A comparison of stochastic inverse methods with sampling and functionalbased linear and non-linear update procedures

In this paper we focus on inverse methods enabling the calibration of input parameters when measurement of the re-sponse of an engineering system is available. Considering only stochastic approaches, different methods can be used to perform the update. In the paper, a comparison of some of these numerical procedures is presented in order to evaluate the capability of the different methods. In particular, simple analysis have been carried out focusing the attention on those aspects that are more crucial in engineering application, such as the linearity/non-linearity of the model and the influence of the prior quality. The results obtained with some toy-examples show that these aspects highly influence the performance of the methods. The Markov Chain Monte Carlo (MCMC) method is computationally expensive, due to slow convergence rate, but it is competitive for capturing multi-modal Bayesian posterior distribution. Efficient methods, such as the Kalman Filter, are suitable for linear models but have limitations when updating the parameters of non-linear models. Non-linear filters, such as the Non Linear Minimum Mean Squared Error (NL-MMSE), lead to better results for highly nonlin-ear models.