A Dynamic Model Incorporated with Delay Estimation and Variable Selection for Control of SCR De-NO x Process

: In order to control NH 3 injection for the selective catalytic reduction of nitrogen oxide (NO x ) denitration (SCR de-NO x ) process, a model that can accurately and quickly predict outlet NO x emissions is required. This paper presents a dynamic kernel partial least squares (KPLS) model incorporated with delay estimation and variable selection for outlet NO x emission and investigated control strategy for NH 3 injection. First, k-nearest neighbor mutual information (KNN_MI) was used for delay estimation, and the e ﬀ ect of historical data lengths on KNN_MI was taken into account. Bidirectional search based on the change rate of KNN_MI (KNN_MI_CR) was used for variable selection. Delay–time di ﬀ erence update algorithm and feedback correction strategy were proposed. Second, the NH 3 injection compensator (NIC) and the outlet NO x emission model constituted a correction controller. Then, its output and the output of the existing controller are added up to suitable NH 3 injection. Finally, the KNN_MI_CR method was compared with di ﬀ erent algorithms by benchmark dataset. The ﬁeld data results showed that the KNN_MI_CR method could improve model accuracy for reconstructed samples. The ﬁnal model can predict outlet NO x emissions in di ﬀ erent operating states accurately. The control result not only meets the NO x emissions standard (50 mg / m 3 ) but also keeps high de-NO x e ﬃ ciency (80%). NH 3 injection and NH 3 escape are reduced by 11% and 39%.


Introduction
How to reduce nitrogen oxide (NO x ) emissions from coal-fired power plants has become an important task of environmental treatment. Selective catalytic reduction denitration (SCR de-NO x ) technology is one of the mature flue gas denitration technologies [1]. Many efforts have been made to optimize the SCR system, such as superior catalyst technology, enhanced de-NO x control strategy, and byproduct limitation [2]. However, it is very difficult to control the amount of NH 3 injection accurately. First, new energy is integrated into the power grid on a large scale in recent years. The boiler load needs to be changed to stabilize the fluctuation from the output power of new energy frequently. Therefore, the wide range of operating states poses certain difficulties in NH 3 injection control. Second, the upper limitation of NO x emission is decreased to 50 mg/m 3 in China. In order to meet the national environmental standard, excessive NH 3 injection occurs easily. Hence, it is required such as the NH 3 valve opening and the increment of NH 3 valve opening, which are neglected in the above literature.
The objective of this paper is to model outlet NO x emissions under the different operating state, thereby to facilitate controller design. The kernel partial least squares (KPLS) model shows a good effect when it deals with the high dimensionality and colinearity data. In this paper, a dynamic KPLS model incorporated with variable selection and delay estimation is proposed. The k-nearest neighbor mutual information (KNN_MI) was used for delay estimation, and the effect of historical data lengths on KNN_MI was taken into account. Based on the results of delay estimation, a bidirectional search based on the change rate of KNN_MI (KNN_MI_CR) was used for variable selection. In order to improve model update accuracy, delay-time difference (DTD) update algorithm and feedback correction strategy are proposed. In order to take advantage of the existing controller, which has rapid response-ability to deal with disturbance signals, a parallel control structure that can identify the dynamic model online by using operation data is proposed. The existing conventional controller is used as the main controller. The NH 3 injection compensator (NIC) combined with the outlet NO x emission model are used as correction controller, which can ensure the outlet NO x emission is stable near the set value. The principle of NIC is to eliminate the adverse effects of the large inertia of the SCR system and the lag of NO x analysis through feed-forward compensation to a certain extent.
The paper is organized as follows: In Section 2, the SCR de-NO x process and its control strategy are described. In Section 3, the delay estimation and variable selection method are presented. The experimental results of the benchmark dataset for variable selection are presented in Section 4. The field data experiment for the SCR de-NO x process is investigated in Section 5, and the predictive accuracy of the outlet NO x emission model and the control effect of the proposed control strategy are analyzed. Finally, concluding remarks are given in Section 6.

The SCR de-NO x Process
For a 1000 MW ultra-supercritical coal-fired power plant, the SCR de-NO x system is shown in Figure 1. The temperature of the SCR de-NO x system is controlled by the bypass gas damper of the economizer in the upstream flue. Mixed with dilution air, the ammonia gas is sprayed by the NH 3 flow rate valve through the ammonia injection grid (AIG). In the reaction zone, the selective catalytic reaction occurs on the stainless steel plates, which are supported by the V 2 O 5 -WO 3 -TiO 2 catalyst. Finally, the NO x in the flue gas is converted into harmless N 2 and H 2 O, and thereby the flue gas is purified. The main reaction of the SCR de-NO x process is described as follows [1]: Actually, adverse side reaction will occur as follows [1]: It can be seen that the excessive NH 3 injection leads to side reaction, and de-NO x efficiency is decreased because of the regeneration of NO x . Excess NH 3 reacts with SO 3 in the flue gas to form NH 4 HSO 4 and (NH 4 ) 2 SO 4 , which not only reduce the catalyst activity but also cause plugging and corrosion in the heated surface of the air preheater. In addition, increased NH 3 escape could lead to secondary pollution. Secondary pollution refers to new pollutants, that is, unreacted ammonia gas.  Figure 1. The selective catalytic reduction nitrogen oxide (NOx) denitration (SCR de-NOx) system.
It can be seen that the excessive NH3 injection leads to side reaction, and de-NOx efficiency is decreased because of the regeneration of NOx. Excess NH3 reacts with SO3 in the flue gas to form NH4HSO4 and (NH4)2SO4, which not only reduce the catalyst activity but also cause plugging and corrosion in the heated surface of the air preheater. In addition, increased NH3 escape could lead to secondary pollution. Secondary pollution refers to new pollutants, that is, unreacted ammonia gas.

