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

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.