Predicting soil electrical conductivity using multi-layer perceptron integrated with grey wolf

Journal of Geochemical Exploration 220 (2021) 106639

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Predicting soil electrical conductivity using multi-layer perceptron integrated with grey wolf optimizer

T

Amirhosein Mosavia,b, , Saeed Samadianfardc, Sabereh Darbandic, Narjes Nabipourd, , ⁎⁎⁎ Sultan Noman Qaseme,f, Ely Salwanag, Shahab S. Bandd,h, ⁎

⁎⁎

a

Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, VietNam Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, VietNam c Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran d Institute of Research and Development, Duy Tan University, Da Nang 550000, VietNam e Computer Science Department, College of Computer and Information Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia f Computer Science Department, Faculty of Applied Science, Taiz University, Taiz, Yemen g Institute of IR4.0, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia h Future Technology Research Center, College of Future, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, ROC b

ARTICLE INFO

ABSTRACT

Keywords: Artificial neural network Grey wolf optimizer algorithm Hybrid predictive model Soil electrical conductivity Machine learning

In irrigation systems, salinity is a critical problem as it has undesirable impacts on crop health, agricultural throughput and farming management. Considering these, it is imperative to regularly monitor and develop measures to predict salinity of the soil to negate the salinization effects on agriculture. This paper constructs and evaluates the performance of the hybrid machine learning model of multilayer perceptron (MLP)-Grey Wolf Optimizer (MLP-GWO) for electrical conductivity (EC). MLP-GWO model is trained with soil sample data (i.e., parameters for organic matter, OM and soil constituents Ca+2, Mg+2, K+, Na+, Cl−, SO4−2, HCO3−) from Khuzestan province in Iran. Seven modelling scenarios representing different combinations of salinity para­ meters are investigated to establish a hybrid MLP-GWO model that aims to reduce the error rate of the resulting forecasts of EC. To ascertain conclusive results, the MLP-GWO model is cross-validated with its classical coun­ terpart without the add-in (i.e., GWO) optimizer, and the model error metrics are evaluated by coefficients of determination (R2), root mean squared error (RMSE) and relative root mean square error (RRMSE) in in­ dependent test data. For all tested predictive models, the performance of the MLP-GWO hybrid model is superior to a classical model, evidenced by larger R2 (~0.552–0.711 relative to ~0.430–0.711) and a lower RMSE and RRSE (~1.293–3.537 vs. 1.616–4.421 and ~3.736–9.899 vs. 4.613–12.133). The proposed GWO as an optimizer leads to a plausible improvement in an MLP model due to the most optimal weights attained in the neuronal layer that facilitates a robust feature extraction process to predict EC. As conclusion, the obtained results proved the effectiveness of the hybrid MLP-GWI model for predicting soil properties, which has potential implications in precision agriculture where salinity needs to be modeled for crop management practices.

1. Introduction Soil salinization, known as the enrichment of the underlying soil with soluble salts, is one of the processes of land degradation, parti­ cularly in arid locations. So, the evaporation of water from lower depths

of the soil and small quantities of rainfall to leach down the salts from the root zones causes the accumulating of excessive soluble salts in soils (Gorji et al., 2015). Under such circumstances, soluble salts are gath­ ered in the soil, impelling the soil properties with a significant weak­ ening in productivity (Asfaw et al., 2018). According to the Food and

Correspondence to: A. Mosavi, Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam. ⁎⁎ Corresponding author. ⁎⁎⁎ Correspondence to: S. S. Band, Institute of Research and Development, Duy Tan University, Da Nang 550000, Viet Nam. E-mail addresses: amirhosein.mosavi@tdtu.edu.vn (A. Mosavi), s.samadian@tabrizu.ac.ir (S. Samadianfard), sdarbandi@tabrizu.ac.ir (S. Darbandi), narjesnabipour@duytan.edu.vn (N. Nabipour), SNMohammed@imamu.edu.sa (S.N. Qasem), elysalwana@ukm.edu.my (E. Salwana), shamshirbands@yuntech.edu.tw, shamshirbandshahaboddin@duytan.edu.vn (S. S. Band). ⁎

https://doi.org/10.1016/j.gexplo.2020.106639 Received 14 April 2020; Received in revised form 5 August 2020; Accepted 1 September 2020 Available online 02 September 2020 0375-6742/ © 2020 Published by Elsevier B.V.

