Relevant bibliographies by topics / General polynomial chaos expansion

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'General polynomial chaos expansion'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "General polynomial chaos expansion"

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SEPAHVAND, K., S. MARBURG, and H. J. HARDTKE. "UNCERTAINTY QUANTIFICATION IN STOCHASTIC SYSTEMS USING POLYNOMIAL CHAOS EXPANSION." International Journal of Applied Mechanics 02, no. 02 (2010): 305–53. http://dx.doi.org/10.1142/s1758825110000524.

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In recent years, extensive research has been reported about a method which is called the generalized polynomial chaos expansion. In contrast to the sampling methods, e.g., Monte Carlo simulations, polynomial chaos expansion is a nonsampling method which represents the uncertain quantities as an expansion including the decomposition of deterministic coefficients and random orthogonal bases. The generalized polynomial chaos expansion uses more orthogonal polynomials as the expansion bases in various random spaces which are not necessarily Gaussian. A general review of uncertainty quantification methods, the theory, the construction method, and various convergence criteria of the polynomial chaos expansion are presented. We apply it to identify the uncertain parameters with predefined probability density functions. The new concepts of optimal and nonoptimal expansions are defined and it demonstrated how we can develop these expansions for random variables belonging to the various random spaces. The calculation of the polynomial coefficients for uncertain parameters by using various procedures, e.g., Galerkin projection, collocation method, and moment method is presented. A comprehensive error and accuracy analysis of the polynomial chaos method is discussed for various random variables and random processes and results are compared with the exact solution or/and Monte Carlo simulations. The method is employed for the basic stochastic differential equation and, as practical application, to solve the stochastic modal analysis of the microsensor quartz fork. We emphasize the accuracy in results and time efficiency of this nonsampling procedure for uncertainty quantification of stochastic systems in comparison with sampling techniques, e.g., Monte Carlo simulation.
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Zhao, Wei, and Ji Ke Liu. "Stochastic Finite Element Method Using Polynomial Chaos Expansion." Advanced Materials Research 199-200 (February 2011): 500–504. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.500.

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We present a new response surface based stochastic finite element method to obtain solutions for general random uncertainty problems using the polynomial chaos expansion. The approach is general but here a typical elastostatics example only with the random field of Young's modulus is presented to illustrate the stress analysis, and computational comparison with the traditional polynomial expansion approach is also performed. It shows that the results of the polynomial chaos expansion are improved compared with that of the second polynomial expansion method.
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SEPAHVAND, K., S. MARBURG, and H. J. HARDTKE. "STOCHASTIC STRUCTURAL MODAL ANALYSIS INVOLVING UNCERTAIN PARAMETERS USING GENERALIZED POLYNOMIAL CHAOS EXPANSION." International Journal of Applied Mechanics 03, no. 03 (2011): 587–606. http://dx.doi.org/10.1142/s1758825111001147.

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In this paper, the application of generalized polynomial chaos expansion in stochastic structural modal analysis including uncertain parameters is investigated. We review the theory of polynomial chaos and relating error analysis. A general formulation for the representation of modal problems by the polynomial chaos expansion is derived. It shows how the modal frequencies and modal shapes are influenced by the parameter uncertainties. The key issues that arise in the polynomial chaos simulation of modal analysis are discussed for two examples: a discrete 2-DOF system and continuous model of a microsensor. In both cases, the polynomial chaos expansion is used for the approximation of uncertain parameters, eigenfrequencies and eigenvectors. We emphasize the accuracy and time efficiency of the method in estimation of the stochastic modal responses in comparison with the sampling techniques, such as the Monte Carlo simulation.
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Yin, Shengwen, Yuan Gao, Xiaohan Zhu, and Zhonggang Wang. "Anisotropy-Based Adaptive Polynomial Chaos Method for Hybrid Uncertainty Quantification and Reliability-Based Design Optimization of Structural-Acoustic System." Mathematics 11, no. 4 (2023): 836. http://dx.doi.org/10.3390/math11040836.

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The evaluation of objective functions and component reliability in the optimisation of structural-acoustic systems with random and interval variables is computationally expensive, especially when strong nonlinearity exhibits between the response and input variables. To reduce the computational cost and improve the computational efficiency, a novel anisotropy-based adaptive polynomial chaos (ABAPC) expansion method was developed in this study. In ABAPC, the anisotropy-based polynomial chaos expansion, namely the retained order of polynomial chaos expansion (PCE) differs from each variable, is used to construct the initial surrogate model instead of first-order polynomial chaos expansion in conventional methods. Then, an anisotropy-based adaptive basis growth strategy was developed to reduce the estimation of the coefficients of the polynomial chaos expansion method and increase its computational efficiency. Finally, to solve problems with probabilistic and interval parameters, an adaptive basis truncation strategy was introduced and implemented. Using the ABAPC method, the computational cost of reliability-based design optimisation for structural-acoustic systems can be efficiently reduced. The effectiveness of the proposed method were demonstrated by solving two numerical examples and optimisation problems of a structural-acoustic system.
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SEPAHVAND, K., S. MARBURG, and H. J. HARDTKE. "NUMERICAL SOLUTION OF ONE-DIMENSIONAL WAVE EQUATION WITH STOCHASTIC PARAMETERS USING GENERALIZED POLYNOMIAL CHAOS EXPANSION." Journal of Computational Acoustics 15, no. 04 (2007): 579–93. http://dx.doi.org/10.1142/s0218396x07003524.

