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Machine Learning-Based Modelling of Soil Properties for Geotechnical Design: Review, Tool Development and Comparison

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Abstract

Machine learning (ML) holds significant potential for predicting soil properties in geotechnical design but at the same time poses challenges, including those of how to easily examine the performance of an algorithm and how to select an optimal algorithm. This study first comprehensively reviewed the application of ML algorithms in modelling soil properties for geotechnical design. The algorithms were categorized into several groups based on their principles, and the main characteristics of these ML algorithms were summarized. After that six representative algorithms are further detailed and selected for the creation of a ML-based tool with which to easily build ML-based models. Interestingly, automatic determination of the optimal configurations of ML algorithms is developed, with an evaluation of model accuracy, application of the developed ML model to the new data and investigation of relationships between the input variables and soil properties. Furthermore, a novel ranking index is proposed for the model comparison and selection, which evaluates a ML-based model from five aspects. Soil maximum dry density is selected as an example to allow examination of the performance of different ML algorithms, the applicability of the tool and the model ranking index to determining an optimal model.

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Abbreviations

b i :

Bias vector of the ith hidden layer

c :

Constant coefficient vector

C :

Regularization parameter

E :

Exponent matrix

F :

Function set

gen :

Number of iterations

H i :

Output of the ith hidden layer

m :

Number of datasets

mtry :

Number of features at each node

n :

Dimension of input variables

n t :

Dimension of transformed variables

ntree :

Number of decision trees

N :

Stochastic calculation times

p :

Dropout probability

p c :

Probability of crossover

p m :

Probability of mutation

pop :

Size of population

r :

Bernoulli distribution with probability of p

W i :

Weight matrix of the ith hidden layer

x i, max :

Maximum value of the variable xi

x i , min :

Minimum value of the variable xi

x norm :

Normalized value of a dataset

X = (x 1, x 2, …, x n):

Matrix of input variables

XT :

Matrix of transformed variables

y a i :

Actual value of the output variable

y p i :

Predicted value of the output variable

\(\bar{y}_{i}^{a}\) :

Mean value of the actual output variable

y = (y 1, y 2, …, y n):

Output of the output layer

γ :

Kernel coefficient

ξ :

Slack parameter (default value: 0.1).

σ :

Activation function

\({\mathbb{E}}\) :

Mean value of output

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Acknowledgements

This research was financially supported by the Research Grants Council (RGC) of Hong Kong Special Administrative Region Government (HKSARG) of China (Grant No.: 15220221, R5037-18F).

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Pin Zhang, Zhen-Yu Yin & Yin-Fu Jin

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  1. Pin Zhang
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Contributions

PZ: conceptualization, methodology, analysis, writing-review and original draft. Z-Yu Y: supervision, methodology, visualization, writing-review and editing. Y-F J: validation, visualization and editing.

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Correspondence to Zhen-Yu Yin.

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The authors declare that the work described has not been published before; that it is not under consideration for publication anywhere else; that its publication has been approved by all co-authors; that there is no conflict of interest regarding the publication of this article.

Data Availability Statement

(GUI download available: https://www.researchgate.net/publication/348617390_ErosMLM). All data used during the study are available from the corresponding author by request.

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Zhang, P., Yin, ZY. & Jin, YF. Machine Learning-Based Modelling of Soil Properties for Geotechnical Design: Review, Tool Development and Comparison. Arch Computat Methods Eng 29, 1229–1245 (2022). https://doi.org/10.1007/s11831-021-09615-5

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