Effect of Limited Modal and Noise Information on Structural Damage Detection

Abstract: The effect of limited modal and noise information on the Transformation Matrix Method is presented. This method detects structural damage and operates on the global stiffness matrix of a structure to condense on the primary degrees of freedom. The method is based on the fact that the transformation matrix for the damaged state can be initially estimated from the corresponding to the non damaged state, by using an iterative procedure. As data, the method is based on the condensed stiffness matrix of the structure that requires modal shapes and vibration frequencies identified from acceleration records. Initially, the localization of seismic instruments is defined. Afterwards, the acceleration records coming from the instrumented floors of the structure are obtained. From these, the dynamic characteristics of the structure are identified to reconstruct the condensed stiffness matrix. This matrix corresponds to the damaged state of the structure. Finally, using the adjusted condensed stiffness matrix with the dynamic characteristics of the structure and the analytically computed condensed stiffness matrix, the Transformation Matrix method locates damage in structural elements as the percentage of loss of stiffness. In this paper, the effect of ignoring all modal shapes and vibration frequencies in the damage detection of structures is studied. Examples are presented and advantages and disadvantages of the Transformation Matrix Method are discussed. The final objective of this work is to present this new formulation applying it to the study of building structures