Product Of Larger Conditional Probabilities Research Articles

Dynamic reliability evaluation of vehicle–track coupled systems considering the randomness of suspension and wheel–rail parameters

The ride quality and running safety of high-speed trains are directly influenced by uncertainties of some key parameters, such as the damping and stiffness coefficients of suspension systems, wheel–rail coefficient of friction and wheel–rail profiles. Dynamic reliability problems of vehicle–track coupled systems under the influence of the above random parameters are studied in this article. An efficient numerical method is presented by combining a prediction-based iterative solution technique with subset simulation method. The solution efficiency of deterministic responses is improved by means of efficient prediction of wheel–rail forces, and the number of deterministic solutions required is reduced by expressing a small failure probability as a product of large conditional probabilities. The accuracy and the efficiency of the present method are verified by comparing with the direct Monte Carlo simulation. The failure probability distribution curves of the lateral ride index on straight track and the derailment coefficient during curve negotiation are obtained and the reliability sensitivity analyses are also carried out. The main conclusions are given as follows: the reliability of the system is higher when the randomness of the parameters with greater sensitivity is not considered; the increase of the damping of anti-yaw damper or the wheel–rail coefficient of friction will improve the ride quality on straight track, but will lower the running safety when negotiating a curved track.

Extracting Rare Failure Events in Composite System Reliability Evaluation Via Subset Simulation

This paper proposes an efficient method for evaluating composite system reliability via subset simulation. The central idea is that a small failure probability can be expressed as a product of larger conditional probabilities, thereby turning the problem of simulating a rare failure event into several conditional simulations of more frequent intermediate failure events. In existing methods, system states are simply assessed in a binary secure/failure manner. To fit into the context of subset simulation, the adequacy of system states is parametrized with a metric based on linear programming, thus allowing for an adaptive choice of intermediate failure events. Samples conditional on these events are generated by Markov chain Monte Carlo simulation. The proposed method requires no prior information before imulation. Different models for renewable energy sources can also be accommodated. Numerical tests show that this method is significantly more efficient than standard Monte Carlo simulation, especially for simulating rare failure events.

Subset Simulation of a reliability model for radioactive waste repository performance assessment

In this paper, we show an original application of the Subset Simulation (SS) technique on a model for the performance assessment of a near surface radioactive waste repository. The logic of the protective barriers of the repository is represented by a reliability model. The SS approach is founded on the idea that a small failure probability can be expressed as a product of larger conditional probabilities of some intermediate events; with a proper choice of the conditional events, the conditional probabilities can be sufficiently large to allow accurate estimation with a small number of samples. In the application, the method allows improving the efficiency of the random sampling for estimating the repository containment failure probability. Moreover, the peculiar set-partitioning scheme of the SS method is exploited for performing the analysis of the sensitivity of the failure probability estimate to the uncertain model parameters.

Estimation of the functional failure probability of a thermal–hydraulic passive system by Subset Simulation

In the light of epistemic uncertainties affecting the model of a thermal–hydraulic (T–H) passive system and the numerical values of its parameters, the system may find itself in working conditions which do not allow it to accomplish its function as required. The estimation of the probability of these functional failures can be done by Monte Carlo (MC) sampling of the uncertainties in the model followed by the computation of the system response by a mechanistic T–H code. The procedure requires considerable computational efforts for achieving accurate estimates. Efficient methods for sampling the uncertainties in the model are thus in order. In this paper, the recently developed Subset Simulation (SS) method is considered for improving the efficiency of the random sampling. The method, originally developed to solve structural reliability problems, is founded on the idea that a small failure probability can be expressed as a product of larger conditional probabilities of some intermediate events: with a proper choice of the conditional events, the conditional probabilities can be made sufficiently large to allow accurate estimation with a small number of samples. Markov Chain Monte Carlo (MCMC) simulation, based on the Metropolis algorithm, is used to efficiently generate the conditional samples, which is otherwise a non-trivial task. The method is here developed for efficiently estimating the probability of functional failure of an emergency passive decay heat removal system in a simple steady-state model of a Gas-cooled Fast Reactor (GFR). The efficiency of the method is demonstrated by comparison to the commonly adopted standard Monte Carlo Simulation (MCS).