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Journal articles on the topic 'General polynomial chaos expansion'

Author: Grafiati

Published: 10 March 2023

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1

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 (June 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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3

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 (September 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 (February 7, 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 (December 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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6

Panayirci, H. M. "Efficient solution for Galerkin-based polynomial chaos expansion systems." Advances in Engineering Software 41, no. 12 (December 2010): 1277–86. http://dx.doi.org/10.1016/j.advengsoft.2010.09.004.

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7

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 (February 7, 2017): 1170–91. http://dx.doi.org/10.1002/nme.5497.

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8

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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9

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 (February 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 (February 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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11

Zhou, Yicheng, Zhenzhou Lu, and Kai Cheng. "Adaboost-based ensemble of polynomial chaos expansion with adaptive sampling." Computer Methods in Applied Mechanics and Engineering 388 (January 2022): 114238. http://dx.doi.org/10.1016/j.cma.2021.114238.

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12

Hadigol, Mohammad, and Alireza Doostan. "Least squares polynomial chaos expansion: A review of sampling strategies." Computer Methods in Applied Mechanics and Engineering 332 (April 2018): 382–407. http://dx.doi.org/10.1016/j.cma.2017.12.019.

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13

Guo, Ling, Yongle Liu, and Liang Yan. "Sparse Recovery via ℓq-Minimization for Polynomial Chaos Expansions." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (September 12, 2017): 775–97. http://dx.doi.org/10.4208/nmtma.2017.0001.

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AbstractIn this paper we consider the algorithm for recovering sparse orthogonal polynomials using stochastic collocation via ℓq minimization. The main results include: 1) By using the norm inequality between ℓq and ℓ2 and the square root lifting inequality, we present several theoretical estimates regarding the recoverability for both sparse and non-sparse signals via ℓq minimization; 2) We then combine this method with the stochastic collocation to identify the coefficients of sparse orthogonal polynomial expansions, stemming from the field of uncertainty quantification. We obtain recoverability results for both sparse polynomial functions and general non-sparse functions. We also present various numerical experiments to show the performance of the ℓq algorithm. We first present some benchmark tests to demonstrate the ability of ℓq minimization to recover exactly sparse signals, and then consider three classical analytical functions to show the advantage of this method over the standard ℓ1 and reweighted ℓ1 minimization. All the numerical results indicate that the ℓq method performs better than standard ℓ1 and reweighted ℓ1 minimization.

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Novák, Lukáš. "On distribution-based global sensitivity analysis by polynomial chaos expansion." Computers & Structures 267 (July 2022): 106808. http://dx.doi.org/10.1016/j.compstruc.2022.106808.

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Son, Jeongeun, and Yuncheng Du. "An Efficient Polynomial Chaos Expansion Method for Uncertainty Quantification in Dynamic Systems." Applied Mechanics 2, no. 3 (July 12, 2021): 460–81. http://dx.doi.org/10.3390/applmech2030026.

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Uncertainty is a common feature in first-principles models that are widely used in various engineering problems. Uncertainty quantification (UQ) has become an essential procedure to improve the accuracy and reliability of model predictions. Polynomial chaos expansion (PCE) has been used as an efficient approach for UQ by approximating uncertainty with orthogonal polynomial basis functions of standard distributions (e.g., normal) chosen from the Askey scheme. However, uncertainty in practice may not be represented well by standard distributions. In this case, the convergence rate and accuracy of the PCE-based UQ cannot be guaranteed. Further, when models involve non-polynomial forms, the PCE-based UQ can be computationally impractical in the presence of many parametric uncertainties. To address these issues, the Gram–Schmidt (GS) orthogonalization and generalized dimension reduction method (gDRM) are integrated with the PCE in this work to deal with many parametric uncertainties that follow arbitrary distributions. The performance of the proposed method is demonstrated with three benchmark cases including two chemical engineering problems in terms of UQ accuracy and computational efficiency by comparison with available algorithms (e.g., non-intrusive PCE).

