Nonhomogeneous Markov chains for degeneration behaviour of RC members’ durability and its Bayesian updating

In the context of reinforced concrete components in chloride-rich environments, establishing a priori models describing the degradation process of component durability by integrating existing research findings, and updating these prior models based on field inspection data has emerged as a hotspot in predicting the service life of reinforced concrete components. At present, such methods can only update some parameters in the prior models based on the introduction of field inspection results. They cannot achieve the information update of the function expression of the prior models by fusing the comprehensive durability evaluation results of the components. Given this, a non-homogeneous Markov chain model has constructed to replace the multivariate display functions nested recursion in describing the long-term performance degradation process of RC members. By utilizing the time series and state-space discretization properties of the Markov model, the multiple time-varying patterns coupled with numerous control parameters in the recursive formulation are transformed into time-dependent equations for the elements of the Markov model's state transition matrix. At the same time, a Bayesian updating method for the time-dependent equations of the non-homogeneous Markov chain state transition matrix elements is proposed, enabling the dynamic updating of the non-homogeneous Markov model using the overall current state assessment of the RC component, rather than relying on the detection results of a single indicator. From the perspective of simplifying the mathematical model, the paper addresses the issue of information updating in the degradation process. It provides a new technical approach for dynamically updating the long-term performance degradation time series model of components using state evaluation results. Manuscript uses a simulated case study and a real case study to illustrate the application process of the proposed method and to examine the predictive performance of the model. The results indicate that the updated model predictions envelop both the predictions from the prior model and the actual state assessment results, effectively integrating common understanding with individualized information.