To control the furnace temperature of a power plant boiler precisely, a dual-optimized adaptive model predictive control (DoAMPC) method is designed based on the data analytics. In the proposed DoAMPC, an accurate predictive model is constructed adaptively by the hybrid algorithm of the least squares support vector machine and differential evolution method. Then, an optimization problem is constructed based on the predictive model and many constraint conditions. To control the boiler furnace temperature, the differential evolution method is utilized to decide the control variables by solving the optimization problem. The proposed method can adapt to the time-varying situation by updating the sample data. The experimental results based on practical data illustrate that the DoAMPC can control the boiler furnace temperature with errors of less than 1.5% which can meet the requirements of the real production process.
Fossil-fuel-fired power plants can produce stable and controllable energy. Despite the quick development of sustainable power generation methods, such as solar power systems and wind power systems, the fossil-fuel-fired power generation system is and will be an import part of the power system. In the meantime, more effort must be made to reduce the waste gas emission of the thermal power production process in order to protect the environment. To realize this target, the boiler furnace temperature should be controlled to follow certain curves. However, there are several challenges that need to be overcome.
To start with, there is a lack of a dynamic and accurate model of the boiler furnace temperature. There are several mechanism models constructed for the boiler. Gao and Dai [
Second, a modern control method should by tailored to fit the boiler furnace temperature control problem. The widely used control method in thermal power plants is PID control method. Although this method is easy to utilize and simple to understand, the control accuracy cannot meet the requirement. Besides the PID method, many other methods are utilized in boiler control. Park et al. [
Motivated by the two mentioned issues, we proposed a dual-optimized adaptive model predictive control (DoAMPC) method. The proposed DoAMPC has the following main features compared with the previous researches: The DoAMPC adopts LSSVM to construct the predictive model for the boiler furnace temperature with high accuracy rapidly. This model considered the main state variables and control variables. Additionally, to improve the prediction accuracy, differential evolution (DE) is utilized to optimize the parameters of LSSVM for each different problem. The DoAMPC includes a rolling optimization problem with a black-box model and bound constraint conditions. Furthermore, DE is employed to solve this nonlinear problem to get optimized control variable values. The DoAMPC presents a new way to realize model predictive control in practical problems by utilizing data-driven algorithm and intelligent optimization algorithms. Instead of the canonical linear predictive model and linear optimization problem, the nonlinear predictive model and optimization problem is constructed and solved in this method.
The remainder of this paper is organized as follows. Section
The production process is shown in Figure
The production process of the boiler.
Suykens and Vandewalle [
The selection of the kernel parameters influences the predictive accuracy significantly. To maintain the predictive accuracy in a different situation, DE is employed to optimize the parameters dynamically.
DE was proposed by Storn and Price [
The dual-optimization model predictive control method is proposed in this section. In Section
The main procedure of DoAMPC is shown in Figure
The main procedure of DoAMPC.
Firstly, the practical data (PD) collected from power industry are preprocessed to reduce the noise and guarantee the effectiveness of the sample data (SD).
Then, to realize the predictive control of boiler furnace temperature, a predictive model of boiler furnace temperature must be constructed. Due to the nonlinearity and time-varying boiler furnace temperature, a black-box model based on data analytics is conducted. The control variables
Thirdly, an optimization problem based on the black-box model and several constraint conditions is given and solved by DE. The solution is the optimized set value of control variables
Finally, a model correction method is proposed to improve the control accuracy.
The practical data are read from the database which stores the real process variables. These data can reflect the state of the boiler which is precious to construct the prediction model. However, due to the tough process environment, there are data missing, outliers in practical data. To ensure the accuracy of the prediction model, the practical data must be preprocessed. In this paper, we utilize two different methods to deal with the missing data and outliers, respectively.
First, to deal with the data missing, the cubic spline interpolation is employed. Actually, the state variables of the boiler are continuous. The cubic spline interpolation is good at solving this kind of question. It can recover the missing data with relatively smooth data. Additionally, the cubic spline interpolation is easy to program with good stability and convergence property.
Second, the outliers are deleted and replaced by the cubic spline interpolation. The 3
After the preprocessing of the practical data, the sample data are utilized in the following procedure. The preprocessing is done repetitively when there are new data collected.
As mentioned before, the traditional boiler furnace temperature models are not good at dealing with the dynamic situation and cannot be utilized in the model predictive control method directly. So, the black-box model based on DE and LSSVM is constructed.
DE is a swarm-based optimization algorithm which was proposed by Storn in 1995. In this algorithm, several particles made up of parameters that need to be determined are initialized with random values within a constraint. Then, the fitness of each particle is calculated. And the particles are updated following certain formulas considering their fitness. Finally, the swarm converges to a global best location which is the solution of the optimization problem.
