A Parameter Optimization for Mode Shapes Estimation Using Kriging Interpolation

Abstract

A parametric study of Kriging interpolation for Optimal Sensor Placement (OSP) is presented in this paper. A Kriging model uses geostatistical information to interpolate and extrapolate the values for unobserved locations with a weighted sum of known neighbors. The accuracy of mode shape estimates is evaluated by Modal Assurance Criteria (MAC), compared to the target mode shapes. The performance of OSP is enhanced by the Kriging results. For the quality estimation of mode shape, a parametric study is conducted in this paper. The Kriging model is composed of linear regression model with random error which is assumed as a realization of a stochastic process. A Gaussian function is used to characterize the covariance function between two random errors in terms of their relative distance. Three parameters are involved to define covariance function: regression model order and two amplification parameters. The parameter optimization approach aims at OSP solution with the minimum number of sensors. The effect of parameters is evaluated using numerically simulated harmonic modes, and modes from Northampton Street Bridge (NSB). Modified Variance (MV) is used to rank the signal strength at candidate sensing locations. The results show that the accuracy of estimated mode shapes is dependent on the eigenvalue of covariance matrix and the number of sensors can be minimized when the Kriging model is optimally designed.