The potential of hybrid evolutionary fuzzy intelligence model for suspended sediment concentration prediction

Catena 174 (2019) 11–23

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The potential of hybrid evolutionary fuzzy intelligence model for suspended sediment concentration prediction Ozgur Kisia, Zaher Mundher Yaseenb, a b

T

⁎

Faculty of Natural Sciences and Engineering, Ilia State University, Tbilisi, Georgia Sustainable Developments in Civil Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam

ARTICLE INFO

ABSTRACT

Keywords: Suspended sediment concentration Hybrid intelligence model River discharge Eel River basin

Providing a robust and reliable prediction model for suspended sediment concentration (SSC) is an essential task for several environmental and geomorphology prospective including water quality, river bed engineering sustainability, and aquatic habitats. In this research, a novel hybrid intelligence approach based on evolutionary fuzzy (EF) approach is developed to predict river suspended sediment concentration. To demonstrate the modeling application, one of the highly affected rivers located in the north-western part of California is selected as a case study (i.e., Eel River). Eel River is considered as one of the most polluted river due to the streamside land sliding, owing to the highly stochastic water river discharge. Thus, the predictive model is constructed using discharge information as it is the main trigger for the SSC amount. The prediction conducted on different locations of the stream (i.e., up-stream and down-stream stations). Three different well-established integrative fuzzy models are developed for the validation purpose including adaptive neuro-fuzzy inference system coupled with subtractive clustering (ANFIS-SC), grid partition (ANFIS-GP), and fuzzy c-means (ANFIS-FCM) models. The predictive models evaluated based on several numerical indicators and two-dimension graphical diagram (i.e., Taylor diagram) that vividly exhibits the observed and predicted values. The attained results evidenced the predictability of the EF model for the SSC over the other models. The discharge information provided an excellent input attributes for the predictive models. In summary, the discovered model showed an outstanding data-intelligence model for the environmental perspective and particularly for Eel River. The methodology is highly qualified to be implemented as a real-time prediction model that can provide a brilliant approach for the river engineering sustainability.

1. Introduction 1.1. Background and research significant Sediment transport in the river considered as one of the significant processes that affect various characteristics of the river system including water health and quality, river geography, channel navigability, and several other water engineering aspects (Sivakumar and Jayawardena, 2002). As a fact, understanding the exact amount of the transported sediment at a particular river is highly essential for hydraulic engineering perspective. This is owing to its importance to the submerged structure in the river and generally on water resources projects (Chang, 2008; Martinez et al., 2009). Nevertheless, the prediction of the suspended sediment is an extremely complicated phenomenon, this is because sediment process is influenced by multiple metrological and hydrological variables in a specific catchment (Frings

⁎

and Kleinhans, 2008). In order to comprehend the transported sediment amount through rivers that usually governed by several hydrological and morphological variables acting in two different scales spatial and temporal (Yaseen et al., 2015); river sediment transport can be modeled either by physical modeling which is required a several efforts and information or conceptually using intelligence models (Kisi, 2015). Intelligence models have been found an appeal in accordance to their advantages (e.g., simplicity, accurate models, less required information, and less time consuming) (Yaseen et al., 2015). 1.2. State-of-the-art Over the past, a few decades, the issue of the complicity in the determination of the dynamism, high non-linearity, and non-stationary of suspended sediment loads have been overcome through the

Corresponding author. E-mail address: [email protected] (Z.M. Yaseen).

https://doi.org/10.1016/j.catena.2018.10.047 Received 19 May 2018; Received in revised form 22 October 2018; Accepted 29 October 2018 0341-8162/ © 2018 Elsevier B.V. All rights reserved.

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sophistication of the computational and artificial intelligence (AI) models. This is due to the limitations indication of the empirical formulations to solve this kind of hydraulic engineering problem (Greimann et al., 1999; Li et al., 2010; Ribbe and Holloway, 2001; Ruessink, 2000; Zhong et al., 2011). Empirical formulations showed a noticeable drawback in the generalization implementation on the sediment transport simulation. This is because sediment transport phenomenon is incorporated with several variables in nature. The major advantages of AI models are their ability to handle the non-linear mechanism, operating large-scale data volumes and mimicking the human brain phenomenon in solving complex problems (Russell and Norvig, 1995). In water resource engineering, sediment transport computing is widely known as a major issue. The sediment load prediction relies not only on the discharge of water into rivers but also relies on other features of the river itself that are prone to seasonal changes (Stott, 2006). A significant increase has been noted in a number of data-based approaches used in hydrologic modeling, especially in the computation of the suspended sediments. The data-based modeling techniques through AI have shown the capability of solving and handling the complexity and the noise problem of data (Yaseen et al., 2016). In modeling sediment transport to be specific, various AI-based techniques have been employed. Among many approaches, couple models have shown noticeable progress in modeling sediment transport such as the traditional artificial neural network (Afan et al., 2014; Agarwal, 2009; Doğan et al., 2007; Huang et al., 2012; Nagy et al., 2002; Tfwala and Wang, 2016; Van Maanen et al., 2010), the theory of fuzzy logic (Bakhtyar et al., 2008; Dogan, 2005; Doğan et al., 2007; Kabiri-Samani et al., 2011; Mianaei and Keshavarzi, 2010), the application of support vector regression (Azamathulla et al., 2010; Buyukyildiz and Kumcu, 2017; Ebtehaj and Bonakdari, 2016; Batt, 2013; Kisi, 2012; Misra et al., 2009; Wei, 2009; Zounemat-Kermani et al., 2016), the employment of evolutionary computing (Altunkaynak, 2009; Aytek and Kişi, 2008; Jaiyeola, 2015; Kizhisseri et al., 2006; Kumar et al., 2014), and most recently the complementary model of wavelet-AI models (Ebtehaj et al., 2016; Goyal, 2014; Liu et al., 2013; Partal and Cigizoglu, 2008; Rajaee, 2011). Despite the extensive researches on the employment of soft computing models, scholars are still seeking for more robust, reliable and effective models that are able to mimic this complex stochastic problem of the suspended sediment transport.

