J. Nig. Soc. Phys. Sci. 5 (2023) 1028 Journal of the Nigerian Society of Physical Sciences Evaluation of ANFIS Predictive Ability Using Computed Sediment from Gullies and Dam Stephen Olushola Oladosua,∗, Alfred Sunday Alademomib,c, James Bolarinwa Olaleyeb, Joseph Olalekan Olusinab, Tosin Julius Salamib aDepartment of Geomatics, Faculty of Environmental Sciences, University of Benin, P.M.B. 1154, Edo State, Nigeria bDepartment of Surveying and Geoinformatics, Faculty of Engineering, University of Lagos, P.M.B. 12003, Akoka, Lagos State, Nigeria cCentre for Multidisciplinary Research and Innovation, Suite C59, New Bannex Plaza, Wuze 2, Abuja, Nigeria Abstract The study proposed an Adaptive Neuro-Fuzzy Inference Systems (ANFIS) model capable of predicting sediment deposited in a dam and sediment loss-in-transit (SLIT) using the potential of a formulated mathematical relation. The input parameters consist of five members viz: the rainfall, the slope, the particle size, the velocity, and the computed total volume of sediment exited from two prominent gullies for 2017, 2018, and 2019. The outputs are the total volume of sediment deposited at the adjoining Ikpoba dam for 2017, 2018, and 2019, respectively. The Ordinary Least Square (OLS) regression model on sediment volume retained all covariates with p<0.05, explaining 93.8% of the variability in the dataset. The multicollinearity effect on the dataset was assessed using the Variance Inflation Factor (VIF) which was found not to pose a problem for (VIF<5). The model was validated using the (MSE), the (MAE), and the correlation coefficient (r). The best prediction was obtained as: (RMSE = 0.0423; R2 = 0.947). The predicted volume of sediment was 842,895.8547m3 with an error of -0.3295344% and the predicted volume of SLIT was 57,787.98m3 which is an indication that ANFIS performs satisfactorily in predicting sediment volume for the gullies and the dam respectively. DOI:10.46481/jnsps.2023.1028 Keywords: ANFIS, Gully Erosion, Ikpoba Dam, Sedimentation Article History : Received: 23 September 2022 Received in revised form: 21 October 2022 Accepted for publication: 21 October 2022 Published: 21 May 2023 © 2023 The Author(s). Published by the Nigerian Society of Physical Sciences under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Communicated by: O. J. Abimbola 1. Introduction There are different ways in which artificial neural networks (ANN) and adaptive neuro-fuzzy inference systems (ANFIS) find application in solving real-life problems that are subject to interpretation using differential or partial differential equa- tions numerically [1]. Water resource is one key area where ∗Corresponding author tel. no: Email address: olushola.oladosu@uniben.edu (Stephen Olushola Oladosu) soft computing, or machine learning and techniques have be- come indispensable for the modelling of complex, non-linear, and dynamic processes in a hydrological system domain [2]. However, their applications are found in other areas [3- 4]. The aspect of the application of soft computing methodologies in sediment study and water resources in Nigeria is quite scanty in literature [5]. Gully erosion, one of the major contributor to channel sed- iment is more profound in the southern part of Nigeria and is known to have contributed sizable amount of sediment as in- 1 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 2 take into dams such as the one under investigation in this work. Notable studies have been conducted in the region in various capacities on gully initiation, development, and remediation in the past as obtained in [6-11]. In 2013, the Nigerian govern- ment established the Nigeria Erosion and Watershed Manage- ment Project (NEWMAP) to oversee how best to mitigate soil erosion (particularly gully erosion) and land degradation in spe- cific watersheds by inclusive approach [12-13]. Most often, ac- tions to salvage the havoc pose by such environmental problem are delayed due to bureaucracy in governance. Approximately 6% of Nigeria’s total landmass, relied upon by many other sec- tors of the economy, has either been badly damaged or degraded by gullying activities [13]. The 2% per annum growth in the population as noted by [13] is an indication that more demand will be on land use; hence, more efforts are required in address- ing the issue of land degradation and gullying in the country. Gully erosion is a process by which soil’s cohesive forces are drastically weakened at particular thresholds by the action of an active run-off leading to the commencement of mass move- ment and the eventual creation of deep channels with a substan- tial amount of sediment deposited downslope [14-15]. The de- velopment of gullies causes a substantial amount of soil loss, especially in badland where sediment from gullies finds its way into the river channel and is later transported as bedload into a dam. The negative impact, in the long run, is the speedy rate of siltation and a drastic reduction in the useful life of a reser- voir which when occurring will require serious attention. Gully erosion has wreaked havoc globally and has been a threat to a free, safe, and life-sustaining environment [16-20]. The moti- vating variables and drivers of gully initiation and development in distinct catchments are present in previous works [21-22]. On a global scale, as reported by [15], [22-23], gully erosion caused between 10 to 94 percent of soil loss, most of which finds its way downstream into a reservoir. Sediment modeling using soft computing methodologies, such as ANN, Wavelet, GA, ANFIS, C-ANFIS, and others, is described in the litera- ture. A researcher’s objective is to ascertain whether combin- ing or complementing any models will produce an improved outcome. According to [24-26], ANN in a broad sense, encompasses a wide range of network designs and configurations. The most common ANN in literature is the multilayer feedforward neural network (MLFFNN), which adopts a form of an interconnected perceptron that makes data and calculations flow ultimately in one direction, starting from the input data to the outputs. The most common attributes of an MLFFNN consist of an input layer, a single or multiple hidden layers, and an output layer [27-28]. During ANFIS internal training of the ANN network, the inputs of the first layer multiply an initial random weight coefficient. This development prompts the network to progress to the neurons in subsequent layers. The resulting sum is then forwarded to an activation function, which processes and trans- forms it to the required output. The network error of the pre- dicted output and target output is calculated and again sent from the last layer to the previous one, thereby updating the weight coefficients. This process is called “error-back-propagation” [28- 29]. In the history of the ANFIS soft computing