Autoregressive modeling with state-space embedding vectors for damage detection under operational variability

A nonlinear time series analysis is presented to detect damage in systems under varying operational and environmental conditions. This paper summarizes the use of a state-space reconstruction to infer the geometrical structure of a deterministic dynamical system from observed time series of the system response at multiple locations. The unique contribution of this paper is using a Multivariate Autoregressive (MAR) model of a baseline health condition to predict the state space, where the model encodes the embedding vectors rather than scalar time series. A hypothesis test is established that the MAR model will fail to predict future response if damage is present in the test condition, and this test is investigated for robustness in the context of operational and environmental variability (nondamage-related events). The applicability of this approach is demonstrated using multi-channel acceleration time series from a base-excited three-story building structure tested in laboratory environment. Under the assumption that many “real-word” damage modes induce transitions from linear to nonlinear response in a system, damage is simulated by a bumper mechanism that creates a repetitive, impact-type nonlinearity. Operational and environmental variations are simulated by changing stiffness and mass conditions, based on the assumption that these sources of variability usually manifest themselves as linear effects on measured data.