Bayesian estimation of cumulative damage from seismic response records of buildings

This paper discusses the estimation of probability distributions of damage using response records from instrumented buildings subjected to seismic excitations. The objective of the paper is to show how the information on the evolution of the mechanical properties of a system can be used to assess the state of cumulative damage. This implies expressing damage on the structural members in terms of its influence on the residual mechanical properties of the system. The information on the inelastic behavior from response records is used in a bayesian formulation along with a damage function to update prior probability distributions of damage. The damage function models the hysteretic cycles of inelastic response in terms of an initial damage and of the displacement amplitudes of the response cycles. It describes the evolution of the secant stiffness through the cycles of inelastic response as a function of cumulative damage and displacement amplitudes. The updating of probability distributions of damage for single degree of freedom systems is presented first. Extensions to the case of non-linear multi-degree of freedom systems are discussed next. Examples of reinforced concrete frames are given for illustrative purposes.