technique, [24- 25] were pioneers. Because of its ability to deal with nonlinear phenomena, it is preferred for simulating and modelling com- plex hydrological systems [29-32]. Applications of ANFIS in diverse fields are quite numerous in the literature. [33], applied an ANFIS-based approach for the prediction of sediment trans- port in clean sewers and affirmed a satisfactory result with (r2 = 0.98 and RMSE = 0.002431) in comparison to other exist- ing predictors. [31-33], adopted an ANFIS-based approach for predicting the bed load for four moderately-sized rivers. While other equations failed to produce an accurate result, the ANFIS results showed an accurate prediction for measured bed-load data based on a regression method used for comparison. This research is aimed at proposing an ANFIS model ca- pable of utilising five input parameters in determining the vol- ume of sediment deposited in Ikpoba dam and the amount not reaching the dam at the time when observations were conducted tagged “sediment-loss-in-transit” (SLIT). The model design links the input parameters to aggregate the devastating effect of sed- iment volume intake of the dam which contribute significantly to early loss of storage capacity. Sediment evaluation at the dam based on the quantity of soil loss from gully erosion trans- ported through the river channel can serve as guide to the water resource managers, hydraulic engineers, and dam operators in taking appropriate decisions on dam water-sharing routine, dam useful life monitoring, dam rejuvenation efforts, cost-effective sediment remediation method, dam management planning, and so on. 2. Materials and Methods 2.1. Study area The study area captured the upstream part of the Ikopba River dam where two prominent gullies, namely, (the Univer- sity of Benin gully and the Iguosa-Oluku gully) are exiting their massive sediment into the Ikpoba river channel within the same catchment in Benin City, Edo State, Southern Nigeria. The geographical location of the study area falls within UTM Zone 31N, 789050.75 mE; 705200.22 mN, and 795500.96 mE; 715950.26 mN). By Koppen classification, Benin City has a tropical savanna climate with rainfall intensities reaching up to 2680mm annually in most cases. The rainfall lasts between eight to nine months, starting in March through October at vary- ing degrees, resulting in a substantial amount of overland flow with impactful erosive energy. The average annual temperature at this location was 25.6 ◦C. The Benin City region is charac- terized by the sedimentary formation underlay of what is called the “South Sedimentary Basin,” with the geology marked by the presence of reddish earth on top, composed of ferruginized or literalized clay sand [34]. The geologic formations in the region are classified into four basic categories: the Benin for- mation; alluvium; drift/topsoil and Azagba-Ogwashi. The type of soil in this region, which has low cohesive aggregate bind- ing force, is highly susceptible to erosion influence, therefore gully formation is always prevalent. The study area including the immediate catchment is shown in Figure 1. 2 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 3 Figure 1. Map showing the study area 2.2. The Description of the Gullies The University of Benin gully and the Iguosa-Oluku gully hereafter referred to as gully (A) and gully (B), respectively, are located in the upper part of the Ikpoba dam. Although there is no specific documentation on the exact date on which Gully (A) began, it started earlier than the year 2005 as captured by Google Earth historical images. Its development has caused some buildings to be completely or partly eroded at the senior staff quarters of the University due to the gradual landslide re- sulting in gully sidewall collapse. The guest house of the Uni- versity is presently under threat. Figure 2 reveals the impacts of gully erosion on some properties and the immediate surround- ings of the invested environment. According to an anonymous resident, the rehabilitation of the Benin/Lagos expressway in 2014 caused the start of the gully (B). Its initiation and subsequent development are tied to the volume of run-off diverted to a drainage system not appro- priately designed to convey such an amount. Hence, the water created an alternative path across the existing settlement, ac- tively creating a bigger and deeper channel. Six years of no visible remedial intervention led to the destruction of more than fifty buildings, including a police station and other utilities. The Federal housing estate located close to where the gully exten- sion has reached is now in grave danger of being eroded. Fig- ure 3 shows the devastation caused by gully erosion (left) and Table 1. Construction information of Ikpoba dam S/No Name of Dam: Ikpoba Remark 1 Type of Dam Earth fill 2 Water production per pump day 34080 m3 3 Catchment area 120 km2 4 Crest level height 35 m (a.m.s.l) 5 Dam length 610 m 6 Active storage capacity 1.5 x 106 m3 7 Reservoir surface area 1.07 x 106m2 8 Service spillway length 60 m 9 Emergency spillway length 4 m 10 Water supply capacity 90,000 m3/day 11 Average monthly discharge 31.9m3/s 12 Average annual run-off 0.9285 x 109m3 13 Population at design 1.0 million 14 First impoundment year 1975 15 Commission year 1987 Source: [38] the massive soil loss deposited along the Ikpoba river course (right). 2.3. Description of Ikpoba river and dam The Ikpoba River originated from the Oluku settlement area in an extension of Benin City’s western highland towards the northern and north-eastern parts [35]. From the identified source, the river flows from east to west; reverses its course and mean- ders through Utekon before changing direction to the southern and eastern banks through the following axes (Ekosodin, Ug- bowo, Okhoro, and New Benin). The river has some level of in- teractions with the exited sediment from the gullies under con- sideration. The Ikpoba dam is an earth dam that is located along the river reach between Okhoro and Teboga. It is a small dam according to the classification of the International Commission on Large Dams [36]. The construction work of the dam be- gan in 1977 and was commissioned in 1987. The Benin-Owena River Basin of Nigeria manages the dam in conjunction with the Edo State Urban Water Board. The geological terrain is ter- tiary and the foundation is pile-based. Four stations are present before reaching the dam’s head [34-37]. These are (Okhoro, Midpoint, Low-lift pump, and Ekiuwa). According to [38], the dam has a length of 610 meters. Table 1 provides useful in- formation on the physical characteristics and parameters of the dam. 2.4. Gully data acquisition and Preparation A Trimble M3 DR 3” Total Station and a Trimble Juno 3B handheld GNSS receiver were used for data collection. Exist- ing ground controls on sites were subjected to an integrity test and found to be stable before proceeding to observations. The cross-sectional design was done in AutoCAD civil 3D for 2017, 2018, and 2019, respectively. Samples are presented in Figure 4. The volume of each gully segment at chainage 20m apart was computed by the average area of the up and downstream cross sections multiplied by their respective segment lengths. 