CN114611398B

CN114611398B - Soft measurement method for nitrogen oxides in urban solid waste incineration process based on brain-like modularized neural network

Info

Publication number: CN114611398B
Application number: CN202210266639.9A
Authority: CN
Inventors: 蒙西; 王岩; 乔俊飞
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2022-03-17
Filing date: 2022-03-17
Publication date: 2023-05-12
Anticipated expiration: 2042-03-17
Also published as: CN114611398A

Abstract

The invention relates to a soft measuring method of nitrogen oxides in urban solid waste incineration process based on brain-like modularized neural network, which realizes NO _X The real-time accurate acquisition of the concentration comprises the following steps: firstly, acquiring data; preprocessing the acquired data to determine an input variable and an output variable of the model; then, a brain-like modularized neural network is adopted to establish a soft measurement model; and finally, taking the test data as the input of the model, and verifying the validity of the model. The invention effectively realizes NO _X The real-time accurate detection of the concentration has important theoretical significance and application value.

Description

Soft measurement method for nitrogen oxides in urban solid waste incineration process based on brain-like modularized neural network

Technical Field

The invention relates to Nitrogen Oxides (NO) in urban solid waste incineration process _X ) A soft measurement method; NO based on Brain-like modularized neural network (Brain-Inspired Modular Neural Network, BIMNN) was established _X Soft measurement model, realize NO _X And (5) accurately acquiring the concentration in real time. Not only belongs to the field of urban solid waste treatment, but also belongs to the field of intelligent modeling.

Background

With the rapid development of Chinese economy and the continuous acceleration of the urban process, the urban solid waste yield is increased, and a plurality of cities face the crisis of 'solid waste surrounding cities'. The solid waste incineration treatment mode becomes a main mode of urban solid waste treatment in China increasingly. And NO _X Is one of main pollutants generated in the urban solid waste incineration process, and seriously affects the health of people and the quality of ecological environment. Along with the increasing environmental protection and treatment requirements of China, the NOx emission control becomes one of key problems to be solved urgently in urban solid waste incineration plants, and the real-time accurate detection of NOx is one of important preconditions for improving the denitration efficiency of the urban solid waste incineration plants. Thus, NO is realized _X The real-time accurate detection of the method has important theoretical significance and application value.

Disclosure of Invention

The invention aims to provide a method for generating NO in the urban solid waste incineration process based on a brain-like modularized neural network _X Soft measurement method for establishing NO by adopting brain-like modularized neural network _X Soft measurement model for implementing NO _X And (5) accurately acquiring the concentration in real time.

The invention adopts the following technical scheme and implementation steps:

1. collecting data;

2. determining input and output variables of a model: determining an input variable of a model by adopting a maximum correlation minimum redundancy (mRMR) algorithm, wherein the output variable of the model is NO at the current moment _X Concentration;

the method for determining the input variable of the model by adopting the mRMR algorithm is as follows:

given two random variables a and b, the mutual information between the two random variables is calculated as follows:

wherein I is mutual information between random variables a and b, and p (a) and p (b) are edge probability distributions of the random variables a and b respectively; p (a, b) is a joint distribution of random variables a and b;

first, based on mutual information, searching a feature subset S with the greatest correlation with a variable c to be measured:

wherein ,m_i For the feature variables in the feature subset S, |s| is the number of the feature variables in the feature subset S, D is the correlation between the selected feature variable and the variable c to be measured, and if D is larger, the correlation between the selected feature variable and the variable c to be measured is higher;

considering that certain similarity exists among the selected feature variables, and eliminating the redundant features does not affect the performance of the model, therefore, the redundancy among the features is calculated, and the mutually exclusive features are found:

wherein ,m_i ，n _j For the feature variables in the feature subset S, R is redundancy among the variables in the feature subset S, and the smaller R is, the lower the redundancy is;

in the mRMR algorithm application process, the maximum correlation index D and the minimum redundancy index R are generally unified into an evaluation function Φ=d-R, and then the optimal feature subset S is determined by searching the maximum value of the evaluation function:

maxΦ(D,R),Φ＝D-R (4)

