scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

2020 ◽  
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Bayesian Inference ◽  
Dynamical Systems ◽  
Uncertainty Quantification ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
User Interest ◽  
Operation Conditions ◽  
Random Material Properties

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

Application of an Adaptive Polynomial Chaos Expansion on Computationally Expensive Three-Dimensional Cardiovascular Models for Uncertainty Quantification and Sensitivity Analysis

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Sjeng Quicken ◽  
Wouter P. Donders ◽  
Emiel M. J. van Disseldorp ◽  
Kujtim Gashi ◽  
Barend M. E. Mees ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Three Dimensional ◽  
Polynomial Chaos Expansion ◽  
Patient Specific ◽  
Chaos Expansion ◽  
Model Input ◽  
Cardiovascular Models

When applying models to patient-specific situations, the impact of model input uncertainty on the model output uncertainty has to be assessed. Proper uncertainty quantification (UQ) and sensitivity analysis (SA) techniques are indispensable for this purpose. An efficient approach for UQ and SA is the generalized polynomial chaos expansion (gPCE) method, where model response is expanded into a finite series of polynomials that depend on the model input (i.e., a meta-model). However, because of the intrinsic high computational cost of three-dimensional (3D) cardiovascular models, performing the number of model evaluations required for the gPCE is often computationally prohibitively expensive. Recently, Blatman and Sudret (2010, “An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis,” Probab. Eng. Mech., 25(2), pp. 183–197) introduced the adaptive sparse gPCE (agPCE) in the field of structural engineering. This approach reduces the computational cost with respect to the gPCE, by only including polynomials that significantly increase the meta-model’s quality. In this study, we demonstrate the agPCE by applying it to a 3D abdominal aortic aneurysm (AAA) wall mechanics model and a 3D model of flow through an arteriovenous fistula (AVF). The agPCE method was indeed able to perform UQ and SA at a significantly lower computational cost than the gPCE, while still retaining accurate results. Cost reductions ranged between 70–80% and 50–90% for the AAA and AVF model, respectively.

scholarly journals Efficient Bayesian inference for large chaotic dynamical systems

2020 ◽  
Author(s):  
Sebastian Springer ◽  
Heikki Haario ◽  
Jouni Susiluoto ◽  
Aleksandr Bibov ◽  
Andrew Davis ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Dynamical Systems ◽  
Spatial Data ◽  
Large Scale ◽  
Likelihood Function ◽  
Computational Cost ◽  
Local Approximation ◽  
Physical Models ◽  
Chaotic Dynamical Systems ◽  
Time Required

Abstract. Estimating parameters of chaotic geophysical models is challenging due to these models' inherent unpredictability. With temporally sparse long-range observations, these models cannot be calibrated using standard least squares or filtering methods. Obvious remedies, such as averaging over temporal and spatial data to characterize the mean behavior, do not capture the subtleties of the underlying dynamics. We perform Bayesian inference of parameters in high-dimensional and computationally demanding chaotic dynamical systems by combining two approaches: (i) measuring model-data mismatch by comparing chaotic attractors, and (ii) mitigating the computational cost of inference by using surrogate models. Specifically, we construct a likelihood function suited to chaotic models by evaluating a distribution over distances between points in the phase space; this distribution defines a summary statistic that depends on the attractor's geometry, rather than on pointwise matching of trajectories. This statistic is computationally expensive to simulate, compounding the usual challenges of Bayesian computation with physical models. Thus we develop an inexpensive surrogate for the log-likelihood via local approximation Markov chain Monte Carlo, which in our simulations reduces the time required for accurate inference by orders of magnitude. We investigate the behavior of the resulting algorithm on model problems, and then use a quasi-geostrophic model to demonstrate its large-scale application.

scholarly journals Efficient Bayesian inference for large chaotic dynamical systems

2021 ◽  
Vol 14 (7) ◽  
pp. 4319-4333
Author(s):  
Sebastian Springer ◽  
Heikki Haario ◽  
Jouni Susiluoto ◽  
Aleksandr Bibov ◽  
Andrew Davis ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Dynamical Systems ◽  
Spatial Data ◽  
Large Scale ◽  
Likelihood Function ◽  
Computational Cost ◽  
Local Approximation ◽  
Physical Models ◽  
Chaotic Dynamical Systems ◽  
Time Required

