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The application of Bayesian model averaging based on artificial intelligent models in estimating multiphase shock flood waves

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Abstract

The multiphase shock wave phenomenon is significantly affected by accumulated upstream sediment deposition and downstream hydraulic conditions. There is a lack of studies evaluating the efficacy of intelligent models in representing multiphase debris flooding over initially dry- or wet-bed tail-waters, or over downstream semi-circular obstacles. To address this, we propose a novel methodology based on Bayesian Model Averaging (BMA), which combines predictions of three individual intelligent models [i.e., “Multi-layer Perceptron” (MLP), “Generalized Regression Neural Network”, and “Support Vector Regression”]. The models were developed through experimental study whereupon high-quality sediment depths and water levels data (n = 9000) were collected from 18 shock wave scenarios with various initial conditions in channel up- and down-stream. Experimental data and related original videos are created accessible in an online repository may be used in other researches. Each model’s results were in close concord with the experimental data; RMRE and RMSE values were in the range of 1.54–5.99 mm and 1.21–40.49 mm, respectively (0.5–2% and 0.4–13.5%) with the MLP model marginally outperforming the other intelligent models. Based on statistical error indices, the BMA model had the best performance (up to 40% better) in estimating most data classes, and was more efficient than the best intelligent model signifying that the proposed methodology is explicit, straightforward, and promising for real-world applications.

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Availability of data and materials

All data, produced and used during the study are available online in a public repository or appear in the submitted article [49,50,51,52].

Abbreviations

BMA:

Bayesian model averaging

MLP:

Multi-layer perceptron

GRNN:

Generalized regression neural network

SVR:

Support vector regression

CFD:

Computational fluid dynamic

ANN:

Artificial neural network

RMSE:

Root mean square error

RMRE:

Root mean relative error

RMSRE:

Root mean square relative error

NSE:

Nash–Sutcliffe efficiency coefficient

SI:

Scatter Index

R 2 :

Coefficient of determination

U S :

Initial depth of sediment in the reservoir

D W :

Initial level of water in downstream bed

T :

Time elapsed after the dam breaks

L :

Distances from reservoir beginning

R :

Radius of a semi-circular obstacle

S d :

Sediment depth

W L :

Water level

H 0 :

Initial height of the water in reservoir

\({M}_{i}\) :

Measured experimental data

\({E}_{i}\) :

Estimated values

\(\overline{M }\) :

Average of measured experimental data

\(\overline{E }\) :

Average of estimated values

\(\beta\) :

Model’s weight

\(\sigma\) :

Model’s standard deviation

\({P}_{i}\) :

A deterministic weighted average prediction

k :

Individual models

\({f}_{k}\) :

Estimation distribution of a model member

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Acknowledgements

The authors wish to express their gratitude to Mr Jasper Vrugt, due to the assistance provided by adopting “MODELAVG toolbox”. The authors are also immensely grateful to Prof. Jan Adamowski for his comments on an earlier version of the manuscript and for sharing his pearls of wisdom with us during the course of this research.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Civil and Environmental Engineering Department, Shiraz University, Shiraz, Iran

    Foad Vosoughi & Gholamreza Rakhshandehroo

  2. Department of Civil and Architectural Engineering, Sultan Qaboos University, Muscat, Oman

    Mohammad Reza Nikoo

  3. Civil and Environmental Engineering Department, Florida State University, Tallahassee, USA

    Nasrin Alamdari

  4. Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia

    Amir H. Gandomi

  5. Department of Soils, Water and Agricultural Engineering, Sultan Qaboos University, SQU, Muscat, Oman

    Malik Al-Wardy

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  1. Foad Vosoughi
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Contributions

FV Conceptualization, Software, Validation, Investigation, Resources, Data Curation, Writing—Original Draft, Visualization, Writing—Review and Editing, MRN Conceptualization, Methodology, Supervision, Reviewing—Original Draft, Validation, Resources, Visualization, Writing—Review and Editing, GR Conceptualization, Methodology, Supervision, Writing—Review and Editing, NA Supervision, Writing—Review and Editing, AHG Supervision, Writing—Review and Editing, MA-W Supervision, Writing—Review and Editing.

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Correspondence to Mohammad Reza Nikoo.

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Vosoughi, F., Nikoo, M.R., Rakhshandehroo, G. et al. The application of Bayesian model averaging based on artificial intelligent models in estimating multiphase shock flood waves. Neural Comput & Applic 34, 20411–20429 (2022). https://doi.org/10.1007/s00521-022-07528-3

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