CN112085277A - SCR denitration system prediction model optimization method based on machine learning - Google Patents

SCR denitration system prediction model optimization method based on machine learning Download PDF

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CN112085277A
CN112085277A CN202010945424.0A CN202010945424A CN112085277A CN 112085277 A CN112085277 A CN 112085277A CN 202010945424 A CN202010945424 A CN 202010945424A CN 112085277 A CN112085277 A CN 112085277A
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易辉
姜子安
徐芳
刘宇芳
费兆阳
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Abstract

The invention provides a machine learning-based SCR denitration system prediction model optimization method, which comprises the following steps: step S1: collecting real-time sample data of NOx concentration at an outlet of a boiler and relevant indexes influencing the NOx concentration in an SCR denitration system; step S2: performing dimensionality reduction treatment by using principal component analysis; step S3: establishing a support vector machine model; step S4: introducing an exponential decay model to iteratively update the step value of the longicorn whisker algorithm, and optimizing the parameters of the vector machine; step S5: simulation of a support vector machine; step S6: steps S1-S5 are repeated. The invention provides a method for optimizing a prediction model of an SCR (selective catalytic reduction) denitration system based on machine learning, which solves the problem that the prior thermal power plant is difficult to realize accurate control of ammonia injection amount.

Description

SCR denitration system prediction model optimization method based on machine learning
Technical Field
The invention discloses a machine learning-based SCR denitration system prediction model optimization method, relates to the fields of geotechnical engineering and tunnel engineering, and particularly relates to the fields of real-time monitoring and forecasting of foundation pit excavation deformation and stability analysis.
Background
More than half of the emission of nitrogen oxides (NOx for short) in China comes from coal combustion, and one of key industries for treating NOx pollution is the fire and electricity industry. The Selective Catalytic Reduction (SCR) technology is characterized in that under the condition of catalyst action, a flue with the smoke temperature of 300-4000 ℃ at the downstream of a boiler is selected, a reducing agent is sprayed into the flue to react with NOx in the flue gas, and the NOx is reduced into pollution-free N2 and H20. The SCR denitration system becomes important equipment for realizing ultralow emission of a large thermal power generating unit.
The main reaction equation is:
Figure BDA0002675158730000011
in practice, however, due to the limitation of site space and the influence of various factors including temporary pressure load and the like, the flue gas flow field at the inlet of the SCR denitration reactor is unevenly distributed, so that NO at the outlet of the reactor is causedXAnd NH3The concentration field of (a) produces a large unevenness. Under environmental policy pressure, power plants need to guarantee NOxThe emission does not exceed the standard, and the consequence of the emission is excessive ammonia injection, the ammonia escape seriously exceeds the standard, and a large amount of NH is caused4Formation of HSO, NH4HSO4The adhesive air preheater is easy to block, and the safe and long-term operation of the boiler is influenced. However, most thermal power plants at present have difficulty in accurately controlling the amount of ammonia injection.
Patent document CN 109062053 a discloses a denitration ammonia injection control method based on multivariate correction. The method comprises the following steps: acquiring measurement data and working condition information of a denitration system instrument in real time; constructing a prediction model of the NOx content at the inlet of the SCR denitration system, and predicting the NOx content at the inlet of the SCR denitration system at the current moment; and based on the predicted NOx content and the measured data of the inlet of the SCR system, performing ammonia injection amount feedforward control and prediction correction, generating an ammonia injection amount control instruction at the current moment, controlling an ammonia injection adjusting valve, and adjusting the ammonia injection amount. The PSO (particle swarm optimization) phase disclosed in the present application may fall into local optimum due to lack of dynamic adjustment of particle velocity, resulting in low convergence accuracy and difficulty in convergence at the later stage of convergence.
Disclosure of Invention
The invention aims to solve the technical problem that the invention provides a machine learning-based SCR denitration system prediction model optimization method, which solves the problem that the existing thermal power plant is difficult to realize accurate control of ammonia injection amount. The method aims at predicting the NOx emission of the power plant, and aims to optimize the ammonia injection amount of the denitration system and prevent the ammonia injection amount from being too much or too little under the condition of meeting the current NOx emission limit. The PCA-BAS-SVM prediction model can improve the prediction accuracy of the concentration of NOx at the inlet of the SCR denitration reactor of the power plant, and lays a foundation for the next step of the optimized operation of the denitration system and the accurate control of ammonia injection amount.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a machine learning-based SCR denitration system prediction model optimization method,
the method comprises the following steps:
step S1: collecting real-time sample data of NOx concentration at an inlet of an SCR denitration reactor in an SCR denitration system and relevant indexes influencing the NOx concentration;
step S2: performing dimensionality reduction on the sample data acquired in the step S1 by using principal component analysis;
step S3: taking the index subjected to dimensionality reduction in the step S2 as model input, taking the NOx concentration at the inlet of the SCR denitration reactor as model output, and establishing a support vector machine model;
step S4: introducing an exponential decay model to iteratively update the step value of the longicorn whisker algorithm, and optimizing the parameters of the vector machine;
step S5: repeating the steps S1-S4, and establishing a final support vector machine prediction model;
step S6: and updating input sample data, predicting the concentration of NOx at the inlet of the SCR denitration reactor, and adjusting the ammonia injection amount.