At all stages of the process, from the initial deformation of sediment to all types of arrival sediment depositions, a multiple variability interacting on the sediment transport phenomena that initiate the complexity, non-linear and dynamic characteristics (Kleinhans and van Rijn, 2002; van Rijn, 1984). The literature had been reported several empirical formulations to comprehend the actual phenomena of sediment flux transport (Greimann et al., 1999; Li et al., 2010; Ribbe and Holloway, 2001; Ruessink, 2000); however, several conclusions evidenced the extreme complexity to candidate a universal formulation for sediment simulation (Fischer et al., 2017; Sivakumar and Wallender, 2005). Hence, exploring more reliable and accurate modeling strategy for this problem is always the motivation for engineers and designers (Alcayaga et al., 2018; Javernick et al., 2018). Nevertheless, the necessity of accurate sediment transport modeling is essential for wide range of engineering applications such as (Afan et al., 2016): i. ii. iii. iv. v.

River engineering sustainability. Design the dead storage for reservoir. Computing the degradation around the bridge piers. Channels design. Assessment of the environmental impact of water quality.

In the United States, the Eel River which drains the coast range of north-western California records the highest average suspended sediment yield per drainage area among all the river of its size and is not affected by active glaciers or volcanic eruptions (Hill et al., 2000; Mackey et al., 2009; Warrick, 2014). Several factors such as the widespread tectonic deformation of the base rocks, landscaping advancements in recent times, high seasonal rainfall, and human ground surface disruption in the last century contribute the high rate of erosion and sediment transport. It is not surprising that the basin boost of most unusual geomorphologic characteristics. The process of sediment transportation on hill-slopes and in channels is closely related, and consequently, there is a significant contribution of high-magnitude and low-frequency climatic events to the formation of channels in this area than in most of other areas. Recently, a new era of soft computing models devoted on the integration of natural-inspired meta-heuristic evolutionary optimization algorithms for the sake of enhancing the predictability of stand-alone AI models within the field of water resources engineering (Yaseen et al., 2017a, 2017b). The motivation of these optimization algorithms is to tune the internal deterministic parameters of AI models based on the concept of natural mechanism behavior (Fahimi et al., 2016). The current study is committed on the implementation of coupled fuzzy logic approach with the genetic algorithm (GA) optimizer. GA optimizer is featured by the potential overcoming the problem of solving the global and local optima effectively. Hence, new intelligence model called evolutionary fuzzy (EF) model is developed to predict sediment transport process.

1.3. Research motivation The surface water quality can be degraded due to the presence of excess sediment in streams and reservoirs, thereby, increasing the cost of treating water for drinking and other usages (Vigiak et al., 2016, 2017). A significant quantity of nutrients, metal, and other hazardous contaminants which can be dangerous to human health might be transported through sediments into the river (Pan et al., 2018). Excess sediments can result in fish mortality in the riverine areas during the embryonic stage of their lives; can also restrict the growth of periphyton and limit primary productivity. Additionally, reservoir storage capacity may be lost to increased sediment loads, thereby, reducing the capability of reservoirs to deliver their services, including hydropower, water supply, and flood control (Afan et al., 2016). Human activities such as deforestation, land use change, agricultural activities, overgrazing, and mismanagement of rivers contribute significantly to the accumulation of sediments in water bodies (Li et al., 2017). It is, therefore, necessary to have a better understanding of the sediment transportation processes, sediment yield, and sediment effects on reservoirs, channels and shallow harbors for appropriate policy and decision making in relation to water resources management (Afan et al., 2016; Wei et al., 2016). There is a need for reliable and accurate models for a perfect understanding of the temporal variations in sediment yield and for the prediction of suspended sediment dynamics at the watershed scale. Several natural processes influence the sediment dynamics in river basins.

1.4. Research objectives Eel River suspended sediment concentration is mainly generated due to the high-intensity monsoon rainfall events. Over the last decades, the river region experienced several attracts of erosion proceedings. This is emphasized in the current study to focus on the implementation of hybrid data-intelligence models for the environmental perspective. The main objectives of this research are: i) investigating new hybrid data-intelligence model called evolutionary fuzzy model for suspended sediment concentration, ii) inspecting the predictability of the proposed model on one of the most affected river in north-western of California (i.e., Eel River), iii) building the predictive model using the historical river discharge as this hydrological variable is the main contributor to the percentage of the SSC, and iv) authenticating the EF model against the predominate integrated version of fuzzy model utilized for suspended sediment transport. 12

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Fig. 1. Eel River morphology map presenting the studied metrological stations.