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Agriculture Organization (FAO, 2007), more than 77 million hectares of land are salt-affected. Assessments specify that about 33% of irrigated areas in most countries are critically affected by salinity or are esti­ mated to be salinized in the near future (Abbas and Khan, 2007). Since measuring and monitoring salty soils is a challenging task due to high costs of soil sample examination, the precise estimation of soil salinity, by means on inexpensive models, is useful for irrigation planning, yield predicting and water management (Rhoades et al., 1999; Darwish et al., 2005; Chen et al., 2005).

In the last decade, only a few studies have been carried out to ad­ dress the challenges in measuring and modelling soil salinity, em­ ploying diverse statistical and artificial intelligence models. For ex­ ample, the study of Cai et al. (2010) implemented SVM classifier models to categorize salt-affected soils with a mix of multispectral and texture features as data input sources. The results advocated that SVM could effectively extract salinization and soil-thematic information from the Yinchuan Plain datasets, leading to a valid classification and modelling soil salinity in that region. Ghorbani et al. (2019) estimated EC values using some factors such as soil texture, cation exchange, drainage conditions, organic matter level, salinity, and subsoil characteristics.

So, they developed a multilayer perceptron optimized with Firefly Al­ gorithm (MLP-FFA) and evaluated its performance with standalone MLP and the ordinary kriging (OK) models. Conclusively, they proved the higher accuracy of MLP-FFA over a standalone MLP and OK ap­ proaches. Singh et al. (2020) implemented five data driven techniques and their wavelet forms to predict soil permeability based on soil physical properties. They stated that among all studied models, the wavelet random forest model had higher efficiency in predicting soil permeability.

One of the most common data-intelligent approaches implemented to forecast environmental properties is the artificial neural network (ANN) model. This can robotically examine the complex and nonlinear association of multi-sourced model inputs through a largely automated, self-learning process (Erzin et al., 2008; Deo and Sahin, 2017; Prasad et al., 2018a, 2018b). ANNs therefore have an excellent capability to model relatively complex input features as they can check for both linear and non-linear interactions among inputs and output variable (Huang and Foo, 2002; Deo and Şahin, 2015; Raheli et al., 2017; Deo et al., 2018). Due to its widespread usage, ANNs have been validated for their effectiveness in different fields such as estimating soil properties using standalone ANN (Zhao et al., 2010), reservoir inflow prediction utilizing wavelet-ANN (Esmaeilzadeh et al., 2017), predicting rockburst risk in deep mines and tunnels employing FFA-ANN (Zhou et al., 2020), predicting compressive strength of recycled aggregate concrete using ICA-XGBoost model (Duan et al., 2020), calculating slope stability safety factors using GA-MLP(Wang et al., 2020) and predicting ripping production in different weathering zones through in situ tests im­ plementing PSO-ANN (Mohamad et al., 2019). Additionally, as the as­ sociation between soil salinity and its related properties may not be linear so the ANN model is beneficial for inspecting such relationships among multivariate data in the soil science area (Shahabi et al., 2017).

Artificial intelligence models are intent to build a model that is predictive and tries to find the hidden patterns of complex problems.

So, proper establishing of these models is vital for accurate prediction of the specific phenomenon. For that purpose, nature inspired techniques such as firefly; fruit fly, etc. have been applied in different fields for optimizing the artificial intelligence model parameters and therefore increasing the prediction accuracy (e.g., Liu et al., 2013; Ghorbani et al., 2017; Samadianfard et al., 2018; Deo et al., 2018; Bhattacharjee and Pant, 2019; Yu et al., 2019; Samadianfard et al., 2019b; Nguyen et al., 2020). Although soil salinization is considered a recognized phenomenon in irrigated agriculture, only a few researchers have de­ veloped data-driven models for salinity and investigated their re­ lationships with other soil parameters. By this deficit and a need to perform research in a diverse range of geographic and hydro-climatic conditions, contemporary explorations have intended to study the

association among EC and other soil properties using hybrid learning models. One such termed as ANN-GWO, where the artificial neural network is integrated with the Grey Wolf Optimization algorithm that has been relatively scarcely utilized. The utility of such models, how­ ever, is expected to have significant implications in maintaining eco­ logical sustainability and empowering agricultural productivity, in­ cluding a significant role in formulating strategic soil management policies by decision-makers in the agricultural sector.

