Multifidelity approaches for uncertainty quantification

Biehler, Jonas; Mäck, Markus; Nitzler, Jonas; Hanss, Michael; Koutsourelakis, Phaedon‐Stelios; Wall, Wolfgang A.

doi:10.1002/gamm.201900008

Cited by 13 publications

(11 citation statements)

References 71 publications

(131 reference statements)

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“…Further research in this regard has been conducted and the means to reduce the computational effort have been developed, such as the elimination of recurring permutations, the treatment of single occurrences of variables through interval arithmetic, and automatic differentiation to test for monotonicity of a model as proposed by Klimke [13]. Recent extensions of the fuzzy arithmetic have been introduced by Mäck et al [14] to perform a structural optimization with uncertain constraints and finally to quantify the fuzziness of complex systems by using multifidelity approaches as shown by Biehler et al in [15].…”

Section: Discussionmentioning

confidence: 99%

Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

2021

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The slightest manufacturing tolerances and variances of material properties can indeed have a significant impact on structural modes. An unintentional shift of eigenfrequencies towards dominant excitation frequencies may lead to increased vibration amplitudes of the structure resulting in radiated noise, e.g., reducing passenger comfort inside an aircraft’s cabin. This paper focuses on so-called non-structural masses of an aircraft, also known as the secondary structure that are attached to the primary structure via clips, brackets, and shock mounts and constitute a significant part of the overall mass of an aircraft’s structure. Using the example of a simplified fuselage panel, the vibro-acoustical consequences of parameter uncertainties in linking elements are studied. Here, the fuzzy arithmetic provides a suitable framework to describe uncertainties, create combination matrices, and evaluate the simulation results regarding target quantities and the impact of each parameter on the overall system response. To assess the vibrations of the fuzzy structure and by taking into account the excitation spectra of engine noise, modal and frequency response analyses are conducted.

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Section: Discussionmentioning

confidence: 99%

Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

2021

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“…For efficient time integration, the method used in the present work relies on well-known projection methods that segregate the solution of velocity and pressure unknowns, where the second-order accurate dual splitting scheme with an explicit treatment of the convective term is used here. 1 In all simulations, the same parameterized mesh according to Fehn et al 49 was used. The simulation domain and the mesh for one sample random input realization ∼ ( ) is shown in Figure 7 for the HF and the LF model version, respectively.…”

Section: Stochastic Flow Past a Cylinder: High-order Discontinuous Ga...mentioning

confidence: 99%

“…We select an initial sample size of N sample = 10000 for the LF model, so that the relative error E ∕ ̂ in the mean estimate is 1%. Afterwards, we successively compute features and choose five features to calculate a Ω × LF -filling subset [ LF ( ), ( )] ⊂ [ LF ( * ), ( * )] , with ∈ N ∶ [1,5]. We choose a data set of size n train = 150, corresponding to 150 HF model simulations to train the Gaussian Process model.…”

Section: Stochastic Flow Past a Cylinder: High-order Discontinuous Ga...mentioning

confidence: 99%

“…One strategy to overcome these problems pertains to multi-fidelity schemes which, by combining information provided by different levels of model sophistication, attempt to decrease the number of high-fidelity model runs required, while retaining the same accuracy 1,2 . Especially sampling based methods for uncertainty propagation, while often being the only choice for nonlinear problems with large variabilities, become unfeasible for costly numerical models.…”

Section: Introductionmentioning

confidence: 99%

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A Generalized Probabilistic Learning Approach for Multi-Fidelity Uncertainty Propagation in Complex Physical Simulations

Nitzler¹,

Biehler²,

Fehn³

et al. 2020

Preprint

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Two of the most significant challenges in uncertainty propagation pertain to the high computational cost for the simulation of complex physical models and the high dimension of the random inputs. In applications of practical interest both of these problems are encountered and standard methods for uncertainty quantification either fail or are not feasible. To overcome the current limitations, we propose a probabilistic multi-fidelity framework that can exploit lower-fidelity model versions of the original problem in a small data regime. The approach circumvents the curse of dimensionality by learning dependencies between the outputs of high-fidelity models and lower-fidelity models instead of explicitly accounting for the high-dimensional inputs. We complement the information provided by a low-fidelity model with a lowdimensional set of informative features of the stochastic input, which are discovered by employing a combination of supervised and unsupervised dimensionality reduction techniques. The goal of our analysis is an efficient and accurate estimation of the full probabilistic response for a high-fidelity model. Despite the incomplete and noisy information that low-fidelity predictors provide, we demonstrate that accurate and certifiable estimates for the quantities of interest can be obtained in the small data regime, i.e., with significantly fewer high-fidelity model runs than state-ofthe-art methods for uncertainty propagation. We illustrate our approach by applying it to challenging numerical examples such as Navier-Stokes flow simulations and monolithic fluid-structure interaction problems.

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“…Le Gratiet [9] introduced multiple ways to include information from different levels in a GP while Bieler et al [10] showed the technique for complex UQ scenarios. Le Gratiet [9] introduced multiple ways to include information from different levels in a GP while Bieler et al [10] showed the technique for complex UQ scenarios.…”

Section: Integration Of Multi-fidelity Informationmentioning

confidence: 99%

Gaussian process based surrogate modelling of acoustic systems

Kohlsche

Lippert

Estorff

2019

Proc Appl Math and Mech

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The numerical simulation of acoustic problems is, for itself, a quite difficult task since the underlying systems are usually highly complex with a broad frequency range and high sensitivity. Due to this complexity and the corresponding computational burden, tasks like optimization and uncertainty quantification (UQ) are seldom performed in acoustics. Especially when dealing with polymorphic uncertainties where combined techniques of UQ might be required, a direct use of the model is not viable. To allow such engineering tasks, the construction of a cheap surrogate or reduced model is common practice in order to allow a large number of model evaluations at low costs. For acoustic systems, the construction of a reasonably accurate surrogate model can become a challenging task since many systems operate in the frequency domain where phenomena like resonance and interference can cause highly nonlinear responses. In this paper, a surrogate model based on the combination of a parametric model for capturing local nonlinearities and a random process regression for modelling the global trend is presented. The basic procedure based on previous works of the authors is extended to a predict the system response both for unobserved parameters and frequencies. The procedure is demonstrated for a representative example namely the acoustic simulation of a car interior, and further improvements in accuracy and efficiency by the usage of multilevel information are discussed.

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Multifidelity approaches for uncertainty quantification

Cited by 13 publications

References 71 publications

Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

A Generalized Probabilistic Learning Approach for Multi-Fidelity Uncertainty Propagation in Complex Physical Simulations

Gaussian process based surrogate modelling of acoustic systems

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