This paper puts forward a new viewpoint on optimization of boiler combustion, namely, reducing NOx emission while maintaining higher reheat steam temperature rather than reducing NOx emission while improving boiler efficiency like traditional practices. Firstly, a set of
Boiler combustion optimization of reducing nitrogen oxide (NOx, for short) has become a hot topic during the past three decades. There exist several currently typical ways in coping with the boiler combustion optimization problem. The first popular method is numerical simulation that is based on computational fluid dynamics (CFD) [
The development of datadriven methods can be divided into two stages. At the first stage, researchers only focus on NOx emission reduction by using evolutional algorithms (EAs) to search the optimal set point of controllable process variables. The typical EAs include genetic algorithm (GA), particle swarm optimization (PSO), and ant colony optimization (ACO). Among them, GA is frequently used on boiler combustion optimization. For example, in [
This issue with multiobjective optimization in boiler combustion systems has gained great attention at the second stage. Traditionally, boiler combustion optimization is implemented to reduce NOx emission and increase boiler efficiency by EAs (for example, see works [
Up to date, to the best of our knowledge, there is few literature on boiler combustion optimization to reduce NOx emission and improve reheat steam temperature simultaneously. Motivated by the above statements, this paper aims to reduce NOx emission while achieving higher reheat steam temperature by proposing a jointed optimization method. More precisely, a Multiple Output version of Nonlinear Partial Least Squares (MONPLS) regression model is first proposed to predict behaviors of NOx emission and reheat steam temperature synchronously. To achieve better performance, the structure and parameters of MONPLS are identified by repeated double cross validation (rdCV) rather than traditional kfold crossvalidation strategy. Then, a multiobjective artificial bee colony (MOABC) algorithm is adopted to search optimal inputs of predictors that can achieve lower NOx emission and higher reheat steam temperature from Pareto front. The modelling data are from a combustion adjustment experiment conducted on a real 1000 MW coalfired boiler. It will be seen that our proposed method outperforms combustion adjustment experimental data and commonly used nondominated sorting genetic algorithm II (NSGAII). Therefore, the main contributions of this paper can be summarized in threefold:
Both NOx emission and reheat steam temperature are firstly proposed in boiler combustion optimization. This strategy can reduce NOx emission while maintaining higher reheat steam temperature to guarantee the safety in boiler combustion system control as well as the improvement of whole plant efficiency.
A MONPLS method with rdCV strategy is raised to establish the predictive model of both NOx emission and reheat steam temperature. This algorithm is powerful due to its strong generalization ability especially with small number of samples.
A MOABCbased multiobjective optimization method is proposed on boiler combustion optimization. On the basis of the rdCVMONPLS modelling method, our proposed MOABC algorithm can reduce NOx emission synchronously and improve reheat steam temperature effectively compared with NSGAII and the experimental data.
The rest of the paper is organized as follows. In Section
In this section, the boiler combustion system is introduced, together with the dynamic characteristics of combustion system. And then, the data source used for modelling establishment and validation is presented.
Figure
Schematic diagram of a 1000 MW boiler combustion system: (1) boiler; (2) burners.
Generally, different coal allocations decided by the coal feeding rate of each mill will lead to different temperature fields and flame centers in the furnace. For instance, if more coal is supplied by bottom mills, the flame center will move downward. As a result, NOx production will reduce due to the extension of reductive zone; however, the reheat steam temperature (Tr) will decrease too because of less quality of heat. In the present work, although the coal feeding rate is a directly manipulated parameter, thermal load (
In contrast to coal allocations, primary air is usually not adjusted because its main task is to transport pulverized power from mills, i.e., to match the pulverized coal. Secondary air, including that in the main combustion zone and separated overfire air (SOFA) in the burningout zone, can be adjusted to improve combustion conditions in the boiler. To enhance reducibility in the main combustion zone so as to reduce NOx production, one can decrease secondary air in the main combustion zone with increase of SOFA ratio (
In addition, notice that the higher the running
In summary, to reduce NOx emission and increase reheat steam temperature synchronously heavily relies on the distribution of thermal loads (
The burners at vertical direction are tilted within a range of ±30° to tune the reheat steam temperature (
The value of reheat steam temperature from actual operational conditions is not accurate as it is controlled by a closedloop temperature system. Therefore, we adopted the data collected from a combustion adjustment experiment shown in Supplementary file of the 1000 MW power plant described in Section
Reheat steam temperature in the experiment was not controlled by a closedloop way, and hence, its values are real. Therefore, all collected experimental data are more useful than data collected in practical running way when validating the performance of our method that will be presented later.
PLS/NPLS algorithms have been applied in engineering (for example, see [
Give inputs
Define
Let
Firstly,
Then, one can fit the polynomial relationship between
So, one can get the polynomial coefficient
After coefficients
Then, update
At this point, we can recalculate the vector
Check the convergence of
Finally, the residual of
Replace
After all
From the above interpretations, the rdCVMONPLS is summarized in Algorithm
Input: data
Output: optimal number of principal component
Split dataset
Select
Split Calibration set equally into
Select
Fit MONPLS based on
Apply the MONPLS models to
Calculate mean square error
Estimate optimum principal components
Make MONPLS models based on Calibration set
Test fitted models on
Find the smallest bias and determine the optimal principal component
One can get
Totally, after a complete rdCV run, we can get
Identify rdCVMONPLS model with database
In this section, rdCVMONPLS is identified, respectively, at 650 MW, 800 MW, and 850 MW. In each case, identification as well as rdCV data are shown in Table
Figure
Percentage of principal components
For better comparison, 5fold cross validation (We call 5foldMONPLS model) is conducted by the same identification data as the rdCV method. After 5fold cross validation process, the optimum principal component
(rdCVMONPLS of 650 MW load condition). Since
Parameters of rdCVMONPLS model at 650 MW.





