TY - JOUR

T1 - Approximate inference of nonparametric Hammerstein models

AU - Risuleo, R.S.

AU - Bottegal, G.

AU - Hjalmarsson, H.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We propose a method for nonparametric identification of Hammerstein models with Gaussian-process models for the impulse response of the linear block and for the input nonlinearity. Interpreting the Gaussian-processes as prior distributions, we can estimate the unknowns using the posterior means given the data. To estimate the hyperparameters we set up an iterative scheme, reminiscent of the expectation-maximization method, where the posterior expectation of the complete likelihood is iteratively maximized. In the Hammerstein case, the posterior density is intractable because, in general, it does not admit a closed form expression. In this work, we propose two approximation approaches to estimate the posterior mean. In the first, we make a particle approximation of the posterior using Markov Chain Monte Carlo. In the second, we use a variational Bayes approach with a mean-field hypothesis. We validate the proposed methods on synthetic datasets of Hammerstein systems.

AB - We propose a method for nonparametric identification of Hammerstein models with Gaussian-process models for the impulse response of the linear block and for the input nonlinearity. Interpreting the Gaussian-processes as prior distributions, we can estimate the unknowns using the posterior means given the data. To estimate the hyperparameters we set up an iterative scheme, reminiscent of the expectation-maximization method, where the posterior expectation of the complete likelihood is iteratively maximized. In the Hammerstein case, the posterior density is intractable because, in general, it does not admit a closed form expression. In this work, we propose two approximation approaches to estimate the posterior mean. In the first, we make a particle approximation of the posterior using Markov Chain Monte Carlo. In the second, we use a variational Bayes approach with a mean-field hypothesis. We validate the proposed methods on synthetic datasets of Hammerstein systems.

KW - Bayesian methods

KW - Nonlinear system identification

KW - Nonparametric methods

UR - http://www.scopus.com/inward/record.url?scp=85031810110&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2017.08.1555

DO - 10.1016/j.ifacol.2017.08.1555

M3 - Conference article

AN - SCOPUS:85031810110

VL - 50

SP - 8333

EP - 8338

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 1

ER -