Model and Parameter Uncertainty in Distributed Systems

Abstract

This paper formulates and solves the problem of model identification and parameter uncertainty in plutonium storage systems. A systematic procedure helps to choose among alternative mathematical models with different properties and degrees of freedom. Rigorous metrics for measuring the statistical alignment between five different physical models and given experimental data are discussed. On the basis of those metrics, the most adequate model is identified and the optimal parameter values for the heat source and the heat transfer coefficients in the packed plutonium bed are calculated. Model confidence and parameter uncertainty are accurately quantified by confidence regions. Rigorous bounds on the uncertain parameter range are computed. Mathematical framework for a flexible design approach and risk minimization is introduced. Flexibility analysis approach is used to detect the worst case temperature hotspots in plutonium storage containers.

Optimal boundary control of a coupled system consisting of Kuramoto–Sivashinsky–Korteweg–de Vries and heat equations

“…However, in realworld applications, there are a lots of distributed parameter systems where the exact model of the system is not known and contains uncertainties. Interested readers can refer to Kulkarni et al (2006) and Rebiai and Zinober (1993) for the corresponding investigations.…”

Optimal boundary control of a continuum model for a highly re-entrant manufacturing system

“…Furthermore, it is possible to find infinitesimal conditions characterizing optimal feedback control in problems of control under disturbance and differential games that are analogous to the Pontryagin maximum principle in optimal control. Interested readers can refer to Kulkarni et al (2006), Ledyaev (1994) and Wang et al (2018) for the corresponding significant investigations.…”

Cerebral Blood Flow Assessment by Digital Subtraction Angiography

“…Independent confidence intervals for confidence level of 99% were calculated based on the covariance method described in. 36 The covariance method requires the sensitivity information; the elements of the Jacobian matrix were computed numerically by repeated simulations with small changes to the flow rates in (5-7) with n is the number of observations, p is the number of parameters, V the covariance matrix, σ the individual variances, ε is the vector of concentration differences between the measurement and the model prediction with t as the student t-value. We computed for four different flow rates with eighty observations, and using 2.63 as t-value with 99% confidence.…”