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16

Tian, Wei, Chuanqi Zhu, Pieter de Wilde, Jiaxin Shi, and Baoquan Yin. "SENSITIVITY ANALYSIS OF BUILDING ENERGY PERFORMANCE BASED ON POLYNOMIAL CHAOS EXPANSION." Journal of Green Building 15, no. 4 (September 1, 2020): 173–83. http://dx.doi.org/10.3992/jgb.15.4.173.

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ABSTRACT Global sensitivity analysis based on polynomial chaos expansion (PCE) shows interesting characteristics, including reduced simulation runs for computer models and high interpretability of sensitivity results. This paper explores these features of the PCE-based sensitivity analysis using an office building as a case study with the EnergyPlus simulation program. The results indicate that the predictive performance of PCE models is closely correlated with the stability of the sensitivity index, depending on sample number and expansion degree. Therefore, it is necessary to carefully assess model accuracy of PCE models and evaluate convergence of the sensitivity index when using PCE-based sensitivity analysis. It is also found that more simulation runs of building energy models are required for a higher expansion degree of the PCE model to obtain a reliable sensitivity index. A bootstrap technique with a random sample can be used to construct confidence intervals for sensitivity indicators in building energy assessment to provide robust sensitivity rankings.

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17

Katagiri, Yuki, Kazuaki Iwamura, Yosuke Nakanishi, Sachio Takano, and Ryohei Suzuki. "Arbitrary polynomial chaos expansion and its application to power flow analysis-Fast approximation of probability distribution by arbitrary polynomial expansion." Journal of Physics: Conference Series 1780, no. 1 (February 1, 2021): 012025. http://dx.doi.org/10.1088/1742-6596/1780/1/012025.

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18

Kaur, Navjot, and Kavita Goyal. "Hybrid Hermite polynomial chaos SBP-SAT technique for stochastic advection-diffusion equations." International Journal of Modern Physics C 31, no. 09 (August 8, 2020): 2050128. http://dx.doi.org/10.1142/s0129183120501284.

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The study of advection–diffusion equation has relatively became an active research topic in the field of uncertainty quantification (UQ) due to its numerous real life applications. In this paper, Hermite polynomial chaos is united with summation-by-parts (SBP) – simultaneous approximation terms (SATs) technique to solve the advection–diffusion equations with random Dirichlet boundary conditions (BCs). Polynomial chaos expansion (PCE) with Hermite basis is employed to separate the randomness, then SBP operators are used to approximate the differential operators and SATs are used to enforce BCs by ensuring the stability. For each chaos coefficient, time integration is performed using Runge–Kutta method of fourth order (RK4). Statistical moments namely mean and variance are computed using polynomial chaos coefficients without any extra computational effort. The method is applied on three test problems for validation. The first two test problems are stochastic advection equations on [Formula: see text] without any boundary and third problem is stochastic advection–diffusion equation on [0,2] with Dirichlet BCs. In case of third problem, we have obtained a range of permissible parameters for a stable numerical solution.

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19

Zhang, Liang, ZhiPing Li, Hong Li, Caspar Daniel Adenutsi, FengPeng Lai, KongJie Wang, and Sen Yang. "Application of Polynomial Chaos Expansion to Optimize Injection-Production Parameters under Uncertainty." Mathematical Problems in Engineering 2020 (April 21, 2020): 1–13. http://dx.doi.org/10.1155/2020/5374523.

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The optimization of oil field development scheme considering the uncertainty of reservoir model is a challenging and difficult problem in reservoir engineering design. The most common method used in this regard is to generate multiple models based on statistical analysis of uncertain reservoir parameters and requires a large number of simulations to efficiently handle all uncertainties, thus requiring a huge amount of computational power. In order to reduce the computational burden, a method which combines reservoir simulation, an economic model, polynomial chaos expansion with response surface methodology, and Levy flight particle swarm optimization (LFPSO) algorithm is proposed to determine the optimal injection-production parameters with reservoir uncertainties at a reasonable computational cost. This approach is applied to a five-spot well pattern optimization design for obtaining the optimal parameters, including oil-water well distance, injection rate, and bottom hole pressure, while considering the uncertainties of porosity, permeability, and relative permeability. The results of the case study indicated that the integrated approach is practical and efficient for performing reservoir optimization with uncertain reservoir parameters.

