Estimating gabion weir oxygen transfer with data mining

Oxygen is vital and indispensable for the sustenance of life on the planet since both the animal and plant kingdoms need oxygen for survival. One of the determinants to measure water quality is dissolved oxygen (D.O.), and water oxygen solubility is directly proportionate to pressure but inversely proportional to temperature (Baylar et al. 2010). Water takes away oxygen by two methods: the first is by the method of aeration, and the second is by the process of photosynthesis. The D.O. level gives information about the degree of contamination of the water and how best the water can support aquatic life (LeFevre et al. 2015). A higher D.O. potential exhibits superior water quality. The deficiency of the D.O. level in the watercourse severely affects the ecological order. To sustain ecological stability and equilibrium, the D.O. level needed for water bodies should be ensured and to meet this requirement, the oxygen of the atmosphere must be transmitted to water. The physiological process of oxygen transmission from the air to water is called aeration, which needs air and water in close touch and link. The efficacy of oxygen transfer depends on its comparison with the existing prototype weir surface contact between water and air, which is regulated eventually by the water drop sizes or bubbles of air. Oxygen transfer in rivers, ponds, lakes, and oceans is significant to the quality and survival of hydro-lives. Oxygen transfer in water bodies is very effective in the survival of aqua life. Entrapped air bubbles would add up to aeration if the water jets fall from drop structures freely into a receiving water pool. Fluidic devices enhance the amount of D.O. in a stream by self-aeration, although the water comes in touch with the hydraulic structure for only a fraction of the clock (Baylar et al. 2010). The volume of aeration usually would take place over numerous miles in a river stream and can occur at a sole fluidic device.

Oxygen transfer of the classical weirs was first investigated by Gameson (1957), but it was followed by many researchers (Van der Kroon & Schram 1969; Avery & Novak 1978; Nakasone 1987) who studied the aeration process at hydraulic structures and developed models for aeration efficiency with discharge and geometry of weir. However, Wilhems et al. (1993) reviewed the above-developed models and made them for many locations where Avery & Novak's (1978) model proved the best. Gulliver & Rindels (1993) analyzed data and recorded inherent errors with measurement tools for prototype aeration. Gabions spillway was studied by Peyras et al. (1992) and explored different forms of flow over the stepped surface. Wuthrich & Chanson (2015) tested the gabion weirs without and with capping and observed significant interactions between the seepage and overflow under-regulated low flow situations. However, lower performances were noticed in energy loss and oxygen transfer efficiency (OTE) for large discharges. Reeve et al. (2019) investigated the hydraulic potential of the gabion-stepped spillways with a numerical model. They concluded that the standard gabion step configuration performed well concerning the energy loss and inception point location.

