Design and implementation of a hybrid model based ...

Science of the Total Environment 648 (2019) 839–853

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Science of the Total Environment journal homepage: www.elsevier.com/locate/scitotenv

Design and implementation of a hybrid model based on two-layer decomposition method coupled with extreme learning machines to support real-time environmental monitoring of water quality parameters Elham Fijani a,⁎, Rahim Barzegar b,f, Ravinesh Deo c, Evangelos Tziritis d, Skordas Konstantinos e a

School of Geology, College of Science, University of Tehran, Tehran, Iran Department of Earth Sciences, Faculty of Natural Sciences, University of Tabriz, Tabriz, Iran c School of Agricultural Computational and Environmental Sciences, International Centre for Applied Climate Sciences, Institute of Agriculture and Environment, University of Southern Queensland, Springfield, Australia d Hellenic Agricultural Organization, Soil and Water Resources Institute, 57400 Sindos, Greece e Department of Ichthyology and Aquatic Environment, School of Agricultural Sciences, University of Thessaly, Fitokou street, 38446 Volos, Greece f Department of Bioresource Engineering, McGill University, 21111 Lakeshore, Ste Anne de Bellevue, Quebec H9X3V9, Canada b

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Designing a new hybrid framework for the water quality parameters (e.g. Chla and DO) estimation in the Prespa Lake • Incorporating a hybrid two-layer decomposition using CEEMDAN and VMD algorithms with LSSVM and ELM models • Improving the performance of the machine learning based water quality parameter estimation models

a r t i c l e

i n f o

Article history: Received 10 June 2018 Received in revised form 15 August 2018 Accepted 17 August 2018 Available online 18 August 2018 Editor: G. Ashantha Goonetilleke Keywords: Water quality modelling Environmental monitoring Complementary ensemble empirical mode decomposition with adaptive noise Variational mode decomposition

a b s t r a c t Accurate prediction of water quality parameters plays a crucial and decisive role in environmental monitoring, ecological systems sustainability, human health, aquaculture and improved agricultural practices. In this study a new hybrid two-layer decomposition model based on the complete ensemble empirical mode decomposition algorithm with adaptive noise (CEEMDAN) and the variational mode decomposition (VMD) algorithm coupled with extreme learning machines (ELM) and also least square support vector machine (LSSVM) was designed to support real-time environmental monitoring of water quality parameters, i.e. chlorophyll-a (Chl-a) and dissolved oxygen (DO) in a Lake reservoir. Daily measurements of Chl-a and DO for June 2012–May 2013 were employed where the partial autocorrelation function was applied to screen the relevant inputs for the model construction. The variables were then split into training, validation and testing subsets where the first stage of the model testing captured the superiority of the ELM over the LSSVM algorithm. To improve these standalone predictive models, a second stage implemented a two-layer decomposition with the model inputs decomposed in the form of high and low frequency oscillations, represented by the intrinsic mode function (IMF) through the

⁎ Corresponding author. E-mail addresses: efi[email protected] (E. Fijani), [email protected] (R. Barzegar), [email protected] (R. Deo), [email protected] (E. Tziritis), [email protected] (S. Konstantinos).

https://doi.org/10.1016/j.scitotenv.2018.08.221 0048-9697/© 2018 Published by Elsevier B.V.

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E. Fijani et al. / Science of the Total Environment 648 (2019) 839–853

Extreme machine learning Small Prespa Lake

CEEMDAN algorithm. The highest frequency component, IMF1 was further decomposed with the VMD algorithm to segregate key model input features, leading to a two-layer hybrid VMD-CEEMDAN model. The VMDCEEMDAN-ELM model was able to reduce the root mean square and the mean absolute error by about 14.04% and 7.12% for the Chl-a estimation and about 5.33% and 4.30% for the DO estimation, respectively, compared with the standalone counterparts. Overall, the developed methodology demonstrates the robustness of the two-phase VMD-CEEMDAN-ELM model in identifying and analyzing critical water quality parameters with a limited set of model construction data over daily horizons, and thus, to actively support environmental monitoring tasks, especially in case of high-frequency, and relatively complex, real-time datasets. © 2018 Published by Elsevier B.V.

1. Introduction Water quality monitoring has a great importance, and is a worldwide growing concern in relation to the quality and quantity of water resources available for multiple purposes. Collecting reliable water quality data is one of the most important aspects of protecting and developing robust management plans for our rivers and lake systems. Monitoring environmental data can also be used to understand the type and severity of water quality impairments and help decision-makers in setting achievable targets for water quality improvement. The concentration of dissolved oxygen (DO), a subject of this paper, is one of the most important water quality parameters since it reflects the equilibrium between oxygen-producing processes (e.g., photosynthesis) and the oxygen-consuming processes (e.g., chemical oxidation). DO itself depends on many interacting factors such as the salinity, temperature, and other water quality parameters (Liu et al., 2012; Missaghi et al., 2017) and is clearly an important element in the assessment and sustainability of complex ecological systems. The eutrophication of pristine as well as actively utilized decisioncentric lakes constitutes an environmental problem, indicating a deterioration of the quality of water in such Lake systems (Huo et al., 2013; ElOtify, 2015; Park et al., 2015). In recent years, natural eutrophication of the surface water has also been expedited due to the presence of anthropogenic activities, and this process is known as the cultural eutrophication (Thevenon et al., 2012). Chlorophyll-a (Chl-a), another subject of this paper, is often used as an indicator of water quality with respect to the eutrophication process, mainly because it is common in most phytoplankton biomass and is a function of the total nutrients in the aquatic ecosystem (Catherine et al., 2010; Lugoli et al., 2012; Carneiro et al., 2014; Park et al., 2015). Despite its importance in water quality management, the current estimation models of Chl-a have largely been based on simple empirical and semi-theoretical relationships that are likely to overlook the non-linearity in various relationships to the pertinent factors that influence the overall presence of this in lake water. Both the DO and the Chl-a indicators are considered as significant parameters that influence the quality of surface waters and will, therefore, alter a natural aquatic ecosystem (Sharma et al., 2007). The regular monitoring of these parameters is therefore very important for environmental managers, research scientists, water resource managers and government agencies. The modelling of the water quality parameters (i.e., DO and Chl-a concentrations) has been carried out by using different methods based on artificial intelligence tools, such as the artificial neural network (ANN) (Noori et al., 2013; Ay and Kisi, 2014; Xu et al., 2015; Ahmed, 2017; Huang and Gao, 2017), fuzzy logic (Chen and Mynett, 2003; Pereira et al., 2009), and neuro fuzzy methods (Noori et al., 2013; Ay and Kisi, 2014; Ay and Kisi, 2017). In recent years, artificial intelligence models have gained significant popularity as a reliable estimation and a prediction tool in order to study the patterns and model a range of environmental parameters (Barzegar et al., 2017a, 2017b). Among the different artificial intelligence models, the extreme learning machines (ELM) and the least squares support vector machines (LSSVM) have gained a lot of attention. The ELM model is a data-intelligent tool that