Wherein, the relevant indexes in the step S1 include boiler load, inlet flue gas temperature, inlet flue gas flow, primary total air volume, secondary total air volume, furnace outlet temperature and flue gas oxygen content.
Step S2 includes the following steps:
2-1 collecting a sample matrix X of relevant indicators affecting NOx concentrationn×(m+a)Wherein (X)1，X2，…，Xm，…Xm+a) M + a correlation indexes of the total X, n is the dimension of a sample collected by one correlation index, m is more than n, and m is more than a;
2-2. matrix X of samplesn×(m+a)Each row of (a) is zero-averaged;
2-3, solving the sample matrix Xn×(m+a)Covariance matrix C of (a):
Figure BDA0002675158730000031
wherein, Xn×(m+a) TRepresenting a sample matrix Xn×(m+a)C represents the sample matrix Xn×(m+a)Covariance of
N is the dimension of a sample collected by a relevant index;
2-4, solving the characteristic value lambda of the covariance matrix CjAnd corresponding feature vector omegajWherein
j＝1,2,...k...,n，λ1≥λ2≥λk……≥λn≥0；
2-5, sorting the eigenvalues from big to small, selecting the eigenvectors corresponding to the first k eigenvalues, and recording the eigenvectors as
Eigenvector matrix D, D ═ ω1，ω2，...ωk]T；
2-6.Z＝Dk×n Xn×(m+a)For data after dimension reduction to k dimension, the matrix Z after dimension reduction is formed by combining m + a column vectors and is recorded as Z ═ Z1，Z2，…，Zm，…Zm+a) Dividing a training set and a test set of a data set Z, and using the first m data Z1＝(Z1,Z2,…,Zm) As training set, the last a pieces of data Z2＝(Zm+1，Zm+2，…，Zm+a) As a set of tests, the test set is,
2-7, when the current k principal components accumulated contribution rate is more than or equal to t, replacing the initial data set X with the data Z after dimensionality reductionn×(m+a)And (5) performing operation analysis.
Wherein t in 2-6 is a constant of 85% or more.
Step S3 includes the following steps:
3-1, constructing an expression of the SVM regression function f (x) in a high-dimensional feature space, and assuming that a training sample set is (x)1,y1)，(x2,y2)…，(xm,ym) And then:
Figure BDA0002675158730000032
wherein, i is 1,2,. m, xiAs an input vector, yiIs the true value of the NOx concentration at the inlet of the SCR denitration reactor, phi (x)i) Is xiMapping to a high-dimensional space, ω and b being the model parameters to be determined;
3-2. introduction of relaxation variable xiiAnd
Figure BDA0002675158730000034
the following objective function is constructed to solve the optimal solution for ω and b:
Figure BDA0002675158730000033
s.t.f(xi)-yi≤+ξi
Figure BDA0002675158730000041
Figure BDA0002675158730000042
where c is a penalty factor, ξ being the deviation that is allowed to existiAnd
Figure BDA0002675158730000043
is a relaxation variable;
3-4, converting the quadratic programming problem of the formula (2) into a dual problem by using an optimization theory, solving the optimal solution of omega and b, and finally obtaining a regression function of the support vector machine as follows:
Figure BDA0002675158730000044
wherein,
Figure BDA0002675158730000045
and alphaiFor lagrange multipliers, k is the kernel function of the support vector machine and b is the model parameter.
3-4, selecting a radial basis kernel function by a kernel function k, wherein the expression is as follows:
Kg(|x-xi|)＝exp(-g|x-xi|2) (5)
in the formula, KgIs a radial basis kernel function, g is a kernel function coefficient, and exp is an exponential function with a natural constant e as a base.
