若干类多变量线性系统模型辨识方法研究

发布时间：2018-02-13 10:50

本文关键词： 多变量线性系统模型迭代或递推参数辨识闭环抗扰设计　出处：《北京化工大学》2016年博士论文　论文类型：学位论文

【摘要】：多数情况下,出于安全和经济方面的考虑,在闭环条件下开展系统辨识的研究十分有必要。另一方面,在不同复杂外部干扰影响下,如何构建出在操作点附近的合理线性化模型以及如何对其进行参数估计,是系统辨识领域具有广泛意义的、极其重要的研究课题。基于上述情形,假定系统模型结构确定或基本确定,本文主要研究针对几种典型多变量线性系统模型的参数抗扰估计新方法,并通过对噪声进行分析、对输入信号以及算法进行精心设计,使得这些改进后的估计方法具有很强的抗扰特性。在开环闭环条件下,本文重点讨论以下几个问题：输入信号的设计、闭环框架的合适选择、不同类型噪声对算法的影响和改造、结构简化带来的辨识误差的有效消除以及复杂算法的收敛性分析。由于不同的线性系统模型之间具有内在联系且在某些条件下能够相互转化,针对不同线性系统开发出的辨识方法既具有特殊性又具有较强的泛化能力。针对不同的多变量线性系统模型,本文的主要工作和创新点表现在如下几个方面：1、针对闭环多变量积分和不稳定过程,提出一种全新的迭代最小二乘辨识方法,这种针对滞后的迭代计算能够有效减小对滞后取一阶泰勒近似所产生的误差,因而在噪声环境中拥有相当快的收敛效率。通过等效的输入和输出,这种新型算法能够拓展到多变量积分和不稳定过程的闭环辨识中,且对生产实践有一定的指导意义。2、在工程实践中,由于测量数据包含离群点,其分布是非高斯的。这种情况会导致参数估计器的表现性能显著下降。针对重尾t分布噪声影响下的离散多输入多输出系统,本文创造性地提出一种迭代再赋权重的相关分析方法。通过将多变量相关分析和以t分布为基础的鲁棒M估计器相结合,该迭代方法能够获得在重尾t噪声下的鲁棒有限脉冲响应(FIR)模型。3、本文针对闭环条件下的离散多变量方程误差类模型开发出一种提升的迭代辨识方法并应用于闭环直接辨识中。该算法基于分层辨识原则对有色噪声进行有效处理,因而具备很强的抗干扰能力。在闭环辨识中,输入测试信号的设计确保了闭环系统的可识别性,弹性化以及独立参数化的噪声模型使得闭环辨识偏差最小化。4、针对带有稀少测量的离散多变量输出误差类模型,本文提出一种新型的以辅助模型为基础的多新息最小二乘算法,该算法将标量新息拓展到新息向量并且利用辅助模型的输出来取代信息矩阵中的内部未知变量。为了很好地处理稀少测量模式,算法采用变间隔递推的形式进而跳过不可用数据(包括离群点)。最后,利用鞅收敛定理,本文证实了该辨识算法的收敛性。
[Abstract]:In most cases, for security and economic reasons, it is necessary to study system identification under closed loop conditions. On the other hand, under the influence of different complex external disturbances, How to construct a reasonable linearization model near the operating point and how to estimate its parameters are of great significance in the field of system identification. Assuming that the system model structure is determined or basically determined, this paper mainly studies a new method of parameter immunity estimation for several typical multivariable linear system models. By analyzing the noise, the input signal and the algorithm are carefully designed. Under the condition of open loop and closed loop, the following problems are discussed in this paper: the design of input signal, the suitable selection of closed loop frame, The influence and modification of different types of noise on the algorithm, The efficient elimination of identification error caused by structural simplification and the convergence analysis of complex algorithms. Due to the inherent relationship between different linear system models and the ability to transform each other under certain conditions, The identification methods developed for different linear systems have both particularity and strong generalization ability. The main work and innovation of this paper are as follows: 1. For closed-loop multivariable integral and unstable process, a new iterative least square identification method is proposed. This iterative computation for delay can effectively reduce the error caused by taking the first order Taylor approximation to delay, and thus has a fairly fast convergence efficiency in noisy environment. This new algorithm can be extended to the closed-loop identification of multivariable integrals and unstable processes, and has a certain guiding significance for production practice. In engineering practice, because the measured data contain outliers, Its distribution is not Gao Si's. This kind of situation will cause the performance of the parameter estimator to degrade significantly. For the discrete multiple-input multi-output system under the influence of the heavy-tailed t distribution noise, In this paper, we creatively propose an iterative re-weighted correlation analysis method, which combines multivariate correlation analysis with robust M-estimator based on t distribution. This iterative method can obtain robust finite impulse response model. 3. This paper develops an improved iterative identification method for the error class model of discrete multivariable equations under closed loop condition and applies it to closed loop. In the direct ring identification, the algorithm is based on the hierarchical identification principle to deal with colored noise effectively. In the closed-loop identification, the design of the input test signal ensures the identifiability of the closed-loop system. The elastic and independent parameterized noise model minimizes the closed-loop identification bias. For the discrete multivariable output error class model with sparse measurements, a new multi-innovation least squares algorithm based on the auxiliary model is proposed in this paper. The algorithm extends the scalar innovation to the innovation vector and uses the output of the auxiliary model to replace the internal unknown variables in the information matrix. The algorithm uses the form of variable interval recursion to skip the unusable data (including outliers). Finally, by using the martingale convergence theorem, the convergence of the identification algorithm is proved in this paper.
【学位授予单位】：北京化工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：N945.14

【参考文献】