3 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 4 Figure 2. Gully (A) and its negative impacts on settlement Figure 3. Devastating impact and soil loss from Gully B The cumulative sum of all sectional volumes represents the to- tal sediment volume contributed by gullies. See Table 2. 2.5. Bathymetric data acquisition and preparation The bathymetric surveys of the reservoir were conducted in 2017, 2018, and 2019, respectively. The procedure involved the coupling of the 15-HP Yamaha engine to the fiber boat and pushing it away from the bank to gain enough depth to allow for the attachment of the transducer and the mounting of the GNSS receiver firmly to their respective positions. The posi- tion fixing was done in RTK mode using the Hi-Target GNSS receiver while depths were measured simultaneously with the aid of the Hi-Target Marine HD-Max Echo Sounder powered by a 12-volt battery. The appropriate bar checks were observed against the standard marks at 1 m, 2 m, and 3 m for consis- tency and the eradication of false depth records. This check was done before and after the bathymetric surveys. Twenty-five transect lines (25) and two longitudinal cross lines (2) were tra- versed. The output from the RTK-GNSS receiver are precise 3-D (X, Y, Z) coordinates with obtained accuracies in the or- der of 0.02m for horizontal and 0.05m for vertical, respectively. Corrections for pitch roll and heave were applied at the soft- ware interface on board to get the corrected depths. During the different campaigns, water level monitoring was performed by planting a levelling staff at the bank of the river, and readings were taken with the aid of Nikon Automatic AC-2s leveling in- strument before and after the bathymetric surveys. For the three campaigns, the average water level recorded at the beginning of work was 3.360m and at the end of work, it was 3.361m. The difference gave 0.001m. This result showed that the water at the dam was non-tidal and relatively calm throughout the time of observations. Note, that water level measurement may not pose a problem with the RTK technique, but when it is taken, it can be used for verification or validation purposes. We com- puted the volume of sediment accumulated in the dam using equation 1 [39]. Table 2, contains the technical parameters of the Hi-Target Marine HD-Max Echo Sounder, while Table 3 provides the summary of the total volume of sediment accumu- lated in the dam for the three years investigated. Figure 5 shows 4 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 5 Figure 4. Sample of cross-sectional design for gullies Table 2. Summary of calculated volume of sediment from Gullies Year Gully ID Vol. loss (m3) Cumulative Vol. loss (m3) Total Vol. (m3) 2017 256791.548 000000.000 2018 A 268363.430 525154.978 2019 277543.350 802698.328* 802698.328 2017 375478.830 000000.000 2018 B 414810.690 790289.520 2019 475275.954 1265565.474* 1265565.474 Grand Total 2068263.802 2068263.802 2068263.802 Note: **are the only final yearly volumes considered in column 4 for to get the grand total the water level monitoring effort at the dam’s location. Rannua = V1 − V f T (1) Where Rannual, represents the annual mean reservoir sedi- mentation volume in (Mm3/year); Vi, refers to the initial reser- voir volume in (Mm3); V f , signifies the final reservoir volume in (Mm3); T, is the number of years since dam had been oper- ated. T V U = ± √ a2 + (b × d)2 (2) 2.6. The ANFIS architecture The input data, the hidden layers, and the output layer are the three fundamental components of the ANFIS architecture. The ANFIS model type used in this study is the Sugeno, with five layers. What necessitate its use was because of its com- pactness and efficient computational capability [42]. Instead of working with linguistic variables on the consequent part as in the Mamdani model, the TSK model [41-45] uses rules as a function of input variables to represent the consequent parts. Its success is due mainly to the ease of generating a set of sys- tem equations for the consequent parts, the parameters of which are simple to estimate using traditional optimization methods. However, the interpretation of the obtained rules is somewhat difficult, which shows their principal shortcoming. The TSK learning algorithm consists of two processes, the forward and the backward stage. The forward phase goes through the five layers to be discussed after in text while the backward stage fine tune the weights of a neural network by using the error rate previous epoch [24]. In a first-order Sugeno fuzzy model, a typ- ical fuzzy rule statement takes the form of say Where: A and B are fuzzy sets in the antecedent, is a crisp function in the con- sequent. The five layers are simplified further to briefly explain what takes place at each layers of the ANFIS model. (i) Layer-1 This layer is the first, and is very critical to the overall pro- cess. Equations 3 or 4 represent what takes place at this phase [42]. O1,i = µAi(x) for i = 1, 2 (3) or O1,i = µ(Bi−2)(y) for i = 3, 4 (4) Where: x or y -represents the input taken by node i, Ai or Bi−2 -signifies a form of linguistic descriptions (e.g. high, low 5 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 6 Figure 5. Bathymetric survey and water level monitoring exercise at Ikpoba dam Table 3. Technical parameters of HD-MAX Echo Sounder S/No (a) Technical parameters 1 CPU speed: 1.6G*2 2 RAM: 2GB 3 Memory space: 16GB SSD 4 Display screen size: 17” 5 Display resolution: 1280*1024 6 Starting time: < 40s 7 High frequency emitted from the probe: 200KHZ 8 Point-positioning precision: <2.5M (built-in GPS function) 9 Input voltage: 10 30V 10 Average power consumption: <40W 11 Operating temperature: 0 50°C (b) Bathymetric Accuracy 12 Horizontal = 0.506m, at 95% confidence level. 