIG. 12 Modular neural network test results

Detailed Description

The text is based on the results of the MSWI factory, Beijing, 10 months, 17 days, 15, 2019: 19: 23-21: 36: a total of 11314 actual data sets were subjected to industrial experiments during 39 hours. After the preprocessing operation, 273 groups of abnormal values are eliminated altogether, and 11041 groups of normal data are reserved. Because MSWI process operating mode is complicated and is influenced by different staff's operation means and presents a plurality of distribution characteristics, in order to make the training process of model cover a plurality of operating modes as far as possible, select 9500 group of data as the training set in the experimentation, 1541 group of data is as the test set. On the training set, the NOx time series data is divided by using a method based on exponential smoothing prediction, and the obtained division result is shown in fig. 5.

In the time series data segmentation stage, two parameters, namely a smoothing factor a and a compression rate p, need to be artificially determined. These two parameters affect the prediction performance and the error distribution, respectively, and therefore, the two parameter values are 0.58 and 0.6, respectively, as determined by trial and error in the experimental process. From the dividing line in fig. 5, 2 dividing points can be obtained: 3658 and 6830. The two division points divide the NOx time sequence data into three subsets, the distribution situation in each subset is different as can be seen from the graph, and when the distribution characteristics are changed, the change can be captured by detecting an error interval based on an exponential smoothing prediction method, so that the division of the working conditions is realized.

And establishing corresponding RBF neural network prediction models aiming at the three subsets. The RBF neural network structure adopted in the method is 11-8-1, 11-8-1, 11-10-1, and the number of nodes of the hidden layer is obtained by a trial and error method. The training results for the subnetworks are shown in fig. 6-8, the training RMSE is 4.0957, and the fitting effect of the modular neural network on the training set is shown in fig. 9. Under different working conditions, the sub-network has good training performance.

And after the network training is finished, testing the network by adopting the test sample. In order to determine the class to which the sample to be tested belongs, the test sample needs to be matched with the training subset, and fig. 10 shows the matching result. The 916 groups of data in the test sample belong to the first class subset, the 617 groups of data belong to the third class subset, and the test results are respectively tested by using the

sub-networks

1 and 3, as shown in fig. 11 and 12, the predicted values of the modular neural network can be better fitted to expected values, have higher prediction accuracy, the test RMSE is 6.0953,

a modular neural network based MSWI process NOx prediction method is presented herein. Different from the traditional modularized neural network method, the method based on exponential smoothing prediction is adopted in the text to segment data so as to complete task decomposition, and the data under different working conditions are divided by capturing the change of data distribution; in addition, the RBF sub-network model established based on the specific subset has high prediction precision, and the prediction performance of the modular neural network model is improved.

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Claims

1. The prediction method of nitrogen oxides in the urban solid waste incineration process based on the modular neural network is characterized by comprising the following steps:

the method comprises four parts, namely data preprocessing, time sequence segmentation, submodule construction and data matching;

first, raw data is collected from the DCS system of the MSWI power plant and X is used^oriIs represented by the formula, wherein X^ori∈R^N×MR represents a real number set in the mathematical definition, N represents the sample size, and M represents the number of auxiliary variables; the data set after preprocessing is expressed as X, and X belongs to R^N×M(ii) a Then, a dividing method based on exponential smoothing prediction is adopted to divide the NOx time sequence set, different operating conditions are established by capturing different distribution characteristics of NOx, and K dividing points SegNum ═ s are obtained₁,s₂,...,s_K+1Dividing the input space X according to K dividing points to obtain K +1 time sequence subsets; then, RBF sub-networks under corresponding working conditions are established for different subsets, and are respectively represented by RBF _1, RBF _2And performing optimal working condition matching on the test sample on the test set according to the distance between the sample point and the center of each time sequence subset, so as to realize the prediction of NOx on the test set.

