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The failure of overhead transmission lines in the United States can lead to significant economic losses and widespread blackouts, affecting the lives of millions. This study focuses on analyzing the failure of transmission lines, specifically considering the effects of wind, ambient temperature, and current demands, incorporating minimal and significant pre-existing damage. We propose a multiphysics framework to analyze the transmission line failures across sensitive and affected states of the United States, integrating historical data on wind and ambient temperature. By combining numerical simulation with historical data analysis, our research assesses the impact of varying environmental conditions on the reliability of transmission lines. Our methodology begins with a deterministic approach to model temperature and damage evolution, using phase-field modeling for fatigue and damage coupled with electrical and thermal models. Later, we adopt the probability collocation method to investigate the stochastic behavior of the system, enhancing our understanding of uncertainties in model parameters, conducting sensitivity analysis to identify the most significant model parameters, and estimating the probability of failures over time. This approach allows for a comprehensive analysis of factors affecting transmission line reliability, contributing valuable insights into improving power line's resilience against environmental conditions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to conduct a thorough investigation of a stochastic eddy-current testing problem, when the geometric parameters of the system under study are characterized by uncertainty. Focusing on the case of subsurface defect detection, we devise reliable surrogates for the quantities of interest (QoI) based on the principles of the generalized polynomial chaos (PC) and using the orthogonal matching pursuit (OMP) solver to promote sparsity in the approximate models. In addition, a variance-based approach is implemented for the sequential construction of the necessary sample set, enabling more accurate estimation of the statistical metrics without imposing additional computational overhead. Apart from quantifying the inherent uncertainty, a sensitivity analysis is performed that assesses the impact of each geometric variable on the QoI, via the computation of Sobol indices. The efficiency of the OMP-PC algorithm is demonstrated in two variants of the subsurface-discontinuity problem, yielding at the same time useful conclusions regarding the properties of the stochastic outputs. [ABSTRACT FROM AUTHOR]

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There is uncertainty in the results of any mathematical model due to different reasons. It is important to estimate this uncertainty. Sensitivity analysis is commonly used to estimate how the changes in the input parameters affect the solutions of the model. In this paper, we discuss different ways of performing local and global sensitivity analyses and apply them to two models: an epidemic model and a new myocardial infarction model, both based on ordinary differential equations. The first model is a simple model used to explain the ideas, while the second one shows how to apply them to a model with more state variables and parameters. We find that if the parameters are not accurately known, local sensitivity analysis can be misleading and that global sensitivity methods that sample the whole parameter space, varying all the values of the parameters at the same time, are the most reliable. We also show how the sensitivity analysis results can be used to determine the uncertainty in the results of the model. We present numerical simulations. [ABSTRACT FROM AUTHOR]

This article introduces and formalizes a novel stochastic method that combines inverse simulation with the theory of generalized Polynomial Chaos (gPC) to solve and study inverse problems under uncertainty in energy system design applications. The method is particularly relevant to design tasks where only a deterministic forward model of a physical system is available, in which a target design quantity is an input to the model that cannot be obtained directly, but can be quantified reversely via the outputs of the model. In this scenario, the proposed method offers an analytical and direct approach to invert such system models. The method puts emphasis on user-friendliness, as it enables its users to conduct the inverse simulation under uncertainty directly in the gPC domain by redefining basic algebra operations for computations. Moreover, the method incorporates an optimization-based approach to integrate supplementary constraints on stochastic quantities. This feature enables the solution of inverse problems bounding the statistical moments of stochastic system variables. The authors exemplify the application of the proposed method with proof-of-concept tests in energy system design, specifically performing uncertainty quantification and sensitivity analysis for a Multi-Energy System (MES). The findings demonstrate the high accuracy of the method as well as clear advantages over conventional sampling-based methods when dealing with a small number of stochastic variables in a system or model. However, the case studies also highlight the current limitations of the proposed method such as slow execution speed due to the optimization-based approach and the challenges associated with, for example, the curse of dimensionality in gPC. [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]

This research introduces a novel global sensitivity analysis (GSA) framework for agent-based models (ABMs) that explicitly handles their distinctive features, such as multi-level structure and temporal dynamics. The framework uses Grassmannian diffusion maps to reduce output data dimensionality and sparse polynomial chaos expansion (PCE) to compute sensitivity indices for stochastic input parameters. To demonstrate the versatility of the proposed GSA method, we applied it to a non-linear system dynamics model and epidemiological and economic ABMs, depicting different dynamics. Unlike traditional GSA approaches, the proposed method enables a more general estimation of parametric sensitivities spanning from the micro level (individual agents) to the macro level (entire population). The new framework encourages the use of manifold-based techniques in uncertainty quantification, enhances understanding of complex spatio-temporal processes, and equips ABM practitioners with robust tools for detailed model analysis. This empowers them to make more informed decisions when developing, fine-tuning, and verifying models, thereby advancing the field and improving routine practice for GSA in ABMs. [ABSTRACT FROM AUTHOR]

A novel and robust slope stability evaluation method based on energy method and radial slices method (RSM) is proposed and validated in terms of strength parameter sensitivity and determination of the critical sliding surface. The sensitivity analysis shows that the deviation from the limit equilibrium method (LEM) does not exceed 1.5%, demonstrating the feasibility of the proposed method. Different from LEM, the proposed framework gets functional enhancements: (1) This method considers the failure mode of the slope as a combination of translation and rotation, which is more in line with the actual monitoring results; (2) if the virtual displacement is regarded as a variable, the effect of accumulated displacement on slope stability can be studied; (3) if the factor of safety (FOS) for the slope is less than 1, this method can be extended to analyze movement of landslide mass after instability using the energy balance. Then, the proposed framework is applied to the 1963 Vajont event and Xinhua event to analyze the slope stability at the changes of reservoir water level and the dynamics after instability. Comparing slopes with different deformation patterns in calculating stability, the paper finds that permeability is the key to understanding the deformation response and summarizes the failure mechanism. For 1963 Vajont landslide, the proposed framework calculates the maximum velocity of the intermediate section to be 21.51 m/s, which is in general agreement with the inference by Hendron and Patton (Eng Geol 24:475–491, 1987), and superior to Zaniboni and Tinti (Nat Hazards 70:567–592, 2014)'s calculation of less than 20 m/s. Through research and application, the superiority of the proposed framework in analyzing slope hazards is shown. [ABSTRACT FROM AUTHOR]

