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Digital twins enable the quantification of the trade-offs in maintaining citrus quality and marketability in the refrigerated supply chain

Abstract

Supply chains of fresh fruit must maintain a very narrow window of hygrothermal conditions after harvest. Any excursions outside this range can markedly lower the consumer acceptability of the fruit. However, the loss in fruit quality and marketability largely remains invisible to stakeholders throughout the supply chain. Here we developed a physics-based digital twin of citrus fruit to pinpoint when, why and to what extent fruit quality and marketability are reduced. Sensor data on 47 commercial shipments are thereby translated into actionable metrics for supply chain stakeholders by mapping the variability using principal component analysis. We unveiled a large spread (between 3% and 60%) in the shipments for different metrics of quality and marketability. Half of the shipments currently lie outside the ideal trade-off range between maintaining quality, killing fruit fly larvae and avoiding chilling injury. The digital twin technology opens the possibility to obtain the real-time coupling with sensor data to monitor food quality and marketability.

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Fig. 1: Overview figure for citrus fruit in a supply chain.
Fig. 2: Descriptive statistics of the input dataset for delivery air temperature.
Fig. 3: Inter-shipment variability in metrics.
Fig. 4: Mapping the correlation landscape for the metrics.
Fig. 5: The invisible quality loss for every shipment.
Fig. 6: Trade-off in maintaining citrus fruit quality.

Data availability

The authors confirm that all relevant data supporting the findings of this study are available within the paper and its Supplementary Information. The source data for the delivery air temperature of the 47 commercially measured shipments and the fruit quality are available as source data files. Source data are provided with this paper.

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Acknowledgements

We thank T. Grout and V. Hattingh for their helpful suggestions. We also thank F. Bahrami for her editorial inputs to this manuscript. We acknowledge the support of K. Shoji in the exploratory work in data processing. The contribution of C.S. was funded by the Swiss National Science Foundation SNSF (project 200021_169372).

Author information

Authors and Affiliations

Authors

Contributions

T.D. conceptualized this study and performed project administration. T.D. wrote the proposal and secured funding for this project. T.D. and C.S. developed the methodology for this study. T.B. and P.C. collected data for citrus cold chains. C.S. performed the simulations, data analysis, interpretation and visualization of results. T.D. supervised the work of C.S. C.S. wrote the original draft of the manuscript with key inputs from T.D. S.S., T.B., P.C. and T.D. critically reviewed and edited the manuscript, and C.S. revised the manuscript based on their suggestions.

Corresponding author

Correspondence to Thijs Defraeye.

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The authors declare no competing interests.

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Nature Food thanks Ettore Settanni and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Variability in input dataset.

Variability in temporal and hygrothermal history of the shipments: (a) Shipment length (days), (b) Average temperature of delivery air (°C), (c) Deviation in delivery air temperature (°C), (d) Average relative humidity of delivery air (%), (e) Deviation in relative humidity of delivery air for the 47 shipments analyzed in this study. Here, the color scale varies from favorable (green) to unfavorable conditions (red). The number over the bar indicates the number of shipments falling into a particular histogram bin. The spread is expressed as a box plot, where the area within the box indicates the interquartile range (IQR = Q3-Q1). The whiskers indicate the minima and maxima of the spread, computed as (Q1 – 1.5xIQR and Q3+1.5xIQR). Outliers are plotted as individual points.

Extended Data Fig. 2 Quantile table for the input parameters and metrics of quality and marketability.

Table presenting the quantiles for the input parameters and metrics of quality and marketability estimated by the digital twin for the 47 shipments.

Extended Data Fig. 3 Mean, standard deviation, and coefficient of variation for the input parameters and metrics of quality and marketability.

Table presenting the mean, standard deviation, and coefficient of variation for the input parameters and metrics of quality and marketability estimated by the digital twin for the 47 shipments.

Extended Data Fig. 4 Goodness-of-fit test, skewness, and kurtosis for the fitted distribution for the input parameters and metrics of quality and marketability.

Table presenting the goodness-of-fit test, skewness, and kurtosis for the fitted distribution for the input parameters and metrics of quality and marketability. Here * indicates that the Chi-squared test is significant (p<0.05), so here the fitted distribution differs significantly from the population. # indicates that the distribution is significantly skewed. A skewness between -0.5 and 0.5 indicates a fairly symmetric distribution, skewness in the range (-1, -0.5) and (0.5, 1) indicates moderately skewed data, and skewness <-1 or >+1 indicates a highly skewed distribution. $ indicates kurtosis is significant. A large, positive kurtosis indicates a leptokurtic distribution (high peak and skinny tails), whereas a small kurtosis (<0) indicates a platykurtic distribution (low peak and heavy tail). Values of skewness and kurtosis close to zero indicate a normal distribution.

Extended Data Fig. 5 Model parameters, constants and variables of interest for the physics-driven model of citrus fruit in a refrigerated container.