Considering the aforesaid, the purpose of this research study is as follows. (1) To construct and evaluate a Multi-Layer Perceptron hybrid forecast model integrated with the Grey Wolf Optimization algorithm (i.e., MLP-GWO) in a problem of predicting soil electrical conductivity.

(2) To apply MLP-GWO hybrid model trained with diverse soil samples extracted from Khuzestan province, Iran with soil parameters based on organic matter (OM) and several soil constituents. (3) evaluate seven unique scenarios applying the optimal MLP-GWO hybrid model that represent different combinations of soil parameters to study their con­ tributory role in predicting electrical conductivity. The rest of the paper is structured as follows. Section 1 introduces a theory of hybrid and standalone models, Section 2 describes the Materials and Method with relevant data and model metrics, Section 3 provides Results and Dis­ cussion and Section 4 shows the conclusions for this study.

2. Materials and method 2.1. Multilayer Perceptron Neural Network In the current study, an ANN based multilayer perceptron (MLP) algorithm in predicting soil electrical conductivity was implemented.

The MLP model is a distinct item of ANN that contains a parallel in­ formation processing system with neurons that are organized in the input, hidden and output layer (McClelland and Rumelhart, 1989). This model has been applied in earlier studies in soil science (e.g., Ghorbani et al., 2017; Samadianfard et al., 2018; Qasem et al., 2019) but its application to the problem of soil electrical conductivity prediction is new. In its elementary form, where an optimizer is not used with the MLP model, it contains input, hidden and output layers. The objective of the backpropagation algorithm is to reduce the global error between predictor and target variables in training stage. In this study, the sig­ moid and linear activation functions are applied in the hidden and output layers, respectively.

2.2. Hybrid MLP-GWO Model To attain accurate predictions of EC, in this study we integrated the MLP model with the Grey Wolf Optimization (GWO) as an ‘add-in’ optimizer algorithm. Fundamentally, it can be construed that the GWO algorithm firstly was recommended by Mirjalili et al. (2014). GWO algorithm can imitate the hunting behavior and group leadership of the grey wolfs. With respect to its competitive counterpart algorithms, GWO has been proven to be a more reasonable and accurate tool for optimization problems (Sweidan et al., 2015). The theory of GWO, converted to an optimization problem for modelling the EC in this re­ search paper, is drawn from the fact that in the wild, the grey wolves typically live in a group with more than ten wolves (Emary et al., 2016).

As it is displayed schematically in Fig. 1, there is an embedded hierarchy system within the groups, which can be converted to an op­ timization algorithm.

Following the notion of Mirjalili et al. (2014), a GWO-based pro­ blem can be scientifically modeled as follows: 1. Social hierarchy: alpha, beta and delta represent the wolves that head the hunting task, whereas the wolf represented by omega lags behind. Therefore, the model can be explained in terms of alpha, which is then led by the wolves beta and delta, and both are thought to be followed by the omega wolves.

2

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2.3. Study area and data This study has utilized a total of 279 soil samples that were collected from different soil types, spread all the Khuzestan Province, southwest of Iran (Fig. 3). Khuzestan has hot and humid climates with usual summer air temperatures of more than 45 °C (113 °F).

Following data collection, HCO3−, SO4−2, Cl−, Na+, K+, Mg+2, Ca+2 and the amount of organic matter (OM) were measured from the soil samples and all data were utilized for training and testing of the developed model. For this reason, a total of 70% of the entire dataset has been used for training while the remaining data has been used for testing purposes. Table 1 represents the statistical parameters of the utilized data. In this table, the minimum, maximum, mean, standard deviation, kurtosis and skewness factors of the training, testing and entire datasets are shown. As shown clearly, the component K+ exhibits the greatest skewness while OM also indicates a skewed distribution, albeit of a smaller magnitude. On the other hand, the constituents HCO3−, SO4−2, Cl−, Na+, Mg+2, Ca+2 reveal normal distributions as evidenced by considerably low skewness values.

Table 2 displays the correlation coefficient among different soil parameters and electrical conductivity (EC). It is evident that Na+, Cl− and Mg+2 have the highest correlation with the present EC in the Khuzestan Province. Ca+2 and SO4−2, on the other hand, have high correlations compared to the other measured variables. Moreover, HCO3−exhibits an inverse (or negatively) correlated relationship with the EC values. It should be noted that all input parameters were nor­ malized before implementing in the computing process. Furthermore, the variations of different soil parameters and EC values are illustrated in Fig. 4.

