Academic literature on the topic 'Multifidelity techniques'

To improve the precision of machine-learning predictions, we investigate various techniques that combine multiple quality sources for the same property. In particular, focusing on the electronic band gap, we aim at having the lowest error by taking advantage of all available experimental measurements and density-functional theory calculations. We show that learning about the difference between high- and low-quality values, considered a correction, significantly improves the results compared to learning on the sole high-quality experimental data. As a preliminary step, we also introduce an extension of the MODNet model, which consists of using a genetic algorithm for hyperparameter optimization. Thanks to this, MODNet is shown to achieve excellent performance on the Matbench test suite.

Bayesian techniques for engineering problems, which rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian process based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data.

Purpose Aerodynamic shape optimisation is complex because of the high dimensionality of the problem, the associated non-linearity and its large computational cost. These three aspects have an impact on the overall time of the design process. To overcome these challenges, this paper aims to develop a method for transonic aerodynamic design with dimensionality reduction and multifidelity techniques. Design/methodology/approach The developed methodology is used for the optimisation of an installed civil ultra-high bypass ratio aero-engine nacelle. As such, the effects of airframe-engine integration are considered during the optimisation routine. The active subspace method is applied to reduce the dimensionality of the problem from 32 to 2 design variables with a database compiled with Euler computational fluid dynamics (CFD) calculations. In the reduced dimensional space, a co-Kriging model is built to combine Euler lower-fidelity and Reynolds-averaged Navier stokes higher-fidelity CFD evaluations. Findings Relative to a baseline aero-engine nacelle derived from an isolated optimisation process, the proposed method yielded a non-axisymmetric nacelle configuration with an increment in net vehicle force of 0.65% of the nominal standard net thrust. Originality/value This work investigates the viability of CFD optimisation through a combination of dimensionality reduction and multifidelity method and demonstrates that the developed methodology enables the optimisation of complex aerodynamic problems.

Abstract Bayesian optimization (BO) is a popular method for expensive black-box optimization problems; however, querying the objective function at every iteration can be a bottleneck that hinders efficient search capabilities. In this regard, multifidelity Bayesian optimization (MFBO) aims to accelerate BO by incorporating lower-fidelity observations available with a lower sampling cost. In our previous work, we proposed an information-theoretic approach to MFBO, referred to as multifidelity max-value entropy search (MF-MES), which inherits practical effectiveness and computational simplicity of the well-known max-value entropy search (MES) for the single-fidelity BO. However, the applicability of MF-MES is still limited to the case that a single observation is sequentially obtained. In this letter, we generalize MF-MES so that information gain can be evaluated even when multiple observations are simultaneously obtained. This generalization enables MF-MES to address two practical problem settings: synchronous parallelization and trace-aware querying. We show that the acquisition functions for these extensions inherit the simplicity of MF-MES without introducing additional assumptions. We also provide computational techniques for entropy evaluation and posterior sampling in the acquisition functions, which can be commonly used for all variants of MF-MES. The effectiveness of MF-MES is demonstrated using benchmark functions and real-world applications such as materials science data and hyperparameter tuning of machine-learning algorithms.

Aircraft design requires a large volume of aerodynamic data to characterize various flight conditions throughout the aircraft’s flight envelope, and the data are typically obtained through wind tunnel testing and numerical analysis. Data acquisition can be costly and inevitably entails multiple sources of uncertainty. Data fusion techniques aim to bring together the strengths and mitigate the limitations of data from various information sources. A multifidelity data fusion framework employing Gaussian process regression is adopted herein and applied to the surface pressure data of a large aircraft wing model. The modeling approach is non-hierarchical in that there is no established hierarchy of accuracy among the information sources. Scalability issues arising from the large volume of data required for the study of pressure distributions are overcome by using an approximate Gaussian process regression based on stochastic variational inference, enabling the data fusion framework to be applied effectively to industry-relevant analysis and design challenges. The approach is demonstrated for a high-dimensional data set generated through wind tunnel testing in an industrial setting and numerical analysis.

In recent years, multifidelity expensive black-box (Mf-EBB) methods have received increasing attention due to their strong applicability to industrial design problems. The challenge, however, is that knowledge of the relationship between decisions and objective values is limited to a small set of sample observations of variable quality. In the field of Mf-EBB, a problem instance consists of an expensive yet accurate source of information, and one or more cheap yet less accurate sources of information. The field aims to provide techniques either to accurately explain how decisions affect design outcome, or to find the best decisions to optimise design outcomes. Many techniques that use surrogate models have been developed to provide solutions to both aims. Only in recent years, however, have researchers begun to explore the conditions under which these new techniques are reliable, often focusing on problems with a single low-fidelity function, known as bifidelity expensive black-box (Bf-EBB) problems. This study extends the existing Bf-EBB test instances found in the literature, as well as the features used to determine when the low-fidelity information source should be used. A literature test suite is constructed and augmented with new instances to demonstrate the potentially misleading results that could be reached using only the instances currently found in the literature, and to expose the criticality of a more heterogeneous test suite for algorithm assessment. Addressing the shortcomings of the existing literature, a new set of features is presented, as well as a new instance creation procedure, and a study of their impact on algorithm assessment is conducted. The low-fidelity information source is shown to be valuable if it is often locally accurate, even when its overall accuracy is relatively low. This contradicts the existing literature guidelines, which indicate the low-fidelity information is only useful if it has a high overall accuracy.

