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Extreme pressure coefficients: modelling a hydraulic jump using deep-learning based methods

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Abstract

Hydraulic jump pressure field analysis is essential to assess slab stability in dissipation basins. This study is aimed to modelling non-dimensional extreme pressure coefficients of the minimum pressure fluctuation (CP−) and maximum pressure fluctuation (CP+) using experimental data with three deep learning (DL) techniques. Pressure coefficients were estimated using Convolutional Neural Network (CNN), Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM) methods. For the CP− coefficient related to the tested dataset, the correlation coefficient (CC)=0.894 and Willmott’s index of agreement (WI)=0.944 are achieved using the LSTM model, compared with 0.892 and 0.936 for CNN; and 0.892 and 0.943 for GRU. For the CP+ coefficient, CC=0.910 and WI=0.950 are attained using the LSTM model, compared with 0.903 and 0.941 with CNN; and 0.905 and 0.945 with GRU. The results indicate the excellent performance of the LSTM model for estimating pressure coefficients. With laboratory conditions and the experimental data domain framework used in this study, it is shown that the DL models have been successful for modelling very complex systems. Therefore, DL techniques are recommended for estimating extreme pressure coefficients with a reduction in the need to perform expensive experiments.

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Abbreviations

C P + :

Non-dimensional coefficient of maximum pressure fluctuation

C P − :

Non-dimensional coefficient of minimum pressure fluctuation

Fr1 :

Incident Froude number of the flow

S r :

Submergence ratio (Tw/d2)

ГX :

Non-dimensional longitudinal position of each point along the basin (X/d1)

ГY :

Non-dimensional transverse position of each point along the basin (Y/d1)

ΔP max :

Maximum pressures fluctuation relative to the mean pressure

ΔP min :

Minimum pressures fluctuation relative to the mean pressure

AI:

Artificial intelligence

CC:

Pearson correlation coefficient

CNN:

Convolutional Neural Network

GRU:

Gated Recurrent Unit

LSTM:

Long Short-Term Memory

MAE:

Mean Absolute Error

RMSE:

Root Mean Squared Error

WI:

Willmott’s Index of Agreement

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Authors and Affiliations

  1. Department of Water Engineering, University of Tabriz, Tabriz, 5166616471, Iran

    Seyed Nasrollah Mousavi & Mohammad Taghi Sattari

  2. Department of Agricultural Engineering, Faculty of Agriculture, Ankara University, Ankara, 06110, Turkey

    Halit Apaydin & Mohammad Taghi Sattari

  3. School of Engineering, University of St. Thomas, Minnesota, 2115 Summit Ave., St. Paul, MN, 55105, USA

    John Patrick Abraham

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  1. Seyed Nasrollah Mousavi
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Mousavi, S.N., Apaydin, H., Sattari, M.T. et al. Extreme pressure coefficients: modelling a hydraulic jump using deep-learning based methods. Sādhanā 49, 151 (2024). https://doi.org/10.1007/s12046-024-02515-x

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