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Sensitivity analysis of parameters affecting scour depth around bridge piers based on the non-tuned, rapid extreme learning machine method

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Abstract

The extreme learning machine (ELM) is a new, non-tuned and fast training algorithm for feedforward neural networks (FFNN). It is highly precise and randomly produces the input weights of single-layer FFNN. In the current study, the scour depth around bridge piers is predicted by ELM as a powerful method of nonlinear system modeling. To predict scour depth, the effective dimensionless parameters are determined through dimensional analysis. Due to the complexity of scour mechanisms around bridges, different models with diverse input numbers are presented. In 5 categories, 31 different models were obtained for modeling and ELM analysis. Following the training and validation of each model presented, the optimum model was selected from each of the 5 categories and its relationship to the respective category was identified to help determine scour depth in practical engineering. For the best models presented in the different input modes, new explicit expressions were deduced. The results show that the most important parameters affecting relative scour depth (ds/y) include ratio of pier width to flow depth (D/y) and ratio of pier length to flow depth (L/y) (RMSE = 0.08; MARE = 0.0.35). The ELM performance was compared for a range of pier geometries with regression-based equations. The results confirm that ELM outperforms other methods.

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Abbreviations

D :

Pier width

d s :

Local scour depth

d 50 :

Median diameter of particles

Fr :

Froude number

g :

Gravitational acceleration

g(x):

Activation function (Eq. 5)

L :

Pier length

l :

Neurons in the hidden layer

Q :

Number of input samples (Eq. 5)

U :

Average velocity of approaching flow

w :

Input-hidden layer

w ij :

Connecting weight between the ith input neuron and the jth hidden neuron (Eq. 3)

Y :

Flow depth

Β :

Hidden-output layer weight

β jk :

Connecting weight between the jth hidden neuron and the kth output neuron (Eq. 3)

σ :

Standard deviation related to bed grain size

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Authors and Affiliations

  1. Department of Civil Engineering, Razi University, Kermanshah, Iran

    Isa Ebtehaj, Hossein Bonakdari, Amir Hossein Zaji & Hassan Sharafi

  2. Environmental Research Center, Razi University, Kermanshah, Iran

    Isa Ebtehaj, Hossein Bonakdari & Amir Hossein Zaji

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  1. Isa Ebtehaj
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Correspondence to Hossein Bonakdari.

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Ebtehaj, I., Bonakdari, H., Zaji, A.H. et al. Sensitivity analysis of parameters affecting scour depth around bridge piers based on the non-tuned, rapid extreme learning machine method. Neural Comput & Applic 31, 9145–9156 (2019). https://doi.org/10.1007/s00521-018-3696-6

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