RLS-based Identification of fractional order H n1,n2 system using the Singularity Function approximation

This paper presents a study of fractional order systems modeling and identification by recursive least squares (RLS) with forgetting factor estimation technique. The fractional order integrators are implemented using the Singularity Function approximation method. Parametric Identification of fractional order differential equations (FDE) is investigated when estimating system parameters by a linear model with respect to parameters, as well as non-integer orders from temporal data (H n1,n2 )-type model. A numerical simulation example illustrates the effectiveness of the proposed identification approach to ensure the convergence of the plant and model outputs even if a bias is persistent in parameters’ values.

Analysis of Stress Singularity near the Tip of Artificial Crack

A generalized expression of the stress-singularity function at the tip of artificial crack is proposed, and a formula to calculate the stress intensity factor of artificial crack is obtained in the paper. The solutions of stress singularity of a cracked bi-materials beam under uniform tension and bending were computed. The results show that the degree of stress-singularity is determined by the exponent λ at the tip of artificial crack, and the exponent λ is, not only determined by materials parameter of artificial crack but also by angle. Key words: artificial crack; bi-material; stress singularity; eigen value; stress extrapolation method