Table listing the model parameters, constants and variables of interest for the physics-driven model of citrus fruit in a refrigerated container.

Extended Data Fig. 6 Death kinetics of Mediterranean fruit fly (MFF) larvae.

Death kinetics of Mediterranean fruit fly (MFF) larvae: (a) Survivor plot of MFF larvae on a logarithmic scale versus the time of exposure (days) at three temperatures (1, 2 and 3 °C). Here, the dotted red line indicates the Probit 9 requirement (99.99683% mortality at 95% confidence interval); (b) Corresponding decimal reduction times or D-value (DT, day) for estimating the temperature dependence as z-value. The z-value is the temperature difference required to change the D-value by a factor of 10.

Extended Data Fig. 7 Comparison between the predicted values and the observed values from experiments and literature for chilling injury in lemon.

Comparison between the predicted values and the observed values from experiments and literature for chilling injury in lemons: (a) Chilling injury index (CI index) takes values between 0 and 3, and is representative of the surface area of the rind that is inflicted with chilling injury. The experiments were conducted for 10 replicates. Experimental data points are plotted as blue dots and the error bars represent the standard deviation. Experiments were conducted on ‘Eureka’ lemon fruit stored at -0.6, 2, and 7 °C for 0, 12, 22, 32, and 42 days. (b) Probability of incidence of chilling injury, expressed as percentage. Error bars are not relevant here for the experimental data, as it was computed as a percentage out of ten replicates. The figure is discussed in the Supplementary information (Section S8). RMSE is the root mean squared error. R2 is the coefficient of determination ranging from 0 to 1 that measures how well the model predicts new observations.

Extended Data Fig. 8 Calibrated thermal damage model for ‘Valencia’ orange.

Calibrated thermal damage model for ‘Valencia’ orange: (a) Iso-effect lines for various combinations of time and temperature exposure, for the severity of chilling injury symptoms, expressed as chilling injury index {0, 1, 2, 3}. (b) Comparison of the predicted values for chilling injury index with other values reported in literature. Iso-effect contours for (c) damage integral (Ω), (d) chilling injury index, and (e) percentage of chilling injury inflicted fruits (%) from the thermal damage model calibrated for ‘Valencia’ orange. The figure is discussed in the Supplementary information (Section S8). RMSE is the root mean squared error. R2 is the coefficient of determination ranging from 0 to 1 that measures how well the model predicts new observations.

Extended Data Fig. 9 Validation of the digital twin for the boxes at the bottom-most pallet layers of the container, near the container floor.

Validation of the digital twin for the boxes at the bottom-most pallet layers of the container, near the container floor: A comparison between measured values for a fruit box in the bottom layer of pallets 1, 5, 9, 14, 17, and 20 and the values predicted by the digital twin based on two sensors measuring delivery air data: (a) Fruit core temperature (°C) - the dotted red lines represent the fruit core temperature predicted by the digital twin based on data from two sensors measuring delivery air temperature and humidity, while the yellow lines correspond to measured fruit core temperature; (b) Moisture loss (%), and the dotted line corresponds to the typically acceptable limit for moisture loss, which is 5%; (c) Box plot for moisture loss (%); (d) Fruit with symptoms of chilling injury (%), here the dotted lines correspond to every additional fruit showing chilling injury; (e) Box plot for fruit with chilling injury (%); (f) Pest mortality (%), and the dotted line corresponds to Probit 9 pest mortality, which is 99.99683% mortality at 95% confidence interval; (g) Box plot for pest mortality. Statistically significant differences were evaluated at a significance level of 0.05 (n.s.: not significant and p>0.05; *: p<0.05; ***: p<0.01). For (c), (e), and (g), the spread is expressed as a box plot, where the area within the box indicates the interquartile range (IQR = Q3-Q1). The whiskers indicate the minima and maxima of the spread, computed as (Q1 – 1.5xIQR and Q3+1.5xIQR). The data are also plotted as individual points.

Extended Data Fig. 10 Validation of the digital twin for the boxes in the middle layer of pallets in the container.

Validation of the digital twin for the boxes in the middle layer of pallets in the container: A comparison between measured values and the values predicted by the digital twin for fruit next to a sensor in the middle layer of pallets 1, 5, 9, 14, 17, and 20: (a) Moisture loss (%), (b) Fruit with symptoms of chilling injury (%); (c) Pest mortality (%); (d) Microbiological risk due to condensation.

Supplementary information

Supplementary Information

Supplementary sections S1–S14, Figs. S1–S6 and Tables S1–S2.

Reporting Summary

Source data

Source Data Fig. 2

Delivery air temperature data for 47 shipments.

Source Data Fig. 4

Fruit quality data for 47 shipments computed by the digital twin.

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Shrivastava, C., Berry, T., Cronje, P. et al. Digital twins enable the quantification of the trade-offs in maintaining citrus quality and marketability in the refrigerated supply chain. Nat Food 3, 413–427 (2022). https://doi.org/10.1038/s43016-022-00497-9

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