2. The investigated case study

2.2. Basin sediment characteristics

2.1. Site description

The high rate of suspended sediments discharged in the Eel River is a result of the combined effects of high sediment concentrations (on the average of 3000 ppm over discharge at Scotia) and the high discharge rates (Holeman, 1968; Nolan et al., 1987). Gullying and mass movement which are encouraged by human activities around the erodible region contribute significantly to the generation of fine sediment which can be easily moved down to stream channels (Lisle, 1982). Increased precipitation events can trigger the surface erosion of exposed grounds as a result of active earth flows, over-grazing, timber harvesting, and road construction. The movement of particles into channels can also be promoted by an increased soil moisture and erosion of the toes of streamside slides and earth flows. However, the high annual precipitation events in a basin do not guarantee a denser protective cover of vegetation than in basins with a lower precipitation. The relatively low level of precipitation encountered in the winter can be utilized for growing plants, and the basin is adequately vegetated naturally except on the steep hill-slopes along down-cutting channels. Based on this, the rate of sediment discharge in the Coast Range increases with annual precipitation compared to the other areas. Table 1 tabulated the statistical properties of the discharge and suspended sediment for both the stations. The statistical variables presented are maximum, mean and minimum values (xmax, xmean, and xmin), standard deviation (Sx), variation coefficient (Cv), skewness coefficient (Csx). It can be observed from the presented information; the river discharge and sediment have a highly skewed distribution (ranges

Daily of discharge and suspended sediment concentration data belong to two different stations are being used in this study. One of the stations is located on the up-stream of the Eel River in California which is named as Dos Rios with a drainage area 1368 km2. The second stream monitoring station is in the down-stream at Scotia with a drainage area 8063 km2. Both stations are maintained by the US Geological Survey (USGS). Fig. 1 demonstrates the Eel River map with the station's location. The span of the utilized historical data to construct the predictive models covers the period (1966–1977). Fig. 2a, b, c, and d show the actual pattern of the discharge and SSC at the up- and down-stream stations. Through these figures, it can be comprehended the clear correlation between the peak discharge values and the amount of the SSC magnitudes. Eel River has the most dynamic river system in California and this is due to the unsteady geology of the site and major Pacific storms effect. The stream flow is very inconsistent through the year whereby it has average flows over January and February but in August and September the discharge is increased by 100 times. Because of the frequent landslides in the region, the river carries the high suspended sediment load. In this area, the increment in suspended sediment amount is being observed.

13

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(a) 1800

(c)

1600

10000

Discharge (m3/s)

9000 1400

Discharge (m3/s)

1200 1000 800 600

8000 7000 6000 5000 4000 3000

400 2000 200

1000

0

01-Oct-1966 18-Jan-1967 07.May.67 24-Aug-1967 11-Dec-1967 29.Mar.68 16-Jul-1968 02-Nov-1968 19-Feb-1969 08-Jun-1969 25-Sep-1969 12-Jan-1970 01.May.70 18-Aug-1970 05-Dec-1970 24.Mar.71 11-Jul-1971 28-Oct-1971 14-Feb-1972 02-Jun-1972 19-Sep-1972 06-Jan-1973 25-Apr-1973 12-Aug-1973 29-Nov-1973 18.Mar.74 05-Jul-1974 22-Oct-1974 08-Feb-1975 28.May.75 14-Sep-1975 01-Jan-1976 19-Apr-1976 06-Aug-1976 23-Nov-1976 12.Mar.77 29-Jun-1977

01-Oct-1966 13-Jan-1967 27-Apr-1967 09-Aug-1967 21-Nov-1967 04.Mar.68 16-Jun-1968 28-Sep-1968 10-Jan-1969 24-Apr-1969 06-Aug-1969 18-Nov-1969 02.Mar.70 14-Jun-1970 26-Sep-1970 08-Jan-1971 22-Apr-1971 04-Aug-1971 16-Nov-1971 28-Feb-1972 11-Jun-1972 23-Sep-1972 05-Jan-1973 19-Apr-1973 01-Aug-1973 13-Nov-1973 25-Feb-1974 09-Jun-1974 21-Sep-1974 03-Jan-1975 17-Apr-1975 30-Jul-1975 11-Nov-1975 23-Feb-1976 06-Jun-1976 18-Sep-1976 31-Dec-1976 14-Apr-1977 27-Jul-1977

0

Date

Date

(b)

(d)

700000

7000000

Suspended Sediment (mg/l)

Suspended Sediment (mg/l)

6000000 600000 500000 400000 300000 200000 100000

5000000 4000000 3000000 2000000 1000000 0

01-Oct-1966 18-Jan-1967 07.May.67 24-Aug-1967 11-Dec-1967 29.Mar.68 16-Jul-1968 02-Nov-1968 19-Feb-1969 08-Jun-1969 25-Sep-1969 12-Jan-1970 01.May.70 18-Aug-1970 05-Dec-1970 24.Mar.71 11-Jul-1971 28-Oct-1971 14-Feb-1972 02-Jun-1972 19-Sep-1972 06-Jan-1973 25-Apr-1973 12-Aug-1973 29-Nov-1973 18.Mar.74 05-Jul-1974 22-Oct-1974 08-Feb-1975 28.May.75 14-Sep-1975 01-Jan-1976 19-Apr-1976 06-Aug-1976 23-Nov-1976 12.Mar.77 29-Jun-1977

01-Oct-1966 18-Jan-1967 07.May.67 24-Aug-1967 11-Dec-1967 29.Mar.68 16-Jul-1968 02-Nov-1968 19-Feb-1969 08-Jun-1969 25-Sep-1969 12-Jan-1970 01.May.70 18-Aug-1970 05-Dec-1970 24.Mar.71 11-Jul-1971 28-Oct-1971 14-Feb-1972 02-Jun-1972 19-Sep-1972 06-Jan-1973 25-Apr-1973 12-Aug-1973 29-Nov-1973 18.Mar.74 05-Jul-1974 22-Oct-1974 08-Feb-1975 28.May.75 14-Sep-1975 01-Jan-1976 19-Apr-1976 06-Aug-1976 23-Nov-1976 12.Mar.77 29-Jun-1977

0

Date

Date

Fig. 2. Discharge and suspended sediment concentration pattern for the up-stream investigated metrological station (a and b), discharge and suspended sediment concentration pattern for the down-stream investigated metrological station (c and d).

