Prediction of scour hole characteristics caused by water jets using metaheuristic artificial bee colony-optimized neural network and pre-processing techniques

B

the plunge pool width of (m)

d

the circular nozzle diameter (m)

D₅₀

median diameter of the sediment particles (m)

F₀

densimetric Froude number (–)

acceleration due to gravity (m s⁻²)

t_d

tailwater depth (m)

H

impingement length (m)

t

time (s)

T

relative tailwater depth (t_d/d)

U₀

jet velocity at the circular nozzle (m s⁻¹)

Δ_m

maximum ridge height (m)

x₁+x₂

scour hole length (m)

ε_m

maximum scour depth (m)

θ

impact angle (angle of jet to the water surface) (°)

ABC

artificial bee colony

ANN

artificial neural network

ANFIS

adaptive neuron-fuzzy inference system

DWT

discrete wavelet transform

EMD

empirical mode decomposition

EEMD

ensemble empirical mode decomposition

GEP

gene expression programming

GMDH

group method of data handling

GBM

gradient boosting machines

GP

genetic programming

LGP

linear genetic programming

ML

machine learning

PSO

particle swarm optimization

REMD

robust empirical mode decomposition

SVM

support vector machines

VMD

variational mode decomposition

Scour is a crucial subject in the application of hydraulic engineering. Scour is a common phenomenon that lowers the riverbed level due to sediment evacuation caused by the erosive activity of a moving stream (Karbasi & Azamathulla 2017). It happens when hydrodynamic shear forces surpass the critical shear stress of sediment. The process appears in cohesive materials such as clay and highly eroded rocks. In other words, scour starts at the plunge pool when the bed shear stress applied by the underwater jet surpasses the critical bed shear stress for bed sediments. Scour can gradually degrade a structure's foundation and cause a devastating threat by decreasing support. Because of this, the prediction of the local scour forming in hydraulic structures has great significance. The engineering treatment of hydraulic structures provided after scour formation is costly. As a result, reliable estimation of scour depth and scour hole slopes can reduce failure risks. Also, understanding the water jets that create local scour downstream is critical to maintaining the safety and integrity of the hydraulic structure.

Numerous studies were conducted (Sarkar & Dey 2004; Pagliara et al. 2006, 2008; Aderibigbe & Rajaratnam 2010; Bombardelli et al. 2018; Kartal 2018; Kartal & Emiroglu 2021, 2022, 2023; Palermo et al. 2021) on jet scours in downstream pools but, Rouse (1939) was the pioneer of the study of scour caused by water jets. Most studies were investigated with circular nozzles in literature; however, the square-shaped, rectangular, and elliptical outlet structures were also utilized in water resources engineering (Canepa & Hager 2003; Kartal & Emiroglu 2023). Kartal & Emiroglu (2021) investigated the water jets scour and found that the water jets scour reduces if the plates are used in the water jets. Kartal & Emiroglu (2022) studied the scour morphology of the impinging jets. They stated that the slope upstream and downstream of the scour hole are nearly equal.

The dimensions of a scour hole are often determined using empirical formulas whose validity is limited to experimental conditions. Since developing physical models are exhausting, the scour hole parameters were used in this paper with previously conducted experimental runs in the literature (Kartal 2018; Kartal & Emiroglu 2021, 2022, 2023) to validate and convince the results were obtained. The safety of the downstream apron is threatened by downstream scour induced by the scour of water jets which can result in the hydraulic structures' failure. Therefore, sufficient preventive measures can only be engineered with a full recognition, location and magnitude prediction or scour extent at downstream. The scour event downstream of a steady or unsteady apron is highly complex because of the change of flow characteristics in the sediment layer over time. The scour depth is a function of jet angle, flow velocity, impingement distance, tailwater depth, median diameter of sediment, operating time, nozzle diameter, and many other parameters.

The scour hole development in the vertical dimension is faster than longitudinal. At the initial stage, sediment suspension is usually the only sediment transport mode. However, when the vertical dimensions of the scour hole decrease, the sediment transport mode becomes a combination of suspended and bed loads. As the scour increment rate nears zero, the equilibrium scour conditions are achieved asymptotically. It is challenging to estimate scour due to turbulent flow in an open channel, irregular and time-varying geometry, and complex sediment transport (Dey & Sarkar 2006).