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20

Prem, Marcel S., Michael Klanner, and Katrin Ellermann. "Identification of Fractional Damping Parameters in Structural Dynamics Using Polynomial Chaos Expansion." Applied Mechanics 2, no. 4 (November 30, 2021): 956–75. http://dx.doi.org/10.3390/applmech2040056.

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In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.

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21

Jakeman, John D., Fabian Franzelin, Akil Narayan, Michael Eldred, and Dirk Plfüger. "Polynomial chaos expansions for dependent random variables." Computer Methods in Applied Mechanics and Engineering 351 (July 2019): 643–66. http://dx.doi.org/10.1016/j.cma.2019.03.049.

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22

Zeng, Xiaoshu, and Roger Ghanem. "Projection pursuit adaptation on polynomial chaos expansions." Computer Methods in Applied Mechanics and Engineering 405 (February 2023): 115845. http://dx.doi.org/10.1016/j.cma.2022.115845.

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23

Son, Jeongeun, and Yuncheng Du. "Probabilistic surrogate models for uncertainty analysis: Dimension reduction‐based polynomial chaos expansion." International Journal for Numerical Methods in Engineering 121, no. 6 (November 14, 2019): 1198–217. http://dx.doi.org/10.1002/nme.6262.

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24

Walters, Gage, Andrew Wixom, and Sheri Martinelli. "Comparison of quadrature and regression based generalized polynomial chaos expansions for structural acoustics." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 6 (August 1, 2021): 863–74. http://dx.doi.org/10.3397/in-2021-1670.

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This work performs a direct comparison between generalized polynomial chaos (GPC) expansion techniques applied to structural acoustic problems. Broadly, the GPC techniques are grouped in two categories: , where the stochastic sampling is predetermined according to a quadrature rule; and , where an arbitrary selection of points is used as long as they are a representative sample of the random input. As a baseline comparison, Monte Carlo type simulations are also performed although they take many more sampling points. The test problems considered include both canonical and more applied cases that exemplify the features and types of calculations commonly arising in vibrations and acoustics. A range of different numbers of random input variables are considered. The primary point of comparison between the methods is the number of sampling points they require to generate an accurate GPC expansion. This is due to the general consideration that the most expensive part of a GPC analysis is evaluating the deterministic problem of interest; thus the method with the fewest sampling points will often be the fastest. Accuracy of each GPC expansion is judged using several metrics including basic statistical moments as well as features of the actual reconstructed probability density function.

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Zhang, Xufang, and Jiafei Sun. "An Effective Approach for Uncertain Aerodynamic Analysis of Airfoils via the Polynomial Chaos Expansion." Mathematical Problems in Engineering 2020 (February 26, 2020): 1–13. http://dx.doi.org/10.1155/2020/7417835.

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This paper presents an effective approach for uncertain aerodynamic analysis of airfoils via the polynomial chaos expansion (PCE). To achieve this, the multivariate polynomial is first setup to represent random factors within the aerodynamic model, whereas the expansion coefficient is expressed as the multivariate stochastic integral of the input random vector. In this regard, the statistical regression in conjunction with a small number of representative samples is employed to determine the expansion coefficient. Then, a combination of the PCE surrogate model with brutal-force Monte Carlo simulation allows to determine numerical results for the uncertain aerodynamic analysis. Potential applications of this approach are first illustrated by the uncertainty analysis of the Helmholtz equation with spatially varied wave-number random field, and its effectiveness is further examined by the uncertain aerodynamic analysis of the NACA 63-215 airfoil. Results for the small regression error and a close agreement between simulated and benchmark results have confirmed numerical accuracy and efficiency of this approach. It, therefore, has a potential to deal with computationally demanding aerodynamical models for the uncertainty analysis.