Fig. 1. Leadership hierarchy of grey wolves.

2. Encircling the prey: the hunting tasks generally initiate with sur­ rounding of the prey. The set of next mathematical equations are suggested to represent the encircling behavior, represented as fol­ lows:

D = C . XP (t )

X (t + 1) = XP (t )

X (t )

A . D

(1)

(2)

where X is the location, XP specifies the place of the prey, t is the present iteration, and A , C are coefficient vectors.

Hunting: Grey wolves are talented in identifying the position of the prey and surrounding it guided by the term, alpha. Nevertheless, in a real sense (i.e., from the model input data), we do not know much about the location of the optimum (prey) in an abstract search space. To perform the mathematical simulation, the hunting beha­ viors of the grey wolf needs to be considered. Suppose that the term alpha, beta, and delta contain more info about the possible situation of the prey. According to this assumption, the first three best ex­ planations about the possible condition of the prey are saved in memory, and the other search agents, such as the omegas, are forced to reconsider their locations conferring to the present first three best locations.

3. Attacking the prey: Following the above operations, the hunting behavior is terminated by attacking the prey when the prey stops its motion. This procedure is usually facilitated mathematically by declining the value of a from 2 to 0, which similarly causes a re­ duction in the value of A . When the values of A are in the interval [−1,1], the grey wolves attack the prey. The attacking behavior identifies the best solution, therefore provides the GWO algorithm an outstanding ability to explore the modelling data (El-Fergany and Hasanien, 2015).

4. Searching for the prey: In reality, the grey wolves frequently search the prey separately and then joined with each other based on the alpha, beta and delta wolves locations. When A is higher than one, the grey wolves are forced to separate from the prey. This se­ paration behavior provides emphasis on the exploration and per­ mission of the GWO algorithm to pursuit the problem quite com­ prehensively. Shortly, the search procedure of the GWO algorithm can initiate the adjustment of the candidate solutions by forming a random population of grey wolves. Through the iteration process, the alpha, beta and delta can approximate the possible location of the prey, and each candidate solution as a result of this updates its location. The exploration and exploitation are underscored by set­ ting the parameter a to linearly decline from 2 to 0 over the se­ quence of iterations. Candidate solutions will then separate from the prey when A > 1 and join toward the prey when A < 1. Lastly, the GWO algorithm is terminated when the completion criteria are fulfilled.

2.4. Model evaluation criteria For statistical evaluation of the performance of MLP-GWO hybrid model with respect to the standalone models, some metrics were im­ plemented to assess the capabilities of developed models. The mathe­ matical formulations are itemized as follows.

I. Coefficient of Determination (R2) (Samadianfard et al., 2018): n

1 n

Oi Pi

i=1

R2 =

n i=1

1 n

Oi 2

n i=1

2

n

Oi

i=1

Oi n

i=1

n

2

Pi

i=1

Pi 2

1 n

n i=1

2

Pi

(3)

II. Root Mean Squared Error (RMSE) (Shamshirband et al., 2020):

RMSE =

1 n

n

Oi )2

(Pi

(4)

i=1

III. Relative Root Mean Squared Error (RRMSE) (Deo et al., 2018):

RRMSE = 100 ×

1 n

n

(Pi

i=1 n i=1

Oi )2

(Oi )

(5) th

where Oi and Pi are the observed and predicted the i value of the EC, n is the number of soil samples in the testing phase.

3. Results and discussion In this study, seven input combinations based on soil parameters were constructed and evaluated to ascertain whether our proposed MLP-GWO hybrid model was a qualified tool for modelling soil elec­ trical conductivity. According to Table 3, the input combinations,

A schematic diagram of the MLP and the hybrid MLP-GWO model is depicted in Fig. 2.

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Fig. 2. A flowchart of MLP-GWO.