Step S4 includes the following steps:
4-1, introducing an exponential decay model for updating the step length of the longicorn whisker
By xlThe coordinates of the left whisker, xr represents the coordinates of the right whisker, and the longicorn is abstracted into a centroid, x0Representing coordinates of the center of mass by d0Representing the distance between two whiskers, setting the variable step length according to an exponential decay model as follows:
Figure BDA0002675158730000046
where t is the number of iterations, stStep size of the t-th iteration, s0Denotes the initial step size, asIs a system of attenuation
Number, TsRepresents an exponential decay time constant;
4-2, calculating the left and right whisker coordinates of the t iteration:
Figure BDA0002675158730000047
Figure BDA0002675158730000048
wherein xl is the left whisker coordinate, xr is the right whisker coordinate,
Figure BDA0002675158730000049
is the centroid coordinate at the t-th iteration,
Figure BDA00026751587300000410
the distance between the left and right whiskers in the t-th iteration is represented by dir, which is a random vector representing the orientation of the longicorn whiskers;
4-3, using f (x) as fitness function, obtaining function value of left and right whiskers by using fitness function f (x)
f (xl) and f (xr), finally determining the centroid position of the longicorn in the next iteration after comparison:
Figure BDA0002675158730000051
where normal is a normalization function, dir represents the random vector of the orientation of the longicorn whiskers, stIs the t th time
Step length of iteration, sign is a sign function;
4-4, establishing an optimizing function minF (c, g) as MSE, wherein the MSE is the mean square error of a support vector machine:
Figure BDA0002675158730000052
in the formula, f (x)i) A predicted value returned for the model; y isiIs the corresponding NOx concentration real value;
centroid position of fitness function value obtained when iteration stops
Figure BDA0002675158730000053
Corresponding parameter (c)*,g*) Namely, the solution is the optimal solution,
4-5, after iteration is stopped, two parameter penalty factors c obtained by optimizing*And kernel function coefficient g*As the parameter value of the support vector machine, the training set data Z1Inputting a support vector machine model for training to obtain a NOx concentration prediction model at the inlet of the SCR denitration reactor, and then inputting test set data Z2Inputting the trained model, and evaluating the prediction effect of the established model.
In step S4, the iteration stop condition is that the maximum iteration number is reached or the MSE reaches a set minimum value, the maximum iteration number is 100, and the MSE sets the minimum value to 2.
In step S4, 4-5, the prediction effect of the model is evaluated, the average absolute error MRE and the root mean square error RMSE are selected as the evaluation indexes of the prediction effect of the model,
Figure BDA0002675158730000054
Figure BDA0002675158730000055
in the formula, f (x)i) A predicted value returned for the model; y isiThe actual value of the NOx concentration corresponding thereto.
MRE < 1% and RMSE < 5.
The invention has the beneficial effects that:
the invention aims to solve the technical problem that the invention provides a machine learning-based SCR denitration system prediction model optimization method, which solves the problem that the existing thermal power plant is difficult to realize accurate control of ammonia injection amount. Different from a general neural network prediction method, the method performs data processing, reduces model dimensionality and improves prediction efficiency. Meanwhile, the improved BAS algorithm is simple in structure, the convergence speed and precision are improved, and the optimized optimal support vector machine parameters can obviously optimize the performance of the support vector machine. For increasing NOXThe speed measurement, the timely guidance of the action of the SCR denitration system and the realization of energy conservation and emission reduction have practical significance.
(1) Different from a general neural network prediction method, the method performs data processing, reduces model dimensionality and improves prediction efficiency. On the premise of ensuring the prediction accuracy of the model, the principal component analysis method is used for carrying out dimensionality reduction on a plurality of auxiliary variables of NOx, so that the dimensionality of the model is effectively reduced, and the prediction efficiency and the operation speed of the field model are improved.
(2) The step size is an important control parameter in the longicorn whisker algorithm, and the size of the step size indicates the moving position of the longicorn. When the step length is larger, the global optimization capability of the algorithm is stronger; the step length is small, and the algorithm local optimization capability is strong. The step length in the standard algorithm is a fixed value, so that the optimization efficiency and the solving precision of the algorithm are low. Therefore, the method is based on the skynet beard algorithm with the step size decreasing, and the exponential decay model is introduced to update the step size value in an iterative mode, so that the algorithm has strong global optimization capability in the early stage and also has excellent local optimization capability in the later stage. The optimization efficiency and the solving precision of the algorithm are improved.
(3) The invention uses the improved longicorn algorithm for optimizing SVM parameter optimization, has simple structure, improves convergence speed and precision, and can obviously optimize the performance of the support vector machine by the optimized optimal support vector machine parameter. The method has practical significance for improving the measuring speed of NOx, guiding the action of the SCR denitration system in time and realizing energy conservation and emission reduction.
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FIG. 1 is a flow chart of a machine learning based SCR denitration system prediction model optimization method of the present invention;
FIG. 2 is a schematic equipment diagram of an application device of the machine learning-based SCR denitration system prediction model optimization method.
Detailed Description
The following describes in detail a machine learning-based SCR denitration system prediction model optimization method according to the present invention with reference to the accompanying drawings and specific embodiments.
