Modeling of the oxygen aeration performance efficiency of gabion spillways

Dissolved oxygen (DO) concentration is essential for determining the health of water bodies. The oxygen content of water is depleted by naturally occurring biological and chemical processes, which puts more stress on aquatic life in bodies of water and reduces DO levels (Baylar & Emiroglu 2004). Reaeration increases the oxygen in the water by drawing air from the surrounding atmosphere. However, for the drop structures like weirs, aeration is connected to form, roughness, plunging velocity, and geometry (Luxmi et al. 2022). By altering the flow using fluidic structures such as hydraulic jumps and hydraulic drops, it is possible to improve aeration.

Hydraulic structures enhance the amount of DO in a stream by self-aeration, even though the water is in contact with the structure for only a fraction of the time (Baylar et al. 2011). The primary cause of this faster oxygen transfer is the extraction of air and its penetration into the flow in the form of an enormous number of tiny bubbles. These micro air bubbles improve the surface area accessible for oxygen transfer, facilitating greater oxygen exchange (Baylar & Bagatur 2000). Gabion spillways are widely employed in an earthen dam, preservation of soil work, retaining structures, river-training work at the bend, and other projects. The gabion is stable, flexible, and simple to construct without losing structural integrity.

Furthermore, they can withstand considerable differential settlements, if any. If materials that may be found locally are readily accessible in large quantities, gabion structures will be a cost-effective solution. It is made up of a porous substance surrounded by a grid of metal wires and filled with coarser materials of various sizes and shapes. Its porosity assists in water drainage, lowering the water load behind the building. It is also possible to design and use stepped spillways in the gabion type.

Additionally, the flow over the steps cascades down the spillway face, causing aeration (Salmasi et al. 2012). Two types of flow over the stepped spillways are defined by Chanson (2002). They are (a) aerated flow and (b) non-aerated flow. Gabions can reduce water pressure by preserving rocks' permeability and flexibility (Aal et al. 2019). Zhang & Chanson (2016) classified flow over stepped spillways into three hydraulic regimes: skimming flow, nappe flow, and transition flow. The research concluded that a stepped weir gives good results compared to a flat one (Wuthrich & Chanson 2015). Wormleaton & Soufiani (1998) studied triangular labyrinth weirs and rectangular labyrinth weirs' oxygen aeration potential. In Africa, Sahel gabion spillways are the most normal spillway (Peyras et al. 1992). Kells (1994) addressed how discharge over the crest and critical depth relates to energy dissipation over gabion-stepped weirs. Chinnarasri et al. (2008) performed experimental research on the sensitivity of hydraulic performance and the properties of the material contained in gabions. The gabion spillway will also produce turbulence, enhancing aeration and enabling the organic materials' aerobic decomposition. It will also help aquatic life to move and migrate more easily (Luxmi et al. 2022). Soft computing data-driven techniques are applied to simulate the effectiveness of oxygen aeration at barrages, spillways, gabion spillways, Parshall flumes, Montana flumes, etc. Soft computing approaches are widely utilized since they are available, have built-in intelligence, and are dependable. In addition, they lessen the scale effect and prevent model creation. In the fields of hydraulic engineering and water resources, a wide variety of soft computing approaches have been used. Researchers have recently expressed interest in applying machine learning (ML)/soft computing approaches to forecast the aeration effectiveness of gabion weirs with and without steps (Luxmi et al. 2022; Srinivas & Tiwari 2022; Verma et al. 2022). Baylar et al. (2011) also studied the prediction of oxygen transfer efficiency in aeration stepped cascades using gene expression programming (GEP) modeling. Aeration efficiency at the Labyrinth Weir was investigated experimentally and through modeling (Singh et al. 2021). Kumar et al’s. (2022) work involves stimulating the oxygen transfer abilities to plunge jets using fundamental flow patterns or flow characteristics and forecasting the volume of oxygen transfer coefficient using modeling approaches such as artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS), multivariate adaptive regression splines (MARS), MNLR, and generalised regression neural network (GRNN). Kumar et al. (2022) aim to investigate the impact of jet velocity, jet length, water depth, and jet thickness of plunging hollow jets in oxygenating the water in the aeration tank. Empirical correlations are proposed for the determination of the volumetric oxygen transfer coefficient, K_LA, based on jet velocities and jet kinetic powers.