The SCR de-NOx Process Control Strategy
Under the variable state of the power plant, the SCR de-NOx process shows nonlinear, strong disturbance and large time-delay in NOx analysis, so it is hard to achieve a good control effect by the existing PID control. Actually, except for controlling the temperature of the reaction zone by the bypass flue gas, it is necessary to design a better automatic control system which can control the NH3 injection strictly. In order to ensure the most suitable NH3/NOx ratio, which is related to de-NOx efficiency and ensure the NH3 escape in a reasonable range, the proposed control system includes the main controller and the correction controller, which are in parallel operation. The main controller is the existing PID controller. The correction controller, which is shown in Figure 1, is investigated in this paper. The parallel control system is shown in Figure 2. The dynamic KPLS model is used as an outlet NOx emission predictive model, which can be identified offline by the field data.  Figure 2. The SCR de-NOx process control system.

The SCR de-NO x Process Control Strategy
Under the variable state of the power plant, the SCR de-NO x process shows nonlinear, strong disturbance and large time-delay in NO x analysis, so it is hard to achieve a good control effect by the existing PID control. Actually, except for controlling the temperature of the reaction zone by the bypass flue gas, it is necessary to design a better automatic control system which can control the NH 3 injection strictly. In order to ensure the most suitable NH 3 /NO x ratio, which is related to de-NO x efficiency and ensure the NH 3 escape in a reasonable range, the proposed control system includes the main controller and the correction controller, which are in parallel operation. The main controller is the existing PID controller. The correction controller, which is shown in Figure 1, is investigated in this paper. The parallel control system is shown in Figure 2. The dynamic KPLS model is used as an outlet NO x emission predictive model, which can be identified offline by the field data.  Figure 1. The selective catalytic reduction nitrogen oxide (NOx) denitration (SCR de-NOx) system.
It can be seen that the excessive NH3 injection leads to side reaction, and de-NOx efficiency is decreased because of the regeneration of NOx. Excess NH3 reacts with SO3 in the flue gas to form NH4HSO4 and (NH4)2SO4, which not only reduce the catalyst activity but also cause plugging and corrosion in the heated surface of the air preheater. In addition, increased NH3 escape could lead to secondary pollution. Secondary pollution refers to new pollutants, that is, unreacted ammonia gas.

The SCR de-NOx Process Control Strategy
Under the variable state of the power plant, the SCR de-NOx process shows nonlinear, strong disturbance and large time-delay in NOx analysis, so it is hard to achieve a good control effect by the existing PID control. Actually, except for controlling the temperature of the reaction zone by the bypass flue gas, it is necessary to design a better automatic control system which can control the NH3 injection strictly. In order to ensure the most suitable NH3/NOx ratio, which is related to de-NOx efficiency and ensure the NH3 escape in a reasonable range, the proposed control system includes the main controller and the correction controller, which are in parallel operation. The main controller is the existing PID controller. The correction controller, which is shown in Figure 1, is investigated in this paper. The parallel control system is shown in Figure 2. The dynamic KPLS model is used as an outlet NOx emission predictive model, which can be identified offline by the field data.  Figure 2. The SCR de-NOx process control system. Figure 2. The SCR de-NO x process control system.
The correction controller includes three parts mainly: outlet NO x emission predictive model, feedback correction and NH 3 injection compensator (NIC).
(1) Outlet NO x emission predictive model In general, a dynamic data-driven model is constructed by adding the model input, such as the historical input data x(t − 1), · · · , x(t − w + 1) and output data y(t − 1), · · · , y(t − w + 1). Therefore, x(t − τ)x(t − τ − 1) and y(t − 1) are selected as the new input variables in this paper. As a kind of model update method, the time difference (TD) algorithm can work out the variable drift and achieve better predictive accuracy. Moreover, the data model based on the TD algorithm does not need frequent reconstruction and parameter updating [21]. The time-delay must be considered in the SCR deNO x process. Hence, the delay-time difference (DTD) algorithm is proposed. Combining with the DTD method and KPLS model, the dynamic KPLS model, which is named DTD-KPLS, is proposed.
In general, the original input variable sample and output variable sample are used in the regression algorithm. However, ∆x(t) is calculated between the input variable x(t) at the time of t and the input variable x(t − i) at the time of t − i through the TD method first. Similarly, ∆y(t) is calculated by the TD method: Then, the relationship between ∆x(t) and ∆y(t) is modeled as: If new data x(t ) is obtained, the TD of input data can be computed as: Thus, the TD of output data can be predicted by the training model as: Finally, the predicted output value at time t is: When the DTD method is used, the time-delay τ needs to be considered in Equations (8) and (10). Hence, the training model becomes: Hence, the actual predicted output is: In this paper, the estimation of the DTD-KPLS model from the training set is depicted as follows [22]: The relevant variable samples are obtained, and the preprocessing, which contains outlier elimination and data filtering, is performed; 2.
The input matrix X real ∈ R n×m and the output matrix Y ∈ R n×1 are confirmed; 3.
The time-delay of each input variable x i (I = 1, . . . ,n) is estimated and the phase space reconstruction is made for X real . Hence, the new input variable matrix X st is obtained; 4.
The ∆x(t − τ) and ∆y(t − 1) of new input are calculated, and the ∆y(t) of output is calculated;

5.
The training set ∆X 0 tr and ∆Y 0 tr are confirmed and ∆X 1 tr and ∆Y 1 tr (z-score normalized) are obtained; 6.
The kernel matrix K 0 tr of the training set is calculated as: Catalysts 2020, 10, 1364 6 of 22 7. The kernel matrix K 0 tr of the training set is centered as: Here, I is a unit matrix, 1 n is a matrix whose all elements are 1 and whose dimension is n.

