Abstract
For the first time, a novel hybrid machine learning model named the least-squares support vector machine-arithmetic optimization algorithm (LSSVM-AOA) was proposed. The performance of LSSVM-AOA was checked on six benchmark data sets (BDSs) to showcase its applicability. After testing the performance of the novel hybrid machine learning model, its performance in electrical conductivity (EC) and total soluble solids (TDS) estimating was developed at six stations in the Karun river basin. For this purpose, effective parameters were selected by the principal component analysis (PCA) method. The results of the technique for order of preference by similarity to ideal solution (TOPSIS) method showed that the LSSVM-AOA has promising results in modeling BDSs and estimating water quality parameters (WQPs) in comparison with classical and hybrid algorithms (artificial neural network (ANN), adaptive neural fuzzy inference system (ANFIS), LSSVM, LSSVM-particle swarm optimization (LSSVM-PSO) and LSSVM-whale optimization algorithm (LSSVM-WOA)). The average values of correlation coefficient (R) in EC and TDS estimates were 0.969 and 0.950, respectively. Eventually, the Monte Carlo method (MCM) showed that the LSSVM-AOA has the lowest uncertainty among other algorithms.
Graphical abstract
Similar content being viewed by others
Data Availability
All data generated or used during the study are applicable if requested. This article contains supplementary information file.
Abbreviations
- A:
-
Addition
- AI:
-
Artificial intelligence
- ANFIS:
-
Adaptive neuro fuzzy inference system
- ANN:
-
Artificial neural network
- AOA:
-
Arithmetic optimization algorithm
- BDS:
-
Benchmark data set
- Ca2+ :
-
Calcium
- \({\mathrm{Cl}}^{-}\) :
-
Chlorine
- CV:
-
Coefficient of variation
- CS:
-
Coefficient of skewness
- CSO:
-
Cat swarm optimization
- D:
-
Division
- DO:
-
Dissolved oxygen
- EC:
-
Electrical conductivity
- FFNN:
-
Feed forward neural network
- GEP:
-
Gene expression programming
- \({\mathrm{HCO}}_{3}^{-}\) :
-
Bicarbonate
- KELM:
-
Kernel extreme learning machine
- LSTM:
-
Long short-term memory network
- LSSVM:
-
Least-square support vector machine
- M:
-
Multiplication
- MAE:
-
Mean absolute error
- MCDM:
-
Multi-criteria decision-making
- MCM:
-
Monte Carlo method
- MFO:
-
Moth flam optimization
- Mg2+ :
-
Magnesium
- MOA:
-
Math optimizer accelerated
- MOP:
-
Math optimizer probability
- Na+ :
-
Sodium
- NIS:
-
Negative ideal solution
- PCA:
-
Principal component analysis
- PIS:
-
Positive ideal solution
- PSO:
-
Particle swarm optimization
- Q:
-
Discharge
- R:
-
Correlation coefficient
- R2 :
-
Coefficient of determination
- RBF:
-
Radial basis function
- RMSE:
-
Root mean squared error
- RRMSE:
-
Relative root mean square error
- S:
-
Subtraction
- SA:
-
Sensitivity analysis
- SAR:
-
Sodium absorption ratio
- SC:
-
Subtractive clustering
- SLA:
-
Superposition-based learning algorithm
- \({\mathrm{So}}_{4}^{2-}\) :
-
Sulfate
- SSA:
-
Sparrow search algorithm
- Sum.A:
-
Sum anion
- Sum.C:
-
Sum cation
- SVM:
-
Support vector machine
- Std:
-
Standard deviation
- TDS:
-
Total dissolved solids
- TOPSIS:
-
Technique for order of preference by similarity to ideal solution
- WOA:
-
Whale optimization algorithm
- WQ:
-
Water quality
- WQP:
-
Water quality parameter
References
Abba SI, Abdulkadir RA, Sammen SS, Pham QB, Lawan AA, Esmaili P, Malik A, Al-Ansari N (2022) Integrating feature extraction approaches with hybrid emotional neural networks for water quality index modeling. Appl Soft Comput 114:108036. https://doi.org/10.1016/j.asoc.2021.108036
Abdel-Fattah MK, Mokhtar A, Abdo AI (2021) Application of neural network and time series modeling to study the suitability of drain water quality for irrigation: a case study from Egypt. Environ Sci Pollut Res 28:898–914. https://doi.org/10.1007/s11356-020-10543-3
