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<p>Operating speed consistency is one of surrogate measure for evaluating geometric design consistency on mountainous highways, yet existing prediction models often fail to account for heteroscedasticity and sampling bias. This study aims to develop reliable and robust operating speed prediction (V<sub>85</sub><sup>P</sup>) models for horizontal and vertical curves of mountainous highways using Weighted Least Squares with Backward Stepwise Regression (WLS-BSR). Continuous speed data were collected using a 5&#xa0;Hz GPS device across 120 horizontal and 60 vertical curves on a representative highway in Himachal Pradesh, India. Ordinary Least Squares (OLS) models exhibited significant heteroscedasticity, confirmed by the Breusch–Pagan test (χ<sup>2</sup> = 86.92, <i>p</i> &lt; 0.01), motivating the weighted approach. Separate models were developed for two-wheelers, passenger cars, and heavy commercial vehicles across curve categories classified by curve orientation and vertical gradient. The final WLS-BSR models achieved R<sup>2</sup> values of 0.791–0.964, substantially outperforming OLS (R<sup>2</sup> = 0.471–0.776). Key predictors included curve radius (R), deflection angle (Δ), gradient (Gc), superelevation (e), and the percentage of horizontal curve within a vertical curve (P<sub>v</sub>). Bootstrap resampling showed that all retained predictors were selected in more than 70% of samples, while five-fold cross-validation indicating minimal overfitting. Models validation on 30 spatially distinct curves and transferability testing demonstrated robust predictive performance. Significantly, curves identified as inconsistent by the WLS-BSR models accounted for 41% of observed crashes, nearly double the detection rate of OLS. These results demonstrate that WLS-BSR effectively addresses heteroscedasticity and sampling bias of geometric design variables, providing reliable and robust models. These models provide a practical tool for screening mountainous highways for geometric design inconsistencies and supporting performance-based safety evaluation at both project and network levels.</p>

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Operating speed prediction modelling on mountainous highway curves using WLS-BSR regression

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Kartick Kumar,
  • Sunil Sharma

摘要

Operating speed consistency is one of surrogate measure for evaluating geometric design consistency on mountainous highways, yet existing prediction models often fail to account for heteroscedasticity and sampling bias. This study aims to develop reliable and robust operating speed prediction (V85P) models for horizontal and vertical curves of mountainous highways using Weighted Least Squares with Backward Stepwise Regression (WLS-BSR). Continuous speed data were collected using a 5 Hz GPS device across 120 horizontal and 60 vertical curves on a representative highway in Himachal Pradesh, India. Ordinary Least Squares (OLS) models exhibited significant heteroscedasticity, confirmed by the Breusch–Pagan test (χ2 = 86.92, p < 0.01), motivating the weighted approach. Separate models were developed for two-wheelers, passenger cars, and heavy commercial vehicles across curve categories classified by curve orientation and vertical gradient. The final WLS-BSR models achieved R2 values of 0.791–0.964, substantially outperforming OLS (R2 = 0.471–0.776). Key predictors included curve radius (R), deflection angle (Δ), gradient (Gc), superelevation (e), and the percentage of horizontal curve within a vertical curve (Pv). Bootstrap resampling showed that all retained predictors were selected in more than 70% of samples, while five-fold cross-validation indicating minimal overfitting. Models validation on 30 spatially distinct curves and transferability testing demonstrated robust predictive performance. Significantly, curves identified as inconsistent by the WLS-BSR models accounted for 41% of observed crashes, nearly double the detection rate of OLS. These results demonstrate that WLS-BSR effectively addresses heteroscedasticity and sampling bias of geometric design variables, providing reliable and robust models. These models provide a practical tool for screening mountainous highways for geometric design inconsistencies and supporting performance-based safety evaluation at both project and network levels.