8.
L is the number of latent variables, i iterates from 1 to L, and initialize the score vector u i of X 1 tr randomly. 9.
The score vector t i is calculated as: 10. The weight vector c i is calculated as: 11. The score vector u i is calculated as: 12.
Step (8) to (11) is repeated until that t i is converged; 13. The matrix K 1 tr and Y 1 tr are reduced as follows: until that t and u are extracted; 14. The regression coefficient B is obtained, and the regression model of the training set is obtained as follows:Ŷ Here, T and U are both matrices, which are formed by score vector t and score vector u.
The prediction for the test set is similar to that for the training set, except the computation of the test kernel matrix K 0 te and the centralization of K 0 te : Here, nt is the number of the test set. In addition, the kernel function uses the radial basis function (RBF) kernel in this paper.
(2) Feedback correction In order to compensate for the prediction error, the feedback correction equation is as follows: Here, ρ is 0.3,ỹ(t) is the corrected predicted value at time t,ŷ(t) is the predicted value at time t, y(t) is the real value at time t. Because the SCR de-NO x process is very complicated, a complete mathematical model of the SCR process has still not been summarized. However, the compensation amount of NH 3 injection ∆y NH 3 can be calculated according to the nonlinear Equation (27): Here, y NH 3 is the demand amount of NH 3 injection at the current operating state. y NH 3 (t) is the NH 3 injection flow rate at the time of t.
In this paper, the TD-KPLS model is used to establish the nonlinear model of the NIC, which is shown in Equation (27). The difference between the TD-KPLS model and DTD-KPLS model is that the samples of the TD-KPLS model are not reconstructed. In the model, the deviation ∆ỹ(t) between the corrected DTD-KPLS model outputỹ(t) and the set value of outlet NO x mission y set is used as the input variables, and the compensation amount of NH 3 injection ∆y NH 3 (t) is used as the output variable. In addition, input variables also include inlet flue gas temperature and inlet NO x concentration, which reflect the changing trend of the boiler load to a certain extent.
The adverse effects brought by the inertia characteristic of the SCR system are eliminated by feed-forward compensation. Hence, the NIC can compensate for the NH 3 injection in time to ensure that the outlet NO x emission is stable at the set value.
In the SCR de-NO x system, the NH 3 injection valve can be seen as a linear part, so the algorithm design and parameter setting are performed on the basis of that. However, the NH 3 injection valve has a certain dead zone and saturation zone, which shows nonlinearity. Therefore, in this paper, the middle curve in the on and off stroke is taken as the fitting curve between the NH 3 injection valve opening and the NH 3 injection flow rate.
In order to avoid valve saturation and action frequently, the following constraints of the NH 3 injection valve need to be considered: Here, U Vmax and U Vmin are the upper and lower limits for the NH 3 valve opening. u Vmax and u Vmin are the upper and lower limits for the increment of the NH 3 valve opening. ∆u V (t + 1|t ) represents the increment of the NH 3 valve opening from the next time t+1 to the current time t.

Delay Estimation
Aiming at nonlinearity and large lag in SCR de-NO x process, this paper proposes the k-nearest neighbor MI(KNN_MI) method to estimate the time-delay of the input variable and the effect of the historical data lengths on KNN_MI was taken into account. The KNN_MI method can be summarized as follows [8].
The KNN_MI of variable X and Y is: Here, n x (i) is the sample number x j whose distance from x i is less than ε i /2 strictly, ε i /2 denotes the distance from x i. to its k-th neighbor, and n y (i) is calculated similarly, i ∈ [1, · · · , n]. Ψ (x) is the Catalysts 2020, 10, 1364 and Ψ (1) ≈ −0.5772156. The symbol · · · denotes the mean of all variables in it.
The KNN_MI of high dimensional variables (X 1 , X 2 , · · · , X m , Y) is: Because of the time-delay between each input variable x .i and the output variable y is different, the phase space of x .i is reconstructed by embedding with time-delay τ i ∈ [min(τ i ), max(τ i )] (min(τ i ) and max(τ i ) are resolved by field experience). In addition, MI value has a relation to the length w of x ·i . Therefore, the time-delay τ i and length w are calculated at the time of t as follows: Here, T max is the maximum reaction time when the SCR system responds. Equation (34) involves constrained multivariable nonlinear optimization. If the number of input variables is m, 2 m parameters need to be obtained. Thus, within the above constraints, a global searcher maximizes the objective function by particle swarm optimization (PSO) algorithm. Hence, the optimal τ = [τ 1 , τ 2 , · · · , τ m ] and w = [w 1 , w 2 , · · · , w m ] are obtained. By estimating the time-delay τ i of input variable x .i , the reconstructed input matrix X st is assumed as follows:

Variable Selection
The subset S, which has m input variables, equals to set (X 1 , X 2 , · · · , X m ). The MI between S and Y is defined as: Information entropy represents a measure of uncertainty. If the added variable d i is irrelevant, the change of uncertainty is less. Therefore, the change rate of KNN_MI, which shown in Equation (37) is larger, when the added variable d i is relevant: The high-dimensional KNN_MI and the impact on original MI(S, Y) are considered in the above equation. Therefore,R ∆MI (S + d i , Y) can be used to select variable subset S in forward-selection (step (2)-step (5)). In addition, the one-dimensional KNN_MI between any two variables in the variable subset S can be used to delete redundant variables in backward selection (step (6)-step (7)). Based on the change rate of KNN_MI (KNN_MI_CR), the algorithm for the variable selection is designed as follows: (1) One-dimensional MI(X i ,Y) between each input variable X i and output variable Y are calculated, i = 1, . . . ,m; (2) Based on one-dimensional KNN_MI values, the input variables are sorted from max to min.
The most relevant variable which corresponds to the maximum KNN_MI value is selected as the initial variable set S; Here, α is a threshold value; (5) Step (3) and step (4) are repeated until all input variables were selected. The relevant variable subset S is finally obtained; (6) Backward selection: The one-dimensional KNN_MI between any two variables in S is calculated, and then the combination of redundant variables which has the max KNN_MI value is selected. (7) The redundant variables are eliminated by combining with the one-dimensional KNN_MI in step (2), and the optimal relevant variable subset S is finally obtained.

