Uncertainty Quantification Of Systems Research Articles

Systematic Uncertainty Quantification of First-Polarity-Based Moment Tensor Inversion Due to Sparse Coverage of Sensor Arrays in Laboratory Acoustic Emission Monitoring

Systematic Uncertainty Quantification of First-Polarity-Based Moment Tensor Inversion Due to Sparse Coverage of Sensor Arrays in Laboratory Acoustic Emission Monitoring

Uncertainty analysis of dynamic mode decomposition for xenon dynamic forecasting

In this paper, a systematic uncertainty quantification of dynamic mode decomposition (DMD) for xenon dynamic prediction is brought out based on HPR1000 reactor. The DMD method is a data-driven approach that decomposes complex systems into spatio-temporal structures and can be used to predict the power distribution in the process of xenon oscillation. To further investigate and improve the robustness of DMD with respect to observation noise, different error metrics are established. The dependence of the prediction error on observation noise level and hyper parameters including the window length and the singular value truncation threshold are investigated. Various numerical experiments based on a typical fuel cycle of the HPR1000 reactor demonstrate that DMD with optimal hyper parameters is robust with respect to observation noise, which confirms that DMD is feasible for real engineering applications.

Uncertainty quantification in a heterogeneous fluvial sandstone reservoir using GPU-based Monte Carlo simulation

The efficient operation and management of a geothermal project can be largely affected by geological, physical, operational and economic uncertainties. Systematic uncertainty quantification (UQ) involving these parameters helps to determine the probability of the focused outputs, e.g., energy production, Net Present Value (NPV), etc. However, how to efficiently assess the specific impacts of different uncertain parameters on the outputs of a geothermal project is still not clear. In this study, we performed a comprehensive UQ to a low-enthalpy geothermal reservoir using the GPU implementation of the Delft Advanced Research Terra Simulator (DARTS) framework with stochastic Monte Carlo samplings of uncertain parameters. With processing the simulation results, large uncertainties have been found in the production temperature, pressure drop, produced energy and NPV. It is also clear from the analysis that salinity influences the producing energy and NPV via changing the amount of energy carried in the fluid. Our work shows that the uncertainty in NPV is much larger than that in produced energy, as more uncertain factors were encompassed in NPV evaluation. An attempt to substitute original 3D models with upscaled 2D models in UQ demonstrates significant differences in the stochastic response of these two approaches in representation of realistic heterogeneity. The GPU version of DARTS significantly improved the simulation performance, which guarantees the full set (10,000 times) UQ with a large model (circa 3.2 million cells) finished within a day. With this study, the importance of UQ to geothermal field development is comprehensively addressed. This work provides a framework for assessing the impacts of uncertain parameters on the concerning system output of a geothermal project and will facilitate analyses with similar procedures.

Fatigue Life Uncertainty Quantification of Front Suspension Lower Control Arm Design

The purpose of this study is to investigate the uncertainty of the design variables of a front suspension lower control arm under fatigue-loading circumstances to estimate a reliable and robust product. This study offers a method for systematic uncertainty quantification (UQ), and the following steps were taken to achieve this: First, a finite element model was built to predict the fatigue life of the control arm under bump-loading conditions. Second, a sensitivity scheme, based on one of the global analyses, was developed to identify the model’s most and least significant design input variables. Third, physics-based and data-driven uncertainty quantification schemes were employed to quantify the model’s input parameter uncertainties via a Monte Carlo simulation. The simulations were conducted using 10,000 samples of material properties and geometrical uncertainty variables, with the coefficients of variation ranging from 1 to 3%. Finally, the confidence interval results show a deviation of about 21.74% from the mean (the baseline). As a result, by applying systematic UQ, a more reliable and robust automobile suspension control arm can be designed during the early stages of design to produce a more efficient and better approximation of fatigue life under uncertain conditions.

