SUMMARYTo support effective decision making, engineers should comprehend and manage various uncertainties throughout the design process. Unfortunately, in today's modern systems, uncertainty analysis can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprised of a large number of components. In many cases, these components may be developed by different groups and even run on different computational platforms. This paper proposes an approach for decomposing the uncertainty analysis task among the various components comprising a feed-forward system and synthesizing the local uncertainty analyses into a system uncertainty analysis. Our proposed decomposition-based multicomponent uncertainty analysis approach is shown to be provably convergent in distribution under certain conditions. The proposed method is illustrated on quantification of uncertainty for a multidisciplinary gas turbine system and is compared to a traditional system-level Monte Carlo uncertainty analysis approach. Copyright © 2014 John Wiley & Sons, Ltd.

This second paper presents the aerothermal optimization of the first stage rotor blade of an axial high pressure (HP) turbine by means of the conjugate heat transfer (CHT) method and lifetime model described in Paper I. The optimization system defines the position and diameter of the cooling channels leading to the maximum lifetime of the blade while limiting the amount of cooling flow. It is driven by the results of a CHT and subsequent stress analysis of each newly designed geometry. Both temperature and stress distributions are the input for the Larson–Miller material model to predict the lifetime of the blade. The optimization procedure makes use of a genetic algorithm (GA) and requires the aerothermal analysis of a large number of geometries. Because of the large computational cost of each CHT analysis, this results in a prohibitive computational effort. The latter has been remediated by using a more elaborate optimization system, in which a large part of the CHT analyzes is replaced by approximated predictions by means of a metamodel. Two metamodels, an artificial neural network and a radial basis function network, have been tested and their merits have been discussed. It is shown how this optimization procedure based on CHT calculations, a GA, and a metamodel can lead to a considerable extension of the blade lifetime without an increase in the amount of cooling flow or the complexity of the cooling geometry.

This first paper describes the conjugate heat transfer (CHT) method and its application to the performance and lifetime prediction of a high pressure turbine blade operating at a very high inlet temperature. It is the analysis tool for the aerothermal optimization described in a second paper. The CHT method uses three separate solvers: a Navier–Stokes solver to predict the nonadiabatic external flow and heat flux, a finite element analysis (FEA) to compute the heat conduction and stress within the solid, and a 1D aerothermal model based on friction and heat transfer correlations for smooth and rib-roughened cooling channels. Special attention is given to the boundary conditions linking these solvers and to the stability of the complete CHT calculation procedure. The Larson–Miller parameter model is used to determine the creep-to-rupture failure lifetime of the blade. This model requires both the temperature and thermal stress inside the blade, calculated by the CHT and FEA. The CHT method is validated on two test cases: a gas turbine rotor blade without cooling and one with five cooling channels evenly distributed along the camber line. The metal temperature and thermal stress distribution in both blades are presented and the impact of the cooling channel geometry on lifetime is discussed.

This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon-Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the L 2 -norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and boxconstrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class