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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., (© 2024 John Wiley & Sons Ltd.)

Objectives: Utility scores associated with preference-based health-related quality-of-life instruments such as the EQ-5D-3L are reported as point estimates. In this study, we develop methods for capturing the uncertainty associated with the valuation study of the UK EQ-5D-3L that arises from the variability inherent in the underlying data, which is tacitly ignored by point estimates. We derive a new tariff that properly accounts for this and assigns a specific closed-form distribution to the utility of each of the 243 health states of the EQ-5D-3L., Methods: Using the UK EQ-5D-3L valuation study, we used a Bayesian approach to obtain the posterior distributions of the derived utility scores. We constructed a hierarchical model that accounts for model misspecification and the responses of the survey participants to obtain Markov chain Monte Carlo (MCMC) samples from the posteriors. The posterior distributions were approximated by mixtures of normal distributions under the Kullback-Leibler (KL) divergence as the criterion for the assessment of the approximation. We considered the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to estimate the parameters of the mixture distributions., Results: We derived an MCMC sample of total size 4,000 × 243. No evidence of nonconvergence was found. Our model was robust to changes in priors and starting values. The posterior utility distributions of the EQ-5D-3L states were summarized as 3-component mixtures of normal distributions, and the corresponding KL divergence values were low., Conclusions: Our method accounts for layers of uncertainty in valuation studies, which are otherwise ignored. Our techniques can be applied to other instruments and countries' populations., Highlights: Guidelines for health technology assessments typically require that uncertainty be accounted for in economic evaluations, but the parameter uncertainty of the regression model used in the valuation study of the health instrument is often tacitly ignored.We consider the UK valuation study of the EQ-5D-3L and construct a Bayesian model that accounts for layers of uncertainty that would otherwise be disregarded, and we derive closed-form utility distributions.The derived tariff can be used by researchers in economic evaluations, as it allows analysts to directly sample a utility value from its corresponding distribution, which reflects the associated uncertainty of the utility score., Competing Interests: The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The authors received no financial support for the research, authorship, and/or publication of this article.

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical models in prediction accuracy, statistical inference, such as estimating the effects of covariates and quantifying the prediction uncertainty, is not trivial due to the highly complicated model structure and overparameterization. To address this challenge, we propose a new Bayesian approach by embedding CNNs within the generalized linear models (GLMs) framework. We use extracted nodes from the last hidden layer of CNN with Monte Carlo (MC) dropout as informative covariates in GLM. This improves accuracy in prediction and regression coefficient inference, allowing for the interpretation of coefficients and uncertainty quantification. By fitting ensemble GLMs across multiple realizations from MC dropout, we can account for uncertainties in extracting the features. We apply our methods to biological and epidemiological problems, which have both high-dimensional correlated inputs and vector covariates. Specifically, we consider malaria incidence data, brain tumor image data, and fMRI data. By extracting information from correlated inputs, the proposed method can provide an interpretable Bayesian analysis. The algorithm can be broadly applicable to image regressions or correlated data analysis by enabling accurate Bayesian inference quickly., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)

Application of deep learning (DL) to the field of healthcare is aiding clinicians to make an accurate diagnosis. DL provides reliable results for image processing and sensor interpretation problems most of the time. However, model uncertainty should also be thoroughly quantified. This paper therefore addresses the employment of Monte Carlo dropout within the DL structure to automatically discriminate presymptomatic signs of spinocerebellar ataxia type 2 in saccadic samples obtained from electrooculograms. The current work goes beyond the common incorporation of this special type of dropout into deep neural networks and uses the uncertainty derived from the validation samples to construct a decision tree at the register level of the patients. The decision tree built from the uncertainty estimates obtained a classification accuracy of 81.18% in automatically discriminating control, presymptomatic and sick classes. This paper proposes a novel method to address both uncertainty quantification and explainability to develop reliable healthcare support systems.

Despite the advantage of model-based design, anaerobic digesters are seldom designed using biokinetic models due to lack of reliable kinetic coefficients and/or systematic approaches for incorporating kinetic models into digester design. This study presents a systematic framework, which couples practical identifiability, uncertainty quantification and attainable region (AR) concepts for defining process performance targets, especially when reliable kinetic coefficients are unavailable. Within the framework, we introduce the concept of self-optimizing ARs, which define performance targets that results in near optimal operation in spite of variations in kinetic coefficients. Using the case of modified Hill model, only 3 out of the 6 model parameters (unidentifiable set) are responsible for the model prediction uncertainty. The uncertainty bands (mean, 10th percentile and 90th percentile) on the model states has been computed using the Monte Carlo Simulation procedure and attainable regions for the different levels of uncertainty has been constructed and the boundaries interpreted into digester structures. The self-optimizing attainable regions have been defined as the intersection region of the attainable regions corresponding to the mean, 10th percentile and 90th percentile. Incorporating uncertainty significantly reduces performance targets of the process but increases self-optimality in defining performance targets. Unlike the attainable region, which represents the limits of achievability for defined kinetics, the self-optimizing attainable region represents the set of all possible states attainable by the system even in cases of kinetic uncertainty. In summary, the concept of self-optimizing ARs provides a systematic way of defining process performance targets and making economic decisions under conditions of uncertainty., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2019 The Authors. Published by Elsevier Ltd.. All rights reserved.)

To enhance the decision-making process and reduce economic losses caused by future flooding, it is critical to quantify uncertainty in each step of flood risk analysis. To address the often-missing uncertainty quantification, we propose a new methodology that combines damage functions and probability bounds analysis. We estimate the likely direct tangible damage to 375,973 residential buildings along the Fraser River through Metro Vancouver, Canada, for a range of climate change driven flood scenarios, while transparently representing the associated uncertainties caused by sampling error, imprecise measurement, and uncertainty in building height and basement conditions. Furthermore, for the purposes of developing effective management strategies, uncertainties in this study are classified into two categories, namely aleatory and epistemic. According to our findings and absent significant action, we should expect an enormous increase in flood damage to the four categories of residential buildings considered in this study by the year 2100. Moreover, the results show that second-order Monte Carlo simulation cannot adequately represent epistemic uncertainty for small sample sizes. In such a case, we recommend employing a probability box to delineate the epistemic uncertainty. [ABSTRACT FROM AUTHOR]

