Optimum design and maintenance of pavements require an accurate prediction of their deterioration process. This process is highly influenced by the uncertainties in traffic load and load distribution, and the parameter and model uncertainties associated with all mechanical properties of materials and structural behavior. This paper presents a model for optimizing the design of flexible asphalt pavement structures. The model takes into account the fatigue damage caused on the asphalt surface and the degradation of granular materials caused by repetitive loading cycles. Mechanical considerations are combined with construction and rehabilitation costs as well as financial factors such as the discount rate. Results of an illustrative example showed that the reliability based design optimization (RBDO) combined with a long-term maintenance policy of pavements produces appropriate integral designs. The analyses of the results have shown the advantages of the procedure proposed.

Adverse environmental conditions cause infrastructure systems to deteriorate (e.g., loss capacity) over time. Modeling system deterioration is essential to define optimum design strategies, and inspection and maintenance (intervention) programs. In particular, the main purpose of maintenance is to increase the system availability by extending the life of the system. Most strategies for maintenance optimization focus on defining long term strategies based on the system's condition at the decision time (e.g., t=0). However, due to the large uncertainty in the system's performance through life, an optimal maintenance policy requires both permanent monitoring and a cost-efficient plan of interventions. This paper presents a model to define an optimal maintenance policy of systems that deteriorate as a result of shocks. Deterioration caused by shocks is modeled as a compound Poisson process, and the optimal maintenance strategy is based on an impulse control model. In the model, the optimal time and size of interventions are executed according to the system state, which is obtained from permanent monitoring.

This work considers the European Resource Adequacy Assessment, which is a pan-European resource adequacy process that is being developed by the European Networks of Transmission System Operators for Electricity (ENTSO-E). A critical part of this process is the so-called Economic Viability Assessment model, which aims at determining future expansion and retirement capacity opportunities for the entire European network. As such, the problem is stochastic. Nevertheless, due to computational constraints, simplified approaches have been followed by ENTSO-E. Our work formulates the problem as a two-stage stochastic problem and proposes two decomposition algorithms for solving the problem which are implemented in a high-performance computing infrastructure. The first is a subgradient-based algorithm, and the second uses a relaxation of the second stage (the economic dispatch) in order to speed up the subgradient calculation thus achieving a considerable reduction in solution time. We compare our schemes against the commonly used Bender's decomposition. We compare the obtained stochastic solution against the deterministic solution proposed by ENTSO-E for their 2021 study and analyze the impact of the stochastic solution on various adequacy indicators.

The moment sum of squares (moment-SOS) hierarchy produces sequences of upper and lower bounds on functionals of the exit time location of a polynomial stochastic differential equation with polynomial constraints, at the price of solving semidefinite optimization problems of increasing size. In this note we use standard results from elliptic partial differential equation analysis to prove convergence of the bounds produced by the hierarchy. We also use elementary convex analysis to describe a super- and sub-solution interpretation dual to a linear formulation on occupation measures. Finally, we introduce a novel Christoffel-Darboux approach for the recovery of the exit location and occupation measures. The practical relevance of these results is illustrated with numerical examples.