Uncertainty evaluation of an on-machine chromatic confocal measurement system

On-machine optical measurement receives growing attention as a viable quality assurance technique to satisfy the increasingly critical requirements for dimensional accuracy and surface finish upon precision components. It preserves the temporal and spatial consistency between manufacturing and measurement activities, allowing for a substantial productivity improvement and a great opportunity for on-line quality control. However, additional uncertainty can be introduced under the harsh on-machine measuring environment degrading the measurement quality. The explicit research on the on-machine measurement uncertainty is therefore essential but rarely carried out to date. To fill this gap, this paper presents the uncertainty investigation of an on-machine areal measuring instrument based on the chromatic confocal scanning principle. The vibration transmitted from neighboring machine tools is found to strengthen the drive vibration and to cause an overestimation of the roughness in the static noise test. The motion-induced disturbance and subdivisional error are recognized as artefacts in the flatness map influencing the evaluation of the flatness deviation, though they can be attenuated by the notch filter. Based on further evaluation on the roughness parameters, the uncertainty contributions from the noise and the corrected flatness deviation are found to be 18nm and 50nm respectively in Sz for the rough surface (pulse energy=250μJ). An uncertainty budget concerning all these influencing factors enables a systematic uncertainty quantification for the on-machine measurement.

Deep capsule encoder–decoder network for surrogate modeling and uncertainty quantification

AbstractWe propose a novel capsule‐based deep encoder–decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into an image‐to‐image regression encoder–decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) – retaining pose and position information related to an entity to name a few. The performance of the proposed approach is illustrated by solving two different variants of elliptic partial differential equations (PDE): a stochastic version without a source term having an input dimensionality of 1024 and a deterministic pressure Poisson equation for flow past a cylinder. The first PDE, that is, the stochastic PDE (SPDE), also governs systems in mechanics such as steady heat conduction, groundwater flow, or other diffusion processes. In this article, the problem definition for this SPDE is such that it does not restrict the random diffusion field to a particular covariance structure, and the more strenuous task of response prediction for an arbitrary diffusion field is solved. Finally, we also evaluate the performance of our model on the uncertainty propagation problem based on this equation. The obtained results from the performance evaluation of the developed model on the mentioned problems indicate that the proposed approach is accurate, data efficient, and robust.

Climate Uncertainty Modelling in Integrated Water Resources Management: Review

Integrated water resources management is exposed to the effects of several risks (climatic, socio-economic, and political). Currently, climate change represents one of the greatest risks for many countries around the world and the agricultural sector in particular. In the literature, climate change is sufficiently researched but there are scarce studies that deal with the theme of risk in agricultural water management and in particular the management under climate change. In the paper, we first define out the characteristics and particularity of climate change risk and then we point the different approaches and methods for taking into consideration for climate change risk in the integrated water resources management models for the agriculture sector. In this work, we aim to appraise the quantification of uncertainties in systems modelling in watersheds and discuss various water resource management and operation models.

Bayesian approach for validation of runaway electron simulations

Plasma-terminating disruptions in future fusion reactors may result in conversion of the initial current to a relativistic runaway electron beam. Validated predictive tools are required to optimise the scenarios and mitigation actuators to avoid the excessive damage that can be caused by such events. Many of the simulation tools applied in fusion energy research require the user to specify input parameters that are not constrained by the available experimental information. The conventional approach, where an expert modeller calibrates these input parameters based on domain knowledge, is prone to lead to an intractable validation challenge without systematic uncertainty quantification. Bayesian inference algorithms offer a promising alternative approach that naturally includes uncertainty quantification and is less subject to user bias in choosing the input parameters. The main challenge in using these methods is the computational cost of simulating enough samples to construct the posterior distributions for the uncertain input parameters. This challenge can be overcome by combining probabilistic surrogate modelling, such as Gaussian process regression, with Bayesian optimisation, which can reduce the number of required simulations by several orders of magnitude. Here, we implement this type of Bayesian optimisation framework for a model for analysis of disruption runaway electrons, and explore for simulations of current quench in a JET plasma discharge with an argon induced disruption. We use this proof-of-principle framework to explore the optimum input parameters with uncertainties in optimisation tasks ranging from one to seven dimensions. The relevant Python codes that are used in the analysis are available via https://github.com/aejarvin/BO_FOR_RE_SIMULATIONS/.

A predictive multiphase model of silica aerogels for building envelope insulations

This work develops a systematic uncertainty quantification framework to assess the reliability of prediction delivered by physics-based material models in the presence of incomplete measurement data and modeling error. The framework consists of global sensitivity analysis, Bayesian inference, and forward propagation of uncertainty through the computational model. The implementation of this framework on a new multiphase model of novel porous silica aerogel materials is demonstrated to predict the thermomechanical performances of a building envelope insulation component. The uncertainty analyses rely on sampling methods, including Markov-chain Monte Carlo and a mixed finite element solution of the multiphase model. Notable features of this work are investigating a new noise model within the Bayesian inversion to prevent biased estimations and characterizing various sources of uncertainty, such as measurements variabilities, model inadequacy in capturing microstructural randomness, and modeling errors incurred by the theoretical model and numerical solutions.