The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep neural networks. Most of these methods require a huge amount of data and computer capacity to train the networks, which often may not be available. Our paper addresses the issue of learning from small data sets by taking patches of very few images into account. We focus on the combination of model‐based and data‐driven methods by approximating just the image prior, also known as regularizer in the variational model. We review two methodically different approaches, namely optimizing the maximum log‐likelihood of the patch distribution, and penalizing Wasserstein‐like discrepancies of whole empirical patch distributions. From the point of view of Bayesian inverse problems, we show how we can achieve uncertainty quantification by approximating the posterior using Langevin Monte Carlo methods. We demonstrate the power of the methods in computed tomography, image super‐resolution, and inpainting. Indeed, the approach provides also high‐quality results in zero‐shot super‐resolution, where only a low‐resolution image is available. The article is accompanied by a GitHub repository containing implementations of all methods as well as data examples so that the reader can get their own insight into the performance. [ABSTRACT FROM AUTHOR]

In the fused filament fabrication (FFF) additive manufacturing process, a part is manufactured by layer-by-layer deposition of thermoplastic filaments extruded from a nozzle. This process results in microscopic voids that are stochastic in size and randomly distributed in space. Also, the elastic properties of the extruded filaments show variation. These uncertainties in the FFF process and the resulting microstructure cause a variation in the structural response (load–displacement curve) of the final printed part. A multiscale uncertainty propagation framework was developed in this study to examine the effect of microscopic inhomogeneity on the variations in the macroscopic structural behavior. Experimental data was used to quantify uncertainty at the micro-scale, while Monte Carlo simulation was used to quantify uncertainty at the meso- and macroscales. A hook model was considered as a case study for uncertainty propagation in the FFF process. [ABSTRACT FROM AUTHOR]

The Windkessel (WK) model is a simplified mathematical model used to represent the systemic arterial circulation. While the WK model is useful for studying blood flow dynamics, it suffers from inaccuracies or uncertainties that should be considered when using it to make physiological predictions. This paper aims to develop an efficient and easy‐to‐implement uncertainty quantification method based on a local gradient‐based formulation to quantify the uncertainty of the pressure waveform resulting from aleatory uncertainties of the WK parameters and flow waveform. The proposed methodology, tested against Monte Carlo simulations, demonstrates good agreement in estimating blood pressure uncertainties due to uncertain Windkessel parameters, but less agreement considering uncertain blood‐flow waveforms. To illustrate our methodology's applicability, we assessed the aortic pressure uncertainty generated by Windkessel parameters‐sets from an available in silico database representing healthy adults. The results from the proposed formulation align qualitatively with those in the database and in vivo data. Furthermore, we investigated how changes in the uncertainty of the Windkessel parameters affect the uncertainty of systolic, diastolic, and pulse pressures. We found that peripheral resistance uncertainty produces the most significant change in the systolic and diastolic blood pressure uncertainties. On the other hand, compliance uncertainty considerably modifies the pulse pressure standard deviation. The presented expansion‐based method is a tool for efficiently propagating the Windkessel parameters' uncertainty to the pressure waveform. The Windkessel model's clinical use depends on the reliability of the pressure in the presence of input uncertainties, which can be efficiently investigated with the proposed methodology. For instance, in wearable technology that uses sensor data and the Windkessel model to estimate systolic and diastolic blood pressures, it is important to check the confidence level in these calculations to ensure that the pressures accurately reflect the patient's cardiovascular condition. [ABSTRACT FROM AUTHOR]

A robust method for uncertainty quantification is undeniably leading to a greater certainty in simulation results and more sustainable designs. The inherent uncertainties of the world around us render everything stochastic, from material parameters, over geometries, up to forces. Consequently, the results of engineering simulations should reflect this randomness. Many methods have been developed for uncertainty quantification for linear elastic material behavior. However, real-life structure often exhibit inelastic material behavior such as visco-plasticity. Inelastic material behavior is described by additional internal variables with accompanying differential equations. This increases the complexity for the computation of stochastic quantities, e.g., expectation and standard deviation, drastically. The time-separated stochastic mechanics is a novel method for the uncertainty quantification of inelastic materials. It is based on a separation of all fields into a sum of products of time-dependent but deterministic and stochastic but time-independent terms. Only a low number of deterministic finite element simulations are then required to track the effect of (in)homogeneous material fluctuations on stress and internal variables. Despite the low computational effort the results are often indistinguishable from reference Monte Carlo simulations for a variety of boundary conditions and loading scenarios. [ABSTRACT FROM AUTHOR]

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]

Due to the complexity of spill fire, predicting heat release rate (HRR) is a challenging aspect, therefore, identifying key contributors to uncertainty is essential to develop reliable models for fire risk assessment. We propose a framework that couples Artificial-Neural-Network (ANN) and Monte Carlo Uncertainty Quantification (UQ) to quantify the uncertainties of spill fire parameters on peak HRR variance. The ANN spill fire model, trained on experimental spill fire data, shows good agreement with measured HRR values. By coupling with Dakota for Monte Carlo uncertainty propagation, the framework identifies major contributors to peak HRR uncertainty for fixed and continuous unconfined spill fires. This is achieved by investigating two uncertainty sources: data scarcity and input parameters. UQ results indicate that the confidence intervals widen at points where data are scarcer. Sensitivity analysis shows that in the case of fixed quantity spills, the fuel amount and properties parameters contribute to 54.4% and 22.6% of peak HRR variance, respectively. For continuous spills, the discharge rate and fuel properties parameters account for 41.8% and 39.3% of peak HRR variance, respectively. This work can be utilized in developing more advanced predictive ANN models for spill fire scenarios, ultimately enhancing fire probabilistic safety analysis in nuclear power plants. [ABSTRACT FROM AUTHOR]

Pavement service life is an important factor that affects both the whole life cost and carbon footprint of a pavement. The service life of a pavement is affected by several different parameters which can be broadly classified into climate conditions, binder and mixture properties, pavement design, workmanship, and maintenance strategies. The current practice for determining service life of pavements involves the use of pavement design tools, which are used while constructing a new pavement or performing a reconstruction/resurfacing or pavement maintenance. In addition, field measurements using ground penetration radar, falling weight deflectometer, traffic speed deflectometer, and other techniques are also used to assess the condition of an existing pavement. The information from these measurements is then combined with pavement design software to predict potential pavement service life. The accuracy of the predicted pavement service life is affected by the associated uncertainties in the parameters that affect pavement life. The following paper presents various approaches that could be potentially used to determine the associated uncertainties in the estimation of pavement service life. The various uncertainty quantification techniques have been applied to a specific design, and the outcomes are discussed in this paper. The Monte Carlo simulation method, a system-level uncertainty quantification technique, can estimate a probabilistic pavement service life. The other uncertainty quantification schemes are software specific and provide probabilistic life factors by assumed statistical distributions. Hence, the Monte Carlo simulation technique could be one potential method that can be used for estimating a generalized pavement service utilizing predictions from various design software. [ABSTRACT FROM AUTHOR]

