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<p>A probabilistic framework for slope safety factor prediction was developed using heterogeneous ensemble learning and Bayesian model averaging to improve predictive reliability and uncertainty quantification under limited geotechnical data conditions. A dataset containing typical slope parameters, including density, cohesion, internal friction angle, slope angle, slope height, and pore water pressure ratio, was used to construct five heterogeneous learning models: support vector regression, random forest, multilayer perceptron, gradient boosting decision tree, and k-nearest neighbor. Bayesian optimization was employed to calibrate model hyperparameters, and posterior model probabilities were estimated through Markov Chain Monte Carlo sampling. The sampled posterior probabilities were normalized as model weights to achieve probabilistic ensemble prediction and uncertainty propagation. Results showed that the proposed framework achieved superior predictive performance, with a mean squared error of 0.0302, a mean absolute error of 0.1242, and a coefficient of determination of 0.8919, while reducing predictive dispersion with a prediction standard deviation of 0.3174 compared with individual models. The framework also quantified prediction uncertainty and reliability through posterior probabilistic inference. The proposed method provides a reliability-oriented strategy for intelligent slope stability evaluation and offers potential applications in transportation geotechnical engineering and hazard prevention.</p>

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Uncertainty Prediction of Slope Safety Factor Based on Heterogeneous Ensemble-Bayesian Model Averaging

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Huajin Zhang,
  • Fangjia Song,
  • Yixiong Gan,
  • Mingzhen Chai

摘要

A probabilistic framework for slope safety factor prediction was developed using heterogeneous ensemble learning and Bayesian model averaging to improve predictive reliability and uncertainty quantification under limited geotechnical data conditions. A dataset containing typical slope parameters, including density, cohesion, internal friction angle, slope angle, slope height, and pore water pressure ratio, was used to construct five heterogeneous learning models: support vector regression, random forest, multilayer perceptron, gradient boosting decision tree, and k-nearest neighbor. Bayesian optimization was employed to calibrate model hyperparameters, and posterior model probabilities were estimated through Markov Chain Monte Carlo sampling. The sampled posterior probabilities were normalized as model weights to achieve probabilistic ensemble prediction and uncertainty propagation. Results showed that the proposed framework achieved superior predictive performance, with a mean squared error of 0.0302, a mean absolute error of 0.1242, and a coefficient of determination of 0.8919, while reducing predictive dispersion with a prediction standard deviation of 0.3174 compared with individual models. The framework also quantified prediction uncertainty and reliability through posterior probabilistic inference. The proposed method provides a reliability-oriented strategy for intelligent slope stability evaluation and offers potential applications in transportation geotechnical engineering and hazard prevention.