Estimating the maximum scour depth with reasonable accuracy is important for properly managing, designing, and planning hydraulic structures. Scour is a dynamic and complex event influenced by several parameters which are related and difficult to comprehend. Nevertheless, deterministic models with different complexity degrees have been utilized to model the scour process with varying degrees of accuracy. As stated above, several researchers have examined scour in the control structures and suggested empirical equations for estimating scour dependent on laboratory experiments under different conditions of time, flow, tailwater, and sediment, etc. They are mainly based on experimental runs to examine scour through physical modeling.

Pal & Goel (2006, 2007) implemented SVMs successfully for estimating the final depth ratio and discharge for trapezoidal, circular, and semi-circular channels and reported good performance compared to empirical relationships. Due to the scour complexity, the proposed empirical formulas based on experimental runs are not precise enough to estimate the scour depth. A new era of data mining approaches, such as machine learning (ML) models for modeling and simulating various hydrological phenomena, has evolved over the past several decades with the development of high-speed processors and novel soft computing techniques (Ikram et al. 2022; Mostafa et al. 2023) The use of hybrid models and artificial intelligence (AI) for engineering applications has also been the subject of a great deal of research with success (Ikram et al. 2023a, 2023b). Besides, AI model creation is fast due to its straightforward architecture and minimal requirements for experimental data collection (Adnan et al. 2023a). Several AI methods such as gene expression programming (GEP), artificial neural networks (ANNs), genetic programming (GP), group method of data handling (GMDH), and model tree (MT) were applied to calculate scour in the hydraulic structures (Lee et al. 2007; Azamathulla et al. 2011; Pal et al. 2012; Akib et al. 2014; Najafzadeh et al. 2016; Shakya et al. 2022). As hydraulic model studies must be undertaken, which takes time and money, there is not currently suitable alternative method except for some soft computing models (Lashkar-Ara et al. 2016). ANNs have the usefulness of being practicable to a wider range of hydraulic conditions than traditional empirical models, which eliminates the need for the designer to choose the appropriate equation for the expected hydraulic conditions. Therefore, this study represents a significant advancement in the field of soft computing. Numerous AI techniques, including as ANNs (Kaya 2010), adaptive neuron-fuzzy inference system (ANFIS) (Farhoudi et al. 2010), decision trees (Etemad-Shahidi & Ghaemi 2011), linear genetic programming (LGP) (Azamathulla et al. 2011), GEP (Moussa 2013) and ML methods have recently been used for modeling difficulties in scour prediction. Liriano & Day (2001) stated that using ANN in scour prediction could result in a miscellaneous tool for engineers. Karbasi & Azamathulla (2017) used GEP, support vector regression (SVM), ANFIS, grouping method of data handling (GMDH) neural network and to estimate maximum scour depth at the downstream for the sluice gates. Their findings revealed that the ANFIS, ANN, GEP, and SVR approaches agreed well with the observed data. Karaboga (2005) introduced the artificial bee colony (ABC) algorithm and used to simulate the foraging behavior of a bee colony and to optimize numerical problems. Although several studies are based on ABC, there is limited study in hydraulic engineering applications. Therefore, the ABC was studied to estimate scour characteristics formed by oblique circular water jets in this study. This approach was chosen to leverage the capabilities of the feed-forward neural network (FFNN), known for its ability to represent intricate and non-linear relationships precisely. Specifically, the model was used to depict the scour hole characteristics caused by water jets, which have been notoriously difficult to capture using traditional linear methods accurately. In order to improve the ability of a regular FFNN to predict water jets, the ABC nature-inspired optimization algorithm was utilized to optimize the parameters of the FFNN. The ABC-FFNN algorithm employed in the study was favored for its capability to handle noisy data, tackle non-linear and intricate problems, and flexibly model the correlation between various datasets. In addition, the ABC-FFNN hybrid model was combined with the VMD and EEMD signal decomposition approaches to evaluate the water jet prediction accuracy of the EEMD-ABC-FFNN and VMD-ABC-FFNN models. Local scour formed by circular water jets in the downstream pool were analyzed for high F₀ (densimetric Froude number) values (34.7–159.22). The impact angle (θ), relative tailwater (T=t_d/d), impingement distance (H), nozzle diameter (d) and densimetric Froude number (⁠⁠) on scour characteristics were analyzed. To the best of our knowledge, numerous studies have introduced with the use of ABC in hydraulic engineering, but no study has conducted its use for water jet scour prediction. VMD and EEMD data pre-processing techniques can transform signals into intrinsic mode functions (IMFs) that reflect the raw data's local properties. Components representing the main dataset are obtained and data noise is removed. In addition, the trends and features in the data are modeled more comprehensively, allowing the prediction model to be developed. The effect of VMD and EEMD methods on the estimation performance of the established model varies according to the data set and data type. These methods can improve the performance of AI models by reducing residuals in the data and modeling each IMF separately, reducing noise and grouping different frequencies (Lei et al. 2019; Xie et al. 2020). The current study aimed to investigate the local scour depth using metaheuristic ABC-optimized feed-forward neural network (ABC-FFNN) and pre-processing techniques. In order to obtain this goal, the accuracy of the ABC and pre-processing techniques were compared with those of the scour depth obtained from the previous studies (Kartal 2018; Kartal & Emiroglu 2021, 2022, 2023).

