Relevant bibliographies by topics / Polynomial chaos expansion

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Academic literature on the topic 'Polynomial chaos expansion'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "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
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Yin, Shengwen, Xiaohan Zhu, and Xiang Liu. "A Novel Sparse Polynomial Expansion Method for Interval and Random Response Analysis of Uncertain Vibro-Acoustic System." Shock and Vibration 2021 (September 23, 2021): 1–15. http://dx.doi.org/10.1155/2021/1125373.

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For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain parameters. This study presents a novel interval and random polynomial expansion method, called Sparse Grids’ Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, to obtain the response of a vibro-acoustic system with interval and random uncertainties. The proposed SGS-IRAPC retains the accuracy and the sim
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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
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Ghanem, R. "The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables." Journal of Applied Mechanics 66, no. 4 (1999): 964–73. http://dx.doi.org/10.1115/1.2791806.

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A procedure is presented in this paper for developing a representation of lognormal stochastic processes via the polynomial chaos expansion. These are processes obtained by applying the exponential operator to a gaussian process. The polynomial chaos expansion results in a representation of a stochastic process in terms of multidimensional polynomials orthogonal with respect to the gaussian measure with the dimension defined through a set of independent normalized gaussian random variables. Such a representation is useful in the context of the spectral stochastic finite element method, as well
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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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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 u
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Abbasi, Mostafa, and Ali Gholami. "Polynomial chaos expansion for nonlinear geophysical inverse problems." GEOPHYSICS 82, no. 4 (2017): R259—R268. http://dx.doi.org/10.1190/geo2016-0716.1.

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There are lots of geophysical problems that include computationally expensive functions (forward models). Polynomial chaos (PC) expansion aims to approximate such an expensive equation or system with a polynomial expansion on the basis of orthogonal polynomials. Evaluation of this expansion is extremely fast because it is a polynomial function. This property of the PC expansion is of great importance for stochastic problems, in which an expensive function needs to be evaluated thousands of times. We have developed PC expansion as a novel technique to solve nonlinear geophysical problems. To be
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Gao, Rugao, Keping Zhou, and Yun Lin. "A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters." Complexity 2018 (December 3, 2018): 1–14. http://dx.doi.org/10.1155/2018/7471460.

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The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computational efficiency and accuracy. But in gPCEM, a nonlinear transformation of random variables should always be used to adapt the generalized Polynomial Chaos theory for the analysis of random problems with complicated probability distributions, which may introduce nonlinearity in the procedure of random u
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Crestaux, Thierry, Olivier Le Maıˆtre, and Jean-Marc Martinez. "Polynomial chaos expansion for sensitivity analysis." Reliability Engineering & System Safety 94, no. 7 (2009): 1161–72. http://dx.doi.org/10.1016/j.ress.2008.10.008.

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LePage, Kevin D. "Polynomial chaos expansions for modelling the statistics of acoustic propagation in random waveguides." Journal of the Acoustical Society of America 155, no. 3_Supplement (2024): A279. http://dx.doi.org/10.1121/10.0027498.

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The use of Polynomial Chaos expansions to model the transfer of the statistical properties of the sound speed in ocean waveguides to those of acoustic waves passing through them is described. A perturbational framework approximating the interaction of acoustic normal modes with fluctuations around a background sound speed is used, with the fluctuations being represented vertically by empirical orthogonal functions and horizontally by correlation functions. The Polynomial Chaos expansions are derived to second order in the uncorrelated random variable representing the sound speed fluctuations f
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Dissertations / Theses on the topic "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'ap
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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
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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 Racew
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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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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 qu
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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 multi
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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 limitatio
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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 p
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Books on the topic "Polynomial chaos expansion"

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Ozen, Hasan Cagan. Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions. [publisher not identified], 2017.

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Book chapters on the topic "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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Syed, Wajih U., and Ibrahim M. Elfadel. "Uncertainty Quantification Using Polynomial-Chaos Expansion." In Tapered Beams in MEMS. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-66391-8_8.

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Marques, Sónia H. "Metamodelling with the Multi-dimensional Hermite Polynomial Chaos Expansion." In Springer Proceedings in Complexity. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-60907-7_30.

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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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Niu, Ruixin, Tao Sun, and Mulugeta Haile. "Polynomial Chaos Expansion-Based Nonlinear Filtering for Dynamic State Estimation." In Handbook of Dynamic Data Driven Applications Systems. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27986-7_3.

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Novák, Jiří, and Peter Chudý. "Dynamic Soaring in Uncertain Wind Conditions: Polynomial Chaos Expansion Approach." In Machine Learning, Optimization, and Data Science. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-53969-5_9.

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An, Qingwei, Jun Zhang, Ling Tao, Ruyi Tao, and Wenjun Ruan. "Uncertainty Quantification in Impulse Thruster Performance Using Polynomial Chaos Expansion." In Lecture Notes in Mechanical Engineering. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-8048-2_183.