is able to attain universal approximation of the input-target features from a dataset to yield a relatively high accuracy, less computational time and human intervention compared to the training of a conventional neural network such as an ANN model (Yaseen et al., 2016; Deo et al., 2017a, 2017b; Yaseen et al., 2018). Likewise, the LSSVM model, a simplified and a more computationally efficient version of the SVM model that uses kernel methods, has the capacity to estimate the output parameters more precisely than a traditional technique such as the ARIMA, ANN, ANFIS, or neuro-fuzzy systems (Hong and Pai, 2006; Wang et al., 2009). The ELM and LSSVM models have been employed in the estimation of water quality parameters (Noori et al., 2015; Barzegar et al., 2017a, 2017b), which has certainly been triggered by their overall preciseness in feature extraction from the historical data. It should be noted that there has been some work (Liu et al., 2009), yet a limited amount of research performed with using LSSVM and ELM models for estimating the Chl-a in the water. In terms of prior research on DO concentration modelling, a recent study performed by Heddam and Kisi (2018) applied different artificial intelligence methods, including the LSSVM model for estimating daily DO concentration using several water quality variables as inputs. In this study, it was found that the DO concentrations in water could be successfully estimated with a reasonable degree of accuracy using the LSSVM model. In another study, Yu et al. (2016) compared the LSSVM and a radial basis function neural network (RBFNN) model for predicting the DO concentrations in crab ponds in China. The results showed that the LSSVM model exhibited considerably better performance compared with the RBFNN model. The ELM model has been also proven to be an effective approach for the modelling of DO concentration in some research works (e.g., (Heddam, 2016; Heddam and Kisi, 2017)). To improve the estimation accuracy of a standalone model (e.g., an ELM or LSSVM without using any optimizer algorithm), a hybrid model can be obtained by applying a data preprocessing or a feature optimization method. Data pre-processing is considered to be an important step in predictive modelling for solving a relatively complex problem, especially where noisy and unreliable data can exist, and the knowledge discovery processes within the learning phase of the standalone model can be tedious. Most of the datasets used with machine learning problems need to be processed and transformed into a simple and an enigmatic-free form, so that the algorithm can be trained on those demarcated datasets where patterns can be recognized relatively easily. In recent years, data-driven modelling approaches, have progressively been executed for solving complex modelling issues in environmental monitoring due to their ability to dominate several limitations related to physically-based methodologies (e.g., Krasnopolsky and Chevallier, 2003; Solomatine, 2005; Haupt et al., 2008). A number of previous researchers (e.g., Hu et al., 2007; Wu et al., 2010; Shiri and Kisi, 2010; Noori et al., 2011; Wu and Chau, 2011; Khadr and Elshemy, 2017; Prasad et al., 2018, 2017; Deo et al., 2017b; Huan et al., 2018) have showed that the forecasting accuracy can be enhanced by removing the noise from the hydrological data and subsequently, finding the useful patterns utilizing proper data preprocessing methods, such as the statistical techniques, the wavelet analysis and, the Gamma test. In order to improve the wavelet analysis technique, Wu and Huang

E. Fijani et al. / Science of the Total Environment 648 (2019) 839–853

(2009) developed a new approach, named the ensemble empirical mode decomposition (EEMD) which is a substantial improvement over the original empirical mode decomposition (EMD), first introduced by Huang et al. (1998). However, the Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) was also established to overcome some issues (e.g. mixing problem) of the EEMD filtering technique, and this technique has recently been used in different fields (e.g., Al-Musaylh et al., 2018). It is important to note that the number of iterations in the CEEMDAN process is less than half of the iterations of the EEMD process and the signal reconstruction is much more accurate than the EEMD process (Torres et al., 2011). Since the CEEMDAN is able to extract the true signals from the data obtained in a noisy, nonlinear and a nonstationary environment, it has been effectively utilized in a large variety of applications as a versatile time-frequency data analysis method (Coughlin and Tung, 2004; Huang and Wu, 2008; Zhang et al., 2008; Wu and Tsai, 2011; Peng et al., 2017; Zhang et al., 2017; Al-Musaylh et al., 2018). Although the estimating capability of a standalone artificial intelligence model (e.g., the ELM or the LSSVM) can be improved using a single data preprocessing techniques, combining a two-layer decomposition technique to develop an integrated hybrid model is expected to further increase the estimation performance of the hybrid model (Wang et al., 2017). To pursue this aim, the variational mode decomposition (VMD) can be applied to conduct a secondary decomposition process where the high frequency CEEMDAN signal is further resolved into finer-scale components for clarity of the inherent features therein. It is imperative to mention that VMD is a relatively new model decomposition method proposed in recent years, which aims to transfer the acquisition of the signal components to a variational framework. The decomposition of the original signal is then realized by constructing and solving constrained variational problems (see Wang et al., 2017). Considering the challenges faced by standalone models, especially when the data are relatively noisy, composed of rapid perturbations, jumps, trends and stochasticity behaviors and they require a data preprocessing scheme, the primary objective of this study is to develop a new prediction tool and demonstrate the ability of two layer decomposition based ELM (i.e., VMD-CEEMDAN-ELM) model. This model is applied in context of a Small Prespa Lake to estimate the concentrations of DO and Chl-a, which are important water quality parameters. To ascertain the preciseness of the hybrid VMD-CEEMDAN-ELM model proposed in this paper, we also applied a competing model: the LSSVM, to benchmark the objective models' testing performances. Although there exist no direct application of a two-layer decomposition approach (i.e., VMD-CEEMDAN-ELM) for the estimation of water quality parameters, a few previous studies in other application domains are notable. For example, the study of Wang et al. (2017) used a two-layer decomposition hybrid-based model with a fast ensemble empirical mode decomposition (FEEMD), VMD, and the back propagation (BP) neural network algorithm optimized by the firefly algorithm to forecast multi-step ahead electricity prices. In another study, Li et al. (2018) proposed a hybrid model based on multi-scale features using EEMD to help increase predictive accuracy of DO in aquaculture, and this particular model yielded a higher efficiency according to their obtained results. These studies have demonstrated the greater preciseness of the hybrid technique in respect to a conventional equivalent model. The present study is therefore, one of the first attempts to develop and apply the secondary decomposition approach (i.e., VMD) in additional to the primary decomposition approach for modelling water quality parameters using a limited set of data for a Small Prespa Lake. 2. Methodology 2.1. Extreme learning machine The ELM model was originally formulated by Huang et al. (2004) as a single hidden layer feed-forward neural network tool. This algorithm

841

aims to generate the hidden node parameters randomly, and then computes the output weights analytically. By contrast, the conventional learning algorithms e.g., SVM or the ANN model require greater human inference and model tuning process (Huang et al., 2006; Bueno-Crespo et al., 2013). The better generalization performance, faster learning speed, and more precise calculation are the most important advantages of the ELM over the conventional algorithms (Barzegar et al., 2018a, 2018b; Deo and Şahin, 2016; Deo et al., 2017b). To formulate the ELM algorithm, let us consider N training samples (xi, yi) incorporated into a neural network architecture with H hidden nodes. The xi and yi time-series are used to denote the input and target vectors, respectively where xi = (xi1,xi2,…, xin) ∈ Rn and yi = (yi1, yi2,…, yim) ∈ Rm. Therefore, the ELM function will be as the following (Huang et al., 2006; Deo et al., 2016; Barzegar et al., 2017a, 2017b; Yadav et al., 2017): H X

H   X   βi f i x j ¼ βi f ai :x j þ bi ;

i¼1

j ¼ 1; …; N

ð1Þ

i¼1

where fi(xj) is the activation function, ai = [ai1, ai2, …, ain]T represents the weight vector between input and hidden nodes, bi is the threshold of the ith hidden node, βi = [βi1, βi2, …, βim]T is the output weights vector connecting the ith hidden node and the output nodes. Eq. (1) in its compact form can be written as follows (Huang et al., 2006; Yadav et al., 2017): H X

