The leading-edge noise generated by turbofan and open rotor engines due to interaction with turbulence can be a significant contributor to the total noise radiated by an aircraft. This noise source is very sensitive to the nature of the turbulence that impinges on the leading edge. Most analytical and numerical models assume that the turbulence is isotropic. This assumption produces satisfactory results for the majority of cases considered. However, there are numerous noise sources in which the anisotropy of the turbulence is significant and the resultant noise is poorly predicted with the use of an isotropic velocity spectrum. One such noise source is the ingestion of a turbulent boundary layer by an open rotor. This paper includes the anisotropic velocity spectrum of Kerschen and Gliebe in Amiet's analytical model for a translating aerofoil. Using the translating model it is shown that the axial length scale shifts the frequency at which the maximum energy in the spectra occurs and moderately alters the resulting sound PoWer Level (PWL) spectra. Conversely, altering the transverse length scale does not change the frequency at which the maximum energy occurs in the spectra but does alter the maximum PWL significantly. The analytical analysis of an aerofoil ingesting anisotropic turbulence provides an insight into how redistributing the energy in the axial and transverse energy spectra, by changing the axial and transverse length scales, can reduce leading-edge noise. The anisotropic turbulence model is compared to two real world anisotropic turbulence datasets available in the literature. These are datasets for boundary-layer turbulence obtained from experiments and direct numerical simulations of a channel flow. When the model spectra is compared to statistics obtained from these datasets, several discrepancies are observed. It is observed that the model spectrum significantly over-predicts the transverse integral length scales and energy spectra.

We present several applications of the bias-variance decomposition, beginning with straightforward Monte Carlo estimation of integrals, but progressing to the more complex problem of Monte Carlo Optimization (MCO), which involves finding a set of parameters that optimize a parameterized integral. We present the similarity of this application to that of Parametric Learning (PL). Algorithms in this field use a particular interpretation of the bias-variance trade to improve performance. This interpretation also applies to MCO, and should therefore improve performance. We verify that this is indeed the case for a particular MCO problem related to adaptive importance sampling.

As part of Aerion’s effort to gain experimental data on natural laminar flow between Mach 1 and 2, a new series of flight tests were conducted in collaboration with NASA. This paper describes the optimization of a test article explicitly designed to maximize the extent of natural laminar flow in supersonic flight. The goal was to obtain extensive laminar flow on a test article mounted underneath NASA’s F-15B which presents challenges due to a complex flow field and due to test article span constraints. We used Cart3D-IBL for steady-state CFD analysis as well as transition prediction, which used data fits to linear stability results from Lastrac. The optimized test article was flown at speeds up to Mach 1.8 and flight data is in good agreement with predictions of laminar extent.

This article concerns "blackbox optimization" algorithms in which one iterates the following procedure: Choose a value x is an element of X, getting statistical information about an associated value G(x), then use the set of all pairs {(x, G(x))} found so far to choose a next x value at which to sample G, the goal being to find xs with as small G(x) as possible, and to do so as fast as possible. Examples of conventional blackbox optimization algorithms are genetic algorithms, simulated annealing, etc. These conventional algorithms work directly with values x, stochastically mapping the set {(x, G(x))} to the next x. The distribution over new xs that gets sampled is never explicitly optimized. In contrast, in the Probability Collectives (PC) approach, one explicitly uses the set {(x, G(x))} to optimize the probability distribution over x that will be sampled. This article reviews some of the work that has been done on Probability Collectives, in particular presenting some of the many experiments that have demonstrated its power.

