## Section: New Results

### Particle–Kalman filter for structural health monitoring

Participant : Frédéric Cérou.

This is a joint work with EPI I4S (Inria Rennes–Bretagne Atlantique).

Standard filtering techniques for structural parameter estimation assume that the input force either is known exactly or can be replicated using a known white Gaussian model. Unfortunately for structures subjected to seismic excitation, the input time history is unknown and also no previously known representative model is available. This invalidates the aforementioned idealization. To identify seismic induced damage in such structures using filtering techniques, a novel algorithm is proposed to estimate the force as additional state in parallel to the system parameters. Two concurrent filters are employed for parameters and force respectively. For the parameters, interacting particle–Kalman filter is employed targeting systems with correlated noise. Alongside a second filter is employed to estimate the seismic force acting on the structure. The proposal is numerically validated on a sixteen degrees–of–freedom mass–spring–damper system. The estimation results confirm the applicability of the proposed algorithm.

In another work, the same approach has been used for varying system parameters with correlated state and observation noise. The idea is to nest a bank of linear KFs (Kalman filters) for state estimation within a PF (particle filter) environment that estimates the parameters. This facilitates employing relatively less expensive linear KF for linear state estimation problem while costly PF is employed only for parameter estimation. Additionally, the proposed algorithm also takes care of those systems for which system and measurement noises are not uncorrelated as it is commonly idealized in standard filtering algorithms. As an example, for mechanical systems under ambient vibration it happens when acceleration response is considered as measurement. Thus the process and measurement noise in these system descriptions are obviously correlated. For this, an improved description for the Kalman gain is developed. Further, to enhance the consistency of particle filtering based parameter estimation involving high dimensional parameter space, a new temporal evolution strategy for the particles is defined. This strategy aims at restricting the solution from diverging (up to the point of no return) because of an isolated event of infeasible estimation which is very much likely especially when dealing with high dimensional parameter space.