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Interval Analysis for System Identification of Linear MDOF Structures in the Presence of Modeling Errors

机译：存在建模误差的线性MDOF结构系统辨识的区间分析

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摘要

Modeling errors, represented as uncertainty associated with the parameters of a mathematical model, inevitably exist in the process of constructing a theoretical model of real structures and limit the practical application of system identification. They are usually represented either in a deterministic manner or in a probabilistic way. However, if the available information is uncertain but of a nonprobabilistic nature, as it may emerge from a lack of knowledge about the sources and characteristics of model uncertainties, a third type of approach may be useful. Presented in this paper is an approach to treat modeling errors with the aid of intervals, resulting in bounded values for the identified parameters. Compared with the traditional identification procedures where model-based forward dynamic analysis is often involved, computing bounded time history responses from a computational model with interval parameters is avoided. Two required submatrices are firstly extracted from identified state-space models by applying a subspace identification method to the measurements, and then interval analysis is performed upon these two matrices to estimate the bounded uncertainty in the identified parameters. The effectiveness of the proposed methodology is evaluated through numerical simulation of a linear multiple–degree-of-freedom (MDOF) system when modeling errors in the mass and damping parameters are taken into account. The results show the ability of the proposed method to maintain sharp enclosures of the identified stiffness parameters.
机译：建模误差（表示为与数学模型的参数相关的不确定性）不可避免地存在于构造实际结构的理论模型的过程中，并限制了系统识别的实际应用。它们通常以确定性方式或概率方式表示。但是，如果可用信息不确定，但具有非概率性质，因为它可能是由于对模型不确定性的来源和特征缺乏了解而产生的，因此第三种方法可能会有用。本文介绍的是一种借助间隔来处理建模错误的方法，该方法可为已确定的参数提供有界值。与通常涉及基于模型的前向动态分析的传统识别过程相比，避免了使用具有间隔参数的计算模型来计算有限的时间历史响应。首先通过将子空间识别方法应用于测量，从已识别的状态空间模型中提取两个所需的子矩阵，然后对这两个矩阵执行间隔分析，以估计所识别参数的有限不确定性。当考虑质量和阻尼参数的建模误差时，通过对线性多自由度（MDOF）系统进行数值模拟，可以评估所提出方法的有效性。结果表明，所提出的方法能够保持所识别的刚度参数的尖锐包围。

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