Fig. 3. Location of the sampling map in the southwest of Iran (URL 1).

deduced carefully after consulting the correlation matrix (Table 2), are the following: (1): OM, Ca+2, Mg+2, K+, Na+, Cl−, SO4−2, HCO3−, (2): Ca+2, Mg+2, K+, Na+, Cl−, SO4−2, HCO3−, (3): Ca+2, Mg+2, Na+, Cl−, SO4−2, HCO3−, (4): Ca+2, Mg+2, Na+, Cl−, SO4−2, (5): Ca+2, Mg+2, Na+, Cl−, (6): Mg+2, Na+, Cl−, (7): Na+. Note that the input

combination (7) has utilized the most highly correlated variable but as a single input only, whereas input combination (6) has incorporated the three most highly correlated variables, and input combination (5) has used the four most relevant variables. Likewise, input combination (1) has used all variables to model EC. The ideal combination of the model 4

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Table 1 Statistical characteristics of data in the Khuzestan Province, southwest of Iran.

Data period Training data

Testing data

All data

Variable −1

EC (dS.m ) OM (%) Ca+2 (meq.l−1) Mg+2 (meq.l−1) K+ (mg.kg−1) Na+ (meq.l−1) Cl− (meq.l−1) SO4−2 (meq.l−1) HCO3− (meq.l−1) EC (dS.m−1) OM (%) Ca+2 (meq.l−1) Mg+2 (meq.l−1) K+ (mg.kg−1) Na+ (meq.l−1) Cl− (meq.l−1) SO4−2 (meq.l−1) HCO3− (meq.l−1) EC (dS.m−1) OM (%) Ca+2 (meq.l−1) Mg+2 (meq.l−1) K+ (mg.kg−1) Na+ (meq.l−1) Cl− (meq.l−1) SO4−2 (meq.l−1) HCO3− (meq.l−1)

Maximum

Minimum

Mean

Std. deviation

Kurtosis

Skewness

191.80 4.80 300.00 500.00 302.00 1943.50 4350.00 322.40 19.20 118.00 8.70 220.00 306.00 99.20 1516.50 2000.00 545.00 11.60 191.80 8.70 300.00 500.00 302.00 1943.50 4350.00 545.00 19.20

0.20 0.10 1.70 0.70 0.00 0.20 0.50 0.00 0.60 0.40 0.10 1.90 0.60 0.00 0.30 0.60 0.00 1.00 0.20 0.10 1.70 0.60 0.00 0.20 0.50 0.00 0.60

28.36 1.01 50.19 54.44 4.33 285.83 359.71 58.34 3.73 32.89 1.10 49.73 55.01 5.85 392.90 436.71 75.15 3.56 29.73 1.04 50.05 54.61 4.79 318.06 382.89 63.40 3.68

36.16 0.68 47.35 85.48 22.45 392.76 556.02 56.70 2.74 36.84 1.10 40.87 69.47 17.42 498.69 559.31 84.51 2.20 36.36 0.79 45.42 80.87 21.04 429.33 557.13 66.77 2.59

4.63 9.06 5.46 8.73 161.69 3.69 14.32 3.67 9.28 −0.69 40.03 2.91 1.84 18.74 −0.10 0.16 10.64 2.83 2.79 34.24 5.04 7.88 146.67 1.95 9.63 10.43 8.71

1.99 2.28 2.02 2.82 12.30 1.90 3.04 1.65 2.49 0.88 5.62 1.40 1.51 4.37 1.14 1.19 2.57 1.59 1.64 4.44 1.89 2.60 11.10 1.62 2.46 2.38 2.37

Table 2 Correlation matrix of the data used.

Variable

EC (dS.m−1)

OM (%)

Ca+2 (meq.l−1)

Mg+2 (meq.l−1)

K+ (mg.kg−1)

Na+ (meq.l−1)

Cl− (meq.l−1)

SO4−2 (meq.l−1)

HCO3− (meq.l−1)

EC (dS.m−1) OM (%) Ca+2 (meq.l−1) Mg+2 (meq.l−1) K+ (mg.kg−1) Na+ (meq.l−1) Cl− (meq.l−1) SO4−2 (meq.l−1) HCO3− (meq.l−1)

1 0.147⁎ 0.648⁎⁎ 0.782⁎⁎ 0.189⁎⁎ 0.878⁎⁎ 0.870⁎⁎ 0.643⁎⁎ −0.369⁎⁎

1 0.140⁎ 0.165⁎⁎ −0.003 0.134⁎ 0.179⁎⁎ 0.123⁎ 0.173⁎⁎

1 0.672⁎⁎ 0.058 0.629⁎⁎ 0.662⁎⁎ 0.410⁎⁎ −0.357⁎⁎

1 0.147⁎ 0.801⁎⁎ 0.825⁎⁎ 0.581⁎⁎ −0.335⁎⁎

1 0.243⁎⁎ 0.233⁎⁎ 0.213⁎⁎ −0.148⁎

1 0.939⁎⁎ 0.759⁎⁎ −0.400⁎⁎

1 0.686⁎⁎ −0.392⁎⁎

1 −0.319⁎⁎

1

⁎⁎ ⁎

Correlation is significant at the 0.01 level (2-tailed).