The Benchmark Dataset Experiment
In order to verify the proposed variable selection method, the Friedman dataset and Housing dataset [23] are used to experiment, and the predictive accuracy of the KPLS model is evaluated by the root mean square error (RMSE).

Friedman Dataset
Friedman function: Here, the input variable X i (1 ≤ i ≤ 10) is a uniform distribution between 0 and 1, ε is the Gaussian noise with a variance of 1. The variables from X 6 to X 10 are irrelevant variables. The variable X 11 = 0.5X 1 + ε is a redundant variable. The sample number is 500. The number of training sets is 338. The number of the test set is 162.
First, this paper uses the proposed variable selection method (KNN_MI_CR) to select variables. In Section 3.2, the one-dimensional MI(X i ,Y) calculated in step (1) is shown in Figure 3.
Here,  is a threshold value; (5) Step (3) and step (4) are repeated until all input variables were selected. The relevant variable subset S is finally obtained; (6) Backward selection: The one-dimensional KNN_MI between any two variables in S is calculated, and then the combination of redundant variables which has the max KNN_MI value is selected. (7) The redundant variables are eliminated by combining with the one-dimensional KNN_MI in step (2), and the optimal relevant variable subset S is finally obtained.

The Benchmark Dataset Experiment
In order to verify the proposed variable selection method, the Friedman dataset and Housing dataset [23] are used to experiment, and the predictive accuracy of the KPLS model is evaluated by the root mean square error (RMSE).

Friedman Dataset
Friedman function: Here, the input variable First, this paper uses the proposed variable selection method (KNN_MI_CR) to select variables. In Section 3.2, the one-dimensional MI(Xi,Y) calculated in step (1) is shown in Figure 3. In Figure 3, if the variable selection is only based on one-dimensional KNN_MI, X8 and X10 are mistakenly selected, X1 and X2 are mistakenly eliminated. In Figure 3, if the variable selection is only based on one-dimensional KNN_MI, X 8 and X 10 are mistakenly selected, X 1 and X 2 are mistakenly eliminated.
In step (2), the most relevant variable X 4, which corresponds to the maximum one-dimensional KNN_MI value, is selected as the initial variable set S. Hence, the initial variable set S is X 4 .
High dimensional KNN_MI and its change rate, which is calculated in step (4), are shown in Figure 4. There, +X 5 represents MI(X 4 , X 5 , Y), +X 3 represents MI(X 4 , X 5 , X 3 , Y) and so on. The threshold value α is 0.1. Therefore, variables from X 6 to X 10 are eliminated, and the relevant variable subset S = (X 4 , X 5 , X 3 , X 2 , X 11 , X 1 ).
KNN_MI value, is selected as the initial variable set S. Hence, the initial variable set S is X4.
In Figure 3, MI(X1, Y), MI(X2, Y) and MI(X11, Y) are relatively close. In addition, MI(X3, Y) and MI(X5, Y) are also relatively close. Therefore, the relevant variable subset S could have a redundant variable. One-dimensional KNN_MI between any two variables in S is shown in Figure 5. It is obvious that MI(X1, X11) is the maximum value. In Figure 3, MI(X1, Y) > MI(X11, Y). Therefore, X11 is a redundant variable. Finally, optimal relevant variable subset S = (X4, X5, X3, X2, X1). This is consistent with Equation (38).  In Figure 3, MI(X 1 , Y), MI(X 2 , Y) and MI(X 11 , Y) are relatively close. In addition, MI(X 3 , Y) and MI(X 5 , Y) are also relatively close. Therefore, the relevant variable subset S could have a redundant variable. One-dimensional KNN_MI between any two variables in S is shown in Figure 5. It is obvious that MI(X 1 , X 11 ) is the maximum value. In Figure 3, MI(X 1 , Y) > MI(X 11 , Y). Therefore, X 11 is a redundant variable. Finally, optimal relevant variable subset S = (X 4 , X 5 , X 3 , X 2 , X 1 ). This is consistent with Equation (38).
Second, the comparison among variable selection methods and the test results of the KPLS model are shown in Tables 1 and 2.
In Tables 1 and 2, it can be seen that BIF, mRMR, MIFS, and CMIM have not selected all valid input variables, and the CMIM method selects redundant variable X 11 in the input variable subset. Compared with the other four variable selection methods, the KNN_MI_CR method selects all relevant input variables. Therefore, the KNN_MI_CR method proposed in this paper can select the input variable subset effectively.  In Tables 1 and 2, it can be seen that BIF, mRMR, MIFS, and CMIM have not selected all valid input variables, and the CMIM method selects redundant variable X11 in the input variable subset. Compared with the other four variable selection methods, the KNN_MI_CR method selects all relevant input variables. Therefore, the KNN_MI_CR method proposed in this paper can select the input variable subset effectively.

Housing Dataset
The Housing dataset is used to predict Boston house price (defined as the output variable Y) by statistic values (defined as input variables X1, ⋅⋅⋅, X13), which represent 13 attributes in each house. The number of training sets is 338. The number of the test set is 168. The comparison of different variable selection methods and test results of the KPLS model are shown in Table 3.

Housing Dataset
The Housing dataset is used to predict Boston house price (defined as the output variable Y) by statistic values (defined as input variables X 1 , · · · , X 13 ), which represent 13 attributes in each house. The number of training sets is 338. The number of the test set is 168. The comparison of different variable selection methods and test results of the KPLS model are shown in Table 3.
It can be seen from the results that the predictive accuracy of the model is highest by using the KNN_MI_CR method. Therefore, the KNN_MI_CR method contributes to establishing a more effective prediction model.