This study presents a data‐driven approach to quantify uncertainties in the ionosphere‐thermosphere (IT) system due to varying solar wind parameters (drivers) during quiet conditions (Kp < 4) and fixed solar radiation and lower atmospheric conditions representative of 16 March 2013. Ensemble simulations of the coupled Whole Atmosphere Model with Ionosphere Plasmasphere Electrodynamics (WAM‐IPE) driven by synthetic solar wind drivers generated through a multi‐channel variational autoencoder (MCVAE) model are obtained. Applying the polynomial chaos expansion (PCE) technique, it is possible to estimate the means and variances of the QoIs as well as the sensitivities of the QoIs with regard to the drivers. Our results highlight unique features of the IT system's uncertainty: (a) the uncertainty of the IT system is larger during nighttime; (b) the spatial distributions of the uncertainty for electron density and zonal drift at fixed local times present 4 peaks in the evening sector, which are associated with the low‐density regions of longitude structure of electron density; (c) the uncertainty of the equatorial electron density is highly correlated with the uncertainty of the zonal drift, especially in the evening sector, while it is weakly correlated with the vertical drift. A variance‐based global sensitivity analysis suggests that the IMF Bz plays a dominant role in the uncertainty of electron density. A further discussion shows that the uncertainty of the IT system is determined by the magnitudes and universal time variations of solar wind drivers. Its temporal and spatial distribution can be modulated by the average state of the IT system. Plain Language Summary: The ionosphere‐thermosphere (IT) is affected by several different drivers, including solar irradiance, geomagnetic activity, and tides and waves from the lower atmosphere. These drivers can interact with each other through multiple dynamic or electrodynamics processes and lead to day‐to‐day variability in the IT system. Quantifying the variability of the IT system due to these different external drivers and their relative importance is key to making a probabilistic prediction of the IT condition. We present a novel framework for uncertainty quantification and sensitivity analysis. Our results show that the solar wind drivers (IMF Bz, solar wind speed, and solar wind density) mainly lead to larger uncertainty in the low‐latitude and equatorial IT at nighttime. The sensitivity analysis shows the dominant role of IMF Bz polarity in the uncertainty of the IT system. Key Points: A novel VAE‐based data‐drive uncertainty representation and PCE‐based uncertainty propagation method is presentedSolar wind associated variability of the equatorial and low‐latitude ionosphere‐thermosphere is larger during nighttimeThe universal time variation of solar wind drivers and IMF Bz polarity is critical to the variability of equatorial IT system [ABSTRACT FROM AUTHOR]

The fate of nutrients and contaminants in fluvial ecosystems is strongly affected by the mixing dynamics between surface water and groundwater within the hyporheic zone, depending on the combination of the sediment's hydraulic heterogeneity and dune morphology. This study examines the effects of hydraulic conductivity stratification on steady‐state, two‐dimensional, hyporheic flows and solute residence time distribution. First, we derive an integral transform‐based semi‐analytical solution for the flow field, capable of accounting for the effects of any functional shape of the vertically varying hydraulic conductivity. The solution considers the uneven distribution of pressure at the water‐sediment interface (i.e., the pumping process) dictated by the presence of dune morphology. We then simulate solute transport using particle tracking. Our modeling framework is validated against numerical and tracer data from flume experiments and used to explore the implication of hydraulic conductivity stratification on the statistics and pdf of the residence time. Finally, reduced‐order models are used to enlighten the dependence of key residence time statistics on the parameters characterizing the hydraulic conductivity stratification. Key Points: A new integral transform‐based semi‐analytical solution for hyporheic flows in stratified sediments is provided and tested against dataThe impact of hydraulic conductivity stratification on residence time distribution and its statistics is quantitatively analyzedROMs are used to approximate key residence time statistics in the space of variability of parameters characterizing the conductivity profile [ABSTRACT FROM AUTHOR]

Computational knee models have shown that predicted condylar reactions are sensitive to the utilized ligament mechanical parameters. These models, however, are computationally expensive with multiple sources of uncertainty. Traditional uncertainty analysis using Monte-Carlo (MC) inspired methods are costly to perform. The purpose of this study was to use two example calibrated knee models to compare quasi-MC versus polynomial chaos expansion (PCE) sensitivity analyses of predicted condylar reactions that included uncertainty in the mechanical parameters of the ligaments. PCE was practically identical versus quasi-MC with 95% and 98% reductions in model evaluations for analyses with 10 and 6 uncertain variables, respectively. [ABSTRACT FROM AUTHOR]

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

The ambient solar wind plays a significant role in propagating interplanetary coronal mass ejections and is an important driver of space weather geomagnetic storms. A computationally efficient and widely used method to predict the ambient solar wind radial velocity near Earth involves coupling three models: Potential Field Source Surface, Wang‐Sheeley‐Arge (WSA), and Heliospheric Upwind eXtrapolation. However, the model chain has 11 uncertain parameters that are mainly non‐physical due to empirical relations and simplified physics assumptions. We, therefore, propose a comprehensive uncertainty quantification (UQ) framework that is able to successfully quantify and reduce parametric uncertainties in the model chain. The UQ framework utilizes variance‐based global sensitivity analysis followed by Bayesian inference via Markov chain Monte Carlo to learn the posterior densities of the most influential parameters. The sensitivity analysis results indicate that the five most influential parameters are all WSA parameters. Additionally, we show that the posterior densities of such influential parameters vary greatly from one Carrington rotation to the next. The influential parameters are trying to overcompensate for the missing physics in the model chain, highlighting the need to enhance the robustness of the model chain to the choice of WSA parameters. The ensemble predictions generated from the learned posterior densities significantly reduce the uncertainty in solar wind velocity predictions near Earth. Plain Language Summary: Predicting the ambient solar wind is an important component of space weather forecasting. We use advanced statistical techniques to analyze the important parameters in a widely used ambient solar wind model. The numerical results show that five specific parameters have the largest impact on solar wind model predictions near Earth and that these parameters can fluctuate considerably over time. The statistical results give us a deeper understanding of the limitations and potential improvements for enhancing the accuracy and reliability of ambient solar wind forecasts. Such an understanding is essential for mitigating the potential impacts of severe geomagnetic storms. Key Points: We quantify and reduce the parametric uncertainties of the Potential Field Source Surface, Wang‐Sheeley‐Arge (WSA), and Heliospheric Upwind eXtrapolation models on the ambient solar wind predictions near EarthGlobal sensitivity analysis shows that the five most influential parameters are all numerical parameters in the WSA modelThe posterior of the influential parameters changes greatly in time, motivating the investigation of the forecasting capability of WSA [ABSTRACT FROM AUTHOR]