are 7.11–14.5 and 8.05–19.5 for the down-stream and up-stream stations). This is clearly obvious over the validation and testing phases of the data set. On the other hand, the ratio (xmax/xmean) of the SSC over the validation and testing data are high. The exhibited statistics evidenced the highly stochastic and redundant between the river flow discharge and the suspended sediment concentration.

simulate human thinking abilities. The fuzzy theory depends on the thought of relatively obtained membership degrees (MDs) range [0,1]. The sets in FL are able to map obscure or questionable data, regularly observed in our life. The FL inference system is illustrated in Fig. 3a. It has 3 parts: i) a fuzzy rule base that includes the IF-THEN rules linked the inputs to the output through the membership functions (MFs), ii) a database comprising MFs utilized in FL rules; iii) a system of inference which combines some rules to identify the relationships between inputs and outputs to acquire a feasible output. Inputs-outputs data are taken into consideration as comprising vague features in the fuzzification and as a result, data are partitioned in sub-sets characterized via linguistic terms such as high and low and MFs are then obtained. A single value is calculated using the linguistic output in defuzzification (Nayak et al., 2005). The part between IF and THEN and the part after THEN are

3. The applied methodology 3.1. Fuzzy logic set (FL) FL approach is utilized in various research areas (Zadeh, 1965). The theory of FL involves a system having linguistic structures e.g. “big”, “small”, “moderate”, “little” etc. Theory of classical binary set defines crisp events whereas fuzzy logic possesses an inference system that can Table 1 The daily statistical parameters of data set for the stations. Set

Station

Training

Upstream (11472150) Downstream (11477000) Upstream (11472150) Downstream (11477000) Upstream (11472150) Downstream (11477000)

Validation

Test

Basin area (km2) 1368 8063 1368 8063 1368 8063

Data type

xmax

xmean

xmin

xmax xmean

Sx

Flow (m3 s−1) Sediment (Mg l−1) Flow (m3 s−1) Sediment (Mg l−1) Flow (m3 s−1) Sediment (Mg l−1) Flow (m3 s−1) Sediment (Mg l−1) Flow (m3 s−1) Sediment (Mg l−1) Flow (m3 s−1) Sediment (Mg l−1)

1270 318,000 7560 4,930,000 1590 661,000 9170 6,230,000 680 86,500 5270 2,870,000

32.7 2790 266 60,966 33.3 2706 296 46,210 12.1 561 131 18,432

0.05 0 2.07 0.23 0.08 0 2.32 0 0 0 0.71 0.06

38.8 114 28.4 80.9 47.7 244 31.0 135 56.1 154 40.3 156

92.8 17,076 625 288,396 95.5 25,108 693 303,083 49.1 4780 408 143,023

14

Cv (Sx/xmean) 2.83 6.12 2.35 4.73 2.86 9.28 2.34 6.55 4.05 8.52 3.12 7.76

Csx 6.31 10.8 5.01 8.50 8.02 19.5 6.32 14.4 8.05 13.1 7.11 14.5

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(a)

(b) (i)

1

1

0

1

0

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(ii)

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(iii)

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1

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(c) (i)

1

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Fig. 3. (a) The general fuzzy inference system procedure, (b) bit-string crossover of parents (i) and (ii) to form offspring (iii) and (iv), (c) bit-flipping mutation of parents (ii) to form offspring (ii), d) the evolutionary fuzzy model flow chart steps, and e) adaptive neuro-fuzzy inference system architecture.

referred as antecedent and consequent, respectively. In the present study, Gaussian fuzzy MFs were used in all fuzzy based models. Let assume that we have 3 input variables containing 2 MFs in the antecedent phase and thus supposed to be there are 23 rules in the fuzzy rule base. The increment in subsets quantity might bring better precision. For this situation, nevertheless, the rule base will be bigger and hard to build (Şen, 1998). Expect that our model has 2 inputs, and each has 2 MFs with “heavy” and “light” labels and 1 output. In this case, we will have 4 rules as: Rule 1: IF x1 is heavy and x2 is heavy THEN y1 Rule 2: IF x1 is heavy and x2 is light THEN y2 Rule 3: IF x1 is light and x2 is heavy THEN y3 Rule 4: IF x1 is light and x2 is light THEN y4where x1 and x2 stand for 1st and 2nd inputs and (yi, …, y4) are linear equations or constants. In the current study, the final output, y was calculated by the following equation: 4

y=

n=1 4

optimization issues (Sivanandam and Deepa, 2008). The main principles of the genetic algorithm are chromosomes population initialization, crossover, mutation and reproduction (Goldberg et al., 1989). Three main steps are comprised in GA followed the established research (Solomatine and Ostfeld, 2008), the steps can be explained as followed: ➢ The production of the preliminary population: GA produces an arrangement of strings, with each string or chromosome including an arrangement of parameters for optimization. ➢ Strings' fitness computation: GA checks each string's fitness (i.e., evaluation of goal function). ➢ Production of a next generation: New generation of chromosomes is initiated by employing the crossover and selection processes. The selection process is used to select the suitable chromosomes from the previous population based on its fitness value. Bit-string crossover is one of the important reproduction operators utilized (Fig. 3b). Two strings (parents) are utilized in this operator and next individuals are produced by exchanging a sub- grouping between the two strings. Bit-flipping mutation is another important operator (Fig. 3c). A single gene (or bit) in the chromosome is flipped in mutation operator to form another offspring chromosome. In GAs, all operators are restricted to handle the chromosome in a parallel mode. For example, 2 genes having the same location on 2 chromosomes might be swapped with the original parents; however, not merged, and that is depending on their values. Individuals are generally selected to be the parents in accordance with the magnitude of the goal or fitness, the formed offspring change the parents (Sivanandam and Deepa, 2008). GA is an effective technique with respect to seek the ideal solution to complicated issues, for instance, the selection of the MFs nearly

wn yn

n=1

wn

(1)

the output value, y, could be easily calculated using Eq. (1) for any set of inputs after determining the fuzzy rule base (Şen, 1998). Detailed information related to FL theory could be obtained from the related books (Kosko, 1993; Ross, 2010). 3.2. Genetic algorithm Genetic algorithms (GAs) firstly reported by (Holland, 1975). GAs have been recently utilized as an effective method for solving 15