13 Vertical = 5m + (-0.30m) at 95% confidence level. Note: We applied the formula provided by the International Hydrographic Organisation, [40] for the determination of horizontal and vertical uncertainties in depth measurement. The maximum depth obtained during sounding was 6.0m, while a and b are constants provided for in the formula. To compute total horizontal uncertainty, we used, THU = 5m + 5/100 of depth. Equation 2 was used to compute the total vertical uncertainty, TVU. The results are contained in the last two rows of Table 3. and so on) assigned to node i, O1,i -represents the member- ship function of fuzzy set Ai which signifies the extent to which the input x or y under consideration satisfies the quantifier Ai. µAi(x) and µBi−2(y) can accommodate any fuzzy membership function assumed to spread between 0 and 1. For example, if the bell-shaped membership function is adopted, µAi(x) follows the equation 5 µAi (x) = 1 1 + [( x−ci ai )2] bi , i = 1, 2 (5) 6 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 7 Table 4. Summary of calculated volume of sediment in Dam Year Ikpoba Dam Annual Sed. Vol. (m3) Cumul. Sed. Vol. (m3) Comp. Bed-load Sed. Vol. (m3) 1987 Base year N/A 000000.000 2017 1st Observation 217336.704 217336.704 2018 2nd Observation 222790.642 440127.346 2019 3rd Observation 400000.000 840127.346* Grand Total 840127.346 840127.346 840127.346 Note:*is the only one considered under column 4 for the ground total Where: ai, bi, and ci in equation 5 are the premise parameters set of the generalized bell shape membership function (MF). The current study adopted the Gaussian membership func- tion (MF) defined by equation 6. µAi (x) = ex p − ( x − ci ai )2 (6) Where: ai and ci in equations 6 are the premise parameters set of the Gaussian MF. Changing the values of these parameters would cause a cor- responding change in the generalize bell-shape behaviour and the Gaussian shape that will make the fuzzy set “Ai” to exhibit various forms of membership functions. In this layer, parame- ters are commonly called premise parameters [42- 45]. (ii) Layer-2 At this layer, each ANFIS node represents a fixed node with an output signal as the product of the contributions of the in- coming signals. O1,i = wi = µAi (x) ∗µ(Bi−2) (y) , f or i = 1, 2 (7) Each node output in this context is a representation of a rule’s firing strength capacity. The node function in this layer will typically be any other T-norm operator that can execute fuzzy (AND). (iii) Layer-3 This layer has a fixed node labeled N. Here, the ith node computes the ratio of the ith rule’s firing strength to the sum of all rules’ firing strengths. The outputs of this layer are the normalized firing strengths, represented as follows: O3, i = wi = wi w1 + w2 : f or i = 1, 2. (8) (iv) Layer-4 Every node i contained in this layer represents an adaptive node with a node function: O4, i = wi fi = wi( pi x + qiy + ri), (9) Where: The ANFIS in this layer represents a normalized firing strength inherited from layer-3, and the quantities represented as: (pi, qi and ri) are the parameters set of this node. Parameters here are termed consequent [41- 45]. (v) Layer-5 This layer is an ANFIS with a fixed node label and a sin- gle node that sums all incoming signals to produce the overall output: O5, i = ∑ i wi fi = ∑ i wi fi∑ i wi = the overall out put (10) Figure 6. ANFIS architecture. Source: [41] These five steps simplify a functional Takagi-Sugeno fuzzy model for an adaptive network design. The backward stage is a useful process in estimating the database; this consists of the parameters of the membership functions in the antecedent part and the coefficients of linear equations in the consequent part. The least-squares method as- sists greatly in parameter learning by utilizing standard fuzzy reasoning to anticipate the outcome of the TSK model in the prediction phase [41- 45]. Figure 6 shows the ANFIS architec- ture. 2.7. Description of ANFIS input parameters The parameters used for the ANFIS model contain the five most important site-specific variables that are either observed, measured, or determined through laboratory analysis for the study area. Rainfall: Rainfall data were collected using two tipping bucket rain gauges located within the catchment of the Ikpoba river close to where gully A and gully B exit their sedi- ment into the river channel in conjunction with rainfall data ob- tained from the Nigerian Meteorological Agency (NiMet). The collected rainfall data was used for validation. The data was resampled and gridded to 220 to comply with the gully cross- section. Volume: For the three years specified earlier, gully A and gully B had 109 and 111 cross-sectional segments, adding up to 220 for which volumes of sediment were calculated and cumu- lated to derive the cumulative volume of sediment deposited. Slope: The slope length was determined as run over the rise at each gully cross-section. The depth of gullies taken at each cross-sections varied from 6.0 m to 11.23 m. Particle size: Particle size was obtained from soil samples taken at 1m to 3m from 20 borehole points dug with a hand 7 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 8 huger at the two gully sites. Sieve analysis was carried out at the University of Benin Civil Engineering Laboratory. Velocity: The velocity was measured manually at pre-defined sections along the gullies on rainy days. The widths were mea- sured with 100 m graduated steel tape, and the upper and lower boundaries of each section were defined with wooden pegs wrapped with caution tape. This information was recorded and kept for further use. On two different rainy days, a floating material (cork) was released from the gully’s head and the time taken for it to travel between the flags was recorded with a stopwatch. Five observers were stationed in succession to record time with a stopwatch until the process was completed. To find the ve- locity in (m/s2), we divided the distance traveled by the average travel time and multiplied the result by a chosen correction fac- tor of 0.9 which is mostly adopted for rivers or flowing water whose bottom consists of smooth mud, and sand, or bedrock. The summary of the description of the ANFIS input param- eters in terms of their minimum and maximum limits and their respective membership functions is presented in Table 5. Each parameter has three (3) membership functions. 2.8. Preliminary investigation on input parameters Ordinary least squares (OLS) regression models on sedi- ment volume retained all covariates with p<0.05, explaining 93.8% variability in the dataset. Assessment of the multicollinear- ity related to the dataset using the variance inflation factor was found not to pose a problem (VIF<5) obtained throughout for covariates is sufficient [46-49]. 2.9. Data normalisation Avoiding data normalisation may lead to a complex situa- tion in the training process and non-convergence of the algo- rithm. The min-max normalisation technique that scales the variables in the interval between (0, 1). The data was ran- domised (the purpose is to reduced bias and make the output more reliable). The data was further divided into training and testing datasets after normalisation. After making a good num- ber of data sharing attempts by trial and error, the choice of 75% was made and used for training, while the remaining 25% was used for testing. This sharing ratio gave the optimal result and accuracy compared to others where less or greater value of sharing resulted in large error. The training data performed the role of the ANFIS training process and the generation of the fuzzy rule-based systems (FRBS), whereas, the testing data served the purpose of verifying the accuracy and effectiveness of the trained ANFIS model. For efficient ANFIS processing, the input dataset used was processed in a data frame in form of a matrix (m × n), where m is the number of instances, n is the number of variables, while the last column in the matrix represents the output. Tables 6 and 7 are excerpts from the nor- malized training and testing data respectively. 