Response surface methodology for damage detection using frequency and mode shapes

Abstract

The model updating method is one popular method in vibration-based damage detection. However, the conventional model updating method requires a finite element (FE) model for sensitive computation during the iteration process, which leads to the problem of slow convergence and high time consumption. Therefore, the response surface methodology (RSM) has emerged as an alternative tool in FE model updating due to easy implementation and time-efficient processing where the computationally expensive analytical FE model is replaced by the simple and inexpensive response surface (RS) model. A recent RSM application in structural damage detection employs frequency as the sole response feature, limiting its ability to localise the existence of damage due to the inability of the frequency to ascertain damage in a symmetric structure. Therefore, a better RSM employing frequency and mode shapes as the response features is proposed in this study, as both parameters are proven sensitive to damage location. The implementation of the proposed method involves a three-phase procedure; (i) sampling, (ii) RS modelling and (iii) model updating. In order to develop the best RS model, two major parameters in the sampling stage, design of experiments (DOEs) and design spaces are carefully assessed through a series of sensitivity studies based on their damage detectability. The applicability of the technique is applied to detect simulated damage in numerical models of simply supported beam and steel frame structures as well as a laboratory tested steel portal frame. The results from sensitivity studies show that central composite design (CCD) with more sampling points in a small design space has better performance in detecting damages due to dense population of data which adequately represents the design space. The results from numerical study demonstrated that the proposed RSM method has a good ability to detect damage due to noise free data while results from experimental study depicted some false detections. It is concluded that the proposed method is reliable in damage detection provided that the data has good precision. Nevertheless, the presence of noise and errors in real practice are inevitable, thus pollute the measured data. Therefore, it is suggested to incorporate the effect of uncertainties in the proposed RSM to improve its applicability in real practice.