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(d) Randomly generation of initial population

Finding optimum parameters of the MFs

Estimating SSC with fuzzy inference method

Calculating objective function (RMSE)

Selecting chromosomes to pass the next generation

Obtaining new chromosomes with crossover and mutation

Yes No

Is objective function optimized?

Is iteration number reached?

No

Yes Solution with optimized parameters

End

Fig. 3. (continued)

3.3. EF approach

cannot be justified optimally (Shoorehdeli et al., 2006). The fundamental distinctions between GAs and traditional optimization techniques are:

In the current study, the evolutionary fuzzy models were obtained by combining two approaches, fuzzy logic, and GA. The best values of the fuzzy model's parameters (e.g., parameters of MFs or linear equations) were computed by utilizing GA. The mechanism of the evolutionary fuzzy model is exhibited in Fig. 3d. GA is employed for minimization of the goal error between the model's results and corresponding observed ones. Mean square error (MSE) is utilized in the present study as a fitness in GA.

➢ In GAs, parameters sets are coded, not the individual parameters. ➢ In GAs, a local minimum is investigated from a population instead of a single point. ➢ In GAs, the information of goal function is utilized, not auxiliary information. ➢ In GAs, the rule of probabilistic evolution is used instead of deterministic ones (Goldberg, 1989).

MSE =

The optimal solutions are investigated by GA. The investigated problem is changed over the binary form and crossover and mate are applied to the solutions with a predetermined evaluation statistic to give the minimum. The detailed GAs theory may be acquired from Ahmed and Sarma (2005) and Wang (1991).

1 N

N

(yiobserved i=1

yimodel ) 2

(2)

where N is the quantity of data in training. In this study, the goal function (Eq. (2)) is optimized via modifying the MFs parameters of each input and output. This issue (optimizing the fuzzy MFs) is very complicated for the scheme of supervised learning. GA, nevertheless, uses a scheme of non-supervised learning and may be effectively employed in the solution of such problems (Goldberg, 1989; Özger, 2009). 16

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Fig. 3. (continued)

3.4. Adaptive neuro-fuzzy inference system model (ANFIS)

validation and testing of the applied models, respectively. The proposed sediment predictive model tested using various input attributes combination that based on the antecedent flow discharge values (as the river flow is the main surface hydrology component stimulus the movement and the concentration of the sediment particles). The input combination structure tabulated in Table 2 that constructed in accordance to the correlation statistics between sediment and river flow discharge. This procedure implemented with harmony with several researches conducted in the literature of the same research field (Afan et al., 2017; Rai and Mathur, 2008; Senthil Kumar et al., 2012; Van Maanen et al., 2010). The presented information of the correlation in Table 2 showed that including current and three antecedent discharge records gave the yield point, in which the fourth day exhibits less correlation with the targeted SSC value. The input combinations are presented as follows:

ANFIS, as a generic approximator, was firstly presented by Jang (1996). It has a system structure involving various nodes linked via directional connections. Every node is portrayed by a node function comprising constant or alterable parameters (Jang et al., 1997). Imagine a FL inference system comprising 3 inputs (x, y, and z) and 1 output (f) and its rules include 2 TS (Takagi and Sugeno) type fuzzy rules (Takagi and Sugeno, 1985):

Rule 1: If x is A1, y is B1 and z is C1 then f1 = p1 x + q1 y + r1 z + s1 (3)

Rule 2: If x is A2, y is B2 and z is C2 then f2 = p2 x + q2 y + r2 z + s2 (4) where f1, f2 demonstrate the function of output for the 1st and 2nd rules. An identical ANFIS structure is illustrated in Fig. 3e. The output of ANFIS includes linear or constant functions. More theory about ANFIS can be obtained from Jang (1996). In the current study, we used three different ANFIS methods, ANFIS with subtractive clustering (ANFIS-SC), ANFIS with grid partition (ANFIS-GP), and ANFIS with fuzzy c-means (ANFIS-FCM). The GP is an input partitioning method and frequently used in the literature (Jang, 1996). In SC method, data are partitioned into clusters and less number of fuzzy rules are obtained compared to GP method. An iterative method used in FCM with the aim of computing cluster centers by minimizing the square error. For the detailed information for these methods, the readers are referred to (Kisi et al., 2017).

(5)

Model 1:

SSC(t ) = Q(t )

Model 2:

SSC(t ) = Q(t ) , Q(t

1)

Model 3:

SSC(t ) = Q(t ) , Q(t

1) ,

Q (t

2)

Model 4:

SSC(t ) = Q(t ) , Q(t

1) ,

Q (t

2) ,

(6) (7)

Q(t

(8)

3)

The proposed and the comparable predictive models were evaluated using four different quantitative statistical metrics including root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe coefficient (NSE) and Willmott's index of agreement (WI). The Table 2 The cross-correlations between discharge and SSC in the upstream and downstream stations.