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This paper presents a numerical algorithm which is using generalized polynomial chaos combined with the finite difference method for the solution of the one-dimensional wave equation with stochastic physical parameters. The stochastic parameters are represented by the Hermite polynomial chaos. A spectral–finite difference model for the numerical solution is introduced using generalized polynomial chaos expansion. The general conditions for convergence and stability of numerical algorithms are derived. Finally, the method is applied to a vibrating string. Results are compared with those of a Monte Carlo simulation.
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Panayirci, H. M. "Efficient solution for Galerkin-based polynomial chaos expansion systems." Advances in Engineering Software 41, no. 12 (2010): 1277–86. http://dx.doi.org/10.1016/j.advengsoft.2010.09.004.

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Jacquelin, E., O. Dessombz, J. J. Sinou, S. Adhikari, and M. I. Friswell. "Polynomial chaos-based extended Padé expansion in structural dynamics." International Journal for Numerical Methods in Engineering 111, no. 12 (2017): 1170–91. http://dx.doi.org/10.1002/nme.5497.

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Novák, Lukáš, Miroslav Vořechovský, Václav Sadílek, and Michael D. Shields. "Variance-based adaptive sequential sampling for Polynomial Chaos Expansion." Computer Methods in Applied Mechanics and Engineering 386 (December 2021): 114105. http://dx.doi.org/10.1016/j.cma.2021.114105.

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Zhang, Wei, Qiang Wang, and Chao Yan. "An intelligent polynomial chaos expansion method based upon features selection." Journal of Physics: Conference Series 1786, no. 1 (2021): 012046. http://dx.doi.org/10.1088/1742-6596/1786/1/012046.

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Chen, Ming, Xinhu Zhang, Kechun Shen, and Guang Pan. "Polynomial chaos expansion for uncertainty analysis and global sensitivity analysis." Journal of Physics: Conference Series 2187, no. 1 (2022): 012071. http://dx.doi.org/10.1088/1742-6596/2187/1/012071.

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Abstract Uncertainty analysis has received increasing attention across all kinds of scientific and engineering fields recently. Uncertainty analysis is often conducted by Monte Carlo simulation (MCS), while with low convergence rate. In this paper, numerical test examples as benchmarks and engineering problems in practice are studied by polynomial chaos expansion (PCE) and compared with the solutions got by MCS. Results show that PCE approach establishes accurate surrogate model for complicated original model with efficiency to conduct uncertainty analysis and global sensitivity analysis. What’s more, sparse PCE is able to tackle problem of high dimension with efficiency. Hence PCE approach can be applied in uncertainty analysis and global sensitivity analysis of engineering problems with efficiency and effectiveness.
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Dissertations / Theses on the topic "General polynomial chaos expansion"

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Szepietowska, Katarzyna. "POLYNOMIAL CHAOS EXPANSION IN BIO- AND STRUCTURAL MECHANICS." Thesis, Bourges, INSA Centre Val de Loire, 2018. http://www.theses.fr/2018ISAB0004/document.

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Cette thèse présente une approche probabiliste de la modélisation de la mécanique des matériaux et des structures. Le dimensionnement est influencé par l'incertitude des paramètres d'entrée. Le travail est interdisciplinaire et les méthodes décrites sont appliquées à des exemples de biomécanique et de génie civil. La motivation de ce travail était le besoin d'approches basées sur la mécanique dans la modélisation et la simulation des implants utilisés dans la réparation des hernies ventrales. De nombreuses incertitudes apparaissent dans la modélisation du système implant-paroi abdominale. L'approche probabiliste proposée dans cette thèse permet de propager ces incertitudes et d’étudier leurs influences respectives. La méthode du chaos polynomial basée sur la régression est utilisée dans ce travail. L'exactitude de ce type de méthodes non intrusives dépend du nombre et de l'emplacement des points de calcul choisis. Trouver une méthode universelle pour atteindre un bon équilibre entre l'exactitude et le coût de calcul est encore une question ouverte. Différentes approches sont étudiées dans cette thèse afin de choisir une méthode efficace et adaptée au cas d’étude. L'analyse de sensibilité globale est utilisée pour étudier les influences des incertitudes d'entrée sur les variations des sorties de différents modèles. Les incertitudes sont propagées aux modèles implant-paroi abdominale. Elle permet de tirer des conclusions importantes pour les pratiques chirurgicales. À l'aide de l'expertise acquise à partir de ces modèles biomécaniques, la méthodologie développée est utilisée pour la modélisation de joints de bois historiques et la simulation de leur comportement mécanique. Ce type d’étude facilite en effet la planification efficace des réparations et de la rénovation des bâtiments ayant une valeur historique<br>This thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair of ventral hernias. Many uncertainties appear in the modelling of the implant-abdominal wall system. The probabilistic approach proposed in this thesis enables these uncertainties to be propagated to the output of the model and the investigation of their respective influences. The regression-based polynomial chaos expansion method is used here. However, the accuracy of such non-intrusive methods depends on the number and location of sampling points. Finding a universal method to achieve a good balance between accuracy and computational cost is still an open question so different approaches are investigated in this thesis in order to choose an efficient method. Global sensitivity analysis is used to investigate the respective influences of input uncertainties on the variation of the outputs of different models. The uncertainties are propagated to the implant-abdominal wall models in order to draw some conclusions important for further research. Using the expertise acquired from biomechanical models, modelling of historic timber joints and simulations of their mechanical behaviour is undertaken. Such an investigation is important owing to the need for efficient planning of repairs and renovation of buildings of historical value
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Nydestedt, Robin. "Application of Polynomial Chaos Expansion for Climate Economy Assessment." Thesis, KTH, Optimeringslära och systemteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223985.