Furthermore, two classical models were developed with regression methods to predict the water depth and the inception point location. Mohamed (2010) performed numerous tests to investigate the flow characteristics of the gabion weir and found that hydraulic characteristics for the gabion weir are different from those of the impervious weir. The head over the previous gabion weir is lower than that of the impervious weir for the same flow rate. Al-Fawzy et al. (2020) investigated the impact of hydraulic jumps on the energy loss in the gabion weirs. Mohamed Al-Mohammed & Hassan Mohammed (2015) conducted laboratory experiments on a gabion weir to examine the flow characteristics and found a relationship between upstream water depth and discharge for the various regimes. However, Shariq et al. (2020) developed the gabion weir discharge model through flow conditions. Kouadri et al. (2021) used eight soft computing methods for prediction of a water quality index (WQI). The artificial neural network (ANN) created a model for the chlorophyll-a levels of a shallow eutrophic lake (Mikri Prespa) located in northern Greece (Hadjisolomou et al. 2021). Forecasting the infiltration rate (IR) of treated wastewater (TWW) is essential in regulating clogging problems. Most investigators that calculate the IR using neural network models consider the characteristics variables of soil without considering those of TWW. So, this work aims to generate a model for forecasting the IR based on various combinations of TWW characteristics parameters. Therefore, two different ANN architectures, the multilayer perceptron model (MLP) and the Elman neural network (ENN), are used to develop the optimal model (Abdalrahman et al. 2022). Computational fluid dynamics (CFD) is considered a robust tool to predict the discharge coefficient. To bypass the computational cost of CFD-based assessment, the present study proposes data-driven modeling techniques, as an alternative to CFD simulation, to predict the discharge coefficient based on an experimental dataset (Chen et al. 2022). This investigation examines the effects of influential dimensionless factors on estimating one of the critical hydraulic characteristics of inflatable dams, namely the discharge capacity. Several parameters such as the proportion of total upstream head to dam height (H₁/D_h), the ratio of overflowing head to dam height (h/D_h), the ratio of discharge per unit width to its maximum value (q/q_max), the ratio of the internal pressure of the tube to its maximum value (p/p_max) and the ratio of the longitudinal coordinate placement of each element to x_max are used. A hybrid model based on the particle swarm optimization (PSO) and the genetic algorithm (GA), PSO–GA, is proposed to improve the accuracy of the estimation by combining the advantages of both algorithms (Zheng et al. 2021). Hu et al. (2021) used different soft computing models in estimating the overflow capacity of a curved labyrinth. For this, a total of 355 empirical data for six different congressional overflow models were extracted from the results of a laboratory study on labyrinth overflow models. The parameters of the upstream water head-to-overflow ratio, the lateral wall angle, and the curvature angle were used to estimate the discharge coefficient of curved labyrinth overflows. Based on various statistical evaluation indicators, the results show that those input parameters can be relied upon to predict the discharge coefficient. Specifically, the least-squares support vector machine–bat algorithm (LSSVM–BA) model showed the best prediction accuracy during the training and test phases. Such a low-cost prediction model may have remarkable practical implications as it could be an economic alternative to the expensive laboratory solution, which is costly and time-consuming.

It is usually recognized that numerous parameters regulate the aeration process. Eggers & Villermaux (2008) reviewed the water jet physics thoroughly. Several engineering and environmental developments involve oxygen transfer by getting the air bubbles generated when the additional liquid of the same or dissimilar properties strikes its surface; e.g., a water jet plunging into a pool, a breaking wave free-falling in the water body, etc. Everyday life is affected by polluted water. The D.O. level in the water bodies is depleted primarily owing to organic contaminants. The silt and sediment, a composition of organic and inorganic materials, offer a perfect ecosystem for the growth of germs, bacteria, microbes, organisms, etc. These organisms disintegrate the organic substance in the silt material utilizing the existing D.O. in the river. Therefore, the D.O. level in the water body depleted with time, and this shortfall is counterbalanced by aeration activity, i.e., oxygen transfers from air to water (Gulliver & Rindels 1993). Recently, Luxmi et al. (2022) used non-dimensional inputs for finding gabion weir aeration while Srinivas & Tiwari (2022) studied the gabion spillways aeration efficiency.

The preceding review study indicates that very few works have been conducted on the gabion weir oxygen transfer efficiency (OTE₂₀), and few or no models have yet been generated. Therefore, the issue of accurate estimation of the OTE₂₀ is left unresolved. Furthermore, ordinary regression models too cannot estimate the precise value of the OTE₂₀ due to the nonlinear and complicated mechanism that occurs during the flow in the gabion weir. So, an alternate way of data mining models could be the most suitable choice owing to their logical, reasonable, and flexible ability in tuning parameters. Recently, data mining models have been employed considerably in water resources and environmental engineering, where neither understanding of mechanisms is needed nor requires a laboratory/field model study (Baylar et al. 2007; Gerger et al. 2017; Sattar et al. 2019; Kumar et al. 2020; Tiwari & Sihag 2020; Tiwari 2021; Tiwari et al. 2022). The data mining models are highly efficient at mapping the actual mechanism of the simulated oxygen transfer applications. Among various data mining models, the proposed back propagation neural network (BPNN) and adaptive neuro-fuzzy inference system (ANFIS) models are the most reliable and robust predictive models.