2.10. Training process The process began by obtaining a training data set (input/output data pairs) and checking of the data sets. Two vectors are used to train the ANFIS system: the input vector and the output vec- tor. ANFIS training rules used was a hybrid learning, which combines the gradient descent and the least-squares method. The training proceeds by determining the fuzzy sets and the number of sets for each input variable and the shape of their membership function. All the training data passes through the neural network, to adjust the input parameters so as to find the relationships between input/output, and to minimize errors propagation. The parameters associated with each membership function kept changing throughout the learning process and a threshold value for the error between the actual and the desired output was determined. If the error is larger than the set thresh- old value, then the premise parameters are updated using the gradient descent method. The consequent parameters are found using the least-squares method. The process is terminated when the error becomes less than the threshold value. We used the checking data set to compare the model with the actual system. The input node received signals from each of the five pre- dictor nodes, connected through intervening hidden nodes. Above each line is the displayed of the respective synoptic weights. The blue circles indicate bias, corresponding to the intercept in the conventional regression model. The variable “sediment volume” represents the output neuron. The network converged when the error reached 0.190791, after 417 steps. The mathe- matics involved in this process is shown in equations 11 and 12. Figures 7 and 8 show the ANN network topology and the flow diagram of the ANN training process, respectively. wi j (t + 1) = wi j (t) + ηδpiOp j (11) δpiwi j (t + 1) = wi j (t)+ηδpiOp j+α [ wi j (t) − wi j (t − 1) ] (12) Where: Weight coefficient in step t+1, from neuron i to neuron j Weight coefficient in step t, from neuron i to neuron j : learning Coefficient : Difference between desired output and network output in neuron p of layer j : Output of neuron p of layer j : Momentum coefficient : Weight coefficient in step t-1, from neuron i to neuron j. 2.11. Model validation metrics In this work, model validation was carried out using the Mean Squared Error (MSE), the Mean Absolute Error (MAE), and the correlation coefficient (r). For simplicity of use, ease of training, and better performance, the rectified linear unit (ReLU) activation function was used. It is a piecewise linear function that will output the input directly if it is positive, otherwise, it will output zero. Equations 13 - 15 are the statistical models adopted in model validation. RMS E = √ ∑N i=0(di − yi) 2 N (13) r = ∑ (yi−ȳ)(di−d̄) N √∑ i (di−d̄)2 N √∑ i (yi−ȳ)2 N (14) 8 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 9 Table 5. Brief description of input parameters Gully A (109 C.S) Gully B (111 C.S) = 220 Parameters Min. Max. Min. Max. MF Rainfall (mm) 55.85 104.49 167.80 215.70 3 Slope-length (m) 29.89 71.99 30.85 63.27 3 Depth (m) 6.45 11.23 4.70 9.61 3 Velocity (m/s) 0.51 1.84 0.44 1.86 3 Particle Size (µm) 28.77 41.69 34.85 47.90 3 Gullies Sed.Vol. x 104 (m3) 5651 8473 8652 13370 3 Note: C.S = Cross-section, MF = Membership Function Table 6. Excerpt from normalised training data index Rainfall(mm) Slope(mm) Depth(mm) Velocity(m/s) P.size(µm) Volume(m3) 139 0.952312 0.325011 0.398463 0.514887 0.60261 0.673596 98 0.003783 0.286023 0.533673 0.78711 0.373132 0.220773 112 0.785692 0.205318 0.206067 0.396444 0.645918 0.756984 144 0.979885 0.646603 0.443222 0.099204 0.763262 0.900655 126 0.864056 0.298648 0.32029 0.365815 0.673003 0.817199 209 0.869185 0.089084 0.251222 0.281811 0.753548 0.860469 35 0.269768 0.842347 0.693181 0.1207 0.446288 0.236462 123 0.818387 0.622698 0.445846 0.925704 0.610277 0.618824 177 0.819464 0.238152 0.499117 0.182115 0.509774 0.612393 212 0.840235 0.554263 0.499378 0.074061 1 1 Table 7. Excerpt from normalised test data index Rainfall(mm) Slope(mm) Depth(mm) Velocity(m/s) P.size(µm) Volume(m3) 7 0.214163 0.958774 0.722309 0.520943 0.491623 0.271775 109 0.074786 0.497832 0.675136 0.925770 0.395535 0.190251 140 0.883963 0.322317 0.279409 0.314403 0.804152 0.706681 74 0.136978 0.710343 0.793520 0.452986 0.266164 0.117517 205 0.725127 0.308324 0.531787 0.103523 0.842459 0.869096 111 0.753561 0.242328 0.000000 0.000000 0.548667 0.693910 187 0.812660 0.211266 0.441200 0.466538 0.485644 0.623276 100 0.152822 0.205663 0.491521 0.274293 0.426886 0.261896 189 0.892676 0.359164 0.323424 0.951899 0.597544 0.580190 88 0.237729 0.535238 0.651543 0.947341 0.349382 0.198406 MAE = 1 N j=1∑ N |yi − ŷi| (15) Where: di : Desired output of i-th data yi : Network output of i-th data N: Number of dataset d̄ : Mean of desired output ȳ : Mean of network outputs RMSE: Root Mean Square Error MAE: Mean Absolute Error r: Correlation coefficient The summary of the investigated neural network algorithms presented in Table 5 shows that: i.) All models have two hidden layer-nodes (5, 3) with ReLU activation function ii.) The learning rule used for model 1 (NN-1) is resilient backward propagation. iii) Levenberg algorithm was adopted for model 2 (NN-2), while iv) Backward propagation algorithm was adopted for model 3 (NN-3). A model that meets all the required evaluation criteria would be the desired model. Therefore, the model with the least RMSE and MAE errors (approaching 0) and the coefficient of determi- nation ”r” (tending to 1) obtained from NN-3 as highlighted in Table 8 is the most acceptable network result chosen. The pre- dictive capability of the best model has an RMSE of 0.0423 with an R2 of 0.947. Table 9 shows the random points to demon- strate normalised and de-normalised for the training and testing datasets. Table 9 presents the comparison of the actual test data and their predicted values based on the fitted training model. The 9 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 10 Figure 7. ANN training network topology Table 8. Summary of Network Algorithms Training Test Model Hidden Layer Nodes Activation Function (F) Learning Rule MAE RMSE r MAE RMSE r NN-1 2 8 ReLU Resilient back- propagation (rprop+) 0.755 0.578 0.903 0.785 