Search

Designing underwater vehicles considering uncertainties in mechanical properties of composites is computationally expensive. In this paper, inexpensive-to-evaluate sparse polynomial chaos expansion (PCE) based on small data is employed to alleviate computational burden arising in uncertainty analysis. Experiments and finite element analysis for buckling are performed. Relative contribution of mechanical properties to critical buckling pressure is quantified. Distribution function histogram and risk of structral failure are obtained by performing Monte Carlo simulation (MCS) on inexpensive-to-evaluate sparse PCE. Mean of critical buckling pressure is 8.27 MPa, with coefficient of variation 8.59%. 95% confidence interval is 6.86 MPa–9.65 MPa. [ABSTRACT FROM AUTHOR]

An aeroengine faces multi-source uncertainty consisting of aeroengine epistemic uncertainty and the control system stochastic uncertainty during operation. This paper investigates actuator fault estimation under multi-source uncertainty to enhance the fault diagnosis capability of aero-engine control systems in complex environments. With the polynomial chaos expansion-based discrete stochastic model quantification, the optimal filter under multi-source uncertainty, the Hyperelliptic Kalman Filter, is proposed. Meanwhile, by treating actuator fault as unknown input, the Two-stage Hyperelliptic Kalman Filter (TSHeKF) is also proposed to achieve optimal fault estimation under multi-source uncertainty. However, considering that the biases of the model are often fixed for the individual, the TSHeKF-based fault estimation is robust and leads to inevitable conservativeness. By adding the additional estimation of the unknown deviation in state function caused by probabilistic system parameters, the hybrid fault observer (HFO) is proposed based on the TSHeKF and realizes conservativeness-reduced estimation for actuator fault under multi-source uncertainty. Numerical simulations show the effectiveness and optimality of the proposed HFO in state estimation, output prediction, and fault estimation for both single and multi-fault modes, when considering multi-source uncertainty. Furthermore, Monte Carlo experiments have demonstrated that the HFO-based optimal fault estimation is less conservative and more accurate than the Two-stage Kalman Filter and TSHeKF, providing better safety and more reliable aeroengine operation assurance. [ABSTRACT FROM AUTHOR]

In the framework of process safety studies, consequence assessment of accidental scenarios is a crucial step affecting the eventual risk profile associated with the facilities under analysis. Conventional models used for consequence assessment are based on integral models, and may not be adequate to cope with the dynamic evolution of accidental scenarios and their three‐dimensional features. On the other hand, consequence assessment models based on computational fluid dynamics (CFD) approaches are promising to cope with complex scenarios and environments, but setting the simulation introduces relevant uncertainties associated with both the input data, assumptions, and with the modelling of physical effects involved. In the present study, uncertainty quantification (UQ) techniques are applied to support advanced safety studies based on CFD simulations of hazardous gas dispersion. Firstly, the accidental scenarios are characterized by defining release scenarios and conditions and quantifying source terms using integral models. At the same time, input meteorological data are gathered. This enables the development of high‐fidelity CFD simulations of gas dispersion based on different input sets and eventually the implementation of UQ techniques. The generalized polynomial chaos (gPC) expansion is employed to obtain hazardous gas concentration based on the variation of wind direction and speed. The present method is applied for the analysis of a real plant featuring a complex layout. The results show the advantages of the present approach by quantifying the influence of meteorological conditions and providing indications for supporting the development of protection systems and emergency measures. [ABSTRACT FROM AUTHOR]

This paper is concerned with a kinetic-fluid model with random initial inputs in the fine particle regime, which is a system coupling the incompressible Navier–Stokes equations and the Vlasov– Fokker–Planck equations that model dispersed particles of different sizes. A uniform regularity for random initial data near the global equilibrium is established in some suitable Sobolev spaces by using energy estimates, and we also prove the energy decays exponentially in time by hypocoercivity arguments, which means that the long time behavior of the solution is insensitive to the random perturbation in the initial data. For the generalized polynomial chaos stochastic Galerkin method (gPC-sG) for the model, with initial data near the global equilibrium and smooth enough in the physical and random spaces, we prove that the gPC-sG method has spectral accuracy, uniformly in time and the Stokes number, and the error decays exponentially in time. [ABSTRACT FROM AUTHOR]

Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample‐based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol' sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three‐dimensional fluid–structure interaction simulations with affordable one‐ and zero‐dimensional reduced‐order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi‐ (1D/0D) and tri‐fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single‐fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol' indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response. [ABSTRACT FROM AUTHOR]

This work proposes a fast, novel, mathematically robust, and elegant unconstrained Method of Uncertainty Quantification (MUQ) for the temperature-dependent Arrhenius rate constant using Cholesky Decomposition (CD) of the covariance matrix of the Arrhenius parameters. The Arrhenius parameters of a reaction are treated as normally distributed correlated random variables. The MUQ method lends itself to an approach for Sampling of Arrhenius Curves (SAC), which automatically ensures that the generated samples are consistent with the distribution of Arrhenius parameters. The Method of Uncertainty Quantification and Sampling of Arrhenius Curves (MUQ-SAC) is used to train a quadratic polynomial response surface (PRS). Three important classes of Arrhenius curves possible within the SAC method are identified. From the total set of targets, a small subset of targets is first used to study the combinations of different classes of Arrhenius curves and their proportions within the design matrix, which is used to train PRS. Based on this understanding, response surfaces are generated for 64 ignition delay targets (Tig), which comprises of a wide range of pressure (P: 1--32.7 atm), temperature (T: 916-DIFadd-2869 K), and equivalence ratio (ϕ: 0.5--6.11), as well as for 74 laminar flame speed targets (Fls), spanning P: 1--25 atm, T: 285--600 K, and ϕ: 0.6--5. The H $ _2 $ 2 /CO sub-mechanism of FFCM1.0 is chosen for the case study in which 22 reactions (66 Arrhenius parameters) are considered active parameters. The quality of the generated PRS is measured using the relative Maximum Residual Error (MRE). The quality of PRS is also checked against the search iterations encountered during mechanism optimisation. Accurate PRS could be generated over the search iterations, validating that the SAC method is able to span the entire uncertainty domain while training the PRS. The implementation of the MUQ-SAC method is made available at . [ABSTRACT FROM AUTHOR]

