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A novel comprehensive quantitative method for various geological disaster evaluations in underground engineering: multidimensional finite interval cloud model (MFICM)

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Abstract

The risk prediction of geological disasters exhibits extreme uncertainty and complexity due to the random distribution of evaluation indexes within a finite interval. To improve the accuracy of disaster prediction results, a new evaluation method is in this study suggested to perform a risk evaluation of geological disasters based on multidimensional finite interval cloud model (MFICM) and combination weighting. The MFICM with a transformation between qualitative concept and quantitative data depicts uncertainties and actual distribution features of indexes in the finite interval. Analytic hierarchy process and principal component analysis are adopted to determine the subjective and objective weights of evaluation indexes, respectively, and the combination weight is calculated by a linear method to reduce the influence of subjective factors. The numerical characteristic parameters of each indexes belonging to various risk levels are first calculated based on established evaluation index system. Subsequently, a multi-dimensional finite interval cloud is generated from a forward cloud generator using MATLAB software. Finally, the comprehensive certainty degrees relative to different levels for each sample are determined combined with combination weight, which achieves a mapping of uncertainty between semantic variables and index values. The proposed method is applied to engineering cases regarding three geological disasters, i.e., water inrush, rock burst and collapse. The obtained results with accuracy and results compared with reference methods show that the MFICM is verified to be practical and universal for the risk evaluation of geological disasters, which improves and enriches the theoretical framework of geotechnical engineering disaster risk evaluation.

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Data availability, Material availability and Code availability

All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

M, M(Ex, En, He):

Qualitative concept

N, N{x 1, x 2, …, x k}:

A universe of discourse

x, x(x 1, x 2, …, x k):

Quantitative number

μ(x), μ(x(x 1, x 2, …, x k)):

Certainty degree

μ c(x(x 1, x 2, …, x k)):

Comprehensive certainty

Ex, (Ex1, Ex2, …, Exk):

Expectation

En, (En1, En2, …, Enk):

Entropy

He, (He1, He2, …, Hek):

Hyper-entropy

[B i min, B i max]:

Bilateral constraints interval

[B i min, + ∞], [0, B i max]:

Unilateral constraint intervals

B i max :

Maximum values of level interval

B i min :

Minimum values of level interval

K :

Cloud droplet number

φ :

Empirical coefficient constant

k :

Dimensions of the cloud model

σ θ/σ c :

Stress coefficient

W et :

Elastic deformation energy

λ max :

Maximum eigenvalues

n :

Order of the judgment matrix

w i :

Subjective weight

P :

Judgment matrix

RI:

Average consistency index

CR:

Consistency index

A t × n :

Data matrix

R :

Correlation coefficient matrix

e i :

Unit eigenvector

f(i):

Principal contribution rate

F(b):

Principal component load

w j :

Objective weight

W :

Combination weight

t :

Risk level number

Q :

Final risk level

σ c / σ t :

Brittle coefficient

K v :

Rock integrity coefficient

AHP:

Analytic hierarchy process

PCA:

Principal component analysis

MFICM:

Multidimensional finite interval cloud model

MNCM:

Multidimensional normal cloud model

RS-TOPSIS:

Rough set-Ideal point method

MABAC:

Multiattributive border approximation area comparison

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Acknowledgements

The research was supported by the National Natural Science Foundation of China (Grant nos. 51504016, 52004017), Fundamental Research Funds for the Central Universities (Grant nos. FRF-BD-17-007A, FRF-TP-19-026A1), and the China Postdoctoral Science Foundation (Grant no. 2020M670138). The authors would like to express appreciation to the Editors and anonymous Reviewers for their valuable and constructive comments relevant to this manuscript.

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Authors and Affiliations

  1. Key Laboratory of Ministry for Efficient Mining and Safety of Metal Mines, University of Science and Technology Beijing, Beijing, 100083, China

    Tianhua Wu, Yongtao Gao, Yu Zhou & Hao Sun

  2. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Tianhua Wu, Yongtao Gao, Yu Zhou & Hao Sun

  3. Department of Resource Engineering, University of Science and Technology Beijing, 30 Xue Yuan Lu (College Road), Beijing, 100083, China

    Yu Zhou

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  1. Tianhua Wu
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  4. Hao Sun
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Contributions

THW conceived and designed the research, wrote the paper and programmed with MATLAB software; YTG drew the figures, collected and analyzed the data; YZ programmed with MATLAB software and contributed ideas concerning the structure and content of the article; HS reviewed and edited the manuscript.

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Correspondence to Yu Zhou.

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Wu, T., Gao, Y., Zhou, Y. et al. A novel comprehensive quantitative method for various geological disaster evaluations in underground engineering: multidimensional finite interval cloud model (MFICM). Environ Earth Sci 80, 696 (2021). https://doi.org/10.1007/s12665-021-10012-1

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