The growing demand for aged care services has become a pressing challenge worldwide. However, the future changes in demand for aged care services and the corresponding socioeconomic consequences in rapidly aging societies are not yet adequately understood. To achieve a better understanding of the future demand for aged care services, this study provides a set of comprehensive projections of the scale of demand for aged care services and the associated economic burdens between 2010 and 2050 in the context of China. Using a research framework based on the life cycle approach and a modified Personal Social Services Research Unit model, the study projects that the size of Chinese elderly population (i.e., aged ≥ 60) demanding aged care services will grow considerably, reaching 127.4 million in 2050 and costing 2.6 trillion yuan (or 1.01% of Chinese gross domestic product). Home-/community-based care services will be the form of aged care most in demand by the 70.21 million Chinese elderly people in 2050, and the most needed types of aged care services will be feeding assistance. The results of the sensitivity analysis indicate that demand for and costs of aged care services are sensitive to the assumptions about patterns of elderly disability and the prices of aged care services. The projected growth in the future demand and costs of aged care services warrants more heightened attention from Chinese policymakers and providers of aged care services. The implications for other rapidly aging societies are also discussed. [ABSTRACT FROM AUTHOR]

Reinforced concrete (RC) is the result of a combination of steel reinforcing rods (which have high tensile) and concrete (which has high compressive strength). Additionally, the prediction of long-term deformations of RC flexural structures and the magnitude of the influence of the relevant material and geometric parameters are important for evaluating their serviceability and safety throughout their life cycles. Empirical methods for predicting the long-term deformation of RC structures are limited due to the difficulty of considering all the influencing factors. In this study, four popular surrogate models, i.e., polynomial chaos expansion (PCE), support vector regression (SVR), Kriging, and radial basis function (RBF), are used to predict the long-term deformation of RC structures. The surrogate models were developed and evaluated using RC simply supported beam examples, and experimental datasets were collected for comparison with common machine learning models (back propagation neural network (BP), multilayer perceptron (MLP), decision tree (DT) and linear regression (LR)). The models were tested using the statistical metrics R 2 , R A A E , R M A E , R M S E ,   V A F ,   P I ,   A 10 − i n d e x   a n d   U 95 . The results show that all four proposed models can effectively predict the deformation of RC structures, with PCE and SVR having the best accuracy, followed by the Kriging model and RBF. Moreover, the prediction accuracy of the surrogate model is much lower than that of the empirical method and the machine learning model in terms of the RMSE. Furthermore, a global sensitivity analysis of the material and geometric parameters affecting structural deflection using PCE is proposed. It was found that the geometric parameters are more influential than the material parameters. Additionally, there is a coupling effect between material and geometric parameters that works together to influence the long-term deflection of RC structures. [ABSTRACT FROM AUTHOR]

Type B aortic dissection (TBAD) carries a high risk of complications, particularly with a partially thrombosed or patent false lumen (FL). Therefore, uncovering the risk factors leading to FL thrombosis is crucial to identify high-risk patients. Although studies have shown that morphological parameters of the dissected aorta are related to FL thrombosis, often conflicting results have been reported. We show that recent models of thrombus evolution in combination with sensitivity analysis methods can provide valuable insights into how combinations of morphological parameters affect the prospect of FL thrombosis. Based on clinical data, an idealized geometry of a TBAD is generated and parameterized. After implementing the thrombus model in computational fluid dynamics simulations, a global sensitivity analysis for selected morphological parameters is performed. We then introduce dimensionless morphological parameters to scale the results to individual patients. The sensitivity analysis demonstrates that the most sensitive parameters influencing FL thrombosis are the FL diameter and the size and location of intimal tears. A higher risk of partial thrombosis is observed when the FL diameter is larger than the true lumen diameter. Reducing the ratio of the distal to proximal tear size increases the risk of FL patency. In summary, these parameters play a dominant role in classifying morphologies into patent, partially thrombosed, and fully thrombosed FL. In this study, we point out the predictive role of morphological parameters for FL thrombosis in TBAD and show that the results are in good agreement with available clinical studies. [ABSTRACT FROM AUTHOR]

The numerical modeling of cardiac electrophysiology has reached a mature and advanced state that allows for quantitative modeling of many clinically relevant processes. As a result, complex computational tasks such as the creation of a variety of electrocardiograms (ECGs) from virtual cohorts of models representing biological variation are within reach. This requires a correct representation of the variability of a population by suitable distributions of a number of input parameters. Hence, the assessment of the dependence and variation of model outputs by sensitivity analysis and uncertainty quantification become crucial. Since the standard metrological approach of using Monte–Carlo simulations is computationally prohibitive, we use a nonintrusive polynomial chaos-based approximation of the forward model used for obtaining the atrial contribution to a realistic electrocardiogram. The surrogate increases the speed of computations for varying parameters by orders of magnitude and thereby greatly enhances the versatility of uncertainty quantification. It further allows for the quantification of parameter influences via Sobol indices for the time series of 12 lead ECGs and provides bounds for the accuracy of the obtained sensitivities derived from an estimation of the surrogate approximation error. Thus, it is capable of supporting and improving the creation of synthetic databases of ECGs from a virtual cohort mapping a representative sample of the human population based on physiologically and anatomically realistic three-dimensional models. [ABSTRACT FROM AUTHOR]

The closure parameters introduced in transition models can compromise the accuracy of prediction results. This paper investigated the uncertainty caused by the closure parameters in transition models (γ and k−ω−γ), and identified the key parameters that have the greatest impact on quantities of interest. The uncertainty was propagated by the point-collocation no-intrusive polynomial chaos method, and the relative contribution of each parameter to uncertainty was assessed by the Sobol index. The natural transition flow (Schubauer–Klebanoff flat plate) and low-velocity airfoil flow (NLF0416 airfoil) were chosen for computational cases. The results, which are highly dependent on the closure parameters, validate the necessity of uncertainty research. The parameters of the k−ω−γ model are more sensitive than those of the γ model. In the γ model, the most critical parameter is CTU2 , which is negatively related to the transition position, i.e., the transition delays when CTU2 increases and advances when CTU2 decreases. In the k−ω−γ model, the most critical parameter is C2 , which is positively related to the transition position. [ABSTRACT FROM AUTHOR]

The utilization of surrogate models to approximate complex systems has recently gained increased popularity. Because of their capability to deal with black-box problems and lower computational requirements, surrogates were successfully utilized by researchers in various engineering and scientific fields. An efficient use of surrogates can bring considerable savings in computational resources and time. Since literature on surrogate modelling encompasses a large variety of approaches, the appropriate choice of a surrogate remains a challenging task. This review discusses significant publications where surrogate modelling for finite element method-based computations was utilized. We familiarize the reader with the subject, explain the function of surrogate modelling, sampling and model validation procedures, and give a description of the different surrogate types. We then discuss main categories where surrogate models are used: prediction, sensitivity analysis, uncertainty quantification, and surrogate-assisted optimization, and give detailed account of recent advances and applications. We review the most widely used and recently developed software tools that are used to apply the discussed techniques with ease. Based on a literature review of 180 papers related to surrogate modelling, we discuss major research trends, gaps, and practical recommendations. As the utilization of surrogate models grows in popularity, this review can function as a guide that makes surrogate modelling more accessible. [ABSTRACT FROM AUTHOR]