3. designed for NO _X A brain-like modularized neural network model for soft concentration measurement;

(1) Task decomposition

In order to measure the modularization degree of the evaluation network and simulate the characteristics of modularization of the brain network, a modularized index (modularity quality, MQ) oriented to a modularized neural network is provided; the modularization index consists of the degree of density in the modules and the degree of sparsity among the modules, wherein the degree of density in the modules is calculated as follows:

wherein ,J_C For the density in the modules, P is the number of modules in the current network, N _l To the number of samples allocated to the first module, x _i To input samples, h _l and r_l Respectively representing the position and the action range of the core node of the first module;

the degree of sparseness between modules is calculated based on the Euclidean distance:

wherein ,J_S For the degree of sparsity between modules, d (h _l ,h _s ) Representing the distance between the core node of the first module and the core node of the second module, comprehensively considering the density J in the modules _C And degree of sparsity J between modules _S The modularization index weighing mode is proposed as follows:

thus, the greater the value of MQ, the higher the modularization degree of the network, and therefore, a brain-like modularization partitioning method is proposed, and the main idea is as follows: firstly, distributing training samples through a core node, and further determining whether the training samples are distributed to a current existing module or a newly added module; the new core node of the existing module is then determined by seeking the greatest "modularization" degree of the network, and thus the modular structure build can be divided into two cases: adding a new module and updating an existing module;

(1) adding new modules

At the initial moment, the number of modules of the whole network is 0;

after the first data sample enters the network, it is set as the core node of the first sub-module:

h ₁ ＝x ₁ (8)

/>

wherein ,h₁ and r₁ Respectively representing the position and the action range of the core node of the first module, x ₁ An input vector, d, for the first training sample _max For training sample x _i And x _j Maximum distance between;

at time t, when the t training sample enters the network, assuming that k modules already exist, finding the core node nearest to the sample:

wherein ,x_t Is the input vector of the t training sample, h _s Representing the position, k, of the core node of the s-th module _min Training sample for representing distanceThe X is _t The nearest core node;

if the t training sample is not at k _min In the scope of the core node, a new module is needed to learn the current sample, and the parameters of the new module corresponding to the core node are set as follows:

h _k+1 ＝x _t (12)

wherein ,h_k+1 ，r _k+1 For the position and the action range of the core node corresponding to the newly added module, x _t Is the input vector for the t-th training sample,

the furthest distance from other core nodes to the newly added module core node is provided;

(2) optimizing existing modules

Otherwise, the sample is considered to be classified as k _min In the module, in order to make the network have the optimal modularization degree, according to the formula (7), respectively calculating the modularization index value MQ of the whole network under the condition that the current sample and the original core node are respectively used as the core nodes _t And

if it is

The network modularization degree of selecting the current input sample as the core node is considered to be higher, and the existing core node is replaced by the sample to become a new core node, and initial parameters are set as follows:

wherein ,

the new core nodes and the new action ranges of the module are respectively provided; n (N) _k For the number of samples assigned to the kth module;

if it is

The location of the current core node +.>

The range of the node is only required to be adjusted>

And (3) the following steps:

wherein ,

is the original core node of the module;

after all training samples are compared, the samples are distributed to different sub-modules, a partition structure is formed, the modularization degree of the current network can be considered to be the largest, and then the sub-network needs to be built aiming at the task of each sub-module;

(2) Sub-network structure design

Training data set

Is divided into M subsets; />

wherein ,x_i ，y _i The input variable and the output variable of the model respectively,

representing the domain, V is the input vector x _i N is the number of the input variable and the output variable data of the model;

an adaptive task-oriented radial basis function neural network (ATO-RBF) is adopted to construct a sub-network corresponding to each module, and the design of the sub-network comprises three parts: network structure growth, network structure pruning and network parameter adjustment;

(1) network structure growth

The center, radius, and connection weight to the output layer of the first hidden layer node of the s-th module are based on the sample with the largest absolute output