Abstract. Estimating parameters of chaotic geophysical models is challenging due to their inherent unpredictability. These models cannot be calibrated with standard least squares or filtering methods if observations are temporally sparse. Obvious remedies, such as averaging over temporal and spatial data to characterize the mean behavior, do not capture the subtleties of the underlying dynamics. We perform Bayesian inference of parameters in high-dimensional and computationally demanding chaotic dynamical systems by combining two approaches: (i) measuring model–data mismatch by comparing chaotic attractors and (ii) mitigating the computational cost of inference by using surrogate models. Specifically, we construct a likelihood function suited to chaotic models by evaluating a distribution over distances between points in the phase space; this distribution defines a summary statistic that depends on the geometry of the attractor, rather than on pointwise matching of trajectories. This statistic is computationally expensive to simulate, compounding the usual challenges of Bayesian computation with physical models. Thus, we develop an inexpensive surrogate for the log likelihood with the local approximation Markov chain Monte Carlo method, which in our simulations reduces the time required for accurate inference by orders of magnitude. We investigate the behavior of the resulting algorithm with two smaller-scale problems and then use a quasi-geostrophic model to demonstrate its large-scale application.

scholarly journals Fast three-dimensional phase retrieval in propagation-based X-ray tomography

2019 ◽  
Vol 26 (3) ◽  
pp. 825-838 ◽  
Author(s):  
Darren A. Thompson ◽  
Yakov I. Nesterets ◽  
Konstantin M. Pavlov ◽  
Timur E. Gureyev
Keyword(s):  
Phase Retrieval ◽  
Noise Suppression ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
Reconstruction Method ◽  
Experimental Conditions ◽  
Modest Improvement ◽  
X Ray ◽  
Noise Characteristics

The following article describes a method for 3D reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogeneous form of the transport of intensity equation (TIE-Hom). Unlike conventional PB-CT algorithms that perform phase retrieval of individual projections, the described post-reconstruction phase-retrieval method is applied in 3D to a localized region of the CT-reconstructed volume. This work demonstrates, via numerical simulations, the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it with both conventional absorption tomography and 2D TIE-Hom phase retrieval applied to projection images. The results indicate that the 3D post-reconstruction method generally achieves a modest improvement in noise suppression over existing PB-CT methods. It is also shown that potentially large computational gains over projection-based phase retrieval for multi-material samples are possible. In particular, constraining phase retrieval to a localized 3D region of interest reduces the overall computational cost and eliminates the need for multiple CT reconstructions and global 2D phase retrieval operations for each material within the sample.

scholarly journals Vibration characteristics of triple-gear-rotor system in compressed air energy storage under variable torque load

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042098705
Author(s):  
Xinran Wang ◽  
Yangli Zhu ◽  
Wen Li ◽  
Dongxu Hu ◽  
Xuehui Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Rotor System ◽  
Dynamic Responses ◽  
System Response ◽  
Rotating Speed ◽  
Torque Load ◽  
Set Up ◽  
Two Stages

This paper focuses on the effects of the off-design operation of CAES on the dynamic characteristics of the triple-gear-rotor system. A finite element model of the system is set up with unbalanced excitations, torque load excitations, and backlash which lead to variations of tooth contact status. An experiment is carried out to verify the accuracy of the mathematical model. The results show that when the system is subjected to large-scale torque load lifting at a high rotating speed, it has two stages of relatively strong periodicity when the torque load is light, and of chaotic when the torque load is heavy, with the transition between the two states being relatively quick and violent. The analysis of the three-dimensional acceleration spectrum and the meshing force shows that the variation in the meshing state and the fluctuation of the meshing force is the basic reasons for the variation in the system response with the torque load. In addition, the three rotors in the triple-gear-rotor system studied show a strong similarity in the meshing states and meshing force fluctuations, which result in the similarity in the dynamic responses of the three rotors.

scholarly journals The ICON Single-Column Mode

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 906
Author(s):  
Ivan Bašták Ďurán ◽  
Martin Köhler ◽  
Astrid Eichhorn-Müller ◽  
Vera Maurer ◽  
Juerg Schmidli ◽  
...  
Keyword(s):  
Data Storage ◽  
Model Development ◽  
Computational Cost ◽  
Three Dimensional ◽  
Shallow Convection ◽  
Modeling Framework ◽  
Additional Tool ◽  
Eddy Simulation ◽  
Single Column ◽  
Stratocumulus Clouds

