On the Use of Artificial Neural Networks to Monitor a Pharmaceutical Freeze-Drying Process

Abstract

This paper is focused on the use of artificial neural networks to monitor a pharmaceutical freeze-drying process. A detailed phenomenological model of the process is used to provide the dataset for the learning phase of the neural network development. Then, a methodology based on a self-adaptive differential evolution scheme is combined with a back-propagation algorithm, as local search method, for the simultaneous structural and parametric optimization of the neural network which models the freeze-drying process. Using some experimentally available measurements at a generic time t, the neural network is able to estimate the temperature of the product and the thickness of the dried cake (the amount of residual ice, as well as the sublimation flux, can be easily calculated from the cake thickness) at a future time t + Δt, for the given operating conditions (the temperature of the heating shelf and the pressure in the drying chamber). Also, the duration of the primary drying phase and the maximum product temperature in the future are predicted, in case the operating conditions are not modified. In this way it is possible to understand if it is necessary to modify the operating conditions, in case the product temperature should trespass the limit value before the ending point of the primary drying. Despite the fact that the artificial neural network is obtained using a learning set determined for specific values of heat transfer coefficient (between the heating shelf and the product at the bottom of the container) and of mass transfer resistance (of the dried cake to vapor flow), reliable and accurate estimations are also obtained in case the sensor is used to monitor a process characterized by different values of heat and mass transfer coefficients.

Keywords:

• Artificial neural network
• Differential evolution
• Freeze-drying
• Mathematical model
• Monitoring
• Soft-sensor

ACKNOWLEDGMENTS

This work was partially done by financial support provided by the EURODOC “Doctoral Scholarships for Research Performance at European Level” project, financed by the European Social Fund and Romanian Government, and by the project PN-II-PT-PCCA-2011-3.2-0732, financed by Romanian Research Agency UEFISCDI.