Field Data and Preselected Input Variables
The inlet NO x concentration and NH 3 injection flow rate reflect the NH 3 /NO x molar ratio, which influences the de-NO x efficiency and the NH 3 escape directly. The NH 3 injection flow rate is controlled to match up the change of boiler load by the NH 3 valve. Inlet O 2 content influences outlet NO x concentration and de-NO x efficiency directly. Moreover, the change in boiler load often influences the inlet flue gas flow rate. Then, the flue gas temperature is changed through heat exchange. The inlet flue gas temperature influences the reaction rate and catalyst activity.
In a word, the outlet NO x emission is related to many factors. In addition, the changes in boiler load, coal quality, and combustion condition could cause a large fluctuation in inlet NO x concentration. Therefore, preselected input variables and the output variable are shown in Table 4. Assuming that coal quality is invariable, the selected field data cover steady state and variable state. One-dimensional linear interpolation is carried out on the measured NO x concentration at the process of blowback. Therefore, 2000 samples were collected, and the sampling period is 10 s. Due to the length of this paper, the samples of part preselected input variables and output variables are shown in Figure 6.

Result Analysis of Delay Estimation and Variable Selection
In general, the maximum time-delay of SCR reaction which includes NOx analysis is 120~400 s, and the maximum time-delay of boiler load which influences inlet NOx concentration is 600 s, so the range of τ is (20,60) from x1 to x3, and (1,40) from x4 to x9. Tmax in Equation (32) is 1200 s, so the range

Result Analysis of Delay Estimation and Variable Selection
In general, the maximum time-delay of SCR reaction which includes NO x analysis is 120~400 s, and the maximum time-delay of boiler load which influences inlet NO x concentration is 600 s, so the range of τ is (20,60) from x 1 to x 3 , and (1,40) from x 4 to x 9 . T max in Equation (32) is 1200 s, so the range of w is (1,120). The time-delay of each input variable is different-in-different operation point. The samples from 200 point to 500 point at 800 MW operating state are taken as an example to analyze the delay estimation and variable selection methods. The size of the SCR reactor is 11.67 m × 13.95 m × 12.6 m. The optimal fitness curves of the PSO algorithm for all preselected input variables are shown in Figure 7, and the results are shown in Table 5.  It can be seen from Figure 7, each preselected variable reaches the optimal global solution before the 10th iteration, and the optimal parameter  τ and ' w are obtained. The optimal result multiplies the sampling period to obtain the time-delay of the preselected variable, which is shown in Table 5.  It can be seen from Figure 7, each preselected variable reaches the optimal global solution before the 10th iteration, and the optimal parameter τ and w are obtained. The optimal result multiplies the sampling period to obtain the time-delay of the preselected variable, which is shown in Table 5.
The effect of time-delay needs to be considered for the variable selection in SCR de-NO x process. Therefore, based on the delay estimation result, the phase space reconstruction on each input variable is performed first, and then the KNN_MI_CR method is used to select a suitable variable.
It can be seen from Table 6 that if the model samples are reconstructed by phase space, the result of variable selection is different. The DTD-KPLS model, whose variables are selected by the KNN_MI_CR method, has the highest predictive accuracy. Although the variable selection result is the same, the predictive accuracy of the DTD-KPLS model whose samples are reconstructed is improved in the BIF and CMIM method. In addition, the sequence of the selected input variable is different, and the model accuracy is different, which indicates that the consideration of high-dimensional KNN_MI is conducive to the selection of suitable input variables.

Analysis of Dynamic Model
In general, dynamic modeling is realized by adding the historical input data x(t − 1), · · · , x(t − w + 1) and output data y(t − 1), · · · , y(t − w + 1) as a new input of the model. The 2000 prediction samples are used to analyze model accuracy by using different input variables. The results are shown in Table 7. Table 7. The predictive accuracy of DT-KPLS and DTD-KPLS model using different input variables.

Model Input Variables Dimension of Input Variable RMSE
DT-KPLS It can be seen from Table 7 when input variables are x(t − τ − 1) , y(t − 1) and x(t − τ), the predictive accuracy of the model is highest. In addition, because the model input is historical input data before the current time t, the DTD-KPLS model can predict the current value of the output variable in advance accurately.
When parameter optimization is used in model control strategies, a large number of calculations need to be avoided. In this paper, the DTD-KPLS model has only one RBF kernel parameter. The predictive accuracy of the DTD-KPLS model in different kernel parameters is analyzed. The results are shown in Figure 8. data before the current time t, the DTD-KPLS model can predict the current value of the output variable in advance accurately.
When parameter optimization is used in model control strategies, a large number of calculations need to be avoided. In this paper, the DTD-KPLS model has only one RBF kernel parameter. The predictive accuracy of the DTD-KPLS model in different kernel parameters is analyzed. The results are shown in Figure 8.  The change rate of the RMSE value was no more than 1%, as shown in Figure 8, which indicates that the predictive accuracy was not sensitive to the kernel parameter. Therefore, the DTD-KPLS model could adopt fixed parameters to avoid a large number of calculations in parameter optimization. In this paper, the single-step prediction time was 1 s, so it could meet the demand for control.
In order to compensate for the prediction error, this paper proposes a feedback correction strategy for the DTD-KPLS model. The predicted value and the corrected predicted value are shown in Figure 9. The change rate of the RMSE value was no more than 1%, as shown in Figure 8, which indicates that the predictive accuracy was not sensitive to the kernel parameter. Therefore, the DTD-KPLS model could adopt fixed parameters to avoid a large number of calculations in parameter optimization. In this paper, the single-step prediction time was 1 s, so it could meet the demand for control.
In order to compensate for the prediction error, this paper proposes a feedback correction strategy for the DTD-KPLS model. The predicted value and the corrected predicted value are shown in Figure 9. It can be seen from Figure 9, and the DTD-KPLS model shows high predictive accuracy with a low RMSE of 3.2933 mg/m 3 and a high determinate coefficient (Q 2 ) of 0.7011 in the whole state. A large amount of NOx was produced in a variable state. Hence the predictive accuracy was lower at the peak of the outlet NOx emission curve. After feedback correction, the predicted values were closer to the real value. Steady state and variable state were covered in the model samples, so the DTD-KPLS model had strong self-adaptability.

