This paper proposes a characteristic time expansion method (CTEM) for estimating nonlinear restoring forces. Because noisy data and numerical instability are the main causes of numerical developing problems in an inverse field, a polynomial to identify restoring forces is usually adopted to eliminate these problems. However, results of the way doing are undesirable for a high order of polynomial. To overcome this difficulty, the characteristic length (CL) is introduced into the power series, and a natural regularization technique is applied to ensure numerical stability and determine the existence of a solution. As compared to previous solutions presented in other researches, the proposed method is a desirable and accurate solver for the problem of restoring the force in the inverse vibration problems.
"Application of the Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forces." J. Appl. Math. 2013 1 - 13, 2013. https://doi.org/10.1155/2013/841690