Observability Gramian for Bayesian Inference in Nonlinear Systems With Its Industrial Application

Abstract

In this paper, we present a novel (empirical) observability Gramian for nonlinear stochastic systems in the light of Bayesian inference. First, we define our observability Gramian, which we refer to as the estimability Gramian, based on the relation to the so-called Bayesian Fisher Information Matrix for initial state estimation. Then, we study the fundamental properties of an empirical version of the estimability Gramian. The practical usefulness of the proposed framework is examined through its application to a parameter and initial state estimation in a natural gas engine cylinder.

Reliability evaluation of meta-action unit based on fault tree Bayesian network

“…Bayesian network [9][10] is a probabilistic graph model and an extension of the Bayesian algorithm. It is used to investigate the properties of a group of random variables {X 1 , X 2 …X n } and n groups of conditional probability distributions (CPD).…”