As magnetic field strength in Magnetic Resonance Imaging (MRI) technology increases, maintaining the specific absorption rate (SAR) within safe limits across human head tissues becomes challenging due to the formation of standing waves at a shortened wavelength. Compounding this challenge is the uncertainty in the dielectric properties of head tissues, which notably affects the SAR induced by the radiofrequency (RF) coils in an ultra-high-field (UHF) MRI system. To this end, this study introduces a computational framework to quantify the impacts of uncertainties in head tissues' dielectric properties on the induced SAR. The framework employs a surrogate model-assisted Monte Carlo (MC) technique, efficiently generating surrogate models of MRI observables (electric fields and SAR) and utilizing them to compute SAR statistics. Particularly, the framework leverages a high-dimensional model representation technique, which constructs the surrogate models of the MRI observables via univariate and bivariate component functions, approximated through generalized polynomial chaos expansions. The numerical results demonstrate the efficiency of the proposed technique, requiring significantly fewer deterministic simulations compared with traditional MC methods and other surrogate model-assisted MC techniques utilizing machine learning algorithms, all while maintaining high accuracy in SAR statistics. Specifically, the proposed framework constructs surrogate models of a local SAR with an average relative error of 0.28% using 289 simulations, outperforming the machine learning-based surrogate modeling techniques considered in this study. Furthermore, the SAR statistics obtained by the proposed framework reveal fluctuations of up to 30% in SAR values within specific head regions. These findings highlight the critical importance of considering dielectric property uncertainties to ensure MRI safety, particularly in 7 T MRI systems. [ABSTRACT FROM AUTHOR]

Blending of partially cracked ammonia with biosyngas is an attractive strategy for improving NH 3 combustion. In practice, products of biomass gasification and those of thermo-catalytic cracking of NH 3 are subject to some compositional uncertainties. Despite their practical importance, so far, the effects of such uncertainties on combustion systems remained largely unexplored. Hence, this paper quantifies the effects of small compositional uncertainties of reactants upon combustion of partially cracked NH 3 /syngas/air mixtures. An uncertainty quantification method, based on polynomial chaos expansion and a data-driven model, is utilised to investigate the effects of uncertainty in fuel composition on the laminar flame speed (S L) and adiabatic flame temperature (T ad) at different inlet pressures (P i). The analysis is then extended to the power output of a combined-cycle gas turbine fuelled by the reactants. It is found that 1.5% fuel compositional uncertainty can cause 12–21% of S L uncertainty depending on the inlet pressure. Furthermore, the effect of compositional uncertainty on T ad increases at higher ratios of H 2 to NH 3. Sensitivity analysis reveals that the uncertainty of CO contribution to S L uncertainty is higher than that of NH 3 , while the trend is reversed for the T ad uncertainty. In addition, the power output from the combined-cycle gas turbine system varies between 4 and 6% with 1.5% of fuel compositional uncertainty. This become more noticeable at elevated P i [5–10 atm], particularly when the fuel mixture contains high H 2 which is the main contributor to T ad variability. • PCE-UQ model to analyse compositional variability effects on flame properties (S L and T ad). • Additional UQ analysis examines the uncertainty impacts on a CCGT system. • H 2 variability is the strongest contributor to the uncertainty in the CCGT power output. • Richer fuel mixtures are most affected (6%) by minor fuel compositional variability. • Uncertainty impact is higher for high H 2 fuel mixtures combustion at elevated pressures. [ABSTRACT FROM AUTHOR]

From a mathematical viewpoint, the frequency domain analysis of vessel motion responses due to wave actions is based on integration of system dynamics idealized in terms of response amplitude operators for six degrees-of-freedom (DOFs) rigid body motions and an input wave spectrum in order to obtain the response spectrum. Various quantities of interest can be deduced from the response spectrum, which are then used for deriving response-based operational limits for marine operations, also including extreme value and fatigue analysis. The variation of such quantities, owing to the uncertainties associated with the vessel system parameters, can be quantified by performing uncertainty propagation and consequent sensitivity analysis. This study emphasizes and proposes a computational-efficient way of assessing the sensitivity of the system model output with respect to the uncertainties residing in the input parameters by operating on a surrogate model representation. In this respect, the global sensitivity analysis was effectively carried out by deploying an efficient nonintrusive polynomial chaos expansion surrogate model built using a point collocation strategy. Successively, Sobol' indices were obtained from the analytical decomposition of the polynomial coefficients. The indices, eventually, are employed to quantitatively measure the effects of input uncertainties on the output 6DOF vessel root-mean-square responses. [ABSTRACT FROM AUTHOR]

Surrogate-based algorithms are indispensable in the aerospace engineering field for reducing the computational cost of optimization and uncertainty quantification analyses, particularly those involving computationally intensive solvers. This paper presents a novel approach for enhancing the efficiency of surrogate-based algorithms through a new multi-fidelity sampling technique. Unlike existing multi-fidelity methods which are based on a single multiplicative acquisition function, the proposed technique decouples the identification of the new infill sample from the selection of the fidelity level. The location of the infill sample is determined by leveraging the highest fidelity surrogate model, while the fidelity level used for its performance evaluation is chosen as the cheapest one within the "accurate enough" models at the infill location. Moreover, the methodology introduces the application of the Jensen–Shannon divergence to quantify the accuracy of the different fidelity levels. Overall, the resulting technique eliminates some of the drawbacks of existing multiplicative acquisition functions such as the risk of continuous sampling from lower and cheaper fidelity levels. Experimental validation conducted in surrogate-based optimization and uncertainty quantification scenarios demonstrates the efficacy of the proposed approach. In an aerodynamic shape optimization task focused on maximizing the lift-to-drag ratio, the multi-fidelity strategy achieved comparable results to standard single-fidelity sampling but with approximately a five-fold improvement in computational efficiency. Likewise, a similar reduction in computational costs was observed in the uncertainty quantification problem, with the resulting statistical values aligning closely with those obtained using traditional single-fidelity sampling. [ABSTRACT FROM AUTHOR]

The probability-based uncertainty quantification (UQ) methods require a large amount of sampled data to construct the probability distribution of uncertain input parameters. However, it is a common situation that only limited and scarce sampled data are available in engineering applications due to expensive tests. In the present paper, the Data-Driven Polynomial Chaos (DDPC) method is adopted, which can propagate input uncertainty in the case of scarce sampled data. The calculation accuracy and convergence of the self-developed DDPC method are validated by a nonlinear test function. Subsequently, the DDPC method is applied to investigate the uncertain impact of stagger angle errors on the aerodynamic performance of a subsonic compressor cascade. A family of manufacturing error data of stagger angles was obtained from the real compressor blades. Based on the limited measurement data, the DDPC method combined with Computational Fluid Dynamics (CFD) simulation is employed to quantify the performance impact of the compressor cascade. The results show that the performance dispersion under off-design conditions is more prominent than that under design conditions. The actual aerodynamic performance deviating from the nominal performance is not a small probability event, and the probability of deviating from the nominal loss coefficient and exit flow angle by more than 1% can reach up to 47.6% and 36.8% under high incidence i = 7°. Detailed analysis shows that stagger angle errors have a significant effect on the flow state near the leading edge, resulting in variations in separation bubble size and boundary layer thickness. [ABSTRACT FROM AUTHOR]