The OAPE is the oxygen aeration performance efficiency, I_d is the intensity of DO downstream of the fluidic device, I_u is the intensity of DO upstream of the fluidic device, and I_S is the saturation intensity of DO. When the downstream water is supersaturated (I_S < I_d), then the OAPE > 1. Similarly, when full oxygen transfer reaches saturation value, then OAE = 1 and OAPE = 0 represent no oxygen transfer.

The importance of the present study was to forecast and examine the usefulness of the gabion spillways by estimating the oxygenation aeration performance efficiency (OAPE₂₀) between the interface of air and water surface overflow and seepage through the previous spillway body. The novelty of the present work had many dimensions, as the current study outlined the evaluation of the OAPE₂₀ by conducting experimental tests varying with dimensionless parameters, such as the Reynolds number (Re), Froude number (Fr), the ratio of the gabion means size particle to its length (d₅₀/L), and porosity (n) of the gabion materials. Second, the OAPE₂₀ was estimated and compared with ML or soft computing models; deep neural network (DNN), neural network (NN), and gradient boosting machine (GBM) utilizing observed datasets. Third, these estimated values of the OAPE₂₀ were further compared with developed multivariable linear regression (MLR) and multivariable nonlinear regression (MNLR) and proposed previous relations. Finally, a sensitivity study was also computed to have the relative impact of input parameters on the outcomes of the OAPE₂₀.

The present study used experimental data to estimate the aeration performance of gabion spillways utilizing traditional approaches such as MLR and MNLR, and proposed existing empirical relations and ML techniques such as NN, GBM, and DNN.

Two regression models were employed in the current investigation to estimate the oxygen aeration performance efficiency (OAPE₂₀). One version of the regression equation uses MLR and the other uses MNLR.

in which p₁, p₂, p₃, … are proportionality constants.

Machine learning includes the NN and the DNN. The NN and the DNN are made up of neurons that resemble those in the nervous system. Neurons are given biases and weights. These neural networks are built to function similarly to how neurons in the human brain do Fischer (1998). A brain neuron works by taking in information and then generating an output utilized by another cell. The NN security training also works on a similar pattern. They stimulate behavior by learning about the collected data and predicting outcomes (Nigrin 1993).

The NN employs a massive number of highly interconnected nodes (neurons) that work to solve specific problems, such as forecast and pattern classification (Bishop 1995). The NN is widely used to solve water resource problems and is a very popular soft computing technique. The NN and DNN include an input, a hidden, and an output layer. Nevertheless, the basic difference between the NN and DNN is that several hidden layers are present, and also several nodes are relatively more in the DNN than NN. In the case of a conventional NN, only one hidden layer is present, but in the DNN, the number of hidden layers is more than one. That is why the DNN is called a deep neural network. In the current study, the NN model was developed using MATLAB software, while the model of the DNN was developed using H₂O software. The structures of the NN and the DNN are shown, respectively, in Figure 1(b) and 1(c).

The water's temperature was measured manually using a thermometer with an accuracy of 0.5 °C in the range of −10 to 50 °C, and the DO was measured using the Azide-modification methods (Winkler method, Raikar & Kamatagi 2015). Configuration and dimension of the gabion spillway models are shown in Table 1. In an experiment, gabion spillway models with the appropriate fixing arrangement were installed at the downstream end of the channel. Underflow rates ranging from 0.5 to 5.2 L/s were used to test each gabion spillway. The porosity (n), Reynolds number (Re), Froude number (Fr), and the ratio of gabion mean sizes to the length of the gabion spillway (d₅₀/L) were calculated from the experimental datasets. See Table 2.