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Yang, Xiu, Xiaoliang Wan, Lin Lin, and Huan Lei. "A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS." International Journal for Uncertainty Quantification 9, no. 3 (2019): 221–43. http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2019027864.

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27

Wei, Xiao, Haichao Chang, Baiwei Feng, and Zuyuan Liu. "Sensitivity Analysis Based on Polynomial Chaos Expansions and Its Application in Ship Uncertainty-Based Design Optimization." Mathematical Problems in Engineering 2019 (January 23, 2019): 1–19. http://dx.doi.org/10.1155/2019/7498526.

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In order to truly reflect the ship performance under the influence of uncertainties, uncertainty-based design optimization (UDO) for ships that fully considers various uncertainties in the early stage of design has gradually received more and more attention. Meanwhile, it also brings high dimensionality problems, which may result in inefficient and impractical optimization. Sensitivity analysis (SA) is a feasible way to alleviate this problem, which can qualitatively or quantitatively evaluate the influence of the model input uncertainty on the model output, so that uninfluential uncertain variables can be determined for the descending dimension to achieve dimension reduction. In this paper, polynomial chaos expansions (PCE) with less computational cost are chosen to directly obtain Sobol' global sensitivity indices by its polynomial coefficients; that is, once the polynomial of the output variable is established, the analysis of the sensitivity index is only the postprocessing of polynomial coefficients. Besides, in order to further reduce the computational cost, for solving the polynomial coefficients of PCE, according to the properties of orthogonal polynomials, an improved probabilistic collocation method (IPCM) based on the linear independence principle is proposed to reduce sample points. Finally, the proposed method is applied to UDO of a bulk carrier preliminary design to ensure the robustness and reliability of the ship.

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28

Dilip, Deepthi Mary, and G. L. Sivakumar Babu. "Influence of Anisotropy on Pavement Responses Using Adaptive Sparse Polynomial Chaos Expansion." Journal of Materials in Civil Engineering 28, no. 1 (January 2016): 04015061. http://dx.doi.org/10.1061/(asce)mt.1943-5533.0001309.

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Zhao, Huan, Zhenghong Gao, Fang Xu, Yidian Zhang, and Jiangtao Huang. "An efficient adaptive forward–backward selection method for sparse polynomial chaos expansion." Computer Methods in Applied Mechanics and Engineering 355 (October 2019): 456–91. http://dx.doi.org/10.1016/j.cma.2019.06.034.

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30

Wei, D. L., Z. S. Cui, and J. Chen. "Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules." Computers & Structures 86, no. 23-24 (December 2008): 2102–8. http://dx.doi.org/10.1016/j.compstruc.2008.07.001.

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Venturi, D., X. Wan, R. Mikulevicius, B. L. Rozovskii, and G. E. Karniadakis. "Wick–Malliavin approximation to nonlinear stochastic partial differential equations: analysis and simulations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2158 (October 8, 2013): 20130001. http://dx.doi.org/10.1098/rspa.2013.0001.

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Approximating nonlinearities in stochastic partial differential equations (SPDEs) via the Wick product has often been used in quantum field theory and stochastic analysis. The main benefit is simplification of the equations but at the expense of introducing modelling errors. In this paper, we study the accuracy and computational efficiency of Wick-type approximations to SPDEs and demonstrate that the Wick propagator, i.e. the system of equations for the coefficients of the polynomial chaos expansion of the solution, has a sparse lower triangular structure that is seemingly universal, i.e. independent of the type of noise. We also introduce new higher-order stochastic approximations via Wick–Malliavin series expansions for Gaussian and uniformly distributed noises, and demonstrate convergence as the number of expansion terms increases. Our results are for diffusion, Burgers and Navier–Stokes equations, but the same approach can be readily adopted for other nonlinear SPDEs and more general noises.

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Schenkendorf, René, Xiangzhong Xie, and Ulrike Krewer. "An efficient polynomial chaos expansion strategy for active fault identification of chemical processes." Computers & Chemical Engineering 122 (March 2019): 228–37. http://dx.doi.org/10.1016/j.compchemeng.2018.08.022.