Introduction: To reliably solve the EEG inverse problem, accurate EEG forward solutions based on a detailed, individual volume conductor model of the head are essential. A crucial--but often neglected--aspect in generating a volume conductor model is the choice of the tissue conductivities, as these may vary from subject to subject. In this study, we investigate the sensitivity of EEG forward and inverse solutions to tissue conductivity uncertainties for sources distributed over the whole cortex surface. Methods: We employ a detailed five-compartment head model distinguishing skin, skull, cerebrospinal fluid, gray matter, and white matter, where we consider uncertainties of skin, skull, gray matter, and white matter conductivities. We use the finite element method (FEM) to calculate EEG forward solutions and goal function scans (GFS) as inverse approach. To be able to generate the large number of EEG forward solutions, we employ generalized polynomial chaos (gPC) expansions. Results: For sources up to a depth of 4 cm, we find the strongest influence on the signal topography of EEG forward solutions for the skull conductivity and a notable effect for the skin conductivity. For even deeper sources, e.g., located deep in the longitudinal fissure, we find an increasing influence of the white matter conductivity. The conductivity variations translate to varying source localizations particularly for quasi-tangential sources on sulcal walls, whereas source localizations of quasi-radial sources on the top of gyri are less affected. We find a strong correlation between skull conductivity and the variation of source localizations and especially the depth of the reconstructed source for quasi-tangential sources. We furthermore find a clear but weaker correlation between depth of the reconstructed source and the skin conductivity. Discussion: Our results clearly show the influence of tissue conductivity uncertainties on EEG source analysis. We find a particularly strong influence of skull and skin conductivity uncertainties. [ABSTRACT FROM AUTHOR]

This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve uncertainties in material properties, external forces, boundary conditions, etc. A stochastic virtual element space that couples the deterministic virtual element space and the stochastic space is constructed for this purpose and used to approximate the unknown stochastic solution. Two numerical frameworks are then developed to solve the derived stochastic virtual element equations, including a Polynomial Chaos approximation based approach and a weakly intrusive approximation based approach. In the Polynomial Chaos based framework, the stochastic solution is approximated using the Polynomial Chaos basis and solved via an augmented deterministic virtual element equation that is generated by applying the stochastic Galerkin procedure to the original stochastic virtual element equation. In the weakly intrusive approximation based framework, the stochastic solution is approximated by a summation of a set of products of random variables and deterministic vectors, where the deterministic vectors are solved via converting the original stochastic problem to deterministic virtual element equations by the stochastic Galerkin approach, and the random variables are solved via converting the original stochastic problem to one-dimensional stochastic algebraic equations by the classical Galerkin procedure. This method avoids the curse of dimensionality in high-dimensional stochastic problems successfully since all random inputs are embedded into one-dimensional stochastic algebraic equations whose computational effort weakly depends on the stochastic dimension. Numerical results on 2D and 3D problems with low- and high-dimensional random inputs demonstrate the good performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Bank vegetation plays a key role in both hydrodynamics and morphodynamics of natural rivers; however, these effects are often unaccounted for in the computational flow dynamics of natural waterways. Recent studies using the large‐eddy simulation (LES), however, have attempted to gain insights into the impacts of bank vegetation on the mean flow field of the natural rivers using a vegetation model, which applies a sink term to the momentum equations of motion. This approach accounts for the effects of the vegetation and provides a practical approach to account for the complex patches of bank vegetation in large‐scale rivers. To implement the vegetation model, a drag coefficient reflecting the overall resistance of vegetal structures to the flow is needed, but due to the lack of calibrated data and range of size, density and type of vegetation, this parameter can be a significant source of uncertainty in the model results. In this study, we use uncertainty quantification (UQ) to investigate the hydrodynamics and bed shear results when a bank vegetation is incorporated in an LES model. To this end, we used the polynomial chaos expansion and Monte Carlo sampling techniques to determine the uncertainties associated with the drag coefficient in the vegetation model and from uncertainties in the bed roughness and inflow discharge. The UQ analysis provided spatially varying confidence levels for the spanwise and vertical distribution of velocity magnitude and for the bed shear stress distributions. In addition, Sobol indices were computed to indicate the relative influence that each parameter had on the overall uncertainty. In general, it was found that uncertainty in flow discharge was the dominant source of uncertainty; however, the drag coefficient in the vegetation model and the bed roughness parameter also made significant contribution to the uncertainty near the banks and bed, respectively. [ABSTRACT FROM AUTHOR]

In the ever-changing marine environment, the key to the optimal design of the towed cable and the precise control of the towed body in the underwater towing system is the quantification of uncertainty at the end of the towed cable. The Monte Carlo(MC) method, a traditional uncertainty quantification method, has high computation costs and low accuracy. In view of this, a method of uncertainty quantization at the end of a towed cable based on polynomial chaos(PC) was proposed. Latin hypercube sampling was used to obtain sample sets of the towed cable parameters, and the sample sets were substituted into the lumped-mass method model to obtain the coordinate of the end position of the towed cable. A proxy model of the end response of the towed cable was generated by the PC method, and the uncertainty of the end was quantified according to the characteristics of the orthogonal polynomials. At the same time, the results of the PC method were compared with those of the MC method. The results show that compared with the MC method, the PC method has a faster convergence speed in terms of sample size and higher accuracy. The uncertainty of motion response is approximately proportional to the axial length of the towed cable; the increase in cable length leads to the increase in uncertainty at the end, and the increasing trend is gradually flattened. When the uncertainty of the towed cable parameters is constant, increasing the speed of the mother ship helps to improve the stability of the towed body at height. The accuracy and efficiency of the PC method have been verified. Meanwhile, the quantitative analysis results of the uncertainty at the end of the towed cable guide engineering problems.

In this paper, we develop surrogate models that can replace expensive predictive models and account for uncertainties in real-time treatment planning for irreversible electroporation of liver tumors. Standard non-intrusive surrogate modeling techniques that account for the model uncertainty and reduce the computational cost, such as polynomial chaos expansion and Gaussian process regression with conventional kernels, often do not capture the true physical behavior of the treatment outcome as required in the context of treatment planning. We improve the Gaussian process regression model by modifying the kernel function to a non-stationary Gibbs kernel with a support vector machine-based classifier in its length scale definition. This proposed model is compared with the standard surrogates in terms of their performance and accuracy. Our model is able to accurately replicate the behavior of the biophysics-based predictive model. There is a decrease of at least 81% in the overall root-mean-square error for treatment outcome when compared to the Gaussian process regression model with conventional kernels. Furthermore, we illustrate the application of the proposed surrogate model in treatment planning to address a voltage optimization problem for complete tumor ablation. Surrogate-assisted treatment planning exhibited good performance while maintaining similar levels of accuracy in comparison to treatment planning based on biophysical models. Finally, the effect of uncertainty in tissue electrical conductivities on the optimal voltage value is discussed. • Gaussian process regression-based surrogates can replace physics-based predictive models for irreversible electroporation. • Gibbs kernel with a support vector machine-based classifier is able to model relative tumor ablation for treatment planning. • Numerical illustrations indicate good accuracy with the use of the proposed kernel when compared to popular kernel choices. • Surrogate-assisted treatment planning was performed to solve a voltage optimization problem for complete tumor ablation. • The effect of uncertainty in electrical conductivities on the optimal voltage for irreversible electroporation is studied. [ABSTRACT FROM AUTHOR]