This paper presents a novel adaptation of the conventional approximate Bayesian computation sequential Monte Carlo (ABC-SMC) sampling algorithm for parameter estimation in the presence of uncertainties, coined combinatorial ABC-SMC. Inference of this type is used in situations where there does not exist a closed form of the associated likelihood function, which is replaced by a simulating model capable of producing artificial data. In the literature, conventional ABC-SMC is utilised to perform inference on continuous parameters. The novel scheme presented here has been developed to perform inference on parameters that are high-dimensional binary, rather than continuous. By altering the form of the proposal distribution from which to sample candidates in subsequent iterations (referred to as waves), high-dimensional binary variables may be targeted and inferred by the scheme. The efficacy of the proposed scheme is demonstrated through application to vibration data obtained in a structural dynamics experiment on a fibre-optic sensor simulated as a finite plate with uncertain boundary conditions at its edges. Results indicate that the method provides sound inference on the plate boundary conditions, which is validated through subsequent application of the method to multiple vibration datasets. Comparisons between appropriate forms of the metric function used in the scheme are also developed to highlight the effect of this element in the schemes convergence. [ABSTRACT FROM AUTHOR]

Stochastic mesoscale inhomogeneity of material properties and material symmetries are investigated in a 3D-printed material. The analysis involves a spatially-dependent characterization of the microstructure in 316 L stainless steel, obtained through electron backscatter diffraction imaging. These data are subsequently fed into a Voigt–Reuss–Hill homogenization approximation to produce maps of elasticity tensor coefficients along the path of experimental probing. Information-theoretic stochastic models corresponding to this stiffness random field are then introduced. The case of orthotropic fields is first defined as a high-fidelity model, the realizations of which are consistent with the elasticity maps. To investigate the role of material symmetries, an isotropic approximation is next introduced through ad-hoc projections (using various metrics). Both stochastic representations are identified using the dataset. In particular, the correlation length along the characterization path is identified using a maximum likelihood estimator. Uncertainty propagation is finally performed on a complex geometry, using a Monte Carlo analysis. It is shown that mechanical predictions in the linear elastic regime are mostly sensitive to material symmetry but weakly depend on the spatial correlation length in the considered propagation scenario. [ABSTRACT FROM AUTHOR]

This research paper presents a new Latin hypercube sampling method, aimed at enhancing its performance in quantifying uncertainty and reducing computation time. The new Latin hypercube sampling (LHS) method serves as a tool in reliability-based design optimization (RBDO). The quantification technique is termed LHSMDF (LHS with maximum diversity factor). The quantification techniques, such as Latin hypercube sampling (LHS), optimum Latin hypercube sampling (OLHS), and Latin hypercube sampling with maximum diversity factor (LHSMDF), are tested against mechanical components, including a circular shaft housing, a connecting rod, and a cantilever beam, to evaluate its comparative performance. Subsequently, the new method is employed as the basis of RBDO in the synthesis of a six-bar high-lift mechanism (HLM) example to enhance the reliability of the resulting mechanism compared to Monte Carlo simulation (MCS). The design problem of this mechanism is classified as a motion generation problem, incorporating angle and position of the flap as an objective function. The six-bar linkage is first adapted to be a high-lift mechanism (HLM), which is a symmetrical device of the aircraft. Furthermore, a deterministic design, without consideration of uncertainty, may lead to unacceptable performance during the manufacturing step due to link length tolerances. The techniques are combined with an efficient metaheuristic known as teaching–learning-based optimization with a diversity archive (ATLBO-DA) to identify a reliable HLM. Performance testing of the new LHSMDF reveals that it outperforms the original LHS and OLHS. The HLM problem test results demonstrate that achieving optimum HLM with high reliability necessitates precision without sacrificing accuracy in the manufacturing process. Moreover, it is suggested that the six-bar HLM could emerge as a viable option for developing a new high-lift device in aircraft mechanisms for the future. [ABSTRACT FROM AUTHOR]

Along with the rapid advancement of additive manufacturing technology, 3D-printed structures and materials have been successfully employed in various applications. Computer simulations of these structures and materials are often characterized by a vast number of spatial-varied parameters to predict the structural response of interest. Direct Monte Carlo methods are infeasible for uncertainty quantification and reliability assessment of such systems as they require a large number of forward model evaluations to obtain convergent statistics. To alleviate this difficulty, this paper presents a convolutional dimension-reduction method with knowledge reasoning-based loss regularization for surrogate modeling and uncertainty quantification of structures with high-dimensional spatial uncertainties. To manage the inherent high-dimensionality, a deep convolutional dimension-reduction network (ConvDR) is constructed to transform the spatial data into a low-dimensional latent space. In the latent space, knowledge reasoning is formulated as a form of loss regularization, and evolutionary algorithms are employed to train both the ConvDR network and a linear regression model as surrogate models for predicting the response of interest. 2D structures with spatial-variated material compositions are used to demonstrate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Tsunamis propagate over long distances and can cause widespread damage even after crossing ocean basins. Prediction of tsunamis in distant areas based on observations near their sources is critical to mitigating damage. In recent years, the accuracy of numerical models of trans‐oceanic tsunami propagation has improved significantly due to the incorporation of effects such as the solid earth response to tsunami loading and wave dispersion. However, these models are computationally expensive and have not been fully utilized for real‐time prediction. Here, we derive the adjoint operator for the linear set of equations describing deep‐ocean tsunami propagation and show how a pre‐computed database of adjoint states can achieve rapid synthesis of tsunami waveforms at target sites from nonpoint arbitrary tsunami sources. The adjoint synthesis method allows for an exhaustive parameter search for tsunami source estimation. A method for simultaneous inversion of fault geometry and slip distribution using adjoint synthesis with Sequential Monte Carlo method was proposed and applied to the 2012 Haida Gwaii earthquake tsunami. The influence of model accuracy and the amount of observed data on the estimation of tsunami sources and waveforms was examined. It was found that with a highly accurate propagation model, using only a limited amount of observed data produced source and waveform estimates very similar to the final models obtained with much larger data sets. The final inferred fault model involved megathrust slip distributed between the Haida Gwaii trench and the Queen Charlotte fault. The proposed method can also quantify the uncertainty of the waveform forecasts. Plain Language Summary: Tsunamis can propagate across the ocean for more than 10,000 km and cause damage even areas far from the source. By observing with new instruments and testing theories over the past decade, far‐reaching tsunamis can now be predicted with high accuracy with the consideration of the effects on the seawater compressibility, seafloor deformation due to tsunami loading, gravitational potential change, and Boussinesq dispersion. Reproducing these effects in numerical simulation has been shown to accurately predict tsunami waveforms at distant locations. However, this type of simulation is time‐consuming and has not been used for real‐time tsunami warnings. In this study, we propose a new waveform calculation method named adjoint synthesis. This method can compute waveforms at target points from an arbitrary tsunami source in short time by synthesizing a pre‐computed database. The database can be efficiently computed by adjoint equations. We also propose a method to simultaneously invert fault geometry and slip distribution for earthquake‐generated tsunamis using adjoint synthesis. A case study of the 2012 Haida Gwaii earthquake tsunami showed that source estimation by exhaustive parameter search can provide highly accurate waveform predictions and uncertainty ranges at distant locations from waveform data observed within 1 hr of the source origin time. Key Points: An exact reciprocity approach for linear deep ocean tsunami waveforms is established by defining a tsunami adjoint operatorA method for simultaneous estimation of fault geometry and slip distribution using a sequential Monte Carlo method is proposedExhaustive parameter search enabled by adjoint synthesis improves waveform prediction accuracy for trans‐oceanic tsunami [ABSTRACT FROM AUTHOR]

