Abstract Monte Carlo and Active Subspace Identification methods are combined with first-
and second-order adjoint sensitivities to perform (forward) uncertainty quantification analysis
of the thermo-acoustic stability of two annular combustor configurations. This method is
applied to evaluate the risk factor, ie, the probability for the system to be unstable. It is shown
that the adjoint approach reduces the number of nonlinear-eigenproblem calculations by as
much as the Monte Carlo samples.

We present an adjoint-based method for the calculation of eigenvalue perturbations in
nonlinear, degenerate and non-self-adjoint eigenproblems. This method is applied to a
thermo-acoustic annular combustor network, the stability of which is governed by a
nonlinear eigenproblem. We calculate the first-and second-order sensitivities of the growth
rate and frequency to geometric, flow and flame parameters. Three different configurations
are analysed. The benchmark sensitivities are obtained by finite difference, which involves …