Fusion of data-driven model and mechanistic model for kiwifruit flesh firmness prediction

Abstract

Kiwifruit are often harvested unripe and stored to ripen in cool storage for extended periods of time. Flesh firmness (FF) is one of the most important postharvest quality attributes for kiwifruit which determines the storability of individual and/or batches of fruit. Pre- and postharvest factors can influence the softening rate of fruit in cool storage, and this results in a wide range of FF retention capabilities creating challenges for prediction of shelf-life performance. Two general streams of modelling methodologies have previously been investigated: 1) mechanistic modelling which attempts to describe the biochemical pathways occurring during fruit softening and environmental interactions which also influence softening rate; and 2) data-driven black-box modelling which utilises sensor data as an input to extrapolate potential firmness outcomes. Both approaches have limitations on their own, and as such adaptation at the industry level is restricted. This work demonstrates the feasibility of a novel model fusion approach which integrates the two types of models by incorporating at-harvest non-destructive sensor data as functional covariates into a mechanistic model. A closed-form solution to a kinetic model was first derived which provides a flexible parametric form for incorporation of covariates utilising non-destructive sensor data and temporal effects. The closed-form model was then integrated with functional regression to enable prediction of post-storage FF values of individual fruit using at-harvest near infrared spectral data obtained from the same fruit. The resulting fused model showed superior performance in forecasting post-storage quality indices of kiwifruit compared with conventional benchmarks including partial least squares and support vector machines regression. However, improvement in prediction accuracy for FF is not yet adequate to justify industrial applicability. Nonetheless, the significance of this work is the demonstration of a physics-guided data-driven modelling approach which is both highly interpretable and flexible in incorporation of other types of measurable covariates such as grading-line sensor data, preharvest growth factors, and harvest conditions. A more generic fused model will need to be developed for future studies in order to allow flexibility in changes in environmental conditions during storage.