0.594 0.916 NN-2 2 8 ReLU Leverberg Algorithm 0.644 0.546 0.924 0.687 0.548 0.919 NN-3 2 8 ReLU Backpropagation (backprop) 0.0456 0.059 0.944 0.048 0.0423 0.947 remaining 25% of input parameters from the test data were fed into the trained ANFIS model to predict the output. It can be observed from the table that the predicted values were close to the original test data. The error rarely exceeds 10%, so the model was able to predict with an acceptable accuracy. The regression plot in Figure 9 (left) displays the network outputs concerning the training and test data. For a perfect fit, the data should fall along a 45-degree line, where the network outputs are equal to the targets. For this particular problem, the fit is reasonably good for all data sets, with a trained coefficient of determination (R2) value in each case of 0.947. Figure 9 (right) depicts the ANFIS training versus validation plot for the test dataset. A close overlap implies a high predictive power of the trained model on the new dataset. i.e., the predicted (purple 10 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 11 Table 9. The predictive power of the model on test data Normalised De-normalised Randomized Index Actual Predicted Actual Predicted %error 7 0.2718 0.2676 7748.541 7716.455 0.414 109 0.1903 0.1923 7119.224 7135.055 -0.222 140 0.7067 0.8422 11105.789 12152.114 -9.421 74 0.1175 0.1527 6557.752 6829.093 -4.138 205 0.8691 0.7942 12359.551 11781.385 4.678 111 0.6939 0.6133 11007.203 10385.319 5.650 187 0.6233 0.5879 10461.952 10189.188 2.607 100 0.2619 0.2948 7672.287 7926.644 -3.315 189 0.5802 0.6580 10129.345 10729.688 -5.927 88 0.1984 0.2140 7182.175 7302.460 -1.675 186 0.6273 0.7331 10492.945 11310.069 -7.787 137 0.7870 0.8188 11725.892 11971.350 -2.093 32 0.1499 0.2065 6807.912 7244.302 -6.410 71 0.2234 0.2255 7375.058 7391.463 -0.222 210 0.7040 0.6087 11084.715 10349.643 6.631 line) has 94.7% predictive accuracy as reported from the value of R2. The attained training error for the test model is obtained as 0.0423. 3. Results and Discussions 3.1. Sediment deposit in dam The total volume of sediment contributed for three years by gullies was 2068263.802 m3. Similarly, the calculated volume of bed-load sediment gained by the dam was 840127.346 m3 (refer to Tables 2 and 4). Here, we are faced with using the model to reproduce the amount of sediment deposited in the dam. Mathematical relationship: VGully − VT ransit = VDam (16) Based on the preamble at the start of this sub-section. Let, 2068263.802VGully = 840127.346VDam Therefore, VDam = ( 2068263.802 840127.346 ) ×γ ⇒ VDam = 2.4618VGullyγ (17) Where: γ is the smoothing parameter or correction factor with value ranging as (0 < γ < 1). %Error = VDamPredicted VDam × 100% (18) Where: VDamPredicted refers to the expected volume of sedi- ment obtainable at the dam that would correspond to the volume computed and VDam is the final volume calculated at the dam’s end. The smoothing parameter is the correction term applied to correct unmeasured external factors such as channel gradient, channel roughness, or corrosion. It helps in computing the volume of sediment in the dam for every combination of hy- perparameters specified by evaluating against a specified (Dam volume constant of 840127.346 m3). The appropriate value of the correction factor can either be learned by trials and error or through cross-validation. This study adopted a cross-validation sequence combining (0.1 and 0.2 step size of 0.005) for hy- perparameters. Table 10 showed the percentage error and the predicted volume of the dam at each iteration of Table 10, reveals the predicted volume of sediment by the ANFIS model. A grid search predicted value of 842895.8547 m3 obtained at 0.165 yielded the best smoothing value for pre- dicting volume of sediment present in the dam with a percent- age error of -0.3295344%. The original volume of sediment computed at the dam was 840127.346 m3 being used as con- stant all through. Initially, the error rate decreases as increases until it attains an optimal value of 0.165. By iterating beyond this value, the error rate starts increasing in the opposite direc- tion. 3.2. Sediment Loss-in-Transit Sediment loss-in-transit per-unit volume is the difference between the calculated amount of sediment exited (deposited) from the gullies and the amount of sediment gained by the dam. This concept forms the basis of the proposed model. Equation 18 expresses another form of equation 15, obtained by making the volume of sediment loss-in-transit the subject of the for- mula of the relation. The deduction from the model shows that it is capable of estimating the computed volume of sediment loss-in-transit by using Equation 19. VT ransit = VGully − VDam (19) Total volume of soil loss (sediment) from gully = 2068263.802 m3= VGully 11 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 12 Figure 8. Flow diagram of ANFIS training process Total volume of bed-load sediment gained by dam = 840127.346 m3= VDam Total volume of soil loss-in-transit (difference) = 1228136.456 m3= VT ransit Note: the difference is the volume of sediment regarded as ”loss-in-transit,” which could not be accounted for at the dam’s end during field campaigns. Therefore, we are faced with the task of using the model to predict the volume of (sediment) loss- in-transit given an array or matrix of input parameters. The proposed ANFIS model was trained to reproduce the Table 10. Percentage error and predicted volume of dam at each iteration of γ γ VDam (m3) VDamPredicted (m3) %Error 0.100 840127.346 510845.9726 39.19422157 0.105 840127.346 536388.2712 36.15393265 0.110 840127.346 561930.5698 33.11364373 0.115 840127.346 587472.8684 30.0733548 0.120 840127.346 613015.1671 27.03306588 0.125 840127.346 638557.4657 23.99277696 0.130 840127.346 664099.7643 20.95248804 0.135 840127.346 689642.0629 17.91219912 0.140 840127.346 715184.3616 14.8719102 0.145 840127.346 740726.6602 11.83162127 0.150 840127.346 766268.9588 8.791332352 0.155 840127.346 791811.2575 5.751043431 0.160 840127.346 817353.5561 2.710754509 0.165 840127.346 842895.8547 -0.3295344** 0.170 840127.346 868438.1533 -3.369823334 0.175 840127.346 893980.452 -6.410112256 0.180 840127.346 919522.7506 -9.450401177 0.185 840127.346 945065.0492 -12.4906901 0.190 840127.346 970607.3479 -15.53097902 0.195 840127.346 996149.6465 -18.57126794 0.200 840127.346 1021691.945 -21.61155686 ** - Optimum smoothing parameter volume of sediment loss-in-transit at 10 randomly selected data points from the test data for (predicted gully volume and pre- dicted dam volume) each, respectively. The results generated by the model for the predicted gully volume, the predicted dam volume, and the volume of sediment loss-in-transit including the final summation for each of the last three column variables are presented in Table 11. From the 11 randomly selected points tested, the was calcu- lated using the mathematical relationship of equation 15. Hence, for a predicted gully volume of 97318.44 m3, a calculated (pre- dicted) volume of 39530.46 m3 would be deposited in the dam. Then, predicted volume loss-in-transit is therefore given as (97318.44 - 39530.46) m3 = 57787.98 m3. This shows that the proposed model is capable of generation output for every in- stance where predicted gully sediment volume and dam’s sedi- ment volume exist. 