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In climate economics integrated assessment models (IAMs) are used to predict economic impacts resulting from climate change. These IAMs attempt to model complex interactions between human and geophysical systems to provide quantifications of economic impact, typically using the Social Cost of Carbon (SCC) which represents the economic cost of a one ton increase in carbon dioxide. Another difficulty that arises in modeling a climate economics system is that both the geophysical and economic submodules are inherently stochastic. Even in frequently cited IAMs, such as DICE and PAGE, there exists a lot of variation in the predictions of the SCC. These differences stem both from the models of the climate and economic modules used, as well as from the choice of probability distributions used for the random variables. Seeing as IAMs often take the form of optimization problems these nondeterministic elements potentially result in heavy computational costs. In this thesis a new IAM, FAIR/DICE, is introduced. FAIR/DICE is a discrete time hybrid of DICE and FAIR providing a potential improvement to DICE as the climate and carbon modules in FAIR take into account feedback coming from the climate module to the carbon module. Additionally uncertainty propagation in FAIR/DICE is analyzed using Polynomial Chaos Expansions (PCEs) which is an alternative to Monte Carlo sampling where the stochastic variables are projected onto stochastic polynomial spaces. PCEs provide better computational efficiency compared to Monte Carlo sampling at the expense of storage requirements as a lot of computations can be stored from the first simulation of the system, and conveniently statistics can be computed from the PCE coefficients without the need for sampling. A PCE overloading of FAIR/DICE is investigated where the equilibrium climate sensitivity, modeled as a four parameter Beta distribution, introduces an uncertainty to the dynamical system. Finally, results in the mean and variance obtained from the PCEs are compared to a Monte Carlo reference and avenues into future work are suggested.<br>Inom klimatekonomi används integrated assessment models (IAMs) för att förutspå hur klimatförändringar påverkar ekonomin. Dessa IAMs modellerar komplexa interaktioner mellan geofysiska och mänskliga system för att kunna kvantifiera till exempel kostnaden för den ökade koldioxidhalten på planeten, i.e. Social Cost of Carbon (SCC). Detta representerar den ekonomiska kostnaden som motsvaras av utsläppet av ett ton koldioxid. Faktumet att både de geofysiska och ekonomiska submodulerna är stokastiska gör att SCC-uppskattningar varierar mycket även inom väletablerade IAMs som PAGE och DICE. Variationen grundar sig i skillnader inom modellerna men också från att val av sannolikhetsfördelningar för de stokastiska variablerna skiljer sig. Eftersom IAMs ofta är formulerade som optimeringsproblem leder dessutom osäkerheterna till höga beräkningskostnader. I denna uppsats introduceras en ny IAM, FAIR/DICE, som är en diskret tids hybrid av DICE och FAIR. Den utgör en potentiell förbättring av DICE eftersom klimat- och kolmodulerna i FAIR även behandlar återkoppling från klimatmodulen till kolmodulen. FAIR/DICE är analyserad med hjälp av Polynomial Chaos Expansions (PCEs), ett alternativ till Monte Carlo-metoder. Med hjälp av PCEs kan de osäkerheter projiceras på stokastiska polynomrum vilket har fördelen att beräkningskostnader reduceras men nackdelen att lagringskraven ökar. Detta eftersom många av beräkningarna kan sparas från första simuleringen av systemet, dessutom kan statistik extraheras direkt från PCE koefficienterna utan behov av sampling. FAIR/DICE systemet projiceras med hjälp av PCEs där en osäkerhet är introducerad via equilibrium climate sensitivity (ECS), vilket i sig är ett värde på hur känsligt klimatet är för koldioxidförändringar. ECS modelleras med hjälp av en fyra-parameters Beta sannolikhetsfördelning. Avslutningsvis jämförs resultat i medelvärde och varians mellan PCE implementationen av FAIR/DICE och en Monte Carlo-baserad referens, därefter ges förslag på framtida utvecklingsområden.
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Koehring, Andrew. "The application of polynomial response surface and polynomial chaos expansion metamodels within an augmented reality conceptual design environment." [Ames, Iowa : Iowa State University], 2008.