3.5. Input variables structure and prediction indicators In the up- and down-stream stations, the data periods October 01, 1966–September 30, 1971, October 01, 1971–September 30, 1974 and October 01, 1974–September 30, 1977 were utilized for training,

Upstream St Downstream St

17

Qt

Qt-1

Qt-2

Qt-3

Qt-4

Qt-5

0.884 0.873

0.545 0.524

0.353 0.358

0.353 0.358

0.310 0.317

0.275 0.259

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mathematical description can be explained as follows (Chai and Draxler, 2014; Nash and Sutcliffe, 1970; Willmott et al., 2012):

1 N

RMSE =

MAE =

1 N

NSE = 1

WI = 1

outperformed the other models (i.e., ANFIS-GP, ANFIS-SC and ANFISFCM) for the up-stream and down-stream stations using the evaluation metrics (i.e., RMSE, MAE, NSE, and WI). For the up-stream station, the optimal antecedent river flow information identified for the proposed (EF) and the comparable (ANFISGP, ANFIS-SC, and ANFIS-FCM) models are (Model 3, Model 4, Model 1 and Model 3). Whereas, the down-stream station attained the best results are (Model 3, Model 4, Model 1 and Model 1). The optimal training (RMSE-MAE-NSE-WI) for the EF are (4579-983-0.928-0.9999) “up-stream station” and (75041-19719-0.932-0.9999) “down-stream station”. Whereas, the testing phase of the modeling attained (RMSEMAE-NSE-WI) values (2583-413-0.708-0.9989) “up-stream station” and (42714-9032-0.911-0.9997) “down-stream station”. The testing phase is the most significant phase that matter for the evaluation of engineering concern. The enhancement of the prediction accuracies through this phase (i.e., RMSE-MAE) using the EF over the other models (i.e., ANFIS-GP, ANFIS-SC and ANFIS-FCM) are ((25.1–6%), (29.3–35.2%), and (10.8–0.4%)) and ((8.8–23.6%), (31–45.2%), and (38.3–12.1%)) for up-stream and down-stream stations. The EF has superior accuracy with respect to the NSE and WI statistics. WI has an advantage over the RMSE and R2 which describe squared differences between measured and predicted SSC and neglect the low values. In WI, however, the ratio of mean square error is considered instead (Diop et al., 2018; Willmott, 1984). It is evident from the Table 5 that the best EF (Model 3 for both stations) have the highest NSE values, 0.708 and 0.911, which indicate ‘good’, and, ‘very good’ efficiencies of the models (Moriasi et al., 2007). The general evaluation of the proposed evolutionary fuzzy model seemed to perform the SSC prediction more precisely than the comparable models (ANFIS-GP, ANFIS-SC, and ANFISFCM). It is important to state that, the proposed and the validation models exhibited no consistency in the input information for the best prediction outcome. Indeed, this is not surprising as the data-intelligent models act differently from one case to another in accordance with the learning process of the model. Also, that is relying on the provided historical information from one case to another. The other important reason for this is the highly complex behavior of discharge-sediment phenomenon (please see the highly skewed distributions of discharge and SSC in Table 1 together with their significantly high xmax/xmax ratio). Moreover, the high different ranges (xmax–xmax) and distributions between

n

Sf )2

(So

(9)

t=1

n

So

Sf

(10)

t=1 N i=1 N i=1

(So

Sf ) 2

(So

So ) 2

N i=1 N i=1

(|Sf

(So

,

NSE

Sf ) 2

So | + |So

So |)2

1

,0

(11)

WI

1

(12)

where the So and Sf are the observed and predicted values of SSC data. Whereas, So and Sf are the mean value of the observed and predicted values of SSC data. 4. Modeling results and discussion The motivation of the current research is to develop new robust intelligent predictive models called evolutionary fuzzy model (EF) for environmental river engineering application (i.e., sediment transport prediction). Sediment concentration prediction as stated in the introductory section can profit significant knowledge to multiple application of water resources engineering and planning including reservoir operation, river topology mechanism, water quality percentage and others. The new EF model was evaluated against the predominant family of the fuzzy logic models such as ANFIS integrated with GP, SC and FCM. The modeling of the SSC established based on river flow discharge information for two different coordinated stations on Eel River upstream and down-stream. In quantitative visualization, Tables 3, 4 and 5 illustrate the training, validation, and testing performance metrics in addition to the optimum parameters of the all developed models (EF, ANFIS-GP, ANFIS-SC and ANFIS-FCM) for up-stream and down-stream stations, respectively. Based on the visualized prediction performance of the daily SSC using discharge information, it can be observed that EF model

Table 3 The training and validation performances of the EF, ANFIS-GP, ANFIS-SC and ANFIS-FCM models in suspended sediment prediction for up-stream station. Models

EF (2,gauss,10000)a EF (2,gauss,1000) EF (3,gauss,5000) EF (3,gauss,5000) ANFIS-GP (3,gauss,100)b ANFIS-GP (2,gauss,70) ANFIS-GP (2,3,3,gauss,10)c ANFIS-GP (2,2,3,3,gauss,100) ANFIS-SC (0.5,50)d ANFIS-SC (1100) ANFIS-SC (1100) ANFIS-SC (1100) ANFIS-FCM (7,30)e ANFIS-FCM (8,00) ANFIS-FCM (5,40) ANFIS-FCM (5,40) a b c d e

Inputs

Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model

Training

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Validation

RMSE (Mg/l)

MAE (Mg/l)

5482 4876 4579 4436 17,297 17,294 17,240 3411 5813 4275 3490 2363 4764 4091 4387 3863

1378 1190 983 1095 2790 2800 2769 742 2148 1483 906 593 961 812 1017 857

NSE

WI

RMSE (Mg/l)

MAE (Mg/l)

NSE

WI

0.897 0.918 0.928 0.932 −0.027 −0.026 −0.020 0.960 0.884 0.937 0.958 0.981 0.922 0.943 0.934 0.949

