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.
Cite This Article
Chen, Y., Chang, J., Hsieh, F., Chen, C. (2013). Application of the Multi Scaling Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forces.
Structural Longevity, 9(1), 37–58.