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Price, Darryl Brian. "Estimation of Uncertain Vehicle Center of Gravity using Polynomial Chaos Expansions." Thesis, Virginia Tech, 2008. http://hdl.handle.net/10919/33625.

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The main goal of this study is the use of polynomial chaos expansion (PCE) to analyze the uncertainty in calculating the lateral and longitudinal center of gravity for a vehicle from static load cell measurements. A secondary goal is to use experimental testing as a source of uncertainty and as a method to confirm the results from the PCE simulation. While PCE has often been used as an alternative to Monte Carlo, PCE models have rarely been based on experimental data. The 8-post test rig at the Virginia Institute for Performance Engineering and Research facility at Virginia International Raceway is the experimental test bed used to implement the PCE model. Experimental tests are conducted to define the true distribution for the load measurement systemsâ uncertainty. A method that does not require a new uncertainty distribution experiment for multiple tests with different goals is presented. Moved mass tests confirm the uncertainty analysis using portable scales that provide accurate results. The polynomial chaos model used to find the uncertainty in the center of gravity calculation is derived. Karhunen-Loeve expansions, similar to Fourier series, are used to define the uncertainties to allow for the polynomial chaos expansion. PCE models are typically computed via the collocation method or the Galerkin method. The Galerkin method is chosen as the PCE method in order to formulate a more accurate analytical result. The derivation systematically increases from one uncertain load cell to all four uncertain load cells noting the differences and increased complexity as the uncertainty dimensions increase. For each derivation the PCE model is shown and the solution to the simulation is given. Results are presented comparing the polynomial chaos simulation to the Monte Carlo simulation and to the accurate scales. It is shown that the PCE simulations closely match the Monte Carlo simulations.<br>Master of Science
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Song, Chen [Verfasser], and Vincent [Akademischer Betreuer] Heuveline. "Uncertainty Quantification for a Blood Pump Device with Generalized Polynomial Chaos Expansion / Chen Song ; Betreuer: Vincent Heuveline." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177252406/34.

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Langewisch, Dustin R. "Application of the polynomial chaos expansion to multiphase CFD : a study of rising bubbles and slug flow." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/92097.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 157-167).<br>Part I of this thesis considers subcooled nucleate boiling on the microscale, focusing on the analysis of heat transfer near the Three-Phase (solid, liquid, and vapor) contact Line (TPL) region. A detailed derivation of one representative TPL model is presented. From this work, it was ultimately concluded that heat transfer in the vicinity of the TPL is rather unimportant in the overall quantification of nucleate boiling heat transfer; despite the extremely high heat fluxes that are attainable, it is limited to a very small region so the net heat transfer from this region is comparatively small. It was further concluded that many of the so-called microlayer heat transfer models appearing in the literature are actually models for TPL heat transfer; these models do not model the experimentally observed microlayer. This portion of the project was terminated early, however, in order to focus on the application of advanced computational uncertainty quantification methods to computational multiphase fluid dynamics (Part II). Part II discusses advanced uncertainty quantification (UQ) methods for long-running numerical models, namely computational multiphase fluid dynamics (CMFD) simulations. We consider the problem of how to efficiently propagate uncertainties in the model inputs (e.g., fluid properties, such as density, viscosity, etc.) through a computationally demanding model. The challenge is chiefly a matter of economics-the long run-time of these simulations limits the number of samples that one can reasonably obtain (i.e., the number of times the simulation can be run). Chapter 2 introduces the generalized Polynomial Chaos (gPC) expansion, which has shown promise for reducing the computational cost of performing UQ for a large class of problems, including heat transfer and single phase, incompressible flow simulations; example applications are demonstrated in Chapter 2. One of main objectives of this research was to ascertain whether this promise extends to realm of CMFD applications, and this is the topic of Chapters 3 and 4; Chapter 3 covers the numerical simulation of a single bubble rising in a quiescent liquid bath. The pertinent quantities from these simulations are the terminal velocity of the bubble and terminal bubble shape. the simulations were performed using the open source gerris flow solver. A handful of test cases were performed to validate the simulation results against available experimental data and numerical results from other authors; the results from gerris were found to compare favorably. Following the validation, we considered two uncertainty quantifications problems. In the first problem, the viscosity of the surrounding liquid is modeled as a uniform random variable and we quantify the resultant uncertainty in the bubbles terminal velocity. The second example is similar, except the bubble's size (diameter) is modeled as a log-normal random variable. In this case, the Hermite expansion is seen to converge almost immediately; a first-order Hermite expansion computed using 3 model evaluations is found to capture the terminal velocity distribution almost exactly. Both examples demonstrate that NISP can be successfully used to efficiently propagate uncertainties through CMFD models. Finally, we describe a simple technique to implement a moving reference frame in gerris. Chapter 4 presents an extensive study of the numerical simulation of capillary slug flow. We review existing correlations for the thickness of the liquid film surrounding a Taylor bubble and the pressure drop across the bubble. Bretherton's lubrication analysis, which yields analytical predictions for these quantities when inertial effects are negligible and Ca[beta] --> o, is considered in detail. In addition, a review is provided of film thickness correlations that are applicable for high Cab or when inertial effects are non-negligible. An extensive computational study was undertaken with gerris to simulate capillary slug flow under a variety of flow conditions; in total, more than two hundred simulations were carried out. The simulations were found to compare favorably with simulations performed previously by other authors using finite elements. The data from our simulations have been used to develop a new correlation for the film thickness and bubble velocity that is generally applicable. While similar in structure to existing film thickness correlations, the present correlation does not require the bubble velocity to be known a priori. We conclude with an application of the gPC expansion to quantify the uncertainty in the pressure drop in a channel in slug flow when the bubble size is described by a probability distribution. It is found that, although the gPC expansion fails to adequately quantify the uncertainty in field quantities (pressure and velocity) near the liquid-vapor interface, it is nevertheless capable of representing the uncertainty in other quantities (e.g., channel pressure drop) that do not depend sensitively on the precise location of the interface.<br>by Dustin R. Langewisch.<br>Ph. D.
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Yadav, Vaibhav. "Novel Computational Methods for Solving High-Dimensional Random Eigenvalue Problems." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4927.

