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Risk Assessment of Scramjet Unstart Using Adjoint-Based Sampling Methods

Summary: Risk Assessment of Scramjet Unstart Using Adjoint-Based
Sampling Methods
Qiqi Wang
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Karthik Duraisamy,
Juan J. Alonso,
and Gianluca Iaccarino§
Stanford University, Stanford, California 94305
DOI: 10.2514/1.J051264
In this paper, we demonstrate an adjoint-based approach for accelerating Monte Carlo estimations of risk, and we
apply it to approximate the unstart probability of a supersonic combustion ramjet (scramjet) engine under changes
in uncertain operating conditions characterized by both Gaussian and non-Gaussian distributions. The adjoint
equation is formulated with respect to an objective function that has been experimentally shown to be indicative of
unstart, and it is used to build a linear surrogate. This surrogate is, in turn, used to divide the uncertain input
parameters into three different strata corresponding to safe operation of the engine, uncertain operation, and
unstart. The probability of unstart within these strata is very different and, as a result, stratified sampling
significantly reduces the variance of the estimator. The efficiency of the stratified sampling procedure is further
improved by optimally allocating the number of solution evaluations within each stratum. Using this technique, the
estimations from straightforward use of the Monte Carlo method were demonstrated to be accelerated by a factor of


Source: Alonso, Juan J. - Department of Aeronautics and Astronautics, Stanford University


Collections: Engineering