The gas turbine cooling system is a typical MIMO system. The complexity focuses on the multivariable, strongly coupled, nonlinear and uncertain characteristics. In order to solve the control problem for the strongly coupled multivariable of pressure, flow, and temperature, an intelligent approach is necessary and more appropriate. The swarm intelligence optimization algorithms have developed rapidly. Scholars propose new swarm intelligence optimization algorithms to solve the scientific problems of complex systems every year, which proves its important position in complex system models. The advantage of swarm intelligence is that it can solve nonlinear, time-varying, black box model problems in multi-dimensional space, and has the ability of global search. Of course, it also has some disadvantages. Every optimization search needs to traverse all agents before completing an iteration. For each agent, it can only move a small step in the process of completing an iteration. For an agent whose initial position is very far away from the point, it will take a long time. If the speed of the agent is set too fast, it will lead to the agent directly jumping out of the optimal solution in an iteration. These problems will lead to slow searching speed of multi-agent cooperation, or premature convergence and local optimal solution. Because of these shortcomings, many scholars have constantly proposed new intelligent optimization algorithms, or improved the original optimization algorithms. Reference [
1] is inspired by the lifestyle, food search and food competition of various vultures on the African continent, proposes a new meta heuristic algorithm, which focuses more on exploration in the early stage of optimization operation. African vulture’s optimization algorithm (AOA) has significant advantages within 95% confidence interval. Its novelty lies in that it not only considers the best fitness individuals but also considers the suboptimal fitness individuals. Reference [
2] is inspired by rabbits in nature. Artificial rabbit optimization (ARO) models the survival strategy of rabbits: detour foraging and random hiding. The novelty of the algorithm is that rabbits are willing to eat distant objects first because of their nature. This interesting phenomenon enables ARO to avoid local extremum and conduct a global search. ARO has significant competitiveness in dealing with engineering tasks of unknown and limited search space. Reference [
3] simulates the foraging and burrowing activities of prairie dogs and the specific response to the unique alarm of prairie dogs performs well in finding the optimal global solution and having more stable convergence. The limitations in Prairie dog optimization algorithm (PDOA) are that only single objective continuous optimization problems are solved, and the performance of algorithms in solving complex industrial systems has not been studied. Beluga whale optimization (BWO) proposed in reference [
4] is inspired by Beluga whale’s behavior, such as swimming, prey, and whale falling. It is composed of three stages: exploration stage, development stage, and whale falling stage, which have achieved very good results in benchmark function testing. The advantage and novelty of the algorithm is that Levy Flight is introduced to enhance the global convergence in the development phase. In addition, there are Harris Hawks Optimizer(HHO) [
5], Red Fox Optimization (RFO) [
6], Artificial Lizard Search Optimization (ALSO) [
7], etc. These optimization algorithms have the same purpose, which is to improve the ability of local development and global exploration and obtain better convergence performance. Egret Swarm Optimization Algorithm (ESOA) is a heuristic algorithm combining the predatory behavior of snow egrets (sit-and-wait strategy) and big egrets (aggressive strategy) [
8]. The advantage is that the performance and robustness of ESOA to typical optimization applications have been proved. The limitation is that other mathematical forms of predator-prey strategies have not been developed. Sine Cosine Algorithm [
9] is an intelligent optimization algorithm proposed by Seyedali Mirjalili in 2016. In SCA, multiple initial random candidate solutions will be generated, and they will fluctuate outward or toward the optimal solution based on the mathematical model of sine and cosine. Multiple random variables and adaptive variables are used to calculate the current position of the solution. The advantage is that the principle of SCA is simple and easy to implement, it can be easily applied to optimization problems in different fields.
Many optimization algorithms will be integrated with SCA, so that different regions in the space can be searched, effectively avoiding local optimization, and converging to the global. References [
10,
11,
12,
13,
14] are respectively the Barnacle Algorithm Optimizer, Arithmetic Optimization Algorithm, Dolphin Swarm Optimization, Crow Search Algorithm and Particle Swarm Optimization of mixed Sine Cosine Algorithm. These hybrid algorithms have verified the strong adaptability of SCA and can obtain good optimization results in different fields, which show their potential to solve many optimization problems in complex system. Algorithm review in the form of tables is shown in
Table 1:
One of the most widely used swarm intelligence optimization algorithms is to optimize the parameters of complex systems [
15,
16]. When the control system has multiple controlled variables, multiple control loops need to be added, which form a MIMO system. In the MIMO system, due to the actual process of industrial systems, there are often some coupling phenomena. The Once-through steam generator (OTSG) in reference [
17] is a strong coupling system. In order to solve the problem of outlet pressure control, Proximal Policy Optimization (PPO) is used to optimize the PID parameters in real time. In addition, take the nozzle of the flame cutting machine as an example. There are dozens of variables, such as the length and diameter of the nozzle of the cutting machine, the pressure of the low-pressure chamber, intermediate pressure chamber and high-pressure chamber, and the length and diameter of the pressure chamber. Because of the serious coupling inside, it is difficult to obtain the relationship between variables through traditional modeling methods. Taking the cooling system of gas turbine as an example, the secondary circuit is designed to realize the cooling of gas turbine by using the secondary water cycle. The functions of target flow, target inlet water temperature and main pipe pressure are difficult to express accurately. In addition, they are also affected by the output temperature of heat exchanger, temperature loss of loop pipe, loop water volume and wastewater volume disturbance. For MIMO systems with large disturbance amplitude, it is difficult to achieve the desired control effect by using the usual control methods. However, if the above complex industrial systems can obtain the input and output conditions under different conditions, set some evaluation functions to obtain the impact of each dimension on the system. Then, set different weights through the swarm intelligence algorithm, the desired combination of parameters can be got to achieve system intelligent and automatic control. In order to solve the problem of real-time control of pressure, flow and temperature of gas turbine cooling system, the research in this paper is as follows: