Effect of inclusion lagrange interpolation method in mode shape curvature based damage detection

Abstract

Mode shape curvature based damage detection capable to detect damage in structure with high sensitivity. Sparse and high density mode shape displacement data obtained experimentally pose difficulties for mode shape curvature algorithm to quantify damage size accurately. The objective of this study is to compare damage detection sensitivity of different mode shape curvature algorithm with the inclusion of Lagrange interpolation to enhance the algorithm damage detection sensitivity for sparse and high density curvature mode shape displacement data. Finite element analysis (FEA) model with free-free boundary condition of an aluminum beam has been carried out to investigate the feasibility of the proposed method. Undamaged curvature mode shape data from the damaged structure was estimated using Gapped Smoothing Method (GSM) and Savitzky-Golay (SG) filters with two different grid points of 149 and 74. Structural Irregularity Index (SII) and Damage Estimate Reliability (DER) were used to evaluate the effectiveness of the proposed algorithm. Numerical results show inclusion of Lagrange interpolation in mode shape curvature algorithm with Savitzky-Golay filter has better performance on estimate damage size by 2.81% of DER value for less dense (74 grid points) compared to GSM. The present method shows the inclusion of Lagrange interpolation has increased the sensitivity of mode shape curvature algorithm to identify damage size in beam-type structures compared to the previous method.