Development of reduced polynomial chaos-Kriging metamodel for uncertainty quantification of computational aerodynamics

2018 Summer.Includes bibliographical references.Computational fluid dynamics (CFD) simulations are a critical component of the design and development of aerodynamic bodies. However, as engineers attempt to capture more detailed physics, the computational cost of simulations increases. This limits the ability of engineers to use robust or multidisciplinary design methodologies for practical engineering applications because the computational model is too expensive to evaluate for uncertainty quantification studies and off-design performance analysis. Metamodels (surrogate models) are a closed-form mathematical solution fit to only a few simulation responses which can be used to remedy this situation by estimating off-design performance and stochastic responses of the CFD simulation for far less computational cost. The development of a reduced polynomial chaos-Kriging (RPC-K) metamodel is another step towards eliminating simulation gridlock by capturing the relevant physics of the problem in a cheap-to-evaluate metamodel using fewer CFD simulations. The RPC-K metamodel is superior to existing technologies because its model reduction methodology eliminates the design parameters which contribute little variance to the problem before fitting a high-fidelity metamodel to the remaining data. This metamodel can capture non-linear physics due to its inclusion of both the long-range trend information of a polynomial chaos expansion and local variations in the simulation data through Kriging. In this thesis, the RPC-K metamodel is developed, validated on a convection-diffusion-reaction problem, and applied to the NACA 4412 airfoil and aircraft engine nacelle problems. This research demonstrates the metamodel's effectiveness over existing polynomial chaos and Kriging metamodels for aerodynamics applications because of its ability to fit non-linear fluid flows with far fewer CFD simulations. This research will allow aerospace engineers to more effectively take advantage of detailed CFD simulations in the development of next-generation aerodynamic bodies through the use of the RPC-K metamodel to save computational cost

Building accurate radio environment maps from multi-fidelity spectrum sensing data

In cognitive wireless networks, active monitoring of the wireless environment is often performed through advanced spectrum sensing and network sniffing. This leads to a set of spatially distributed measurements which are collected from different sensing devices. Nowadays, several interpolation methods (e.g., Kriging) are available and can be used to combine these measurements into a single globally accurate radio environment map that covers a certain geographical area. However, the calibration of multi-fidelity measurements from heterogeneous sensing devices, and the integration into a map is a challenging problem. In this paper, the auto-regressive co-Kriging model is proposed as a novel solution. The algorithm is applied to model measurements which are collected in a heterogeneous wireless testbed environment, and the effectiveness of the new methodology is validated

Técnicas para el desarrollo de metamodelos aplicadas a problemas

Metamodels, also known as surrogate models, can be used in place of computationally expensive simulation models to increase computational efficiency for the purposes of design optimization or design space exploration. Metamodel-based design optimization is especially advantageous for ship design problems that require either computationally expensive simulations or costly physical experiments. In this paper, three metamodeling methods are evaluated with respect to their capabilities for modeling highly nonlinear, multimodal functions with incrementally increasing numbers of independent variables. Methods analyzed include kriging, radial basis functions (RBF), and support vector regression (SVR). Each metamodeling technique is used to model a set of single-output functions with dimensionality ranging from one to ten independent variables and modality ranging from one to twenty local maxima. The number of points used to train the models is increased until a predetermined error threshold is met. Results show that each of the three methods has its own distinct advantages.Los metamodelos, también conocimos como modelos substitutos, pueden ser utilizados en lugar de modeloscuyas simulaciones tienen un costo computacional muy alto, incrementado con esto la eficiencia en procesos de optimización de diseños o en el diseño de exploraciones espaciales. La optimización de diseños basados en metamodelos es especialmente ventajosa en problemas de diseño relacionado con vehículos marinos en los cuales serequieran simulaciones con un alto costo computacional o bien de experimentos con una alta inversión en equipos.En este artículo se evalúan tres métodos para el desarrollo de metamodelos. La evaluación de estos métodos es desarrollada teniendo en cuenta la capacidad de cada uno de ellos para modelar funciones multimodales no lineales con un número creciente de variables independientes. Dentro de los métodos analizados se encuentran el método de kriging, el método de funciones de base radiales, y el método de regresión con vector de apoyo. Cada una de las anteriores técnicas para la generación de metamodelos es utilizada para modelar un grupo de funciones de una salida con dimensiones variando desde uno hasta diez variables independientes y una modalidad variando entre uno y veinte máximos locales. El número de puntos utilizados para entrenar los modelos es incrementado hasta que el error alcanza una tolerancia predeterminada. Los resultados obtenidos muestran que cada uno de los tres modelos tiene sus propias ventajas distintivas

Fast Yield Estimation of Multi-Band Patch Antennas by PC-Kriging

The PC-Kriging metamodeling method is proposed for yield estimation of multi-band patch antennas. PC-Kriging is a combination of polynomial chaos expansion (PCE) and Kriging metamodeling, where PCE is used as a trend function for the Kriging interpolation metamodel. The method is demonstrated on the Ishigami analytical function and a dual-band patch antenna. The PC-Kriging is shown to reach the prescribed accuracy limit with significantly fewer training points than both PCE and Kriging. This translates into considerable computational savings of yield estimation over alternative metamodel-based procedures and direct EM-driven Monte Carlo simulation. The saving are obtained without compromising evaluation reliability