Water was mixed with sodium sulfite (Na₂SO₃) and cobalt chloride (COCl₂) in the proper amounts to lower the oxygen level between 1 and 2 mg/L, which was used to compute the DO level in each run. Water samples were analyzed using the azide-modification method after the flume had run for 85 s (Kumar et al. 2021). Care was also made to prevent water from coming into contact with air, except for models where air mixing happens due to gravity.

The model performance metrics of the proposed models were analyzed by statistical measures, i.e., the correlation of coefficient (CC) and root mean square error (RMSE), MSE, and mean absolute error (MAE).

A total number of 161 experimental readings were utilized for making the model. The input datasets comprise the Reynolds number (Re), mean sizes of gabion (d₅₀), Froude number (Fr), the ratio of mean sizes of gabion to the length of gabion spillway (d₅₀/L), porosity(n), and output data were the oxygen aeration performance efficiency (OAPE₂₀). For training, 75% of the total data were taken, and the net left out 25% of the total datasets were utilized for testing. The statistical summary details of training and testing are shown in Table 3.

Table 3

Statistical summary for training and test data

Variables .	Mini .	Max .	Mean .	Std. .	Kurtosis .	Skewness .
Train
Re	2000	20,400	12836.67	5869.848	−1.1799	−0.4612
Fr	7.504	22.686	11.112	3.470	2.5780	1.6542
	0.04	0.314	0.138	0.0725	0.1778	0.7393
N	24	57	41.368	8.084	0.1666	0.2725
OAPE20	0.013	0.559	0.341	0.116	0.0513	−0.6163
Test
Re	3200	20,400	13,380	6209.96	−1.3793	−0.4666
Fr	7.595	3200	10.583	2.514	−0.5271	0.7879
	0.04	0.314	0.1266	0.0684	1.0998	1.0918
N	24	57	39.821	7.269	1.0839	0.1998
OAPE20	0.039	0.584	0.321	0.154	−0.9897	−0.2886

Variables .	Mini .	Max .	Mean .	Std. .	Kurtosis .	Skewness .
Train
Re	2000	20,400	12836.67	5869.848	−1.1799	−0.4612
Fr	7.504	22.686	11.112	3.470	2.5780	1.6542
	0.04	0.314	0.138	0.0725	0.1778	0.7393
N	24	57	41.368	8.084	0.1666	0.2725
OAPE20	0.013	0.559	0.341	0.116	0.0513	−0.6163
Test
Re	3200	20,400	13,380	6209.96	−1.3793	−0.4666
Fr	7.595	3200	10.583	2.514	−0.5271	0.7879
	0.04	0.314	0.1266	0.0684	1.0998	1.0918
N	24	57	39.821	7.269	1.0839	0.1998
OAPE20	0.039	0.584	0.321	0.154	−0.9897	−0.2886

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The dataset was obtained from experimental observations, and proposed traditional methods (MLR and MNLR), existing predictive equations, and soft computing or ML techniques (GBM, NN, and DNN) are used as modeling techniques.

The GBM model was developed using free auto-ML H₂O software. Many models were developed by changing the percentage of the division of training data (calibrating data) and testing data (validating data). A total number of 161 datasets were used for modeling. Finally, 75% of training data (124) and 25% of testing data (37) were found suitable for estimating the best model. A new model was fitted when each weak learner was added to give a more precise estimate of the response variable. The negative gradient of the function linked to the entire ensemble and the new weak learners were most strongly coupled. The GBM's primary goal was to produce a better prediction model by combining several relatively weak prediction models. These were essential in estimating accurate values by considering the minimum reckoning cost. The calibrating (training) data dataset was split into five folds, each comprising 25 data, whereas testing (validating) data was equally split into five folds, each comprising secen data. The principal parameters were tuned by methods of hit-and-trial, as shown in Table 4.