Correlation is significant at the 0.05 level (2-tailed).

inputs aimed to create accurate models that represented the most sig­ nificant variables, as well as a carefully selected combination of these variables to check their influence on the testing performances.

It is important to note that the optimal configurations for standalone MLP and the hybrid MLP-GWO models are designated based on trial and error. This followed the notion that there is no definite or uni­ versally testified procedure for choosing the optimum number of hidden neurons and these are normally designated in iteratively. Fig. 5. shows a schematic structure of the hybrid MLP-GWO model used for EC prediction.

In MLP models, trial and error is typically implemented to screen the ideal number of hidden neurons in each hidden layer. This optimal number of hidden neurons was then examined by training the network in 100 epochs, with a learning rate of 0.0012 and a momentum coef­ ficient of 0.84 to accord with the approaches in recent studies (e.g., (Ghorbani et al., 2017; Raheli et al., 2017)). For each neuronal ar­ rangement and model structure, the best performing model (according to the lowest root mean square error, RMSE criterion) was then screened from a total of 20 different modelling topologies.

For both the hybrid MLP-GWO and standalone model, Table 4 il­ lustrates the designated models, neuronal arrangements and the RMSE

values. It is noticeable that when the effect of the GWO algorithm on the enactment of the established models was checked, the predictive performance in terms of the RMSE value led to a meaningfully lower value of the error for all model input combinations. This implied that the exploiting the ‘add-in’ optimization algorithm into a standalone MLP model generated more accurate neuronal weights within the hidden layers. This led to an enhancement in the overall model accu­ racy, demonstrating that the hybrid MLP-GWO model was trained more accurately than the MLP model, and is likely to lead to a better per­ formance for the prediction of electrical conductivity in the testing dataset.

In all modelling scenarios, we followed the notion that there is no rule of thumb for that the universal way the training and testing data are partitioned. For example, the study of Kurup and Dudani (2002) used a total of their 63% of data for model development while Samadianfard et al. (2013, 2014) used 67%, Samadianfard et al.

(2018), Deo et al. (2018), Qasem et al. (2019) utilized 67% of data and Samadianfard et al. (2019a, 2019b) used 70% and Zounemat-Kermani et al. (2019) implemented 80% of total data to develop their models.

Considering these studies, the data in the present study were separated into two distinct parts; training (70%) and testing (30%) for all of the 5

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Fig. 4. The variations of different soil parameters and EC values.

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Table 3 The implemented input combinations and model designations.

No.

1 2 3 4 5 6 7

Input combination

+2

+2

Model designation

+

+

−

OM, Ca , Mg , K , Na , Cl , SO4−2,HCO3− Ca+2, Mg+2, K+, Na+, Cl−, SO4−2,HCO3− Ca+2, Mg+2, Na+, Cl−, SO4−2,HCO3− Ca+2, Mg+2, Na+, Cl−, SO4−2 +2 +2 + − Ca , Mg , Na , Cl Mg+2, Na+, Cl− Na+

MLP

MLP-GWO

MLP1 MLP 2 MLP 3 MLP 4 MLP 5 MLP 6 MLP 7

MLP-GWO1 MLP-GWO2 MLP-GWO3 MLP-GWO4 MLP-GWO5 MLP-GWO6 MLP-GWO7

Fig. 5. Schematic structure of the hybrid MLP-GWO model developed for EC prediction.

Fig. 6. The observed and predicted electrical conductivity (EC) in the testing phase by optimal (i.e., MLP-GWO and MLP) models.

chosen input combinations. The statistical parameters of developed models are shown in Table 4, and the corresponding time series plots of observed and predicted EC values are demonstrated in Fig. 6.