Analysis of Control Effect
Two kinds of NH3 injection control modes have mainly existed in China. One is fixed NH3/NOx molar ratio control, and the other one is fixed outlet NOx value control. In this paper, the fixed outlet NOx value control was analyzed. First, the NOx flow rate was determined by the inlet NOx concentration and the flue gas flow rate, and the preset molar ratio was calculated. Then, the NH3/NOx molar ratio was corrected based on the measured value and the set value of outlet NOx emission. The amount of NH3 injection was determined by the corrected NH3/NOx molar ratio and the calculated NOx flow rate. Finally, the fixed outlet NOx emission was achieved.
In order to obtain the demand amount of NH3 injection 3 ' NH y at the current operating state, the transfer function from the NH3 injection to the decreased amount of outlet NOx emission was investigated through a dynamic characteristic test as follows: Then, the control structure diagram set up in MATLAB/SIMULINK is shown in Figure 10. It can be seen from Figure 9, and the DTD-KPLS model shows high predictive accuracy with a low RMSE of 3.2933 mg/m 3 and a high determinate coefficient (Q 2 ) of 0.7011 in the whole state. A large amount of NO x was produced in a variable state. Hence the predictive accuracy was lower at the peak of the outlet NO x emission curve. After feedback correction, the predicted values were closer to the real value. Steady state and variable state were covered in the model samples, so the DTD-KPLS model had strong self-adaptability.

Analysis of Control Effect
Two kinds of NH 3 injection control modes have mainly existed in China. One is fixed NH 3 /NO x molar ratio control, and the other one is fixed outlet NO x value control. In this paper, the fixed outlet NO x value control was analyzed. First, the NO x flow rate was determined by the inlet NO x concentration and the flue gas flow rate, and the preset molar ratio was calculated. Then, the NH 3 /NO x molar ratio was corrected based on the measured value and the set value of outlet NO x emission. The amount of NH 3 injection was determined by the corrected NH 3 /NO x molar ratio and the calculated NO x flow rate. Finally, the fixed outlet NO x emission was achieved.
In order to obtain the demand amount of NH 3 injection y NH 3 at the current operating state, the transfer function from the NH 3 injection to the decreased amount of outlet NO x emission was investigated through a dynamic characteristic test as follows: Then, the control structure diagram set up in MATLAB/SIMULINK is shown in Figure 10. In the field data in Figure 6, the inlet NOx and the flue gas flow rate fluctuated from 135~230 mg/m 3 to 120~160 km 3 /h. During the simulation, the inlet NOx, the flue gas flow rate and the set value of outlet NOx were set to 160 mg/m 3 , 1300 km 3 /h and 37 mg/m 3 , which were consistent with the field data. PID tuning program was used to get optimal PID parameters. The results are shown in Figures 11-13.  In the field data in Figure 6, the inlet NO x and the flue gas flow rate fluctuated from 135~230 mg/m 3 to 120~160 km 3 /h. During the simulation, the inlet NO x , the flue gas flow rate and the set value of outlet NO x were set to 160 mg/m 3 , 1300 km 3 /h and 37 mg/m 3 , which were consistent with the field data. PID tuning program was used to get optimal PID parameters. The results are shown in Figures 11-13. In the field data in Figure 6, the inlet NOx and the flue gas flow rate fluctuated from 135~230 mg/m 3 to 120~160 km 3 /h. During the simulation, the inlet NOx, the flue gas flow rate and the set value of outlet NOx were set to 160 mg/m 3 , 1300 km 3 /h and 37 mg/m 3 , which were consistent with the field data. PID tuning program was used to get optimal PID parameters. The results are shown in Figures 11-13.     If the inlet NOx value and the set value of outlet NOx were fixed, as the deviation between them decreased, the PID controller reduced the actual NH3/NOx molar ratio; thereby, the amount of NH3 injection was reduced gradually. After the system was stabilized, the outlet NOx emission, the NH3 injection flow rate and the NH3/NOx molar ratio were stable at 37 mg/m 3 (set value), 60 kg/h and 0.8857, which were close to the average value of field data. So the demand amount of NH3 injection 3 ' NH y corresponding to the set value of outlet NOx emission was 59.6 kg/h, and this method could accurately simulate the fixed outlet NOx control mode. The control process lasted for nearly 1000 s before the system became stable. Hence, the existing system could not meet real-time control because of the long adjustment time.
The predicted value of the TD-KPLS model was taken as the output of NIC in each model update. The input variables included the deviation between the corrected predicted NOx emission value and the set value of outlet NOx emission, inlet flue gas temperature and inlet NOx concentration. The output variable was the amount of NH3 injection compensation. The output of the NIC is shown in Figure 14. If the inlet NO x value and the set value of outlet NO x were fixed, as the deviation between them decreased, the PID controller reduced the actual NH 3 /NO x molar ratio; thereby, the amount of NH 3 injection was reduced gradually. After the system was stabilized, the outlet NO x emission, the NH 3 injection flow rate and the NH 3 /NO x molar ratio were stable at 37 mg/m 3 (set value), 60 kg/h and 0.8857, which were close to the average value of field data. So the demand amount of NH 3 injection y NH 3 corresponding to the set value of outlet NO x emission was 59.6 kg/h, and this method could accurately simulate the fixed outlet NO x control mode. The control process lasted for nearly 1000 s before the system became stable. Hence, the existing system could not meet real-time control because of the long adjustment time.
The predicted value of the TD-KPLS model was taken as the output of NIC in each model update. The input variables included the deviation between the corrected predicted NO x emission value and the set value of outlet NO x emission, inlet flue gas temperature and inlet NO x concentration. The output variable was the amount of NH 3 injection compensation. The output of the NIC is shown in Figure 14.
of the long adjustment time.
The predicted value of the TD-KPLS model was taken as the output of NIC in each model update. The input variables included the deviation between the corrected predicted NOx emission value and the set value of outlet NOx emission, inlet flue gas temperature and inlet NOx concentration. The output variable was the amount of NH3 injection compensation. The output of the NIC is shown in Figure 14.  Figure 14 shows that the output of the NIC was consistent with the trend of the expected value of NH3 injection compensation. Therefore, the predictive accuracy of TD-KPLS was high. In addition, the predicted value was a mostly negative value indicating that the amount of NH3 injection was reduced by 11% after adding the NIC. Assuming that the price of NH3 water was about 3000 RMB per ton, the data used in this paper was taken as an example. After the application of the NIC, the cost of de-NOx could be saved by 531.2 RMB per day.  Figure 14 shows that the output of the NIC was consistent with the trend of the expected value of NH 3 injection compensation. Therefore, the predictive accuracy of TD-KPLS was high. In addition, the predicted value was a mostly negative value indicating that the amount of NH 3 injection was reduced by 11% after adding the NIC. Assuming that the price of NH 3 water was about 3000 RMB per ton, the data used in this paper was taken as an example. After the application of the NIC, the cost of de-NO x could be saved by 531.2 RMB per day.
Because the SCR de-NO x system had large inertia and had a large delay in NO x analysis; hence, the following analysis started from the 100th point. The control effect of outlet NO x emission is shown in Figure 15. Because the SCR de-NOx system had large inertia and had a large delay in NOx analysis; hence, the following analysis started from the 100th point. The control effect of outlet NOx emission is shown in Figure 15.  Figure 15 shows the control effect of the existing controller was not ideal, and the outlet NOx emission produced drastic fluctuation when the load changes. For example, the outlet NOx emission exceeded the national NOx emission standard (50 mg/m 3 ) at the 500, 1400 and 1800 points. In contrast, after the NIC was added, the outlet NOx emission whose fluctuation ranged in ±5 mg/m 3 was stable near the set value. Therefore, the outlet NOx emission was far lower than the national NOx emission standard.
It can be seen from Figure 16 that the minimum value of the de-NOx efficiency after adding the NIC (76.31%) was higher than the minimum value of the de-NOx efficiency of the existing controller (73.79%). The average de-NOx efficiency was 80.12% by using the existing controller, and the average de-NOx efficiency was 80.15% after adding the NIC. This indicated that the de-NOx efficiency was basically unchanged after adding the NIC.  Figure 15 shows the control effect of the existing controller was not ideal, and the outlet NO x emission produced drastic fluctuation when the load changes. For example, the outlet NO x emission exceeded the national NO x emission standard (50 mg/m 3 ) at the 500, 1400 and 1800 points. In contrast, after the NIC was added, the outlet NO x emission whose fluctuation ranged in ±5 mg/m 3 was stable near the set value. Therefore, the outlet NO x emission was far lower than the national NO x emission standard.
It can be seen from Figure 16 that the minimum value of the de-NO x efficiency after adding the NIC (76.31%) was higher than the minimum value of the de-NO x efficiency of the existing controller (73.79%). The average de-NO x efficiency was 80.12% by using the existing controller, and the average de-NO x efficiency was 80.15% after adding the NIC. This indicated that the de-NO x efficiency was basically unchanged after adding the NIC.

