(612a) Using Paralllel Tempering to Evaluate Optimum Parameter Estimates in Nonlinear Dynamic Simulation Models

The evaluation of multiple parameters involved in nonlinear dynamic simulation models based on a minimization of the sum of the squares of the differences between the predictions and experimental data is often a non-trivial step.  Classical least squares minimization methods are all local methods that only converge to a local minimum that is not necessarily the global one, the answer depending crucially of the initial guess.  The evaluation of the sensitivity of the local minimization solution to the initial guess can be quite time-consuming, especially when the model predictions involve the solution of a set of ODEs the time-integration of which requires by itself a non-negligible computational time.   In this work we present a stochastic method to evaluate that dependence effectively with an application to the evaluations of parameters in the dynamic simulation of a thixotropic concentrated suspension system using Large Amplitude Oscillatory Shear (LAOS) Data.

The approach developed in the present work incorporates a hybrid parallel, simulated annealing, “Metropolis” –like algorithm, within a least squares fitting algorithm.  The parallel simulated annealing is used to develop a good initial guess of the values of the parameters space using as an objective function the squares of the differences of the model predictions from oscillatory in time experimental data obtained over a period.  The selection of the initial guess is followed by an application of a modified least squares local minimization procedure to determine accurately the “global” minimum.  An important advantage of the proposed method is that all parameters needed to execute it are evaluated numerically based on few simulated annealing runs.  A further advantage of the proposed algorithm is the potential speedup by executing its most time-consuming step, a series of simulated annealing simulations, in parallel.

The above-described method is then applied to the multiple parameter estimation problem involved in the modeling of thixotropy exhibited by concentrated suspensions using several LAOS data at varying frequency and strain amplitude.   Several different models are used to fit thixotropic systems LAOS data from the literature as well as obtained within our own research group.  With the developed method, we have been able to fit very complicated thixotropic models involving upwards of 5-9 parameters.  Furthermore, it is shown that our approach ensures the precise location of the global minimum independent of the initial guess in a systematic way and without involving the need of any adjustable parameters.  In contrast, we show that often the use of direct local minimization methods leads to local minima with the values of the parameters significantly different and the fitting substantially poorer that the results obtained with our global minimization scheme.  Thus, the potential of the application of the proposed method to many other parameter fitting in dynamic simulations applications.