基于多种算法的果树果实生长模型研究—以云南昭通苹果为例

【目的】针对果树果实与生长过程中的气象因子关联密切,且生长过程多为非线性、非平稳序列,直接对其连续测定难度较大的问题,对比多种模型对果实直径的模拟能力,为果树及其果实的生长发育监测和预测、适时灌溉施肥、生长环境调控等提供科学参考。【方法】以云南昭通苹果为例,分析2019和2020年果实生长期间直径变化特征及其与环境气候因子的关系。引入深度学习中的长短期记忆模型（LSTM）,使用LSTM模型对苹果果实直径进行模拟及预测,与多元线性回归模型（MLR）和机器学习模型中的决策树（DT）及随机森林（RF）模型的模拟结果进行对比分析,并使用3种采样方法对不同模型模拟的结果进行评估。【结果】苹果果实直径有明显日变化特征,呈夜间直径增长而白天缩小为主的规律,一般早晨直径达到最大,然后逐渐微缩,在日落前后直径到达当日最小。苹果果实直径的增长速率在果实膨大初期较高,在果实生长后期降低。苹果果实小时和日平均直径与土壤温度和土壤湿度呈中度或高度正相关,与紫外线指数（UVI）呈高度负相关。苹果果实直径的日平均增长量（FMDG）、日增长量（FDG）、日最大变化量（MDFS）与60 cm土壤温度和20 cm、40 cm土壤湿度呈低负相关（-0.5≤R<-0.3）。4个模型的模拟结果相比,LSTM模型的模拟精度高于MLR、DT和RF模型。LSTM模型比MLR模型在相关系数R增加3%—20%的情况下,RMSE和MAE下降约50%—75%,而机器学习模型DT和RF对苹果果实直径的预测相对较差,可能存在过度拟合。【结论】对比统计学、机器学习和深度学习等方法,LSTM模型在苹果果实直径的模拟中表现出更高的精度和可靠性,能更好地解决果实生长过程中的复杂非线性问题。

Fruit Growth Modelling Based on Multi-Methods - A Case Study of Apple in Zhaotong,Yunnan

【Objective】 Meteorological factors are closely related to fruit diameter during growth process, but this relationship between them tends to be non-linear and non-stationary, thus making it hard to monitor the fruit and trunk diameter continuously. Comparing the simulation capabilities of various growth models for fruit diameter could provide scientific support for fruit growth monitoring and predicting, timely irrigation and fertilization, and the regulation of growth environment. 【Method】 Taking apples in Zhaotong, Yunan Province as an example, this study first analyzed the characteristics of diameter change during apple growth in 2019 and 2020 and its relationship with environmental and climate factors. Subsequently, a deep learning method of Long Short-Term Memory (LSTM) model was adopted to simulate and predict the fruit diameter by integrating these factors, which was evaluated with the multi-linear regression (MLR) model and machine learning methods including Decision Tree (DT) and Random Forests (RF) using three sampling methods. 【Result】 The apple diameter had obvious diurnal cycle characteristics, which shrunk in the daytime and expanded in the nighttime. The maximum diameter was in the morning, while the minimum diameter was near the sunset. The growth rate of apple diameter was higher in the early growth period than near mature. The hourly and daily mean apple diameters were moderately or highly-positive correlated with soil temperature and soil moisture, while there was a highly-negative correlation with UVI. The daily mean increase (FMDG), daily increase (FDG), and maximum daily shrinkage (MDFS) of apple diameter had a weak negative correlation with 60 cm soil temperature as well as 20 and 40 cm soil moisture (-0.5≤R<-0.3). The simulation accuracy of the LSTM model was significantly higher than that of MLR, DT and RF model. The correlation coefficient (R) of LSTM model increased (3% -20%) compared with MLR, and the RMSE and MAE were approximately decreased by 50%-75%. The machine learning methods showed relatively poor performance in apple diameter simulation and might have overfitting problems. 【Conclusion】 Compared to statistics and machine learning approaches, the LSTM model demonstrated higher accuracy and robust performance because of the incapability of considering the complex non-linear correlations in the fruit growth simulation.