A surrogate model for a perfect electric conductor plate is built by using the polynomial chaos expansion method. The plate is excited via four capacitive coupling elements for which the locations are determined by the analysis of the current distribution for each mode provided by the characteristic mode analysis. A numerical model based on the method of moments is then created to generate a database needed to build the surrogate model. Radiation patterns calculated by the surrogate model are compared with those given by the numerical model. The results show that the surrogate model can mimic the numerical model and it can be used to replace complex numerical models to save computation time and to alleviate the burden on the computation resources. Then, a sensitivity analysis is conducted to exhibit the effect of the parameter deviations on the overall antenna performance and to reveal the influential input parameters. The results of sensitivity analysis are used to reduce the complexity of the overall structure. [ABSTRACT FROM AUTHOR]

Aseisimic earth fissures are complex consequences of groundwater withdrawal and natural hydrogeologic conditions. This paper aims to improve the understanding of the mechanism of earth fissuring and investigate the relative importance of various factors to fissure activity, including bedrock geometry, piezometric depletion, compressibility and thickness of the exploited aquifer. For these purposes, a test case characterized by an impermeable and incompressible rock ridge in a subsiding basin is developed, where stress/displacement analyses and fissure state are predicted using an interface-finite element model. Three different methods for global sensitivity analysis are used to quantify the extent of the fissure opening to the aforementioned factors. The conventional sampling based Sobol' sensitivity analysis is compared to two surrogate based methods, the general polynomial chaos expansion based Sobol' analysis and a feature importance evaluation of a gradient boosting decision tree model. Numerical results indicate that earth fissure is forming in response to tensile stress accumulation above the ridge associated to pore-pressure depletion, inducing the fissure opening at land surface with further downward propagation. Sensitivity analysis highlights that the geometry of bedrock ridge is the most influential feature. Specifically, the fissure grows more when the ridge is steeper and closer to the land surface. Pore pressure depletion is a secondary feature and required to reach a certain threshold to activate the fissure. As for this specific application, the gradient boosting tree is the most suitable method for its better performance in capturing fissure characteristics. [ABSTRACT FROM AUTHOR]

To disclose the pathophysiological mechanism of schizophrenia from the general connectivity among distinct brain regions, the computational model proposed by Szalisznyó et al. is generalized by incorporating the effects of the hippocampus. Based on the center manifold theorem and normal form theory, the emergence of abnormal alpha oscillations, which are directly associated with symptoms of schizophrenia, is analyzed in this network with Hopf bifurcation as a precursor. It is found that the clinically significant hypoconnectivities between the anterior cingulate and the dorsolateral prefrontal cortex or from the dorsolateral prefrontal cortex to the hippocampus are helpful in inhibiting the abnormal alpha oscillations, while disconnection of the coupling from the anterior cingulate cortex to the striatum can induce schizophrenia. Moreover, polynomial chaos expansion and variance-based sensitivity analysis are applied to determine the contributions of these connection strengths to the variance of the neuronal population activity. Our model results are consistent with experimental observations and thus might be meaningful for clinical interference. [ABSTRACT FROM AUTHOR]

Aerodynamic optimization of the airfoil is of great significance to the shape design for wind turbine blade. However, it is tough to calculate the aerodynamic forces of airfoil with random shape variations. In response to this challenge, a stochastic parameterized model based on uncertainty quantification method is proposed. And the influence of non-deterministic airfoil geometry caused by designed parameters on the aerodynamic characteristics is evaluated through the combination of sparse grid-based polynomial chaos (SGPC) and computational fluid dynamic (CFD) taking two airfoils at different Reynolds numbers as examples. OpenFOAM is employed as CFD solver and connected with the in-house stochastic parametric analysis code in a non-intrusive way. Finally, the aerodynamic responses of lift, drag, as well as the surface pressure coefficients are obtained, and the sensitivity of the lift and drag coefficients to the stochastic designed parameters are evaluated. It can be concluded that for the same type airfoil, the sensitive parameters after stall behavior are effected to some extent by increasing Reynolds number, that is, the impact of the maximum curvature index on pressure surface is weakened. As for two kinds of airfoils, S809 is sensitive to parameters near the maximum curvature of the airfoil and the trailing edge of the suction surface under attached flow, while convert to those near the leading edge and maximum curvature of suction face once stalled. FFA-W3-241 airfoil has no sensitivity factors in attached flow and features the same sensitive indicators after stall. These results will provide a reference for coarse-to-fine strategy in optimizing the sample library which is generally the first step of airfoil design process. [ABSTRACT FROM AUTHOR]

Uncertainty quantification and sensitivity analysis are crucial tools in the development and evaluation of mathematical models. In enhanced oil recovery, the co-injection of foam in porous media has been investigated through laboratory experiments and mathematical models as a promising technique for improving sweep efficiency. In this work, we study two mathematical models of foam flow in porous media. First, we present a foam quality-scan experiment using nitrogen and low concentration of an alpha-olefin sulfonate surfactant in brine using Indiana limestone carbonate core. Second, we evaluate the models based on their ability to represent the experimental data using inverse uncertainty quantification techniques. Third, the parameters' estimated distributions are used to perform both forward uncertainty quantification and sensitivity analysis. We also present a detailed comparison of the models, and analyses on the experimental data, model discrepancy, and sources of uncertainties. The experimental results of foam apparent viscosity in carbonate rocks are consistent with other experiments in sandstones: The foam quality transition is present; the difference in apparent viscosity values is of the same magnitude as the difference in permeability. Propagation of uncertainties from the estimated parameter distributions through the models showed a good match between experimental data and model predictions. The sensitivity analysis showed that the model's parameters play different roles and depend on the quantity of interest, the foam quality regime, and limiting water saturation. To summarize, this study provides essential information for possible improvements in the experiments and mathematical models of foam flow in EOR processes. [ABSTRACT FROM AUTHOR]