As shown in FIG. 1, the pulverized coal forms flue gas containing NO after being combusted in the boilerX、SO2Cooling pollutants by a heat exchanger, then feeding the pollutants into an SCR denitration reactor, installing an ammonia spraying grid (the ammonia spraying grid refers to an ammonia spraying pipeline and a grid) at the inlet of the reactor, mixing ammonia gas from a liquid ammonia evaporator with diluted air, and then mixing the ammonia gas with NO in flue gasXAnd carrying out selective reduction reaction under the action of a catalyst to generate water and ammonia gas. At present, most coal-fired power plants are difficult to realize accurate control of ammonia injection amount, and insufficient ammonia injection amount can cause NOXThe emission can not reach the environmental protection standard required by the state. In order to ensure that the emission does not exceed the standard, the problem of excessive ammonia spraying is commonly existed on the site, and secondary pollution is caused. Therefore, during the operation of the system, the ammonia injection amount is a key control index, and the ammonia injection amount is based on NO at the inlet of the SCR denitration reactorXThe concentration is determined, and the boiler load, the inlet flue gas temperature and flow, the primary total air volume and the secondary total air volume are determined by establishing a prediction model of the denitration reactorTotal air volume, hearth outlet temperature and total 7 pairs of variables of flue gas oxygen content are used as input of a model, and NO at an SCR inletxThe concentration is used as the output of the model, and the ammonia injection amount is further determined according to the predicted value. The denitration system prediction model can lay a foundation for the operation of a next denitration system and the accurate control of ammonia injection amount.
The method comprises the following steps: the relevant input variables influencing the NOx concentration at the inlet of the SCR denitration reactor in the denitration process are determined by comprehensively analyzing each real-time monitoring data on site, and the acquired data are processed by utilizing principal component analysis.
Collecting power plant operation data 800 group as total X, considering that the fluctuation of NOx emission is not big under stable condition, this patent selects the data under the starting condition to carry out the simulation prediction. Is provided with (X)1，X2，…，X800) For 800 samples of the total X, each sample corresponds to a 7-dimensional variable, conventionally, a record is represented by a column vector, and the corresponding data matrix is X7×800The 7-dimensional variables include: boiler load, inlet flue gas temperature and flow, primary total air quantity and secondary total air quantity, hearth outlet temperature and flue gas oxygen content. Mixing X7×800Is zero-averaged, i.e. the average of this line is subtracted:
Figure BDA0002675158730000071
in the formula, X7×800In the form of a matrix of data,
Figure BDA0002675158730000072
is a row average matrix, X, of a data matrix7×800' is a data matrix after zero equalization;
then, determine X7×800Covariance matrix of's:
Figure BDA0002675158730000081
wherein (X)7×800')TRepresentation matrix X7×800' ofTranspose, C represents the matrix X7×800' covariance matrix, 7 is the dimension of the sample collected for a correlation index;
the covariance matrix C of the selected data matrix can be directly calculated using the self-contained function cov of the software Matlab.
Determining an eigenvalue λ of a covariance matrixjAnd corresponding feature vector omegaj(j 1, 2.. 7), the eigenvalues and eigenvectors of the matrix C can be directly solved using the eig (C) function, where larger eigenvalues represent more important information of the variables, and conversely smaller values can be considered as secondary information.
After sorting the eigenvalues from large to small, the first k largest ones are selected. Then, k eigenvectors corresponding to the eigenvalues are respectively used as row vectors to form an eigenvector matrix D, wherein D is [ omega ]1，ω2，…ωk]T；
Z＝Dk×7X7×800I.e. data after dimension reduction to k dimension, dimension reduction matrix Zk×800＝Dk×7X7×800。
The matrix Z after dimensionality reduction is formed by combining 800 column vectors and is recorded as Z ═ Z1，Z2，…，Z800) Dividing a data set Z into a training set and a test set, and using the first 600 data Z1＝(Z1,Z2,…,Z600) The residual 200 data Z are used as training set to train the model2＝(Z601，Z602，，Z800) The model is validated as a test set.
The contribution ratio of the jth principal component is lambdajP (j ═ 1,2, 3, …, 7); wherein P is equal to
Figure BDA0002675158730000082
The cumulative contribution rate of the first k principal components is
Figure BDA0002675158730000083
When the accumulated contribution rate of the current k principal components is larger than or equal to t (t is larger than 85%), replacing the initial data set X with the data set Z after dimensionality reduction7×800To perform an operationAnalysis, generally satisfactory. the larger t is, the more the characteristic value is retained, and the specific value is set according to the actual requirement.
Step two: and establishing a basic SVM model, and establishing a basic prediction model by adopting a single-output (the output is the concentration of NOx at the inlet of the SCR denitration reactor) support vector machine regression model.
The support vector machine is a machine learning method developed from statistical theory, and a training sample set after principal component analysis has seven-dimensional characteristics and is expressed as (x)1,y1)，(x2,y2)…，(x600,y600)，xiAs input vectors (reduced-dimension matrix Z)1Of 600 total), yiIs the actual value of the NOx concentration at the inlet of the SCR denitration reactor corresponding to the actual value.