In the gas turbine industry, computational fluid dynamics (CFD) simulations are often used to predict and visualize the complex reacting flow dynamics, combustion environment and emissions performance of a combustor at the design stage. Given the complexity involved in obtaining accurate flow predictions and due to the expensive nature of simulations, conventional techniques for CFD based combustor design optimization are often ruled out, primarily due to the limits on available computing resources and time. The design optimization process normally requires a large number of analyses of the objective and constraint functions which necessitates a careful selection of fast, reliable and efficient computational methods for the CFD analysis and the optimization process. In this study, given a fixed computational budget, an assessment of a co-Kriging based optimization strategy against a standard Kriging based optimization strategy is presented for the design of a 2D combustor using steady and unsteady Reynolds-averaged Navier Stokes (RANS) formulation. Within the fixed computational budget, using a steady RANS formulation, the Kriging strategy successfully captures the underlying response; however with unsteady RANS the Kriging strategy fails to capture the underlying response due to the existence of a high level of noise. The co-Kriging strategy is then applied to two design problems, one using two levels of grid resolutions in a steady RANS formulation and the other using steady and unsteady RANS formulations on the same grid resolution. With the co-Kriging strategy, the multifidelity analysis is expected to find an optimum design in comparatively less time than that required using the high-fidelity model alone since less high-fidelity function calls should be required. However, using the applied computational setup for co-Kriging, the Kriging strategy beats the co-Kriging strategy under the steady RANS formulation whereas under the unsteady RANS formulation, the high level of noise stalls the co-Kriging optimization process.

