Soft Computing

, Volume 23, Issue 14, pp 5913–5929 | Cite as

Applying various hybrid intelligent systems to evaluate and predict slope stability under static and dynamic conditions

  • Mohammadreza KoopialipoorEmail author
  • Danial Jahed Armaghani
  • Ahmadreza Hedayat
  • Aminaton Marto
  • Behrouz Gordan
Methodologies and Application


The evaluation and precise prediction of safety factor (SF) of slopes can be useful in designing/analyzing these important structures. In this study, an attempt has been made to evaluate/predict SF of many homogenous slopes in static and dynamic conditions through applying various hybrid intelligent systems namely imperialist competitive algorithm (ICA)-artificial neural network (ANN), genetic algorithm (GA)-ANN, particle swarm optimization (PSO)-ANN and artificial bee colony (ABC)-ANN. In fact, ICA, PSO, GA and ABC were used to adjust weights and biases of ANN model. In order to achieve the aim of this study, a database composed of 699 datasets with 5 model inputs including slope gradient, slope height, friction angle of soil, soil cohesion and peak ground acceleration and one output (SF) was established. Several parametric investigations were conducted in order to determine the most effective factors of GA, ICA, ABC and PSO algorithms. The obtained results of hybrid models were check considering two performance indices, i.e., root-mean-square error and coefficient of determination \((R^{2})\). To evaluate capability of all hybrid models, a new system of ranking, i.e., the color intensity rating, was developed. As a result, although all predictive models are able to approximate slope SF values, PSO-ANN predictive model can perform better compared to others. Based on \(R^{2}\), values of (0.969, 0.957, 0.980 and 0.920) were found for testing of ICA-ANN, ABC-ANN, PSO-ANN and GA-ANN predictive models, respectively, which show higher efficiency of the PSO-ANN model in predicting slope SF values.


Slope stability Hybrid model Genetic algorithm Particle swarm optimization Imperialist competitive algorithm Artificial bee colony 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Mohammadreza Koopialipoor
    • 1
    Email author
  • Danial Jahed Armaghani
    • 2
    • 3
  • Ahmadreza Hedayat
    • 4
  • Aminaton Marto
    • 3
  • Behrouz Gordan
    • 5
  1. 1.Faculty of Mining and MetallurgyAmirkabir University of TechnologyTehranIran
  2. 2.Faculty of Civil and Environmental EngineeringAmirkabir University of TechnologyTehranIran
  3. 3.Environmental Engineering and Green Technology Department, Malaysia-Japan International Institute of TechnologyUniversiti Teknologi MalaysiaKuala LumpurMalaysia
  4. 4.Faculty of Civil and Environmental EngineeringColorado School of MinesGoldenUSA
  5. 5.Department of Geotechnics and Transportation, Faculty of Civil EngineeringUniversiti Teknologi Malaysia (UTM)SkudaiMalaysia

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