The high computational expense of peridynamic models remains a major limitation, hindering 'outer-loop' applications that require a large number of simulations, for example, uncertainty quantification. This contribution presents a framework that makes such computations feasible. By employing a Multilevel Monte Carlo framework, where the majority of simulations are performed using a coarse mesh, and performing relatively few simulations using a fine mesh, a significant reduction in computational cost can be realised, and statistics of structural failure can be estimated. The maximum observed speed-up factor is 16 when compared to a standard Monte Carlo estimator, thus enabling the efficient forward propagation of uncertain parameters in a computationally expensive peridynamic model. Furthermore, the multilevel method provides an estimate of both the discretisation error and sampling error, thereby improving confidence in numerical predictions. The performance of the approach is demonstrated through an examination of the statistical size effect in quasi-brittle materials. • First use of the Multilevel Monte Carlo method with a peridynamic model. • Two case studies examining the statistical size effect in quasi-brittle materials. • Maximum 16x speed improvement over standard Monte Carlo for presented case studies. • Efficient estimation of failure probabilities using a peridynamic model. • Provides an estimate of both the discretisation error and sampling error. [ABSTRACT FROM AUTHOR]

Reactive chromatography overcomes many disadvantages of conventional separation processes by improving yields and reduces costs by combining reaction and separation in a single operation. Model-based optimization is essential to realize industrial applications of this process. Parameters in the model must be estimated accurately, and evaluating the uncertainty of the model parameters is crucial. However, uncertainty quantification of model parameters has not been performed for reactive chromatography processes. In this study, we propose an approach to estimate the parameter uncertainty of reactive chromatography processes using Bayesian inference and parallel sequential Monte Carlo. As an example, the esterification synthesis of acetic acid and methanol catalyzed by a cation exchange resin was considered. Parameter estimation was performed using a reactive chromatography experiment and a non-reactive experiment in which only the products were injected. The results of the analysis showed that using both the reactive and non-reactive chromatography experimental data simultaneously improved the accuracy of the estimation. In addition, correlations between some parameters were revealed. [Display omitted] • Bayesian inference for reactive chromatography parameter estimation is performed. • Sequential Monte Carlo method is applied to estimate the parameter uncertainty. • Two types of experimental data are used for parameter estimation. • The parameter uncertainty is reduced by combining the two data sets. [ABSTRACT FROM AUTHOR]

Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one is interested in analyzing the stochastic response of the PDE subject to input uncertainty, which usually involves solving high-dimensional integrals of the PDE output over a sequence of stochastic variables. In practical computations, one typically needs to discretize the problem in several ways: approximating an infinite-dimensional input random field with a finite-dimensional random field, spatial discretization of the PDE using, e.g., finite elements, and approximating high-dimensional integrals using cubatures such as quasi--Monte Carlo methods. In this paper, we focus on the error resulting from dimension truncation of an input random field. We show how Taylor series can be used to derive theoretical dimension truncation rates for a wide class of problems and we provide a simple checklist of conditions that a parametric mathematical model needs to satisfy in order for our dimension truncation error bound to hold. Some of the novel features of our approach include that our results are applicable to nonaffine parametric operator equations, dimensionally truncated conforming finite element discretized solutions of parametric PDEs, and even compositions of PDE solutions with smooth nonlinear quantities of interest. As a specific application of our method, we derive an improved dimension truncation error bound for elliptic PDEs with lognormally parameterized diffusion coefficients. Numerical examples support our theoretical findings. [ABSTRACT FROM AUTHOR]

Coupled simulations of surface and variably saturated subsurface flow, termed integrated hydrologic models (IHMs), can provide powerful insights into the complex dynamics of watersheds. The system of governing equations solved by an IHM is non‐linear, making them a significant computational burden and challenging to accurately parameterize. Consequently, a large fraction of the IHM studies to date have been "numerical hypothesis testing" studies, but, as parallel computing continues to improve, IHMs are approaching the point where they might also be useful as predictive tools. For this to become reality, the predictive uncertainty of such highly parameterized simulations must be considered. However, uncertainty is seldom considered in the IHM literature, likely due to the long runtimes of the complex simulations. The questions considered herein are how much uncertainty is there in an IHM for a common watershed simulation scenario, and how likely is it that any one realization of a system will give the same relative change as any other due to a perturbation in recharge? A stochastic ensemble of 250 permeability field realizations was used to show that uncertainty in a high‐mountain headwaters systems is dominated by the subsurface. Recharge perturbation scenarios echo these results, but the uncertainty of changes in streamflow or groundwater pressure heads were significantly smaller than the uncertainty in their base‐case values. The main finding is that IHMs do provide confident, predictive estimates of relative changes in watersheds, even when uncertainty in specific simulation outputs may be high. Plain Language Summary: Watershed simulations that consider stream‐groundwater interactions require the specification of lots of parameters to define the model but there is often little data to base those parameters on. Consequently, simulation results have uncertainty and if it is not quantified then any predictions made by these models have no "plus‐or‐minus" factors, giving an illusion of high confidence. The catch is that quantifying uncertainty is computationally expensive, which is why it is seldom done, yet at some point the uncertainty must be explored if these models are to be used for predictions. The work in this paper assesses the variability of predictions for a "typical" watershed simulation under three different rainfall scenarios using an ensemble of 250 random versions of the system. The results show that groundwater has higher variability than surface flows, meaning the latter is simulated with higher confidence. However, an important finding is that the relative changes due to the changes in the rainfall were generally consistent across the ensemble. The main point is that even with limited confidence in what an output will be, the relative change of that output (e.g., a 10% increase in recharge increases streamflow by 10%) can likely be inferred with much greater confidence. Key Points: Ensemble simulations of coupled surface‐subsurface flows in a high mountain watershed were performed using the numerical model ParFlowUncertainty throughout the simulation domain was significant and was dominated by the subsurface domainRelative changes in the surface‐ and groundwater values due to a perturbation had smaller confidence intervals than the base‐case values [ABSTRACT FROM AUTHOR]

