A Non-Tuned Machine Learning Technique for Abutment Scour Depth in Clear Water Condition

Abstract

Abutment scour is a complex three-dimensional phenomenon, which is one of the leading causes of marine structure damage. Structural integrity is potentially attainable through the precise estimation of local scour depth. Due to the high complexity of scouring hydrodynamics, existing regression-based relations cannot make accurate predictions. Therefore, this study presented a novel expansion of extreme learning machines (ELM) to predict abutment scour depth (ds) in clear water conditions. The model was built using the relative flow depth (h/L), excess abutment Froude number (Fe), abutment shape factor (Ks), and relative sediment size (d50/L). A wide range of experimental samples was collected from the literature, and data was utilized to develop the ELM model. The ELM model reliability was evaluated based on the estimation results and several statistical indices. According to the results, the sigmoid activation function (correlation coefficient, R = 0.97; root mean square error, RMSE = 0.162; mean absolute percentage error, MAPE = 7.69; and scatter index, SI = 0.088) performed the best compared with the hard limit, triangular bias, radial basis, and sine activation functions. Eleven input combinations were considered to investigate the impact of each dimensionless variable on the abutment scour depth. It was found that ds/L = f (Fe, h/L, d50/L, Ks) was the best ELM model, indicating that the dimensional analysis of the original data properly reflected the underlying physics of the problem. Also, the absence of one variable from this input combination resulted in a significant accuracy reduction. The results also demonstrated that the proposed ELM model significantly outperformed the regression-based equations derived from the literature. The ELM model presented a fundamental equation for abutment scours depth prediction. Based on the simulation results, it appeared the ELM model could be used effectively in practical engineering applications of predicting abutment scour depth. The estimated uncertainty of the developed ELM model was calculated and compared with the conventional and artificial intelligence-based models. The lowest uncertainty with a value of ±0.026 was found in the proposed model in comparison with ±0.50 as the best uncertainty of the other models.

A comparison between advanced hybrid machine learning algorithms and empirical equations applied to abutment scour depth prediction

“…This is in accordance with the outcomes of the r value and the determination of the most effective input parameter combination. Also, our result is in accordance with Bonakdari et al (2020) which stated that the relative median sediment diameter (d50/l) is the most effective parameter for the prediction of scour depth. Bonakdari et al…”

“…Our results show that the approach flow depth (h) is not very effective on the overall scour depth, while flow velocity, transverse abutment length, and median sediment diameter are important. Azimi et al, (2019), Moradi et al, (2019) and Bonakdari et al, (2020) revealed that their best input combination was a combination of Fe, h/l, Ks, d50/l. This definitely shows that the structure of the modeling approach has a crucial role on the selection of the input combination, which is resulting from different structure of each model.…”

“…Indeed, experiments can be designed with a certain rate of sediment supply from upstream (as generally expected in the field during flood events) or without coarse sediment supply (i.e., clear water conditions). Overall, the scour depth abutment has been considered as a function of sediment size, flow parameters, and the geometrical characteristics of the structure (Bonakdari et al, 2020;Firat and Gungor, 2009;Raudkivi and Ettema, 1983;Sheppard et al, 2004). This can be written as follows:…”

“…In addition, Froehlich (1989) showed that the excess Froude influence the scour depth in a uniform sediment bed, under clear-water condition, and our results are in agreement with that. The other AI models proposed by Azimi et al (2019), Bonakdari et al (2020), Moradi et al (2019) and Najafzadeh et al (2013b) all mentioned that the influence of Fe parameter in the prediction of scour depth is remarkable.…”

“…Ebtehaj et al (2018) reported that the ELM model has a higher performance than ANN and SVM models to predict scour depth. In a recent study, Bonakdari et al (2020) used the ELM technique to predict scour depth in clear-water condition considering four different nondimensional input parameters to estimate scour depth. About 11 different input combinations were tested to find the best one and they finally concluded that the model which contains all input variables allowed to obtain a better performance.…”