A robust singular value decomposition for damage detection under changing operating conditions and structural uncertainties
Introduction
In recent decades many techniques have been proposed for detecting damage based on changes of modal parameters. Unfortunately, the modal parameter changes due to varying operating conditions and structural uncertainties (e.g. due to inter-product variability) are often much more important, and hence they mask the information on the damage state of the structure. Therefore, most vibration-based damage detection techniques only give good results in well-controlled laboratory conditions.
During the last decades many techniques were proposed to detect damage based on changes of modal parameters (see the literature survey in Ref. [1]). A common property of these methods—based on changes in modal parameters—is that they are very sensitive to changes in: (a) the environment, (b) the operational conditions, and (c) structural uncertainties. Recently, a few publications appeared that aim at removing the influence of these variations. In Ref. [2] a technique is proposed to eliminate the influence of operational conditions. The technique is based on a singular value decomposition (SVD) of a frequency response function (FRF) matrix , where are FRFs at N conditions. In Ref. [3] another matrix decomposition (principal component analysis or PCA) of a matrix of estimated features (i.e. resonance frequencies) is used to eliminate the influence of environmental changes. Both authors have shown that matrix decompositions can help in removing the influence of varying conditions of the structure/measurement. However, when damaged features (FRFs or estimated parameters) are included in the matrix , the decomposition largely deviates from the one based on merely features from intact structures. This is true since damaged features are outliers, as was recognized by Worden in Ref. [4] (in the paper [4] the fact that a damaged feature is an outlier with respect to the features of intact samples is used to separate damaged and intact observations). This means that existing SVD damage detection techniques [5], [3] only work well when the SVD of the data matrix from intact observations can be computed (in general, however, it is not known beforehand if an observation is intact or damaged).
The purpose of this article is to present a robust SVD which computes the SVD of the intact structures from a set of observations of both intact and damaged structures, which are possibly measured in different conditions. In order to guarantee the success of the proposed technique, it is assumed that there are at least as many intact as damaged observations (FRFs, response spectra or estimated parameters) are present in the observation matrix which has to be decomposed.
In the next section the theory behind the method will be described. Firstly, in Section 2.2 a review of damage detection using the least-squares SVD will be given. Next, in Section 2.3, a somewhat more robust iterative SVD (ISVD) is introduced. The proposed robust SVD (RSVD) is described in Section 2.4. All three methods are validated on an extensive experimental case study of an aluminium beam measured under various conditions. The results of the experimental validation can be found in Section 4. Finally conclusions will be drawn in Section 5.
Section snippets
Motivation of SVD-based damage detection techniques
Depending on the material type of a structure and the loading scenario, different types of damage can be present in a structure: (fatigue) cracks, delaminations, wear, etc. From a structural behaviour point of view, damage is characterized by a local reduction in the stiffness near the location where the damage is present. This local stiffness reduction effect can be used to separate damage with changes due to environmental conditions. Indeed, the latter usually introduces a global change in
Simulation results
In order to quantify the sensitivity of the proposed technique a simulation is performed in this section. Twelve cases of a 10 degree-of-freedom (dof) system (with mass 1 kg and stiffness ) are considered:
In the first 6 cases a uniform reduction of the stiffness is applied to all 10 dofs (Case 1: 0.1%, Case 2: 0.5%, Case 3: 1%, Case 4: 2%, Case 5: 5% and Case 6: 7.5%). This is used to simulate the global influence of environmental changes.
In the last 6 cases a reduction is applied to only
Set-up
In this paper, nine different experimental cases are considered in order to be able to compare the sensitivity of the proposed damage detection technique (see Section 2) in the presence of structural uncertainties with respect to:
the structures’ geometry (product variability);
the surface treatment and boundary conditions.
The following cases are tested:
- Case 1:
Aluminium beam 1 (dimensions ), intact.
- Case 2:
Beam from Case 1 covered with plastic tape (see Fig. 3a).
- Case 3:
Beam from Case 1 covered with acoustic
Conclusions
In this article, a technique was proposed to detect damage in structures from measurements taken under different conditions (i.e. different operational excitation levels, geometrical uncertainties and surface treatments of the structure). From the experimental results in the article it can be concluded that the classical least-squares SVD approach gives incorrect decomposition (and hence an incorrect classification between damaged and intact samples) when both damaged and intact measurements
Acknowledgements
The financial support of the Fund for Scientific Research (FWO Vlaanderen), the Concerted Research Action “OPTIMech’’ of the Flemish Community, the Research Council (OZR) of the Vrije Universiteit Brussel (VUB) are gratefully acknowledged. The first author holds a Postdoctoral Research Grant of the Fund for Scientific Research—Flanders (Belgium) (F.W.O.—Vlaanderen) at the mechanical engineering department of the Vrije Universiteit Brussel.
References (11)
- et al.
Using svd to detect damage in structures with different operating conditions
Journal of Sound and Vibration
(1999) - et al.
Damage detection using outlier analysis
Journal of Sound and Vibration
(2000) - S.W. Doebling, C.R. Farrar, M.B. Prime, D.W. Shevitz, Damage identification and health monitoring of structural and...
Elimination of environment influences from damage-sensitive features in a structural health monitoring system
- W. Heylen, S. Lammens, P. Sas, Modal Analysis Theory and Testing, PMA, KU Leuven, Leuven, Belgium,...
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