2. The method of claim 1, wherein:

removing abnormal values in original data by adopting a Rajda criterion, namely a method of three times of standard deviation higher than data, as shown in formula (1):

Removing from the data set;

then, the raw variables are normalized by a Z-score method, as shown in formula (2):

wherein x is^mRepresenting normalized data of the mth auxiliary variable, x^ori_mRepresenting the m auxiliary variable, mu, in the acquired raw data set^mAnd σ^mRespectively, mean and standard deviation of the mth process variable.

3. The method of claim 1, wherein:

a time sequence segmentation method based on exponential smoothing prediction is adopted to divide time sequence data into different stages, and the exponential smoothing method is shown as a formula (3):

S_t＝a·y_t-1+(1-a)S_t-1 (3)

wherein S is_tAnd S_t-1Respectively representing time t and time t-1Exponential smoothing value of scale, y_t-1Is the real value sampled at the time of t-1, and a represents an exponential smoothing factor;

by iterative computation, equation (3) is written as:

wherein

Denotes the initial value of the smoothing at the initial time, a denotes the smoothing factor, y_iRepresenting the true value of NOx, t, at the i-th moment₀Indicating the initial time, smoothing the initial value

Determined by equation (5):

wherein, y₁And y₂The real NOx values sampled at the time t-1 and t-2 are respectively shown;

step 1: initializing a segmentation point set SegNum, the number of segmentation points num, an absolute error vector Err and a smooth initial value

A compression rate p, wherein SegNum [ [ alpha ] ]]，Err＝[]Num is 0, smoothing the initial value

Calculated from equation (5), the compression ratio p and the smoothing factor a are respectively p ═ 0.6, and a ═ 0.45;

step 2: calculating a smoothed value S at the ith time according to equation (4)_i；

Step 3: calculating an absolute prediction error at the ith time according to equation (8);

err_i＝||y_i-S_i|| (6)

step 4: updating the Err mean value μ according to the equations (5) and (6)^ErrAnd standard deviation σ^Err；

Step 5: determination of err_iIf err is_iIn the interval [ mu ]^Err-p*σ^Err,μ^Err+p*σ^Err]Wherein, mu^ErrAnd σ^ErrRespectively representing the mean and standard deviation of the absolute prediction error vector Err, and p represents the compression ratio, then y is determined_iAs the division points, the number of the division points is calculated as

num＝num+1 (9)

Segnum (num) y_iAnd reinitializing according to equation (5)

Otherwise, return to Step 2;

wherein, y_t+1And y_t+2After the division point is determined, real values obtained by sampling at the time t +1 and the time t +2 respectively are represented,

representing the initial value smooth value after reinitialization;

after the time-series data has been segmented,the resulting number of segmentation points is denoted by K, which divides the data set into K +1 subsets, denoted X respectively₁,X₂,...,X_K+1The K value does not need to be specified, and is automatically determined by an algorithm according to the distribution interval of the absolute prediction error;

the method based on exponential smoothing prediction is finally determined as two division points, namely K is 2, the NOx time sequence data is divided into three parts, each divided subset has obvious data distribution difference, and the initial value is smoothed

The value of (b) is calculated according to equation (5).

4. The method of claim 1, wherein:

aiming at each subset, establishing a corresponding RBF neural network, wherein the RBF neural network consists of three parts, namely an input layer, a hidden layer and an output layer; the input layer transmits potential auxiliary variables affecting NOx into the network in a first subset X of segments₁For example, the input of the neural network is

x_1,nRepresenting the nth sample in the segment 1 subset,

the chalk representing a first subset X of segments₁The 1 st, 2 th, the.. multidot.M auxiliary variables under the nth training sample, wherein M represents the number of the auxiliary variables of the training sample, namely the number of neurons in an input layer; the number of hidden nodes in the hidden layer is represented by H, and each node selects a Gaussian kernel function as a basis function and uses the Gaussian kernel function as the basis function