0.1084  −1.0821  −0.2037  0.7211  
0.7642  1.7506  2.7657  0.6928  
−0.2669  −2.0513  0.9019  
−0.5667  1.7544  
−0.0943  −1.3794  
0.0555  1.7356  







−0.2521  1.3719  −0.0598  0.5585  
−0.5344  −1.1655  1.1211  −0.8295  
−0.5870  0.1064  0.6167  
−0.5105  −1.2466  
0.1779  0.0342  
0.1181  1.2109  







0.7658  1.7521  0.0860  0.8038  
−0.0421  −0.7898  0.2901  0.5949  
−0.5367  0.0805  −0.5950  
0.3318  −0.6007  
0.0995  −1.1659  
0.0608  −0.2728 
(rdCVMONPLS of 800 MW load condition). The first two components (
Parameters of rdCVMONPLS model at 800 MW.





−0.4416  −0.0237  −0.2057  0.7513  
−0.3083  −0.2094  1.4695  0.6600  
0.3598  0.0880  0.2770  
−0.1139  0.2170  
−0.1758  −0.0283  
−0.5304  −1.0054  
0.5053  0.7517  







0.3187  0.9644  −0.0116  0.7014  
−0.0164  0.1064  0.4219  −0.7128  
−0.2241  −0.2031  0.0257  
−0.0662  −0.4456  
0.3286  −0.9193  
0.2724  0.3618  
0.8133  1.0018 
(rdCVMONPLS of 850 MW load condition). Similar as Case 2, the first two components (
Parameters of rdCVMONPLS model at 850 MW.





