Ion-selective electrodes (ISEs) have recently become the most attractive tools for the development of efficient hydroponic systems. Nevertheless, some inherent shortcomings such as signal drifts, secondary ion interferences, and effected high ionic strength make them difficult to apply in a hydroponic system. To minimize these deficiencies, we combined the multivariate standard addition (MSAM) sampling technique with the deep kernel learning (DKL) model for a six ISEs array to increase the prediction accuracy and precision of eight ions, including $N{O}_3^{-}$, $N{H}_4^{+}$, $K^{+}$, $C{a}^{2+}$, $N{a}^{+}$, $C{l}^{-}$, $H_{2}P{O}_4^{-}$, and $M{g}^{2+}$. The enhanced data feature based on feature enrichment (FE) of the MSAM technique provided more useful information to DKL for improving the prediction reliability of the available ISE ions and enhanced the detection of unavailable ISE ions (phosphate and magnesium). The results showed that the combined MSAM–feature enrichment (FE)–DKL sensing structure for validating ten real hydroponic samples achieved low root mean square errors (RMSE) of 63.8, 8.3, 29.2, 18.5, 11.8, and 8.8 $\mathrm{mg}·{\mathrm{L}}^{-1}$ with below 8% coefficients of variation (CVs) for predicting nitrate, ammonium, potassium, calcium, sodium, and chloride, respectively. Moreover, the prediction of phosphate and magnesium in the ranges of 5–275 mg·L⁻¹ and 10–80 $\mathrm{mg}·{\mathrm{L}}^{-1}$ had RMSEs of 29.6 and 8.7 $\mathrm{mg}·{\mathrm{L}}^{-1}$ respectively. The results prove that the proposed approach can be applied successfully to improve the accuracy and feasibility of ISEs in a closed hydroponic system.

中文翻译：

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多元标准添加技术与深度核学习模型相结合，确定水培营养液中的多种离子。

离子选择电极（ISE）最近已成为开发高效水培系统的最有吸引力的工具。然而，一些固有的缺点，例如信号漂移，次级离子干扰和有效的高离子强度，使其难以应用于水培系统。为了最大程度地减少这些缺陷，我们将多元标准加法（MSAM）采样技术与深度核学习（DKL）模型结合在一起，用于六个ISEs阵列，以提高八种离子的预测精度和精度，包括$ñ{Ø}_3^{-}$， $ñH_4^{+}$， ${ķ}^{+}$， $C{\mathrm{一种}}^{2+}$， $ñ{\mathrm{一种}}^{+}$， $C{升}^{-}$， $H_{2}P{Ø}_4^{-}$和 $\mathrm{中号}{G}^{2+}$。基于MSAM技术的特征丰富（FE）的增强数据特征为DKL提供了更多有用的信息，以改善可用ISE离子的预测可靠性，并增强了对不可用ISE离子（磷酸盐和镁）的检测。结果表明，用于验证十个真实水培样品的组合MSAM-特征富集（FE）-DKL传感结构实现了63.8、8.3、29.2、18.5、11.8和8.8的低均方根误差（RMSE）$\mathrm{毫克}·{\mathrm{大号}}^{-\mathrm{1个}}$变异系数（CV）低于8％，分别用于预测硝酸盐，铵，钾，钙，钠和氯化物。此外，对磷酸盐和镁的预测范围为5–275 mg·L ^-1和10–80$\mathrm{毫克}·{\mathrm{大号}}^{-\mathrm{1个}}$ RMSE为29.6和8.7 $\mathrm{毫克}·{\mathrm{大号}}^{-\mathrm{1个}}$分别。结果证明，所提出的方法可以成功地用于提高封闭式水培系统中ISE的准确性和可行性。