Dharmendra K. Mishra

Parameter Estimation in Food Science

Modeling includes two distinct parts, the forward problem and the inverse problem. The forward problem-computing y(t) given known parameters-has received much attention, especially with the explosion of commercial simulation software. What is rarely made clear is that the forward results can be no better than the accuracy of the parameters. Therefore, the inverse problem-estimation of parameters given measured y(t)-is at least as important as the forward problem. However, in the food science literature there has been little attention paid to the accuracy of parameters. The purpose of this article is to summarize the state of the art of parameter estimation in food science, to review some of the common food science models used for parameter estimation (for microbial inactivation and growth, thermal properties, and kinetics), and to suggest a generic method to standardize parameter estimation, thereby making research results more useful. Scaled sensitivity coefficients are introduced and shown to be important in parameter identifiability. Sequential estimation and optimal experimental design are also reviewed as powerful parameter estimation methods that are beginning to be used in the food science literature.

Optimal Experimental Design to Estimate Thermal Degradation Kinetic Parameters for Nutraceuticals in Intermediate-Moisture Foods

Optimal experimental design for nonlinear models is important to enhance accuracy of parameter estimates. Analysis for optimal design was conducted for the thermal processing of grape pomace (moisture content 42% wb) at constant retort temperarture of 126.7oC. The optimum heating time is proposed that minimizes the hypervolume of the confidence region of the parameters. Degradation of anthocyanins followed a first-order reaction, and the rate followed an Arrhenius model. Sensitivity coefficients for rate constant and activation energy were estimated to optimize the determinant of the delta (XTX) matrix, where X is the sensitivity matrix. It was found that for a given temperature history, to estimate only rate constant, the optimal heating time would be 30 min. For estimating only activation energy in the model, the optimal time to take measurements would be 12 minutes. The maximum value of the delta function occurred at 31 min. indicating that if one wishes to estimate both parameters simultaneously, then measurements should be concentrated around this time. The optimal time corresponded to 10% retention of anthocyanins. This method will be helpful in determining optimal design for non-isothermal processes.