Quantifying Staircase Wear in Historic Buildings Using GMM and MCMC Methods

This paper proposes a GMM and MCMC based model to estimate the wear and tear of stair steps. The total wear is calculated by using the Archard model. Next, the model used cluster analysis to count stepping points. Finally, the model estimates the frequency of pedestrian traffic at each step. Given the absence of wear data on ancient staircases, an exponential decay model of wear versus time was developed. This model estimated the service life of the staircase to be approximately 144.4 years. Subsequently, a Gaussian Mixture Model (GMM) combined with an Expectation Maximization (EM) algorithm was used to cluster discrete wear points. The experimental results demonstrate that the wear predicted by the model is almost 85% accurate in comparison to the actual data. This paper presents a quantitative analysis model that aims to elucidate the wear mechanism of ancient staircases. It offers novel concepts and directions for archaeological research and cultural heritage preservation.