Hybrid method for full-field response estimation using sparse measurement data based on inverse analysis and static condensation

Abstract

In structural health monitoring, measuring the accurate and spatially dense response near critical locations of the structure can be advantageous to estimate damage to the structure. Due to several physical restrictions or limitations of the sensing method, it may not always be possible to generate reliable data at critical locations. In this study, a hybrid method is presented that makes use of the measured displacement data and finite element (FE) model of the structure to predict dense full-field response. The presented method can incorporate unknown boundary conditions and unknown body forces by applying correction/fictitious forces to match predicted and measured responses. Using static condensation followed by inverse analysis, these additional forces are found by setting up a least square problem. Due to the problem being ill-posed, L2-penalty is used to control the prediction error. Numerical simulation of a plate subjected to body force showed an accurate prediction of full-field response except for a few boundary locations. To handle this, the proposed method is used in conjunction with linear interpolation near boundary locations. The method is validated in a laboratory experiment for a plate with a notch having displacement measured using Digital Image Correlation (DIC). On comparing strains calculated using predicted displacements, FEM, and DIC, the predicted strains show better agreement with the FEM than DIC. This affirms that the proposed hybrid technique can be used at critical locations where DIC fails to provide reliable strain data.