Purpose: The geometric parameters of the compressor blade have a noteworthy influence on compressor stability, which should be meticulously designed. However, machining inaccuracies cause the blade geometric parameters to deviate from the ideal design, and the geometric deviation exhibits high randomness. Therefore, the purpose of this study is to quantify the uncertainty and analyze the sensitivity of the impact of blade geometric deviation on compressor stability. Design/methodology/approach: In this work, the influence of blade geometric deviation is analyzed based on a subsonic compressor rotor stage, and three-dimensional numerical simulations are used to compute samples with different geometric features. A method of combining Halton sequence and non-intrusive polynomial chaos is adopted to carry out uncertainty quantitative analysis. Sobol' index and Spearman correlation coefficient are used to analysis the sensitivity and correlation between compressor stability and blade geometric deviation, respectively. Findings: The results show that the compressor stability is most sensitive to the tip clearance deviation, whereas deviations in the leading edge radius, trailing edge radius and chord length have minimal impact on the compressor stability. And, the effects of various blade geometric deviations on the compressor stability are basically independent and linearly superimposed. Originality/value: This work provided a new approach for uncertainty quantification in compressor stability analysis. The conclusions obtained in this work provide some reference value for the manufacturing and maintenance of rotor blades. [ABSTRACT FROM AUTHOR]

Purpose: This paper studies the nonlinear free and forced vibration of in-plane bi-directional functionally graded (FG) metal nanocomposite plates considering uncertain material elastic properties in the pre/post buckling states. Initially, the distribution of the nano-reinforcement volume fraction is designed through an optimization process to minimize the amount of the reinforcement in case of simply supported and clamped plates. Methods: The elastic modulus of the nanocomposite is modeled as a non-stationary random field using the Karhunen–Loève expansion (KLE) technique while the uncertain output variables are modeled using the polynomial chaos expansion (PCE). The considered plates are thin, so the classical plate theory with the von Kármán nonlinear strain field is used for the analysis. The harmonic balance method and the fourth-order Runge Kutta method are used to estimate the vibration responses. Results: The in-plane optimization process of the nonreinforcement volume fraction distribution yielded a 14% and 70% saving in the reinforcement amount in the case of the simply supported plate and the clamped plate respectively. The uncertainty in the vibration amplitude in the pre-buckled state can be multiples of the uncertainty in the elastic modulus and follows near normal distributions. In the post-buckled state, the nature of the probability distribution depends on the excitation force and frequency. In general, the FG plates can have similar or more uncertainty levels compared to the equivalent homogenous plates. Conclusion: The uncertainty in the nonlinear vibration of in-plane functionally graded plates depends on the boundary conditions, modeling definition of the input uncertainty, the excitation force and frequency. [ABSTRACT FROM AUTHOR]

Traditional designing of ethylene-cracking furnaces by computational fluid dynamics (CFD) does not consider the uncertainties in actual engineering. This paper introduces one uncertainty analysis framework based on non-intrusive polynomial chaos expansion (NIPCE) and multi-order Sobol indices to perform uncertainty quantification (UQ) and sensitivity analysis for NOx and CO emissions in the combustion process. In this framework, several operating parameters of the bottom burners that easily cause uncontrollable fluctuations in the flame and emission characteristics are selected as uncertainty variables and characterized as a probability distribution. Computationally expensive CFD simulation of cracking furnace is used to generate a small number of samples, which are carried out to develop high-precision sparse PCE models by the degree-adaptive scheme and least angle regression (LAR) algorithm. And multi-order Sobol sensitivity analysis based on PCE models is performed efficiently to research the influence of uncertain parameters on pollution generation. Under 3% of burner's uncertainty operating parameters, the results find that the excess air coefficient of 1.20 can obviously reduce the generation of NOx and CO emissions and control the fluctuation caused by uncertainties. Moreover, sensitivity analysis determines the critical variables that affect pollutant emissions to help the actual process avoid the unknown effects of uncertainties. [ABSTRACT FROM AUTHOR]

Low-fidelity, cost-effective, physics-based models are useful for assessing the environmental performance of novel combustion systems, especially those utilizing alternative fuels, like hydrogen and ammonia. However, these models require calibration and quantification of their limitations to be reliable predictive tools. This paper presents a framework for calibrating a simplified Chemical Reactor Network model using higher-fidelity Computational Fluid Dynamics data from a micro-gas-turbine-like combustor fuelled with pure ammonia. A Bayesian inference strategy that explicitly accounts for model error is used to calibrate the most relevant CRN parameters based on NO emissions data from CFD simulations and to estimate the model's structural uncertainty. The calibrated CRN model accurately predicts NO emissions within the design space and can extrapolate reasonably well to conditions outside the calibration range. By utilizing this framework, low-fidelity models can be employed to explore various operating conditions during the preliminary design of innovative combustion systems. • Bayesian calibration with model error embedding of Chemical Reactor Network (CRN) parameters is performed. • 15 RANS simulations of an ammonia-fuelled, multi-stage, mGT-like combustor are used as higher-fidelity samples. • Polynomial Chaos Expansion is used for likelihood construction and global sensitivity analysis. • Calibration enables quantifying parametric and model-form uncertainties in the CRN predictions of NO. • CRN allows performing optimisation under uncertainty to minimise NO at the combustor outlet. [ABSTRACT FROM AUTHOR]

The Fokker–Planck equation is a partial differential equation that describes how the probability density function of an object state varies, when subject to deterministic and random forces. The solution to this equation is crucial in many space applications, such as space debris trajectory tracking and prediction, guidance navigation and control under uncertainties, space situational awareness, and mission analysis and planning. However, no general closed-form solutions are known and several methods exist to tackle its solution. In this work, we use a known technique to transform this equation into a set of linear ordinary differential equations in the context of orbital dynamics. In particular, we show the advantages of the applied methodology, which allows to decouple the time and state-dependent components and to retain the entire shape of the probability density function through time, in the presence of both deterministic and stochastic dynamics. With this approach, the probability density function values at future times and for different initial conditions can be computed without added costs, provided that some time-independent integrals are solved offline. We showcase the efficacy and use of this method on some orbital dynamics example, by also leveraging the use of automatic differentiation for efficiently computing the involved derivatives. [ABSTRACT FROM AUTHOR]

