【作者】 吴亚锋；

【导师】 姜节胜；

【作者基本信息】 西北工业大学 ， 一般力学， 2000， 博士

【摘要】 本文基于基本的状态空间子空间系统辨识（4SID）理论和算法，对子空间辨识算法的特性，适用性及其在复杂结构系统中的应用进行研究。具体内容如下： 系统地总结了子空间辨识方法的基本理论及算法。基于实现理论讨论了线性系统的随机特性及其子空间结构。概括了子空间辨识算法的三个主要运算步骤：首先由LQ分解计算特定Hankel矩阵的行空间投影；再对该投影进行SVD，获取系统的可观测矩阵及状态序列的Kalman滤波器估计；最后由可观测矩阵和／或估计的状态序列确定系统矩阵。 构建了子空间辨识算法的统一理论框架。通过对不同子空间算法相似性的分析、比较，说明了已有的各种子空间算法都是一个统一理论下的特例；不同的算法均采用了完全相同的子空间来确定系统的阶次和广义可观测矩阵，其差异仅在于计算观测矩阵列空间基的加权矩阵有所不同。 研究了闭环系统的子空间辨识算法。基于闭环子空间投影和辨识理论，仿照开环子空间辨识算法，推导了两种直接从输入输出数据应用状态序列和／或观测矩阵获取系统矩阵的闭环辨识算法。通过一个仿真算例，比较了这两种闭环算法和开环算法在闭环系统中的应用特性。 提出了一种适用于多数据组子空间辨识算法。通过理论分析和数学推导，将前述用于单个数据组的算法改造成一种极具工程实用价值的新算法。该算法的特点是允许处理在同一系统上、不同初始条件下获取的多组试验数据，并可取得良好的辨识结果。两个仿真算例分别用于说明该算法的适用性和正确性。 基于上述研究，将单数据组和多数据组子空间辨识方法应用于二个复杂结构中—航空发动机的数学建模和桁架结构缩型铁塔的模态参数辨识，取得了满意的结果。同时也进一步表明了子空间辨识算法使用简单，数值稳定，尤其适用于高阶多变量复杂系统的辨识。更多还原

【Abstract】 This thesis focuses on the performances, extensions of subspace identification methods and their applications to complicated structures, based on the basic theory of subspace-based state-space system identifica- tion (4SID). 1 .The theory of subspaee identification algorithms is summarized systematically. Based on the realization theory, the stochastic properties and subspace structures of linear system are described. And three main steps of all subspace algorithms are explored. First, using an LQ-decomposition, the projection of the row space of specific data Hankel matrices is calculated. Next, the SV-decomposition of the projection is calculated to directly lead to the observability matrices and a Kalman filter estimation of the state sequences. Last, the system matrices are extracted from the observability matrices and/or the estimated state sequences. 2.A unified framework of subspace algorithm is structured through analyzing and comparing of the similarities among various subspace algorithms. It is shown that all these are special cases of one unified theorem. The results reveal that existing 4SID methods use exactly the same subspace to determine the order and the extended observability matrix, but that the weighting matrix, to calculate a basis for the column space of observability matrix is different among them. 3.The closed-loop subspace identification methods are studied in order to apply the 4SID to engineering practices. In terms of the theories of the projection and identification for closed-loop system, as the open-loop does, two identification algorithms are presented using the observability matrices and/or the estimated state sequences directly from closed-loop input-output data. A simulation is carried out to compare the differences between the closed-loop algorithms and open-loop one. 4.A subspace identification method with multiple-data sets is proposed to adapt 4SID to practical problems. Via the theoretical and mathematical derivation, the 4SID methods of single input-output data set are readily ii 2 .2 ABSTRACT modified to handle the cases of multiple data sets. It is very useful for most of practices where the multiple data sets related the same dynamic system are collected, but with possibly different initial conditions. By means of two examples, the algorithm is shown good efficiency and feasibility. 5.The given subspace identification methods are applied to two complicated structures: to model an aero-engine and to estimate the modal parameters of a Mini-Mast, and the satisfied results are obtained. Which show that the subspace methods have the advantages of simple operation and good numerical stability, and prove that it is an excellent method for the identification of high order, multi-variable complicated system.更多还原