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Bazyleva, Valentina, Victoria M. Garibay, and Debraj Roy. "Global Sensitivity Analysis Using Polynomial Chaos Expansion on the Grassmann Manifold." In Computational Science – ICCS 2023. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-36030-5_46.

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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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Conference papers on the topic "Polynomial chaos expansion"

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Kumar, Kundan, and Simo Särkkä. "Polynomial Chaos Expansion Based Rauch–Tung–Striebel Smoothers." In 2024 27th International Conference on Information Fusion (FUSION). IEEE, 2024. http://dx.doi.org/10.23919/fusion59988.2024.10706310.

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Ou, Zhongxi, Lihong Qian, Sui Peng, et al. "A Polynomial Chaos Expansion-Based Reserve Capacity Optimization Method Considering Reliability." In 2025 7th Asia Energy and Electrical Engineering Symposium (AEEES). IEEE, 2025. https://doi.org/10.1109/aeees64634.2025.11020389.

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Li, Zheng, Ze-Ming Wu, and Xiao-Chun Li. "Deep Kernel Polynomial Chaos Expansion Technique for Uncertainty Quantification of Electronic Circuits." In 2024 IEEE International Symposium on Radio-Frequency Integration Technology (RFIT). IEEE, 2024. https://doi.org/10.1109/rfit60557.2024.10812522.

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Zhang, Yiwen, and Vikass Monebhurrun. "Non-Intrusive Polynomial Chaos Expansion for Uncertainty Quantification in Specific Absorption Rate Calculations." In 2024 IEEE International Symposium on Antennas and Propagation and INC/USNC‐URSI Radio Science Meeting (AP-S/INC-USNC-URSI). IEEE, 2024. http://dx.doi.org/10.1109/ap-s/inc-usnc-ursi52054.2024.10686256.

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Jiang, Haolin, Francesco Ferranti, and Giulio Antonini. "Sparse polynomial chaos expansion for high-dimensional uncertainty quantification of braided shielded cables." In 2024 International Symposium on Electromagnetic Compatibility – EMC Europe. IEEE, 2024. http://dx.doi.org/10.1109/emceurope59828.2024.10722165.

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Yurtseven, Kaan, Hakan Ergun, and Dirk Van Hertem. "Risk-based Stochastic Optimal Power Flow for AC/DC Grids Using Polynomial Chaos Expansion." In 2024 IEEE PES Innovative Smart Grid Technologies Europe (ISGT EUROPE). IEEE, 2024. https://doi.org/10.1109/isgteurope62998.2024.10863605.

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Gill, Hyunjune, and Seongkyu Lee. "Uncertainty Quantification of Unsteady Loading Noise of a Hovering Rotor Using Polynomial Chaos Expansion." In Vertical Flight Society 81st Annual Forum and Technology Display. The Vertical Flight Society, 2025. https://doi.org/10.4050/f-0081-2025-60.

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In this study, we employ the Polynomial Chaos Expansion (PCE) and Monte Carlo (MC) methods to quantify the uncertainty of unsteady loading noise generated by a hovering rotor under the presence of vertical gust. The unsteady loading noise is predicted using a frequency-domain approach combined with a quasi-steady Blade Element Momentum Theory, accounting for time-varying aerodynamic forces. A sinusoidal gust is modeled using two parameters: gust length and gust amplitude. Then, the uncertainty quantification (UQ) of the unsteady loading noise is performed using the PCE and MC with these two gu
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Codecasa, Lorenzo, and Luca Di Rienzo. "Stochastic thermal modeling by polynomial chaos expansion." In 2013 19th International Workshop on Thermal Investigations of ICs and Systems (THERMINIC). IEEE, 2013. http://dx.doi.org/10.1109/therminic.2013.6675234.

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Novák, Lukáš, Miroslav Vořechovský, and Václav Sadílek. "ADAPTIVE SEQUENTIAL SAMPLING FOR POLYNOMIAL CHAOS EXPANSION." In 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Institute of Research and Development for Computational Methods in Engineering Sciences (ICMES), 2021. http://dx.doi.org/10.7712/120221.8038.18955.

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Xiong, Fenfen, Bin Xue, Zhang Yan, and Shuxing Yang. "Polynomial chaos expansion based robust design optimization." In 2011 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (ICQR2MSE). IEEE, 2011. http://dx.doi.org/10.1109/icqr2mse.2011.5976745.

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Reports on the topic "Polynomial chaos expansion"

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Jakeman, John, Fabian Franzelin, Akil Narayan, Michael Eldred, and Dirk Pflueger. Polynomial chaos expansions for dependent random variables. Office of Scientific and Technical Information (OSTI), 2019. http://dx.doi.org/10.2172/1762354.

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