Inlet and Outlet Boundary Conditions and Uncertainty Quantification in Volumetric Lattice Boltzmann Method for Image-Based Computational Hemodynamics

Inlet and outlet boundary conditions (BCs) play an important role in newly emerged image-based computational hemodynamics for blood flows in human arteries anatomically extracted from medical images. We developed physiological inlet and outlet BCs based on patients’ medical data and integrated them into the volumetric lattice Boltzmann method. The inlet BC is a pulsatile paraboloidal velocity profile, which fits the real arterial shape, constructed from the Doppler velocity waveform. The BC of each outlet is a pulsatile pressure calculated from the three-element Windkessel model, in which three physiological parameters are tuned by the corresponding Doppler velocity waveform. Both velocity and pressure BCs are introduced into the lattice Boltzmann equations through Guo’s non-equilibrium extrapolation scheme. Meanwhile, we performed uncertainty quantification for the impact of uncertainties on the computation results. An application study was conducted for six human aortorenal arterial systems. The computed pressure waveforms have good agreement with the medical measurement data. A systematic uncertainty quantification analysis demonstrates the reliability of the computed pressure with associated uncertainties in the Windkessel model. With the developed physiological BCs, the image-based computation hemodynamics is expected to provide a computation potential for the noninvasive evaluation of hemodynamic abnormalities in diseased human vessels.

Uncertainty Quantification for Fatigue Life of Offshore Wind Turbine Structure

Abstract This study aims to address the question: can the structural reliability of an offshore wind turbine (OWT) under fatigue loading conditions be predicted more consistently? To respond to that question this study addresses the following specific aims: (1) to obtain a systematic approach that takes into consideration the amount of information available for the uncertainty modeling of the model input parameters and (2) to determine the impact of the most sensitive input parameters on the structural reliability of the OWT through a surrogate model. First, a coupled model to determine the fatigue life of the support structure considering the soil-structure interaction under 15 different loading conditions was developed. Second, a sensitivity scheme using two global analyses was developed to consistently establish the most and least important input parameters of the model. Third, systematic uncertainty quantification (UQ) scheme was employed to model the uncertainties of model input parameters based on their available—data-driven and physics-informed—information. Finally, the impact of the proposed UQ framework on the OWT structural reliability was evaluated through the estimation of the probability of failure of the structure based on the fatigue limit state design criterion. The results show high sensitivity for the wind speed and moderate sensitivity for parameters usually considered as deterministic values in design standards. Additionally, it is shown that applying systematic UQ not only produces a more efficient and better approximation of the fatigue life under uncertainty, but also a more accurate estimation of the structural reliability of offshore wind turbine's structure during conceptual design. Consequently, more reliable, and robust estimations of the structural designs for large offshore wind turbines with limited information may be achieved during the early stages of design.

Lagrangian models of particle-laden flows with stochastic forcing: Monte Carlo, moment equations, and method of distributions analyses

Deterministic Eulerian–Lagrangian models represent the interaction between particles and carrier flow through the drag force. Its analytical descriptions are only feasible in special physical situations, such as the Stokes drag for low Reynolds number. For high particle Reynolds and Mach numbers, where the Stokes solution is not valid, the drag must be corrected by empirical, computational, or hybrid (data-driven) methods. This procedure introduces uncertainty in the resulting model predictions, which can be quantified by treating the drag as a random variable and by using data to verify the validity of the correction. For a given probability density function of the drag coefficient, we carry out systematic uncertainty quantification for an isothermal one-way coupled Eulerian–Lagrangian system with stochastic forcing. The first three moment equations are analyzed with a priori closure using Monte Carlo computations, showing that the stochastic solution is highly non-Gaussian. For a more complete description, the method of distributions is used to derive a deterministic partial differential equation for the evolution of the joint PDF of the particle phase and drag coefficient. This equation is solved via Chebyshev spectral collocation method, and the resulting numerical solution is compared with Monte Carlo computations. Our analysis highlights the importance of a proper approximation of the Dirac delta function, which represents deterministic (known with certainty) initial conditions. The robustness and accuracy of our PDF equation were tested on one-dimensional problems in which the Eulerian phase represents either a uniform flow or a stagnation flow.