4. Conclusion This work was carried out to examine the capability of the ANFIS hybrid model to predict sediment volume supplied from upstream by two prominent gullies through the Ikpoba river channel and the amount of sediment accumulated (gained), as much as can be accounted for at the Ikpoba dam’s end. Three- year consecutive field campaigns at the gullies’ location and dam’s end enabled us to prepare, refine, normalise, and modify the input parameters for optimum model performance. We first applied the ANFIS model to reproduce the volume of sediment deposited in the dam as calculated and proposed a mathematical relationship that incorporated the ANFIS model 12 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 13 Figure 9. Regression (left) and Validation (right) plots Table 11. Predicted volume loss-in-transit from a random selection of 10 data points index Rainfall (mm) Slope (mm) Depth (m) Velocity (m/s) P. size (µm) Volume (m3) Predicted Gully Volume (m3) Predicted Dam Volume (m3) Volume Loss-in- Transit (m3) 100 80.280 38.545 7.908 0.827 36.934 7672.287 7926.644 3219.779 4706.865 186 202.963 38.118 6.522 1.412 41.182 10492.945 11310.07 4594.116 6715.953 189 198.573 45.008 6.811 1.791 40.199 10129.345 10729.69 4358.367 6371.321 210 176.937 37.126 5.928 1.210 39.141 11084.715 10349.64 4203.994 6145.649 159 193.554 39.714 6.411 1.463 38.102 9951.850 10079.82 4094.394 5985.429 13 84.328 53.774 8.771 1.823 38.317 7544.943 7750.151 3148.088 4602.063 131 203.851 57.883 8.819 1.505 45.722 11620.630 12271.57 4984.675 7286.895 205 171.784 42.867 8.170 0.584 44.885 12359.551 11781.39 4785.563 6995.822 51 78.476 60.745 9.439 1.320 36.152 7370.700 7215.381 2930.866 4284.515 52 82.163 64.956 9.576 1.656 39.972 8256.199 7904.086 3210.616 4693.470 SUM 97318.44 39530.46 57787.98 to generate output in form of a computed volume of sediment loss-in-transit as a function of the normalised gully sectional sediment loss and dam’s sediment accumulation. Our investi- gations showed that the ANFIS model could estimate sediment deposited in the dam effectively while, at the same time, it was able to determine the volume of sediment loss-in-transit using the established mathematical equation. The best ANN model with the least error and the most accurate predictive result was selected and presented. However, we made some assumptions. For example, we assume no silt (sediment) escapes from the dam by any means, (that is, the dam traps all the sediment be- hind it). The combined volume of sediment exited from the two gullies was treated as stagnant to be able to arrive at a nu- merical value. The volume of sediment deposited in the dam is treated as being localized (i. e. confined); such that numeri- cal values can be obtained for location-based sediment volume actualisation. For these reasons, sediment transport equations were not incorporated. Furthermore, rather than converting the estimated sediment volume to weight equivalent, we left it in meters cubed to save processing time and computational space. 4.1. Recommendations According to our discoveries in this work, we recommend the following: Due to the fast rate of siltation, there is an urgent need to dredge the dam. At present, sediment impact has rendered the Ikpoba dam a failed infrastructure, hence we propose a holistic desilting or dredging for the rejuvenation of the dam to return it back to its original purpose of providing domestic water for the teeming population. Gully remediation action should be prioritize and attracts necessary attention from relevant government agencies and decision- 13 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 14 makers to enhance a safe environment devoid of land degrada- tion. Acknowledgements The authors are grateful to Iterlen Industrial Services Ltd, Km 1 Effurun-DSC Express Road, Ugbolokposo, Delta State for the release of the Hi-Target echo-sounder and accessories, the Department of Geomatics, University of Benin, for the as- sistance with the Total Station equipment used for data collec- tion, the Department of Civil Engineering for allowing the lab- oratory to be used for soil analysis. The authors are also grate- ful to the Federal Government of Nigeria for providing part of the funding for this research through the tertiary education trust fund (TETFUND) initiative with grant No: REG/SSA/P.15799/83 (2018 intervention). References [1] S. Chakraverty & S. Mall, “Artificial Neural Networks for Engineers and ScientistsSolving Ordinary Differential Equations”, CRC Press 168 (2017) 80. [2] S. Akram & R. Hossien, “Improving one-dimensional pollution disper- sion modeling in rivers using ANFIS and ANN-based GA optimized mod- els”, Environmental Science and Pollution Research (2018). [3] V. Umarania, A. Juliana & J. Deepa, “Sentiment Analysis using various Machine Learning and Deep Learning Techniques”, J. Nig. Soc. Phys. Sci. 3 (2021) 308. [4] C. I. Udeze, I. E. Eteng & A. E. Ibor, “Application of Machine Learning and Resampling Techniques to Credit Card Fraud Detection” J. Nig. Soc. Phys. Sci. 4 (2022) 769. [5] B. N. Hikona, G. G. Yebpellaa, L. Jafiyab & S. Ayuba, “Preliminary In- vestigation of Microplastic as a Vector for HeavyMetals in Bye-ma Salt Mine, Wukari, Nigeria”, J. Nig. Soc. Phys. Sci. 3 (2021) 259. [6] G. O. Aigbadon, A. Ocheli, & E. O. Akudo, “Geotechnical evaluation of gully erosion and landslides materials and their impact in Iguosa and its environs, southern Nigeria”, Environ Syst Res 10 (2021) 36. [7] J. C. Egbueri, O. Igwe & C. O. Unigwe, “Gully slope distribution char- acteristics and stability analysis for soil erosion risk ranking in parts of southeastern Nigeria: a case study”, Environ Earth Sci 80 (2021) 292. [8] J. O. Ehiorobo & O. C. Izinyon, “Monitoring Gully Formation and De- velopment for Effective Remediation and Control”, TS09I - Engineering Surveying, 5919. FIG Working Week 2012. Knowing to manage the ter- ritory, protect the environment, evaluate the cultural heritage Rome, Italy (2012) 6. [9] J. O. Ehiorobo, & O. C. Izinyon, “Monitoring of Soil Loss from Erosion Using Geoinformatics and Geotechnical Engi- neering Methods”. (2011). Retrieved June 10, 2021, from https://www.fig.net/resources/proceedings/2011. [10] O. Igwe, U. I. John, O. Solomon & O. Obinna., “GIS-based gully erosion susceptibility modeling, adapting bivariate statistical method and AHP