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The primary objective of this study is to develop new computational methods for solving a general random eigenvalue problem (REP) commonly encountered in modeling and simulation of high-dimensional, complex dynamic systems. Four major research directions, all anchored in polynomial dimensional decomposition (PDD), have been defined to meet the objective. They involve: (1) a rigorous comparison of accuracy, efficiency, and convergence properties of the polynomial chaos expansion (PCE) and PDD methods; (2) development of two novel multiplicative PDD methods for addressing multiplicative structures in REPs; (3) development of a new hybrid PDD method to account for the combined effects of the multiplicative and additive structures in REPs; and (4) development of adaptive and sparse algorithms in conjunction with the PDD methods. The major findings are as follows. First, a rigorous comparison of the PCE and PDD methods indicates that the infinite series from the two expansions are equivalent but their truncations endow contrasting dimensional structures, creating significant difference between the two approximations. When the cooperative effects of input variables on an eigenvalue attenuate rapidly or vanish altogether, the PDD approximation commits smaller error than does the PCE approximation for identical expansion orders. Numerical analysis reveal higher convergence rates and significantly higher efficiency of the PDD approximation than the PCE approximation. Second, two novel multiplicative PDD methods, factorized PDD and logarithmic PDD, were developed to exploit the hidden multiplicative structure of an REP, if it exists. Since a multiplicative PDD recycles the same component functions of the additive PDD, no additional cost is incurred. Numerical results show that indeed both the multiplicative PDD methods are capable of effectively utilizing the multiplicative structure of a random response. Third, a new hybrid PDD method was constructed for uncertainty quantification of high-dimensional complex systems. The method is based on a linear combination of an additive and a multiplicative PDD approximation. Numerical results indicate that the univariate hybrid PDD method, which is slightly more expensive than the univariate additive or multiplicative PDD approximations, yields more accurate stochastic solutions than the latter two methods. Last, two novel adaptive-sparse PDD methods were developed that entail global sensitivity analysis for defining the relevant pruning criteria. Compared with the past developments, the adaptive-sparse PDD methods do not require its truncation parameter(s) to be assigned a priori or arbitrarily. Numerical results reveal that an adaptive-sparse PDD method achieves a desired level of accuracy with considerably fewer coefficients compared with existing PDD approximations.
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Mühlpfordt, Tillmann [Verfasser], and V. [Akademischer Betreuer] Hagenmeyer. "Uncertainty Quantification via Polynomial Chaos Expansion – Methods and Applications for Optimization of Power Systems / Tillmann Mühlpfordt ; Betreuer: V. Hagenmeyer." Karlsruhe : KIT-Bibliothek, 2020. http://d-nb.info/1203211872/34.

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Scott, Karen Mary Louise. "Practical Analysis Tools for Structures Subjected to Flow-Induced and Non-Stationary Random Loads." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/38686.

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There is a need to investigate and improve upon existing methods to predict response of sensors due to flow-induced vibrations in a pipe flow. The aim was to develop a tool which would enable an engineer to quickly evaluate the suitability of a particular design for a certain pipe flow application, without sacrificing fidelity. The primary methods, found in guides published by the American Society of Mechanical Engineers (ASME), of simple response prediction of sensors were found to be lacking in several key areas, which prompted development of the tool described herein. A particular limitation of the existing guidelines deals with complex stochastic stationary and non-stationary modeling and required much further study, therefore providing direction for the second portion of this body of work. A tool for response prediction of fluid-induced vibrations of sensors was developed which allowed for analysis of low aspect ratio sensors. Results from the tool were compared to experimental lift and drag data, recorded for a range of flow velocities. The model was found to perform well over the majority of the velocity range showing superiority in prediction of response as compared to ASME guidelines. The tool was then applied to a design problem given by an industrial partner, showing several of their designs to be inadequate for the proposed flow regime. This immediate identification of unsuitable designs no doubt saved significant time in the product development process. Work to investigate stochastic modeling in structural dynamics was undertaken to understand the reasons for the limitations found in fluid-structure interaction models. A particular weakness, non-stationary forcing, was found to be the most lacking in terms of use in the design stage of structures. A method was developed using the Karhunen Loeve expansion as its base to close the gap between prohibitively simple (stationary only) models and those which require too much computation time. Models were developed from SDOF through continuous systems and shown to perform well at each stage. Further work is needed in this area to bring this work full circle such that the lessons learned can improve design level turbulent response calculations.<br>Ph. D.
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Segui, Vasquez Bartolomé. "Modélisation dynamique des systèmes disque aubes multi-étages : Effets des incertitudes." Phd thesis, INSA de Lyon, 2013. http://tel.archives-ouvertes.fr/tel-00961270.

