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Sampling-based methods are general but time consuming for solving a Reliability-Based Design Optimization (RBDO) problem. In order to alleviate the computation burden, score function together with the Monte Carlo method was used to compute the stochastic sensitivities of reliability functions. In literature, re-weighting schemes were shown to converge faster than the regular Monte Carlo method. In this paper, a reweighting scheme together with score function is employed to perform sampling-based stochastic sensitivity analysis to improve the computational efficiency and accuracy. An analytical example is used to show the advantages of the proposed method. Comparisons to the conventional methods are made and discussed. Two RBDO problems are solved to demonstrate the use of the proposed method.

The proper formation of fuel-air mixture, which depends to a large extend on the complex in-cylinder air flow, is an important criterion to control the clean and reliable combustion process in spark-ignition direct-injection (SIDI) engines. The in-cylinder flow vorticity field presents highly transient complex characteristics, and the corresponding vorticity field also evolves in the entire engine cycle from intake to exhaust strokes. It is also widely recognized that the vorticity field plays a key role in the in-cylinder turbulent field because it influences the air-fuel mixing and flame development process. In this investigation, the in-cylinder vortex structure and vorticity field characteristics are analyzed using the phase-invariant proper orthogonal decomposition (POD) method.