0.2595  0.3142  0.0113  0.8622  
0.4561  0.0651  1.5380  0.5066  
−0.3307  −0.6749  −0.0266  
−0.5786  0.0298  
−0.0490  −0.2947  
0.05273  1.2676  







0.1698  −1.6923  0.0092  0.5021  
0.0401  −2.2468  1.1094  −0.8648  
0.5532  −0.5951  −0.1266  
−0.6529  −2.4330  
0.0806  −0.2785  
−0.4804  −0.2926 
In general, generalization ability of a prediction model is more important than its fitting ability. Therefore, it is necessary to validate aforementioned models to get their generalization ability. Validation samples in three cases are seen in Table
To state the superiority of the rdCVMONPLS model, another three wellknown methods: 5foldMONPLS, support vector regression (SVR), and artificial neural network (ANN) are employed to establish models of NOx emission and reheated steam temperature. All methods are on the same identification and validation data. Figures
Comparisons among different predictors at 650 MW.
Comparisons among different predictors at 800 MW.
Comparisons among different predictors at 850 MW.
Loads  Methods 







650 MW  rdCVMONPLS  0.1346  0.0193 

0.8458  0.1138  0.9596 
5foldMONPLS  0.1354  0.0192  0.1546  0.8458  0.1138  0.9596  
SVR  0.1407  0.0294  0.1701  0.8705  0.1347  1.0052  
ANN  0.1360  0.0336  0.1696  0.7806  0.1342 




800 MW  rdCVMONPLS  0.0985  0.0140 

0.5368  0.1139 

5foldMONPLS  0.1397  0.0098  0.1495  0.5368  0.1139  0.6507  
SVR  0.1318  0.0295  0.1613  1.3079  0.1580  1.4659  
ANN  0.1633  0.0214  0.1847  1.1438  0.2416  1.3854  


850 MW  rdCVMONPLS  0.0931  0.0141 

2.4469  0.2517  2.6986 
5foldMONPLS  0.1068  0.0136  0.1204  2.4469  0.2517  2.6986  
SVR  0.1073  0.0165  0.1238  2.5070  0.1665 


ANN  0.1416  0.0139  0.1555  2.9540  0.2784  3.2324 
^{1}The values in bold are the optimal in their columns. ^{2}
It can be seen from Figures
Compared with kfold cross validation, rdCV can achieve more robust ability. This also shows that rdCV can be successfully used in NPLS. Besides, rdCVMONPLS is more powerful than SVR and ANN in generalization ability on the modelling of NOx emission and reheat steam temperature.
Artificial bee colony (ABC) is a wellknown intelligent optimization algorithm proposed in 2005 [
The objective of combustion optimization is to minimize NOx emission and maximize reheat steam temperature (Tr) through searching optimal inputs (
To solve problem 4.1, a MOABC is applied step by step as follows:
(solutions initialization). New variables named
In addition, assign each food source with a trial index
(solutions evolve in employed bee phase). The initial solutions in (
(solutions evolve in onlooker bee phase). The quality of solution
Once a solution is selected, this solution will evolve to a new position according to formula (
(solutions evolve in scout bee phase). There is at most one scout bee in the colony. This means if the maximal
(solution archive updates). A fixedsize archive (e.g.,
All the above steps are repeated until the maximum iteration,
Schematic diagram of the MOABC algorithm.
The specific values of
To implement MOABC as shown above, some parameters should be preset including
Furthermore, another popular multiobjective EA (MOEA), NSGAII, is also conducted for comparison. Values of
In the present work, we use the number of function evaluations (
The optimization results of MOABC and NAGAII are presented in Figures
Pareto frontier by MOEAs at 650 MW.
Pareto frontier by MOEAs at 800 MW.
Pareto frontier by MOEAs at 850 MW.
To assess the solution sets shown in Figures
Given a solution set
Specifically, for a twoobjective optimization problem, HV can be calculated by the following steps. Firstly, the nondominated points in set
The
HV indicator and time consumption by MOEAs.
Loads  MOEAs 

HV  Time consuming ( 

650 MW  MOABC  (1200, 0.002) 

36.503 
NSGAII  (1200, 0.002) 

37.021  


800 MW  MOABC  (500, 0.002) 

38.105 
NSGAII  (500, 0.002) 

37.929  


850 MW  MOABC  (500, 0.002) 

30.856 
NSGAII  (500, 0.002) 

29.499 
Table
Furthermore, we can present our findings in our current study whether the nondominated solutions by MOABC shown in Figures
Recommended setpoints for inputs at 650 MW.