A set of global metamodeling uncertainty quantification (UQ) techniques belonging to non-intrusive and forward propagation categories; Polynomial Chaos Expansion (PCE), Kriging, Canonical Low Rank Approximation (LRA), and Polynomial Chaos Kriging (PC-Kriging) and global sensitivity analysis (SA) techniques, Sobol' indices, Borgonovo, and Morris were compared to a benchmark methodology of direct Monte Carlo Simulation (MCS). The comparative analysis was demonstrated on a CO 2 capture absorber model with MEA solvent. Our analysis concluded as follows; (1) although significant variation in the CO 2 capture ratio in the prediction profile is shown, there is no apparent advantage of using a larger sample size via direct MCS except achieving a higher clarity in the output distribution, (2) while a very little effect on the convergence was observed which confirms the number of sample size, the fraction of computational time is enhanced by using Sobol sampling method, (3) the benefit of using metamodeling techniques compared to direct MCS was proven as they provide equal predictions in the output statistical measures with fewer evaluations of the original model and are therefore computationally cheaper, and (4) the global SA results showed Sobol indices is computationally more efficient while sharing similar ranking for the most influential parameter with Borgonovo and Morris. [Display omitted] • We integrated global UQ and SA methodologies with a CO 2 absorber with MEA model. • We performed a comparative analysis of global UQ and SA methodologies. • We compared direct Monte Carlo simulation (MCS) with metamodeling techniques. • We compared sampling strategies, Latin Hypercube, Halton, and Sobol sequence. • We showed ranking of the influential parameter using Sobol, Morris, and Borgonovo. [ABSTRACT FROM AUTHOR]

The computational fluid dynamics-based design of next-generation aeronautical combustion chambers is challenging due to many geometrical and operational parameters to be optimized and several sources of uncertainty that arise from numerical modeling. The present work highlights the potential benefits of exploiting Bayesian uncertainty quantification at the preliminary design stage. A prototypical configuration of an acetone/air spray swirling jet is investigated through an Eulerian–Lagrangian method under non-reactive conditions. Two direct numerical simulations (DNSs) provide reference data, coping with different vortex breakdown states. Consequently, a set of Reynolds-averaged Navier–Stokes simulations is conducted. Polynomial chaos expansion (PCE) is adopted to propagate the uncertainty associated with the spray dispersion model and the turbulent Schmidt number, delivering confidence intervals and the sensitivity of the output variance to each uncertain input. Consequently, the most significant sources of modeling uncertainty may be identified and eventually removed via a calibration procedure, thus making it possible to carry out a combustion chamber optimization process that is no longer affected by numerical biases. The uncertainty quantification analysis in the current study demonstrates that the spray dispersion model slightly affects the fuel vapor spatial distribution under vortex breakdown flow conditions, compared with the output variance induced by the selection of the turbulent Schmidt number. As a result, additional high-fidelity experimental and numerical campaigns should exclusively address the development of an ad hoc model characterizing the spatial distribution of the latter in the presence of vortex breakdown phenomenology, discarding any effort to improve the spray dispersion formulation. [ABSTRACT FROM AUTHOR]

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm. The source code is made publicly available for reproducibility. [ABSTRACT FROM AUTHOR]

Full-scale dome structures intrinsically have numerous sources of irreducible aleatoric uncertainties. A large-scale numerical simulation of the dome structure is required to quantify the effects of these sources on the dynamic performance of the structure using the finite element method (FEM). To reduce the heavy computational burden, a surrogate model of a dome structure was constructed to solve this problem. The dynamic global sensitivity of elastic and elastoplastic structures was analyzed in the uncertainty quantification framework using fully quantitative variance- and distribution-based methods through the surrogate model. The model considered the predominant sources of uncertainty that have a significant influence on the performance of the dome structure. The effects of the variables on the structural performance indicators were quantified using the sensitivity index values of the different performance states. Finally, the effects of the sample size and correlation function on the accuracy of the surrogate model as well as the effects of the surrogate accuracy and failure probability on the sensitivity index values are discussed. The results show that surrogate modeling has high computational efficiency and acceptable accuracy in the uncertainty quantification of large-scale structures subjected to earthquakes in comparison to the conventional FEM. [ABSTRACT FROM AUTHOR]

Uncertainties in the atmosphere and flight conditions can drastically impact the performance of an aircraft and result in certification delays. However, uncertainty propagation in high-fidelity simulations, which have become integral to the design process, can pose intractably high computational costs. This study presents a non-intrusive, parametric reduced order modeling (ROM) method to enable the prediction of uncertain fields with thousands of random variables and nonlinear features under limited sampling budgets. The methodology combines linear dimensionality reduction with sparse polynomial chaos expansions and is assessed in a variety of CFD-based test cases, including 3D supersonic flow over a passenger aircraft with uncertain flight conditions. Each problem has strong nonlinearities, such as shocks, to investigate the effectiveness of models in real-world aerodynamic simulations that may arise during conceptual or preliminary design. The performance is assessed by comparing the uncertain mean, variance, point predictions, and integrated quantities of interest obtained using the ROMs to Monte Carlo simulations. It is observed that if the flow is entirely supersonic or subsonic, then the method can predict the pressure field accurately and rapidly. Moreover, it is also seen that statistical moments can be efficiently obtained using closed-form analytical expressions and closely match Monte Carlo results. [ABSTRACT FROM AUTHOR]

Many probability-based uncertainty quantification (UQ) schemes require a large amount of sampled data to build credible probability density function (PDF) models for uncertain parameters. Unfortunately, the amounts of data collected as to compressor blades of aero-engines are mostly limited due to the expensive and time-consuming tests. In this paper, we develop a preconditioner-based data-driven polynomial chaos (PDDPC) method that can efficiently deal with uncertainty propagation of limited amounts of sampled data. The calculation accuracy of a PDDPC method is closely related to the sample size of collected data. Therefore, the influence of sample size on this PDDPC method is investigated using a nonlinear test function. Subsequently, we consider the real manufacturing errors in stagger angles for compressor blades. Under three different operating conditions, the PDDPC method is applied to investigate the effect of stagger-angle error on UQ results of multiple aerodynamic parameters of a two-dimensional compressor blade. The results show that as the sample-size of measured data increases, UQ results regarding aerodynamic performance obtained by the PDDPC method gradually converge. There exists a critical sample size that ensures accurate UQ analysis of compressor blades. The probability information contained in the machining error data is analyzed through Kullback–Leibler divergence, and the critical sample size is determined. The research results can serve as a valuable reference for the fast and cheap UQ analysis of compressor blades in practical engineering. [ABSTRACT FROM AUTHOR]

The paper is focused on recent advances in uncertainty quantification using polynomial chaos expansion (PCE). PCE is a well-known technique for approximation of costly mathematical models with random inputs - surrogate model. Although PCE is a widely used technique and it has several advantages over various surrogate models, it has still several limitations and research gaps. This paper reviews some of the recent theoretical developments in PCE. Specifically a new active learning method optimizing the experimental design and an extension of analytical statistical analysis using PCE will be reviewed. These two topics represent crucial tools for efficient applications: active learning leads generally to a significantly more efficient construction of PCE and improved statistical analysis allows for analytical estimation of higher statistical moments directly from PCE coefficients. Higher statistical moments can be further used for the identification of probability distribution and estimation of design quantiles, which is a crucial task for the probabilistic analysis of structures. Selected applications of the theoretical methods are briefly presented in a context of civil engineering as well as some preliminary results of further research. A part of the paper also presents UQPy package containing state-of-the-art implementation of the PCE theory. [ABSTRACT FROM AUTHOR]

In this work, we describe an algorithm based on Polynomial-Chaos (PC) expansions for the study of uncertainty quantification problems involving grating filters. The proposed method adaptively builds anisotropic PC models for the quantities of interest, considering varying polynomial orders. In addition, optimal experimental designs are constructed that exploit the local variance of the samples, further increasing the reliability of the computations. The method is applied to the uncertainty quantification of a typical resonant grating filter, where the efficiency of the proposed approach over standard techniques is demonstrated.

