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New Methods in Systems Reliability
The dissertation comprises three areas of research: reliability analysis of truss and frame structures, parametric sensitivity analysis and use of simulation based techniques to estimate reliability.
In the first part of the thesis, we extend currently used reliability analysis procedures for truss and frame structures to allow more realistic modeling of non-linear behaviour. Current procedures are restricted to structure models with "two-state" elements and static proportional loads. The elements, semi-brittle truss members and rigid-plastic hinges, can be in either their initial (safe) state or their yielded (failed) state. Structure failure can be defined in terms of sequences of element failures and the structure failure event can be formulated as a union of intersections of element failure events. First order reliability methods are then used to compute the structure
reliability. We extend this methodology to truss structures with multi-state elements under proportional and non-proportional loads. We also extend it to frame structures with moment/axial-force interaction effects.
The second part of the thesis focuses on a different aspect of system reliability, namely the sensitivity of the failure probability to the distribution parameters (e.g., the means and variances of the random variables). A new method is presented for estimating the sensitivity in the context of simulation schemes. The method requires only marginally extra computation and can be used with a wide range of simulation techniques including Monte Carlo simulation, Latin hypercube sampling, stratified sampling, importance sampling and conditional expectation. A new approach to estimate sensitivities in the context of First and Second Order Reliability Methods is also presented. This approach can be used for component and system problems.
The last part of the thesis advances the use of simulation based methods for estimating reliability. These methods can be applied to a wider range of problems than currently popular first and second order reliability methods. But these methods are efficient only if one has a priori knowledge about the important regions of the failure domain [i.e., which regions have a significant contribution to the failure probability). Usually, such a priori knowledge is not available. However, as the simulation proceeds, knowledge about the failure domain increases and it is possible to develop adaptive schemes which constantly modify themselves to incorporate the increasing knowledge base. In this last part of the thesis, two such adaptive scheme are presented. One of the schemes is based on importance sampling while the other involves a combination of importance sampling and conditional expectation. Both schemes are found to far more effective than existing simulation methods .