A computer-aided methodology for the optimization of electrostatic separation processes in recycling

The rapid growth of technological products has led to an increasing volume of waste electrical and electronic equipments (WEEE), which could represent a valuable source of critical raw materials. However, current mechanical separation processes for recycling are typically poorly operated, making it impossible to modify the process parameters as a function of the materials under treatment, thus resulting in untapped separation potentials. Corona electrostatic separation (CES) is one of the most popular processes for separating fine metal and nonmetal particles derived from WEEE. In order to optimize the process operating conditions (i.e., variables) for a given multi-material mixture under treatment, several technological and economical criteria should be jointly considered. This translates into a complex optimization problem that can be hardly solved by a purely experimental approach. As a result, practitioners tend to assign process parameters by few experiments based on a small material sample and to keep these parameters fixed during the process life-cycle. The use of computer experiments for parameter optimization is a mostly unexplored area in this field. In this work, a computer-aided approach is proposed to the problem of optimizing the operational parameters in CES processes. Three metamodels, developed starting from a multi-body simulation model of the process physics, are presented and compared by means of a numerical and simulation study. Our approach proves to be an effective framework to optimize the CES process performance. Furthermore, by comparing the predicted response surfaces of the metamodels, additional insight into the process behavior over the operating region is obtained

Identification of critical mechanical parameters for advanced analysis of masonry arch bridges

The response up to collapse of masonry arch bridges is very complex and affected by many uncertainties. In general, accurate response predictions can be achieved using sophisticated numerical descriptions, requiring a significant number of parameters that need to be properly characterised. This study focuses on the sensitivity of the behaviour of masonry arch bridges with respect to a wide range of mechanical parameters considered within a detailed modelling approach. The aim is to investigate the effect of constitutive parameters variations on the stiffness and ultimate load capacity under vertical loading. First, advanced numerical models of masonry arches and of a masonry arch bridge are developed, where a mesoscale approach describes the actual texture of masonry. Subsequently, a surrogate kriging metamodel is constructed to replace the accurate but computationally expensive numerical descriptions, and global sensitivity analysis is performed to identify the mechanical parameters affecting the most the stiffness and load capacity. Uncertainty propagation is then performed on the surrogate models to estimate the probabilistic distribution of the response parameters of interest. The results provide useful information for risk assessment and management purposes, and shed light on the parameters that control the bridge behaviour and require an accurate characterisation in terms of uncertainty

Otimização eficiente global dirigida por metamodelos combinados : novos caminhos abertos pela aproximação por mínimos quadrados

Orientador: Alberto Luiz SerpaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O presente trabalho representa a compilação dos resultados anteriores dessa pesquisa no campo de metamodelos combinados e otimização eficiente global (EGO), os quais foram sumetidos para publicação em periódicos especializados. Recentemente foi implementado nesse trabalho de doutorado o algoritmo LSEGO que é uma abordagem para conduzir algoritmos tipo EGO, baseando-se em metamodelos combinados através da aproximação por mínimos quadrados (metamodelos combinados LS). Através dos metamodelos combinados LS é possível estimar a incerteza da aproximação usando qualquer tipo de metamodelagem (e não somente do tipo kriging), permitindo estimar a função de expectativa de melhora para a função objetivo. Nos experimentos computacionais anteriores em problemas de otimização sem restrições, a abordagem LSEGO mostrou-se como uma alternativa viável para conduzir otimização eficiente global usando metamodelos combinados, sem se restringir a somente um ponto adicional por ciclo de otimização iterativa. Na presente tese o algoritmo LSEGO foi extendido de modo a tratar também problemas de otimização com restrições. Os resultados de testes numéricos com problemas analíticos e de referência e também em um estudo de caso de engenharia em escala industrial mostraram-se bastante promissores e competitivos em relação aos trabalhos similares encontrados na literaturaAbstract: In this work we review and compile the results of our previous research in the fields of ensemble of metamodels and efficient global optimization (EGO). Recently we implemented LSEGO that is an approach to drive EGO algorithms, based on LS (least squares) ensemble of metamodels. By means of LS ensemble of metamodels, it is possible to estimate the uncertainty of the prediction by using any kind of model (not only kriging) and provide an estimate for the expected improvement function. In previous numerical experiments with unconstrained optimization problems, LSEGO approach has shown to be a feasible alternative to drive efficient global optimization by using multiple or ensemble of metamodels, not restricted to kriging approximation or single infill point per optimization cycles. In the present work we extended the previous LSEGO algorithm to handle constrained optimization problems as well. Some numerical experiments were performed with analytical benchmark functions and also for industry scale engineering problems with competitive resultsDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânic