Improved Experimental Ritz Vector Extraction With Application to Damage Detection

Abstract

Load-dependent Ritz vectors, or Lanczos vectors, are alternatives to mode shapes as a set of orthogonal vectors used to describe the dynamic behavior of a structure. Experimental Ritz vectors are extracted recursively from a state-space system realization, and they are orthogonalized using the Gram–Schmidt process. In addition to the Ritz vectors themselves, the associated nonorthogonalized vectors are required for application to damage detection. First, this paper presents an improved experimental Ritz vector extraction algorithm to correctly extract the nonorthogonalized Ritz vectors. Second, this paper introduces a Ritz vector accuracy indicator for use with noisy data. This accuracy indicator is applied as a tool to guide the deflation of a state-space system realization identified from simulated noisy data. The improved experimental Ritz vector extraction algorithm produces experimental nonorthogonalized Ritz vectors that match the analytically computed vectors. The use of the accuracy indicator with simulated noisy data enables the identification of a state-space realization for Ritz vector extraction from which damage location and extent are correctly estimated. The improved Ritz vector extraction algorithm improves the application of Ritz vectors to damage detection, more accurately estimating damage location and extent. The accuracy indicator extends the application of Ritz vectors to damage detection in noisy systems as well.