Identification of flexural rigidity for Euler–Bernoulli beam by an iterative algorithm based on least squares and finite difference method

Abstract

In this paper, a method combining finite differences and least squares is investigated to determine the unknown flexural rigidity EI(x) governed by the Euler–Bernoulli beam. First, by discretizing the Euler–Bernoulli beam, a partial differential equation, in space and time using the finite difference method, further collation will result in a simplified expression form, similar to the discrete expression form of a system of ordinary differential equations. At this point, the parameters to be identified will be hidden in the coefficient matrix of this expression in a linear combination. Using the least squares method, we can determine the individual elements of the coefficient matrix. Through a series of iterative inverse solutions, we can identify the discrete parameters. The final results of the flexural rigidity identification will be obtained by choosing a suitable fitting method. We demonstrate the identifiability of our coefficient matrix and analyze the causes of error accumulation during the iterative inverse solution. The simulation results show that with a reasonable discretization, the identification results are still very accurate despite the noise in the collected output data. At the end of the paper, an example of applying flexural rigidity in the simulation process of the Euler–Bernoulli beam control system is also presented.