A wind turbines' power curve is an easily accessible form of damage-sensitive data, and as such is a key part of structural health monitoring (SHM) in wind turbines. Power curve models can be constructed in a number of ways, but the authors argue that probabilistic methods carry inherent benefits in this use case, such as uncertainty quantification and allowing uncertainty propagation analysis. Many probabilistic power curve models have a key limitation in that they are not physically meaningful – they return mean and uncertainty predictions outside of what is physically possible (the maximum and minimum power outputs of the wind turbine). This paper investigates the use of two bounded Gaussian processes (GPs) in order to produce physically meaningful probabilistic power curve models. The first model investigated was a warped heteroscedastic Gaussian process, and was found to be ineffective due to specific shortcomings of the GP in relation to the warping function. The second model – an approximated GP with a Beta likelihood was highly successful and demonstrated that a working bounded probabilistic model results in better predictive uncertainty than a corresponding unbounded one without meaningful loss in predictive accuracy. Such a bounded model thus offers increased accuracy for performance monitoring and increased operator confidence in the model due to guaranteed physical plausibility. [ABSTRACT FROM AUTHOR]

This paper investigates the adequacy of radial basis function (RBF)-based models as surrogates in uncertainty quantification (UQ) and CFD shape optimization; for the latter, problems with and without uncertainties are considered. In UQ, these are used to support the Monte Carlo, as well as, the non-intrusive, Gauss Quadrature and regression-based polynomial chaos expansion methods. They are applied to the flow around an isolated airfoil and a wing to quantify uncertainties associated with the constants of the γ − R ˜ e θ t transition model and the surface roughness (in the 3D case); it is demonstrated that the use of the RBF-based surrogates leads to an up to 50% reduction in computational cost, compared with the same UQ method that uses CFD computations. In shape optimization under uncertainties, solved by stochastic search methods, RBF-based surrogates are used to compute statistical moments of the objective function. In applications with geometric uncertainties which are modeled through the Karhunen–Loève technique, the use on an RBF-based surrogate reduces the turnaround time of an evolutionary algorithm by orders of magnitude. In this type of applications, RBF networks are also used to perform mesh displacement for the perturbed geometries. [ABSTRACT FROM AUTHOR]

The accurate simulation of complex turbulent flow has remained a challenging issue in computational fluid dynamics and plays a crucial role in engineering practice. Due to computational limitations, the Reynolds Averaged Navier-Stokes (RANS) simulation method continues to be the preferred choice for engineers to solve practical problems. Nonetheless, there are concerns regarding the applicability of RANS models to complex flows such as those with large-scale separation or jet interaction, as recommended coefficients may not be suitable. This work aims to perform a specified analysis of parameters' uncertainty in the Speziale-Sarkar-Gatsk/Launder-Reece-Rodi (SSG/LRR)-ω turbulence model. This work employs the non-intrusive polynomial chaos (NIPC) method to establish a surrogate model between parameters and computational results for uncertainty quantification. Sensitivity analysis is conducted via the Sobol index to identify key parameters critical for different flow structures. Then, Bayesian inference is applied for calibrating parameters by leveraging calculation results and two groups of experimental data, respectively. The results show that the calibrated values for the key parameters could significantly improve prediction accuracy. Subsequently, the work also delves into the inadequacies of SSG/LRR-ω models when applied to separated flows, revealing an underestimation of Reynolds stress in the separation zone as a primary source of poor predictions. Furthermore, it is considered that using a set of parameter combinations with a larger value of C 3 ω after the separation of the flow will obtain better calculation results in the separation zone. • Uncertainty quantification is performed by a surrogate model constructed by the non-invasive polynomial chaos method. • The Bayesian method is employed to evalute and correct the SSG/LRR-ω model. • The specific reasons for the inaccurate predictions of the model applied to separated flows are analyzed. • The improvement measures of the SSG/LRR-ω model are discussed. [ABSTRACT FROM AUTHOR]

The assessment of the future thermodynamics performance of a retrofitted heat and power production unit is prone to many uncertainties due to the large number of parameters involved in the modeling of all its components. To carry out uncertainty quantification analysis, alternatives to the traditional Monte Carlo method must be used due to the large stochastic dimension of the problem. In this paper, sparse polynomial chaos expansion (SPCE) is applied to the retrofit of a large coal-fired power plant into a biomass-fired combined heat and power unit to quantify the main drivers and the overall uncertainty on the plant's performance. The thermodynamic model encompasses over 180 components and 1500 parameters. A methodology combining the use of SPCE and expert judgment is proposed to narrow down the sources of uncertainty and deliver reliable probability distributions for the main key performance indicators (KPIs). The impact of the uncertainties on each input parameter vary with the considered KPI and its assessment through the computation of Sobol' indices. For both coal and biomass operations, the most impactful input parameters are the composition of the fuel and its heating value. The uncertainty on the performance and steam quality parameters is not much affected by the retrofit. Key furnace parameters exhibit a skewed probability distribution with large uncertainties, which is a strong attention point in terms of boiler operation and maintenance. [ABSTRACT FROM AUTHOR]

Robust optimization design (ROD) is playing an increasingly significant role in aerodynamic shape optimization and aircraft design. However, an efficient ROD framework that couples uncertainty quantification (UQ) and a powerful optimization algorithm for three-dimensional configurations is lacking. In addition, it is very important to reveal the maintenance mechanism of aerodynamic robustness from the design viewpoint. This paper first combines gradient-based optimization using the discrete adjoint-based approach with the polynomial chaos expansion (PCE) method to establish the ROD framework. A flying-wing configuration is optimized using deterministic optimization and ROD methods, respectively. The uncertainty parameters are Mach and the angle of attack. The ROD framework with the mean as an objective achieves better robustness with a lower mean (6.7% reduction) and standard derivation (Std, 18.92% reduction) compared to deterministic results. Moreover, we only sacrifice a minor amount of the aerodynamic performance (an increment of 0.64 counts in the drag coefficient). In comparison, the ROD with Std as an objective obtains a very different result, achieving the lowest Std and largest mean The far-field drag decomposition method is applied to compute the statistical moment variation of drag components and reveal how the ROD framework adjusts the drag component to realize better aerodynamic robustness. The ROD with the mean as the objective decreases the statistical moment of each drag component to improve aerodynamic robustness. In contrast, the ROD with Std as an objective reduces Std significantly by maintaining the inverse correlation relationship between the induced drag and viscous drag with an uncertainty parameter, respectively. The established ROD framework can be applied to future engineering applications that consider uncertainties. The unveiled mechanism for maintaining aerodynamic robustness will help designers understand ROD results more deeply, enabling them to reasonably construct ROD optimization problems. [ABSTRACT FROM AUTHOR]

