# An Improved Particle-Swarm-Optimization Algorithm for a Prediction Model of Steel Slab Temperature
## 1 Introduction  
In the steel industry, the reheating furnace must reheat the material (slabs) to the desired uniformity temperature profiles at the exit. However, the slab reheating furnace's operation is a complex physical and chemical process [1]. To better control and optimize the furnace's operations, there should be a suitable temperature prediction model to predict the accurate temperatures for the slabs inside the furnace. Given the continuous development of artificial intelligence techniques, the demand for a suitable temperature prediction model is increasing [2]. Therefore, a suitable mathematical model which can predict the discharge temperatures of billets accurately and quickly should be proposed for the control and optimization of the reheating furnaces. In general, the prediction models can be divided into two categories [3]: the mechanism models based on first principles [4] and the empirical models based on the production data and black-box approaches [5]. The first kind of model needs to fully understand the physical and chemical processes inside the reheating furnace--e.g., [1, 6, 7, 8]. The computational requirements of these models vary widely depending on the level of complexity [3]. Finally, the heat-transfer process is often summarized by partial differential equations (PDEs). Usually, mechanism models are complicated and nonlinear (such as those in ([9, 10, 11, 12, 13, 14]). [PERSON] et al. [13] investigated the sequential function specification coupled with the Broyden combined method (BC-SFSM) to obtain the temperature field of a steel billet based on the inverse heat-conduction problem. The resultsillustrate that the majority of relative errors during the whole reheating time are less than 5%. [PERSON] et al. [14] presented a novel method to obtain these parameters by combining a \"black box\" test with a billet heat transfer model. The surface temperature and center temperature's relative error were 2.34% and 3.51%, respectively. The numerical computation of PDEs will require a lot of computational time, which will exceed a practical time criterion. Therefore, this kind of model cannot satisfy the requirements for an online system. The empirical models are often determined by identification methods involving the genetic algorithm (GA), support vector machines (SVMs), neural networks (NNs), particle swarm optimization (PSO) and other intelligent techniques ([15; 16; 17; 18]). For instance, [PERSON] et al. [19] investigated a prediction model using the production data from Ratchasima Steel Products Company. The GA method was used to identify the model's unknown factors. [PERSON] et al. [20] presented the SVM predictive model for the temperature control problem. The PSO was applied to determine proper parameters for the SVM model and finally obtained good performance. [PERSON] et al. [21] constructed a prediction model of slab discharging temperature by combining GA with a BP neural network. The mean-square error of the network was 72.3477, and the error was lower than 20 \({}^{\circ}\)C. [PERSON] et al. [22] used the relevance vector machine (RVM) method to predict the slab temperature. The maximum prediction error of slab temperature was 10.46 \({}^{\circ}\)C. In general, the empirical model is often simplified to a simple formula, so the calculation time is small enough to satisfy online production [23]. The production data and the performance of the intelligent algorithm used will determine the advantages and disadvantages of an empirical model. As the industrial software and database techniques continue developing, more production data are being obtained [24]. Thus, an intelligent algorithm with excellent performance is indispensable, and it behooves us to study the intelligent algorithms carefully. The PSO algorithm has the characteristics of high solution accuracy and a fast approach to the optimal solution. However, the basic PSO varies in its ability to solve problems in different application contexts. It also easily falls into local optima.