Setting:

wherein ,

for the sample with the largest absolute output, +.>

Respectively representing the input variable and the output variable corresponding to the sample with the largest absolute output, r _s For the range of the s-th module, N _s For samples assigned to the s-th moduleA number;

the center and the radius of the first hidden layer node of the s-th module and the connection weight value to the output layer are respectively;

at time t _s Time, training error vector e (t _s ) Obtained by the formula:

wherein ,y_f Is the desired output of the f-th sample,

is the f sample at time t _s Is calculated by the following formula:

wherein H is the number of neurons in the hidden layer,

is the function of the jth hidden layer node of the s-th module, +.>

For the connection weight of the jth hidden layer node of the s-th module to the output layer, < ->

The center and the radius of the j hidden layer node of the s-th module;

finding a sample with the largest difference between the desired output and the network output

Then, a RBF neuron pair is newly added

The initial parameters of the newly added neurons are as follows:

wherein

and />

Respectively representing the center of the newly added neuron of the s-th module and the connection weight value to the output layer; />

Is->

Input variable corresponding to each sample, +.>

Respectively +.>

The expected output sum for each sample is at t _s A network output value at a moment;

existing neurons have less effect on newly added neurons when the following relationship is satisfied:

wherein

Is the center of the neuron closest to the newly added neuron;

the radius of the newly added neuron is defined by equations (27) and (28):

when neurons are newly added each time, the network parameters are adjusted through a second-order learning algorithm; when reaching the preset maximum structure J _max Or desired training accuracy E ₀ Ending the network structure growth process; in the experimental process J _max ＝10，E ₀ =0.0001, the training accuracy of the network was measured using Root Mean Square Error (RMSE), calculated as follows:

wherein ,y_i and y_i The expected outputs and network outputs of the ith sample, respectively;

(2) network structure pruning

To avoid redundancy in the network structure, it is proposed to measure the contribution value of hidden layer neurons based on the index of the connection weights:

wherein SI (j) is the contribution value of the j-th hidden layer node,

is the weight from the jth hidden layer node of the s-th module to the output layer;

searching for an hidden layer node with the smallest contribution value:

wherein ,

the hidden layer node with the smallest contribution value in the s-th module is J, and the J is the number of hidden layer nodes in the network;

therefore, deleting the hidden node with the smallest contribution, adjusting parameters through a second-order learning algorithm, and comparing the root mean square error value (RMSE_1) after deleting the node with the root mean square error value (RMSE_0) when not deleting the node, wherein the calculation formula of the RMSE is shown as a formula (30); if RMSE_1 is less than or equal to RMSE_0, pruning the selected node under the condition of not sacrificing the network learning capability, and then repeating the process, wherein the selected node cannot be deleted; at this time, the network structure pruning process is finished, and the sub-network construction is completed; each time neurons are deleted, a second-order learning algorithm is used for adjusting parameters;

(3) network parameter adjustment

The second order learning algorithm is as follows:

θ _L+1 ＝θ _L -(Q _L +μ _L E) ^-1 g _L (33)

wherein θ refers to parameters to be adjusted, including center, radius and connection weight, Q is a Hessian-like matrix, μ is a learning coefficient (0.01 in experiment), E is a identity matrix, g is a gradient vector, and L is the number of iteration steps (50 in experiment);

to reduce memory requirements and computation time, the computation of the Hessian-like matrix Q and gradient vector g is converted into a Hessian-like sub-matrix summation and a gradient sub-vector summation:

q _z is a Hessian-like submatrix, eta _z The gradient sub-vectors can be calculated by the following formula:

wherein ,e_z Expected output y for sample z _z Output with network prediction

Is the difference of j _z For the jacobian vector, the following is calculated:

according to the chain derivative rule, each component in the jacobian vector in equation (39) is calculated as follows:

wherein

The center, radius and connection weight to the output layer of the jth neuron of the s-th module, x _z Is the input vector of the z-th training sample;

