Regularization of Noisy Displacement Data to Estimate Magnitude and Distribution of Antecedent Beam Loads

Abstract

The magnitude and distribution of antecedent loads on a beam from the acquired data of discrete displacements is of great interest in structural health monitoring. This requires solving an inverse problem that is ill-posed due to data noise emerging from instrument’s precisions. Real data would contain apparent noise because of simplifications made in the mathematical simulation. In this paper. the Euler-Bernoulli beam theory is adopted that transforms known beam loads into unknown displacements. Theoretical displacement data are obtained by solving the direct problem. and then replicated noisy by adding random numbers to simulate a certain level of noise. This paper follows the Tikho nov Regularization Method to solve ill-posed inverse problem that would transform measured displacement data into unknown antecedent loads. Presented results are consistent within themselves and thus establish field application of the method.