NOx 

Thermal load (C)  Thermal load (D)  Thermal load (E)  Thermal load (F) 

Running 



1 


146.6  167.5  154.7  205.8  0.225  4.805  6.26  0.28 
2 


143.8  171.0  150.0  209.9  0.209  4.742  1.67  0.59 
3 


146.6  167.6  155.9  205.7  0.229  4.672  9.19  0.02 
4 


146.6  171.3  147.1  209.4  0.190  4.782  3.65  0.38 
5 


140.1  169.5  147.1  210.0  0.203  4.791  0.61  0.81 
6 


142.1  170.4  147.1  209.2  0.211  4.423  1.01  0.90 
7 


Recommended setpoints for inputs at 800 MW.

NOx 

Thermal load (B)  Thermal load (C)  Thermal load (D)  Thermal load (E)  Thermal load (F) 

Running 



1 


123.1  156.0  166.6  172.9  203.4  0.253  2.211  87.9  0.46 
2 


123.1  155.9  166.6  173.2  203.4  0.253  2.237  86.2  0.61 
3 


123.1  155.4  166.5  173.0  203.4  0.210  2.237  47.8  2.06 
4 


122.4  155.9  166.6  173.5  203.4  0.208  2.236  39.9  2.25 
5 


123.1  157.3  166.2  173.1  203.4  0.196  2.224  56.1  2.92 
6 


123.1  160.0  166.2  173.1  203.4  0.196  2.236  15.0  2.94 
7 


Recommended setpoints for inputs at 850 MW.

NOx 

Thermal load (C)  Thermal load (D)  Thermal load (E)  Thermal load (F) 

Running 



1 


151.1  164.4  206.4  251.3  0.243  2.171  67.1  0.87 
2 


152.6  164.4  205.7  251.3  0.197  2.171  64.7  1.09 
3 


151.3  164.4  186.3  251.3  0.184  2.229  56.6  2.18 
4 


153.1  164.4  186.3  251.3  0.184  2.948  46.4  2.57 
5 


151.1  164.4  186.3  251.3  0.201  4.479  13.6  3.36 
6 


151.1  164.4  186.3  251.0  0.185  4.478  13.0  3.42 
7 


In order to quantify the degree of reduction of NOx and increase of Tr relative to the experimental value, percentage improvement (
By comparing results in Figures
This paper puts a new point on optimizing NOx emission and reheat steam temperature simultaneously using a joint optimization method, in which a set of rdCVMONPLS strategies were proposed as predictors in three cases of load such as 650 MW, 800 MW, and 850 MW. Compared with another three wellknown methods (kfoldMONPLS, SVR, and ANN), this method can achieve higher predictive accuracies. Then, MOABC was applied to search the optimal set point of controllable process variables to reduce NOx emission and improve reheat steam temperature. Results showed that our joint optimization of boiler combustion with MOABC provided a set of tradeoff solutions and outperformed that obtained by NSGAII and experimental data. This implies that our proposed method on boiler combustion optimization can guarantee higher economy as well as safety control of combustion systems.
The data used to support the findings of this study are included within the supplementary information file.
The authors declare no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (Grant no. 51676034) and the Fundamental Research Funds for the Central Universities (Grant no. 2242019K40002).
Appendix A: experimental data are provided when the boiler worked stably, respectively, at 650 MW, 800 MW, and 850 MW. More details can be viewed in Tables A1–A3. Table A1: the steadystate experimental data of 650 MW. Table A2: the steadystate experimental data of 800 MW. Table A3: the steadystate experimental data of 850 MW. Appendix B: Table B1: lower and upper bounds of inputs of the rdCVMONPLS model at 650 MW. Table B2: lower and upper bounds of inputs of the rdCVMONPLS model at 800 MW. Table B3: lower and upper bounds of inputs of the rdCVMONPLS model at 850 MW.