Major difficulties and challenges are faced in computing the porosity and the mean size of gabion particles resolved by the volumetric displacement method and sieve analysis technique, respectively. Besides, the other difficulty and challenge is that the water jet through gabion weirs strikes the middle of the aeration tank to acquire uniform aeration. Furthermore, finding optimal values for tuning parameters of proposed data mining methods is equally challenging, which are calculated by trial and error methods.

The novelty of the current study has many facets, as it outlines the estimation of the OTE₂₀ by performing laboratory tests with varying discharge per unit width, drop height, porosity, and mean sizes of gabion particles. Secondly, the OTE₂₀ is estimated and compared with data mining models; BPNN, and ANFIS utilizing observation data. Thirdly, these estimated values of the OTE₂₀ are compared with developed multivariate linear relation (MVLR) and multivariate nonlinear relation (MVNLR) models. Finally, the sensitivity investigation was also executed to get the comparative significance of input variables on the output results of the OTE₂₀. The performance potential of these models is evaluated in terms of statistical metrics.

In this section, basic backgrounds, experimental methodology, and proposed data mining techniques have been discussed.

OTE is oxygen transfer efficiency at any water temperature and the OTE₂₀ is oxygen transfer efficiency at 20 °C.

Proposed data mining methods have been discussed in this section as

The BPNN is a soft computing method extensively applied in civil engineering (Tiwari & Sihag 2020). It is inspired by the human mind and based upon human brain structure divided into input, intermediate/hidden, and output layers. These layers are connected with weights, and each layer has a different number of neurons/nodes but operates in association to resolve even a complex problem.

During the last two decades, numerous neural network water quality modeling works are carried out with very good predicting results (Hadjisolomou et al. 2021). The advantages of the BPNN are that it can learn and model nonlinear and complex relationships, and it can manage the relationship between inputs and outputs, as this is rarely simple. The BPNN also does not restrict the input variables, unlike other prediction techniques.

ANFIS is a soft hybrid method, denoted as an adaptive neuro-fuzzy inference system that amalgamated neural networks (NNs) and fuzzy inference systems (FISs) to gain their benefits and ever first coined by Jang (1993). An ANFIS technique utilizes NNs for resolving nonlinear and complex cases and their capability to distinguish and establish relationships between different variables. It also uses FIS to rationalize complex scenarios, utilizing the ideologies extracted from human decision-making (Tiwari & Sihag 2020). To get rid of the weaknesses of NNs and FIS, ANFIS techniques have already been successfully utilized as a reliable estimating tool for OTE, sediment trapping efficiency, a discharge correction factor of Parshall flume and plunging hollow jet penetration depth, and many more problems related to the discipline of water resources, environmental, etc. of civil engineering (Tiwari et al. 2020; Saran & Tiwari 2020; Sharafati et al. 2021; Tiwari et al. 2022). The ANFIS technique creates an association between input and output variables by applying the linguistic terminologies. These If-Then rules have a large capacity to deal with nonlinearity or stochastic or dynamical problems. From fuzzy logic, each input (in terms of x and y) is expressed as a fuzzy set (P_i and Q_i) with one output f_i (Jang 1993). The rules are utilized as

The ANFIS model has the advantage of having both numerical and linguistic knowledge. ANFIS also uses the BPNN's ability to classify data and identify patterns. Compared to the BPNN, the ANFIS model is more transparent to the user and causes fewer memorization errors.

It is a well understood and popular algorithm in statistical soft computing. It has been proved to have one of the best performing potentials in prediction of water quality (Chou et al. 2018; Luxmi et al. 2022).

The most important advantage of multivariate linear regression is that it helps us to understand the relationships among variables present in the dataset. This will further help in understanding the correlation between dependent and independent variables.

Nonlinear regression is a mathematical function that uses a generated line – typically a curve – to fit an equation to some data. The sum of squares is used to determine the fitness of a regression model, which is computed by calculating the difference between the mean and every point of data.

For the invoking of data mining models, a total of 60 observations of OTE₂₀ are determined employing the weirs with different discharge per unit width (q), porosity (n), mean size (d₅₀)_, and drop height (h). Two groups are created from the total observations for training (70% observations) and testing (30%). Data grouping is carried out randomly. The statistical characteristics of both groups of data are described in Table 2.