4、NO _X soft measurement of concentration;

taking the test sample data as input of the brain-like modularized neural network, and outputting the model as NO _X Soft measurement of concentration; at time T, after the T test sample enters the BIMNN, searching a core node closest to the sample, and activating a sub-module to which the core node belongs:

wherein ,x_T An input vector, h, for the T-th test sample _s Is the core node of the s-th module, l _act For distance from the T test sample x _T The nearest core node belongs to a sub-network, A is the number of sub-network modules;

therefore, the actual output of BIMNN is the first _act Output of the sub-network:

wherein ,

for the actual output of BIMNN at time T, < >>

Is the first _act Actual output of the sub-network;

the test precision is quantitatively evaluated by adopting a Root Mean Square Error (RMSE), an average percentage error (MAPE) and a Correlation Coefficient (CC), wherein the calculation formula of the RMSE is shown as a formula (30), and the calculation formulas of the MAPE and the CC are as follows:

/>

in the formula ,y_i And

desired output and network output of the ith sample, N _T To test the number of samples.

The invention has the following obvious advantages and beneficial effects:

1 the invention establishes stable and effective NO based on good nonlinear mapping capability and generalization capability of the brain-like modularized neural network _X Concentration soft measurement model, can realize NO _X Accurate acquisition of concentration in real time, NO in urban solid waste incineration process _X Emission control is of great importance.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a block diagram of a brain-like modular neural network;

FIG. 3 is a block diagram of an ATO-RBF neural network;

fig. 4 is a training result diagram of the sub-network 1;

fig. 5 is a training result diagram of the subnetwork 2;

fig. 6 is a training result diagram of the subnetwork 3;

FIG. 7 is a BIMNN soft measurement model test output diagram;

fig. 8 is a BIMNN soft measurement test error chart.

Detailed Description

The present invention utilizes training data to build a training data for NO _X A brain-like modularized neural network model for soft concentration measurement; verifying NO output by brain-like modularized neural network soft measurement model by using test data set _X Accuracy of real-time concentration.

As an example, the validity of the method provided by the invention is verified by adopting actual data from a solid waste incineration plant in a certain Beijing city. After eliminating obvious abnormal data, 1000 groups of 96-dimensional experimental data are obtained. Based on the obtained data sample, adopting mRMR algorithm to make feature selection, selecting NO _X The 20 variables with larger correlation are used as soft measurement model input variables, and are specifically shown in table 1.

TABLE 1

/>

For 1000 groups of data after dimension reduction, 750 groups of data are used for establishing a soft measurement model, and the rest 250 groups of data are used for testing the performance of the model;

(1) Based on 750 groups of training data, adopting a brain-like modularized partitioning method, dividing the 750 groups of training data into three subsets, wherein the sample number of each subset is 215, 273 and 262 respectively; correspondingly, the BIMNN is formed by 3 sub-networks, and the sub-networks are built through the sub-network building method in the step 3; fig. 4, 5, and 6 are training result diagrams of respective sub-networks, respectively, along the X-axis: training samples number, units are individual/sample, Y-axis: NO (NO) _X Concentration in mg/Nm ³ ；

(2) NO through brain-like modularized neural network based on 250 groups of test data _X Concentration soft measurement, test results are shown in fig. 7, X-axis: the number of samples tested, in units of units/sample, Y-axis: NO (NO) _X Concentration in mg/Nm ³ The method comprises the steps of carrying out a first treatment on the surface of the Test errors as shown in fig. 8, X-axis: training sample number, unit isSample, Y-axis: NO (NO) _X Concentration test error in mg/Nm ³ ；

(3) The test accuracy was quantitatively evaluated using the root mean square error RMSE, the average percent error MAPE, and the correlation coefficient CC, with the calculation result rmse=6.5031, mape= 3.8514, cc= 0.9777.

It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. It should be noted that the above-mentioned embodiments are merely examples of the present invention, and are not intended to limit the invention, but all modifications and optimization within the spirit and scope of the present invention are included in the following claims.