We develop a probabilistic approach to map parametric uncertainty to output state uncertainty in first‐order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two‐phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from incomplete descriptions of either porosity field, injection flux, or both. This uncertainty leads to spatiotemporal uncertainty in the saturation field. Given information about spatial/temporal statistics of spatially correlated heterogeneity, we leverage the method of distributions to derive deterministic equations that govern the evolution of pointwise cumulative distribution functions (CDFs) of saturation for a vertical reservoir, while handling the manipulation of multiple shocks arising due to buoyancy forces. Unlike the Buckley‐Leverett equation, the equation describing the fine‐grained CDF is linear in space and time. Ensemble averaging of the fine‐grained CDF results in the CDF of saturation. Thus, we give routes to circumventing the computational cost of Monte Carlo simulations (MCS), while obtaining a pointwise description of the saturation field. We conduct a set of numerical experiments for one‐dimensional transport, and compare the obtained saturation CDFs, against those obtained using MCS as our reference solution, and the statistical moment equation method. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties, that is, standard deviation and correlation length of the underlying random fields, whereas the corresponding low‐order statistical moment equations significantly deviate from the MCS results, except for very small values of standard deviation and correlation length. Key Points: Our cumulative distribution function method provides pointwise probabilistic descriptions of two‐phase transport, handling multiple shocks arising due to buoyancy forcesOur results match Monte Carlo (MC) simulations and statistical moment equations for a wide range of statistical properties of the random inputsThe numerical comparisons confirm the robustness and efficiency of our method over MC simulations and statistical moment equations [ABSTRACT FROM AUTHOR]

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer. Firstly, the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel. Subsequently, the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform. Furthermore, the probability density evolution method (PDEM) is developed to high-dimensional uncertainty quantification of projectile motion. The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation (MCS). Finally, the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed. The results show that the disturbance of the pitch angular, pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle, and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle. [ABSTRACT FROM AUTHOR]

Bayesian physics-informed neural networks (B-PINNs) have emerged as an efficient tool for uncertainty quantification in partial differential equations (PDEs). However, their applicability has been limited to accounting for noisy data. They fail to effectively address the uncertainty arising from the randomness of physical parameters in stochastic PDEs (SPDEs). To this end, we propose a novel Bayesian deep learning framework designed for uncertainty quantification in SPDE problems. We model the solution of an SPDE using a Bayesian neural network (BNN), where the posterior distribution of the parameters is constructed by Bayes' rule. We incorporate the governing physical laws into the likelihood distribution through automatic differentiation and estimate the likelihood using a Gaussian mixture model. To effectively learn the posterior distribution of BNN parameters, we employ a Hamiltonian Monte Carlo method, an efficient method for high-dimensional sampling. We propose a parallel algorithm to mitigate the high computational cost associated with the Hamiltonian Monte Carlo, thereby enhancing its efficiency. We provide numerical examples for both forward and inverse SPDE problems to demonstrate the effectiveness of our proposed method for uncertainty quantification in SPDEs. Notably, it is demonstrated that the computational cost is almost unaffected by the number of BNN parameters and the random dimension of the problem, underscoring its computational efficiency. [ABSTRACT FROM AUTHOR]

The gust factor commonly is used in wind engineering community to convert mean wind speeds into gusty winds, which exhibit significant variability in real observations of typhoon winds. This study proposes a probabilistic gust factor model that accounts for uncertainties of wind speed statistics. The statistical characteristics of wind speed from nine typhoons, including the mean, standard deviation, skewness, kurtosis, power spectral density (PSD) parameter, peak factor, and gust factor, were examined. The effects of nonstationary characteristics in terms of time-varying mean wind speed and non-Gaussian attributes of fluctuating winds on the gust factor are discussed. These wind speed statistics were incorporated into a non-Gaussian moment-based translation model to perform the Monte Carlo simulation of peak factor and gust factor. The simulation results for different gust durations were juxtaposed with observations to substantiate the accuracy of the probabilistic model. Subsequently, a standardization framework for estimating site-specific probabilistic gust factor curves was developed. This approach was applied to determine the gust typhoon wind speed hazard curve at a real bridge site with flat open terrain. The present model enables the consideration of gust factor dispersion to achieve a probabilistic gust wind hazard curve and facilitate the development of performance-based wind engineering. [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]

Urban canopy models simplify urban morphology and physical processes such as radiative transfer to calculate the urban surface energy balance as a lower boundary condition for atmospheric models at low computational cost. The present study uses a reference model of urban radiative transfer based on the Monte Carlo method, which solves the radiative transfer equation by taking into account the complex geometry of buildings and vegetation. Procedurally-generated urban morphologies similar to the local climate zones (LCZ) are studied to cover the variety of urban forms that exist globally. The uncertainties arising from the simplification of the urban morphology as an infinitely-long street canyon or a regular array of square blocks are quantified. In addition, uncertainties due to the neglect of specular or spectral material reflectivities and the involved atmosphere are investigated. It is found that for all LCZ, the street canyon and block morphologies lead to a systematic overestimation (underestimation) of the fraction of solar radiation absorbed by the walls (ground). The neglect of pitched roofs has a strong influence on the simulated urban solar radiation budget for low solar elevation angles. Neglecting the spectral reflectivity of urban materials does not lead to relevant uncertainties in the broadband radiative fluxes. Specularly reflecting windows only change the urban solar radiation budget for a central business district morphology with a high glazing ratio. The participating atmosphere can strongly influence the urban terrestrial radiation budget, especially for high-rise districts. Future urban canopy models should therefore improve the realism of the urban morphology, and consider a participating atmosphere for the calculation of terrestrial radiation. [ABSTRACT FROM AUTHOR]

