Modeling Staircase Wear Using Logistic Growth and Clustering Analysis

Abstract

This study develops a novel framework for assessing staircase wear in high-traffic environments by integrating logistic growth modeling with clustering-based crowd behavior analysis. Traditional visual inspection methods often fail to provide quantitative wear assessments, necessitating data-driven approaches to evaluate deterioration patterns and predict service life. The proposed two-phase logistic model distinguishes between natural degradation (unrepaired state) and post-repair recovery, incorporating adjusted growth rates and maximum wear capacities to reflect maintenance impacts. Clustering techniques analyze pedestrian flow patterns, revealing an annual usage frequency of 75.002 million people and identifying predominant upward movement tendencies (82.4% side-by-side walking). Spatial wear analysis demonstrates concentrated degradation on step outer edges and right sides, correlating with biomechanical movement patterns. Results demonstrate the model's effectiveness in quantifying wear progression, offering actionable insights for maintenance planning and stair design optimization. The hybrid approach bridges theoretical wear mechanics with real-world usage dynamics, providing a scalable solution for infrastructure management that could be extended to other high-traffic structures.