LSSVM was proposed in 1995 by Suykens as a variant of SVM. A linear programming problem instead of the quadratic programming problem is solved in LSSVM, which accelerates the calculation while inheriting the ability to solve nonlinear problems. Additionally, LSSVM shows an outstanding generalization ability. The selections of kernel function parameters and regularization parameter are the keys to maintain the predictive accuracy. Due to the complexity of the selection, an optimization problem is constructed and then solved by DE.
Assume that the sample data used to train the predictive model is
Assume that
To calculate the fitness of particles, the kernel parameter
To update particles, the particles change their location by the following equation:
After the update, run Step
If one of the termination conditions is met, stop the algorithm and output the predictive model. If not, go to Step
The termination conditions utilized in this paper are as follows: (
The outputs stored in a specified file for further application include the best parameters, the coefficients
To control the boiler furnace temperature, we attempt to control the temperature to change following a certain curve. This curve named reference curve is given considering the practical requirement. In other words, the objective target is to minimize the error between the outputs and reference curve. After discretization of the reference curve, assume that
To solve the problem, DE is utilized to obtain the optimized control variables. The flowchart of the procedure is shown in Figure
The flowchart of solving the rolling optimization.
Initialize the swarm. As in Section
To calculate the fitness of each particle, the predictive values are calculated. Then, the error between the predictive outputs and reference curve is calculated by formula (
The terminal conditions and the method to update the particle are the same as the ones in Section
The result outputted by DE includes the optimized control variables and the objective value for further analysis.
The state of the boiler is dynamic. And the boiler load should change with the requirement. In this case, the prediction model needs to be corrected if the predictive error exceeds the acceptable range. In this paper, considering that the modeling can be done in seconds, a reconstruction strategy is employed.
If the relative predictive error is bigger than 1% for continuous
To testify the performance of the proposed algorithm, experiments based on the practical production data are carried out. Both the accuracy of the predictive model and the effectiveness of the DoAMPC method are testified. All the algorithms are implemented using VC++. All the following experiments are run on a PC with Intel Core i7-4712MQ CPU (2.30 GHz), 4.00 GB RAM, and Windows 10 operating system.
The data utilized in the following experiments are collected from a Chinese thermal power plant. The details of the data are shown in Table
The details of the datasets.
Name of the dataset | Number of instances | Number of inputs | Number of outputs |
---|---|---|---|
Case | 500 | 12 | 1 |
Case | 500 | 12 | 1 |
Case | 500 | 12 | 1 |
To utilize DE to solve the two optimization problems, some of the DE parameters need to be set up. By the commonly used trial-and-error method, the parameters are set up as follows:
To verify the accuracy of the proposed black-box model, several experiments based on the datasets mentioned in Section
The experimental results of the proposed modeling method.
The predictive results based on case 1
The predictive results based on case 2
The predictive results based on case 3
The boxplot of predictive errors based on case 1
The boxplot of predictive errors based on case 2
The boxplot of predictive errors based on case 3
The results in subplots (a)–(c) illustrate that (
All the results illustrate that the proposed modeling method can construct an accurate model for nonlinear problems.
The control results of the proposed DoAMPC method and the widely used PID control method are shown in Figure
The control results of the proposed DoAMPC.
The control result of scene 1
The control result of scene 2
The control result of scene 3
The boxplot of the control errors
From subplots (a)–(c), the following results can be concluded. (
Similar to the predictive results, the control errors are bigger in the load change point than in a stable situation. This may be caused by the lag of model reconstruction. That is, the predictive model needs several sample times to reconstruct the model. However, the good performance of the reconstructed model demonstrates the effectiveness of the model correction strategy.
All the results demonstrate that the DoAMPC can handle nonlinear and dynamic problems with good performance. The generalization ability of the proposed method is outstanding. With the update of the sample data, this method can be utilized in other boilers in other thermal power plants.
A dual-optimized adaptive model predictive control method based on black-box model and DE algorithm is proposed in this paper in order to control the boiler furnace temperature accurately. One major feature of the proposed DoAMPC method is that it uses a black-box model based on LSSVM and DE. The DE optimizes the parameters of the LSSVM to maintain the high predictive accuracy. Another main feature is that it contains a minimization problem with nonlinear model and bound constraint conditions for the boiler furnace temperature control problem. To solve this nonlinear problem, DE is employed to obtain the optimized control variables. The practical data are assessed to test the performance of the proposed methods. And the results show that the proposed strategies in both modeling and controlling are effective. The proposed method is comparative or superior to some commonly used algorithms. In the future, we will make more effort in improving the prediction accuracy and trying to utilize other data-mining methods in this structure.
The authors declare that there are no competing interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grants 61503072, 71402021, and 51376042, Northeast Electric Power University BSJXM-201434.