Structural health monitoring with non-linear sensor measurements robust to unknown non-stationary input forcing

Abstract

Bayesian filtering based structural health monitoring algorithms typically assume stationary white Gaussian noise models to represent an unknown input forcing. However, typical structural damages occur mostly under the action of extreme loading conditions, like earthquake or high wind/waves, which are characteristically non-stationary and non-Gaussian. Clearly, this invalidates this basic assumption, causing these algorithms to perform poorly under non-stationary noise conditions. This paper extends an existing interacting filtering algorithm to efficiently estimate structural damages while being robust to unknown non-stationary non-Gaussian input forcing. Furthermore, this approach is generalized beyond linear measurements to encompass the case of non-linear measurements such as strains. The joint estimation of state and parameters is performed by combining Ensemble Kalman filtering, for non-linear system state estimation, and Particle filtering to estimate changes in the structural parameters. The robustness against input forcing is achieved through an output injection approach embedded in the state filter equation. Numerical simulations for two kinds of response measurements (acceleration and strain) are performed on a 3D frame structure under different damage location and severity scenarios. The sensitivity with respect to noise and the impact of different sensor combinations have also been investigated.

Switching Kalman filter for damage estimation in the presence of sensor faults

“…Focusing on joint state-parameter estimation, JEKF has been established as an efficient method to estimate the state and the augmented health parameters (HIs) simultaneously. At the expense of a higher computational cost, this method has been improved upon by decoupling the estimation approaches [7,[18][19][20], but traditional joint estimation approach is still impelling for handling systems of moderate dimension, because of its excellent computational performance.…”

Strain‐based joint damage estimation approach robust to unknown non‐stationary input force

“…This re‐centring is actually a second step evolution in which particles are pushed towards the particle mean. For this, the same evolution strategy is adopted, as has been adopted in Sen et al 18,55 and is reproduced here as where denotes the particle mean of the parameters till time step and denotes the shifted position for the particle. For detailed evolution strategy, readers may refer Sen et al 18 These particles are further employed to define the system matrices , , and , and the KF can then be employed to estimate the response states.…”

“…This re-centring is actually a second step evolution in which particles are pushed towards the particle mean. For this, the same evolution strategy is adopted, as has been adopted in Sen et al 18,55 and is reproduced here as…”

“…To achieve this, output injection approach introduced by Zhang and Zhang 54 is integrated within the IPKF environment that rejects the unknown inputs by simply transforming the system model, so that state and/or parameter estimation algorithms can be applied as if the rejected unknown inputs no longer exist. This noise robust filtering approach is extended to ensemble Kalman filter (r‐EnKF) in Sen et al, 55 which is however computationally expensive since a good amount of state ensembles are required to be propagated in each time update. For the considered case of linear dynamics, a computationally lighter state estimation through Kalman filtering is preferred.…”

Response and input time history dataset and numerical models for a miniaturized 3D shear frame under damaged and undamaged conditions

“…Further, few example cases of damages in both the real structure and its numerical replica are performed with frequencies comparison ( Table 3 , Table 4 , Table 5 ). The resulting data can be employed for validating damage detection approaches [ 3 , 5 , 6 ]. All details pertaining to the real experiment and modeling have been vividly demonstrated in the following.…”