This patent need use support vector regression machine (SVR), establishes the model mathematical expression that divides hyperplane and correspond in the feature space and is:
y＝ωTφ(x)+b (15)
it is desirable to learn a regression model so that f (x) and y are as close as possible. (x) predicted values returned for the SVR model; and y is the corresponding true NOx concentration value.
Where φ (x) is a mapping where sample data is converted to a high-dimensional space; omega is a normal vector of the hyperplane and determines the direction of the hyperplane; b is a displacement term and determines the distance between the hyperplane and the origin. ω and b are the model parameters to be determined, and the problem of finding the hyperplane can be directly considered as the problem of finding ω and b.
The limiting conditions of the optimal hyperplane are as follows:
Figure BDA0002675158730000091
s.t.yi(wTx+b)≥1(i＝1,2,…,m)，
this is the basic SVM model. (in the following, the derivation is shown by m for the number of samples and n for the dimension of the variables)
For the optimization problem with a plurality of inequality constraint conditions, the dual problem is easier to solve, and a Lagrange multiplier method is required to be utilized and the KKT condition is satisfied:
Figure BDA0002675158730000092
to minimize the lagrange function, let function L (ω, b, α) separately make the partial derivatives of ω, b equal to 0, as follows:
Figure BDA0002675158730000093
Figure BDA0002675158730000094
substituting the first formula into L (ω, b, α), ω and b in the formula can be eliminated, and considering the constraint of the second formula, the dual problem is obtained:
Figure BDA0002675158730000101
Figure BDA0002675158730000102
after solving alpha, obtaining omega and b to obtain a model:
Figure BDA0002675158730000103
the above derivation all needs to satisfy the KKT condition:
Figure BDA0002675158730000104
in practice there is almost no completely linearly separable data, and to solve this problem, some points may be allowed to fail the constraint, i.e. allow a deviation to exist. In contrast to conventional regression models which typically compute the loss directly based on the difference between the model output f (x) and the true output y, Support Vector Regression (SVR) assumes that we can tolerate at most e deviation between f (x) and y, i.e. the loss is computed only if the absolute value of the difference between f (x) and y is greater than e, the original optimization problem can be rewritten as:
Figure BDA0002675158730000105
wherein c is a penalty factor; lIs the insensitive loss (∈ -insensitive loss) function:
Figure BDA0002675158730000106
introducing a relaxation variable xiiAnd
Figure BDA0002675158730000107
the formula can be rewritten as:
Figure BDA0002675158730000108
s.t.f(xi)-yi≤+ξi
Figure BDA0002675158730000111
Figure BDA0002675158730000112
the quadratic programming problem with complex formula is converted into a dual problem by utilizing the optimization theory
Figure BDA0002675158730000113
Figure BDA0002675158730000114
In the formula, alpha*μ，μ*Is a Lagrange multiplier, xi*Question is relaxation factor
Then let L (omega, b, alpha)*,ξ，ξ*,μ，μ*) For omega, b, xi*A partial derivative of 0 gives:
Figure BDA0002675158730000115
the process meets the KKT condition:
Figure BDA0002675158730000116
from the KKT condition, it can be seen that for each sample there is (C- α)i)ξiIs equal to 0, and αi(f(xi)-yi--ξi) 0. Then, α is obtainediThen, take 0 < alphaiIf < C, xi must be presenti＝0，
Figure BDA0002675158730000117
In actual operation, a plurality of or all of the alpha-alphaiThe samples < C are averaged after solving for b.
The regression function of the support vector machine is finally obtained as follows:
Figure BDA0002675158730000118
wherein,
Figure BDA0002675158730000121
is a kernel function of a support vector machine, which can map a sample space to oneThe high-dimensional feature space enables the low-dimensional nonlinear problem to be solved in the high-dimensional feature space through a support vector machine linear regression method. Without knowing the form of the feature map, we generally do not know what kernel functions are appropriate. In this case, the linear kernel, the polynomial kernel, the gaussian kernel, the laplace kernel, and the Sigmoid kernel can be tested one by one, and the one with the best selectivity can be used as the kernel function of a certain problem.
The kernel function selected by the patent is a Radial Basis Function (RBF) kernel function, and the expression is as follows:
Kg(|x-xi|)＝exp(-g|x-xi|2) (29)
in the formula, g is a kernel function coefficient, and exp is an exponential function with a natural constant e as a base.
Step three: SVM parameter optimization based on the improved BAS algorithm. Support vector machine regression requires optimization of 2 important parameters, penalty factor c (control model complexity and generalization ability) and kernel function coefficient g (determining input spatial range and width). Therefore, when the SVM regression algorithm is used for data prediction, in order to improve the prediction accuracy and efficiency of the model, the values of the two parameters need to be continuously adjusted until the training network meets the set requirements.
