Orthogonal polynomials or wavelet analysis for mechanical system direct identification

A Direct Method for Numerically Solving Integral Equations System Using Orthogonal Triangular Functions

Wavelet for System Identification

A new scheme of Wavelets based system identification for structures with multi-coupled modes is presented in this paper. The advantages of using Wavelets for system identification are that good localization and hierarchical multi-resolution can be achieved in both time and frequency domains. Consequently, the system model for different modes can be identified more efficiently and accurately, es...

Complexity analysis of hypergeometric orthogonal polynomials

The complexity measures of the Crámer-Rao, Fisher-Shannon and LMC (López-Ruiz, Mancini and Calvet) types of the Rakhmanov probability density ρn(x) = ω(x)p 2 n(x) of the polynomials pn(x) orthogonal with respect to the weight function ω(x), x ∈ (a, b), are used to quantify various two-fold facets of the spreading of the Hermite, Laguerre and Jacobi systems all over their corresponding orthogona...

Orthogonal Functions Techniques for the Identification of Mechanical Systems

This paper presents orthogonal function techniques for the identitication of mechanical systems. For this purpose, mechanical systems are represented by state-space equations and the input and output signals are developed in series of orthogonal functions. The equation of motion can be integrated using numerical techniques together with integration properties specific for orthogonal functions. ...

Orthogonal Polynomials

The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipl...