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Introducing a Novel Hybrid Machine Learning Model and Developing its Performance in Estimating Water Quality Parameters

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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.

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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

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Funding

The research has not been supported through any funds.

Author information

Authors and Affiliations

  1. Department of Water Engineering and Hydraulic Structures, Faculty of Civil Engineering, Semnan University, Semnan, 35131-19111, Iran

    Mojtaba Kadkhodazadeh & Saeed Farzin

Authors
  1. Mojtaba Kadkhodazadeh
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  2. Saeed Farzin
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Corresponding author

Correspondence to Saeed Farzin.

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The authors have made a significant contribution to this manuscript, have seen and approved the final manuscript.

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The authors have agreed to publish the study in Water Resources Management.

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The authors declare that they have no conflict of interest.

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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

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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

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  • DOI: https://doi.org/10.1007/s11269-022-03238-6

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