Increasing interest in natural laminar flow technology has created a need for improved techniques for predicting instability growth and transition for aircraft. At the conceptualdesign stage, there is a need for rapid and reliable methods that facilitate exploration of a large number of designs. While it is believed that linear stability theory in conjunction with the e n criterion provides adequate accuracy for conceptual design, existing linear stability codes are too slow to be used so early in the design process, often requiring significant user interaction and human-in-the-loop iteration to yield reasonable results. In this paper, we present an improved methodology for rapid and robust transition prediction. The technique uses a database of linear stability results on representative boundary layers and constructs a machine-learning fit to those results. Unlike many fit-based transition prediction methods, we do not attempt to model the behavior of n-factor envelopes. Rather, we closely mimic the procedure followed in linear stability computations by modeling the local growth rate of individual modes as a function temporal frequency, spatial wave number, and several boundary-layer parameters. This enables us to reproduce sophisticated n-factor behavior that previous techniques could not. While there have been other techniques that use databases, they have generally been restricted to incompressible flows and provide no way of extending their applicability or improving their accuracy. Our methodology is far less restrictive and is easily extended to specific applications by adding relevant data based on flow conditions and aircraft geometries of interest. Recent additions to the methodology include a modal description of the velocity and temperature profiles using singular value decomposition.

In many stochastic optimization algorithms there is a hyperparameter that controls how the next sampling distribution is determined from the current data set of samples of the objective function. This hyperparameter controls the exploration /exploitation trade-off of the next sample. Typically heuristic rules of thumb are used to set that hyperparameter, e.g., a pre-fixed annealing schedule. We show how machine learning provides more principled alternatives to (adaptively) set that hyperparameter, and demonstrate that these alternatives can substantially improve optimization performance.

L'invention porte sur un appareil de traitement comprenant un ou plusieurs processeurs et une memoire, qui obtient une ou plusieurs mesures de capteur generees par un ou plusieurs capteurs de surveillance d'un ou plusieurs dispositifs, comprenant une ou plusieurs mesures de capteur de surveillance provenant d'un capteur de surveillance respectif d'un dispositif respectif et qui obtient un ou plusieurs signaux de systeme comprenant un signal de systeme respectif correspondant a un fonctionnement courant du dispositif respectif. L'appareil de traitement determine des informations de contexte de dispositif pour le dispositif respectif sur la base de la ou des mesures de capteur et du ou des signaux de systeme et regle le fonctionnement du dispositif selon les informations de contexte de dispositif.

In this paper, we examine the CE method in the broad context of Monte Carlo Optimization (MCO) and Parametric Learning (PL), a type of machine learning. A well-known overarching principle used to improve the performance of many PL algorithms is the bias-variance tradeoff. This tradeoff has been used to improve PL algorithms ranging from Monte Carlo estimation of integrals, to linear estimation, to general statistical estimation. Moreover, as described by, MCO is very closely related to PL. Owing to this similarity, the bias-variance tradeoff affects MCO performance, just as it does PL performance. In this article, we exploit the bias-variance tradeoff to enhance the performance of MCO algorithms. We use the technique of cross-validation, a technique based on the bias-variance tradeoff, to significantly improve the performance of the Cross Entropy (CE) method, which is an MCO algorithm. In previous work we have confirmed that other PL techniques improve the perfomance of other MCO algorithms. We conclude that the many techniques pioneered in PL could be investigated as ways to improve MCO algorithms in general, and the CE method in particular.

The use of expensive simulations in engineering design optimization often rules out conventional techniques for design optimization for a variety of reasons, such as lack of smoothness, unavailability of gradient information, presence of multiple local optima, and most importantly, limits on available computing resources and time. Often, the designer also has access to lower-fidelity simulations that may suer from poor accuracy in some regions of the design space, but are much cheaper to evaluate than the original expensive simulation. We can accelerate the design process by eciently managing these models of various fidelities. There has been previous research in this area: some algorithms in the literature first estimate of the relationships between these models, and then perform optimization on the corrected low-fidelity models. Others adaptively select new high-fidelity designs, but these usually require gradient information; those that relax this requirement use a trust-region-based local search method. In contrast, most global optimization methods in the literature require smoothness, and do not incorporate multifidelity analyses. We would like to combine the advantages of all these techniques, and in this paper, we describe a method to incorporate models of two fidelities and perform a gradient-free global search on expensive functions that are not necessarily smooth everywhere. The main contribution of this paper is an extension of the well-known technique of maximization of expected improvement to the two-fidelity case. We demonstrate this improved technique on some academic problems with an artificially constructed ‘low-fidelity’ approximation, and also on a simple application problem in supersonic design optimization.