Uncertainty Quantification in Water Resource Systems Modeling: Case Studies from India

Regional water resource modelling is important for evaluating system performance by analyzing the reliability, resilience and vulnerability criteria of the system. In water resource systems modelling, several uncertainties abound, including data inadequacy and errors, modeling inaccuracy, lack of knowledge, imprecision, inexactness, randomness of natural phenomena, and operational variability, in addition to challenges such as growing population, increasing water demands, diminishing water sources and climate change. Recent advances in modelling techniques along with high computational capabilities have facilitated rapid progress in this area. In India, several studies have been carried out to understand and quantify uncertainties in various basins, enumerate large temporal and regional mismatches between water availability and demands, and project likely changes due to warming. A comprehensive review of uncertainties in water resource modelling from an Indian perspective is yet to be done. In this work, we aim to appraise the quantification of uncertainties in systems modelling in India and discuss various water resource management and operation models. Basic formulation of models for probabilistic, fuzzy and grey/inexact simulation, optimization, and multi-objective analyses to water resource design, planning and operations are presented. We further discuss challenges in modelling uncertainties, missing links in integrated systems approach, along with directions for future.

Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation

Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of one or more system parameters are not normal, uniform, or closely related distributions, due to the computational issues that arise when one wishes to define interpolation nodes for general distributions. This paper examines the use of the recently introduced weighted Leja nodes for that purpose. Weighted Leja interpolation rules are presented, along with a dimension-adaptive sparse interpolation algorithm, to be employed in the case of high-dimensional input uncertainty. The performance and reliability of the suggested approach is verified by four numerical experiments, where the respective models feature extreme value and truncated normal parameter distributions. Furthermore, the suggested approach is compared with a well-established polynomial chaos method and found to be either comparable or superior in terms of approximation and statistics estimation accuracy.

Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation

Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of one or more system parameters are not normal, uniform, or closely related distributions, due to the computational issues that arise when one wishes to define interpolation nodes for general distributions. This paper examines the use of the recently introduced weighted Leja nodes for that purpose. Weighted Leja interpolation rules are presented, along with a dimension-adaptive sparse interpolation algorithm, to be employed in the case of high-dimensional input uncertainty. The performance and reliability of the suggested approach is verified by four numerical experiments, where the respective models feature extreme value and truncated normal parameter distributions. Furthermore, the suggested approach is compared with a well-established polynomial chaos method and found to be either comparable or superior in terms of approximation and statistics estimation accuracy

Enhancing industrial X-ray tomography by data-centric statistical methods

AbstractX-ray tomography has applications in various industrial fields such as sawmill industry, oil and gas industry, as well as chemical, biomedical, and geotechnical engineering. In this article, we study Bayesian methods for the X-ray tomography reconstruction. In Bayesian methods, the inverse problem of tomographic reconstruction is solved with the help of a statistical prior distribution which encodes the possible internal structures by assigning probabilities for smoothness and edge distribution of the object. We compare Gaussian random field priors, that favor smoothness, to non-Gaussian total variation (TV), Besov, and Cauchy priors which promote sharp edges and high- and low-contrast areas in the object. We also present computational schemes for solving the resulting high-dimensional Bayesian inverse problem with 100,000–1,000,000 unknowns. We study the applicability of a no-U-turn variant of Hamiltonian Monte Carlo (HMC) methods and of a more classical adaptive Metropolis-within-Gibbs (MwG) algorithm to enable full uncertainty quantification of the reconstructions. We use maximum a posteriori (MAP) estimates with limited-memory BFGS (Broyden–Fletcher–Goldfarb–Shanno) optimization algorithm. As the first industrial application, we consider sawmill industry X-ray log tomography. The logs have knots, rotten parts, and even possibly metallic pieces, making them good examples for non-Gaussian priors. Secondly, we study drill-core rock sample tomography, an example from oil and gas industry. In that case, we compare the priors without uncertainty quantification. We show that Cauchy priors produce smaller number of artefacts than other choices, especially with sparse high-noise measurements, and choosing HMC enables systematic uncertainty quantification, provided that the posterior is not pathologically multimodal or heavy-tailed.

