Study On The Structural Time-dependent Reliability Analysis And The Optimization Design

In practical engineering, due to the effects of loads, environments and interior factors of materials, system performance is time-dependent and reliability of structures or conponents will deteriorate gradually before final failure. This produces an effect on service. In order to guarantee structural safety during its service lifetime, it is urgent to carry out structural time-dependent reliability analysis and optimization design.Structural time-dependent reliability analysis has the following features: 1) external loads or performance degradation rules are generally described by stochastic processes; 2) limit state functions often exist in an implicit form; 3) small failure probabilities are desined for structures in practical engineering; 4) traditional reliability methods is time-consuming and inefficient. Therefore, it is necessary to develop an effective time-dependent reliability method, establish a comprehensive time-dependent reliability analysis model, which can effectively solve reliability analysis and RBDO problems for complex structrues.Aiming at the problems mentioned above, the main contents and achievements in this paper are listed as follows:(1) A reliability method(AK-SS) is proposed aiming at the case of implicit limit state functions and small failure probabilities in structural reliability analysis. A Kriging model is utilized to replace the true performance function based on small size of sample points, and then the Kriging model is updated progressively through active learning method. Based on the Kriging model, the Subset simulation(SS) method is adopted to evaluate the failure probabilies. The new method AK-SS is applied to the reliability analysis of a shield tunnel. The AK-SS method provides accurate solutions more efficiently, making it a promising approach for deteriorating tructural reliability analyses with small failure probabilities in practical engineering.(2) Based on the mixed stochastic processes, a time-dependent reliability analysis model of deteriorating structures considering both ageing effects and random shocks is proposed. The ageing effect is modeled as a Gamma process while the random shock is described by a Poisson process. A more comprehensive deteriorating model is estiabilished. To incorporate effects of model uncertainties, Bayesian inference methods are further integrated with the reliability model to update the uncertain parameters in the model using sampling data. The uncertainty in deteriorating model is therefore reduced.Numerical examples demonstrate that the proposed model provides a reasonable method for evaluating the reliability of deteriorating structures containing model uncertainties.(3) Aming at the case of non-monotonic performance variation, a mixed EGO-AK-SS method is proposed for time-dependent reliability analysis. In the proposed method, the Mixed-EGO(Mixed Efficient Global Optimization) algorithm is utilized to build an initial Kriging extreme response surface, which is improved gradually by adding the best next points based on AK-SS. Simultaneously, the time-dependent reliability can be obtained. This proposed method has advantages to deal with time-dependent reliability analysis with very small failure probabilities in practical engineering.(4) Aiming at the reliability-based design optimization(RBDO) with time-dependent reliability constraints, a mixed EGO-SORA method for time-dependent RBDO is proposed. The time-dependent reliability constraint is converted to time-independent one with the Mixed-EGO method. The RBDO problem is devided into two loops by using sequential optimization and reliability assessment(SORA) approach: deterministic optimization loop and the reliability analysis loop. During the reliability index evaluation and the optimal solution searching process, the Kriging extreme response surface for the time-dependent reliability constraint is updated gradually by adding an approximate most probable point(MPP) to the design of experiment(Do E). The proposed method possesses the merit of the SORA in solving RBDO problems efficiently and the merit of extreme response surface in dealing with time-dependent constraints accurately.