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A New Criterion for the Stabilization Diagram Used with Stochastic Subspace Identification Methods: An Application to an Aircraft Skeleton

DOI: 10.1155/2014/409298

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The modal parameters of a structure that is estimated from ambient vibration measurements are always subject to bias and variance errors. Accordingly the concept of the stabilization diagram is introduced to help users identify the correct model. One of the most important problems using this diagram is the appearance of spurious modes that should be discriminated to simplify modes selections. This study presents a new stabilization criterion obtained through a novel numerical implementation of the stabilization diagram and the discussion of model validation employing the power spectral density. As an application, an aircraft skeleton is used. 1. Introduction The vibration and acoustical behaviors of a mechanical structure are determined by its dynamic characteristics. This dynamic behavior is typically described with a linear system model. The procedure for the estimation of modal parameters of structures from measured data can be split into three distinct steps [1]: data collection, system identification, and determination of modal parameters from the identified system description. Stochastic identification methods for systems with unknown input have been introduced decades ago. Among the most robust and accurate system identification methods for output-only modal analysis of mechanical structures is the stochastic subspace identification method. Two types of implementation are available: the covariance-driven (SSI-cov) [2] implementation and the data-driven (SSI-data) [3] implementation. For the first one (SSI-cov), three methods can be implemented: the balanced realization (BR), the principal component (PC), and the canonical variate analysis (CVA). For dynamic structures such as the aircraft skeleton studied in this paper, the major setback in applying system identification for large-scale structures is the selection of the model order and the corresponding system poles. To address this problem, the concept of the “stabilization diagram” is introduced, overestimating the structure model order. Therefore, spurious modes are going to surface out and we have to discriminate them. For this matter, many stabilization criteria have been implemented. The most recent one was the modal transform norm [4]. In this paper, a new stabilization criterion is implemented and a validation method is discussed. The stochastic subspace identification method used is the balanced realization. 2. Stochastic State Space Models for Vibrating Structures The finite element method [4] is one of the most common tools for modeling mechanical structures. In the case of a linear


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