Abualigah L, Diabat A, Mirjalili S, Elaziz MA, Gandomi AH (2021a) The arithmetic optimization algorithm. Comput Methods Appl Mech Engrg 376:113609. https://doi.org/10.1016/j.cma.2020.113609
Abualigah L, Yousri D, Elaziz MA, Ewees AA, Al-qaness MAA, Gandomi AH (2021b) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250. https://doi.org/10.1016/j.cie.2021.107250
Ahmadianfar I, Heidari AA, Gandomi AH, Chu X, Chen H (2021) RUN beyond the metaphor: an efficient optimization algorithm based on Runge Kutta method. Expert Syst Appl 181:115079. https://doi.org/10.1016/j.eswa.2021.115079
Alizamir M, Kisi O, Adnan RM, Kuriqi A (2020) Modelling reference evapotranspiration by combining neuro-fuzzy and evolutionary strategies. Acta Geophys 68:1113–1126. https://doi.org/10.1007/s11600-020-00446-9
Anaraki MV, Farzin S, Mousavi SF, Karami H (2021) Uncertainty analysis of climate change impacts on flood frequency by using hybrid machine learning methods. Water Resour Manag 35:199–223. https://doi.org/10.1007/s11269-020-02719-w
Azad A, Farzin S, Sanikhani H, Karami H (2021) Approaches for optimizing the performance of adaptive neuro-fuzzy inference system and least-squares support vector machine in pecipitation modeling. J Hydrol Eng 26(4). https://doi.org/10.1061/(ASCE)HE.1943-5584.0002069
Banadkooki FB, Ehteram M, Panahi F, Sammen SS, Othman FB, EL-Shafie A (2020) Estimation of total dissolved solids (TDS) using new hybrid machine learning models. J Hydrol 587:124989. https://doi.org/10.1016/j.jhydrol.2020.124989
Choubin B, Borji M, Hosseini FS, Mosavi A, Dineva AA (2020) Mass wasting susceptibility assessment of snow avalanches using machine learning models. Sci Rep 10:18363. https://doi.org/10.1038/s41598-020-75476-w
Chowdhury S, Husain T (2020) Reducing the dimension of water quality parameters in source water: an assessment through multivariate analysis on the data from 441 supply systems. J Environ Manage 274:111202. https://doi.org/10.1016/j.jenvman.2020.111202
Deng T, Chau KW, Duan HF (2021) Machine learning based marine water quality prediction for coastal hydro-environment management. J Environ Manage 284:112051. https://doi.org/10.1016/j.jenvman.2021.112051
Egbueri JC, Agbasi JC (2022) Data-driven soft computing modeling of groundwater quality parameters in southeast Nigeria: comparing the performances of different algorithms. Environ Sci Pollut. https://doi.org/10.1007/s11356-022-18520-8
Farzin S, Chianeh FN, Anaraki MV, Mahmoudian F (2020) Introducing a framework for modeling of drug electrochemical removal from wastewater based on data mining algorithms, scatter interpolation method, and multi criteria decision analysis (DID). J Clean Prod 266:122075. https://doi.org/10.1016/j.jclepro.2020.122075
Guvenir HA, Uysal I (2000) Regression on feature projections. Knowl Based Syst 13(4):207–214. https://doi.org/10.1016/S0950-7051(00)00060-5
Hojjatnooghi F, Shirani H, Pazira E, Besalatpour AA, Torkashvand AM (2021) Determination of soil properties affecting soil aggregate tensile strength in a semiarid region of Iran using a hybrid algorithm. Commun Soil Sci Plant Anal 52(17):1981–1992. https://doi.org/10.1080/00103624.2021.1908321
Ighalo JO, Adeniyi AG, Marques G (2021) Artificial intelligence for surface water quality monitoring and assessment: a systematic literature analysis. Model Earth Syst Environ 7:669–681. https://doi.org/10.1007/s40808-020-01041-z
Jang JS (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23:665–685. https://doi.org/10.1109/21.256541
JannatKhah M, Akbari A, Basmanji AB, Rahmani E, Cox JP (2021) Estimation of monthly total dissolved solids using ANN and LS-SVM techniques in the Aji Chay river, Iran. J Civil Eng Construct 10. https://doi.org/10.32732/jcec.2021.10.1.1