  βi f i x j ¼ Gβ

ð2Þ

i¼1

2 G¼4

f ða1 :x1 þ b1 Þ ⋮ f ða1 :xN : þ b1 Þ

2

3 βT1 β¼4 ⋮ 5 βTL Hm

… … …

3 f ðaH :x1 þ bH Þ 5 ⋮ f ðaH :xN : þ bH Þ NH

3 yT1 Y¼4 ⋮ 5 yTL Nm

ð3Þ

2

ð4Þ

where G is called the hidden layer output matrix, β represents the output weight matrix and, T is the transport operator. The output weights are computed using the least squares solution. The result can be written as (Huang et al., 2011): β ¼ H† Y

ð5Þ

where H† known as the Moore–Penrose generalized inverse solution for the hidden layer output matrix Y and can be obtained from the singular value decomposition (SVD) (Yadav et al., 2017). As recommended by Liu and Wang (2010), the ensemble learning technique and cross-validation method are embedded into the training phase, so as to alleviate the overtraining problem and enhance the predictive stability of ELM model. Details on the stability and generalization of the ELM algorithm can be found in Huang et al. (2015). 2.2. Least square support vector machine The LSSVM model was originally proposed by Suykens and Vandewalle in 1999. LSSVM aims to employ the least-squares loss functions while the original support vector machine (SVM) uses the quadratic program solving approach (Suykens et al., 2002). A data set comprised of xt as the inputs, yt as the target, and w as the ddimentional weight vectors, where xt ∈ Rd and yt ∈ R, is considered. The LSSVM non-linear function is expressed as (Suykens and Vandewalle, 1999; Cao et al., 2008; Vapnik, 2013): f ðX Þ ¼ wT ∅ðX Þ þ b

ð6Þ

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where the term b represents bias, and ∅ is the mapping function that maps X into a d-dimensional feature vector. In a regression problem, the structural minimization principle considers the complexity of function and fitting error as (Noori et al., 2009, 2015, 2016): minJ ðw; eÞ ¼

d 1 T γX e2 w wþ 2 2 t¼1 t

ð7Þ

oscillations within a time-series data used to construct a model (Rilling et al., 2003). The algorithm is used to decompose a signal into a series of IMFs. An IMF has two general features: (1) it has the same number of zero-crossings and extrema, and (2) it has a set of symmetric envelopes that are defined by the local maxima, and minima, respectively. In the EMD technique, the decomposition of the data series x(t) is defined as follows (Huang et al., 1998, 1999): xðt Þ ¼

By considering the following constraints to the function:

n X

c j þ rn

ð14Þ

j¼1

yt ¼ wT ∅ðxt Þ þ b þ et

ðt ¼ 1; 2; …; dÞ

ð8Þ

where et is the slack variable for xt. And γ is the margin parameter. The objective function can be obtained to solve the optimization problems in Eq. (15) by introducing the Lagrange multipliers αt and converting the constraint problem into an unconstrained one: Lðw; b; e; α∝Þ ¼ J ðw; eÞ−

d X

  ∝t wT ∅ðxt Þ þ b þ et −yt

ð9Þ

t¼1

The optimal condition can be achieved according to Karush-KuhnTucker (KKT) by taking the partial derivatives of Eq. (17): 8 > > > > > > > > < > > > > > > > > :

w¼

d X t¼1 d X

∝t ∅ðxt Þ ð10Þ

∝t

t¼1 ∝t ¼

γet wT ∅ðxt Þ þ b þ et −yt ¼ 0 Therefore, the linear equations are produced as:



0 y

−yT ZZ þ I=γ T

    0 b ¼ 1 ∝

ð11Þ

where t = (1, …, d), y = (y1,…, yd), Z = ∅ (x1)Tyt, …, ∅ (xd)Tyd, and ∝ = (∝1, …, ∝i). The kernel function k(x,xt) = ∅ (x)T ∅ (xi), i = 1, …, d is defined to the LSSVM and new points are generated as: ^f ðxÞ ¼

d X

∝t kðxnew ; xi Þ þ b

ð12Þ

t¼1

Different kernel functions e.g., linear, polynomial, radial basis, and sigmoidal are employed for LSSVM modelling. The radial basis function (RBF) kernel is the most commonly employed function in regression problems (Kisi, 2012), and is denoted as (Cao et al., 2008):  kðx; xt Þ ¼ exp −kx−xt k2 =2σ 2

ð13Þ

where σ2 is the bandwidth of the RBF, which is determined by a grid search method (Deo et al., 2017a, 2017b). 2.3. Complementary ensemble empirical mode decomposition with adaptive noise In this paper, we adopt the Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise, an improved multiresolution tool that was developed following its predecessor, the Empirical Mode Decomposition algorithm. The EMD algorithm was firstly proposed by Huang et al. in 1998 in order to analyze nonlinear and nonstationary characteristics of a time-series data (Huang et al., 1998, 1999). This algorithm considers the low and high-frequency oscillatory signals at a number of decomposition levels to reveal their local

where n is the number of IMFs, cj is jth IMF and rn represents the residue of the data series x(t). It should be noted that the original EMD algorithm has a mode mixing issue (Wu and Huang, 2009). This typically arises due to a single IMF either consisting of widely disparate scales, or a similar scale residing in different IMF components (Lei et al., 2009). According to Huang et al. (1998), the IMFs extracted from the EMD process should be complete and orthogonal since the orthogonality of the IMFs helps to prevent the mode mixing issue. Therefore, the EEMD process (with an ensemble method) was developed to overcome this problem. In the EEMD approach, the added white noise is applied to complete the entire time-frequency space consistently, which can facilitate a natural separation of the frequency scales, and to diminish the mode mixing occurring during the decomposition process. Importantly, noise is expected to remain in the corresponding IMF(s) if the ensemble number of the EEMD is relatively small. Therefore, the added white noise is not eliminated entirely, and different modes may be produced by the interaction between the signal and the noise. To generate a noise-free IMF, the complementary ensemble empirical mode decomposition utilized in this paper, was introduced by Yeh et al. (2010). In the CEEMD algorithm, the white noise is added into the original data series (i.e., one positive and one negative set) to construct two new sets of ensemble IMFs. Contrary to the EEMD algorithm, the CEEMD algorithm is able to eliminate the residue of the added white noises completely, regardless of how many noises were used initially (Yeh et al., 2010). However, the high computational load in the decomposition process can be the resultant issue of the CEEMD algorithm. To ameliorate the computational cost with the reconstruction error to be almost zero and to maintain the ability to eliminate mode mixing, CEEMDAN algorithm, which has adaptive noise component to address the issues with EMD and CEEMD, was introduced by Torres et al. (2011). The CEEMDAN decomposition process is described as the following steps (Torres et al., 2011; Antico et al., 2014; Li et al., 2015): 1) Obtain the first EMD mode by decomposition of signal x (t) + w0 εi (t); 1 N ð15Þ c1 ðt Þ ¼ ∑i¼1 ci1 i∈f1…Ng N where w0 represents the amplitude of the added white noise, and ε (t) denotes the unit variance white noise. 2) Calculate the difference signal; r 1 ðt Þ ¼ xðt Þ–c1 ðt Þ

ð16Þ

3) Decompose r1(t) + w1E1(εi(t)) to obtain the first mode and define the second mode by:   1 N ð17Þ c2 ðt Þ ¼ ∑i¼1 E1 r 1 ðt Þ þ w1 E1 εi ðt Þ N 4) For k = 2. K, calculate the kth residue and obtain the first mode. Define the (k + 1)th mode as:   1 N ð18Þ ckþ1 ðt Þ ¼ ∑i¼1 E1 r k ðt Þ þ wk Ek εi ðt Þ N where Ej(.) is a function to extract the jth IMF decomposed by EMD.