Dimension reduction in heterogeneous neural networks: Generalized Polynomial Chaos (gPC) and ANalysis-Of-VAriance (ANOVA)

We propose, and illustrate via a neural network example, two different approaches to coarse-graining large heterogeneous networks. Both approaches are inspired from, and use tools developed in, methods for uncertainty quantification in systems with multiple uncertain parameters - in our case, the parameters are heterogeneously distributed on the network nodes. The approach shows promise in accelerating large scale network simulations as well as coarse-grained fixed point, periodic solution and stability analysis. We also demonstrate that the approach can successfully deal with structural as well as intrinsic heterogeneities.

Systematic selection of amine mixtures as post-combustion CO2 capture solvent candidates

A systematic approach is proposed for the preliminary screening of binary amine mixtures as CO2 capture candidates considering several important properties as selection criteria. The approach consists of several decision making stages which account for solvent–solvent and solvent–solvent–CO2 interactions using standard group contribution models as well as equations of state and activity coefficient models for a wide range of molecular structures. A multi-criteria assessment methodology is combined with a systematic uncertainty quantification approach to unveil important trade-offs among several important properties and to propose the mixtures that appear to be promising as CO2 capture candidates. The aim of the proposed approach is to support the identification of few valid amine combinations which may then be evaluated using rigorous prediction models or experiments, while quickly avoiding amine options of poor performance. The proposed method is applied in mixtures resulting from numerous binary combinations of amines which have been previously investigated in their pure aqueous form as CO2 capture solvents. A mixture of 4-diethylamino-2-butanol (DEAB) and 2-amino-1-hexanol (2A1H) appears to be promising among other useful options.

Evolved chiralNN+3NHamiltonians forab initionuclear structure calculations

We discuss the building blocks for a consistent inclusion of chiral three-nucleon (3N) interactions into ab initio nuclear structure calculations beyond the lower p-shell. We highlight important technical developments, such as the similarity renormalization group (SRG) evolution in the 3N sector, a JT-coupled storage scheme for 3N matrix elements with efficient on-the-fly decoupling, and the importance truncated no-core shell model with 3N interactions. Together, these developments make converged ab initio calculations with explicit 3N interactions possible also beyond the lower p-shell. We analyze in detail the impact of various truncations of the SRG-evolved Hamiltonian, in particular the truncation of the harmonic-oscillator model space used for solving the SRG flow equations and the omission of the induced beyond-3N contributions of the evolved Hamiltonian. Both truncations lead to sizable effects in the upper p-shell and beyond and we present options to remedy these truncation effects. The analysis of the different truncations is a first step towards a systematic uncertainty quantification of all stages of the calculation.

An efficient framework for optimization and parameter sensitivity analysis in arterial growth and remodeling computations

Computational models for vascular growth and remodeling (G&R) are used to predict the long-term response of vessels to changes in pressure, flow, and other mechanical loading conditions. Accurate predictions of these responses are essential for understanding numerous disease processes. Such models require reliable inputs of numerous parameters, including material properties and growth rates, which are often experimentally derived, and inherently uncertain. While earlier methods have used a brute force approach, systematic uncertainty quantification in G&R models promises to provide much better information. In this work, we introduce an efficient framework for uncertainty quantification and optimal parameter selection, and illustrate it via several examples. First, an adaptive sparse grid stochastic collocation scheme is implemented in an established G&R solver to quantify parameter sensitivities, and near-linear scaling with the number of parameters is demonstrated. This non-intrusive and parallelizable algorithm is compared with standard sampling algorithms such as Monte-Carlo. Second, we determine optimal arterial wall material properties by applying robust optimization. We couple the G&R simulator with an adaptive sparse grid collocation approach and a derivative-free optimization algorithm. We show that an artery can achieve optimal homeostatic conditions over a range of alterations in pressure and flow; robustness of the solution is enforced by including uncertainty in loading conditions in the objective function. We then show that homeostatic intramural and wall shear stress is maintained for a wide range of material properties, though the time it takes to achieve this state varies. We also show that the intramural stress is robust and lies within 5% of its mean value for realistic variability of the material parameters. We observe that prestretch of elastin and collagen are most critical to maintaining homeostasis, while values of the material properties are most critical in determining response time. Finally, we outline several challenges to the G&R community for future work. We suggest that these tools provide the first systematic and efficient framework to quantify uncertainties and optimally identify G&R model parameters.