Kadkhodazadeh M, Farzin S (2021) A novel LSSVM model integrated with GBO algorithm to assessment of water quality parameters. Water Resour Manag 35:3939–3968. https://doi.org/10.1007/s11269-021-02913-4
Kadkhodazadeh M, Valikhan Anaraki M, Morshed-Bozorgdel A, Farzin S (2022) A new methodology for reference evapotranspiration prediction and uncertainty analysis under climate change conditions based on machine learning, multi criteria decision making and Monte Carlo methods. Sustainability 14(5):2601. https://doi.org/10.3390/su14052601
Karabašević D, Stanujkić D, Zavadskas EK, Stanimirović P, Popović G, Predić B, Ulutaş A (2020) A novel extension of the TOPSIS method adapted for the use of single-valued neutrosophic sets and hamming distance for e-commerce development strategies selection. Symmetry 12(8):1263. https://doi.org/10.3390/sym12081263
Karami H, Anaraki MV, Farzin S, Mirjalili S (2021) Flow direction algorithm (FDA): a novel optimization approach for solving optimization problems. Comput Ind Eng 156:107224. https://doi.org/10.1016/j.cie.2021.107224
Khan FM, Gupta R, Sekhri S (2021) Superposition learning-based model for prediction of E.coli in groundwater using physico-chemical water quality parameters. Groundw Sustain Dev 13:100580. https://doi.org/10.1016/j.gsd.2021.100580
Khullar S, Singh N (2022) Water quality assessment of a river using deep learning Bi-LSTM methodology: forecasting and validation. Environ Sci Pollut Res 29:12875–12889. https://doi.org/10.1007/s11356-021-13875-w
Mahmood T, Ali Z (2021) Entropy measure and TOPSIS method based on correlation coefficient using complex q-rung orthopair fuzzy information and its application to multi-attribute decision making. Soft Comput 25:1249–1275. https://doi.org/10.1007/s00500-020-05218-7
Meng X, Zhang Y, Qiao J (2021) An adaptive task-oriented RBF network for key water quality parameters prediction in wastewater treatment process. Neural Comput & Applic 33:11401–11414. https://doi.org/10.1007/s00521-020-05659-z
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
Monticeli FM, Neves RM, Júnior HLO (2021) Using an artificial neural network (ANN) for prediction of thermal degradation from kinetics parameters of vegetable fibers. Cellulose 28:1961–1971. https://doi.org/10.1007/s10570-021-03684-2
Najafzadeh M, Niazmardi S (2021) A novel multiple-kernel support vector regression algorithm for estimation of water quality parameters. Nat Resour Res 30:3761–3775. https://doi.org/10.1007/s11053-021-09895-5
Ouiyangkul P, Tantishaiyakul V, Hirun N (2020) Exploring potential coformers for oxyresveratrol using principal component analysis. Int J Pharm 587:119630. https://doi.org/10.1016/j.ijpharm.2020.119630
Panahi M, Gayen A, Pourghasemi HR, Rezaie F, Lee S (2020) Spatial prediction of landslide susceptibility using hybrid support vector regression (SVR) and the adaptive neuro-fuzzy inference system (ANFIS) with various metaheuristic algorithms. Sci Total Environ 741:139937. https://doi.org/10.1016/j.scitotenv.2020.139937
Pham QB, Yang TC, Kuo CM, Tseng HW, Yu PS (2021) Coupling singular spectrum analysis with least square support vector machine to improve accuracy of SPI drought forecasting. Water Resour Manag 35:847–868. https://doi.org/10.1007/s11269-020-02746-7
Pipelzadeh S, Mastouri R (2021) Modeling of contaminant concentration using the classification-based model integrated with data preprocessing algorithms. J Hydroinformatics 23(3):639–654. https://doi.org/10.2166/hydro.2021.138
Rehamnia I, Benlaoukli B, Heddam S (2020) Modeling of seepage flow through concrete face rockfill and embankment dams using three heuristic artificial intelligence approaches: a comparative study. Environ Process 7:367–381. https://doi.org/10.1007/s40710-019-00414-6
