Stochastic Renewal Process Models for Structural Reliability Analysis

Abstract

Reliability analysis in structural engineering is utilized in the initial design phase and its application continues throughout the service life of a structural system in form of maintenance planning and optimization. Engineering structures are usually designed with extremely high reliability and with a long service life. However, deterioration with time and exposure to external hazards like earthquakes, strong winds etc., increase the structure's vulnerability to failure.

In structural reliability analysis, stochastic processes have been utilized to model timedependent uncertain variations in environmental loads and structural resistance. The Homogeneous Poisson Process (HPP) is most commonly used as the driving process behind environmental hazards and shocks causing structural deterioration. The HPP model is justi ed on account of an asymptotic argument that exceedances of a process to a high threshold over a long lifetime converge to HPP model. This approach serves the purpose at the initial design stages. The combination of stochastic loads is an important part of design load estimation. Currently, solutions of the load combination problem are also based on HPP shock and pulse processes. The deterioration is typically modelled as a random variable problem, instead of a stochastic process. Among stochastic models of deterioration, the gamma process is popularly used. The reliability evaluation by combining a stochastic load process with a stochastic process of deterioration, such as gamma process, is a very challenging problem, and so its discussion is quite limited in the existing literature.

In case of reliability assessment of existing structures, such as nuclear power plants nearing the end of life, an indiscriminate use of HPP load models becomes questionable as asymptotic arguments may not be valid over a short remaining life. Thus, this thesis aims to generalize stochastic models used in the structural reliability analysis by considering more general models of environmental hazards based on the theory of the renewal process. These models include shock, pulse and alternating processes. The stochastic load combination problem is also solved in a more general setting by considering a renewal pulse process in combination with a Poisson shock process. The thesis presents a clear exposition of the stochastic load and strength combination problem. Several numerical algorithms have been developed to compute the stochastic reliability solution, and results have been compared with existing approximations. Naturally, existing approximations serve adequately in the routine design. However, in case of critical structures with high consequences to safety and reliability, the use of proposed methods would provide a more realistic assessment of structural reliability.

In summary, the results presented in this thesis contribute to the advancement in stochastic modeling of structural reliability analysis problems.