Claims

1. A soft measuring method of nitrogen oxides in urban solid waste incineration process based on brain-like modularized neural network is characterized by comprising the following steps:

step 1, acquiring data of an urban solid waste incineration plant, and removing abnormal data to obtain a data sample;

step 2, determining input and output variables of a model, and based on the obtained data samples, training a set of the model;

the input variables of the model training set are determined by a maximum correlation minimum redundancy mRMR algorithm, and the input variables comprise: primary air flow, secondary air flow, grate left air flow, dry grate left air flow, inlet flue gas O ₂ Concentration, boiler outlet flue gas accumulation, primary combustion chamber temperature, primary combustion chamber left side temperature, primary combustion chamber right side temperature, hearth average temperature, primary combustion chamber right side flue gas temperature, urea solvent supply flow accumulation, furnace urea solution amount accumulation, active carbon storage bin feeding amount accumulation, lime feeder accumulation, hearth water supply accumulation, main steam flow accumulation, economizer water supply accumulation, boiler outlet main steam flow and boiler drum water level;

the output variable of the model training set is NO at the current moment _X Concentration;

step 3, designing a brain-like modularized neural network, and establishing a soft measurement model;

step (a)4. The test set data uses the same input variable as the training set as the input of the model, and the output of the model is NO at the current moment _X A concentration measurement;

in step 2, the input variable selection method based on the mRMR algorithm is as follows:

wherein ,m_i S is the number of the feature variables in the feature subset S, D is the correlation between the selected feature variable and the variable c to be measured, and if D is larger, the correlation between the selected feature variable and the variable c to be measured is higher;

calculating redundancy among features, and finding a mutual exclusion feature:

in the application process of the mRMR algorithm, unifying the maximum correlation index D and the minimum redundancy index R into an evaluation function Φ=d-R, and then determining an optimal feature subset S by searching the maximum value of the evaluation function:

maxΦ(D,R),Φ＝D-R (4)

in step 3, the soft measurement model design method based on the brain-like modularized neural network is as follows:

(1) Task decomposition;

the modularized index MQ consists of the density degree in the modules and the sparsity degree among the modules, wherein the density degree in the modules is calculated as follows:

/>

wherein ,J_S For the degree of sparsity between modules, d (h _l ,h _s ) Representing the distance between the core node of the first module and the core node of the second module according to the density J in the module _C And degree of sparsity J between modules _S The modular index is obtained by the following measurement modes:

the greater the value of MQ, the greater the degree of modularity of the network, and the modular structure construction can be divided into two cases: adding a new module and updating an existing module;

(1) adding a new module:

at the initial moment, the number of modules of the whole network is 0;

h ₁ ＝x ₁ (8)

wherein ,h₁ and r₁ Respectively representing the position and the action range of the core node of the first module, x ₁ An input vector, d, for the first training sample _max Input vector x for training samples _i And x _j Maximum distance between;

at time t, when the input vector of the t training sample enters the network, k modules exist, and the core node closest to the input vector of the sample is found:

wherein ,x_t Is the input vector of the t training sample, h _s Representing the position, k, of the core node of the s-th module _min Input vector x representing distance training samples _t The nearest core node;

if the input vector x of the t training sample _t Not at k _min In the scope of the core node, a module is newly added to learn the current sample, and the parameters of the newly added module corresponding to the core node are set as follows:

h _k+1 ＝x _t (12)

wherein ,h_k+1 ，r _k+1 The position and the action range of the core node corresponding to the newly added module，x _t Is the input vector for the t-th training sample,

the furthest distance from other core nodes to the newly added module core node is provided; />

(2) Optimizing existing modules:

the sample is classified as k _min In the module, according to the formula (7), respectively calculating the modularized index value MQ of the whole network under the condition that the current sample and the original core node are respectively used as the core nodes _t And

if it is

The network modularization degree of selecting the current sample as the core node is higher, and the original core node is replaced by the sample to become a new core node, and the initial parameters are set as follows:

wherein ,

the position and the action range of a new core node of the module are respectively; n (N) _k For the number of samples assigned to the kth module;

if it is

The location of the current core node +.>

Remain unchanged, adjust only the nodeScope of action->

wherein ,

is the original core node of the module;

after all training samples are compared, the samples are distributed to different sub-modules, a partition structure is formed, the modularization degree of the current network is considered to be the largest, and then the sub-network is required to be built for the task of each sub-module;

