Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition
Abstract Permeability index (PI) and magnesium absorption ratio (MAR) are both primary irrigation water quality indicators (IWQI) used to evaluate the efficacy of agricultural water supplies. This is considered a complex environmental issue to reliably forecast IWQI parameters without its appropriat...
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Nature Portfolio
2025-05-01
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| Online Access: | https://doi.org/10.1038/s41598-025-99341-w |
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| author | Marjan Kordani Mohsen Bagheritabar Iman Ahmadianfar Arvin Samadi-Koucheksaraee |
| author_facet | Marjan Kordani Mohsen Bagheritabar Iman Ahmadianfar Arvin Samadi-Koucheksaraee |
| author_sort | Marjan Kordani |
| collection | DOAJ |
| description | Abstract Permeability index (PI) and magnesium absorption ratio (MAR) are both primary irrigation water quality indicators (IWQI) used to evaluate the efficacy of agricultural water supplies. This is considered a complex environmental issue to reliably forecast IWQI parameters without its appropriate time series and limited input sequences. Hence, this research develops an innovative hybrid intelligence framework for the first time to forecast the PI and MAR indices at the Karun River, Iran. The proposed framework includes a new hybrid machine learning (ML) model based on generalized ridge regression and kernel ridge regression with a regularized locally weighted (GRKR) method. This research developed an optimized multivariate variational mode decomposition (OMVMD) technique, optimized by the Runge-Kutta algorithm (RUN), to decompose the input variables. The light gradient boosting machine model (LGBM) is also implemented to select the influential input variables. The main contribution of the intelligence framework lies in developing a new hybrid ML model based on GRKR coupled with OMVMD. Five water quality parameters from the Karun River at two stations (Ahvaz and Molasani) over 40 years are used to forecast the PI and MAR indices monthly. Statistical metrics confirmed that the proposed OMVMD-GRKR model, concerning the best efficiency in the Ahvaz (R = 0.987, RMSE = 0.761, and U95% = 2.108) and Molasani (R = 0.963, RMSE = 1.379, and U95% = 3.828) stations, outperformed the OMVMD and simple-based methods such as ridge regression (Ridge), least squares support vector machine (LSSVM), deep random vector functional link (DRVFL), and deep extreme learning machine (DELM). For this reason, the suggested OMVMD-GRKR model serves as a valuable framework for predicting IWQI parameters. |
| format | Article |
| id | doaj-art-f66feeffc7f64bfebd68db67a5e3ba16 |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-f66feeffc7f64bfebd68db67a5e3ba162025-08-20T03:09:34ZengNature PortfolioScientific Reports2045-23222025-05-0115112410.1038/s41598-025-99341-wForecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decompositionMarjan Kordani0Mohsen Bagheritabar1Iman Ahmadianfar2Arvin Samadi-Koucheksaraee3Department of Hydrology and Water Resources, Shahid Chamran University of AhvazDepartment of Electrical Engineering, University of CincinnatiDepartment of Civil Engineering, Behbahan Khatam Alanbia University of TechnologyDepartment of Civil, Construction and Environmental Engineering (Dept 2470), North Dakota State UniversityAbstract Permeability index (PI) and magnesium absorption ratio (MAR) are both primary irrigation water quality indicators (IWQI) used to evaluate the efficacy of agricultural water supplies. This is considered a complex environmental issue to reliably forecast IWQI parameters without its appropriate time series and limited input sequences. Hence, this research develops an innovative hybrid intelligence framework for the first time to forecast the PI and MAR indices at the Karun River, Iran. The proposed framework includes a new hybrid machine learning (ML) model based on generalized ridge regression and kernel ridge regression with a regularized locally weighted (GRKR) method. This research developed an optimized multivariate variational mode decomposition (OMVMD) technique, optimized by the Runge-Kutta algorithm (RUN), to decompose the input variables. The light gradient boosting machine model (LGBM) is also implemented to select the influential input variables. The main contribution of the intelligence framework lies in developing a new hybrid ML model based on GRKR coupled with OMVMD. Five water quality parameters from the Karun River at two stations (Ahvaz and Molasani) over 40 years are used to forecast the PI and MAR indices monthly. Statistical metrics confirmed that the proposed OMVMD-GRKR model, concerning the best efficiency in the Ahvaz (R = 0.987, RMSE = 0.761, and U95% = 2.108) and Molasani (R = 0.963, RMSE = 1.379, and U95% = 3.828) stations, outperformed the OMVMD and simple-based methods such as ridge regression (Ridge), least squares support vector machine (LSSVM), deep random vector functional link (DRVFL), and deep extreme learning machine (DELM). For this reason, the suggested OMVMD-GRKR model serves as a valuable framework for predicting IWQI parameters.https://doi.org/10.1038/s41598-025-99341-wPermeability indexMagnesium absorption ratioGeneralized ridge regressionOptimized MVMDKernel ridge regressionWater quality |
| spellingShingle | Marjan Kordani Mohsen Bagheritabar Iman Ahmadianfar Arvin Samadi-Koucheksaraee Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition Scientific Reports Permeability index Magnesium absorption ratio Generalized ridge regression Optimized MVMD Kernel ridge regression Water quality |
| title | Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition |
| title_full | Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition |
| title_fullStr | Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition |
| title_full_unstemmed | Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition |
| title_short | Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition |
| title_sort | forecasting water quality indices using generalized ridge model regularized weighted kernel ridge model and optimized multivariate variational mode decomposition |
| topic | Permeability index Magnesium absorption ratio Generalized ridge regression Optimized MVMD Kernel ridge regression Water quality |
| url | https://doi.org/10.1038/s41598-025-99341-w |
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