The standard longicorn stigma search algorithm:
the longicorn stigma search algorithm is an efficient intelligent optimization algorithm, is similar to a particle swarm algorithm, a simulated annealing algorithm and the like, and can realize efficient optimization without knowing a specific form of a function or gradient information. The biological principle is that when the longicorn is looking for food, the specific position of the food is unknown. The longicorn senses the strong and weak smell of food through the antenna positioned at the head, and flies leftwards when the left antenna senses stronger smell of the food, and flies rightwards when the left antenna senses the stronger smell of the food. The process of searching for food by longicorn is an optimization process in nature.
PCA reduces the data from 7-dimensions to k-dimensions, and for an optimization problem in k-dimensional space, represents the left whisker coordinate by xl, the right whisker coordinate by xr,
Figure BDA0002675158730000124
representing coordinates of the centroid at the t-th iteration by
Figure BDA0002675158730000125
The distance between two whiskers at the t-th iteration is represented, and step is the step size (constant value) of the forward progress of the longicorn. According to the assumption that the head of the longicorn is oriented arbitrarily, the vector of the direction of the antenna towards the right and left is random, so a random vector dir can be generated to represent the orientation of the longicorn whisker, and the random vector is normalized:
Figure BDA0002675158730000122
where rands (k,1) is a random vector in k-dimension space, which can be obtained
Figure BDA0002675158730000123
Obviously, xl, xr can also be expressed as an expression for the centroid:
Figure BDA0002675158730000131
the second step is that: and (x) is used as a fitness function, function values f (xl) and f (xr) of the left and right whiskers are obtained, and the barnyard beetle mass center position is updated by judging the sizes of the two values.
If f (xl) < f (xr), the longicorn travels a distance step in the direction of the left hair, i.e.
Figure BDA0002675158730000132
If f (xl) > f (xr), the longicorn travels a distance step in the direction of the right whisker, i.e.
Figure BDA0002675158730000133
The above two cases can be uniformly written using sign function sign:
Figure BDA0002675158730000134
where normal is a normalization function, sign () is a sign function, dir represents a random vector of skyhook orientation, and step is the step size of skyhook travel.
Judging whether a termination condition is met, if so, immediately terminating the calculation and outputting an optimal solution; if not, returning to the second step to continue the next cycle.
Improved longicorn whisker algorithm:
the BAS algorithm has the advantages of high optimizing speed, high convergence and small operand. The selection of the step size has great influence on the convergence performance and the search efficiency of the algorithm: the step length is large, and the global optimization capability of the algorithm is strong; the step length is small, and the algorithm has strong local optimization capability. The step length in the traditional algorithm is a fixed value, so that the optimization efficiency and the solving precision of the algorithm are low.
Fixed size steps are difficult to satisfy both the rapidity and accuracy of the algorithm. The method adopts the step length attenuated according to the iteration times to give consideration to the convergence speed and the precision of the optimal solution. For this purpose, an exponential decay model is introduced to continuously update the step value.
The attenuation model is:
Figure BDA0002675158730000135
where t is the number of iterations, stStep size of the t-th iteration, s0Denotes the initial step size, asFor attenuation coefficient, TsRepresents an exponential decay time constant;
the longicorn centroid position expression is changed to:
Figure BDA0002675158730000141
Figure BDA0002675158730000142
is the centroid position at the t +1 th iteration, stSign () is a sign function and dir is a random vector representing the orientation of the longicorn whiskers for a variable step size set according to an exponential decay model;
the improvement is significant in dynamically adjusting the step size, and when the optimization reaches a certain bottleneck, the fixed step size is not suitable for the optimization. Through the step change of the attenuation formula, the algorithm has strong global optimization capability (the attenuation of the exponential function at the early stage) at the early stage, the rough result of the optimal solution is obtained, and meanwhile, fine search can be performed near the optimal point at the later stage of iteration (the attenuation at the later stage is slow). Therefore, the time-varying step size can improve the problem that the traditional BAS algorithm has insufficient local searching capability.
And establishing an optimizing function minF (c, g) ═ MSE, wherein the MSE is the mean square error of the support vector machine. Meaning that the parameters c and g are used as optimization variables to search for the best support vector machine parameters so that the MSE is minimized. Centroid position of fitness function value obtained when iteration stops
Figure BDA0002675158730000143
Corresponding parameter (c)*,g*) I.e. the optimal solution.
Figure BDA0002675158730000144
The iteration stop condition is that the precision requirement is met (MSE is less than or equal to 2) or the maximum iteration number is reached (set as 100 times).