Le problème de la propagation non linéaire d’incertitude est crucial en astrodynamique, car tous les systèmes d’intérêt pratique, allant de la navigation à la détermination d’orbite et au suivi de cibles, impliquent des non-linéarités dans leurs modèles dynamiques et de mesure. Un sujet d’intérêt est la propagation précise d’incertitude à travers la dynamique orbitale non linéaire, une exigence fondamentale dans plusieurs applications telles que la surveillance de l’espace, la gestion du trafic spatial et la fin de vie des satellites. Étant donnée une représentation dimensionnelle finie de la fonction de densité de probabilité (pdf) de l’état initial, l’objectif est d’obtenir une représentation similaire de cette pdf à tout moment futur. Ce problème a été historiquement abordé avec des méthodes linéarisées ou des simulations de Monte Carlo (MC), toutes deux inadaptées pour satisfaire la demande d’un nombre croissant d’applications. Les méthodes linéarisées sont très performantes, mais ne peuvent pas gérer de fortes non-linéarités ou de longues fenêtres de propagation en raison de la validité locale de la linéarisation. En revanche, les méthodes MC peuvent gérer tout type de non-linéarité, mais sont trop coûteuses en termes de calcul pour toute tâche nécessitant la propagation de plusieurs pdf. Au lieu de cela, cette thèse exploite des méthodes multi-fidélité et des techniques d’algèbre différentielle (DA) pour développer des méthodes efficaces pour la propagation précise des incertitudes à travers des systèmes dynamiques non linéaires. La première méthode, appelée low-order automatic domain splitting (LOADS), représente l’incertitude avec un ensemble de polynômes de Taylor du deuxième ordre et exploite une mesure de non-linéarité basée sur la DA pour ajuster leur nombre en fonction de la dynamique locale et de la précision requise. Un modèle adaptatif de mélange Gaussien (GMM) est ensuite développé en associant chaque polynôme à un noyau pondéré pour obtenir une représentation analytique de la pdf d’état. En outre, une méthode multi-fidélité est proposée pour réduire le coût computationnel des algorithmes précédents tout en conservant une précision similaire. La méthode GMM est dans ce cas exécutée sur un modèle dynamique à faible fidélité, et seules les moyennes des noyaux sont propagées ponctuellement dans une dynamique à haute fidélité pour corriger la pdf à faible fidélité. Si les méthodes précédentes traitent de la propagation d’une incertitude initiale dans un modèle dynamique déterministe, les effets des forces mal ou non modélisées sont enfin pris en compte pour améliorer le réalisme des statistiques propagées. Dans ce cas, la méthode multi-fidélité est d’abord utilisée pour propager l’incertitude initiale dans un modèle dynamique déterministe de faible fidélité. Les propagations ponctuelles sont ensuite remplacées par une propagation polynomiale des moments de la pdf dans un système dynamique stochastique. Ces moments modélisent les effets des accélérations stochastiques sur les moyennes des noyaux, et couplés à la méthode GMM, ils fournissent une description de la pdf qui tient compte de l’incertitude initiale et des effets des forces négligées. Les méthodes proposées sont appliquées au problème de la propagation d’incertitude en orbite, et leurs performances sont évaluées dans différents régimes orbitaux. Les résultats démontrent leur efficacité pour une propagation précise de l’incertitude initiale et des effets du bruit du processus à une fraction du coût de calcul des simulations MC. La méthode LOADS est ensuite utilisée pour résoudre le problème de la détermination initiale d’orbite en exploitant les informations sur l’incertitude des mesures, et pour développer une méthode de prétraitement des données qui améliore la robustesse des algorithmes de détermination d’orbite. Ces outils sont enfin validés sur des observations réelles d’un objet en orbite de transfert géostationnaire
The problem of nonlinear uncertainty propagation (UP) is crucial in astrodynamics since all systems of practical interest, ranging from navigation to orbit determination (OD) and target tracking, involve nonlinearities in their dynamics and measurement models. One topic of interest is the accurate propagation of uncertainty through the nonlinear orbital dynamics, a fundamental requirement in several applications such as space surveillance and tracking (SST), space traffic management (STM), and end-of-life (EOL) disposal. Given a finite-dimensional representation of the probability density function (pdf) of the initial state, the main goal is to obtain a similar representation of the state pdf at any future time. This problem has been historically tackled with either linearized methods or Monte Carlo (MC) simulations, both of which are unsuitable to satisfy the demand of a rapidly growing number of applications. Linearized methods are light on computational resources, but cannot handle strong nonlinearities or long propagation windows due to the local validity of the linearization. In contrast, MC methods can handle any kind of nonlinearity, but are too computationally expensive for any task that requires the propagation of several pdfs. Instead, this thesis leverages multifidelity methods and differential algebra (DA) techniques to develop computationally efficient methods for the accurate propagation of uncertainties through nonlinear dynamical systems. The first method, named low-order automatic domain splitting (LOADS), represents the uncertainty with a set of second-order Taylor polynomials and leverages a DA-based measure of nonlinearity to adjust their number based on the local dynamics and the required accuracy. An adaptive Gaussian mixture model (GMM) method is then developed by associating each polynomial to a weighted Gaussian kernel, thus obtaining an analytical representation of the state pdf. Going further, a multifidelity method is proposed to reduce the computational cost of the former algorithms while retaining a similar accuracy. The adaptive GMM method is in this case run on a low-fidelity dynamical model, and only the expected values of the kernels are propagated point-wise in high-fidelity dynamics to compute a posteriori correction of the low-fidelity state pdf. If the former methods deal with the propagation of an initial uncertainty through a deterministic dynamical model, the effects of mismodeled or unmodeled forces are finally considered to further enhance the realism of the propagated statistics. In this case, the multifidelity GMM method is used at first to propagate the initial uncertainty through a low-fidelity, deterministic dynamical model. The point-wise propagations are then replaced with a DA-based algorithm to efficiently propagate a polynomial representation of the moments of the pdf in a stochastic dynamical system. These moments model the effects of stochastic accelerations on the deterministic kernels’ means, and coupled with the former GMM provide a description of the propagated state pdf that accounts for both the uncertainty in the initial state and the effects of neglected forces. The proposed methods are applied to the problem of orbit UP, and their performance is assessed in different orbital regimes. The results demonstrate the effectiveness of these methods in accurately propagating the initial uncertainty and the effects of process noise at a fraction of the computational cost of high-fidelity MC simulations. The LOADS method is then employed to solve the initial orbit determination (IOD) problem by exploiting the information on measurement uncertainty and to develop a preprocessing scheme aimed at improving the robustness of batch OD algorithms. These tools are finally validated on a set of real observations for an object in geostationary transfer orbit (GTO)

This work illustrates the effect of a rotor blade's boundary layer on the broadband laminar boundary layer vortex shedding (LBL-VS) self-noise emitted from an optimum hovering rotor through experimental and multifidelity computational studies. Blade surface roughness effects associated with different manufacturing techniques and the effect of adding a boundary layer trip were shown to decrease LBL-VS noise by upwards of 30 dB at the frequency of maximum emission with as light penalty in aerodynamic performance when compared with smooth rotor blades. Low-fidelity 2-D viscous flow analysis verified the presence of laminar separation bubbles on the rotor blades, which are responsible for LBL-VS noise. Three high-fidelity lattice-Boltzmann simulations were conducted with different wall-functions to predict the boundary layer character correspondent to their experimental counterpart and the resultant presence or absence of LBL-VS noise. Excellent aerodynamic and aeroacoustic agreement was seen between the lattice-Boltzmann simulations and the experimental data for the cases with surface roughness and the boundary layer trip.The broadband noise results from the simulation with fully turbulent wall-functions diverged from the experimental results above 5 kHz. The transitional wall-function simulation, which emulated the smooth experimental blades, under predicted thrust by 14% and broadband noise by a minimum of 10dB with an accurately predicted broadband noise trend.