Open Access

ARTICLE

Application of the Multi Scaling Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forces

Yung-Wei Chen¹, Jiang-Ren Chang², Fu-Hsuan Hsieh², Che-Wei Chen²

1 Department of Marine Engineering, National Taiwan Ocean University, 2, Pei-Ning Road, Keelung 20224, Taiwan, ROC.
2 Department of Systems Engineering & Naval Architecture, National Taiwan Ocean University, 2, Pei-Ning Road, Keelung 20224, Taiwan, ROC.

Structural Longevity 2013, 9(1), 37-58. https://doi.org/10.3970/sl.2013.009.037

Abstract

Since numerical instability phenomena always arise in the solving process for parameters identification of structural vibration. To resolve such a problem, the multi scaling characteristic time expansion method (MSCTEM) in conjunction with the natural regularization method is adopted to overcome the higher order numerical oscillation problem when polynomial series expansion is necessary. Due to inclusion of the characteristic length (CL) in the scheme, the ill-posed problem of the constructed Vandwemonde matrix will be overcome and will also increase the term number of polynomial series. Thus, the ill condition and numerical instability of numerical calculations can be resolved. Besides, to overcome the numerical instability problem of a noise disturbance, in contrast to the conventional Tikhonov regularization method, the natural regularization method is again adopted to resolve the problem. It is shown that the MSCTEM with the natural regularization method can effectively resolve those above mentioned problems through three benchmark examples.

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