On parameter estimation of linear time invariant (LTI) systems using bootstrap filters

Abstract

In this paper, sequential Markov Chain Monte Carlo (MCMC) simulation based algorithm (aka Particle Filter) is used for parameter estimation of a three storied shear building model subjected to recorded earthquake ground motions with different non-stationary features (i.e. pga, strong motion durations, amplitude and frequency content). The forward problem is solved using time integration schemes and synthetic measurements are generated by adding simulated zero mean Gaussian noise. Using these synthetic data, stiffness and damping values are identified at different degrees of freedom (dof). Initially, random values (i.e. particles) of these parameters are generated from a pre-selected probability distribution function (e.g. uniform distribution). Each particle is then passed through the model equation and the state is updated using the measurement at each time step. A weight is then assigned to each particle by evaluating their likelihood to the measurement. Once the likelihoods for all particles are evaluated, the new samples for the next iteration are drawn from the simulated initial pool of particles as per the estimated likelihoods. For this purpose, four different re-sampling strategies (e.g. simple, wheel, systematic and stratified) are used to test their relative performance. The performances of the re-sampling algorithms are compared on the basis on number of convergence steps, computational time and the accuracy of the identified parameters. The efficiency of the Bootstrap identification algorithm is also discussed in the light of noise contamination of different intensity.