standard.
It can be seen from Figure 16 that the minimum value of the de-NOx efficiency after adding the NIC (76.31%) was higher than the minimum value of the de-NOx efficiency of the existing controller (73.79%). The average de-NOx efficiency was 80.12% by using the existing controller, and the average de-NOx efficiency was 80.15% after adding the NIC. This indicated that the de-NOx efficiency was basically unchanged after adding the NIC. In order to calculate the NH3 escape further, the following formula was introduced.
Here, t represents the sampling time; Wm is the measured NH3 injection flow rate, kg/h; Wc is the NH3 injection consumption, kg/h; Vgas is the inlet flue gas flow rate, m 3 /h; p is the NH3 escape, μg/m 3 .
Because the compensation amount of NH3 injection in this paper was negative value mostly, the consumption of NH3 injection was regarded unchanged basically. Figure 17 was the comparison between the NH3 escape of the existing controller and the NH3 escape after NH3 injection compensation. In order to calculate the NH 3 escape further, the following formula was introduced.
Here, t represents the sampling time; W m is the measured NH 3 injection flow rate, kg/h; W c is the NH 3 injection consumption, kg/h; V gas is the inlet flue gas flow rate, m 3 /h; p is the NH 3 escape, µg/m 3 .
Because the compensation amount of NH 3 injection in this paper was negative value mostly, the consumption of NH 3 injection was regarded unchanged basically. Figure 17 was the comparison between the NH 3 escape of the existing controller and the NH 3 escape after NH 3