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5) Repeat step (4), until the residue contains no more than two extrema. The residue mode is then defined as: K

Rðt Þ ¼ xðt Þ−∑k¼1 ck ðt Þ

K

2.5. Model performance and accuracy criteria

ð20Þ

The performance of the predictive models was evaluated in terms of the correlation coefficient (r), root mean square error (RMSE), mean absolute error (MAE), and their normalized equivalents expressed as a percentage and bias error (BIAS) defined by the following equations:

2.4. Variational mode decomposition The purpose of this research paper is to develop and evaluate a twolayer hybrid predictive model; hence we also apply VMD, a newlydeveloped methodology for adaptive and quasi-orthogonal signal decomposition (Dragomiretskiy and Zosso, 2014). The VMD algorithm is able to decompose a signal x(t) into K discrete number of sub-signals or modes uk, where each component is considered compact around their respective center frequency wk. The VMD is applied as a constrained optimization problem, formulated as (Dragomiretskiy and Zosso, 2014): ( 2 ) 

  X X ∂t δðt Þ þ j  uk ðt Þ e− jωk t subject to uk min πt fu g;fω g k

k

¼f

2

k

k

ð21Þ

2 

 X ∂t δt þ j  uk ðt Þe− jωk t πt 2 + 2 * k X þ f ð t Þ− ∑ u ð t Þ þ λ ð t Þ; f ð t Þ− u ð t Þ ð22Þ k k

Lðfuk g; fωk g; λÞ ¼ α

2

k

Eq. (22) can be solved with the alternative direction method of multipliers. The optimization of Eq. (22) can be illustrated as following steps: 1) Minimization of uk: ^f ðωÞ− ^ nþ1 u ¼ k

X

^ i ðωÞ þ u

i≠k

^ ðωÞ λ 2

1 þ 2α ðω−ωk Þ2

ð23Þ

2) Minimization of ωk: R∞ ^ k ðωÞj2 dω ωju ωnþ1 ¼ R0 ∞ k 2 ^ 0 juk ðωÞj dω

  i¼N  ∑i¼1 Obsi −Est ∙ Predi −Est ffi where; −1≤r ≤1 r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  i¼N i¼N  ∑i¼1 Obsi −Obs ∙ ∑i¼1 Predi −Est

ð25Þ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 i¼N 2 ∑ ðObsi −Est i Þ RMSE ¼ N i¼1

ð26Þ

MAE ¼

1 i¼N ∑ jObsi −Est i j N i¼1

RRMSE ¼ 100∙

where {uk} : {u1, u2,…, uk} and {ωk} : {ω1, ω2,…,ωk} are shorthand notations for the set of all modes and their center frequencies, respectively. δ(t) is the Dirac distribution and * denotes convolution. The quadratic penalty term and Lagrangian multipliers are introduced to convert the above optimization problem into an unconstraint one (Dragomiretskiy and Zosso, 2014):

k

accurately modelling the chlorophyll-a and dissolved oxygen timeseries.

ð19Þ

Thus, the signal x(t) can be represented as: xðt Þ ¼ ∑k¼1 ck ðt Þ þ Rðt Þ

843

ð24Þ

n+1 ^ ^ ^ i ðωÞ, u ^ nþ1 where u , k , f ðωÞ, λðωÞ denote the Fourier transform of ui(ω), uk f(ω), λ(ω), respectively, and n is the number of iterations. The advantage of the VMD process is that there is no residual noise in the modes, and that it can avoid the redundant modes compared with the CEEMD method. Moreover, the VMD is an adaptive signal decomposition technique, which can non-recursively decompose a multi-component signal into a number of quasi-orthogonal intrinsic mode functions (Liu et al., 2016). By a combination of VMD with CEEMDAN approaches, we aim to further resolve low frequency patterns that are contained in the IMF1 signal, to enable the artificial intelligence model to be more responsive to the fine-scale data patterns for

RMAE ¼ 100∙

BIAS ¼

ð27Þ

RMSE

ð28Þ

Obs

MAE

ð29Þ

Obs

i¼N 1X ðObsi −Est i Þ N i¼1

ð30Þ

In Eqs. (25)–(30), N is the number of data points; Obsi and Esti are the ith measured and estimated values, respectively; and Obs and Est are the mean of observed and estimated values, respectively. The physical interpretation of the performance metrics is as follows. The correlation coefficient (r) is employed to describe the covariance in observed data that can be explained by the estimation model. The estimation accuracy of the models, via the goodness-of-fit, is assessed by the RMSE and MAE indicators. The RMSE and MAE values range between zero and ∞. An RMSE value of zero and ∞ indicates perfect match and no match respectively between the estimated and the observed outputs. Moreover, the models' precision is evaluated by the RRMSE in which percentage deviation is compared versus estimated data. The RMAE demonstrates the average percentage magnitude of total absolute bias errors between estimated and measured data. The BIAS indicates the overestimation and underestimation of the model. The abovementioned statistical metrics show the linear agreement between observed and estimated values in the modelling. Also, they can be overly sensitive to extreme values (outliers) in the observed data and somewhat insensitive to the additive or proportional differences between estimations and observations (Legates and McCabe, 1999; Willmott, 1981; Yaseen et al., 2018). To overcome these limitations, the Willmott's Index (WI) and Legates and McCabe Index (LMI) (Legates and McCabe, 1999), the normalized performance indicators, were considered. The mathematical formulations are given in Eqs. (31) and (32). 2

3 i¼N

2

∑i¼1 ðObsi −Est i Þ 6 7 WI ¼ 1−4    2 5     i¼N  ∑i¼1 Est i −Obs þ Obsi −Obs 3  i¼N   ∑ Obs −Est i 6 i¼1 7 LMI ¼ 1−4 i¼N 5  ∑i¼1 Obsi −Obs

ð31Þ

2

ð32Þ

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It is important to note that the LMI used in this paper present an advantage over the WI when relatively high estimated values are expected, even for a poorly fitted model (Legates and McCabe, 1999). 2.6. Case study area and environmental monitoring data collection The case study area in this paper used to demonstrate the design and implementation of the two-layer hybrid model is a Small Prespa Lake, located in western Macedonia, Greece (Fig. 1). The Prespa area, located in the Balkan Peninsula is a region of great significant environmental, aesthetical, and cultural value, shared among three different countries (Greece, Albania, and FYROM). Prespa region consists of two renowned lakes, namely small (Mikri) and great (Megali) Prespa that form a transboundary unique natural monument protected by RAMSAR convention as a wetland of international importance (RAMSAR, 1974). The two lakes lie at an altitude of 850 m A.S.L., though many of the mountainous surrounding areas exceed about 2000 m. The significance of Prespa Lakes is that it is related to their exceptional biodiversity reflected to the great number of life forms concentrated in such a small geographical area; as a result, the region has been recognized as a European and Global Hotspot of Biodiversity (Albrecht et al., 2008; UNDP GEF, 2013). The climate of Prespa area is characterized as a hot and dry Mediterranean type during summer (July, 23.6 °C) and midEuropean type during winter with long periods of high rainfall, snow, increased cloudiness and low temperatures (January, 0.8 °C) (Hollis and Stevenson, 1997). Under an Emberger bioclimatic classification the area is typical of a humid Mediterranean type (Emberger, 1963). Previous researchers reported that mean annual rainfall varies from 647 to 742 mm (Kassioumis, 1991) which is typical for low-lying agricultural lands. Taking into account that mean annual snowfall is about 300 mm (Kassioumis, 1991) the total precipitation is likely to reach up to 1000 mm per year, denoting significant amount of water recharge to