To analyze scour due to water jets, ABC, the FFNN metaheuristic logarithms, variational mode decomposition (VMD), ensemble empirical mode decomposition (EEMD), and Rank Analysis were applied.

The effectiveness of the Metaheuristic ABC-Optimized Neural Network and Pre-processing Techniques for modeling scour in water jets was evaluated using the experimental data sets conducted by (Kartal 2018; Kartal & Emiroglu 2021, 2022, 2023). Experimental data set has 144 runs with six nozzle diameter (10, 15, 20, 28, 34, 40 mm) and three impact angles (30°, 45°, 60°), four impingement distances (10, 15, 20, 30 cm) were get from the studies of them. Median diameter of sand and tailwater depth was kept constant. All experiments were conducted in unsubmerged flow conditions.

The algorithm was introduced in 2005 by Karaboga (2005). It is modeled from the behavior of a honey bee colony. It can be used for smart system models due to its several features (communication, task selection, foraging, decision-making of the collection, etc). Every model for a particular task describes every behavior. By performing a series of movements referred to as a waggle dance, the bees communicate information about the location of food sources. The queen produces all the eggs in a bee honey colony. It is classified into three groups: employed bees, looker bees, and scouts. The utilized bees are located in the first colony part, whereas the on-lookers are in the second part. The employed bee's source of food consumed by the bees will be scouted to search for new food sources randomly (Karaboga & Basturk 2007, 2008).

Metaheuristic algorithms are applied techniques to various problems to obtain near-optimal solutions at a competitive computation cost-efficiently (Hemeida et al. 2020). They are intelligent approaches to handling various complex issues efficiently. Deterministic methods execute analyses based on their strong analytical capabilities. However, heuristic methods are typically more adaptable and less likely to produce generic or confusing solutions throughout the implementation phase (Adnan et al. 2023b). Such methods depend on distinct agents, ensure global population optimization, and avoid suboptimal local optimization. The most important key in designing meta-heuristics is the ability to conduct large-scale exploitation and exploration. Meta-heuristics fall into two categories: single solution-based methods and population-based methods. While single solution-based methods such as tabu search (Elhedhli et al. 2014), emulated annealing (Liu et al. 2017), etc., population-based methods contain evolutionary methods such as particle swarm optimization (PSO) (Rathore & Sharma 2017), ABC optimizations (Alatas 2010), cuckoo search algorithm (CS) (Shehab et al. 2017). PSO was introduced as a global optimization method in 1995 (Sharma & Pandey 2016; Morra et al. 2018). PSO employs to model the loose and unpredictable behavior of flocks of birds to get a solution for the optimization problem.

The scour prediction performance of models is compared with ABC-FFNN, EEMD-ABC-FFNN, and VMD-ABC-FFNN hybrid algorithms. In the selection of ML algorithms, 80% of the data were utilized for training, while %20 of data was used for testing (Katipoğlu 2022). In addition, five parameters were used as an input.