The single-column mode (SCM) of the ICON (ICOsahedral Nonhydrostatic) modeling framework is presented. The primary purpose of the ICON SCM is to use it as a tool for research, model evaluation and development. Thanks to the simplified geometry of the ICON SCM, various aspects of the ICON model, in particular the model physics, can be studied in a well-controlled environment. Additionally, the ICON SCM has a reduced computational cost and a low data storage demand. The ICON SCM can be utilized for idealized cases—several well-established cases are already included—or for semi-realistic cases based on analyses or model forecasts. As the case setup is defined by a single NetCDF file, new cases can be prepared easily by the modification of this file. We demonstrate the usage of the ICON SCM for different idealized cases such as shallow convection, stratocumulus clouds, and radiative transfer. Additionally, the ICON SCM is tested for a semi-realistic case together with an equivalent three-dimensional setup and the large eddy simulation mode of ICON. Such consistent comparisons across the hierarchy of ICON configurations are very helpful for model development. The ICON SCM will be implemented into the operational ICON model and will serve as an additional tool for advancing the development of the ICON model.

scholarly journals Updated Kriging-Assisted Shape Optimization of a Gravity Dam

Water ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 87
Author(s):  
Yongqiang Wang ◽  
Ye Liu ◽  
Xiaoyi Ma
Keyword(s):  
Surrogate Model ◽  
Computational Cost ◽  
Region Of Interest ◽  
Optimization Procedure ◽  
Optimal Shape ◽  
Small Sample ◽  
Gravity Dam ◽  
Kriging Surrogate Model ◽  
Gravity Dams ◽  
Sample Set

The numerical simulation of the optimal design of gravity dams is computationally expensive. Therefore, a new optimization procedure is presented in this study to reduce the computational cost for determining the optimal shape of a gravity dam. Optimization was performed using a combination of the genetic algorithm (GA) and an updated Kriging surrogate model (UKSM). First, a Kriging surrogate model (KSM) was constructed with a small sample set. Second, the minimizing the predictor strategy was used to add samples in the region of interest to update the KSM in each updating cycle until the optimization process converged. Third, an existing gravity dam was used to demonstrate the effectiveness of the GA–UKSM. The solution obtained with the GA–UKSM was compared with that obtained using the GA–KSM. The results revealed that the GA–UKSM required only 7.53% of the total number of numerical simulations required by the GA–KSM to achieve similar optimization results. Thus, the GA–UKSM can significantly improve the computational efficiency. The method adopted in this study can be used as a reference for the optimization of the design of gravity dams.

scholarly journals Retinal vessel segmentation with constrained-based nonnegative matrix factorization and 3D modified attention U-Net

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang Yu ◽  
Hongqing Zhu
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Three Dimensional ◽  
Nonnegative Matrix ◽  
Retinal Vessel ◽  
Classification Problem ◽  
Image Resolution ◽  
Retinal Vessels ◽  
Segmentation Task

AbstractDue to the complex morphology and characteristic of retinal vessels, it remains challenging for most of the existing algorithms to accurately detect them. This paper proposes a supervised retinal vessels extraction scheme using constrained-based nonnegative matrix factorization (NMF) and three dimensional (3D) modified attention U-Net architecture. The proposed method detects the retinal vessels by three major steps. First, we perform Gaussian filter and gamma correction on the green channel of retinal images to suppress background noise and adjust the contrast of images. Then, the study develops a new within-class and between-class constrained NMF algorithm to extract neighborhood feature information of every pixel and reduce feature data dimension. By using these constraints, the method can effectively gather similar features within-class and discriminate features between-class to improve feature description ability for each pixel. Next, this study formulates segmentation task as a classification problem and solves it with a more contributing 3D modified attention U-Net as a two-label classifier for reducing computational cost. This proposed network contains an upsampling to raise image resolution before encoding and revert image to its original size with a downsampling after three max-pooling layers. Besides, the attention gate (AG) set in these layers contributes to more accurate segmentation by maintaining details while suppressing noises. Finally, the experimental results on three publicly available datasets DRIVE, STARE, and HRF demonstrate better performance than most existing methods.

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