Stochastic Petri net-based modelling of the durability of renderings

In this study, a methodology to model and predict the life-cycle performance of building façades based on Stochastic Petri Nets is proposed. The proposed model evaluates the performance of rendered façades over time, evaluating the uncertainty of the future performance of these coatings. The performance of rendered façades is evaluated based on a discrete qualitative scale composed of five condition levels, established according to the physical and visual degradation of these elements. In this study, the deterioration is modelled considering that the transition times between these condition states can be modelled as a random variable with different distributions. For that purpose, a Stochastic Petri Nets model is used, as a formal framework to describe this problem. The model's validation is based on probabilistic indicators of performance, computed using Monte-Carlo simulation and the probability distribution parameters leading to better fit are defined as those maximizing the likelihood, computed using Genetic Algorithm. In this study, a sample of 99 rendered façades, located in Portugal, is analysed, and the degradation condition of each case study is evaluated through in-situ visual inspections. The model proposed allows evaluating: i) the transition rate between degradation conditions; ii) the probability of belonging to a given degradation condition over time; and iii) the mean time of permanence in each degradation condition. The use of Petri Nets shows to be more accurate than a more traditional approach based on Markov Chains, but also allows developing future research to consider different environmental conditions, maintenance actions or inspections, amongst other aspects of life-cycle analysis of existing assets.