After iteration is stopped, the obtained penalty factor c and kernel function coefficient g are used as parameter values of a support vector machine, and training set data Z1And inputting a support vector machine model for training to obtain a NOx concentration prediction model at the inlet of the SCR denitration reactor. Then test set data Z2Inputting the trained model, and evaluating the prediction effect of the established model.
In order to evaluate the performance and prediction accuracy of the model, the patent uses the average relative error (MRE) and the Root Mean Square Error (RMSE) as evaluation criteria, and the formula is as follows:
Figure BDA0002675158730000145
Figure BDA0002675158730000146
in the formula, f (x)i) A predicted value returned for the SVR model; y isiThe actual value of the NOx concentration corresponding thereto. The RMSE and the MRE both represent the prediction effect of the established model on the target variable, can reflect the quality of the test effect of the model, and if the predicted value completely follows the actual value change, the two results are zero, and the prediction precision of the model is the highest, but because the influence of the actual condition cannot be zero, the evaluation standard is that the smaller the two values is, the better the evaluation standard is. The specific precision requirement can be set according to the actual condition, and the model prediction effect reaches the standard when MRE is less than 1% and RMSE is less than 5.
In the description provided herein, numerous specific details are set forth. It is understood, however, that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
In the description of the present invention, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.
Similarly, it should be appreciated that in the foregoing description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. However, the disclosed method should not be interpreted as reflecting an intention that: that the invention as claimed requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.
As used herein, unless otherwise specified the use of the ordinal adjectives "first", "second", "third", etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. Furthermore, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter. Accordingly, many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the appended claims. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (10)

1. A machine learning-based SCR denitration system prediction model optimization method is characterized in that,
the method comprises the following steps:
step S1: collecting real-time sample data of NOx concentration at an inlet of an SCR denitration reactor in an SCR denitration system and relevant indexes influencing the NOx concentration;
step S2: performing dimensionality reduction on the sample data acquired in the step S1 by using principal component analysis;
step S3: taking the index subjected to dimensionality reduction in the step S2 as model input, taking the NOx concentration at the inlet of the SCR denitration reactor as model output, and establishing a support vector machine model;
step S4: introducing an exponential decay model to iteratively update the step value of the longicorn whisker algorithm, and optimizing the parameters of the vector machine;
step S5: repeating the steps S1-S4, and establishing a final support vector machine prediction model;
step S6: and updating input sample data, predicting the concentration of NOx at the inlet of the SCR denitration reactor, and adjusting the ammonia injection amount.
2. The machine learning-based SCR denitration system prediction model optimization method of claim 1, wherein the relevant indexes in step S1 comprise boiler load, inlet flue gas temperature, inlet flue gas flow, primary total air volume, secondary total air volume, furnace outlet temperature and flue gas oxygen content.
3. The machine learning-based SCR denitration system prediction model optimization method of claim 1, wherein the step S2 comprises the following steps:
2-1 collecting a sample matrix X of relevant indicators affecting NOx concentrationn×(m+a)Wherein (X)1，X2，…，Xm，…Xm+a) M + a correlation indexes of the total X, n is the dimension of a sample collected by one correlation index, m is more than n, and m is more than a;
2-2. matrix X of samplesn×(m+a)Each row of (a) is zero-averaged;
2-3, solving the sample matrix Xn×(m+a)Covariance matrix C of (a):
Figure FDA0002675158720000011
wherein, Xn×(m+a) TRepresenting a sample matrix Xn×(m+a)C represents the sample matrix Xn×(m+a)N is the dimension of a sample collected by a correlation index;
2-4, solving the characteristic value lambda of the covariance matrix CjAnd corresponding feature vector omegajWherein j is 1,2, k1≥λ2≥λk……≥λn≥0；
2-5, sorting the eigenvalues from big to small, selecting the eigenvectors corresponding to the first k eigenvalues, and recording the eigenvector matrix D as an eigenvector matrix D, D ═ omega1，ω2，...ωk]T；
2-6.Z＝Dk×nXn×(m+a)For data after dimension reduction to k dimension, the matrix Z after dimension reduction is formed by combining m + a column vectors and is recorded as Z ═ Z1，Z2，…，Zm，…Zm+a) Dividing a training set and a test set of a data set Z, and using the first m data Z1＝(Z1,Z2,…,Zm) As training set, the last a pieces of data Z2＝(Zm+1，Zm+2，…，Zm+a) As a set of tests, the test set is,
2-7, when the current k principal components accumulated contribution rate is more than or equal to t, replacing the initial data set X with the data Z after dimensionality reductionn×(m+a)And (5) performing operation analysis.
4. The machine learning-based SCR denitration system prediction model optimization method of claim 3, wherein t is a constant of 85% or more in 2-6.