the entire hydrological system. The mean air temperature remains above freezing throughout the year but Lake small Prespa is frequently frozen probably due to the descending cold air-streams from the surrounding mountains. The present research is focused on the Small Prespa Lake where the main inputs of water recharge are the surface runoff and lateral sub-surface flow that occur as a result of cross flows with the interacting aquifer systems of the area (Tziritis, 2014). Temporarily, the Small Prespa Lake is also fed by the inflows of Devoll River (SW part of Small Prespa Lake) originating westwards in Albania. A real-time multi-probe sensor CYCLOPS-7 of TURNER DESIGS® was installed at a constant depth of 1.5 m below the lake's surface (i.e., total depth in that point was nearly 3 m with minor fluctuations during the year) at the northern side of the lake and recorded values during June 2012–May 2013. The sensor included a submersible fluorometer with an optical Chl-a kit, light emitting diode as a light source, excitation wavelength of 460 nm, photodiode detector and emission wave length between 620 and 715 nm for Chl-a measurement. The descriptive statistics of the measured Chl-a and DO parameters are given in Table 1. The Chl-a and DO values range between 1 and 8.4 μg/L (with a median value of 2.5 μg/L) and 4.8 and 12.6 mg/L (with a median value of 8.0 mg/L) in the Lake. 2.7. Model development In this study, a total of 363 Chl-a and DO measurements over a daily time-scale (from 01 June 2012–31 May 2013), were collected from a station in the Small Prespa lake, and used to conduct the predictive models. For each dataset, a total of 70% (or 254 points) of them were used for training the models, 15% (or 54 points) were used for the validation purposes where the optimal model was selected independent of the training stage, while the remaining 15% (or 55 points) were used as the testing partition for all data-driven models. The number of data points required for any model depends on at least two things: the

Fig. 1. Location map of the Prespa Lake.

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Table 1 Descriptive statistics of the measured water quality parameters in the Small Prespa Lake (2012−2013). Water quality parameter

Unit

Maximum

Minimum

Median

Std. dev.

Skewness

Kurtosis

Chlorophyll-a Dissolved oxygen

μg/L mg/L

8.4 12.6

1.0 4.8

2.5 8.0

1.2 2.0

1.3 0.2

3.2 −1.4

number of model parameters to estimate and the amount of randomness in the data (Hyndman and Kostenko, 2007). In the current study, the data revealed little random variations, and therefore were deemed suitable to estimate a reasonable model with a limited number of available observations. This paper has used daily data over a period of 1 year, and this was implemented purposely to cover the variation of predictor data over a seasonal cycle during the model development, validation and testing phases, in accordance with earlier studies. For example, the study of Deo and Samui (2017) developed an evaporative loss model using only the limited set of daily data from March 1, 2014 to March 31, 2015, whereas Deo and Şahin (2017) used monthly data from 2012 to 2014 to develop efficient solar radiation models. In another study (Deo et al., 2016), a wavelet-coupled support vector machine model was developed for forecasting solar radiation using limited meteorological dataset where a year of daily meteorological data were used to attain efficient models. To prevent a bias within the predictor variables with large numerical ranges to dominate over those with smaller numeric ranges in the predictive models, and also to increase the execution speed of the model training and the convergence of the trained model during the training process, the input variables were scaled prior to the modelling processes (Deo et al., 2016; Barzegar et al., 2016a, 2016b; Barzegar and Asghari Moghaddam, 2016): xnorm ¼

xt −xmin xmax −xmin

ð33Þ

where, is the original value of input variable that is to be normalized, is the minimum value of variable x, is the maximum value of variable x, and is the normalized value (between 0 and 1) of the input variable In this study, the correlation coefficient (r) and partial autocorrelation function (PACF) values of the time series with 95% confidence level were calculated to extract the relevant and important input variables of the models. Fig. 2 shows the PACF analysis for the Chl-a and DO time series. It is observed that two and six lags are significant for standalone modelling e.g. ELM and LSSVM of the Chl-a and DO, respectively. Moreover, the r-values confirm these suitable input selections. Therefore, the values of r between the Chl-a (t) and Chl-a (t − 1) and Chl-a (t − 2) were 0.93 and 0.92, respectively. For the DO time series, those values were 0.95, 0.93, 0.92, 0.90, 0.88 and 0.86 between DO (t) and DO (t − 1)… DO (t − 6), respectively. To develop the LSSVM model, the input variables (Chl-a (t − 1) and Chl (t − 2) for Chl-a modelling and DO (t − 1), DO (t − 2), …, DO (t − 6) for DO modelling) were served to the models and different kernel functions e.g. radial basis function (RBF), linear, polynomial were tested. A grid search approach (e.g., Deo et al., 2016) with k-fold cross-validation process was employed to deduce the optimal parameter values and to prevent over-fitting of the LSSVM models. The RBF function with γ = 16.11 and σ2 = 0.89 for Chl-a modelling and γ = 23.14 and σ2 = 8.36 for DO modelling obtained the best performances. For the ELM model, the input time-series composed of Chl-a (t − 1) and Chl (t − 2) for the purpose of Chl-a modelling and the DO (t − 1), DO (t − 2), …, DO (t − 6) for the purpose of DO modelling together with the output Chl-a (t) for Chl-a modelling and DO (t) for DO xi xmin xmax xnorm

modelling variables were incorporated into the predictive model. The ELM models with different activation functions within its hidden layer, e.g., RBF, sigmoid, linear, hard-limit were used and a randomization of the hidden layer up to 1000 folds was performed following earlier studies (Deo et al., 2017a, 2017b; Deo et al., 2016). A total of 150 hidden neurons was set for executing the ELM model. The optimal model structures, determined randomly, with 5 and 10 hidden neurons and sigmoid function for the Chl-a and DO models, respectively were selected based on the lowest RMSE in the validation phase. To develop the two-phase hybrid, CEEDMAN-based LSSVM and ELM model, the non-stationary and non-linear Chl-a and DO time series were decomposed into several different IMFs and one residual component, which provided details of the high to low frequencies contained within the model input data series. It is noteworthy that the studies of Colominas et al. (2012) and Antico et al. (2014) have indicated that the added noise level and number of realizations can be adjusted depending on the application in the CEMDAN based modelling, as also verified by a recent study that has implemented these recommendations (Al-Musaylh et al., 2018). Therefore, a noise level of 0.1, a realization of 100, and a maximum of 1000 sifting iteration was set to the CEEMDAN based decomposition of the Chl-a and DO time series. Fig. 3 presents the decomposed time series of the Chl-a dataset decomposed into eight IMFs and a residual component. For conciseness of this paper, the IMFs and residual time series plot of the DO, a second objective variable to be modeled, has been presented in the supplementary materials (Fig. S1). Subsequent to this process, the PACF and correlation analyses were used for each IMFs and residual time series to deduce the significant lagged dataset that were correlated with the non-shifted (zero-lag) data. Fig. 4 illustrate the PACF and the significantly lagged data for each IMFs and the residual component for the Chl-a modelling process. The PACF analysis for each IMFs and the residual component of the DO time series is presented in the supplementary material (Fig. S2). The computed correlation values, as evidenced from this data, confirmed the input selection. These significantly lagged dataset were served as the models' inputs for each IMF and residual time series estimation; and then the estimated IMFs and residual were summed to obtain the final CEMDAN-machine learning based output values (e.g., Al-Musaylh et al., 2018). The CEEMDAN preprocessing method shows that the IMF1 for the both water quality parameters have a high frequency oscillatory behavior. Therefore, a secondary decomposition of the IMF1signal, by means of the VMD approach, was performed. It is important to note that the determination of the number of intrinsic modes is crucial in the VMD process as it must represent an adequately resolved data series for an accurate estimation model. If this process is not followed, the hidden characteristics of the original time series data may not be extracted fully and come with too fewer components. In contrast, too many intrinsic modes may lead to a poor estimation performance because of the error accumulation effects from each component estimation in the aggregation step as stipulated in earlier studies (Niu et al., 2016, 2017). Notwithstanding this requirement, the intrinsic modes obtained by the VMD process can be much smoother than components decomposed by the traditional methods, e.g., the complementary ensemble empirical mode decomposition (CEEMD) alone and the wavelet decomposition technique (Niu et al., 2018) so that the error accumulation effects can be partly, if not totally, mitigated to attain an optimized predictive model. To construct the VMD decomposition, six parameters of the algorithm must be set. Recall that the study of Li et al. (2017) has