The DNN model was also developed using the free auto-ML H2O software. Several models were created by changing the ratio of the division between training data and testing datasets. For modeling, a total of 161 datasets were employed. Finally, 25% of the testing data (40) and 75% of the training data (121) are considered appropriate for predicting the best model. In a DNN, the initial stage was to find the number of epochs. These were essential in forecasting accurate values by considering minimum reckoning costs. The dataset of training records was split into five folds, each comprising 25 data, whereas testing data were split into five folds, each comprising eight data. The optimized key parameters were tuned by methods of trial-and-error, as shown in Table 7.

The models developed using datasets of gabion spillways were compared using appraisal parameters shown in Table 5. All the proposed models, namely MLR, MNLR, GBM, NN, and DNN models are efficiently predicted the OAPE₂₀ of the gabion spillways. However, the DNN model outperformed all the proposed models in estimating the OAPE of the gabion spillways. The DNN model has the highest CC value and lowest error values, as shown in Table 5. However, all proposed soft computing models performed better than traditional models. However, both the MLR and MNLR models performed well and could be utilized in estimating the OPAE₂₀.

The above contention was further corroborated by Figure 7, where it is clear that predicted values by the DNN model were lying near the observed values, followed by NN and GBM models. Besides, Table 5 also further substantiated that the value of the correlation coefficient (CC = 0.9713) was the highest, and the value of errors (RMSE = 0.1684, MSE = 0.06953, and MAE = 0.1532 were lowest for the DNN model which shows the best-performing model followed by the NN model. Nevertheless, the GBM model performed at par with the proposed ML-based models. But, in the case of traditional models, both MLR and MVLR models were giving comparable performance but the proposed previously existing models (Tiwari 2021; Luxmi et al. 2022) were performing very poorly for training and testing datasets. The summary statistics of predicted results by all proposed models are presented in Table 8 for the training and testing dataset.

In the present study, the modeling of OAPE of gabion spillways (OAPE₂₀) was investigated by traditional methods, including MLR and MNLR, and considered existing empirical relations and proposed ML techniques, namely GBM, NN, and DNN using an experimental dataset. From the above works, the following key conclusions were drawn.

The performance evaluation of the three ML techniques was carried out based on statistical indices like the CC, RMSE, MSE, and MAE. These three ML techniques models utilized experimental datasets to estimate the OAPE₂₀ of the gabion spillways. Out of these three ML models, it was observed that the DNN model was the best performing in both training and testing as the highest values of CC = 0.9744, and lowest values of RMSE = 0.1430, MSE = 0.02040, and MAE = 0.1297 for the training and highest value CC = 0.9713, and lowest values of RMSE = 0.1684, MSE = 0.0283, and MAE = 0.1532 for the testing in comparison to other proposed models.

• This study further presented that the NN model (CC = 0.9368, RMSE = 0.1867, MSE = 0.0348, and MSE = 0.1639 in testing) had sufficient potential for estimating gabion spillway OAPE. It was the second-best-performing model after the DNN, in which the number of neurons in the hidden layer was found to be more sensitive, and its optimum value was eight.

• The GBM model with metrics of CC = 0.93167, RMSE = 0.1850, MSE = 0.0342, and MSE = 0.1665 in testing could be used to estimate the OAPE₂₀ of the gabion spillways but was found to be the least-performing model compared to the other proposed ML-based models.

• Both MLR and MNLR models were also executing well, but the MLR with CC = 0.9253, in testing, performed better than the MNLR with a CC value of 0.9045 in the estimating gabion spillways oxygen aeration performance efficiency (OAPE₂₀). However, the proposed previous models are performing poorly due to high errors and small correlation values for these datasets.

• The sensitivity study suggests that the Reynolds number (Re) was the most sensitive. At the same time, the ratio of the mean size gabion material to the length of the gabion spillway (d₅₀/L) is the least sensitive parameter.

R.S. is thankful to the Ministry of Human Resources, Government of India, and the Director, National Institute of Technology Kurukshetra (Haryana) for the monetary support of the present work for the Master Degree (MTech) scholarship (32012514).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.