The coefficient of correlation (cc) represents goodness of fitting. A correlation helps to identify the absence or presence of a relationship between two variables, i.e., awareness of behavior between two parameters. The best possible value is 1. It can have negative value as well but it signifies that the model is worse performing as variables change in the opposite directions. While rmse is the most widely used for evaluating the potential for the assessment of the model in prediction of quantitative dataset. The rmse gives a relatively high weight to large errors. This means the rmse is the most useful when large errors are particularly undesirable. The rmse can range from zero to infinitive.

This work uses ANFIS to model the correlation between inputs and output variables. The model utilizes MATLAB-fuzzy rules based upon the membership function (mf). No definite rule exists for generating the ANFIS model, and selecting ANFIS tuning parameters requires a hit and trial method. ANFIS model generation is somewhat identical to the BPNN model and involves hidden layers, neurons in the hidden layer, mfs as well as optimization processes.

The addition of mf numbers is done one after the other to each parameter and models with four different shapes, i.e., triangular mf (Tri), trapezoidal mf (Trap), generalized bell-shaped mf (Gbell), and Gaussian mf (Gauss) are trained and tested. Thus, the ANFIS model is checked for accuracy and error on the testing datasets with the performance metrics. Depending on numerous training and corresponding testing of the models, (2-3-2-2) is the input combination of the mf number utilized in the present study. Model-specific parameters chosen in the current work are listed in Table 5.

To work out the effective input parameters in the computation of the OTE at the gabion weir_, a sensitivity investigation was performed with the BPNN as this model depicted the highest computed accuracy for this dataset. Firstly, models utilizing different parameters are made out, and corresponding values of cc and rmse are measured (Table 7). The model's performance potential during training and testing is checked by eliminating each input parameter one after the other. The highest fluctuation in the results of cc and rmse is noted when discharge per unit length (q) is pulled out from the input grouping in testing, which implies the critical importance of q in affecting the computation of OTE_20, followed by the size of gabion particle (d₅₀) input parameter

A gabion weir is supposed to be more ecologically responsive than a conventional one, as its perviousness permits materials and water-living animals to move through it. Fluidic devices have a rejuvenating effect on D.O. levels in a water body, though the water is in contact with the fluidic device for a shorter time. Fluidic devices can produce turbulence in which bubbles are carried away to the flow end and, in turn, enhance D.O. concentrations, though the water would be in contact with the device for only a brief period. The present study used MVLR, MVNLR, BPNN, and ANFIS with mfs to compute the oxygen aeration efficiency. Four key input parameters, q, n, d₅₀, and h, are considered, and 60 observations were collected from experimental tests. The following crucial takeaways could be drawn from this investigation:

• The BPNN is found to be the outperforming model where neurons in the hidden layer are the most sensitive tuning parameters, and its optimal value is found to be nine and also optimized values of their other significant parameters; learning rate, momentum, and the number of epochs are 0.3, 0.2, and 1,500, respectively.

• The triangular mf-based ANFIS, MVNLR, and MVLR give comparable results. However, the least performing model is generalized mf-based ANFIS.

• Outcomes of a single-factor ANOVA suggest that insignificant differences between experimental and computed values have been found using all considered models.

• Results of the sensitivity investigation show that discharge per unit width (q) is the most sensitive variable in the computation of the oxygen transfer efficiency (OTE₂₀)_, while the second significant sensitive variable is the mean size (d₅₀) of gabion material.

Due to constraints of the study, the limited number of datasets is taken, so for the improvement in the work, more dataset is required from the same source or another for reaching out with definite inference; nevertheless, these models may assist the researchers and project engineers in computing the OTE₂₀. Furthermore, the considered models may also be compared with other data mining algorithms and classical models.

N.K.T., K.L., and S.R. conceptualized the study; N.K.T. and K.L. did formal analysis and investigation; N.K.T. wrote and prepared the original draft; N.K.T. and S.R. wrote, reviewed, edited, and supervised the article.

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

The authors declare there is no conflict.