Coherence analysis of systems with feedback and its application to a BWR noise investigation

Abstract

Two new methods for coherence analysis are presented with the aim of analyzing dynamic characteristics of systems with feedback which include closed-loops among measured variables. In order to investigate feedback effects implicit in measured ordinary coherence, this paper proposes a method of evaluating system dynamics by comparison of the ordinary coherence and noise power contribution ratio derived from an autoregressive modeling. It is theoretically shown that the comparison of these two functions enables us to evaluate the property of a feedback effect in the system if it exists. Concerning the coherence analysis of multivariable systems, this paper discusses, through numerical examples, some difficulties which are encountered in the conventional partial coherence analysis if there exists feedback loops connecting the output to the inputs. In order to obviate these difficulties this paper introduces a new method called extended partial coherence analysis which ensures the evaluation of direct correlation existing between two variables of interest by eliminating the effect of the remaining variables, regardless of whether or not the system contains feedback loops. Through application to simulation data as well as to actual BWR noise data, it is shown that the methods presented here have a potential applicability to various studies of at-power reactor noise, especially of its generation and propagation mechanisms.