A reservoir is formed due to geologic deposition processes and is not created randomly. However, because of subsurface complexity and limited data, there are many uncertainties in reservoir characterization. Uncertainties can be reduced by gathering more data and/or employing improved technology and scientific methods. Under uncertainty and risk, uncertainty analysis should be performed for investigational analyses as well as decision-making. The main focus of uncertainty analysis in reservoir characterization and management should be to understand what needs to be known and what can be known. Therefore, there are several reservoir parameters’ uncertainties and their quantitative influence on cumulative oil production and water cut were studied. In this paper, sensitivity analysis and uncertainty quantification were conducted for several parameters to study their effect on cumulative oil production. The Monte Carlo method was used to carry out the uncertainty quantification. In this study, we examined two methods which are the Monte Carlo simulation using a Reservoir simulator (MCRS) and the Monte Carlo simulation using a Proxy (MCP) to overcome the issue of the high number of simulation runs requirement and to reduce time consumption. The results showed that The MCP method is a very useful and powerful tool to conduct the uncertainty quantification than the MCRS because the MCP performs the objective function with extremely less time-consuming and very accurate and identical results compared to the results of the MCRS method. The results of uncertainty quantification for production forecast show there is a low risk due to the small gap difference between the P50 and P90. While the sensitivity analysis results showed that the oil-water-contact depth is the dominant parameter that affects cumulative oil production while porosity is the less influential parameter. [ABSTRACT FROM AUTHOR]

Stochastic variations of the operation conditions and the resultant variations of the aerodynamic performance in Low-Pressure Turbine (LPT) can often be found. This paper studies the aerodynamic performance impact of the uncertain variations of flow parameters, including inlet total pressure, inlet flow angle, and turbulence intensity for an LPT cascade. Flow simulations by solving the Reynolds-averaged Navier–Stokes equations, the SST turbulence model, and γ − R e ˜ θ t transition model equations are first carried out. Then, a Gaussian process (GP) based on an adaptive sampling technique is introduced. The accuracy of adaptive GP (ADGP) is proven to be high through a function experiment. Using ADGP, the uncertainty propagation models between the performance parameters, including total pressure-loss coefficient, outlet flow angle, Zweifel number, and the uncertain inlet flow parameters, are established. Finally, using the propagation models, uncertainty quantifications of the performance changes are conducted. The results demonstrate that the total pressure-loss coefficient and Zweifel number are sensitive to uncertainties, while the outlet flow angle is almost insensitive. Statistical analysis of the flow field by direct Monte Carlo simulation (MCS) shows that flow transition on the suction side and viscous shear stress are rather sensitive to uncertainties. Moreover, Sobol sensitivity analysis is carried out to specify the influence of each uncertainty on the performance changes in the turbine cascade. [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]

Slope stabilities are mainly designed using the conventional design approach (CDA), where the limit equilibrium methods (LEMs) are performed. Fellenius and Bishop's simplified methods are the two commonly LEMs adopted as recommended in most design codes. In the design process of CDA, the safety factors (FS) of slopes are checked with specified FSs to ensure stability. The CDA has inherent drawbacks because the design process does not account for uncertainties. Moreover, different LEMs using different assumptions to solve the safety factors might include some amount orders of approximations. This study conducts probabilistic analyses, i.e., Monte Carlo simulations (MCSs) and uncertainty quantification, to obtain insights into the two LEMs applied to clay and sand slopes. The results reveal that the reliability indexes (RIs) obtained from the two LEMs-based MCSs are relatively identical for the same slope. Concerning the soil types, however, the RIs of the clay slope are significantly lower than those estimated for the sand slope, regardless of the LEMs used. The uncertainty quantifications for the clay slopes reveal that the two LEMs have relatively similar bias factors regarding FSs. Nevertheless, using the Fellenius method underestimates the probabilistic safety (about 17% in terms of the mean of FSs) for the sand slope compared to Bishop's simplified method. Moreover, the coefficients of variation of FS obtained from the clay slope are consistently larger than those from the sand slope. These observations imply that the clay slope is more uncertain than the sand slope, and the Fellenius method results in lower FSs for sand slopes. Therefore, the FSs specified in the design codes should be connected to the soil type or the LEMs used to achieve the same probabilistic safety levels. Finally, the equivalent FSs associated with a RI of 1.75 are derived for each slope and each LEM used. [ABSTRACT FROM AUTHOR]

Uncertainties are essential, yet often neglected, information for evaluating the reliability in forest carbon balance projections used in national and regional policy planning. We analysed uncertainties in the forest net biome exchange (NBE) and carbon stocks under multiple management and climate scenarios with a process-based ecosystem model. Sampled forest initial state values, model parameters, harvest levels and global climate models (GCMs) served as inputs in Monte Carlo simulations, which covered forests of the 18 regions of mainland Finland over the period 2015–2050. Under individual scenarios, the results revealed time- and region-dependent variability in the magnitude of uncertainty and mean values of the NBE projections. The main sources of uncertainty varied with time, by region and by the amount of harvested wood. Combinations of uncertainties in the representative concentration pathways scenarios, GCMs, forest initial values and model parameters were the main sources of uncertainty at the beginning, while the harvest scenarios dominated by the end of the simulation period, combined with GCMs and climate scenarios especially in the north. Our regionally explicit uncertainty analysis was found a useful approach to reveal the variability in the regional potentials to reach a policy related, future target level of NBE, which is important information when planning realistic and regionally fair national policy actions. [ABSTRACT FROM AUTHOR]

Uncertainty quantification is a critical aspect of distribution logistics, particularly unpredictable travel times caused by traffic congestion and varying transportation conditions. This paper explores the modeling of uncertainty in dealing with travel times in the context of distribution logistics using the collocation method. First, we employ Monte Carlo simulations to assess the efficacy of the collocation method in modeling the variability and uncertainty associated with travel times. Second, we implement the collocation method in Casablanca, Morocco, a city renowned for its extensive distribution logistics operations and its dynamic traffic. Four distinct scenarios are considered: morning peak, inter-peak, evening peak, and off-peak periods. Our study explores two scenarios: one with recurrent congestion, representing typical daily conditions, and the other with unpredictable uncertainties in travel times, accounting for unexpected events that may occur during a distribution day. Our research findings enhance our understanding of the probabilistic nature of travel times in distribution logistics. This knowledge provides valuable insights applicable to both routine situations with recurrent congestion and non-recurrent congestion. The results' findings contribute to a better understanding of the probabilistic nature of travel times in distribution logistics, offering valuable insights for optimizing route planning and scheduling. [ABSTRACT FROM AUTHOR]