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Fig. 2. The PACF analysis of the a) Chl-a and b) DO time series data used to construct the predictive models. Note: The blue lines denote the boundaries of statistical significance of the correlations at a 95% confidence internal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

recommended that the EMD process can be used to deduce the maximum value of the decomposition modes. In this study, based on the data, the EMD was able to generate 9 IMFs for the both IMF1 signals of the Chl-a and DO time series, so the maximum number of decomposition modes was set to this value and the moderate bandwidth constraint was set to 1000. The parameter τ was set to zero, which means that the Lagrangian multiplier was effectively shut off. The parameter init was set to be one, which suggested that center frequencies of all the modes were initialized in the uniform distribution (Zhu et al.,

2017; Li et al., 2017). The parameter DC was set to zero, for no DC part imposed the parameter tol for tolerance, a measure of the process efficiency, was set as default value 1E−7. By using the VMD algorithm, the time-series for IMF1 was decomposed into 9 different variational components for both IMF1 of the Chl-a and DO time series, denoted as Mode1, Mode2… Mode9, respectively. Fig. 5 shows the decomposed time-series of the Chl-a IMF1 data using the VMD method and the VMD decomposed series of DO is presented in the supplementary materials (Fig. S3). Following this, the

Fig. 3. The IMFs and the residual components of the Chl-a time series generated by the CEEMDAN method.

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Fig. 4. The PACF of each IMF and the residual Chl-a time series after the CEEMDAN process was implemented.

PACF analysis was employed to extract the significantly lagged dataset and consequently, these lagged dataset were served into the LSSVM and ELM models in order to estimate their output values (Mode1′, Mode2′, …, Mode9′). An aggregation of the estimated values from these intrinsic modes was used to obtain the estimated value for IMF1. Finally, the VMD-CEEMDAN based estimated values were obtained from aggregation of estimated value from IMF1 decomposed through VMD and other IMFs (e.g., IMF2, IMF3… Residual). A flow chart of the developed two layer decomposition based artificial intelligence models is presented in Fig. 6. For developing the LSSVM

models, the RBF function was applied with a grid search process and a Kfold cross validation in the validation phase and for the ELM model, the algorithm was executed with sigmoid function and hidden layer randomizations by a 1000 fold following earlier research works (e.g., Deo and Şahin, 2016; Deo et al., 2017a, 2017b). 3. Results and discussion In this study, based on the decomposition of model input data and ensemble approaches, a two layer hybrid decomposition model utilizing

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Fig. 5. The decomposed series of Chl-a IMF1 using VMD method.

the CEEMDAN and VMD tools integrated with the ELM and LSSVM algorithms was constructed for an estimation of the concentration of Chl-a (μg/L) and DO (mg/L) in a Small Prespa Lake. The performance statistics obtained from the modeled results using the standalone LSSVM, ELM and the hybrid CEEMDAN-based LSSVM and ELM models, and the hybrid CEEMDAN-VMD-based LSSVM and ELM models for estimating the Chl-a (μg/L) and DO (mg/L) in the training and validation periods, are provided in the supplementary material (Tables S1 and S2). Evidently, the hybrid models appear to be trained and validated more accurately than their standalone counterparts (i.e., the ELM and the LSSVM model). After the training and validation phases for the developed models, the testing phase was implemented to establish the viability of the models for the estimation of Chl-a (μg/L) and DO (mg/L) data. Table 2 shows the statistical metrics for models' performance evaluation in the testing period. In comparison to the standalone LSSVM and ELM models where no decomposition of model inputs were performed, the performance of the ELM model (with r = 0.849, RMSE = 0.310 m, MAE = 0.187 m, BIAS = 1.035 m, MAEP = 10.082%, RMSEP = 17.752%, LMI = 0.617 and WI = 0.918 for the Chl-a (μg/L) estimation and with r = 0.957, RMSE = 0.481 m, MAE = 0.369 m, BIAS = 1.012 m, MAEP = 4.829%, RMSEP = 5.960%, LMI = 0.760 and WI = 0.974 for the DO (mg/L) estimation) were far better than those of the

LSSVM model. The latter model generated a r value of 0.828, RMSE = 0.353 m, MAE = 0.221 m, BIAS = 1.024 m, MAEP = 11.797%, RMSEP = 20.181%, LMI = 0.548 and WI = 0.918 for the estimation of Chl-a (μg/L) and an r value of 0.939, RMSE = 0.614 m, MAE = 0.472 m, BIAS = 1.007 m, MAEP = 6.232%, RMSEP = 7.610%, LMI = 0.693 and WI = 0.941 for the estimation of DO (mg/L) during the testing phase. Therefore, this study has confirmed the better capability of the ELM model compared to the LSSVM model for estimating water quality parameters in the Small Prespa Lake. The primary advantage, and the verified accuracy of the ELM over the SVM model for regression purposes is also found in Barzegar et al. (2017a). Generally, it is true that the output weights of the ELM model are computed analytically, and its learning is considerably faster and the computation complexity is also less than SVM model (Wang et al., 2015; Barzegar et al., 2018b). In the case of the integrated CEEMDAN-based and the respective standalone models, it is observable that this decomposition method was able to improve the implementation of the standalone model. The results show that this first decomposition process (out of the two phases applied) on the data time series was able to reduces the percentage value of the relative root mean square error (RMSEP) and mean absolute error (MAEP) generated by the LSSVM model by about 8.91% and 1.18%, respectively for the estimation of Chl-a (μg/L). In contrast, the same model was able to reduce the RMSEP and MAEP of the ELM

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Fig. 6. Flow chart to represent two-layer decomposition modelling for the water quality parameters estimation.