Uncertainty quantification (UQ) is deemed critical in steel reheating simulations due to the significant input uncertainties arising when defining steel surface properties and atmospheric furnace conditions. In order to conduct UQ, the study utilizes polynomial chaos expansion, which has been found to significantly curtail the computational effort needed to obtain reliable convergent statistics for the model of interest. Results from a comprehensive UQ analysis of a walking‐beam reheat furnace simulated using Tata Steel's reheat furnace control model, online slab temperature calculation, are presented. Slab temperature evolution and oxide scale growth are chosen as the study's QoIs. The analysis reveals that at the earlier stages of reheating, the majority of the output variance in slab temperature can be traced back exclusively to the emissivity of the slab surface, and the majority of the output variance in oxide scale growth is traced back to the combination of slab's surface emissivity and the initial scale thickness found on steel products prior to reheating. However, as the steel product advances toward the furnace's discharge end, inputs related to oxide scale growth become increasingly important, ultimately becoming the most influential input parameters, although the dynamics of this transition differ between the QoIs. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid–porous interface. These models include a porous-medium model using Darcy's law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems' behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model's predictive capabilities, and make a probabilistic model comparison. [ABSTRACT FROM AUTHOR]

Modern astronautics problems require methods of tractable uncertainty quantification for problems with data in a variety of mathematical spaces. Polynomial Chaos Expansions (PCEs) enable tractable uncertainty propagation, sensitivity analysis, and provide a surrogate model to efficiently solve stochastic optimization problems. Existing PCE methods are mostly isolated to bases defined via tensor products of univariate functions over subdomains of the real line or integers. The goal of this work is to incorporate random vectors on the n-dimensional sphere, thereby extending the use of PCEs to problems that include spacecraft attitude uncertainty. Random inputs with probability densities on the n-sphere are generally correlated. When directional random inputs are independent, products of univariate functions fail to produce an orthogonal basis. Basis functions must preserve the periodic response of the system produced by the underlying structure of the domain. This paper presents an approach to generating an orthogonal basis with respect to a density function on the n-sphere by combining hyperspherical harmonics with an orthogonalization procedure based on the raw moments of the harmonic functions. For highly concentrated densities on the unit sphere, the spherical cap harmonics provide a more numerically stable solution while preserving periodicity. Numeric errors in the proposed procedure are presented for multiple cases. Performance of the PCEs is quantified when propagating uncertainty for a highly eccentric orbit with a random translational maneuver error, and a second case based on rigid-body dynamics with the attitude state parameterized as a quaternion. [ABSTRACT FROM AUTHOR]

The slipstream effect of propeller aircraft has a major impact on aircraft aerodynamic characteristics. Predicting the interaction of propeller slipstream on flow field over a complete aircraft has been an important topic in the field of fluid mechanics. In the flight test, we found that parameters in the flight data of propeller aircraft exhibit significant stochastic characteristics, and the mechanism of the influence of these stochastic parameters on aerodynamic characteristics of propeller aircraft needs to be further studied. Therefore, we combine arbitrary Polynomial Chaos method with Computational Fluid Dynamics (CFD) according to the characteristics of stochastic parameter distribution, propose an uncertainty CFD analysis method, and apply it to the aerodynamic uncertainty analysis of propeller aircraft. Results show that the standard deviation (Std) of the pressure coefficient C p on the wing surface will form an extreme region at windward side and separation position, respectively, which will gradually decrease with the flow direction. Furthermore, the slipstream will reduce the local Std on wing surface, and the downwash caused by slipstream will change the Std distribution on the leading edge of the horizontal tail. [ABSTRACT FROM AUTHOR]

With the rapid development of the mobile communication technology, the design of mobile phones has become more complex, and research on the electromagnetic radiation from mobile phones that reaches the human head has become important. Therefore, first of all, a model of mobile phone daily use was established. Then, based on the established simulation model, the safety of human head exposure to mobile phones was evaluated. The generalized polynomial chaos (gPC) method was used to establish a proxy model of the specific absorption rate (SAR) of the human head at different frequencies to perform a parameter uncertainty quantification (UQ). Finally, the Sobol method was used to quantify the influence of relevant variables on the SAR. The simulation results showed that the gPC method can save time and cost while ensuring accuracy, and the SAR value is greatly influenced by the electromagnetic materials of the mobile phone shell. Combined with the above analysis, this paper can provide reasonable suggestions for the design of mobile phone electromagnetic materials. [ABSTRACT FROM AUTHOR]

The impact of uncertainty on the flexural response of sandwich beams is studied in this paper. The study focuses on the unique features of typical soft-core sandwich beams, including local effects and stresses concentrations. Those are critical for the integrity and performance of the structural system and, to the best knowledge of the authors, were never considered from a stochastic viewpoint. Several structural features of the beam are considered, separately, as uncertain, and the stochastic characteristics of the distributions of the displacements and stresses are investigated. To capture the unique local effects, the extended high-order sandwich panel theory is adopted. Numerical solutions of the stochastic ordinary differential equations use the finite element (FE) method. The parametric uncertainty and its spatial distribution are modeled by random fields. The stochastic analysis uses both the Karhunen-Loeve polynomial-chaos and the perturbation-based stochastic finite element methods. The two approaches are compared and comprehensively validated against Monte Carlo simulations. The numerical results quantify the impact of uncertainty on the response, but show significant disagreements between the two stochastic approaches, and the perturbation-based stochastic finite element method is chosen as the most suitable one. The effects of the coefficient of variation of the uncertain input parameter and its correlation length are also studied. Highly amplified levels of uncertainty are revealed by the stochastic analysis near points of local stress concentration. These localized yet significant uncertainties, reported here for the first time, shed new light on the design, analysis, and safety of such sandwich beams. [ABSTRACT FROM AUTHOR]

The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexity of the model. In this work, we propose a multidimensional Galerkin proper orthogonal decomposition that optimally reduces each dimension of a tensorized product space. We provide the analytical framework and results that define and quantify the low‐dimensional approximation. We illustrate its application for uncertainty modeling with polynomial chaos expansions and show its efficiency in a numerical example. [ABSTRACT FROM AUTHOR]

Surrogate models are widely used to improve the computational efficiency in various geophysical simulation problems by reducing the number of model runs. Conventional one-layer surrogate representations are based on global (e.g. polynomial chaos expansion, PCE) or on local kernels (e.g., Gaussian process emulator, GPE). Global representations omit some details, while local kernels require more model runs. The existing multi-resolution PCE is a promising hybrid: it is a global representation with local refinement. However, it can not (yet) estimate the uncertainty of the resulting surrogate, which techniques like the GPE can do. We propose to join multi-resolution PCE and GPE s into a joint surrogate framework to get the best out of both worlds. By doing so, we correct the surrogate bias and assess the remaining uncertainty of the surrogate itself. The resulting multi-resolution emulator offers a pathway for several active learning strategies to improve the surrogate at acceptable computational costs, compared to the existing PCE-kriging approach it adds the multi-resolution aspect. We analyze the performance of a multi-resolution emulator and a plain GPE using didactic test cases and a CO2 benchmark, that is representative of many alike problems in the geosciences. Both approaches show similar improvements during the active learning, but our multi-resolution emulator leads to much more stable results than the GPE. Overall, our suggested emulator can be seen as a generalization of multi-resolution PCE and GPE concepts that offers the possibility for active learning. [ABSTRACT FROM AUTHOR]