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Les conceptions récentes de turbomachines ont tendance à évoluer vers des liaisons entre étages de plus en plus souples et des niveaux d'amortissement faibles, donnant lieu à des configurations où les modes sont susceptibles de présenter des niveaux de couplages inter-étages forts. En général, les ensembles disques aubes multi-étagés n'ont aucune propriété de symétrie cyclique d'ensemble et l'analyse doit porter sur un modèle de la structure complète donnant lieu à des calculs très coûteux. Pour palier ce problème, une méthode récente appelée symétrie cyclique multi-étages peut être utilisée pour réduire le coût des calculs des rotors composés de plusieurs étages, même lorsque les étages ont un nombre différent de secteurs. Cette approche profite de la symétrie cyclique inhérente à chaque étage et utilise une hypothèse spécifique qui aboutit à des sous-problèmes découplés pour chaque ordre de Fourier spatial. La méthodologie proposée vise à étudier l'effet des incertitudes sur le comportement dynamique des rotors en utilisant l'approche de symétrie cyclique multi-étages et l'expansion en Chaos Polynomial. Les incertitudes peuvent découler de l'usure des aubes, des changements de température ou des tolérances de fabrication. En première approche, seules les incertitudes provenant de l'usure uniforme de l'ensemble des aubes sont étudiées. Celles-ci peuvent être modélisées en considérant une variation globale des propriétés du matériau de l'ensemble des aubes d'un étage particulier. L'approche de symétrie cyclique multi-étages peut alors être utilisée car l'hypothèse de secteurs identiques est respectée. La positivité des matrices aléatoires concernées est assurée par l'utilisation d'une loi gamma très adaptée à la physique du problème impliquant le choix des polynômes de Laguerre comme base pour le chaos polynomial. Dans un premier temps des exemples numériques représentatifs de différents types de turbomachines sont introduits dans le but d'évaluer la robustesse de la méthode de symétrie cyclique multi-étages. Ensuite, les résultats de l'analyse modale aléatoire et de la réponse aléatoire obtenus par le chaos polynomial sont validés par comparaison avec des simulations de Monte-Carlo. En plus des résultats classiquement rencontrés pour les fréquences et réponses forcées, les incertitudes considérées mettent en évidence des variations sur les déformées modales qui évoluent entre différentes familles de modes dans les zones de forte densité modale. Ces variations entraînent des modifications sensibles sur la dynamique globale de la structure analysée et doivent être considérées dans le cadre des conceptions robustes.
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Book chapters on the topic "General polynomial chaos expansion"

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Chu, Liu. "Polynomial Chaos Expansion." In Uncertainty Quantification of Stochastic Defects in Materials. CRC Press, 2021. http://dx.doi.org/10.1201/9781003226628-5.

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Lacor, Chris, and Éric Savin. "General Introduction to Polynomial Chaos and Collocation Methods." In Uncertainty Management for Robust Industrial Design in Aeronautics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77767-2_7.

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Chikhaoui, K., N. Kacem, N. Bouhaddi, and M. Guedri. "Uncertainty Propagation Combining Robust Condensation and Generalized Polynomial Chaos Expansion." In Model Validation and Uncertainty Quantification, Volume 3. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15224-0_24.

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Marchi, Mariapia, Enrico Rigoni, Rosario Russo, and Alberto Clarich. "Percentile via Polynomial Chaos Expansion: Bridging Robust Optimization with Reliability." In EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49325-1_3.

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Hu, Junjun, S. Lakshmivarahan, and John M. Lewis. "Quantification of Forecast Uncertainty and Data Assimilation Using Wiener’s Polynomial Chaos Expansion." In Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. III). Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43415-5_7.

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Zhao, Huan, and Zhenghong Gao. "Uncertainty-Based Design Optimization of NLF Airfoil Based on Polynomial Chaos Expansion." In Lecture Notes in Electrical Engineering. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3305-7_126.

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Du, Yuncheng, and Dongping Du. "Cardiac Image Segmentation Using Generalized Polynomial Chaos Expansion and Level Set Function." In Level Set Method in Medical Imaging Segmentation. CRC Press, 2019. http://dx.doi.org/10.1201/b22435-9.