0.9998 0.9999 0.9999 0.9999 0.9972 0.9972 0.9972 0.9999 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

9704 9783 9973 12,232 25,242 25,240 25,171 12,364 9753 9562 36,653 7,981,014 6965 7364 8998 14,628

1604 1415 1259 1610 2705 2716 2684 1508 1780 1497 3061 346,190 1119 1021 1247 1625

0.850 0.848 0.842 0.762 −0.012 −0.012 −0.006 0.757 0.849 0.855 −1.133 −1011 0.923 0.914 0.871 0.660

0.9990 0.9990 0.9990 0.9985 0.9897 0.9896 0.9897 0.9986 0.9990 0.9991 0.9910 0.5385 0.9995 0.9995 0.9992 0.9978

2 Gaussian MFs for each input and 10,000 generations. 3 Gaussian MFs for each input and 100 iterations. 2,3,3 Gaussian MFs for the inputs Qt, Qt-1, Qt-2, respectively and 10 iterations. 0.5 radii value and 50 iterations. 7 clusters and 30 iterations. 18

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Table 4 The training and validation performances of the EF, ANFIS-GP, ANFIS-SC and ANFIS-FCM models in suspended sediment prediction for down-stream station. Models

Inputs

EF (2,gauss,20000)a EF (5,gauss,1000) EF (2,gauss,50,000) EF (4,gauss,5000) ANFIS-GP (3,gauss,100)b ANFIS-GP (3,gauss,100) ANFIS-GP (3,gauss,100) ANFIS-GP (2,gauss,100) ANFIS-SC (1100)c ANFIS-SC (1100) ANFIS-SC (0.3,70) ANFIS-SC (1100) ANFIS-FCM (2100)d ANFIS-FCM (8,10) ANFIS-FCM (7,10) ANFIS-FCM (5,80) a b c d

Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model

Training

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Validation

RMSE (Mg/l)

MAE (Mg/l)

NSE

WI

RMSE (Mg/l)

MAE (Mg/l)

NSE

WI

85,898 63,122 75,041 72,437 294,692 294,692 294,692 64,740 90,461 64,107 53,369 39,785 87,062 79,485 87,877 336,012

23,182 16,028 19,719 19,282 60,966 60,966 60,966 20,388 35,472 21,007 17,070 12,203 24,860 17,499 19,304 56,333

0.911 0.952 0.932 0.937 −0.045 −0.045 −0.045 0.950 0.902 0.951 0.966 0.981 0.909 0.924 0.907 −0.358

0.9999 0.9999 0.9999 0.9999 0.9982 0.9982 0.9982 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9988

164,866 168,184 214,455 182,543 306,449 306,449 306,449 207,596 156,225 377,626 360,274 1,382,684 157,881 222,667 167,361 747,048

32,127 31,977 40,579 34,471 46,210 46,210 46,210 39,893 37,656 42,714 47,307 120,462 34,649 29,080 32,601 86,449

0.704 0.692 0.499 0.637 −0.023 −0.023 −0.023 0.530 0.734 −0.554 −0.414 −19.83 0.728 0.460 0.695 −5.081

0.9991 0.9990 0.9985 0.9989 0.9943 0.9943 0.9943 0.9986 0.9992 0.9958 0.9965 0.9727 0.9992 0.9985 0.9991 0.9894

2 Gaussian MFs for each input and 10,000 generations. 3 Gaussian MFs for each input and 100 iterations. 1 radii value and 100 iterations. 2 clusters and 100 iterations.

the training and validation/test data bring additional difficulties to the applied models. Scatter plot generated between the observed SSC values and predicted values over the testing phase of the modeling for both investigated stations (see Fig. 4a and b). The determination coefficient (R2) demonstrated an excellent correlation to the ideal line of the 45° for the EF. To have a more detailed inspection of the four data-intelligence predictive models, a combination of three metrics including standard deviation, correlation, and root mean square error is constructed to be visualized as a Taylor diagram (Fig. 5) (Taylor, 2001). The main point of this diagram is to summarize multiple performance metrics in one combination and statistically quantify the degree of similarity between the observed (actual suspended sediment concentration) and the predicted values. Based on the graphical presentation, the EF model located closer to the benchmark observed record in comparison with ANFIS-GP, ANFIS-SC, and ANFIS-FCM models. It can be seen very obvious for the up-stream station and with slight difference between EF and ANFIS-SC. This is not surprising as ANFIS-SC model showed the

excellent performance of prediction in the last decade within the field of hydrology and environment (Kisi et al., 2015; Kisi and ZounematKermani, 2014; Orouji and Haddad, 2013; Sanikhani et al., 2012). The analyzed data of the suspended sediment of the two stations in up-stream and down-stream of the Eel River, it is very clear the SSC amount values of the down-stream station is highly greater than the upstream. This is owing to the uplifting of the streamside land sliding which presents the main source of the sediment. Here the uplifting of the soil originally materialized due to the high event of river flow discharge. It is worth it to validate the current research results with the established literature. Rajaee et al. (2009) applied ANFIS and neural networks (NN) for daily suspended sediment (SS) concentration of Little Black River and Salt River, USA. Previous streamflow and SS values were used as inputs to the applied models. Authors used simple two data separation rule, training, and testing. Skewness coefficients of the SS data used vary from 4.63 to 6.69. ANFIS model attained R2 value of 0.697. Senthil Kumar et al. (2012) modeled SS concentration of Kasol, Sutlej basin, India using various AI models including: NN, radial basis

Table 5 The testing performances of the EF, ANFIS-GP, ANFIS-SC and ANFIS-FCM models in suspended sediment prediction for the up-stream and down-stream stations. Models