model by about 11.17% and 6.05%, respectively, which are indeed the indicators of a better performance of the ELM model. Also, the error reductions noted for the modelling of the DO data was found to be about 3.34% and 2.29% based on the RMSEP and MAEP values for the LSSVMbased models while, those for the ELM-based models were found to be about 3.67% and 3.03%, respectively. By contrast, the hybrid CEEMDAN-ELM model (which attained a value of r = 0.979, RMSE = 0.115 m, MAE = 0.077 m, BIAS = 0.997 m, MAEP = 4.028%, RMSEP = 6.577%, LMI = 0.842 and WI = 0.988 for the estimation of Chl-a (μg/L) and a value of r = 0.993, RMSE = 0.185 m, MAE = 0.140 m, BIAS = 1.002 m, MAEP = 1.799%, RMSEP = 2.290%, LMI = 0.908 and WI = 0.996 for the estimation of DO (mg/L)) clearly outperformed the CEEMDAN-LSSVM model. For the latter model, a value of r = 0.969, RMSE = 0.194 m, MAE = 0.164 m, BIAS = 1.072 m, MAEP = 10.616%, RMSEP = 11.268%, LMI = 0.664 and WI = 0.962 were obtained for

the estimation of Chl-a (μg/L) and a value of r = 0.992, RMSE = 0.345 m, MAE = 0.308 m, BIAS = 0.964 m, MAEP = 3.945%, RMSEP = 4.279%, LMI = 0.800 and WI = 0.989 were obtained for the estimation of DO (mg/L) in the testing phase. In the case of the two-layer decomposition-based models (i.e., VMDCEEMDAN-LSSVM and VMD-CEEMDAN-ELM), the present results showed that the ELM based models yielded r = 0.993, RMSE = 0.064 m, MAE = 0.051 m, BIAS = 1.003 m, MAEP = 2.962%, RMSEP = 3.707%, LMI = 0.894 and WI = 0.996 for Chl-a (μg/L) estimation and r = 0.999, RMSE = 0.051 m, MAE = 0.040 m, BIAS = 1.000 m, MAEP = 0.523%, RMSEP = 0.634%, LMI = 0.973 and WI = 0.999 for DO (mg/L) estimation. The two-layer decomposed LSSVR model, however, yielded r = 0.989, RMSE = 0.167 m, MAE = 0.144 m, BIAS = 1.077 m, MAEP = 9.868%, RMSEP = 9.537%, LMI = 0.704 and WI = 0.975 for the estimation of Chl-a (μg/L) and r = 0.999, RMSE = 0.307 m, MAE = 0.300 m,

Table 2 Statistical metrics for models' performance evaluation in the testing phase. Model

LSSVM CEEMDAN-LSSVM VMD-CEEMDAN-LSSVM ELM CEEMDAN-ELM VMD-CEEMDAN-ELM

Chlorophyll-a (μg/L) estimation

Dissolved oxygen (μg/L) estimation

r

RMSE

MAE

BIAS

MAEP

RMSEP

LMI

WI

r

RMSE

MAE

BIAS

MAEP

RMSEP

LMI

WI

0.828 0.969 0.989 0.849 0.979 0.993

0.353 0.194 0.167 0.310 0.115 0.064

0.221 0.164 0.144 0.187 0.077 0.051

1.024 1.072 1.077 1.035 0.997 1.003

11.797 10.616 9.868 10.082 4.028 2.962

20.181 11.268 9.537 17.752 6.577 3.707

0.548 0.664 0.704 0.617 0.842 0.894

0.918 0.962 0.975 0.918 0.988 0.996

0.939 0.992 0.999 0.957 0.993 0.999

0.614 0.345 0.307 0.481 0.185 0.051

0.472 0.308 0.300 0.369 0.140 0.040

1.007 0.964 0.962 1.012 1.002 1.000

6.232 3.945 3.908 4.829 1.799 0.523

7.610 4.279 3.806 5.960 2.290 0.634

0.693 0.800 0.805 0.760 0.908 0.973

0.941 0.989 0.991 0.974 0.996 0.999

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BIAS = 0.962 m, MAEP = 3.908%, RMSEP = 3.806%, LMI = 0.805 and WI = 0.991 for the estimation of DO (mg/L) estimation, indicating a much worse performance than the ELM-equivalent models. In order to enable a comparison based on normalized errors, the present stud found that the two-layer decomposition model led to decrease in the RMSEP and MAEP value of the ELM-based model by about 2.87% and 1.06%, respectively, compared to the one-layer decomposition (i.e., CEEMDAN-based model) for the estimation of Chl-a (μg/L). Similarly, a reduction in the errors encountered by the LSSVMbased model was also observed. For the estimation of DO (mg/L), we noted that the error reduction in terms of the RMSEP and MAEP values of the ELM-based model were about 1.66% and 1.27% while those of the LSSVM-based model were very low. However, the results obtained for the both water quality parameters showed that two-layer decomposition technique acted to reduce the errors compared with the onelayer decomposition technique. A comparison of the two-layer hybrid VMD-CEEMDAN-ELM and the standalone ELM models' performance

indicated a reduction in the RMSEP and MAEP values that were about 14.04% and 7.12%, respectively, which also indicated a significant improvement of the standalone ELM model compared to the standalone LSSVM model. The scatter plots of the estimated vs. observed water quality parameters are depicted in Fig. 7. It is observed that the scatter points of the VMD-CEEMDAN-ELM model are most concentrated around the regression line, with the highest r-value and lowest error, and also closest to the line which display that this model generates a superior estimation result compared with the other developed models. Overall, it is concluded that two-layer decomposition (VMD-CEEMDAN) model improves the performance of the model in comparison with standalone and one-layer decomposition (CEEMDAN) models. The water quality parameter estimation results for all developed models in the testing phase are shown in Fig. 8. As it can be seen, the standalone models (i.e., LSSVM and ELM) are not able to capture the minimum and maximum values of the water quality parameters. It is

Fig. 7. Scatter plots of the estimated Chl-a and DO values vs. the observed Chl-a and DO values in the testing phase.

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Fig. 8. Estimation results of the developed models in the testing phase.

observed that decomposition based models, particularly the two-layer decomposition based models, are most effective in estimating the peak values of data in the testing phase. In accordance with results presented so far, this study clearly demonstrates the implementation of a low cost modelling for critical water quality parameters (Chl-a and DO in this study) using the antecedent time series of the desired variables, can significantly support an integrated environmental monitoring program, along with the other monitoring means (conventional sampling and/or real-time high-frequency measurements); thus provide stakeholders with the means to effectively responding to alerts, upcoming events and outbreaks and, ultimately support strategic planning towards sustainable water resources management. The implementation of the proposed low-cost modelling techniques may therefore provide a substantial contribution to the holistic co-management of the biosphere and the geosphere, with regards to the critical water quality parameters that directly or indirectly affect biota. Overall, incorporated monitoring and modelling frameworks could give better knowledge than monitoring or modelling alone for the same total cost (Loucks and van Beek, 2005), a fact which is rather important in the light of limited financial sources or infrastructures. In spite of the superb skills of the two-phase model for an estimation of Chl-a and DO, this study has some limitations. Firstly, this study has utilized a limited set of data over a one-year period, typically to capture the seasonal dynamics of environmental flows over an annual cycle and also to be a viable tool for data sparse regions. An independent study could apply the two-phase hybrid model with data for relatively longer time periods. Secondly, this study has utilized only the antecedent behavior of Chl-a and DO time-series to predict these data, however, in a follow-up study, researchers could also employ exogenous variables (e.g., rainfall, heal fluxes, temperature etc.) that could act to moderate the dynamics of dissolved oxygen and chlorophyll-a concentration. Finally, in view of the advanced capability of the ELM (over the LSSVM model), one could also develop a real-time environmental modelling tool using the online sequential and self-adaptive ELM model as a future implementation tool (e.g., Ali et al., 2018). 4. Conclusions In this research paper, the performance of a newly constructed two-phase hybrid decomposition model embedded with the

complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) integrated with variational mode decomposition (VMD) as a preprocessing scheme was adopted. Subsequently, the LSSVM and ELM models were used in the hybrid scheme for an estimation of chlorophyll-a (Chl-a) and dissolved oxygen (DO), as important water quality parameters in a Small Prespa Lake, Greece. For the purpose of model development and evaluation using a limited set of predictor data, daily time-series of Chl-a and DO measurements were collected during the period 01 June 2012–31 May 2013. The PACF, which aimed to identify the statistically significant lagged data to construct the models, was employed to select the relevant input variables of the final model. The inputs and the target values of the models were split into three subsets including training (70% of total dataset), validation (15% of total dataset) and testing (15% of total dataset) phases. The performance of the developed models was evaluated in terms of r, RMSE, MAE, RMSEP, MAEP, BIAS, LMI and WI. The results of the standalone models indicated that performance of the ELM model is far better than the LSSVM model during the testing period in estimating the daily Chl-a and DO concentrations. In order to improve the performance of the models, the decomposition of Chl-a and DO time series using the CEEMDAN algorithm was applied, resulting in an improved performance of the standalone model. In this respect, the RMSEP and MAEP values of the CEEMDAN-ELM model for Chl-a estimation were reduced to 11.17% and 6.05%, respectively compared with the standalone ELM model. The error reduction for the CEEMDAN LSSVM-based model, based on the RMSEP and MAEP values, were 3.331% and 2.387%, respectively for DO estimation. While the CEEMDAN led to an improved performance compared to the standalone models, high frequency oscillatory behaviors within the IMFs can lead to a poor estimation of the Chl-a time series Therefore, in the next stage, the IMF1 generated from the timer series from first decomposition (i.e., CEEMDAN) were decomposed using the VMD as the second decomposition and the VMD-CEEMDAN-based LSSVM and VMD-CEEMDAN-based ELM models were constructed. The results showed that the two-layer decomposition method (VMD-CEEMDAN) decreased 2.87% and 1.06% of the RMSEP and MAEP, respectively compared with the one-layer decomposition for the ELM-based Chl-a modelling. Similarly, for the LSSVM based models, the VMDCEEMDAN decreased 1.73% and 0.74% of the RMSEP and MAEP, respectively compared with CEEMDAN method. This error decreasing was

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also observed in DO modelling. Overall, the VMD-CEEMDAN-ELM model with an r of 0.999, RMSE of 0.051 m, MAE of 0.040 m, BIAS of 1.000 m, MAEP of 0.523%, RMSEP of 0.634%, LMI of 0.793 and WI of 0.999 had the best performance among the developed models for DO concentration estimation in the Prespa Lake. Although, the VMDCEEMDAN based models outperformed the standalone models, the results also indicated that they were capable of estimating the minimum and maximum concentrations of Chl-a and DO satisfactory. Acknowledgments Data acquisition was performed in the context of “Vodafone World of Difference” program which constitutes a charitable volunteering initiative delivered by Vodafone Foundations and funded by Vodafone Greece. The project was supported by the Society for the Protection of Prespa (SPP) as a host organization in liaison with Prespa Municipality. The authors wish to express their acknowledgments to the above for their fruitful contribution and overall support. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.scitotenv.2018.08.221. References Ahmed, A.A.M., 2017. Prediction of dissolved oxygen in Surma River by biochemical oxygen demand and chemical oxygen demand using the artificial neural networks (ANNs). J. King Saud Univ. Eng. Sci. 29 (2), 151–158. Albrecht, C., Wolff, C., Gloer, P., Wilke, T., 2008. Concurrent evolution of ancient sister lakes and sister species: the freshwater gastropod genus Radix in lakes Ohrid and Prespa. Hydrobiologia 615, 157–167. Ali, M., Deo, R.C., Downs, N.J., Maraseni, T., 2018. Multi-stage hybridized online sequential extreme learning machine integrated with Markov Chain Monte Carlo copula-bat algorithm for rainfall forecasting. Atmos. Res. 213, 450–464. Al-Musaylh, M.S., Deo, R.C., Adamowski, J.F., Li, Y., 2018. Two-phase particle swarm optimized-support vector regression hybrid model integrated with improved empirical mode decomposition with adaptive noise for multiple-horizon electricity demand forecasting. Appl. Energy 217, 422–439. Antico, A., Schlotthauer, G., Torres, M.E., 2014. Analysis of hydroclimatic variability and trends using a novel empirical mode decomposition: application to the Paraná River basin. J. Geophys. Res. Atmos. 119 (3), 1218–1233. Ay, M., Kisi, O., 2014. Modelling of chemical oxygen demand by using ANNs, ANFIS and kmeans clustering techniques. J. Hydrol. 511, 279–289. Ay, M., Kisi, O., 2017. Estimation of dissolved oxygen by using neural networks and neuro fuzzy computing techniques. KSCE J. Civ. Eng. 21 (5), 1631–1639. Barzegar, R., Asghari Moghaddam, A., 2016. Combining the advantages of neural networks using the concept of committee machine in the groundwater salinity prediction. Model. Earth Syst. Environ. 2 (26). https://doi.org/10.1007/s40808-015-0072-8. Barzegar, R., Adamowski, J., Asghari Moghaddam, A., 2016a. Application of waveletartificial intelligence hybrid models for water quality prediction: a case study in Aji-Chay River, Iran. Stoch. Environ. Res. Risk Assess. 30 (7), 1797–1819. Barzegar, R., Asghari Moghaddam, A., Baghban, H., 2016b. A supervised committee machine artificial intelligent for improving DRASTIC method to assess groundwater contamination risk: a case study from Tabriz plain aquifer, Iran. Stoch. Environ. Res. Risk Assess. 30 (3), 883–899. Barzegar, R., Asghari Moghaddam, A., Adamowski, J., Fijani, E., 2017a. Comparison of machine learning models for predicting fluoride contamination in groundwater. Stoch. Env. Res. Risk A. 31 (10), 2705–2718. Barzegar, R., Fijani, E., Asghari Moghaddam, A., Tziritis, E., 2017b. Forecasting of groundwater level fluctuations using ensemble hybrid multi-wavelet neural network based models. Sci. Total Environ. 599–600, 20–31. Barzegar, R., Asghari Moghaddam, A., Adamowski, J., Ozga-Zielinski, B., 2018a. Multi-step water quality forecasting using a boosting ensemble multi-wavelet extreme learning machine model. Stoch. Env. Res. Risk A. 32 (3), 799–813. Barzegar, R., Asghari Moghaddam, A., Deo, A., Fijani, E., Tziritis, E., 2018b. Mapping groundwater contamination risk of multiple aquifers using multi-model ensemble of machine learning algorithms. Sci. Total Environ. 621, 697–712. Bueno-Crespo, A., García-Laencina, P.J., Sancho-Gómez, J.-L., 2013. Neural architecture design based on extreme learning machine. Neural Netw. 48, 19–24. Cao, S., Liu, Y., Wang, Y., 2008. A forecasting and forewarning model for methane hazard in working face of coal mine based on LS-SVM. J. China Univ. Min. Technol. 18 (2), 172–176. Carneiro, F.M., Nabout, J.C., Vieira, L.C.G., Roland, F., Bini, L.M., 2014. Determinants of chlorophyll-a concentration in tropical reservoirs. Hydrobiologia 740 (1), 89–99. Catherine, A., Mouillot, D., Escoffier, N., Bernard, C., Troussellier, M., 2010. Cost effective prediction of the eutrophication status of lakes and reservoirs. Freshw. Biol. 55 (11), 2425–2435.

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