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Cedeño, Naomi, and Saba Infante. "Estimation of Ordinary Differential Equations Solutions with Gaussian Processes and Polynomial Chaos Expansion." In Information and Communication Technologies. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89941-7_1.

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Liatsikouras, Athanasios G., Varvara G. Asouti, Kyriakos Giannakoglou, and Guillaume Pierrot. "Aerodynamic Shape Optimization by Considering Geometrical Imperfections Using Polynomial Chaos Expansion and Evolutionary Algorithms." In Computational Methods in Applied Sciences. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89890-2_28.

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Dutta, Subhrajit, and Chandrasekhar Putcha. "Reliability-Based Design Optimization of a Large-Scale Truss Structure Using Polynomial Chaos Expansion Metamodel." In Reliability, Safety and Hazard Assessment for Risk-Based Technologies. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9008-1_39.

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Conference papers on the topic "General polynomial chaos expansion"

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Liu, Jingyu, Xiaoting Wang, and Xiaozhe Wang. "A Sparse Polynomial Chaos Expansion-Based Method for Probabilistic Transient Stability Assessment and Enhancement." In 2022 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2022. http://dx.doi.org/10.1109/pesgm48719.2022.9916882.

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Wang, F., F. Xiong, S. Yang, and Y. Xiong. "A Sparse Data-Driven Polynomial Chaos Expansion Method for Uncertainty Propagation." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59795.

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The data-driven polynomial chaos expansion (DD-PCE) method is claimed to be a more general approach of uncertainty propagation (UP). However, as a common problem of all the full PCE approaches, the size of polynomial terms in the full DD-PCE model is significantly increased with the dimension of random inputs and the order of PCE model, which would greatly increase the computational cost especially for high-dimensional and highly non-linear problems. Therefore, a sparse DD-PCE is developed by employing the least angle regression technique and a stepwise regression strategy to adaptively remove some insignificant terms. Through comparative studies between sparse DD-PCE and the full DD-PCE on three mathematical examples with random input of raw data, common and nontrivial distributions, and a ten-bar structure problem for UP, it is observed that generally both methods yield comparably accurate results, while the computational cost is significantly reduced by sDD-PCE especially for high-dimensional problems, which demonstrates the effectiveness and advantage of the proposed method.
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Shen, Danfeng, Hao Wu, Lu Liu, and Deqiang Gan. "Solving Probabilistic Power Flow with Wind Generation by Polynomial Chaos Expansion Method from the Perspective of Parametric Problems." In 2020 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2020. http://dx.doi.org/10.1109/pesgm41954.2020.9281771.

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Fan, Miao, Xiaoyu Wang, Lengcheng Huang, and Feng Dong. "Data-Driven Probabilistic Dynamic Analysis for Power Systems with Correlated Renewable Energy Sources based on Polynomial Chaos Expansion." In 2022 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2022. http://dx.doi.org/10.1109/pesgm48719.2022.9916667.

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Wang, Xiaoting, Xiaozhe Wang, Hao Sheng, and Xi Lin. "A Data-Driven Sparse Polynomial Chaos Expansion Method to Assess Probabilistic Total Transfer Capability for Power Systems with Renewables." In 2022 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2022. http://dx.doi.org/10.1109/pesgm48719.2022.9916717.

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Panizza, Andrea, Dante Tommaso Rubino, and Libero Tapinassi. "Efficient Uncertainty Quantification of Centrifugal Compressor Performance Using Polynomial Chaos." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-25081.

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This paper presents a fully automated procedure to estimate the uncertainty of compressor stage performance, due to impeller manufacturing variability. The methodology was originally developed for 2D stages, i.e., stages for which the impeller blade angle and thickness distribution are only defined at the hub end-wall. Here, we extend the procedure to general 3D stages, for which blade angle and thickness distributions can be prescribed independently at the shroud and hub endwalls. Starting from the probability distribution of the impeller geometrical parameters, 3D sample geometries are generated and 1D/2D aerodynamic models are created, which are used to predict the performance of each sample geometry. The original procedure used the Monte Carlo method to propagate uncertainty. However, this requires a large number of samples to compute accurate performance statistics. Here we compare the results from Monte Carlo, with those obtained using Sparse Grid Polynomial Chaos Expansion (PCE) and a Multidimensional Cubature Rule for uncertainty propagation. PCE has exponential convergence in the stochastic space for smooth functions, and the use of sparse grids mitigates the increase of sample points due to the increase in the number of uncertain parameters. The cubature rule has accuracy limitations, but sample points increase only linearly with the number of parameters. For a 3D stage, the probability distributions of the performance characteristics are computed, as well as the sensitivity to the design parameters. The results show that PCE and Multidimensional Cubature give similar results to MC computations, with a much lower computational effort.
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Babaee, Hessam, Xiaoliang Wan, and Sumanta Acharya. "Effect of Uncertainty in Blowing Ratio on Film Cooling Effectiveness." In ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/ht2013-17159.