Because careful selection of suitable input combinations is a vital phase in a data-driven model, the influence of different input ar­ rangements can be seen clearly in Table 4. This result indicates that optimal models need to be developed by a careful construction of the pertinent model inputs variables, and a preliminary assessment of their correlations with the target variable (Table 2). In terms of the tested results, the R2 value of the standalone MLP model ranges from 0.430–0.597, whereas the corresponding values for the MLP-GWO hy­ brid model vary from 0.552–0.711. This higher coefficient of determi­ nation indicates that the hybrid MLP-GWO model can generate the forecasts where the net variance in the tested EC agree more closely to the variance in the real dataset, compared to the standalone MLP model. Moreover, RMSE values of the standalone MLP are seen to fluctuate between 1.616 and 4.421, whereas these are generally lower,

and occupy a range of 1.293–3.537 in hybrid MLP-GWO model. Similar to the RMSE values, RRMSE (i.e., the relative normalized errors) re­ gistered noticeably lower values (i.e., in the range 3.736–9.899%) for the hybrid MLP-GWO models compared to a higher range of 4.613–12.133% for the standalone MLP model.

In fact, the performance of the hybrid MLP-GWO model stood out superior to that of the standalone MLP model. For example, if we ex­ amined both types of data-driven models that utilized all input vari­ ables (i.e., OM, Ca+2, Mg+2, K+, Na+, Cl−, SO4−2,HCO3−), this led to a testing performance metric of R2, RMSE and RRMSE of 0.597, 2.675 dS.m−1 and 7.426%, respectively, for model MLP1 whereas the model MLP-GWO1 registered values of 0.711, 2.140 dS.m−1 and 6.046%, respectively. In other words, the hybrid MLP-GWO1 model in com­ parison with the MLP1 model led to an increase in the R2 value by approximately 19.1%, and a decrease in the RMSE and RRMSE values by about 20.0% and 18.6%, respectively.

Table 4 The performance evaluation criteria of developed models. The optimal MLP-GWO hybrid and the comparative standalone MLP model are indicated in the boldfaced row Model

1 2 3 4 5 6 7 1 2 3 4 5 6 7

Model designation

MLP1 MLP 2 MLP 3 MLP 4 MLP 5 MLP 6 MLP 7 MLP -GWO1 MLP -GWO2 MLP -GWO3 MLP -GWO4 MLP -GWO5 MLP -GWO6 MLP -GWO7

Structure

8-9-1 7-8-1 6-7-1 5-6-1 4-5-1 3-4-1 1-2-1 8-9-1 7-8-1 6-7-1 5-6-1 4-5-1 3-4-1 1-2-1

R2

RMSE (dS.m−1)

RRMSE (%)

Training

Testing

Training

Testing

Training

Testing

0.934 0.897 0.902 0.935 0.918 0.899 0.907 0.963 0.943 0.946 0.963 0.954 0.943 0.950

0.597 0.430 0.533 0.581 0.555 0.566 0.570 0.711 0.552 0.678 0.698 0.687 0.695 0.691

2.238 0.022 0.625 0.574 0.720 1.659 2.751 1.679 0.016 0.469 0.431 0.540 1.244 2.419

2.675 3.619 4.421 1.616 1.669 2.352 3.401 2.140 2.895 3.536 1.293 1.335 1.882 3.537

7.843 0.078 2.014 2.058 2.605 5.554 9.920 5.891 0.058 1.544 1.537 1.941 4.219 8.672

7.426 8.580 12.133 4.613 4.930 6.547 9.269 6.046 7.180 9.899 3.736 3.967 5.328 9.844

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can be seen in Table 4 that the fourth set of models generated the best results compared with the other modelling scenarios. That is, the standalone MLP4 and the hybrid MLP-GWO4 model attained R2, RMSE and RRMSE values of approximately 0.581–0.698, 1.616–1.293 (dS.m−1) and 4.613–3.736%, respectively, and these model can be classified as the best models in the present problem of the EC predic­ tion. Moreover, comparing the obtained results from the current re­ search with other studies indicated that the RMSE value of MLP-GWO4 in the testing phase (1.293 dS.m−1) is lower than the RMSE values of OK, MLP and MLP-FFA models reported in Ghorbani et al. (2019). So, the GWO had a significant role in increasing the accuracy of standalone MLP models.