approach in Gombe town and environs Northeast Nigeria”, Geoenviron- mental Disasters 7 (2020) 32. [11] S. E. Okonofua & N. O. Uwadia, “Evaluating Factors Responsible for Gully Development at the University of Benin. Scholarlink Research In- stitute Journals”, Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 4 (2013) 5. [12] S. Dahiru, “Nigeria Erosion and Watershed Management Project”, (NEWMAP). (2020). Retrieved July 20, 2021, from https://newmap.gov.ng/index.php. [13] World Bank, “Nigeria Erosion and Watershed Manage- ment Project (NEWMAP) Additional Financing” (2017). https://documents1.worldbank.org/curated/en/193161525194153230. Deposited July 10, 2022. [14] N. Q. Sultan, E. Isa & R. M. Hossien, “Optimizing ANFIS for sediment transport in open channels using different evolutionary algorithms”, Jour- nal of Applied Research in Water and Wastewater 4 (2017) 1. [15] X. Zhang, J. Fan, Q. Liu & D. Xiong, “The contribution of gully ero- sion to total sediment production in a small watershed in Southwest China”, Physical Geography 39 (2018) 3. [16] Y. Guan, S. Yang, C. Zhao, H. Lou, K. Chen, C. Zhang & B. Wu, “Moni- toring long-term gully erosion and topographic thresholds in the marginal zone of the Chinese Loess Plateau”, Soil and Tillage Research 205 (2021) 104800. [17] I. Ionita, M. A. Fullen, W. Zgłobicki & J. Poesen, “Gully erosion as a natural and human-induced hazard”, Nat Hazards 79 (2015) 1. [18] C. Jiang, W. Fan, N. Yu & E. Liu, “Spatial modeling of gully head ero- sion on the Loess Plateau using a certainty factor and random forest model”, Science of the Total Environment 783 (2021). [19] I. Marzolff, J. Poeen & J. B. Ries, “Short to medium-term gully devel- opment: human activity and gully erosion variability in selected Spanish gully catchments”, Landform Anal 17 (2011) 111. [20] P. K. Shit, G. Bhunia & R. Maiti, “Morphology and development of se- lected Badlands in South Bengal (India)”, Indian Journal of Geography and Environment 13 (2014) 161. [21] G. Chen, “A simple way to deal with multicollinearity”, Journal of Ap- plied Statistics 39 (2012) 9. [22] J. Poesen, J. Nachtergaele, G. Verstraeten & C. Valentin, “Gully erosion and environmental change: Importance and research needs”, Catena 50 (2003) 91. [23] A. Majhi, J. Nyssen & A. Verdoodt, “What is the best technique to es- timate topographic thresholds of gully erosion? Insights from a case study on the permanent gullies of Rarh plain, India”, Geomorphology 375 (2021) 107547. [24] J. S. R. Jang, “ANFIS: adaptive-network-based fuzzy inference system”, IEEE Trans. Syst. Man Cybern. 23 (1993) 665. [25] J. S. R. Jang, “Input selection for ANFIS learning” In Proceedings of the Fifth IEEE International Conference on Fuzzy Systems (1996) 1493. [26] J. S. R. Jang & E. Mizutani, “Levenberg–Marquardt method for ANFIS learning”, In Fuzzy Information Processing Society, Biennial Conference of the North American (1996) 87. [27] D. K. Ghosea, S. S. Pandab & P. C. Swainc, “Prediction and optimization of runoff via ANFIS and GA”, Alexandria Engineering Journal 52 (2013) 2. [28] T. Gokmen, O. Serhan & P. S. Vijay, “Fuzzy logic algorithm for runoff- induced sediment transport from bare soil surfaces”, Advances in Water Resources 26 (2003) 1249. [29] A. B. Dariane & S. H. Azimi, “Forecasting streamflow by combination of genetic input selection algorithm and wavelet transform using ANFIS model”, Hydrolog. Sci. J. 61 (2016) 585. [30] A. Mustafa, “Evaluation of different types of artificial intelligence meth- ods to model the suspended sediment load in Tigris River”, MATEC Web of Conferences 162 (2018) 2. [31] H. M. Azamathulla & A. A. Ghani, “ANFIS-based approach for predict- ing the scour depth at culvert outlets”, Journal of Pipeline Systems Engi- neering and Practice 2 (2011). [32] H. M. Azamathulla, A. A. Ghani & S. Y., Fei, “ANFIS-based approach for predicting sediment transport in clean sewer”, Applied soft computing 12 (2012) 3. [33] H. M. Azamathulla, K C. Chun, A. A. Ghani, A. Junaidah, N. A., Zakaria & Z. A. Hasan, “An ANFIS-based approach for predicting the bed load for moderately sized rivers”, Journal of Hydro-environment Research 3 (2009) 35. [34] C. I. Ikhile, “Geomorphology and Hydrology of the Benin Region, Edo State, Nigeria”, International Journal of Geosciences 7 (2016). [35] C. N. Akujieze, “Effects of Anthropogenic Activities (Sand Quarrying and Waste Disposal) on Urban Groundwater System and Aquifer Vul- nerability Assessment in Benin City, Edo State, Nigeria”. PhD Thesis, University of Benin, Benin City, Nigeria (2004). [36] P. Hjorth & L. Bengtsson, “Large Dams, Statistics and Critical Review”. In: Bengtsson L., Herschy R.W., Fairbridge R.W. (eds) Encyclopedia of Lakes and Reservoirs, Encyclopedia of Earth Sciences Series, Springer, Dordrecht (2012). [37] C. N. Ezugwu, B. U. Anyata & E. O. Ekenta, “Estimation of The Life of Ikpoba River Reservoir”, International Journal of Engineering Research & Technology (IJERT) 2 (2013) 8. [38] Edo State Urban Water Board, Construction information of Ikpoba Dam Archive (2007). 14 Oladosu et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1028 15 [39] S. O. Oladosu, L. M. Ojigi, V. E. Aturuocha, C. O. Anekwe & R. Tanko, “An investigative study on the volume of sediment accumulation in Tag- wai dam reservoir using bathymetric and geostatistical analysis tech- niques”, SN Applied Sciences 1 (2019) 492. [40] International Hydrographic Organization (IHO) Standards for Hydro- graphic Surveys 6th Edition IHO Publication (2020) 44. [41] B. Selma, S. Chouraqui & H. Abouaı̈ssa, “Optimization of ANFIS con- trollers using improved ant colony to control an UAV trajectory tracking task”, SN Appl. Sci. 2 (2020) 878. [42] M. Sugeno, T. Kang & G. Kang, “Structure Identification of Fuzzy Model. Fuzzy Sets and Systems”, 28 (1988) 9. [43] T. Takagi & M. Sugeno, “Fuzzy Identification of Systems and Its Appli- cation to Modeling and Control”, IEEE Transactions on Systems, Man, and Cybernetics, SMC-15 (1985). [44] A. Tarno, Rusgiyono & Sugito, “Adaptive Neuro Fuzzy Inference System (ANFIS) approach for modeling paddy production data in Central Java”, IOP Conf. Series: Journal of Physics: Conf. Series 1217 (2019) 012083. [45] N. A. Adnan, H. Maizah & R. A. Adnan, “Comparative study on some methods for handling multicollinearity problems”, Mathematika 22 (2006) 2. [46] M. Kutner, C. J. Nacctsheim & J. Neter, “Applied Linear Regression Model”. Technometrics 26 (2004) 4. [47] D. W. Marquardt, “Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation”, Technometrics 12 (1970) 59. [48] D. O’brien & P. S. Scott, “Correlation and Regression”, in Approaches to Quantitative Research-A guide for Dissertation Students, Ed, Chen, H, Oak Tree Press (2012). [49] R. M. O’brien, “A Caution Regarding Rule of Thumb for Variance Infla- tion Factor”, Qual Quant. 41 (2007) 673. 15