基于关键项分离的输入非线性系统参数辨识

发布时间：2018-05-02 01:28

本文选题：系统辨识 + 随机梯度　；参考：《江南大学》2017年博士论文

【摘要】：输入非线性系统由一个静态无记忆的非线性模块串联一个动态线性系统构成,通过构建不同形式的非线性模块可以满足不同工程的需要,也正因为其结构的灵活性和实用性,受到人们广泛的关注.输入非线性系统存在未知参数的乘积项,常用的过参数化算法会引入大量冗余参数,不适用于多变量输入非线性系统的参数辨识.在这样的背景下,论文选题“基于关键项分离的输入非线性系统参数辨识”,具有重要的理论意义和研究价值.取得的研究成果如下.1.针对标量输入非线性系统的参数空间存在两个参数集的乘积项,而常用的过参数化算法将参数乘积项作为独立待辨识参数进行辨识,从而导致一个可产生冗余参数估计的问题,论文采用关键项分离技术,将系统的输入输出之间复杂的映射关系分解成两部分,一种是直观的外部映射关系,另一种是隐含但明确的内部映射关系,从而得到一个无冗余参数的辨识模型.进一步,将提出的方法推广到多变量输入非线性系统.2.针对输入非线性系统的辨识模型中包含未知的关键项、噪声项和中间项导致辨识参数困难,采取辅助模型辨识思想,在实现辨识算法的过程中,将信息向量中的未知项用其估计值代替,并利用相应的辨识算法得到参数估计,然后利用得到的参数估计估算未知项的估计,不断循环得到满意的辨识结果.3.针对多变量输入非线性系统存在结构复杂、参数空间维数高、各通道间存在耦合等特点导致递推算法辨识效率低下的问题,利用模型分解的方法,将系统分解为两个或多个子系统,并结合递阶辨识理论,实现子系统参数之间的交互估计,最后将递推辨识算法推广到多变量输入非线性系统.4.在上述基础上,根据最小二乘原理和梯度搜索方法,推导了多变量输入非线性系统的最小二乘迭代算法和梯度迭代算法.不同于递推辨识算法,迭代算法利用采集到的一组输入输出数据,进行反复迭代运算,更充分地利用了数据,因而具有更快的收敛速度和更高的辨识精度.论文最后对提出的参数辨识算法都用计算机进行仿真,验证其有效性,并对不同的参数辨识算法进行了比较分析.
[Abstract]:The input nonlinear system is composed of a static memoryless nonlinear module in series and a dynamic linear system. By constructing different forms of nonlinear modules, it can meet the needs of different projects, and also because of the flexibility and practicability of its structure. Received widespread attention. There is a product term of unknown parameters in the input nonlinear system. The commonly used overparameterization algorithm will introduce a large number of redundant parameters, which is not suitable for parameter identification of multivariable input nonlinear systems. Under this background, it is of great theoretical significance and research value to select the topic of "input nonlinear system parameter identification based on the separation of key terms". The results of the research are as follows. There are two product terms of two parameter sets in the parameter space of scalar input nonlinear system. The commonly used over-parameterization algorithm identifies the parameter product as an independent parameter to be identified, which leads to a problem of redundant parameter estimation. In this paper, the key item separation technique is used to decompose the complex mapping relationship between the input and output of the system into two parts, one is the intuitionistic external mapping relationship, the other is the implicit but explicit internal mapping relationship. Thus, an identification model with no redundant parameters is obtained. Furthermore, the proposed method is extended to multivariable input nonlinear systems. In view of the difficulty of identifying parameters caused by the unknown key items in the identification model of input nonlinear system, the noise term and the intermediate term lead to the difficulty of identification parameters, the idea of auxiliary model identification is adopted, and the identification algorithm is realized. The unknown term in the information vector is replaced by its estimated value, and the parameter estimation is obtained by using the corresponding identification algorithm. Then, the estimated unknown term is estimated by the obtained parameter estimation, and the satisfactory identification result is obtained continuously. In view of the complex structure of multivariable input nonlinear system, the high dimension of parameter space and the coupling between different channels, the recursive algorithm is inefficiently identified, and the method of model decomposition is used to solve the problem. The system is decomposed into two or more subsystems, and the interactive estimation of the subsystem parameters is realized by combining the hierarchical identification theory. Finally, the recursive identification algorithm is extended to the multivariable input nonlinear system .4. On the basis of the above, the least squares iterative algorithm and gradient iterative algorithm for multivariable input nonlinear systems are derived according to the least square principle and gradient search method. Different from the recursive identification algorithm, the iterative algorithm makes use of a collection of input and output data to iterate over and over again, making full use of the data, so it has faster convergence speed and higher identification accuracy. At the end of the paper, the algorithms of parameter identification are simulated by computer to verify its validity, and the different parameter identification algorithms are compared and analyzed.
【学位授予单位】：江南大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：N945.14

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