Abstract Total dissolved solids (TDS) are recognized as an essential indicator of surface water quality. The current research investigates the potential of a novel computer aid approach based on the hybridization of wavelet pre-processing with multigene genetic programming (W-MGGP) for monthly TDS prediction at the Sefid Rud River in Northern Iran. 20-year historical monthly river flow (Q) and TDS data measured at the Astaneh station were used for the model training and testing. The employed time series data were decomposed into several sub-series using three mother wavelets (i.e., Daubechies4 (db4), biorthogonal (bior6.8), and discrete meyer (dmey)) to assess appropriate combinations of the time series and their lag times, which were further used for prediction process. The W-MGGP model was compared against the wavelet-gene expression programming (W-GEP), stand-alone MGGP, and GEP models. Results were evaluated using several performance metrics including root mean square error (RMSE), correlation coefficient (R), and Nash-Sutcliffe efficiency (NSE). Modeling results indicated that W-MGGP and W-GEP provided a superior prediction capacity for the TDS in comparison with the other stand-alone artificial intelligence (AI) models. The discrete meyer method exhibited the best performance in time series data decomposition as a pre-processing approach. The proposed W-MGGP model based on the dmey mother wavelet attained the best statistical metrics (R = 0.942, RMSE = 90.383, and NSE = 0.862). The research findings demonstrated the hybridization of the wavelet pre-processing approach with MGGP predictive model for the TDS simulation.

中文翻译：

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使用杂交小波-多基因遗传编程预测地表水总溶解固体：新方法

摘要 总溶解固体 (TDS) 被公认为地表水水质的重要指标。目前的研究调查了一种基于小波预处理与多基因遗传编程 (W-MGGP) 杂交的新型计算机辅助方法的潜力，用于在伊朗北部的 Sefid Rud 河进行每月 TDS 预测。在 Astaneh 站测量的 20 年历史月河流量 (Q) 和 TDS 数据用于模型训练和测试。使用三个母小波（即 Daubechies4 (db4)、双正交 (bior6.8) 和离散迈耶 (dmey)）将采用的时间序列数据分解为几个子序列，以评估时间序列的适当组合及其滞后时间，进一步用于预测过程。W-MGGP 模型与小波基因表达编程 (W-GEP)、独立 MGGP 和 GEP 模型进行了比较。使用多种性能指标评估结果，包括均方根误差 (RMSE)、相关系数 (R) 和 Nash-Sutcliffe 效率 (NSE)。建模结果表明，与其他独立的人工智能 (AI) 模型相比，W-MGGP 和 W-GEP 为 TDS 提供了更好的预测能力。作为一种预处理方法，离散迈耶方法在时间序列数据分解中表现出最好的性能。提出的基于 dmey 母小波的 W-MGGP 模型获得了最好的统计指标（R = 0.942，RMSE = 90.383，NSE = 0.862）。