It is also noteworthy that the hybrid MLP-GWO4 model that utilized input variables of Ca+2, Mg+2, Na+, Cl−, SO4−2 led to a significant reduction in the RMSE and RRMSE values relative to the MLP model by approximately 20.0% and 19.0%, respectively, and can be selected as the best and the most precise model for soil EC prediction. When we scan through the results of Models 5 to Models 7, we note an increasing trend of the prediction errors (i.e., Table 4) where the RMSE and RRMSE values increased from approximately 1.335 (dS.m−1) and 3.967% to 3.537 (dS.m−1) and 9.844% in the testing phase. It is therefore ascertained that the elimination of the input variables (Ca+2, Mg+2, Cl− and SO4−2) had a negative influence in reducing the pre­ diction errors.

For the additional investigation of the accuracy of the studied models, Fig. 7 illustrates the scatter plots of the observed and the es­ timated EC values of the best models (i.e., standalone MLP4 and the hybrid MLP-GWO4 models) where the predictions are evaluated as a regression line between the two datasets. The R2-value proves the su­ perior precision of the hybrid ML-GWO4 model comparing to the standalone MLP4 model. Additionally, residual errors of both of the selected best models (MLP4 and MLP-GWO4) are displayed in Fig. 8. It can be comprehended that the fluctuations of the presented errors in MLP4 are higher than the corresponding error of the hybrid MLPGWO4.

A more in-depth inspection of the capabilities of the best studied models (i.e., MLP4 and MLP-GWO4) in EC prediction has been depicted in Fig. 9, which shows the probability distribution of the testing data. It is understandable from Fig. 9 that the probability distributions of the predicted EC value of the MLP-GWO4 are adjacently located to the observed EC values for most intervals.

Fig. 7. Scatter plots of measured and estimated values of EC for the optimal models (MLP4 and MLP-GWO4).

It is interesting to note that in the second set of models (i.e., MLPGWO2 & MLP2), the elimination of the OM from the input variable list led to a mild increase in the error of EC prediction. In that case, al­ though the prediction accuracy was lower the equivalent mode1 in the first set (i.e., MLP-GWO1), the RMSE and RRMSE values of the hybrid MLP-GWO2 were less than corresponding values of the standalone MLP2 model. In the other words, using the GWO as an optimizer al­ gorithm has led to improved performance in terms of the RMSE and RRMSE values of the standalone MLP model by 20.0% and 16.3%, re­ spectively. A closer examination of these results shows that the input variables in the third set of models (i.e., MLP-GWO3 & MLP3) resulted in the lowest prediction accuracy among all of the other input combi­ nations. It is therefore conclusive that the hybrid MLP-GWO3 model that included the input variables denoted as Ca+2, Mg+2, Na+, Cl−, SO4−2, HCO3− was unable to attain a low prediction error. Moreover, it

4. Concluding remark In predictive modelling, a substantial challenge confronted by ar­ tificial intelligence methods is searching optimal weights in a neuronal layer to facilitate the extraction of appropriate input features in the input data as requirements for creating an ideal predictive model. For

Fig. 8. Residual error of estimated electrical conductivity (EC) for the best models (i.e., MLP4 and MLP-GWO4) in the testing phase.

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Fig. 9. Histograms of different electrical conductivity (EC) values during the testing period.

accurate forecasting of soil EC values, designing optimum data-driven models with minimum input variables is considered as a vital tool for researchers and engineers employed in the soil science area. Here, in this paper, we validated the effectiveness of a reliable, robust and consistent predictive methodology for EC estimation, where the input data of several other soil parameters were exploited as the predictor variables to forecast the future EC values. In this study, we inspected the predictive proficiency of the recommended hybrid MLP-GWO model where the Grey Wolf Optimization algorithm was joined with a standard MLP model and applied for EC prediction. The results attained revealed that the fourth input combination (utilizing Ca+2, Mg+2, Na+, Cl−, SO4−2) generated the most precise results in the independent testing phase. Moreover, the hybrid MLP-GWO4 model produced a substantial reduction in RMSE and RRMSE values compared to the standalone MLP model by approximately 20.0% and 19.0%, respec­ tively, and therefore, is designated as the optimal model for of the prediction of soil EC. The present results confirmed that the hybrid MLP-GWO model can improve the prediction accuracy, perhaps due to its ability to acquire more accurate neuronal weights in the hidden layer compared to the standalone non-optimized (MLP) model.

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Declaration of competing interest The authors declare no conflict of interest.

Acknowledgement All data were obtained from the data agency in Khuzestan Province, southwest of Iran.

Data availability Data and codes will be available upon request through corre­ sponding authors.

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