In this study, the aerodynamic uncertainty analysis and optimization of a conventional axisymmetric vehicle with an aerodynamic configuration were investigated. The prediction precision of the typical aerodynamic performance estimating methods, namely, engineering estimation and numerical simulation, was compared using the wind tunnel test data of the vehicle. Then, using a modified missile data compendium (DATCOM) software, a high-efficiency and high-precision method was developed, which was applied to analyze and characterize the aerodynamic parameters of the axisymmetric vehicle. To enhance the robustness and reliability of aerodynamic performance, an uncertainty-based design optimization (UDO) framework was established. The design space was scaled by parameter sensitivity analysis, and improved computational efficiency was achieved by developing parallel polynomial chaos expansions (PCEs). The optimized results show that the modified method exhibits high accuracy in predicting aerodynamic performance. For the same constraints, the results of the deterministic design optimization (DDO) showed that compared with the initial scheme, the probability of the controllability-to-stability ratio satisfying the constraint decreased from 98.8% to 72.4%, and this value increased to 99.9% in the case of UDO. Compared with the results of the initial scheme and DDO, UDO achieved a considerable reduction in mean values and standard deviation of aerodynamic performances, which can ensure a higher probability of constraints meeting the design requirements, thereby, realizing a reliable and robust design. [ABSTRACT FROM AUTHOR]

Parametric variability is inevitable in actual energy harvesters. It can significantly affect crucial aspects of the system performance, especially in harvesting systems that present geometric parameters, material properties, or excitation conditions that are susceptible to small perturbations. This work aims to develop an investigation to identify the most critical parameters in the dynamic behavior of asymmetric bistable energy harvesters with nonlinear piezoelectric coupling, considering the variability of their physical and excitation properties. For this purpose, a global sensitivity analysis based on orthogonal variance decomposition, employing Sobol indices, is performed to quantify the effect of the harvester parameters on the variance of the recovered power. This technique quantifies the variance concerning each parameter individually and collectively regarding the total variation of the model. The results indicate that the frequency and amplitude of excitation, asymmetric terms and electrical proprieties of the piezoelectric coupling are the most critical parameters that affect the mean power harvested. It is also shown that the order of importance of the parameters can change according to the stability of the harvester's dynamic response. In this way, a better understanding of the system under analysis is obtained since the study allows the identification of vital parameters that rule the change of dynamic behavior and therefore constitutes a powerful tool in the robust design, optimization, and response prediction of nonlinear harvesters. [ABSTRACT FROM AUTHOR]

Numerical models can be used for many purposes in oil and gas engineering, such as production optimization and forecasting, uncertainty analysis, history matching, and risk assessment. However, subsurface problems are complex and non-linear, and making reliable decisions in reservoir management requires substantial computational effort. Proxy models have gained much attention in recent years. They are advanced non-linear interpolation tables that can approximate complex models and alleviate computational effort. Proxy models are constructed by running high-fidelity models to gather the necessary data to create the proxy model. Once constructed, they can be a great choice for different tasks such as uncertainty analysis, optimization, forecasting, etc. The application of proxy modeling in oil and gas has had an increasing trend in recent years, and there is no consensus rule on the correct choice of proxy model. As a result, it is crucial to better understand the advantages and disadvantages of various proxy models. The existing work in the literature does not comprehensively cover all proxy model types, and there is a considerable requirement for fulfilling the existing gaps in summarizing the classification techniques with their applications. We propose a novel categorization method covering all proxy model types. This review paper provides a more comprehensive guideline on comparing and developing a proxy model compared to the existing literature. Furthermore, we point out the advantages of smart proxy models (SPM) compared to traditional proxy models (TPM) and suggest how we may further improve SPM accuracy where the literature is limited. This review paper first introduces proxy models and shows how they are classified in the literature. Then, it explains that the current classifications cannot cover all types of proxy models and proposes a novel categorization based on various development strategies. This new categorization includes four groups multi-fidelity models (MFM), reduced-order models (ROM), TPM, and SPM. MFMs are constructed based on simplifying physics assumptions (e.g., coarser discretization), and ROMs are based on dimensional reduction (i.e., neglecting irrelevant parameters). Developing these two models requires an in-depth knowledge of the problem. In contrast, TPMs and novel SPMs require less effort. In other words, they do not solve the complex underlying mathematical equations of the problem; instead, they decouple the mathematical equations into a numeric dataset and train statistical/AI-driven models on the dataset. Nevertheless, SPMs implement feature engineering techniques (i.e., generating new parameters) for its development and can capture the complexities within the reservoir, such as the constraints and characteristics of the grids. The newly introduced parameters can help find the hidden patterns within the parameters, which eventually increase the accuracy of SPMs compared to the TPMs. This review highlights the superiority of SPM over traditional statistical/AI-based proxy models. Finally, the application of various proxy models in the oil and gas industry, especially in subsurface modeling with a set of real examples, is presented. The introduced guideline in this review aids the researchers in obtaining valuable information on the current state of PM problems in the oil and gas industry. [ABSTRACT FROM AUTHOR]

This paper aims at presenting a novel effective approach to probabilistic analysis of distribution power grid with high penetration of PV sources. The novel method adopts a Gaussian Mixture Model for reproducing the uncertainty of correlated PV sources along with a piece-wise-linear approximation of the voltage-power relationship established by load flow problem. The method allows the handling of scenarios with a large number of uncertain PV sources in an efficient yet accurate way. A distinctive feature of the proposed probabilistic analysis is that of directly providing, in closed-form, the joint probability distribution of the set of observable variables of interest. From such a comprehensive statistical representation, remarkable information about grid uncertainty can be deduced. This includes the probability of violating the safe operation conditions as a function of PV penetration. [ABSTRACT FROM AUTHOR]

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti‐platelet therapies. In this work, an uncertainty quantification analysis of a multi‐constituent thrombosis model is performed considering a common assay for platelet function (PFA‐100®). The analysis is facilitated thanks to time‐evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA‐100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti‐platelet therapies to identify scenarios that preserve the hematological balance. [ABSTRACT FROM AUTHOR]

A surrogate model is developed to accurately approximate a two-dimensional hydrodynamics numerical solver in order to conduct a reduced-cost variance-based global sensitivity analysis of the hydraulic state. The impact of uncertainties in river bottom friction and boundary conditions on the simulated water depth is analyzed for quasi-unsteady flows. An autoencoder technique adapted to non-linear variable dimension reduction is used to reduce the multi-dimensional model output so that the formulation of the surrogate remains computationally parsimonious. In addition, following the divide-and-conquer principle, a mixture of local polynomial chaos expansions is proposed to deal with non-linearity in the hydraulic state with respect to uncertain inputs. Machine learning techniques are used to automatically partition the input space into clusters that are not affected by non-linearities and support accurate surrogates. This combined strategy is applied to a reach of the Garonne River where river and floodplains dynamics are simulated by the numerical solver Telemac-2D. The merits of this strategy are highlighted when the flood front reaches regions where the topography features a strong gradient and where, consequently, strong non-linearities occur between the water depth and friction as well as hydrologic input forcing. By applying this strategy, the Q 2 metric improves by 90% compared to a classical polynomial chaos expansion surrogate, resulting in a much more reliable sensitivity analysis. This is particularly important in floodplain areas where human and economic activities are at stake. [ABSTRACT FROM AUTHOR]