(2) And (3) structural design of a sub-network:

training data set

Is divided into M subsets;

wherein ,x_i ，y _i The input vector and the output vector of the ith training sample of the model respectively,

representing the domain, V is the input vector x _i N is the number of the input vector and the output vector data of the model;

constructing a sub-network corresponding to each module by adopting an adaptive task-oriented radial basis function neural network ATO-RBF, wherein the design of the sub-network comprises three parts: network structure growth, network structure pruning and network parameter adjustment;

(1) network structure growth:

Setting:

wherein ,

for the sample with the largest absolute output, +.>

Respectively representing an input vector and an output vector corresponding to a sample with the largest absolute output, r _s For the range of the s-th module, N _s For the number of samples assigned to the s-th module; />

at time t _s Time, training error vector e (t _s ) Obtained by the formula:

/>

wherein ,y_f Is the desired output of the f-th sample,

is the f sample at time t _s Is calculated by the following formula:

wherein H is the number of neurons in the hidden layer,

is the function of the jth hidden layer node of the s-th module, +.>

The center and the radius of the j hidden layer node of the s-th module; x is x _f An input vector for the f training sample;

Then, a RBF neuron pair is newly added

The initial parameters of the newly added neurons are as follows:

wherein

and />

Is->

Input vector corresponding to each sample,/>

Respectively +.>

wherein

Is the center of the neuron closest to the newly added neuron; />

The center of the neuron is newly added for the s-th module,

newly adding the radius of the neuron for the s-th module;

the radius of the newly added neuron is set as:

when neurons are newly added each time, the network parameters are adjusted through a second-order learning algorithm; when reaching the preset maximum structure J _max Or desired training accuracy E ₀ Ending the network structure growth process; in the experimental process J _max ＝10，E ₀ =0.0001, the training accuracy of the network is measured using root mean square error RMSE, calculated as follows:

wherein ,y_i And

the expected outputs and network outputs of the ith sample, respectively;

(2) and (3) pruning a network structure:

measuring contribution values of hidden layer neurons based on an exponent of the connection weight:

wherein SI (j) is the contribution value of the j-th hidden layer node,

searching for an hidden layer node with the smallest contribution value:

wherein ,

deleting the hidden node with the smallest contribution, adjusting parameters through a second-order learning algorithm, and comparing the root mean square error value RMSE_1 after deleting the node with the root mean square error value RMSE_0 when not deleting the node, wherein the calculation formula of the RMSE is shown as a formula (30); if RMSE_1 is less than or equal to RMSE_0, pruning the selected node under the condition of not sacrificing the network learning capability, and then repeating the process, wherein the selected node cannot be deleted; at this time, the network structure pruning process is finished, and the sub-network construction is completed; each time neurons are deleted, a second-order learning algorithm is used for adjusting parameters;

(3) and (3) network parameter adjustment:

the second order learning algorithm is as follows:

θ _L+1 ＝θ _L -(Q _L +μ _L E) ^-1 g _L (33)

wherein θ refers to parameters to be adjusted, including center, radius and connection weight, Q is a Hessian-like matrix, μ is a learning coefficient, and 0.01 is taken; e is an identity matrix, g is a gradient vector, L is an iteration step number, and the iteration step number is set to be 50;

converting the computation of the Hessian-like matrix Q and the gradient vector g into a Hessian-like submatrix summation and a gradient submatrix summation:

q _z is a Hessian-like submatrix, eta _z Is a gradient sub-directionThe amount can be calculated from the following formula:

wherein ,e_z Expected output y for sample z _z Output with network prediction

Is the difference of j _z Is the jacobian vector which is the vector,

the calculation is as follows:

according to the chain derivative law, each component in the jacobian vector in equation (39) is calculated as follows:

/>

wherein

The s-th module respectivelyThe center, radius and connection weight to the output layer of j neurons, x _z Is the input vector of the z-th training sample; />

The function of the j hidden layer node of the s-th module;

in step 4, the test data is used as the input of the model, and the output of the model is NO at the current moment _X A concentration measurement;

at time T, after the T test sample enters the BIMNN, searching a core node closest to the sample, and activating a sub-module to which the core node belongs:

wherein ,

for the actual output of BIMNN at time T, < >>

Is the first _act The actual output of the sub-network. />