Kimberley B. McAuley

A maximum-likelihood method for estimating parameters, stochastic disturbance intensities and measurement noise variances in nonlinear dynamic models with process disturbances

Abstract An improved approximate maximum likelihood algorithm is developed for estimating measurement noise variances along with model parameters and disturbance intensities in nonlinear stochastic differential equation (SDE) models. This algorithm uses a Laplace approximation and B-spline basis functions for approximating the likelihood function of the parameters given the measurements. The resulting Laplace approximation maximum likelihood estimation (LAMLE) algorithm is tested using a nonlinear continuous stirred tank reactor (CSTR) model. Estimation results for four model parameters, two process disturbance intensities and two measurement noise variances are obtained using LAMLE and are compared with results from two other maximum-likelihood-based methods, the continuous-time stochastic method (CTSM) of Kristensen and Madsen (2003) and the Fully Laplace Approximation Estimation Method (FLAEM) (Karimi and McAuley, 2014). Parameter estimations using 100 simulated data sets reveal that the LAMLE estimation results tend to be more precise and less biased than corresponding estimates obtained using CTSM and FLAEM.

A Numerical Study of Channel-to-Channel Flow Cross-Over Through the Gas Diffusion Layer in a PEM Fuel Cell Type Flow System Using a Sepentine Flow Channel With a Trapezoidal Cross-Sectional Shape

On the cathode side of a PEM fuel cell, the air usually flows through serpentine channels in a flow plate, these channels usually having a square cross-sectional shape. There is a porous diffusion layer adjacent to the flow plate. Flow cross-over of air through the porous diffusion layer from one part of the channel to another can occur. This flow cross-over is a result of the pressure differences between different parts of the channel and it causes the flow rate through the channel to vary with the distance along the channel. A numerical study of the pressure distribution and flow cross-over through the gas diffusion layer (GDL) in a PEMFC flow plate system that uses a serpentine channel system has therefore been undertaken for the case where the channel has a trapezoidal cross-sectional shape. The purpose of the present work was to study the effect of the flow plate geometry on the basic fluid flow through the plate. The flow has been assumed to be three-dimensional, steady, incompressible and single-phase. The flow through the porous diffusion layer has been described using the Darcy model. The dimensionless governing equations have been written in dimensionless form and solved by using the commercial CFD solver, FIDAP. The solution depends on (1) the Reynolds number, Re, based on the mean channel width and on the mean velocity at the channel inlet, (2) the gas Prandtl number, Pr, a value of 0.7 being assumed here, (3) the permeability of the diffusion layer, (4) the ratio, R, of the length of the wide side of the trapezoidal channel to the length of the narrow side of the channel. Values of Re between 50 and 200 and of R between 1 and 7 have been considered. The results obtained indicate that: (1) the width ratio, R, of the trapezoidal channel cross-sectional shape has a significant effect on the flow cross-over As R increases the flow cross-over through GDL increases, (2) The ratio R also has a significant effect on the pressure variation in the flow field for both cross-over and no cross-over cases. (3) Flow cross-over has a significant influence on the pressure variation through the channel, tending to decrease the pressure drop across the channel. (4) An increase in Re can lead to a slight increase in the flow cross-over.Copyright