Wavelets or Chebyshev polynomials continuous-time identification of mechanical systems

This paper focuses on the identification of mechanical modal characteristics by comparing two different approaches based on function basis expansion. The main framework of such approaches is to transform a set of differential equations into easier to solve algebraic equations. From a general point of view, the proposed approaches, using wavelets or Chebyshev polynomial functions, achieve signal expansion in a first step, then the selection of informative points and finally the parameter estimation in the last step. The comparison of the two methods on the same discrete mechanical system makes it possible showing numerical differences and describing each step of the identification problem. The formulations, expressed in three kinds of differential equations, are tested on a linear 3- DOF mechanical system for different excitation signals taking into account drawbacks and advantages of each method. From this comparison, it is shown that the selection of points where parameters are estimated can deeply improve this estimation even if the signal expansions are not satisfactory. Moreover, the selection of the expansion basis is shown to be important not only for the quality of signal expansion but also for the transformation of differential equations.