Polynomial Chaos Expansion method
Stochastic porous model of a bone-implant healing process using polynomial chaos expansion
... The polynomial chaos expansion method is a parametric approach to describe uncertain ...The polynomial chaos expansion was first introduced as the homogeneous chaos ...
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Identification of random shapes from images through polynomial chaos expansion of random level-set functions
... Element Method (X-SFEM) [5, 6] has been ...X-FEM method [7, 8, 9, 10, 11], relies on the implicit representation of complex geometries using random level-set functions and on the use of a Galerkin ...
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Efficient sparse polynomial chaos expansion methodology for the probabilistic analysis of computationally-expensive deterministic models
... SPARSE POLYNOMIAL CHAOS EXPANSION METHODOLOGY In this section, one first presents the PCE and then its extension, the ...non-intrusive method is the regression approach [1 –11]. This ...
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Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion
... sparse polynomial chaos expansion developed by Blatman and Sudret [18] in the framework of the non-intrusive approaches is used ...This method is based on an adaptive regression-based ...
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Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion
... Carlo method is not applicable and a surrogate model has to be ...methods, polynomial chaos expansion is one of the most efficient to calculate variance- based sensitivity ...the ...
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Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system
... series expansion on a set of zero mean random variables [21, ...so-called Polynomial Chaos Expansions and was first introduced in the field of structural dynamics by Ghanem and Spanos ...new ...
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Analyzing the dynamic response of a rotor system under uncertain parameters by Polynomial Chaos Expansion
... expansion [Benaroya and Rehak (1988); Yamazaki et ...this method, a very high number of samples is necessary then if solving the deterministic problem is already computationally intensive, the ...
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ON OPTIMAL EXPERIMENTAL DESIGNS FOR SPARSE POLYNOMIAL CHAOS EXPANSIONS
... 5.2.1 Sparse PCE: Least Angle regression The LAR algorithm is an iterative regression method applied in the context of PCE for ba- sis selection (Blatman and Sudret, 2011a). The basic idea of LAR is to select a ...
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A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter
... robust method: it is not sensitive to possible polynomial trends as soon as the number of vanishing moments Q is large ...This method has been introduced by Flandrin [15] in the case of fBm and later ...
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Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion
... This paper proposes to take advantage of the PCE in the estimation of variance based sensitivity indices. Then, in order to know if this approximation is accurate enough to estimate partial variances, a way to construct ...
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Bayesian sparse polynomial chaos expansion for global sensitivity analysis
... Regarding the parameter estimation, we assume that the prior parame- ter and error distributions are both Gaussian. Thus the parameters can be estimated by the analytical expression of the MAP as described in Section 4. ...
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Efficient sparse polynomial chaos expansion methodology for computationally expensive deterministic models
... SPARSE POLYNOMIAL CHAOS EXPANSION (SPCE) METHODOLOGY In this section, one first presents the polynomial chaos expansion (PCE) and then its extension, the sparse polynomial ...
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A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry
... the polynomial chaos (PC) theory has originally been introduced by Wiener in the case of Gaussian random input variables as the finite-dimensional Wiener polynomial chaos ...This ...
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Propagation of modeling uncertainty by polynomial chaos expansion in multidisciplinary analysis
... a polynomial chaos expansion (PCE) based approach to propagate modeling uncertainties in ...proposed method emphasizes an important particular case in which each disciplinary solver is ...
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Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification
... generalized polynomial-chaos basis functions and Gauss quadrature rules from a general surrogate ...Our method is based on the ideas of changing variables and monotone interpolation ...generalized ...
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Determination of Bootstrap confidence intervals on sensitivity indices obtained by polynomial chaos expansion
... 4.3. Results with the LAR strategy The major advantage of this basis construction method is that polynomials are chosen a priori within a full basis reaching a given degree. Moreover the size of the basis have not ...
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A Method for Invariant Generation for Polynomial Continuous Systems
... for polynomial ODEs [14] allow deductive provers to work with arbitrary semi-algebraic invariants, yet few methods for invariant generation are able to synthesize interesting invariants with boolean structure that ...
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On Continued Fraction Expansion of Real Roots of Polynomial Systems, Complexity and Condition Numbers
... the depth of the subdivision tree. 7. Implementation and Experimentation We have implemented the algorithm in the C++ library realroot of Mathemagix 1 , which is an open source effort that provides fundamental algebraic ...
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A polynomial chaos approach for uncertainty analysis of chloride-induced corrosion in concrete structures
... a polynomial chaos approach for the probabilistic modeling of chloride-induced corrosion that takes into account the uncertainties in the parameters that govern the physical ...
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Stein's method on the second Wiener chaos : 2-Wasserstein distance
... i=1 α n,i (N i 2 − 1) still with {N i } i≥1 i.i.d. standard Gaussian and now {α n,i } i≥1 not necessarily distinct real numbers. As mentioned above, the fact that we bound the Wasserstein-2 distance is not anecdotal : ...
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