In this paper, a mixed spectral technique is suggested for the analysis of stochastic models with parameters having random variations. The proposed mixed technique considers a Volterra-like expansions for all types of randomness. Particularly, the generalized polynomial chaos (gPC) expansion is used for the random parameters and the Wiener–Hermite functionals (WHF) technique is used for the noise. The statistical properties of the functionals enables to derive a deterministic system used to evaluate the solution statistical moments. The new mixed technique is shown to be efficient compared with the classical techniques and analytical solutions could be obtained in many cases. The suggested technique allows to separate the contributions of the different random sources and hence enables to evaluate variance components which are used to estimate the sensitivity indices. The technique is applied successfully to different models with additive and multiplicative noise and compared with the classical sampling techniques. The stochastic nuclear reactor model with random parameters is analyzed with the new technique. [ABSTRACT FROM AUTHOR]

The method of connection weights in neural networks was used to analyze the sensitivity of the compressor rotor, and the Back Propagation Neural Network (BPNN) was used to construct the analysis relationship between the compressor rotor's geometries and the performance based on the training and learning of the data base, and the prediction accuracy can reach more than 99.99%. Then the modified Grason Algorithm based on the neural network connect weights was used to quantify the contribution of the geometrical effects on its performance. The result shows that the tip clearance contributes 11.43% (efficiency sensitivity analysis) and 10.18% (pressure ratio sensitivity analysis) to compressor performance changes. This study focuses mainly on the robust optimization of tip clearance. Non-intrusive probability collection point method (NIPC) was adopted for the uncertainty propagation. The robust optimization method based on BPNN agent model coupled with multi-objective genetic algorithm Non-dominated sorting genetic algorithm-II (NSGA II) was used to perform the optimization. Compared to the design prototype, the variance of robust compressor rotor's efficiency could be reduced by 21.04%. [ABSTRACT FROM AUTHOR]

Sensitivity analysis investigates how the change in the output of a computational model can be attributed to changes of its input parameters. Identifying the input parameters that propagate more uncertainty on the ruin probability associated with insurance risk models is a challenging problem. In this paper, we consider the classical risk model, where an epistemic-uncertainty veils the true values of the claim size distribution rate and the Poisson arrival rate. Based on the available data for calibrating the probability distributions that model gaps of knowledge on these rates, and using the Taylor-series expansion methodology, we obtain the ruin probability under polynomial form in uncertain rates as a computational model. Specifically, we get a new sensitivity estimate of the ruin probability with respect to uncertain parameters. We provide a coherent framework within which we can accurately characterize statistically the uncertain ruin probability. In addition, we use the Markov's inequality to estimate the risk incurred by working with uncertain ruin probability rather than that evaluated at fixed parameters. A series of numerical experiments are presented to illustrate the potential of the proposed approach. [ABSTRACT FROM AUTHOR]

We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-valued outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Loéve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs. [ABSTRACT FROM AUTHOR]

Queueing systems are modeled by equations which depend on a large number of input parameters. In practice, significant uncertainty is associated with estimates of these parameters, and this uncertainty must be considered in the analysis of the model. The objective of this paper is to propose a sensitivity analysis approach for a queueing model, presenting parameters that follow a Gaussian distribution. The approach consists in decomposing the output of the model (stationary distribution of the model) into a polynomial chaos. The sensitivity indices, allowing to quantify the contribution of each parameter to the variance of the output, are obtained directly from the coefficients of decomposition. The proposed approach is then applied to M/G/1/N queueing model. The most influential parameters are highlighted. Finally several numerical and data examples are sketched out to illustrate the accuracy of the proposed method and compare them with Monte Carlo simulation. The results of this work will be useful to practitioners in various fields of theoretical and applied sciences. [ABSTRACT FROM AUTHOR]

Pulmonary hypertension (PH), defined as an elevated mean blood pressure in the main pulmonary artery (MPA) at rest, is associated with vascular remodeling of both large and small arteries. PH has several sub‐types that are all linked to high mortality rates. In this study, we use a one‐dimensional (1‐D) fluid dynamics model driven by in vivo measurements of MPA flow to understand how model parameters and network size influence MPA pressure predictions in the presence of PH. We compare model predictions with in vivo MPA pressure measurements from a control and a hypertensive mouse and analyze results in three networks of increasing complexity, extracted from micro‐computed tomography (micro‐CT) images. We introduce global scaling factors for boundary condition parameters and perform local and global sensitivity analysis to calculate parameter influence on model predictions of MPA pressure and correlation analysis to determine a subset of identifiable parameters. These are inferred using frequentist optimization and Bayesian inference via the Delayed Rejection Adaptive Metropolis (DRAM) algorithm. Frequentist and Bayesian uncertainty is computed for model parameters and MPA pressure predictions. Results show that MPA pressure predictions are most sensitive to distal vascular resistance and that parameter influence changes with increasing network complexity. Our outcomes suggest that PH leads to increased vascular stiffness and decreased peripheral compliance, congruent with clinical observations. [ABSTRACT FROM AUTHOR]

Many countries are currently dealing with the COVID-19 epidemic and are searching for an exit strategy such that life in society can return to normal. To support this search, computational models are used to predict the spread of the virus and to assess the efficacy of policy measures before actual implementation. The model output has to be interpreted carefully though, as computational models are subject to uncertainties. These can stem from, e.g., limited knowledge about input parameters values or from the intrinsic stochastic nature of some computational models. They lead to uncertainties in the model predictions, raising the question what distribution of values the model produces for key indicators of the severity of the epidemic. Here we show how to tackle this question using techniques for uncertainty quantification and sensitivity analysis. We assess the uncertainties and sensitivities of four exit strategies implemented in an agent-based transmission model with geographical stratification. The exit strategies are termed Flattening the Curve, Contact Tracing, Intermittent Lockdown and Phased Opening. We consider two key indicators of the ability of exit strategies to avoid catastrophic health care overload: the maximum number of prevalent cases in intensive care (IC), and the total number of IC patient-days in excess of IC bed capacity. Our results show that uncertainties not directly related to the exit strategies are secondary, although they should still be considered in comprehensive analysis intended to inform policy makers. The sensitivity analysis discloses the crucial role of the intervention uptake by the population and of the capability to trace infected individuals. Finally, we explore the existence of a safe operating space. For Intermittent Lockdown we find only a small region in the model parameter space where the key indicators of the model stay within safe bounds, whereas this region is larger for the other exit strategies. Author summary: Many countries are currently dealing with the COVID-19 epidemic and are looking for an exit strategy such that life in society can return to normal. For that purpose computational models are used to predict the spread of the virus and to assess the efficacy of policy measures before putting them into practice. These models are subject to uncertainties (due to, for instance, limited knowledge of the parameter values), which can lead to a large variability in model predictions. It is therefore fundamental to assess which range of values a model produces for key indicators of the severity of the epidemic. We present here the results of the uncertainty and sensitivity analysis of four exit strategies simulated with an individual-based model of the COVID-19 transmission. As key indicators of the severity of the pandemic we consider the maximum number of cases in intensive care and the total number of intensive care patient-days in excess. Our results show the crucial role of the intervention uptake by the population, of the reduction in the level of transmission by intervention and of the capability to trace infected individuals. [ABSTRACT FROM AUTHOR]