injection compensation.
Catalysts 2020, 10, x FOR PEER REVIEW 20 of 23 Figure 17. The NH3 escape of the existing controller and the NH3 escape after NH3 injection compensation.
In Figure 17, after the NIC was added, although the average of de-NOx efficiency did not change, the NH3 escape was reduced by 39% after NH3 injection compensation.
Actually, in order to avoid actuator saturation, the NH3 injection valve opening was restrained by conditions (23) and (24) in the NH3 injection control. The NH3 valve opening of the existing controller and NH3 valve opening after NH3 injection compensation are shown in Figure 18.  The NH 3 escape of the existing controller and the NH 3 escape after NH 3 injection compensation.
In Figure 17, after the NIC was added, although the average of de-NO x efficiency did not change, the NH 3 escape was reduced by 39% after NH 3 injection compensation.
Actually, in order to avoid actuator saturation, the NH 3 injection valve opening was restrained by conditions (23) and (24) in the NH 3 injection control. The NH 3 valve opening of the existing controller and NH 3 valve opening after NH 3 injection compensation are shown in Figure 18.
Due to the lag of NO x analysis, the NH 3 control valve was prevented from being over-opened or over-closed. Therefore, when the NH 3 control valve was in automatic mode, the NH 3 valve opening was limited from U Vmin = 20% to U Vmax = 50%. In Figure 18, the NH 3 valve opening of the existing controller reached 50% from 1300 points to 1500 points, which indicated that the actuator reached saturation in automatic control. When the NIC was used, the average of the NH 3 valve opening was reduced, thereby actuator saturation was avoided.
In Figure 17, after the NIC was added, although the average of de-NOx efficiency did not change, the NH3 escape was reduced by 39% after NH3 injection compensation.
Actually, in order to avoid actuator saturation, the NH3 injection valve opening was restrained by conditions (23) and (24) in the NH3 injection control. The NH3 valve opening of the existing controller and NH3 valve opening after NH3 injection compensation are shown in Figure 18. Due to the lag of NOx analysis, the NH3 control valve was prevented from being over-opened or over-closed. Therefore, when the NH3 control valve was in automatic mode, the NH3 valve opening was limited from UVmin = 20% to UVmax = 50%. In Figure 18, the NH3 valve opening of the existing controller reached 50% from 1300 points to 1500 points, which indicated that the actuator reached saturation in automatic control. When the NIC was used, the average of the NH3 valve opening was reduced, thereby actuator saturation was avoided.
The upper limitation uVmax and the lower limitation uVmin of the increment of NH3 valve opening were 2% and −2%, respectively. Figure 19 shows that the increment of NH3 valve opening after NH3 injection compensation was within limitation. Therefore, the NH3 valve was protected, and the control accuracy was improved. The upper limitation u Vmax and the lower limitation u Vmin of the increment of NH 3 valve opening were 2% and −2%, respectively. Figure 19 shows that the increment of NH 3 valve opening after NH 3 injection compensation was within limitation. Therefore, the NH 3 valve was protected, and the control accuracy was improved. In all, the proposed control strategy had a good control effect. Through the NH3 injection was adjusted by NIC continually, the controller could decrease the NH3 injection and decrease the NH3 escape as much as possible while ensuring that the high de-NOx efficiency and NOx emission meets the national NOx emission standard. Therefore, the operation cost was reduced, and secondary pollution caused by the incomplete reaction of NH3 was avoided.

Conclusions
A dynamic KPLS model incorporated with variable selection and delay estimation was proposed for the prediction of outlet NOx emission in advance. The KNN_MI method was used to estimate the time-delay, and the effect of historical data lengths on the KNN_MI value was considered. Bidirectional search, which is based on the change rate of KNN_MI (KNN_MI_CR), was used for variable selection, which avoids using a single evaluation strategy and considers the effect of highdimensional KNN_MI. Finally, the DTD update method and feedback correction strategy are proposed, so the fixed parameter is used in the final model. Therefore, the final model could be identified offline by using field data and have high predictive accuracy. The proposed control system includes the main controller and the correction controller. The main controller is the existing PID controller. The combination of NIC and the outlet NOx emission model is used as the correction controller. According to the results of the field data experiment, the proposed control strategy has several findings as follows: (1) In the aspect of the control effect, the outlet NOx emission meets the national NOx emission standard, whose fluctuation range in ±5 mg/m 3 is stable near the set value, and the system maintains high de-NOx efficiency; the NH3 escape is reduced by 39% after NIC. (2) Compared with the conventional PID control, the proposed control strategy not only protects the NH3 injection valve but also reduces the operation cost because of the reduction of NH3 injection; Figure 19. The increment of NH 3 valve opening after NH 3 injection compensation.
In all, the proposed control strategy had a good control effect. Through the NH 3 injection was adjusted by NIC continually, the controller could decrease the NH 3 injection and decrease the NH 3 escape as much as possible while ensuring that the high de-NO x efficiency and NO x emission meets the national NO x emission standard. Therefore, the operation cost was reduced, and secondary pollution caused by the incomplete reaction of NH 3 was avoided.

Conclusions
A dynamic KPLS model incorporated with variable selection and delay estimation was proposed for the prediction of outlet NO x emission in advance. The KNN_MI method was used to estimate the time-delay, and the effect of historical data lengths on the KNN_MI value was considered. Bidirectional search, which is based on the change rate of KNN_MI (KNN_MI_CR), was used for variable selection, which avoids using a single evaluation strategy and considers the effect of high-dimensional KNN_MI. Finally, the DTD update method and feedback correction strategy are proposed, so the fixed parameter is used in the final model. Therefore, the final model could be identified offline by using field data and have high predictive accuracy. The proposed control system includes the main controller and the correction controller. The main controller is the existing PID controller. The combination of NIC and the outlet NO x emission model is used as the correction controller. According to the results of the field data experiment, the proposed control strategy has several findings as follows: (1) In the aspect of the control effect, the outlet NO x emission meets the national NO x emission standard, whose fluctuation range in ±5 mg/m 3 is stable near the set value, and the system maintains high de-NO x efficiency; the NH 3 escape is reduced by 39% after NIC. (2) Compared with the conventional PID control, the proposed control strategy not only protects the NH 3 injection valve but also reduces the operation cost because of the reduction of NH 3 injection; (3) The reduction of NH 3 escape avoids operating accidents and secondary pollution.
The potential disadvantage of the proposed control strategy is that the calculation of the demand amount of NH 3 injection y NH 3 at the current operating state involves a dynamic characteristic test. For different operating states, y NH 3 will be different. If the operating state changes frequently, it will not be easy to determine y NH 3 accurately.