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In this study the effect of randomness of blowing ratio on film cooling performance is investigated by combining direct numerical simulations with a stochastic collocation approach. The geometry includes a 35-degree inclined jet with a plenum attached to it. The blowing ratio variations are assumed to have a truncated Gaussian distribution with mean of 0.3 and the standard variation of approximately 0.1. The parametric space is discretized using Multi-Element general Polynomial Chaos (ME-gPC) with five elements where general polynomial chaos of order 3 is used in each element. A fast convergence of the polynomial expansion in the random space was observed. Direct numerical simulations were carried out using spectral element method to sample the governing equations in space and time. The probability density function of the film cooling effectiveness was obtained and the standard deviation of the adiabatic film cooling effectiveness on the blade surface was calculated. A maximum standard deviation of 15% was observed in the region within a four-jet-diameter distance downstream of the exit hole. The spatially-averaged adiabatic film cooling effectiveness was 0.23 ± 0.02. The calculation of all the statistical properties were carried out as off-line post-processing. Overall the computational strategy is shown to be very effective with the total computational cost being equivalent to solving twenty independent direct numerical simulations that are performed concurrently.
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Pepper, Nick, Francesco Montomoli, Francesco Giacomel, et al. "Uncertainty Quantification and Missing Data for Turbomachinery With Probabilistic Equivalence and Arbitrary Polynomial Chaos, Applied to Scroll Compressors." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-16139.

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Abstract This work presents a framework for predicting unknown input distributions for turbomachinery applications starting from scarce experimental measurements. The problem is relevant to turbomachinery where important parameters are obtained using indirect measurements. In this paper a scroll compressor is used as example but the suggested framework is completely general and can be used to infer missing data on material composition (carbon fiber properties, laser melted specimens for additive manufacturing etc) or input data (such as the turbine inlet temperature). Scroll compressors are small devices with a very complex geometry that is difficult to measure. Moreover these compressors are highly sensitive to manufacturing errors and clearances. For these reasons we have chosen this example as an ideal candidate to prove the effectiveness of the framework. An input probability distribution for the scroll height is recovered based on a scarce, synthetic data set. The scroll height is used as an example of a missing distribution for a geometric parameter as it has the highest variance and is challenging to measure experimentally. The framework consists of two main building blocks: an equivalence in a probabilistic sense and a Non-Intrusive Polynomial Chaos formulation able to deal with scarce data. The probabilistic equivalence is defined by a Probability Density Function (PDF) matching approach in which the statistical distance between probability distributions is quantified by either the Kolmogorov-Smirnov (KS) distance or the Kullback-Leibler (KL) divergence. By representing the missing inputs with a generalised Polynomial Chaos Expansion (gPCE) the back-calculation problem can be recast as an optimisation problem in which an arbitrary Polynomial Chaos (aPC) formulation was used to propagate the uncertain input distributions through a computational model of the system and generate a probability distribution for the Quantity of Interest (QoI). The framework has been tested with multiple non-Askey scheme distributions to prove the generality of the proposed approach.
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Geroulas, Vasileios, Zissimos P. Mourelatos, Vasiliki Tsianika, and Igor Baseski. "Reliability of Nonlinear Vibratory Systems Under Non-Gaussian Loads." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67313.

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A general methodology is presented for time-dependent reliability and random vibrations of nonlinear vibratory systems with random parameters excited by non-Gaussian loads. The approach is based on Polynomial Chaos Expansion (PCE), Karhunen-Loeve (KL) expansion and Quasi Monte Carlo (QMC). The latter is used to estimate multi-dimensional integrals efficiently. The input random processes are first characterized using their first four moments (mean, standard deviation, skewness and kurtosis coefficients) and a correlation structure in order to generate sample realizations (trajectories). Characterization means the development of a stochastic metamodel. The input random variables and processes are expressed in terms of independent standard normal variables in N dimensions. The N-dimensional input space is space filled with M points. The system differential equations of motion are time integrated for each of the M points and QMC estimates the four moments and correlation structure of the output efficiently. The proposed PCE-KL-QMC approach is then used to characterize the output process. Finally, classical MC simulation estimates the time-dependent probability of failure using the developed stochastic metamodel of the output process. The proposed methodology is demonstrated with a Duffing oscillator example under non-Gaussian load.
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Greene, M. Steven, Yu Liu, Wei Chen, Wing Kam Liu, and Hong-Zhong Huang. "Enabling Integrated Material and Product Design Under Uncertainty Through Stochastic Constitutive Relations." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28917.

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This paper presents a computational framework that mathematically propagates material microstructure uncertainties to coarser system resolutions for use in multiscale design frameworks. The computational framework uses a homogenized stochastic constitutive relation that links microstructure uncertainty with stochastic material properties. The stochastic constitutive relation formulated in this work serves as the critical link between the material and product domains in integrated material and product design. Ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized, and stochastic cell averaging is achieved by two advanced uncertainty quantification methods: random process polynomial chaos expansion and statistical copula functions. Both methods confront the mathematical difficulty in randomizing constitutive law parameters by capturing the marked correlation among them often seen in complex materials, thus the results proffer a more accurate probabilistic estimation of constitutive material behavior. The method put forth in this research, though quite general, is applied to a plastic, high strength steel alloy for demonstration.
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