Large scale random fields generation using localized Karhunen–Loève expansion

Panunzio, Alfonso M.; Cottereau, Régis; Puel, Guillaume

doi:10.1186/s40323-018-0114-7

Cited by 15 publications

(12 citation statements)

References 50 publications

(42 reference statements)

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“…representing the convolution kernel in local coordinates, or graph NNs [112]. The scaling of random field generation to large domains was addressed in [76,77]. However, practical limitations could again be the computational budget for data generation, i.e.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

Ranftl¹,

Rolf-Pissarczyk²,

Wolkerstorfer³

et al. 2022

Preprint

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Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape, and type, are difficult to predict. Motivated by this observation, we describe the heterogeneous distribution of elastic fiber degradation in the dissected aortic wall using a stochastic constitutive model. For this purpose, random field realizations, which model the stochastic distribution of degraded elastic fibers, are generated over a non-equidistant grid. The random field then serves as input for a uniaxial extension test of the pathological aortic wall, solved with the finite-element (FE) method. To include the microstructure of the dissected aortic wall, a constitutive model developed in a previous study is applied, which also includes an approach to model the degradation of interlamellar elastic fibers. Then to assess the uncertainty in the output stress distribution due to this stochastic constitutive model, a convolutional neural network, specifically a Bayesian encoderdecoder, was used as a surrogate model that maps the random input fields to the output stress distribution obtained from the FE analysis. The results show that the neural network is able to predict the stress distribution of the FE analysis while significantly reducing the computational time. In addition, it provides the probability for exceeding critical stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.

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Section: Discussionmentioning

confidence: 99%

Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

Ranftl¹,

Rolf-Pissarczyk²,

Wolkerstorfer³

et al. 2022

Preprint

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“…Those spatial heterogeneities are often modeled by random fields generated either by a Karhunen-Loève expansion (e.g., Karhunen 1947;Loève 1968) or by a power spectral density function (e.g., Pardo-Iguzquiza & Chica-Olmo 1993). Such random fields are not considered in our study because solving the Karhunen-Loève expansion modal decomposition when the domain is much larger than the correlation length (which is our case) represents a computational issue that can quickly become unaffordable (e.g., Panunzio et al 2018). In addition, considering a large number of Karhunen-Loève modes as uncertain parameters would compromise the feasability of a GSA.…”

Section: O R I Gmentioning

confidence: 99%

Influential parameters on 3-D synthetic ground motions in a sedimentary basin derived from global sensitivity analysis

Martin

Chaljub

Thierry³

et al. 2021

Geophysical Journal International

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Summary Which physical parameters are the most influential when predicting earthquake ground motions in a 3-D sedimentary basin? We answer quantitatively by doing a global sensitivity analysis of two quantities of interest: the peak ground motions (PGMs) and a time-frequency representation (the S transform) of ground motions resulting from the synthetic anelastic responses of the EUROSEISTEST. This domain of interest is modeled by two layers with uncertain depth-dependent mechanical properties and is illuminated by a plane S-wave propagating vertically upward in an uncertain homogeneous elastic bedrock. The global sensitivity analysis is conducted on 800+ physics-based simulations of the EUROSEISTEST requiring 8+ million core-hours (i.e., ≈ 900 years of mono-core computation). The analysis of the PGMs at the free surface displays the spatial influence of the uncertain input parameters over the entire basin scale, while the analysis of the time-frequency representation shows their influence at a specific location inside the basin. The global sensitivity analysis done on the PGMs points out that their most influential parameter in the middle of the basin is the quality factor QS (it controls up to 80 per cent of the PGMs in certain locations where the sediments thickness is larger than 200 m). On the other hand, the geological layering configuration (here represented by the depth of a gelological interface controlling the geological layering) strongly influences the PGMs close to the basin edges, up to 90 per cent. We also found that the shear-wave velocity at the free surface of the basin and the one of the bedrock underlying the basin are to be considered on an equal footing, both influencing the PGMs in the middle of the basin and close to its edges. We highlight that the bedrock to basin amplification of the PGMs shows a clear increase with respect to the thickness of the sediments, but this amplification saturates from 200 m of sediments around the value of three and is frequency dependent. This PGMs amplification starts from about one tenth of the mean S-wavelength propagating in the basin. The global sensitivity analysis done on the S transform of the ground motions shows that (i) the own effect of the parameters fully controls the first S-wave train and mostly controls the direct arrival of the basin-induced surfaces waves, (ii) the quality factor QS controls 40 to 60 per cent of the decay of amplitude of coda waves, the remaining part being mainly controlled by interaction effects due to the coupling effect of several parameters, and (iii) the interaction effects between the parameters increases with time, suggesting under the hypotheses of our study that the own effects control the ballistic wave propagation while the interaction effects control the diffusive wave propagation.

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“…A first numerical model is therefore selected to try and understand the implications of truncating the computa- Table 1), with correlation length c = 100 m. Realizations of the fluctuating constitutive tensor C 1 can be obtained using various schemes [45], and a classical spectral representation approach was chosen in this work [46]. In that technique, the realizations of the random fields are generated in the spectral domain, as sums of cosine functions with increasing frequency and random phases, and with an amplitude controlled by the power spectral density.…”

Section: Choice Of An Initial Numerical Modelmentioning

confidence: 99%

Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium

Khazaie

Cottereau

2020

Wave Motion

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At long lapse times in randomly fluctuating media with macroscopic isotropy (texture-less media), the energy of elastic waves is equipartitioned between compressional (P) and shear (S) waves. This property is independent of the local isotropy or anisotropy of the heterogeneous constitutive tensor and of the type of source. However the local symmetry of the constitutive tensor does influence the rate of convergence to equipartition and this paper discusses the precise influence of local anisotropy on the time required to reach equipartition. More particularly, a randomlyfluctuating medium is considered, whose behavior is statistically isotropic, and locally cubic. After calculating all the differential and total scattering cross-sections in that case, an analytical formula is derived for the rate of convergence to the equipartition regime, function of the second-order statistics of the mechanical parameter fields (bulk and shear moduli and anisotropy parameter). The local anisotropy is shown to influence strongly that transition rate, with a faster transition when the fluctuations of the anisotropy parameter are positively correlated to those of the shear modulus. A numerical model is constructed to illustrate numerically these results. Since the asymptotic regime of equipartition cannot be simulated directly because it would require too large a computational domain, boundaries are introduced and mechanical properties are chosen so as to minimize their influence on equipartition.

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Large scale random fields generation using localized Karhunen–Loève expansion

Cited by 15 publications

References 50 publications

Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

Influential parameters on 3-D synthetic ground motions in a sedimentary basin derived from global sensitivity analysis

Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium

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