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A Hybrid Machine Learning Model for Modeling Nitrate Concentration in Water Sources

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Abstract

Nitrate is one of the most dangerous contaminants that can pollute water sources; as a result, it is always tried to use accurate methods to monitor its quantity. The goal of this study is to develop a hybrid machine learning model (HELM) for modeling nitrate concentration in water resources. For this purpose, 1453 samples were collected over a 20-year period (from 2000 to 2020). To develop the HMLM, the concentrations of nitrate data were first clustered using the Jenks natural breaks method (JNBA). After that, a support vector machines (SVM) model was developed for each cluster. In this case, the trial-and-error (TaE) method was used to determine the parameters of kernel functions. However, the sequential forward floating selection (SFFS) technique was employed to select the optimal input parameters to simulate the nitrate content in each cluster. In the last step, to improve the efficiency of the SVM model, the parameters of the kernel functions were determined using the Harris-Hawkes optimization (HHO) algorithm. The HHO algorithm is used because of its ability to intelligently shift between the exploration and exploitation phases during optimization. To develop all of the models, 80% of the data was utilized for training and the remaining for testing. Finally, indices such as root mean square error (RMSE), mean absolute error (MAE), Willmott’s index agreement (WI), explained variance score (EVS), Kling-Gupta efficiency (KGE), and coefficient of determination (\({R}^{2}\)) were used to evaluate different models. Based on the results of this study, HMLM can be used to accurately model nitrate concentration. Furthermore, using the HHO optimization algorithm instead of the TaE method considerably improves the SVM model’s performance.

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Data Availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

ANFIS:

Adaptive neuro-fuzzy inference system

AUC:

Area under the receiver operating characteristic curve method

ANN:

Artificial neural network

AT:

Air temperature

ARIMA:

Autoregressive integrated moving average

BRT:

Boosted regression trees

\({\mathrm{R}}^{2}\)  :

Coefficient of determination

DE:

Differential evolution algorithm

EVS:

Explained variance score

FLS:

Fuzzy logic supervised

GA:

Genetic algorithm

GVF:

Goodness of variance fit

GAPM:

Groundwater aquifer potential mapping

HM-SVMS:

Hard-margin support vector machines

HHO:

Harris-Hawkes optimization algorithm

HMLM:

Hybrid machine learning model

JNB:

Jenks natural breaks algorithm

KGE:

Kling-Gupta efficiency

LK:

Linear kernel

LR:

Logistic regression

MAE:

Mean absolute error

MCM:

Million cubic meters

MQ:

Multi quadric

MABLR:

Multi-adaptive boosting logistic regression

MPL:

Multiple-layer perception

MDA:

Multivariate discriminant analysis

OOB:

Out-of-bag error

PSO:

Particle swarm optimization

PK:

Polynomial kernel

RBF:

Radial basis function

ROC:

Receiver operating characteristic curve

SFF:

Sequential forward floating selection technique

SK:

Sigmoid kernel

SM-SVMS:

Soft-margin support vector machines

SVM:

Support vector machines

TH:

Total hardness

TAE:

Trial-and-error method

WT:

Water temperature

WI:

Willmott’s index agreement

MA:

Mean absolute error

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Authors and Affiliations

  1. Department of Geology, Faculty of Earth Sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Adnan Mazraeh

  2. Department of Civil, Faculty of Engineering, Shushtar Branch, Islamic Azad University, Shushtar, Iran

    Meysam Bagherifar

  3. Department of Water Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

    Saeid Shabanlou

  4. Guilan University, Rasht, Iran

    Reza Ekhlasmand

Authors
  1. Adnan Mazraeh
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  2. Meysam Bagherifar
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  3. Saeid Shabanlou
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  4. Reza Ekhlasmand
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All authors (Adnan Mazraeh, Meysam Bagherifar, Saeid Shabanlou, Reza Ekhlasmand) have an equal share in writing all parts of the article.

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Correspondence to Saeid Shabanlou.

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Mazraeh, A., Bagherifar, M., Shabanlou, S. et al. A Hybrid Machine Learning Model for Modeling Nitrate Concentration in Water Sources. Water Air Soil Pollut 234, 721 (2023). https://doi.org/10.1007/s11270-023-06745-3

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