A range of different techniques for determining the unknown coefficients of Polynomial Chaos Expansion (PCE) models for antenna structures, are presented. PCE models offer significant advantages over Monte Carlo analysis, for the modeling of the statistical behavior of structures, but the different approaches for calculating the PCE model coefficients exhibits a large variation in the number of required basis points, that number also being problem specific. A range of model coefficient calculation techniques are evaluated in this article, for the problem of modeling cross‐polarization of an inset‐fed patch antenna. This structure is one of the most widely used antenna structures, often produced in high‐volume, and serves as an excellent example to emphasize the variation in performance between the different techniques, and problem‐specific nature of finding an optimal solution. It is shown that the most optimal method requires fewer than 10% analysis points of the least optimal, and a factor of 100 fewer points than Monte‐Carlo analysis. [ABSTRACT FROM AUTHOR]

During the past few decades, uncertainty quantification (UQ) techniques have been developed and applied to many applications. The majority of these techniques have been applied directly to specifically defined problems, that is, problems described by a mathematical operator and a specific source term, both which may be endowed with uncertainty. In this article, we take an alternative approach: applying UQ techniques to probe the operator. The goal is to extract intrinsic structures of the problem, particularly operator structures that reveal the propagation of uncertainty which a UQ analysis of a specific problem may not accurately extract. There are many practical reasons for this. For example, the operator often contains more aspects of uncertainty than the forcing term, and the operator is often computationally expensive to form and hence, wasteful to use only for determining the solution of a sample instantiation. The anticipation is that the detailed information can lead to more accurate and efficient UQ analysis of the general problem. In this article, we consider only linear problems since we want to explore the potential benefits of this approach without the added complexities introduced by nonlinearities. This linearity assumption allows us to explore structures exposed by the spectrum of the operator. We explore sensitivity of the eigenvectors to determine a relationship between the spatial and uncertainty parameter dimensions, and then construct an adaptive parameter procedure based on this relationship. We also explore the propagation of uncertainties in multicomponent systems, like in multiphysics applications, by examining the coupling in the smooth‐frequency eigenvectors; and explore componentized UQ processing based on the eigenvalues/vectors of the state‐equation operator in goal‐oriented multiple‐input/multiple‐output systems. Analysis and numerical examples demonstrating the applicability of the methods are presented. [ABSTRACT FROM AUTHOR]

This study introduces a computational framework for efficient and accurate seismic fragility analysis based on a combination of artificial ground motion modeling, polynomial‐chaos‐based global sensitivity analysis, and hierarchical kriging surrogate modeling. The framework follows the philosophy of the Performance‐Based Earthquake Engineering PEER approach, where the fragility analysis is decoupled from hazard analysis. This study addresses three criticalities that are present in the current practice. Namely, reduced size of hazard‐consistent size‐specific ensembles of seismic records, validation of structural simulators against large‐scale experiments, high computational cost for accurate fragility estimates. The effectiveness of the proposed framework is demonstrated for the Rio Torto Bridge, recently tested using hybrid simulation within the RETRO project. [ABSTRACT FROM AUTHOR]

We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev‐Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance‐based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra‐subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high‐fidelity, full‐order computational model obtained by approximating the coupled monodomain/Aliev‐Panfilov system through the finite element method. To mitigate this computational burden, we replace the full‐order model with computationally inexpensive projection‐based reduced‐order models (ROMs) aimed at reducing the state‐space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)‐based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics‐based ROMs outperform regression‐based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency. [ABSTRACT FROM AUTHOR]

Materials accumulate energy around voids and defects under external loading, causing the formation of microcracks. With increasing or repeated loads, those microcracks eventually coalesce to form macrocracks, which in a brittle material can cause catastrophic failure without apparent permanent deformation. At the continuum level, a stochastic phase‐field model is employed to simulate failure through introducing damage and fatigue variables. The damage phase‐field is introduced as a continuous dynamical variable representing the volumetric portion of fractured material and fatigue is treated as a continuous internal field variable to model the effects of microcracks arising from energy accumulation. We formulate a computational‐mathematical framework for quantifying the corresponding model uncertainties and sensitivities in order to unfold and mitigate the salient sources of unpredictability in the model, hence, leading to new possible modeling paradigms. Considering an isothermal isotropic linear elastic material with viscous dissipation under the hypothesis of small deformations, we employed Monte Carlo and probabilistic collocation methods to perform the forward uncertainty propagation, in addition to local‐to‐global sensitivity analysis. We demonstrate that the model parameters associated with free‐energy potentials contribute significantly more to the total model output uncertainties, motivating further investigations for obtaining more predictable model forms, representing the damage diffusion. [ABSTRACT FROM AUTHOR]

Disturbed flow and the resulting non‐physiological wall shear stress (WSS) at the graft‐vein anastomosis play an important role in arteriovenous graft (AVG) patency loss. Modifying graft geometry with helical features is a popular approach to minimise the occurrence of detrimental haemodynamics and to potentially increase graft longevity. Haemodynamic optimisation of AVGs typically requires many computationally expensive computational fluid dynamics (CFD) simulations to evaluate haemodynamic performance of different graft designs. In this study, we aimed to develop a haemodynamically optimised AVG by using an efficient meta‐modelling approach. A training dataset containing CFD evaluations of 103 graft designs with helical features was used to develop computationally low‐cost meta‐models for haemodynamic metrics related to graft dysfunction. During optimisation, the meta‐models replaced CFD simulations that were otherwise needed to evaluate the haemodynamic performance of possible graft designs. After optimisation, haemodynamic performance of the optimised graft design was verified using a CFD simulation. The obtained optimised graft design contained both a helical graft centreline and helical ridge. Using the optimised design, the magnitude of flow disturbances and the size of the anastomotic areas exposed to non‐physiological WSS was successfully reduced compared to a regular straight graft. Our meta‐modelling approach allowed to reduce the total number of CFD model evaluations required for our design optimisation by approximately a factor 2000. The applied efficient meta‐modelling technique was successful in identifying an optimal, helical graft design at relatively low computational costs. Future studies should evaluate the in vivo benefits of the developed graft design. [ABSTRACT FROM AUTHOR]

