Applying the Continuous Hidden Markov Model to Structural State Estimation

Assessing large structures on the basis of multivariate static data sets is a challenging task for a number of reasons. One is that a low-frequency sample does not consistently capture longitudinal discrepancies in the data and thus cannot translate multivariate information into structural conditions and performance metrics. Another is the fluctuation in the data due to the synergy between loading and environmental factors. The precise elimination of these factors is difficult and can lead to inaccuracies in a structural condition assessment. In this study, an advanced machine learning framework employing the Continuous Hidden Markov Model (CHMM) is proposed to address this challenge using multivariate static data flows. Trained CHMMs are used to determine the probabilistic states of given degrees of freedom (e.g., a member or element within the structure) with respect to the input data. To build reliable training sets, two key factors need to be accounted for: (1) the numerical modeling errors inherent in training data, and (2) the sensitivity of the data to localized damage (e.g., the decrement of stiffness in a component). To handle Factor (1), an inversion-based regime is adopted to account for modeling errors by modifying the global (finite element) stiffness matrix. For Factor (2), the use of amplifying functions effectively increases the distinguishability of data and CHMMs to state changes. The efficacy of the CHMM-based framework is numerically demonstrated on a simple support beam and then on a cable-stayed bridge section. In both cases, the results demonstrate that the proposed method can capture the damage location and detect damage extent when the noise is below an acceptable level.