## 1 Introduction  
The control valve is a common element in modem process control, which is used to control the flow of a fluid. Its mathematical model is usually necessary in designing the automatic control or fault diagnosis systems. [PERSON]. _et al._[1, 2] described the system of control valve based on fluid mechanics. However, there are a lot of limitations for the theory analysis method because of the complexity of the structure, nonlinearity and time-lag of the control valve. This makes it is quite difficult to accurately forecast the physical variable of control valve. To overcome this problem, some simulation calculation methods are used, such as bondgraph approach [3] and system identification. Especially the latter is wildly used. [PERSON] [4] predicted the characteristics of hydraulic valve using support vector machine. [PERSON] [5] deduced the dynamic mathematic model of the control valve using neural network.  
The least squares support vector machine (LS-SVM) is a reformulation of the support vector machine (SVM) which solves linear programming problem rather than quadratic programming problem [6, 7]. LS-SVM can approach the nonlinear system with high precision, making it an excellent method for modeling nonlinear systems [8, 9]. The LS-SVM model has been successfully used to solve forecasting problems in many fields, such as CO concentration [10], gas [11, 12], short term electric load [13, 14, 15], revenue [16], precipitation [17], wind speed [18], hydropower consumption forecasting [19], and so on. However, we regret that few literatures study the modeling of control valve using LS-SVM. This paper explores the feasibility of using the LS-SVM model to forecast the upstream pressure of control valve. The forecasting performance of the LS-SVM model largely depends on the values of its two parameters. Currently, several meta-heuristic algorithms have been used to determine the optimal values of these two parameters, including particle swarm optimization [11], genetic algorithm [12], chaotic differential evolution approach [20], artificial bee colony algorithm [21], and simulated annealing algorithm [22]. However, these algorithms have some drawbacks such as being hard to understand and reaching the global optimal solution slowly.  
The fruit fly optimization algorithm (FOA) is a novel evolutionary optimization technique, which was proposed by [PERSON] in 2011 [23]. This new optimization algorithm has the advantages of being easy to understand and of reaching the global optimal solution fast. Recently, the FOA has been applied for different problems, for example PID controller tuning [24], power load forecasting [25, 26], web auction logistics service [27] and financial distress [23]. Therefore, this paper attempts to use the FOA to optimize the two necessary parameters in order to improve the performance of the LSSVM model in upstream pressure forecasting of the control valve.  
The outline of the paper is as follows. Section 2 introduces the physical model and LS-SVM model of upstream pressure. Section 3 studies the influence of the LS-SVM parameters on identification performance. Then, in Section 4, the process of optimizing the parameters of LS-SVM based on FOA is introduced in detail. Section 5 introduces the method of sampling the test data, the predicting results and comparison between FOA, the particle swarm optimization (PSO) and the grid search method. Finally, the proposed modeling method is concluded in Section 6.