COMPUTING OPTIMAL DYNAMIC EXPERIMENTS FOR MODEL CALIBRATION IN PREDICTIVE MICROBIOLOGY

Abstract

ABSTRACT The potential of mathematical models describing the microbial behavior during food processing and storage largely depends on their predictive capabilities and, in this concern, model calibration plays a crucial role. Unfortunately, model calibration may only be performed successfully if the sources of information are sufficiently rich. Therefore, a careful experimental design is required. This contribution formulated the optimal experimental design (OED) problem as a general dynamic optimization problem where the objective was to optimize a certain criterion depending on the Fisher information matrix. This formulation allows for more flexibility in the experimental design, including initial conditions, sampling times, experimental durations, time‐dependent manipulable variables and number of experiments as degrees of freedom. Moreover, the use of robust confidence regions for the parameter estimates was suggested as an alternative to evaluate the quality of the proposed experimental schemes. The OED for the calibration of the thermal death time and Ratkowsky‐type secondary models was considered for illustrative purposes, showing how the usually disregarded E‐optimality criterion results in the experimental schemes offering the best compromise precision/decorrelation among the parameters.PRACTICAL APPLICATIONSThis work addresses a general methodology for designing optimal dynamic experiments for the purpose of model calibration. This methodology is general in the sense that it may be applied to any type of food processing model, being particularly relevant for predictive microbiology and quality assessment as the experimentation is both time consuming and expensive.The main advantages of the proposed technique are twofold: on one hand, it is able to significantly reduce the overall experimental burden, contributing not only to simplify the experimental planning, devising the most adequate experiments, but also minimizing the number of experiments, and on the other hand, the resultant experiments provide the maximum quantity and quality of information to improve the predictive capabilities of the models under consideration, of key importance for process design, optimization and control.