A novel hybrid surrogate intelligent model for creep index prediction based on particle swarm optimization and random forest

Pin Zhang, Zhen Yu Yin, Yin Fu Jin, Tommy H.T. Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

122 Citations (Scopus)


Long-term settlement issues in engineering practice are controlled by the creep index, Cα, but current empirical models of Cα are not sufficiently reliable. In a departure from previous correlations, this study proposes a hybrid surrogate intelligent model for predicting Cα. The new combined model integrates a meta-heuristic particle optimization swarm (PSO) in the random forest (RF) to overcome the user experience dependence and local optimum problems. A total of 151 datasets having four parameters (liquid limit wL, plasticity index Ip, void ratio e, clay content CI) and one output variable Cα are collected from the literature. Eleven combinations of these four parameters (one with four parameters, four with three parameters and six with two parameters) are used as input variables in the RF algorithm to determine the optimal combination of variables. In this novel model, PSO is employed to determine the optimal hyper-parameters in the RF algorithm, and the fitness function in the PSO is defined as the mean prediction error for 10 cross-validation sets to enhance the robustness of the RF model. The performance of the RF model is compared specifically with the existing empirical formulae. The results indicate that the combinations IP–e, CI–IP–e and CI–wL–Ip–e are optimal RF models in their respective groups, recommended for predicting Cα in engineering practice. What's more, these three proposed models demonstrably outperform empirical methods, featuring as they do lower levels of prediction error. Parametric investigation indicates that the relationships between Cα and the four input variables in the proposed RF models harmonize with the physical explanation. A Gini index generated during the RF process indicates that Cα is much more sensitive to e than to CI, Ip and wL, in that order – although the difference among the latter three variables can be negligible.

Original languageEnglish
Article number105328
JournalEngineering Geology
Publication statusPublished - Feb 2020


  • Correlation
  • Creep
  • Machine learning
  • Optimization
  • Physical properties
  • Soft clay

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Geology


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