And (3) representing that the nonlinear mapping from the input space to the hidden layer space is completed, and the calculation of the Gaussian kernel function is shown as the formula (11):

wherein x_1,nRepresents a subset X₁The nth sample in (1), c_hAnd σ_hRespectively representing the center and width of the h hidden layer neuron,

and the output of the h hidden layer node is shown, the subscript h represents the h node in the hidden layer, and the output of the RBF neural network for predicting the NOx concentration is as follows:

wherein, w₀Indicates a deviation, w_h(H1, … H.., H) denotes the weight between the H-th hidden layer neuron and the output node, x_1,nDenotes the nth sample in the 1 st subset, c_hAnd σ_hRespectively representing the center and width of the h hidden layer neuron;

by c_h，σ_h，w_hRespectively representing the center, width and weight of the h-th neuron of the hidden layer, training and adjusting the parameters by adopting a second-order LM algorithm until the expected precision is reached, wherein the updating rule of the algorithm is as follows:

Δ_n+1＝Δ_n-(Q+μ_nI)^-1g (13)

where Δ is all the parameters to be trained of the network, including center c, width σ and weight w, i.e., Δ ═ c₁,...,c_h,...,c_H,σ₁,...,σ_h,...,σ_H,w₀,w₁,...,w_h,...,w_H]Wherein c is_h，σ_hAnd w_hRespectively representing the center, width and weight of the H hidden layer neuron, wherein the value range of H is [1,2]H represents the number of hidden layer neurons, Q is a Hessian matrix, mu_nIs step size, I is identity matrix, g represents gradient vector；

The Hessian matrix Q is calculated as:

wherein N is₁Is a subset X₁Number of samples j contained in_nWhen the input is x_1,nA Jacobian component corresponding to the time; x is the number of_1nRepresents the nth sample in the first subset, represented by equation (15):

wherein,

indicating the difference between the predicted and expected values of NOx concentration for the nth sample, w₀,...,w_HAnd σ₁,...,σ_HWeight and width, w, for the 1 st through H th hidden layer neurons, respectively₀Denotes an offset, c_1,1,...,c_1,M1 st to Mth components representing the 1 st hidden layer neuron center vector, c_H,1,...,c_H,M1 st to Mth components representing the H-th hidden layer neuron center vector, c_hRepresenting the central vector of the h-th neuron in the hidden layer,c_h,mthe mth component, x, representing the center of the h neuron in the hidden layer_nDenotes the nth sample, x_n,mRepresenting the input of the nth sample on the mth input neuron, σ_hRepresenting the width of the h-th hidden layer neuron,

representing the output of the H-th neuron of the hidden layer, the following table H represents the number of neurons of the hidden layer, M represents the number of input nodes, n represents the nth sample, H and M represent the indexes of the input neuron and the hidden layer neuron respectively, and a gradient vector g is obtained by summing gradient sub-vectors:

wherein,

expressed as when the input is x_1,nThe Jacobian component, x, corresponding to time_1,nRepresenting the nth sample in the first subset, calculated as shown in equation (15),

predicted value indicating NOx concentration

And expected value

The difference of (a):

the Root Mean Square Error (RMSE) is used as a model performance index, and is shown as a formula (21):

wherein,

a predicted value that indicates the NOx concentration is indicated,

representing the desired value of the NOx concentration.

5. The method of claim 1, wherein:

with a first subset X₁For example, using x_cen,1Denotes the center point of the subset, subscript cen,1 denotes the center of the first subset, x_cen,1The following conditions should be satisfied: except for the central point x_cen,1Except that the sum of the distances from all the other points to the point is minimum, i.e. the distance between the other points and the point is less than

Wherein x is_nPoint x representing the nth sample and satisfying the equations (22) and (23)_cen,1As subset X₁Center point of (1), same principle, x_cen,2,...,x_cen,(K+1)Is a subset X₂,...,X_K+1A center point of (a);

cluster(x_test)＝min dist(x_test,x_cen,k),k＝1,2,...,K+1 (24)

the k value satisfying the formula (24) is taken as a test sample x_testIs of a membership class of x_testBy the sub-network RBF_kGiven, as shown in equation (25):

wherein the subscript k denotes the test sample x_testClass of activated sub-network, denoted RBF_k，c_k，σ_k，w_kAre sub-networks RBF respectively_kCenter, width and weight parameters obtained after training.