Optimal dynamic heat generation profiles for simultaneous estimation of thermal food properties using a hotwire probe: Computation, implementation and validation

Abstract The methodology of dynamic optimal experimental design was applied to estimate the thermal conductivity and the volumetric heat capacity of conduction heated foods simultaneously. For this purpose, a hotwire probe was used to generate heat in the thermal center of a food product. The temperature response was measured at a specified location inside the food. In order to minimize the effect of experimental input errors on the estimates, the information content of the measured temperature profiles was maximized. Optimal (dynamic) heat generation profiles as well as an optimal location to measure the temperature response in the food product were computed based on modern global optimization algorithms. These heating profiles were implemented and it was shown that the methodology guarantees an optimal regime for simultaneous parameter estimation. Pulse heating with two peaks – one at the beginning and one at the end of the experiment – was found to be an optimal heating profile. The optimal measurement position was located at some distance from, and close to, the heating probe. The mathematical and numerical outcomes of the applied methodology were interpreted in a physical context. Validation experiments with a food simulator (Tylose) were done, and coefficients of variation of 4% and 2% were obtained for the thermal conductivity and volumetric heat capacity, respectively.

[1]  O. C. Zienkiewicz,et al.  The Finite Element Method: Basic Formulation and Linear Problems , 1987 .

[2]  KARINA J. VERSYCK,et al.  OPTIMAL DESIGN OF A CLOSED LOOP CONTROLLER FOR ESTIMATION OF PARAMETER COUPLES OF MICROBIAL GROWTH KINETICS , 2000 .

[3]  Eva Balsa-Canto,et al.  Improving food processing using modern optimization methods , 2003 .

[4]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[5]  S. Sahin,et al.  Physical properties of foods , 2006 .

[6]  Bart Nicolai,et al.  Optimal experimental design for the parameter estimation of conduction heated foods , 2001 .

[7]  Bart Nicolai,et al.  FINITE ELEMENT COMPUTATION OF UNSTEADY PHASE CHANGE HEAT TRANSFER DURING FREEZING OR THAWING OF FOOD USING A COMBINED ENTHALPY AND KIRCHHOFF TRANSFORM METHOD , 2001 .

[8]  Eric Walter,et al.  Qualitative and quantitative experiment design for phenomenological models - A survey , 1990, Autom..

[9]  N. F. Thornhill,et al.  Computer Applications in Fermentation Technology: Modelling and Control of Biotechnological Processes , 1989 .

[10]  Erwin Lutwak,et al.  Crame/spl acute/r-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information , 2005, IEEE Transactions on Information Theory.

[11]  Julio R. Banga,et al.  A model-based approach to develop periodic thermal treatments for surface decontamination of strawberries , 2004 .

[12]  R. Horton,et al.  Measurement of Soil Thermal Properties with a Dual‐Probe Heat‐Pulse Technique , 1994 .

[13]  Axel Munack,et al.  Optimal Feeding Strategy for Identification of Monod-Type Models by Fed-Batch Experiments , 1989 .

[14]  Jan Van Impe,et al.  Computation of optimal identification experiments for nonlinear dynamic process models: a stochastic global optimization approach , 2002 .

[15]  Bart Nicolai,et al.  Optimization of the temperature sensor position in a hot wire probe set up for estimation of the thermal properties of foods using optimal experimental design , 2003 .

[16]  Frank P. Incropera,et al.  Fundamentals of Heat and Mass Transfer , 1981 .

[17]  J. Carson,et al.  Predicting the effective thermal conductivity of unfrozen, porous foods , 2006 .

[18]  L. Riedel.  Eine Prüfsubstanz für Gefrierversuche , 1960 .

[19]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[20]  Raman K. Mehra,et al.  Optimal input signals for parameter estimation in dynamic systems--Survey and new results , 1974 .

[21]  R. Horton,et al.  Test of a dual-probe heat-pulse method for determining thermal properties of porous materials , 1998 .

[22]  J. Carson,et al.  Experimental measurements of the effective thermal conductivity of a pseudo-porous food analogue over a range of porosities and mean pore sizes , 2004 .

[23]  Donald J. Cleland,et al.  A new approach to modelling the effective thermal conductivity of heterogeneous materials , 2006 .

[24]  Keith L. Bristow,et al.  COMPARISON OF TECHNIQUES FOR EXTRACTING SOIL THERMAL PROPERTIES FROM DUAL‐PROBE HEAT‐PULSE DATA , 1995 .