5. The machine learning-based SCR denitration system prediction model optimization method of claim 3, wherein the step S3 comprises the following steps:
3-1, constructing SVM regression function f (x) in high-dimensionalExpression of eigenspace, assuming a training sample set of (x)1,y1)，(x2,y2)…，(xm,ym) And then:
yi＝ωTφ(xi)+b (2)
wherein, i is 1,2iAs an input vector, yiIs the true value of the NOx concentration at the inlet of the SCR denitration reactor, phi (x)i) Is xiMapping to a high-dimensional space, ω and b being the model parameters to be determined;
3-2. introduction of relaxation variable xiiAnd
Figure FDA0002675158720000021
the following objective function is constructed, and the optimal solution of ω and b is solved:
Figure FDA0002675158720000022
s.t.f(xi)-yi≤+ξi
Figure FDA0002675158720000023
Figure FDA0002675158720000024
where c is a penalty factor, ξ being the deviation that is allowed to existiAnd
Figure FDA0002675158720000025
is a relaxation variable;
3-4, converting the quadratic programming problem of the formula (2) into a dual problem by using an optimization theory, solving the optimal solution of omega and b, and finally obtaining a regression function of the support vector machine as follows:
Figure FDA0002675158720000026
wherein,
Figure FDA0002675158720000027
and alphaiFor lagrange multipliers, k is the kernel function of the support vector machine and b is the model parameter.
6. The machine learning-based SCR denitration system prediction model optimization method of claim 5, wherein the kernel function k in 3-4 is a radial basis kernel function, and the expression is as follows:
Kg(|x-xi|)＝exp(-g|x-xi|2) (5)
in the formula, KgIs a radial basis kernel function, g is a kernel function coefficient, and exp is an exponential function with a natural constant e as a base.
7. The machine learning-based SCR denitration system prediction model optimization method of claim 1, wherein the step S4 comprises the following steps:
4-1, introducing an exponential decay model for updating the step length of the longicorn whisker
Using xl to represent coordinates of left whisker, using xr to represent coordinates of right whisker, abstracting longicorn to be a centroid, x0Representing coordinates of the center of mass by d0Representing the distance between two whiskers, setting the variable step length according to an exponential decay model as follows:
Figure FDA0002675158720000031
where t is the number of iterations, stStep size of the t-th iteration, s0Denotes the initial step size, asFor attenuation coefficient, TsRepresents an exponential decay time constant;
4-2, calculating the left and right whisker coordinates of the t iteration:
Figure FDA0002675158720000032
Figure FDA0002675158720000033
wherein xl is the left whisker coordinate, xr is the right whisker coordinate,
Figure FDA0002675158720000034
is the centroid coordinate at the t-th iteration,
Figure FDA0002675158720000035
the distance between the left and right whiskers in the t-th iteration is represented by dir, which is a random vector representing the orientation of the longicorn whiskers;
4-3, taking f (x) as a fitness function, obtaining function values f (xl) and f (xr) of the left and right whiskers through the fitness function f (x), and finally determining the centroid position of the longicorn for the next iteration after comparison:
Figure FDA0002675158720000036
where normal is a normalization function, dir represents the random vector of the orientation of the longicorn whiskers, stSign is a sign function for the step length of the t iteration;
4-4, establishing an optimizing function minF (c, g) as MSE, wherein the MSE is the mean square error of a support vector machine:
Figure FDA0002675158720000037
in the formula, f (x)i) A predicted value returned for the model; y isiIs the corresponding NOx concentration real value;
centroid position of fitness function value obtained when iteration stops
Figure FDA0002675158720000038
Corresponding parameter (c)*,g*) Namely, the solution is the optimal solution,
4-5, after the iteration is stopped, two parameters obtained by optimization, namely a penalty factor c*And kernel function coefficient g*As the parameter value of the support vector machine, the training set data Z1Inputting a support vector machine model for training to obtain a NOx concentration prediction model at the inlet of the SCR denitration reactor, and then inputting test set data Z2Inputting the trained model, and evaluating the prediction effect of the established model.
8. The machine-learning-based SCR denitration system prediction model optimization method of claim 7, wherein the iteration stop condition in step S4 is that the maximum iteration number is reached or MSE reaches a set minimum value, the maximum iteration number is 100, and the MSE is set to a minimum value of 2.
9. The machine learning-based SCR denitration system prediction model optimization method of claim 7, wherein the prediction effect of the model is evaluated in 4-5 of step S4, the average absolute error MRE and the root mean square error RMSE are selected as the evaluation indexes of the model prediction effect,
Figure FDA0002675158720000041
Figure FDA0002675158720000042
in the formula, f (x)i) A predicted value returned for the model; y isiThe actual value of the NOx concentration corresponding thereto.
10. The machine-learning-based SCR denitration system prediction model optimization method of claim 9, wherein MRE < 1% and RMSE < 5.
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