EMD presents adaptive instantaneous frequency-based IMFs, extensively deployed to flexibly analyze multichannel data with linear and non-stationary time series (Sarıgöl & Katipoğlu 2023). Every IMF is representative of a simple oscillation in the signal. The frequencies and amplitudes of IMFs are not steady but can vary with time. If x(n) is stated as a time series:

Here, r_N(t): residual of signal, C_i(t): ith IMF x(t) (Kedadouche et al. 2016).

Even though EMD is extensively employed in non-stationary and/or non-linear signal analysis, its decomposition results are subject to various problems due to mode mixing. The EMD ensemble method was developed to eliminate this problem. When repeatedly decomposing the signal into IMFs with the EMD method, finite-amplitude white noise is injected into the original signal. The averages of the IMFs produced from each trial are denoted as the IMFs of the EEMD method. In this way, the mode mixing problem is canceled by EEMD (Wu et al. 2009; Zhang et al. 2010).

Individual ranking values were calculated within this study to determine the best model from the models in which many statistical indicators were employed. A rank was assigned to each performance parameter, the best-performing model was placed third, and the lowest-performing model was given the first rank. While the model with the highest overall ranking value is considered the best, the model with the lowest is regarded as the worst (Zhang et al. 2020).

In this section, the developed approaches for scour prediction are evaluated, and statistical parameters for accuracy assessment are given based on the scour characteristics in Figure 1.

The estimation success of the model results designed in Table 1 was evaluated according to various statistical parameters. The model with the smallest error coefficient, the Bias Factor and R² value closest to 1 was evaluated as the best. Accordingly, the AI predictions with Models 1, 2 and 3 are compared. As seen from Table 1, the ABC-FFNN model produced the most successful predictions. The EEMD-ABC-FFNN hybrid algorithm showed the weakest predictions in the M2 combination, while the VMD-ABC-FFNN hybrid algorithm showed the weakest predictions in the M1 and M2 combination. Furthermore, out of all the input combinations, the ABC-FFNN algorithm with Model 1 structure yielded the most accurate predictions, with R² values of 0.778 for training and 0.680 for testing.

The study presents the results of scour prediction in non-cohesive sediments by oblique circular jets through experimental observations and modeling analysis. The present study was carried out to Metaheuristic ABC-FFNN and pre-processing techniques in scour prediction due to water jets using experimental data sets. The Metaheuristic ABC-FFNN and pre-processing techniques produced satisfactory results compared to backpropagation with experimental data for Kartal & Emiroglu (2021, 2022, 2023) data sets. Furthermore, significant differences in scour depth can affect the estimation of scale-up, flow, geometry, and material conditions. Nevertheless, the results of this study may encourage the use of EMD, EEMD, FFNN, VMD, ABC and pre-processing techniques in predicting the scour in water jets. It is seen that the prediction performance of all models is satisfactory. However, the ABC-FFNN algorithm showed more accurate results, the albeit slightly. It is also seen that the box structure of the prediction results of the EEMD-ABC-FFNN algorithm in the training phase and the ABC-FFNN algorithms in the testing phase is the closest to the real data. In M3 model combination predictions, the ABC-FFNN algorithm in training phase and the VMD-ABC-FFNN algorithm in the test phase showed the best results the ABC-FFNN model produced the most successful predictions, while the EEMD-ABC-FFNN model showed the weakest predictions. In addition, among all input combinations, the ABC-FFNN algorithm with Model 1 structure with training: 0.778 and testing: 0.680 produced the most accurate predictions. Although the model produced good estimation, it has some drawbacks including being a complex and have need of more parameters for training. In order to train the network and verify its efficacy, a comprehensive data set must be provided in further investigation.

Special thanks to Firat University Scientific Research Projects (FÜBAP: MF.17.38) Unit for funding.

Each author participated in the concept and design of the study and contributed the draft of manuscript. V.K. and M.E.E. prepared the material, collected, and analyzed the data. E.K. drafted and edited the manuscript. O.M.K. conducted the analysis. All authors read and approved the final manuscript.

Firat University Scientific Research Projects (FUBAP) Unit funded the present study with the project number MF.17.38.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.