Improved State Space Model Using Iterative PSO for Unsteady Aerodynamic System at High AOA

Improved State Space Model Using Iterative PSO for Unsteady Aerodynamic System at High AOA

Guiming Luo (School of Software, Tsinghua University, Beijing, China), Boxu Zhao (School of Software, Tsinghua University, Beijing, China) and Mengqi Jiang (School of Software, Tsinghua University, Beijing, China)
DOI: 10.4018/IJCINI.2018070101

Abstract

Due to the complex hysteresis phenomenon at a high angle of attack (AOA), modeling of unsteady aerodynamic coefficients usually encounters the problem that the parameter vector is too long and the simulation accuracy is not high. The article proposes an improved state-space model based on aerodynamics, applying Fourier analysis and the principal component analysis for model optimization. The likelihood criterion and GOIPSO (Iterative Particle Swarm Optimization Based on Genetic Operator) algorithm are established under the Gaussian assumption. The iterative PSO, into which the genetic algorithm's operators are integrated to calculate the optimization of the likelihood function, greatly reduced the probability of local optimization. Experiments show that the algorithm and model proposed in this paper greatly improves the model-fitting accuracy.
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1. Introduction

When the Wright brothers conducted the first controllable flight, the flight control system was born (Jakab, 2014). Aerodynamic coefficients are important parameters during the operation of an aircraft and in the process of establishing a dynamic model in a flight control system. They are also of great significance in the research and design of new aircraft. Along with the development of aircraft technology, research on identification of aerodynamic coefficients has not stopped.

Currently, the flight envelope of an aircraft has expanded from a smooth movement state at a low angle of attack to an unsteady flow state at a high angle (Gad-el-Hak, & Ho, 1986; Lutze, & Fan, 1998). Aerodynamic force data and oscillatory data at a high angle of attack can be obtained through wind-tunnel experiments. The data shows strong inconsistency and time-related complexity compared to that of a low angle of attack. Therefore, aerodynamic coefficients of a flight system have become a focus of the present research. By analyzing the data obtained from wind-tunnel experiments, different aspects of the aircraft system can be modeled. Through computer modeling and simulation experiments, the model is improved to enhance the accuracy of aerodynamic coefficients and provide effective support for aircraft design and control.

The study of identifying aerodynamic coefficients is conducted from static data to dynamic unsteady data, from the initial linear model to the nonlinear model. At present, static pneumatic experiments and linear aerodynamic coefficient model can meet the basic industrial requirements. (Baker, Yuan, & Goggin, 1998) Under the flight conditions of a high angle of attack, aircraft flights demonstrate a high degree of non-linearity and strong hysteresis performance, which have uncovered phenomena calling for new research. To identify the aerodynamic coefficients in complex situations, many aspects of the experimental process and modeling studies have been improved (Denoël, 2009; Meng, Li, & Veres, 2010). This paper is based on the experimental data generated by a wind tunnel in large amplitude oscillation.

In view of the non-linear and unsteady phenomena of aircraft at a high angle of attack, the research addresses mainly three aspects. First, from the perspective of mathematical research to establish a corresponding algebraic model directly for the aircraft, the main idea is to approximate the wind tunnel experimental data or real flight data by using an algebraic model, such as a polynomial model (Lin et al., 1997). Because the length of the parameter vector is guaranteed, a pure algebraic model is generally more accurate, and the model is also simple. In recent years, such methods have been often used at a low angle of attack or in static wind tunnel data modeling.

The second model category is established based on aerodynamics research. For example, in the 1970s, Tobak proposed step theory (Tobak, & Schiff, 1981) to model unsteady aerodynamic coefficients; here, the variation of the aerodynamic coefficients is regarded as a set of a series of step responses. The feature of this model is the viewpoint of physical analysis: using hydrodynamics to analyze the flight processes which result in non-linear aerodynamic phenomena at a high angle of attack and using mathematical expressions to represent the physical phenomena that occur during flight. In addition to an integral model based on step theory, there are also a pure step-response model and a model of differential forms in such models (Wang, Lan, & Brandon, 2000). Additionally, the state space is an important research point for the modeling of aerodynamic coefficients (Taha, Hajj, & Beran, 2014).

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