In three‐dimensional (3D) equilibrium, reconstruction defining parameters of an ideal magneto‐hydrodynamic equilibrium are inferred from a set of plasma diagnostic measurements. For the reconstructed parameters, various forms of uncertainty estimates exist within common 3D reconstruction frameworks. These estimates often assume a Gaussian posterior distribution. The validity of this assumption is not obvious in such highly nonlinear inverse problems, and therefore the accuracy of the estimates cannot be guaranteed. In this work, we formulate the problem of 3D equilibrium reconstruction in a Bayesian sense and explore the posterior distribution of reconstruction parameters via Markov chain Monte Carlo (MCMC) sampling. The target reconstruction parameters, that is, shape and scaling factors of the pressure and toroidal current‐density profiles as well as the total toroidal flux, are taken from a reduced subspace of Wendelstein 7‐X equilibrium configurations. Since the corresponding forward model evaluations are computationally demanding, we replace the forward model via a polynomial chaos expansion surrogate. We compare the posterior distribution obtained via MCMC sampling to Laplace's approximation, which assumes a Gaussian posterior. We find that the two approaches provide similar results in regimes where the uncertainty on the plasma diagnostic signals is low. However, discrepancies between the posteriors are observed in cases of higher diagnostic signal uncertainty. Therefore, we provide further validation of the commonly used Laplace's approximation as a method of uncertainty quantification in 3D equilibrium reconstruction and showcase some of its limitations. [ABSTRACT FROM AUTHOR]

Objective: pulsed fields or waveforms with multi-frequency content have to be assessed with suitable methods. This paper deals with the uncertainty quantification associated to these methods. Approach: among all possible approaches, the weighted peak method (WPM) is widely employed in standards and guidelines, therefore, in this paper, we consider its implementation both in time domain and frequency domain. For the uncertainty quantification the polynomial chaos expansion theory is used. By means of a sensitivity analysis, for several standard waveforms, the parameters with more influence on the exposure index are identified and their sensitivity indices are quantified. The output of the sensitivity analysis is used to set up a parametric analysis with the aim of evaluating the uncertainty propagation of the analyzed methods and, finally, also several measured waveforms generated by a welding gun are tested. Main results: it is shown that the time domain implementation of the weighted peak method provides results in agreement with the basilar mechanisms of electromagnetic induction and electrostimulation. On the opposite, the WPM in frequency domain is found to be too sensitive to parameters that should not influence the exposure index because its weight function includes sharp variations of the phase centered on real zeros and poles. To overcome this issue, a new definition for the phase of the weight function in frequency domain is proposed. Significance: it is shown that the time domain implementation of the WPM is the more accurate and precise. The standard WPM in frequency domain has some issues that can be avoided with the proposed modification of the phase definition of the weight function. Finally, all the codes used in this paper are hosted on a GitHub and can be freely accessed at https://github.com/giaccone/wpm_uncertainty. [ABSTRACT FROM AUTHOR]

The design of naval exhaust funnels has to take into account the interaction between the hot gases and topside structures, which usually includes critical electronic devices. Being able to predict the propagation trajectory, shape and temperature distribution of an exhaust gas plume is highly strategic in different industrial sectors. The propagation of a stack plume can be affected by different uncertainty factors, such as those related to the wind flow and gas flow conditions at the funnel exit. The constant growth of computational resources has allowed simulations to gain a key role in the early design phase. However, it is still difficult to model all the aspects of real physical problems in actual applications and, therefore, to completely rely upon the quantitative results of numerical simulations. One of the most important aspects is related to input variable uncertainty, which can significantly affect the simulation result. With this aim, the discipline of Uncertainty Quantification provides several methods to evaluate uncertainty propagation in numerical simulations. In this paper, UQ procedures are applied to a CFD simulation of a single plume in a crossflow. The authors test the influence of the uncertainty propagation of the chimney exit velocity and the main flow angle on the plume flow development. Two different UQ methods are applied to the analysis: the surrogate-based approach and the polynomial chaos expansion method. A comparison of the two methods is performed in order to find their pros and cons, focusing on the different and detailed quantities of interest. [ABSTRACT FROM AUTHOR]

As one of the main methods to study ice formation of aircraft, numerical simulation introduces a lot of parameter uncertainties when calculating ice formation, which affects the accuracy and reliability of the numerical simulation. It is important to develop methods of uncertainty quantification and quantify the uncertainty scientifically for evaluating numerical simulation results. To solve the problem of high-dimensional input-output that is difficult to be solved by traditional parameter uncertainty quantification methods, an ice shape prediction proxy model is proposed based on the proper orthogonal decomposition and error back-propagation neural network. The proxy model is proved to have high accuracy and excellent generalization ability under single input and double input parameters by taking the droplet median size and temperature as examples. Finally, on the basis of ice shape calculated by the proxy model with Monte Carlo sampling, the icing range is established by criteria 2σ. It is found that the uncertainty of droplet median size mainly affects the ice angle growth of glaze ice, while the superposition of temperature and droplet median size uncertainty affect the frost ice thickness. This study establishes a method for the subsequent impact analysis of multi-icing conditions and provides ideas for the uncertainty quantification of multi-dimensional input-output.. [ABSTRACT FROM AUTHOR]

We continue our study [R. Aylwin, C. Jerez-Hanckes, C. Schwab and J. Zech, Domain uncertainty quantification in computational electromagnetics, SIAM/ASA J. Uncertain. Quant.8 (2020) 301–341] of the numerical approximation of time-harmonic electromagnetic fields for the Maxwell lossy cavity problem for uncertain geometries. We adopt the same affine-parametric shape parametrization framework, mapping the physical domains to a nominal polygonal domain with piecewise smooth maps. The regularity of the pullback solutions on the nominal domain is characterized in piecewise Sobolev spaces. We prove error convergence rates and optimize the algorithmic steering of parameters for edge-element discretizations in the nominal domain combined with: (a) multilevel Monte Carlo sampling, and (b) multilevel, sparse-grid quadrature for computing the expectation of the solutions with respect to uncertain domain ensembles. In addition, we analyze sparse-grid interpolation to compute surrogates of the domain-to-solution mappings. All calculations are performed on the polyhedral nominal domain, which enables the use of standard simplicial finite element meshes. We provide a rigorous fully discrete error analysis and show, in all cases, that dimension-independent algebraic convergence is achieved. For the multilevel sparse-grid quadrature methods, we prove higher order convergence rates free from the so-called curse of dimensionality. Numerical experiments confirm our theoretical results and verify the superiority of the sparse-grid methods. [ABSTRACT FROM AUTHOR]