多新息辨识方法及性能分析

发布时间：2018-06-29 00:41

本文选题：多新息辨识 + 递阶辨识　；参考：《江南大学》2017年博士论文

【摘要】：多新息辨识通过推广单新息修正理念,扩展辨识新息的维数,充分利用新息作为有用信息能改善参数估计和状态估计精度的特性,提高辨识效果。论文研究多新息辨识方法及其收敛性,选题具有理论意义和学术价值。论文主要工作如下。(1)针对Box-Jenkins系统,利用随机鞅理论分析了辅助模型多新息广义增广随机梯度算法的收敛性,在持续激励的条件下,证明了参数估计收敛于真实参数。为了减少有色噪声对系统参数估计的影响,通过线性滤波器对观测数据进行滤波,提出了基于数据滤波的多新息广义增广随机梯度算法,提高了多新息辨识算法在同等新息长度下的参数辨识精度。进一步,将提出的算法推广到多变量Box-Jenkins系统的辨识。(2)针对双线性参数系统,利用过参数化技术将系统的输出表达成观测数据与参数乘积的线性组合,结合多新息辨识理论与负梯度搜索,推导了基于过参数化模型的多新息随机梯度算法。为了避免过参数化导致的冗余参数问题,利用递阶辨识理论,推导了递阶多新息随机梯度算法,并从理论上分析了算法的性能。为了获取更高的参数估计精度,将数据滤波技术与多新息辨识理论相结合,提出了有色噪声干扰下双线性参数系统基于数据滤波的多新息随机梯度算法。进一步,将提出的算法推广用于估计多变量双线性参数系统的参数。(3)针对输入非线性状态空间系统,基于动态线性子系统的能观测性规范型,导出了系统的辨识模型,其特征是既含有线性子模块和非线性输入的参数乘积,又含有不可量测的系统状态。针对上述特点,将辨识模型分解为两个子模型,信息向量中未知状态用估计的状态代替以估算系统参数,根据量测数据和已计算的参数估计,利用Kalman滤波原理估计系统的状态,执行交互运算,提出了基于Kalman滤波的递阶多新息随机梯度算法,实现系统参数和状态的联合估计。进而在设计状态观测器的基础上,利用数据滤波技术,推导了基于状态观测器和数据滤波的多新息辨识算法,提高参数估计精度。论文对提出的一些辨识方法都利用数值例子进行了仿真研究,验证了提出方法的性能,对几个重要辨识算法在理论上进行了收敛性能分析。
[Abstract]:By popularizing the idea of single innovation correction and extending the dimension of identification innovation, multi-innovation identification can improve the accuracy of parameter estimation and state estimation by fully utilizing innovation as useful information and improve the identification effect. This paper studies the multi-innovation identification method and its convergence, the topic has theoretical significance and academic value. The main work of this paper is as follows: (1) for Box-Jenkins system, the convergence of generalized augmented stochastic gradient algorithm with auxiliary model is analyzed by means of stochastic martingale theory. Under the condition of continuous excitation, the convergence of parameter estimation to real parameters is proved. In order to reduce the influence of colored noise on the parameter estimation of the system, a generalized augmented stochastic gradient algorithm with multiple innovations based on data filtering is proposed by using linear filter to filter the observed data. The parameter identification accuracy of the multi-innovation identification algorithm under the same innovation length is improved. Furthermore, the proposed algorithm is extended to the identification of multivariable Box-Jenkins systems. (2) for bilinear parametric systems, the output of the system is expressed as a linear combination of the observed data and the product of the parameters by using the over-parameterization technique. Based on the multi-innovation identification theory and the negative gradient search, a multi-innovation stochastic gradient algorithm based on the over-parameterized model is derived. In order to avoid the redundant parameter problem caused by over-parameterization, the hierarchical multi-innovation stochastic gradient algorithm is derived by using hierarchical identification theory, and the performance of the algorithm is analyzed theoretically. In order to obtain higher precision of parameter estimation, a multi-innovation stochastic gradient algorithm based on data filtering for bilinear parametric systems with colored noise interference is proposed by combining the data filtering technique with the theory of multi-innovation identification. Furthermore, the proposed algorithm is extended to estimate the parameters of multivariable bilinear parameter systems. (3) for input nonlinear state space systems, an identification model is derived based on the observability canonical form of dynamic linear subsystems. Its characteristic is that it contains not only the parameter product of linear submodule and nonlinear input, but also the unmeasurable state of the system. In view of the above characteristics, the identification model is decomposed into two sub-models. The unknown state in the information vector is replaced by the estimated state to estimate the system parameters, and the state of the system is estimated by the Kalman filter principle according to the measured data and the calculated parameters. A hierarchical multi-innovation stochastic gradient algorithm based on Kalman filter is proposed to realize the joint estimation of system parameters and states. Based on the design of the state observer, the multi-innovation identification algorithm based on the state observer and the data filter is derived by using the data filtering technology to improve the precision of parameter estimation. In this paper, some of the proposed identification methods are simulated with numerical examples to verify the performance of the proposed method, and the convergence performance of several important identification algorithms is analyzed theoretically.
【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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