Sales AK, Gul E, Safari MJS, Gharehbagh HG, Vaheddoost B (2021) Urmia lake water depth modeling using extreme learning machine-improved grey wolf optimizer hybrid algorithm. Theor Appl Climatol 146:833–849. https://doi.org/10.1007/s00704-021-03771-1
Sha J, Li X, Zhang M, Wang ZL (2021) Comparison of forecasting models for real-time monitoring of water quality parameters based on hybrid deep learning neural networks. Water 13(11):1547. https://doi.org/10.3390/w13111547
Shah MI, Abunama T, Javed MF, Bux F, Aldrees A, Tariq MAUR, Mosavi A (2021a) Modeling surface water quality using the adaptive neuro-fuzzy inference system aided by input optimization. Sustainability 13(8):4576. https://doi.org/10.3390/su13084576
Shah MI, Javed MF, Alqahtani A, Aldrees A (2021b) Environmental assessment based surface water quality prediction using hyper-parameter optimized machine learning models based on consistent big data. Process Saf Environ Prot 151:324–340. https://doi.org/10.1016/j.psep.2021.05.026
Song C, Yao L, Hua C, Ni O (2021a) Comprehensive water quality evaluation based on kernel extreme learning machine optimized with the sparrow search algorithm in Luoyang river basin. China Environ Earth Sci 80:521. https://doi.org/10.1007/s12665-021-09879-x
Song C, Yao L, Hua C, Ni Q (2021b) A water quality prediction model based on variational mode decomposition and the least squares support vector machine optimized by the sparrow search algorithm (VMD-SSA-LSSVM) of the Yangtze river. China Environ Monit Assess 193:363. https://doi.org/10.1007/s10661-021-09127-6
Taghizadeh S, Khani S, Rajaee T (2021) Hybrid SWMM and particle swarm optimization model for urban runoff water quality control by using green infrastructures (LID-BMPs). Urban for Urban Green 60:127032. https://doi.org/10.1016/j.ufug.2021.127032
Tikhamarine Y, Malik A, Souag-Gamane D, Kisi O (2020) Artificial intelligence models versus empirical equations for modeling monthly reference evapotranspiration. Environ Sci Pollut Res 27:30001–30019. https://doi.org/10.1007/s11356-020-08792-3
Tizro AT, Fryar AE, Vanaei A, Kazakis N, Voudouris K, Mohammadi P (2021) Estimation of total dissolved solids in Zayandehrood river using intelligent models and PCA. Sustain Water Resour Manag 7:22. https://doi.org/10.1007/s40899-021-00497-w
Zeng N, Wang Z, Liu W, Zhang H, Hone K, Liu X (2020) A dynamic neighborhood-based switching particle swarm optimization algorithm. IEEE Trans Cybern 33170793:1–12. https://doi.org/10.1109/TCYB.2020.3029748
Funding
The research has not been supported through any funds.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical Approval
Not applicable.
Consent to Participate
The authors have made a significant contribution to this manuscript, have seen and approved the final manuscript.
Consent to Publish
The authors have agreed to publish the study in Water Resources Management.
Competing Interests
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Highlights
• Introducing a novel hybrid machine learning model, namely LSSVM-AOA.
• Proving the performance of the LSSVM-AOA by using several benchmark data sets (BDSs).
• Developing the application of LSSVM-AOA in estimation of water quality parameters (WQPs).
• Comparing the performance of LSSVM-AOA with classical and hybrid algorithms.
• Uncertainty analysis of machine learning algorithms by Monte Carlo method (MCM).
• The proposed hybrid machine learning model has potential to analyse other engineering problems.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Kadkhodazadeh, M., Farzin, S. Introducing a Novel Hybrid Machine Learning Model and Developing its Performance in Estimating Water Quality Parameters. Water Resour Manage 36, 3901–3927 (2022). https://doi.org/10.1007/s11269-022-03238-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-022-03238-6