• Structural Engineering and Mechanics
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• v.47 no.1
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• pp.45-58
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• 2013

In structural reliability analysis, the response surface method is a powerful method to evaluate the probability of failure. However, the location of experimental points used to form a response surface function must be selected in a judicious way. It is necessary for the highly nonlinear limit state functions to consider the design point and the nonlinear trend of the limit state, because both of them influence the probability of failure. In this paper, in order to approximate the actual limit state more accurately, experimental points are selected close to the design point and the actual limit state, and consider the nonlinear trend of the limit state. Linear, quadratic and cubic polynomials without mixed terms are utilized to approximate the actual limit state. The direct Monte Carlo simulation on the approximated limit state is carried out to determine the probability of failure. Four examples are given to demonstrate the efficiency and the accuracy of the proposed method for both numerical and implicit limit states.

• Journal of the Korean Society of Propulsion Engineers
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• v.15 no.6
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• pp.98-106
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• 2011

This paper reviews the state-of-the-art thermoacoustic(TA) modeling techniques and research trend to predict major parameters determining combustion instabilities in lean premixed gas turbine combustors. Linear TA modeling results give us an information on eigenfrequencies and initial growth rate of the instabilities. For the prediction, linear relation equation between acoustic waves and heat release oscillations should be derived in the determined system. Key information for this analysis is to determine the heat release fluctuations in the combustor, which is typically obtained by using n-${\tau}$ function from flame transfer function measurements and/or predictions. Great advancement in the linear TA modeling has been made over a couple of decades, and some successful prediction results have been reported in actual gas turbine combustors. However nonlinear TA model developments which are required to analyze nonlinear system behaviors such as limit cycle saturation and transition phenomena are still limited in a very simple system. In order to fully understand combustion instabilities in a complicated real system, nonlinear flame dynamics and acoustic wave interaction with nonlinear system boundary conditions should be explained from the nonlinear TA model developments.