EF EF EF EF ANFIS-GP ANFIS-GP ANFIS-GP ANFIS-GP ANFIS-SC ANFIS-SC ANFIS-SC ANFIS-SC ANFIS-FCM ANFIS-FCM ANFIS-FCM ANFIS-FCM

Inputs

Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model

Up-stream

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Down-stream

RMSE (Mg/l)

MAE (Mg/l)

2588 2654 2583 2685 4810 4808 4772 3449 2719 3271 3655 20,679 3482 3060 2898 3510

503 445 413 476 561 585 558 444 1339 976 638 1879 434 393 415 426

NSE

WI

RMSE (Mg/l)

MAE (Mg/l)

NSE

WI

0.707 0.691 0.708 0.684 −0.014 −0.013 0.003 0.479 0.676 0.531 0.415 −17.74 0.469 0.590 0.632 0.460

0.9990 0.9989 0.9989 0.9989 0.9918 0.9914 0.9917 0.9982 0.9994 0.9989 0.9982 0.9712 0.9980 0.9985 0.9987 0.9981

47,773 44,593 42,714 45,493 144,141 144,141 144,141 48,915 50,972 65,172 122,783 358,188 50,489 72,319 75,641 337,632

10,285 8414 9032 10,149 18,432 18,432 18,432 11,023 22,568 15,352 17,019 29,063 11,007 9573 11,154 28,816

0.888 0.903 0.911 0.899 −0.017 −0.017 −0.017 0.883 0.873 0.792 0.262 −5.278 0.875 0.744 0.720 −4.578

0.9996 0.9996 0.9997 0.9996 0.9929 0.9929 0.9929 0.9996 0.9997 0.9993 0.9978 0.9834 0.9996 0.9991 0.9990 0.9865

19

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Fig. 4. Scatter plot graphical presentation between the observed and the predictive intelligence models, a) the upstream investigated metrological station b) the downstream investigated metrological station.

function (RBF), fuzzy logic, M5 model tree and REPTree. Input variables were antecedent values of rainfall, streamflow, and SS. The best model (NN) provided the NSE of 0.91. Vafakhah (2012) developed neuro-fuzzy, ANN and cokriging based models for daily SS estimation.

Various input combinations based on the current and past daily rainfall and streamflow data obtained from the Kojor forest watershed near the Caspian Sea. The achieved results of the model's predictability displayed a value of NSE 0.64, 0.79 and 0.85 for the best neuro-fuzzy, 20

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attributes for the developed model. This is very significant for limited hydrological data catchments. Nearly 90% of the conducted literature studies were modeled using sediment information in addition to other hydrological variables as an input attribute. Indeed, this is not recommended practically due to the measurement of SS is a very difficult task from the engineering point of view. Also, the SS value of the current day should be measured and applied as an input to estimate tomorrow's value. However, streamflow can be measured or calculated from river stage data much easier than the SS. To conclude the discussion section, the proposed EF demonstrates an adequate predictive model for the investigated environmental problem over the other version of the integrated ANFIS models. The main merit of the EF in its integration with the nature-inspired genetic algorithm. On the contrary with ANFIS model, the gradient descent algorithm is used to define the MFs, in which several disadvantages can be faced such as tapped in the local minima (Piotrowski and Napiorkowski, 2011). Note that GA is a combination of stochastic and direct searching solution that never tapped in the local optima problem (David and Greental, 2014; Garousi-Nejad et al., 2016). 5. Conclusion and remarks In this research, a new hybrid intelligence model called evolutionary fuzzy is proposed to predict SSC at El River, one of the very big and problematic rivers in northern California. Different data-intelligence models of the same family of the fuzzy logic set (ANFIS-SC, ANFIS-GP, and ANFIS-FCM) were developed for validation purpose of the EF. The prediction models built using the information of river flow discharge as this hydrological process is the main casual correlated variable to the SSC. The modeling carried out on two different locations of the river (i.e., up-stream and down-stream). The results indicated the potential of the evolutionary fuzzy predictive model to mimic the SSC pattern with a high level of accuracy over the comparable models. The predictability effectiveness of the EF attributed to several aspects of the environmental concerns. It is highly recommended to integrate the applicability of this evolutionary predictive model with the typical monitoring expert system of the Eel River. The current findings of this research can be expanded for future research by employing more hydrological or climatological or even morphological information to the predictive model. In addition, other water quality parameters that are associated with the percentage of the SSC can be included in the modeling for inspection.

Fig. 5. Tayler diagram exhibition denoting the prediction skill between the data-intelligence models and the observed record of SSC a) the upstream investigated metrological station b) the downstream investigated metrological station.

References

ANN, and cokriging models, respectively. Another study conducted on modeling daily SS of Kopili River, India, using NN, RBF, least square support vector regression (LS-SVR), multi-linear regression (MLR), Classification and Regression Tree (CART) and M5 model tree (Kumar et al., 2016). The scholars included various combinations of current and past rainfall, streamflow, SS data in the model inputs. They used two data separation rule, calibration and validation. LS-SVR attained the best prediction results with NSE value equal to 0.89. Most of the studies in the related literature used simple two data-splitting rule, training and testing. Throughout the numerical statistic performance of the literature studies, it is very obvious that the proposed modeling strategy of the evolutionary fuzzy model successfully estimates SS of Eel River using only the current and antecedent streamflow values. In the present study, three data splitting procedures (i.e., training, validation and testing), were applied. Here, the optimal model was designated using training and validation data sets where the validation phase was used for controlling the overfitting learning process. The testing data phase was performed as independent dataset which is not known by the developed model. The other advantage of the present study is the use of the individual streamflow information as input

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