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Ma, Zeyu, Jinglai Wu, Yunqing Zhang, and Ming Jiang. "Recursive parameter estimation for load sensing proportional valve based on polynomial chaos expansion." Engineering Computations 32, no. 5 (July 6, 2015): 1343–71. http://dx.doi.org/10.1108/ec-05-2014-0116.

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Purpose – The purpose of this paper is to provide a new computational method based on the polynomial chaos (PC) expansion to identify the uncertain parameters of load sensing proportional valve (LSPV), which is commonly used to improve the efficiency of brake system in heavy truck. Design/methodology/approach – For this investigation, the mathematic model of LSPV is constructed in the form of state space equation. Then the estimation process is implemented relying on the experimental measurements. With the coefficients of the PC expansion obtained by the numerical implementation, the output observation function can be transformed into a linear and time-invariant form. The uncertain parameter recursively update functions based on Newton method can therefore be derived fit for computer calculation. To improve the estimation accuracy and stability, the Newton method is modified by employing the acceptance probability to escape from the local minima during the estimation process. Findings – The accuracy and effectiveness of the proposed parameter estimation method are confirmed by model validation compared with other estimation methods. Meanwhile, the influence of measurement noise on the robustness of the estimation methods is taken into consideration, and it is shown that the estimation approach developed in this paper could achieve impressive stability without compromising the convergence speed and accuracy too much. Originality/value – The model of LSPV is originally developed in this paper, and then the authors propose a novel effective strategy for recursively estimating uncertain parameters of complicate pneumatic system based on the PC theory.

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Jia, Wei, Brian McPherson, Feng Pan, Zhenxue Dai, and Ting Xiao. "Uncertainty quantification of CO2 storage using Bayesian model averaging and polynomial chaos expansion." International Journal of Greenhouse Gas Control 71 (April 2018): 104–15. http://dx.doi.org/10.1016/j.ijggc.2018.02.015.

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Pan, Qiujing, Xingru Qu, Leilei Liu, and Daniel Dias. "A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations." International Journal for Numerical and Analytical Methods in Geomechanics 44, no. 6 (April 25, 2020): 874–89. http://dx.doi.org/10.1002/nag.3044.

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Qiu, Chan, Xiang Peng, Zhenyu Liu, and Jianrong Tan. "Sensitivity Analysis of Random and Interval Uncertain Variables Based on Polynomial Chaos Expansion Method." IEEE Access 7 (2019): 73046–56. http://dx.doi.org/10.1109/access.2019.2919714.

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Cheng, Kai, Zhenzhou Lu, and Ying Zhen. "Multi-level multi-fidelity sparse polynomial chaos expansion based on Gaussian process regression." Computer Methods in Applied Mechanics and Engineering 349 (June 2019): 360–77. http://dx.doi.org/10.1016/j.cma.2019.02.021.

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Luu Trung Duong, Pham, Le Quang Minh, Muhammad Abdul Qyyum, and Moonyong Lee. "Sparse Bayesian learning for data driven polynomial chaos expansion with application to chemical processes." Chemical Engineering Research and Design 137 (September 2018): 553–65. http://dx.doi.org/10.1016/j.cherd.2018.08.006.

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Pascual, B., and S. Adhikari. "Combined parametric–nonparametric uncertainty quantification using random matrix theory and polynomial chaos expansion." Computers & Structures 112-113 (December 2012): 364–79. http://dx.doi.org/10.1016/j.compstruc.2012.08.008.

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Zhao, Jianyu, Shengkui Zeng, Jianbin Guo, and Shaohua Du. "Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion." Entropy 20, no. 3 (March 16, 2018): 202. http://dx.doi.org/10.3390/e20030202.

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Avdonin, Alexander, Stefan Jaensch, Camilo F. Silva, Matic Češnovar, and Wolfgang Polifke. "Uncertainty quantification and sensitivity analysis of thermoacoustic stability with non-intrusive polynomial chaos expansion." Combustion and Flame 189 (March 2018): 300–310. http://dx.doi.org/10.1016/j.combustflame.2017.11.001.

