Mechanistic-informed statistical modelling for pre-harvest apple firmness prediction using sensor-based data : a thesis submitted for the degree of Master of Information Science, College of Sciences, Massey University, New Zealand

Abstract

Accurately predicting pre-harvest apple fruit firmness is important for supporting harvest planning, fruit quality control, and post-harvest management. This thesis develops a mechanistic informed statistical framework for predicting pre-harvest firmness in ‘Royal Gala’ apples. The proposed approach combines biological information about apple softening with fruit quality measurements, Near-Infrared (NIR) spectral data, and environmental data. More specifically, a two phase one-knot spline model is first used to construct a biologically meaningful population-level baseline firmness trajectory over days after full bloom (DAFB). Two sequential statistical correction components are then considered: the h(·) model uses fruit-level variables and destructive NIR spectra, while the g(·) model uses date-level environmental information and longitudinal non-destructive NIR spectra. The model was developed using data from the 2021–2022 sea son. For the held-out cross-season evaluation using the 2024–2025 season, the two-phase decline structure was retained, the first assessment date was used to calibrate the season-specific initial firmness, and the two later assessment dates were used to evaluate prediction performance. The baseline model captured the broad decline in pre-harvest firmness. In the development season, the correction components produced only negligible improvements over the baseline, with RMSE remaining approximately 1.07 kgf and RPD remaining below 1.2. In the 2024–2025 evaluation, the environmental g(·) correction provided the best fruit-level performance, improving RMSE from 1.009 to 0.979 kgf and R² from 0.330 to 0.369. However, the corresponding RPD was only 1.285, indicating limited utility for precise individual-fruit prediction. Prediction errors were smaller when evaluated using assessment-date mean firmness, with an RMSE of 0.272 kgf for the environmental correction model, although this result was based on only two post-calibration dates. Overall, the results demonstrate a practical framework for integrating biological information with heterogeneous sensor-based data. The framework shows greater potential for describing population-level pre-harvest firmness development than for predicting individual-fruit firmness. More complete and consistently matched multi-season data are required before the model can be considered sufficiently robust for practical prediction.