Damage Identification of a Mechanical Structure with a Non-Minimum Phase Based on Singular Value Decomposition
This paper presents experimental results of source identification for a non-minimum phase system. Generally, a causal linear system may be described by matrix form. The inverse problem is considered as a matrix inversion. Direct inverse method cannot be applied for a non-minimum phase system, because the system has ill-conditioning. Therefore, in this study the SVD inverse technique is introduced to execute an effective inversion. In a non-minimum phase system, its system matrix may be singular or near-singular and has very small singular values. These very small singular values have information about a phase of the system and ill-conditioning. Using this property we could solve the ill-conditioned problem of the system and then verify it for the practical system (cantilever beam). The experimental results show that the SVD inverse technique works well for a non-minimum phase system. This inverse technique can be applied to the estimation of the magnitude of impact force, which becomes often a cause of damage to a mechanical system.
W.M. Ostachowicz, J.M. Dulieu-Barton, K.M. Holford, M. Krawczuk and A. Zak
S. K. Lee et al., "Damage Identification of a Mechanical Structure with a Non-Minimum Phase Based on Singular Value Decomposition ", Key Engineering Materials, Vols. 293-294, pp. 119-126, 2005