Swift hardening law is one of the widely used phenomenological model to describe the stress–strain behavior in sheet metal forming simulations. In the present study, a statistical approach was used to investigate the effect of the variation in material model parameters on estimated values of the stress–strain data obtained using Swift hardening law. This estimation employed values of the Swift hardening law parameters as reported in the literature and those from three uniaxial tensile tests conducted in this study. Uncertainties in the flow stress were estimated using Monte Carlo (MC) simulations. A detailed sensitivity analysis was performed to determine the most sensitive parameter influencing the flow stress estimation. It was found that the sensitivity coefficients of the Swift hardening parameters are dependent on the true plastic strain. At lower plastic strains, ϵ 0 was found to be most sensitive parameter whereas at larger pre-strains K was observed to be the critical parameter affecting the flow stress estimation. Further, computed hardening curves were used to simulate the deformation in hole expansion tests (HET) of dual phase steel (DP600) steel specimens using an explicit finite element analysis (FEA) technique. The effects of the material property variation on the thinning rate of the sheet with punch displacement were estimated with a mean (μ ) and standard deviations (σ ) for determining (± 1 ± 2 σ ) statistical limits. FEA predictions were compared with measured data obtained from HET conducted using specimens with holes fabricated with both drilling and boring processes. A reasonable agreement was achieved. Furthermore, the experimental values of the final sheet thicknesses were found to lie within the statistical limits using finite element simulations. [ABSTRACT FROM AUTHOR]

In the present work, a stochastic framework, which combines the well‐recognized linear damage rule (LDR) and the uncertainty of material properties under constant amplitude loading, is proposed to improve the accuracy in prediction of remaining fatigue life. The uncertainty quantification approach based on parametric statistics is employed together with the Monte‐Carlo simulation method for modeling the randomness of remaining fatigue life. The impact of several commonly‐used parametric statistics is investigated, and the pertinent one is identified utilizing the Kullback‐Leibler divergence. The proposed framework is validated through the use of experimental fatigue life data under two‐step loading test. [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]

Flexible metal–organic frameworks (flexible MOFs) are considered promising adsorbents for CO2 capture, some of which have sigmoidal isotherm shapes that allow adsorption and desorption operations within a narrow partial pressure range. Nevertheless, modeling of adsorption processes employing flexible MOFs remains a challenge due to the unique isotherm shapes and kinetics. In this work, a Bayesian estimation framework is applied sequentially to handle two experimental data sets: isotherm and breakthrough measurements. The computational challenge for estimating the isotherm and kinetic parameters from the isotherm measurements and breakthrough experiments is resolved by Markov chain and sequential Monte Carlo methods. The uncertainties of the model parameters are obtained as probability distributions. [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]

This paper studies a new and highly efficient Markov chain Monte Carlo (MCMC) methodology to perform Bayesian inference in low-photon imaging problems, with particular attention given to situations involving observation noise processes that deviate significantly from Gaussian noise, such as binomial, geometric, and low-intensity Poisson noise. These problems are challenging for many reasons. From an inferential viewpoint, low-photon numbers lead to severe identifiability issues, poor stability, and high uncertainty about the solution. Moreover, low-photon models often exhibit poor regularity properties that make efficient Bayesian computation difficult, e.g., hard nonnegativity constraints, nonsmooth priors, and log-likelihood terms with exploding gradients. More precisely, the lack of suitable regularity properties hinders the use of state-of-the-art Monte Carlo methods based on numerical approximations of the Langevin stochastic differential equation (SDE), as both the SDE and its numerical approximations behave poorly. We address this difficulty by proposing an MCMC methodology based on a reflected and regularized Langevin SDE, which is shown to be well-posed and exponentially ergodic under mild and easily verifiable conditions. This then allows us to derive four reflected proximal Langevin MCMC algorithms to perform Bayesian computation in low-photon imaging problems. The proposed approach is demonstrated with a range of experiments related to image deblurring, denoising, and inpainting under binomial, geometric, and Poisson noise. [ABSTRACT FROM AUTHOR]

Surrogate models have been used to emulate mathematical simulators of physical or biological processes for computational efficiency. High‐speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation must repeat over many randomly sampled input points (aka the Monte Carlo method). A simulator can be so computationally intensive that UQ is only feasible with a surrogate model. Recently, deep neural network (DNN) surrogate models have gained popularity for their state‐of‐the‐art emulation accuracy. However, it is well‐known that DNN is prone to severe errors when input data are perturbed in particular ways, the very phenomenon which has inspired great interest in adversarial training. In the case of surrogate models, the concern is less about a deliberate attack exploiting the vulnerability of a DNN but more of the high sensitivity of its accuracy to input directions, an issue largely ignored by researchers using emulation models. In this paper, we show the severity of this issue through empirical studies and hypothesis testing. Furthermore, we adopt methods in adversarial training to enhance the robustness of DNN surrogate models. Experiments demonstrate that our approaches significantly improve the robustness of the surrogate models without compromising emulation accuracy. [ABSTRACT FROM AUTHOR]

The effects of inflow variations due to the working environment and flight attitude changes on turbomachines are considerable in the real world. Nevertheless, uncertainty quantification can be adopted to assess mean performance changes and perform the aerodynamic shape design as well as optimization. Thus, an uncertainty quantification method of adaptive sparse grid collocation (ASGC) was first introduced to address the inflow uncertainties’ effect issue effectively and accurately. Then, ASGC was utilized to evaluate the impacts of inlet incidence perturbations at different perturbation scales and reference inflow Mach numbers on the aerodynamic performance of a controlled diffusion cascade. The results showed that compared with the Monte Carlo simulation and static sparse gird collocation, the statistical accuracy and response accuracy of ASGC were maintained, and meanwhile its model construction efficiency was significantly improved because of the nested adaptive sampling feature. Under the perturbations of inlet incidences with high reference incidences, the mean aerodynamic loss always aggravates. The changes in aerodynamic loss nonlinearly depend on the inlet incidence perturbations, and the nonlinear dependence becomes greater when the perturbation scale. expands. At the same perturbation scale, the nonlinear dependence on the inlet incidence perturbations is further enhanced when the reference inflow Mach number rises. Finally, uncertainty quantification of the flow field revealed that the fluctuation of flow accelerations at the leading edge plays a fundamental role in determining the uncertainty of the aerodynamic loss. [ABSTRACT FROM AUTHOR]

The flood peak is commonly estimated using the rational method for the design of hydraulic structures. The method is mainly used in a deterministic context. However, there is often uncertainty in flood predictions, which should be incorporated in the design of mitigation schemes. This research proposes a methodology to cope with uncertainty in the rational method via the application of a stochastic framework. Data from 158 storms, recorded in the period 1984–1987 in 19 subbasins in the southwestern part of Saudi Arabia, were used to implement the proposed methodology. A tri-variate log-normal probability density function was used to model the joint relationship between the rational method parameters. The model considered the parameters as random variables. The uncertainty in the rainstorms was represented by intensity or depth; the uncertainty in basin delineation (due to the use of different digital elevation model resolution) was represented by the basin area; and the uncertainty in the land use/land cover was represented by the runoff coefficient. The Monte Carlo method was used to generate realizations of the peak flow and runoff volume with 95% and 99% confidence levels from the input parameters. Although the correlation between the parameters was weak, the model was capable of simulating the rational model parameters and estimating the peak flow and runoff volume relatively well, and the generated realizations fell within the confidence levels, except for a few marginal cases. The model can be used to generate peak flows and the associated confidence limits in ungauged basins from the statistics of the input parameters using the equations developed in this study. [ABSTRACT FROM AUTHOR]

Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin and stochastic collocations methods. This work is concerned with a nonintrusive generalization of the adaptive Galerkin finite element method with residual-based error estimation. It combines the nonintrusive character of a randomized least squares method with the a posteriori error analysis of stochastic Galerkin methods. The proposed approach uses the variational Monte Carlo method to obtain a quasi-optimal low-rank approximation of the Galerkin projection in a highly efficient hierarchical tensor format. We derive an adaptive refinement algorithm which is steered by a reliable error estimator. Opposite to stochastic Galerkin methods, the approach is easily applicable to a wide range of problems, enabling a fully automated adjustment of all discretization parameters. Benchmark examples with affine and (unbounded) lognormal coefficient fields illustrate the performance of the nonintrusive adaptive algorithm, showing the expected convergence rates of single-level strategies. [ABSTRACT FROM AUTHOR]

The dynamic responses of bridges with uncertain parameters under moving loads were analyzed, and a polynomial dimensional decomposition method for the analysis of structural responses induced by moving loads was proposed for the first time. The uncertain parameters were regarded as independent random variables, and the random response function about these uncertain parameters was constructed. The dimensional decomposition of the function was further performed with a group of component functions with a gradually increasing number of variables, and the approximate expressions of the component functions were derived through the Fourier polynomial expansion. Then, the expansion coefficients were efficiently calculated through the introduction of the dimension-reduction integration method. The numerical examples give response estimation of bridges with uncertain parameters under moving loads, which in comparison with those from the Monte-Carlo simulation, verify the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Based on polynomial dimensional decomposition (PDD), a novel method for analysing nonstationary random vibration of structures with uncertain parameters is proposed in this paper. The uncertain structural parameters are assumed to be independent random variables, with certain types of probability distributions; thus, the nonstationary random vibration responses of the structures become stochastic functions of these uncertain parameters. A dimensional decomposition and Fourier expansion were applied to calculate the statistical characteristics of the nonstationary random vibration responses of the structures. To calculate the conditional power spectral density (CPSD) and conditional standard deviation (CSD) of the nonstationary random vibration responses, CPSD and CSD were explicitly expressed using expansion coefficients and polynomial basis. Subsequently, the probability distributions of the structural responses can be effectively calculated in terms of these explicit expressions. Dimension‐reduction integration and Gauss numerical integration were applied to calculate expansion coefficients. The validity of the proposed method was verified by numerical examples, including a single‐degree‐of‐freedom system and a multi‐degree‐of‐freedom system (reinforced concrete shear wall). The results indicate that the proposed method is as accurate as Monte Carlo simulation (MCS), whereas the proposed method requires considerably smaller number of nonstationary random vibration analyses than MCS. Moreover, the nonstationary random vibration analysis of a long‐span cable‐stayed bridge demonstrates that the proposed method is feasible for quantifying the uncertainties of the nonstationary random vibration responses of complex engineering structures with uncertain parameters. [ABSTRACT FROM AUTHOR]

Purpose: In the present study, vibration analyses of cracked plates having uncertain input parameters are investigated by developing a probabilistic methodology. The crack length, crack location, the module of elasticity and material density of the plate are considered as random variables. Methods: In this paper, a non-intrusive Chaotic radial basis function computational scheme is developed, and it is combined with an enriched element-free Galerkin approach to obtain the statistics of the natural frequencies of the cracked plates. Results: Two types of moderately thick cracked plates, including the internally cracked and side-cracked plates are considered and the results of the developed computational scheme for obtaining the statistics of natural frequencies of the system are compared with those of the Monte Carlo simulation. Also, through various numerical results, the effects of uncertain parameters are investigated on the vibration behavior of cracked plates. Conclusion: It is shown that the developed method produces accurate results with significantly less computing time compared with the Monte Carlo simulation. Besides, it is indicated that the statistics of the fundamental natural frequency of the internally cracked plate is reduced by increasing the mean value of the crack length and it is increased by increasing the coefficients of variation of the crack position. It is shown that increasing the uncertainty in the crack length has a small influence on the mean value of the fundamental frequency, while it has an important impact on the variance of the vibration. In addition, it is demonstrated that the uncertainty parameters can importantly change the shape of the probability distribution of the plate natural frequencies. Furthermore, it is seen that, the mean value and the variance of the fundamental natural frequency of side-cracked plates are slightly affected by increasing the coefficient of variation of the side crack position. [ABSTRACT FROM AUTHOR]

Silicon carbide fiber and silicon carbide matrix (SiCf/SiCm) tubes produced through the chemical vapor infiltration process have become a candidate cladding material in nuclear applications. The performance of this composite is influenced by many variables such as braiding angle, porosity, material properties, etc., which vary over a range of values due to the inherent fluctuations in the manufacturing process. In this study, the variability in elastic constants of SiCf/SiCm composite has been quantified through multiscale finite element (FE) simulations, variable screening, and high-fidelity surrogate modeling. The key variables dominantly affecting the elastic constants of SiCf/SiCm tubes were identified using global sensitivity analysis. A surrogate to the high-fidelity FE-based model was used in Monte Carlo simulations to generate a hundred thousand samples from which the uncertainty in elastic constants was assessed. It turned out that the coefficient of variation was less than 10%. [ABSTRACT FROM AUTHOR]

In uncertainty quantification, the quantity of interest is usually the statistics of the space and/or time integration of system solution. In order to reduce the computational cost, a Bayes estimator based on multilevel Monte Carlo (MLMC) is introduced in this paper. The cumulative distribution function of the output of interest, that is, the expectation of the indicator function, is estimated by MLMC method instead of the classic Monte Carlo simulation. Then, combined with the corresponding probability density function, the quantity of interest is obtained by using some specific quadrature rules. In addition, the smoothing of indicator function and Latin hypercube sampling are used to accelerate the reduction of variance. An elliptic stochastic partial differential equation is used to provide a research context for this model. Numerical experiments are performed to verify the advantage of computational reduction and accuracy improvement of our MLMC-Bayes method. [ABSTRACT FROM AUTHOR]