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A novel TS Fuzzy-GMDH model optimized by PSO to determine the deformation values of rock material

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Abstract

Since determining the rock deformation directly in the laboratory is costly and time consuming, it is important to reliably determine/estimate this parameter through the use of several simple rock index tests. This study develops a new hybrid intelligent technique according to Takagi–Sugeno Fuzzy Inference System-Group Method of Data Handling optimized by the particle swarm optimization, called TS Fuzzy-GMDH-PSO for prediction of the rock deformation. The PSO role in this advanced system is to optimize the membership functions of TS Fuzzy-GMDH model for enhancing the level of prediction capacity. In this research, four rock index tests including Schmidt hammer, p-wave velocity, porosity and point load were selected and conducted in laboratory in order to establish a suitable database for prediction purposes. To demonstrate the feasibility and applicability of the advanced hybrid model, two base models of TS Fuzzy and GMDH were also modeled to forecast rock deformation. After conducting several sensitivity analyses on the mentioned models to get the highest performance capacity, their prediction levels were evaluated using some statistical indices, such as root mean square error and correlation coefficient (R). The comparative results confirmed the superiority of the TS Fuzzy-GMDH-PSO over other two models, namely TS Fuzzy and GMDH in terms of both train and test phases. It can be concluded that the TS Fuzzy-GMDH-PSO can be recommended as a powerful, capable and new model to solve the problems related to rock strength and deformation.

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Abbreviations

AI:

Artificial intelligence

ANN:

Artificial neural network

C 1 and C 2 :

Coefficients of velocity equation

E :

Young’s modulus

EC:

External criterion

E rm :

Rock mass Young’s modulus

FFN:

Feed-forward network

FIS:

Fuzzy inference system

FS:

Fuzzy set

GMDH:

Group method of data handling

ICA:

Imperialism competitive algorithm

Is(50) :

Point load strength index

MAPE:

Mean absolute percentage error

MF:

Membership function

ML:

Machine learning

MSE:

Mean square error

n :

Porosity

PD:

Partial description

PI:

Performance index

PSO:

Particle swarm optimization

R 2 :

Coefficient of determination

R a :

Cluster radius parameter

R b :

Cluster neighborhood

RMSE:

Root mean square error

Rn:

Schmidt hammer rebound number

SVR:

Support vector regression

TBM:

Tunnel boring machine

TS:

Takagi–Sugeno

UCS:

Uniaxial compressive strength

Vp:

P-wave velocity

w :

Inertia weight

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Acknowledgements

The authors wish to express their appreciation to Universiti Teknologi Malaysia for supporting this study and making it possible.

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Pajoohesh Sq., Imam Khomeni Highway, P.O. Box 76169133, Kerman, Iran

    Hooman Harandizadeh

  2. Department of Urban Planning, Engineering Networks and Systems, Institute of Architecture and Construction, South Ural State University, 76, Lenin Prospect, Chelyabinsk, 454080, Russia

    Danial Jahed Armaghani

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Mahdi Hasanipanah

  4. Centre for Infrastructure Engineering, Western Sydney University, Penrith, NSW, 2751, Australia

    Soheil Jahandari

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  1. Hooman Harandizadeh
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Harandizadeh, H., Armaghani, D.J., Hasanipanah, M. et al. A novel TS Fuzzy-GMDH model optimized by PSO to determine the deformation values of rock material. Neural Comput & Applic 34, 15755–15779 (2022). https://doi.org/10.1007/s00521-022-07214-4

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