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Piprek, Patrick, Sébastien Gros, and Florian Holzapfel. "Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation." Processes 7, no. 4 (March 30, 2019): 185. http://dx.doi.org/10.3390/pr7040185.

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This study develops a ccoc framework capable of handling rare event probabilities. Therefore, the framework uses the gpc method to calculate the probability of fulfilling rare event constraints under uncertainties. Here, the resulting cc evaluation is based on the efficient sampling provided by the gpc expansion. The subsim method is used to estimate the actual probability of the rare event. Additionally, the discontinuous cc is approximated by a differentiable function that is iteratively sharpened using a homotopy strategy. Furthermore, the subsim problem is also iteratively adapted using another homotopy strategy to improve the convergence of the Newton-type optimization algorithm. The applicability of the framework is shown in case studies regarding battery charging and discharging. The results show that the proposed method is indeed capable of incorporating very general cc within an ocp at a low computational cost to calculate optimal results with rare failure probability cc.

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Guo, Xiangfeng, Qiangqiang Sun, Daniel Dias, and Eric Antoinet. "Probabilistic assessment of an earth dam stability design using the adaptive polynomial chaos expansion." Bulletin of Engineering Geology and the Environment 79, no. 9 (May 25, 2020): 4639–55. http://dx.doi.org/10.1007/s10064-020-01847-2.

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Ding, Shuoliang, and Lionel Pichon. "Sensitivity Analysis of an Implanted Antenna within Surrounding Biological Environment." Energies 13, no. 4 (February 23, 2020): 996. http://dx.doi.org/10.3390/en13040996.

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The paper describes the sensitivity analysis of a wireless power transfer link involving an implanted antenna within the surrounding biological environment. The approach combines a 3D electromagnetic modeling and a surrogate model (based polynomial chaos expansion). The analysis takes into account geometrical parameters of the implanted antenna and physical properties of the biological tissue. It allows researchers to identify at low cost the main parameters affecting the efficiency of the transmission link.

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Weise, Konstantin, Erik Müller, Lucas Poßner, and Thomas R. Knösche. "Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion." Mathematical Biosciences and Engineering 19, no. 8 (2022): 7425–80. http://dx.doi.org/10.3934/mbe.2022351.

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<abstract><p>As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of $ < 0.1 $%, $ < 1 $%, and $ < 10 $%, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions.</p></abstract>

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Umesh, K., and Ranjan Ganguli. "Material Uncertainty Effect on Vibration Control of Smart Composite Plate Using Polynomial Chaos Expansion." Mechanics of Advanced Materials and Structures 20, no. 7 (August 9, 2013): 580–91. http://dx.doi.org/10.1080/15376494.2011.643279.

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Al-Bittar, Tamara, and Abdul-Hamid Soubra. "Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion." International Journal for Numerical and Analytical Methods in Geomechanics 37, no. 13 (July 31, 2012): 2039–60. http://dx.doi.org/10.1002/nag.2120.

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Thapa, Mishal, Sameer B. Mulani, and Robert W. Walters. "Adaptive weighted least-squares polynomial chaos expansion with basis adaptivity and sequential adaptive sampling." Computer Methods in Applied Mechanics and Engineering 360 (March 2020): 112759. http://dx.doi.org/10.1016/j.cma.2019.112759.

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Zhang, Yu, and Jun Xu. "Efficient reliability analysis with a CDA-based dimension-reduction model and polynomial chaos expansion." Computer Methods in Applied Mechanics and Engineering 373 (January 2021): 113467. http://dx.doi.org/10.1016/j.cma.2020.113467.

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Jiang, Changwei, Yi Jiang, and Er Shi. "UNCERTAINTY QUANTIFICATION FOR NATURAL CONVECTION IN RANDOM POROUS MEDIA WITH INTRUSIVE POLYNOMIAL CHAOS EXPANSION." Journal of Porous Media 23, no. 7 (2020): 641–61. http://dx.doi.org/10.1615/jpormedia.2020033288.

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