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<p>The study integrates the First-Order Reliability Method (FORM) with a K-Nearest Neighbours (KNN) regression model to estimate reliability indices of bridge deep-beam components. The novelty lies in developing a data-driven reliability evaluation framework that compares analytical and machine-learning-based reliability indices. The main aim of this paper is to analyse the reliability of deep beams using both traditional probabilistic methods and machine learning approaches. The study addresses key challenges by evaluating the performance and safety of structural elements under varying loads and material conditions. We created 250 datasets by varying the live load and the concrete’s characteristic compressive strength, fck. Shear stress and deflection, the main outputs, were calculated using structural design principles. We first evaluated the reliability of deep beams using the First-Order Reliability Method on a real dataset. The reliability index (β) values were 1.50 for deflection and 13.61 for shear stress, showing strong structural safety, especially for shear that suggests a serviceability limit state concern. Next, a KNN model was developed to predict deflection and shear stress. The KNN model demonstrated high predictive power, with R² values of 0.998 and 0.996, and Mean Squared Error values of 0.00001 (training) and 0.0003 (testing). Applying FORM to the KNN-predicted outputs yielded β values of 13.61 for shear stress and 1.51 for deflection. The small difference between reliability indices and failure probabilities in actual and predicted datasets validates the effectiveness of the KNN model. Results indicate close agreement between analytical and predicted outcomes, demonstrating the applicability of ML-assisted reliability analysis. The findings demonstrate that the KNN algorithm is highly effective for reliability analysis and prediction of structural responses. Integrating machine learning with traditional probabilistic methods provides a strong framework for assessing safety and performance in complex structural systems such as deep beams. The study also highlights computational efficiency and practical limitations of the proposed approach.</p>

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Reliability analysis of components of bridge beam structure

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Abhishek Kumar Singh,
  • Pijush Samui

摘要

The study integrates the First-Order Reliability Method (FORM) with a K-Nearest Neighbours (KNN) regression model to estimate reliability indices of bridge deep-beam components. The novelty lies in developing a data-driven reliability evaluation framework that compares analytical and machine-learning-based reliability indices. The main aim of this paper is to analyse the reliability of deep beams using both traditional probabilistic methods and machine learning approaches. The study addresses key challenges by evaluating the performance and safety of structural elements under varying loads and material conditions. We created 250 datasets by varying the live load and the concrete’s characteristic compressive strength, fck. Shear stress and deflection, the main outputs, were calculated using structural design principles. We first evaluated the reliability of deep beams using the First-Order Reliability Method on a real dataset. The reliability index (β) values were 1.50 for deflection and 13.61 for shear stress, showing strong structural safety, especially for shear that suggests a serviceability limit state concern. Next, a KNN model was developed to predict deflection and shear stress. The KNN model demonstrated high predictive power, with R² values of 0.998 and 0.996, and Mean Squared Error values of 0.00001 (training) and 0.0003 (testing). Applying FORM to the KNN-predicted outputs yielded β values of 13.61 for shear stress and 1.51 for deflection. The small difference between reliability indices and failure probabilities in actual and predicted datasets validates the effectiveness of the KNN model. Results indicate close agreement between analytical and predicted outcomes, demonstrating the applicability of ML-assisted reliability analysis. The findings demonstrate that the KNN algorithm is highly effective for reliability analysis and prediction of structural responses. Integrating machine learning with traditional probabilistic methods provides a strong framework for assessing safety and performance in complex structural systems such as deep beams. The study also highlights computational efficiency and practical limitations of the proposed approach.