One of the critical factors in the optimal design of drip-fertigation systems is determining the distribution of nitrate in the soil. Handling such a complex non-linear process is challenging. The main goal of this study is to develop an accurate hybrid Boruta Random Forest (BRF)-Whale Optimization Algorithm (WOA) integrated with an Artificial Neural Network (ANN) to estimate the nitrate concentration ($N{O}_3^{-}$) in the distribution system. In addition to applying ANN and support vector regression (SVR) methods, various training algorithms and kernel functions are used as standalone validation models to evaluate the robustness of the WOA-ANN model for nitrate pattern estimation. The algorithm uses 11 variables extracted from the experimental study, which are optimally arranged in five input combinations employing the BRF Feature Selection (FS) and regression analyses. The statistical and diagnostic analyses showed that the BRF-FS is the best approach to optimize the WOA-ANN model. The proposed approach provided the best metrics (i.e. R=0.962, RMSE=0.029 mg/L, MAE=0.024, and U_95%=0.056) and improved the ANN’s accuracy by 30%. It also outperformed the ANN (R=0.913 and RMSE=0.042 mg/L) and SVR (R=0.901 and RMSE=0.045 mg/L) when applied to estimate the $N{O}_3^{-}$ values. An external validation analysis showed the robustness of all applied machine learning models. Moreover, the significant scoring assessment also showed that when using the BRF-FS approach, the initial nitrate concentration in soil (N₀) and nitrate concentration in irrigation water ($F-N{O}_3^{-}$) had the most influence on the estimation of nitrate pattern, respectively.

滴灌系统优化设计的关键因素之一是确定土壤中硝酸盐的分布。处理如此复杂的非线性过程具有挑战性。本研究的主要目标是开发一种精确的混合 Boruta 随机森林 (BRF)-鲸鱼优化算法 (WOA) 与人工神经网络 (ANN) 集成以估计硝酸盐浓度 ($ñ{○}_3^{-}$) 在分配系统中。除了应用 ANN 和支持向量回归 (SVR) 方法外，各种训练算法和核函数被用作独立的验证模型来评估 WOA-ANN 模型在硝酸盐模式估计中的稳健性。该算法使用从实验研究中提取的 11 个变量，这些变量采用 BRF 特征选择 (FS) 和回归分析以最佳方式排列在五个输入组合中。统计和诊断分析表明，BRF-FS 是优化 WOA-ANN 模型的最佳方法。建议的方法提供了最佳指标（即 R=0.962，RMSE=0.029 mg/L，MAE=0.024，和 U _95%=0.056) 并将 ANN 的准确率提高了 30%。当应用于估计$ñ{○}_3^{-}$价值观。外部验证分析显示了所有应用的机器学习模型的稳健性。此外，显着性评分评估还表明，当使用 BRF-FS 方法时，土壤中的初始硝酸盐浓度（N ₀）和灌溉水中的硝酸盐浓度（$F-ñ{○}_3^{-}$) 分别对硝酸盐模式的估计影响最大。