# Improvement of Wheat Grain Yield Prediction Model Performance Based on Stacking Technique
###### Abstract
In this growth period, there is a transition from vegetative growth to reproductive growth, and the nutrient transfers from the leaves to the ear, so it is the key period of grain formation and accumulation. After the anthesis stage, the number of grains per panicle is determined. The thousand seed weight of wheat is mainly determined by the intensity of photosynthesis and the rate of energy transfer from the anthesis to the grain filling stage [26; 27]. Therefore, the physiology, shape, and structure of the crop vary throughout the growth cycle from germination, flowering, and fruiting to senescence and death, and the formation of GY occurs sequentially and overlappingly at different growth stages [28]. A study has shown that each key growth period of crop is closely related to the formation of the final GY [4]. Most existing studies considered the grain filling stage as the key stage of GY formation; therefore, it was considered to have the best prediction accuracy in many studies [29]. [PERSON] et al. [30] reached a similar conclusion in that a penalized ridge regression model constructed using spectral reflectance data at the anthesis or grain filling stages could effectively predict GY at different water levels. However, the GY prediction model constructed using only a single critical growth stage will lose part of GY correlation information, and the prediction results may vary with the changes in the vegetation types, growth stages, and environmental conditions. Moreover, the robustness of the model is not strong, and the generalization ability is weak [31; 32]. Based on this, many researchers have proposed multitemporal vegetation index-based GY prediction models to improve the accuracy and universality of model prediction. For example, [PERSON] et al. [33] used multitemporal Terra /MODIS satellite data to simulate GY in the west of Uttar Pradesh, India. [PERSON] et al. [34] used the support vector regression method to construct a GY prediction model based on the normalized vegetation index obtained from multitemporal Landsat TM images, which effectively improved the prediction accuracy. [PERSON] et al. [35] used a large regional remote sensing GY estimation model based on multifertility MODIS-NDVI data and obtained a higher estimation accuracy than the single-fertility GY prediction model. [PERSON] et al. [36] obtained multispectral data of the four key growth periods of wheat based on the UAV remote sensing platform and estimated GY using the method of random forest combined with the vegetation index. To the best of our knowledge, there are no studies related to the ensemble of ground spectral data and LAI data from multiple growth stages of crops for yield prediction. Therefore, it is important to find a method that can combine the advantages of multiple growth stages to achieve an improved prediction accuracy and robustness for grain yield prediction. As an important part of ensemble learning, the stacking method trains a secondary model through \"learning method\", which is used to combine other primary models. Most existing studies applied this method to heterogeneous models to integrate and improve the final prediction accuracy of the model using the differences between the primary models [37]. Currently, this method has been applied to the prediction of plant photosynthesis capacity, map synthesis, and forest coverage monitoring [38; 39; 40]. Considering the heterogeneity of the canopy spectral information in the different growth stages of crops, multiple key growth stages related to GY formation were selected, and the integration of hyperspectral data and phenotypic data of the multiple growth stages based on the stacking method was studied. This was helpful to improve the estimation accuracy and generalization ability of the GY prediction model. In recent years, machine-learning techniques using spectral reflectance data as input to build predictive models for plant traits have been employed and have shown improved prediction accuracy and robustness [41].