Polynomial chaos (PC) methods with Gauss-type quadrature formulae have been widely applied for robust design optimization. During the robust optimization, gradient-based optimization algorithms are commonly employed, where the sensitivities of the mean and variance of the output response with respect to design variables are calculated. For robust optimization with computationally expensive response functions, although the PC method can significantly reduce the computational cost, the direct application of the classical finite difference method for the analysis of the design sensitivity is impractical with a limited computational budget. Therefore, in this paper, a semi-analytical design sensitivity analysis method based on the PC method is proposed, in which the sensitivity is directly derived based on the Gauss-type quadrature formula without additional function evaluations. Comparative studies conducted on several mathematical examples and an aerodynamic robust optimization problem revealed that the proposed method can reduce the computational cost of robust optimization to a certain extent with comparable accuracy compared with the finite difference-based PC method. [ABSTRACT FROM AUTHOR]

In this paper, a framework for the stochastic progressive failure analysis (PFA) of fiber-reinforced composites is presented. The nonlinear responses of composite structures are hugely influenced by the randomness in material properties of plies, thereby yielding significantly different responses compared with that with deterministic simulations. Moreover, performing PFA using finite element analysis (FEA) is a computationally intensive process that becomes unaffordable while performing uncertainty analysis that requires numerous FEA runs. So, to alleviate this computational cost while maintaining an acceptable accuracy, an efficient technique called polynomial chaos expansion (PCE) was implemented. Another advantage of PCE is that it allows performing global sensitivity analysis (GSA) to estimate the influence of the random inputs on the stochastic responses as a post-processing step without any additional cost. The effects of randomness in material properties on the first ply failure load and ultimate failure responses of a composite laminate were compared with the framework using PCE as well as 5000 LHS simulations and the results underlined the cost-effectiveness as well as the high accuracy of PCE. Moreover, the GSA successfully identified the influential random material properties that correlated well with the failure modes. Thus, the presented approach and the results of this study will be instrumental in understanding the failure as well as improving the design of composite structures. [ABSTRACT FROM AUTHOR]

Electrical impedance tomography (EIT) is a boundary measurement inverse technique targeting reconstruction of the conductivity distribution of the interior of a physical body based on boundary measurement data. Typically, the measured data are uncertain because of various error sources; thus, there are many uncertainties in the reconstructed image. This study attempts to quantify the effects of these measurement errors on EIT reconstruction. A comprehensive framework that combines uncertainty quantification techniques and EIT reconstruction techniques is proposed. In this framework, a polynomial chaos expansion method is used to construct a surrogate model of the conductivity field with respect to the measurement errors. Two shape detection indices are introduced to show the EIT reconstruction quality. Finally, under certain detection index constraints, statistical and sensitivity analyses are performed using the properties of the surrogate model. Several EIT problems are examined in this study, involving one or two anomalies in a circular domain or two asymmetric anomalies in a body-like domain. The results show that the proposed framework can quantify the effects of measurement errors on EIT reconstruction at reasonable cost. Further, for the test cases, the measurement errors at the electrodes close to the anomalies are shown to have the greatest influence on the image reconstruction. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic model for performing the uncertainty and sensitivity analysis of a Jeffcott rotor system with fixed-point rub-impact and multiple uncertain parameters. A probabilistic nonlinear formulation is developed based on the combination of the harmonic balance method and an alternate frequency/time procedure (HB-AFT) in stochastic form. The non-intrusive generalized polynomial chaos expansion (gPCE) with unknown deterministic coefficients is employed to represent the propagation of uncertainties on rotor dynamics. In conjunction with the path continuation scheme and the Floquet theory, the developed model enables one to expediently evaluate the uncertainty bounds and probability density functions (PDFs) on periodic solution branches and associated stabilities. A global sensitivity analysis is then carried out by evaluating Sobol's indices from gPCE to quantitatively ascertain the relative influence of different stochastic parameters on vibrational behaviors and conditions for the occurrence of rub-impact. The efficiency of the proposed algorithm for nonlinear stochastic dynamics of rub-impact rotors is validated with Monte Carlo simulation. Parametric studies are finally carried out to investigate the effects of multiple random parameters on the probabilistic variability in nonlinear responses of rub-impact rotors, which reveals the necessary to consider input uncertainties in analyses and designs to ensure the sustainable system performance. [ABSTRACT FROM AUTHOR]

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient‐specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least‐squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application. [ABSTRACT FROM AUTHOR]

Chloride‐induced corrosion is one of the main causes leading to the lifetime reduction of reinforced concrete (RC) structures in marine environments or subjected to de‐icing salts. Modeling chloride ingress into concrete in a comprehensive way is therefore a crucial task to evaluate corrosion initiation risk and carry out preventive maintenance. Nevertheless, this comprehensive modeling is a challenging task that requires solving simultaneously a set of coupled non‐linear partial differential equations. This task becomes more complex if the inherent uncertainties of the process are considered for probabilistic lifetime assessment. The present research aims to assess the probability of corrosion initiation of RC structures. The polynomial chaos expansion (PCE) method is employed to propagate uncertainties in a chloride ingress model requiring significant computational time to perform one deterministic simulation. PCE is also applied to perform a sensitivity analysis to determine which are the more influential random variables in the problem. The proposed methodology is applied to RC structures placed in several locations in France (Brest, Marseille, and Strasbourg) and subjected to realistic environmental conditions including climate change. The results show that the PCE‐based model is accurate and efficient for lifetime assessment of RC structures subject to chloride‐induced corrosion. [ABSTRACT FROM AUTHOR]

The effects of uncertainty in flow conditions, namely angle of attack, Reynolds number, and freestream Mach number, on airfoil characteristics in the low-Reynolds-number regime are evaluated. The Ishii airfoil, a thin-cambered airfoil known to have high aerodynamic performance in this regime, is analyzed. The NACA0012 airfoil is also analyzed as a comparative study. The results for two sets of nominal flow conditions are compared to comprehensively characterize performance in the low-Reynolds-number regime. Statistical quantities of aerodynamic coefficients are computed by coupling the stochastic spectral projection method based on polynomial chaos expansion with two-dimensional flow simulations. The relative contribution of the uncertainty of each flow parameter to the variance of outputs is computed using Sobol's global sensitivity analysis. It is shown that, for the Ishii airfoil, the lift coefficient is highly sensitive to the uncertainty, while the lift-to-drag ratio has a high statistical mean and the pitching moment coefficient has low sensitivity. This indicates that, for thin-cambered airfoils, attention should be given to rapid degradation due to unexpected variation in the angle of attack. [ABSTRACT FROM AUTHOR]