Hammerstein非线性系统辨识算法研究

发布时间：2018-01-05 13:09

本文关键词：Hammerstein非线性系统辨识算法研究　出处：《浙江大学》2017年博士论文　论文类型：学位论文

【摘要】：在现实生活中,实际系统几乎都是非线性的,而只有当研究对象的非线性程度不强时,才可将对象看成线性模型处理。随着科学技术的迅猛发展,工业中控制系统越来越复杂,对控制精度的要求越来越高,具有复杂非线性的系统不能用线性模型来近似,所以非线性系统的建模逐渐成为非线性系统研究的重要方向。然而辨识非线性系统的难点之一就是缺乏描述各种非线性系统特性的统一的数学模型。Hammerstein非线性模型由于其结构简单且灵活多变,被普遍应用到诸多领域。本文在此开展工作,针对HammersteinARMAX模型,从确定性的线性算法、到非确定性辨识算法,再到非线性辨识算法、最后到辨识算法中的参数优化问题,以此为脉络针对性地展开研究,提出了多种新的HammersteinARMAX辨识算法,以提高非线性模型的辨识精度。本文的主要工作及创新如下:1.针对 Hammerstein ARMAX模型,提出了 Hammerstein ARMAX 递推辅助变量法(Recursive Instrumental Variables,RIV),并对该算法的均方收敛性进行了严格证明。将该算法进行了数值例子研究,并与经典的RLS算法进行了对比。辨识结果表明了该算法的有效性。在有色噪声干扰下,该算法在辨识精度和收敛速度两方面均优于RLS算法;2.针对 Hammerstein ARMAX 模型,提出了 Hammerstein ARMAX 递推极大似然法(Recursive Maximum Likelihood,RML),详细地给出了该算法的推导过程及流程框图。该算法既可以避免过参数化,也可以对噪声模型进行辨识。将该算法进行了数值例子研究,并与经典的RLS算法进行了对比。辨识结果表明了该算法的有效性。该算法在辨识精度上优于RLS算法;3.针对Hammerstein ARMAX模型,提出了一种基于自适应粒子群优化算法(APSO)和鲁棒最小二乘向量机(WLSSVM)相结合的Hammerstein ARMAX APSO_WLSSVM算法。在粒子群优化算法(PSO)的基础上,引入进化状态估计(ESE)技术,对粒子的惯性系数及加速因子进行调整,从而加快算法的收敛速度;同时,变异操作也避免了算法陷入局部最优解,增强了算法的搜索能力。将该算法进行了数值例子研究,并与多种算法进行了对比。辨识结果表明了该算法的有效性。该算法不仅辨识精度高,同时收敛速度优于PSO_WLSSVM算法;4.针对Hammerstein ARMAX模型,提出了一种基于自适应变异果蝇优化算法(AM_FOA)和鲁棒最小二乘法支持向量机(WLSSVM)相结合的Hammerstein ARMAXAM_FOA_WLSSVM 算法。在果蝇优化算法(FOA)的基础上,通过对群体适应度方差和全局最优值判定来进行变异操作,既避免了算法陷入局部最优解,又增强了算法的搜索能力。将该算法进行了数值例子研究,并与多种算法进行了对比。辨识结果表明了该算法的有效性。该算法不仅辨识精度高,同时收敛速度优于FOA_WLSSVM算法。
[Abstract]:In real life, the real system is almost nonlinear, but only when the degree of nonlinearity of the research object is not strong, can the object be treated as a linear model. With the rapid development of science and technology. The control system in industry is becoming more and more complex and the requirement of control precision is higher and higher. The system with complex nonlinear can not be approximated by linear model. Therefore, modeling of nonlinear systems has gradually become an important research direction of nonlinear systems. However, one of the difficulties in identifying nonlinear systems is the lack of a unified mathematical model to describe the characteristics of various nonlinear systems. Hamme. The rstein nonlinear model is simple and flexible because of its simple structure. It has been widely used in many fields. This paper focuses on the HammersteinARMAX model, from deterministic linear algorithm to non-deterministic identification algorithm. Then to the nonlinear identification algorithm, and finally to the parameter optimization problem in the identification algorithm. Based on this research, a variety of new HammersteinARMAX identification algorithms are proposed. In order to improve the identification accuracy of nonlinear model, the main work and innovation of this paper are as follows: 1. Aiming at Hammerstein ARMAX model. Hammerstein ARMAX recursive auxiliary variable method is proposed. The mean square convergence of the algorithm is proved strictly. A numerical example is given to study the algorithm. And compared with the classical RLS algorithm, the identification results show the effectiveness of the algorithm. Under the colored noise interference, the algorithm is superior to the RLS algorithm in terms of identification accuracy and convergence speed. 2. Aiming at the Hammerstein ARMAX model. A recursive Maximum Likelihoodo Hammerstein ARMAX recursive maximum likelihood method is proposed. The derivation process and flow chart of the algorithm are given in detail. The algorithm can not only avoid over-parameterization but also identify the noise model. And compared with the classical RLS algorithm, the identification results show the effectiveness of the algorithm. The algorithm is superior to the RLS algorithm in the accuracy of identification. 3. Aiming at Hammerstein ARMAX model. An adaptive particle swarm optimization algorithm (APSO) and robust least squares vector machine (WLSSVM) are proposed. Based on the particle swarm optimization (PSO) algorithm. The evolutionary state estimation (ESE) technique is introduced to adjust the inertial coefficient and acceleration factor of particles to speed up the convergence of the algorithm. At the same time, the mutation operation also avoids the algorithm falling into the local optimal solution, and enhances the search ability of the algorithm. Compared with many algorithms, the identification results show that the algorithm is effective. This algorithm not only has high identification accuracy, but also has better convergence speed than PSO_WLSSVM algorithm. 4. Aiming at Hammerstein ARMAX model. An adaptive mutation Drosophila optimization algorithm (AMFOAA) and robust least square support vector machine (WLSSVM) are proposed. Combined with Hammerstein ARMAXAM_FOA_WLSSVM algorithm. Based on the Drosophila optimization algorithm (FOAA). By determining the variance of population fitness and the global optimal value, the mutation operation can not only avoid the algorithm falling into the local optimal solution, but also enhance the search ability of the algorithm. A numerical example is given to study the algorithm. The results show that the algorithm is effective and the convergence speed of the algorithm is higher than that of FOA_WLSSVM algorithm.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：N945.14

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