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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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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]

This paper demonstrates the use of generalized polynomial chaos expansion for the propagation of uncertainties present in various dynamical models. Specifically, a sampling based non-intrusive approach using pseudospectral stochastic collocation is employed to obtain the coefficients required for the generalized polynomial chaos expansion. Various recently developed quadrature techniques are employed within the generalized polynomial chaos expansion framework in order to illustrate their efficacy. In addition to that, the paper also provides an efficient numerical quadrature technique to be used as a sampling technique in stochastic collocation to quantify the uncertainties which are governed by different distribution functions. Results are presented for the orbital motion of a 2U CubeSat subject to initial condition uncertainty and drag related parametric uncertainty demonstrating the accuracy and effectiveness of the proposed technique. Further, stochastic sensitivity analysis is performed to gain insight into the impact of uncertain variables on the evolution of the quantities of interest. [ABSTRACT FROM AUTHOR]

Surrogate models are popular tool to approximate the functional relationship of expensive simulation models in multiple scientific and engineering disciplines. Successful use of surrogate models can provide significant savings of computational cost. However, with a variety of surrogate model approaches available in literature, it is a difficult task to select an appropriate one at hand. In this paper, we present an overview of surrogate model approaches with an emphasis of their application for variance-based global sensitivity analysis, including polynomial regression model, high-dimensional model representation, state-dependent parameter, polynomial chaos expansion, Kriging/Gaussian Process, support vector regression, radial basis function, and low rank tensor approximation. The accuracy and efficiency of these approaches are compared with several benchmark examples. The strengths and weaknesses of these surrogate models are discussed, and the recommendations are provided for different types of applications. For ease of implementations, the packages, as well as toolboxes, of surrogate model techniques and their applications for global sensitivity analysis are collected. [ABSTRACT FROM AUTHOR]

Computational models of the heart have reached a level of maturity that enables sophisticated patient-specific simulations and hold potential for important applications in diagnosis and therapy planning. However, such clinical use puts strict demands on the reliability and accuracy of the models and requires the sensitivity of the model predictions due to errors and uncertainty in the model inputs to be quantified. The models typically contain a large number of parameters, which are difficult to measure and therefore associated with considerable uncertainty. Additionally, patient-specific geometries are usually constructed by semi-manual processing of medical images and must be assumed to be a potential source of model uncertainty. In this paper, we assess the model accuracy by considering the impact of geometrical uncertainties, which typically occur in image-based computational geometries. An approach based on 17 AHA segments diagram is used to consider uncertainties in wall thickness and also in the material properties and fiber orientation, and we perform a comprehensive uncertainty quantification and sensitivity analysis based on polynomial chaos expansions. The quantities considered include stress, strain and global deformation parameters of the left ventricle. The results indicate that important quantities of interest may be more affected by wall thickness, and highlight the need for accurate geometry reconstructions in patient-specific cardiac mechanics models. [ABSTRACT FROM AUTHOR]

Thrombus formation is one of the main issues in the development of blood-contacting medical devices. This article focuses on the modeling of one aspect of thrombosis, the coagulation cascade, which is initiated by the contact activation at the device surface and forms thrombin. Models exist representing the coagulation cascade by a series of reactions, usually solved in quiescent plasma. However, large parameter uncertainty involved in the kinetic models can affect the predictive capabilities of this approach. In addition, the large number of reactions of the kinetic models prevents their use in the simulation of complex flow configurations encountered in medical devices. In the current work, both issues are addressed to improve the applicability and fidelity of kinetic models. A sensitivity analysis is performed by two different techniques to identify the most sensitive parameters of an existing detailed kinetic model of the coagulation cascade. The results are used to select the form of a novel reduced model of the coagulation cascade which relies on eight chemical reactors only. Then, once its parameters have been calibrated thanks to the Bayesian inference, this model shows good predictive capabilities for different initial conditions. [ABSTRACT FROM AUTHOR]

Hydrologic flood prediction has been a quite complex and difficult task because of various sources of inherent uncertainty. Accurately quantifying these uncertainties plays a significant role in providing flood warnings and mitigating risk, but it is time-consuming. To offset the cost of quantifying the uncertainty, we adopted a highly efficient metamodel based on polynomial chaos expansion (PCE) theory and applied it to a lumped, deterministic rainfall–runoff model (Nedbør–Afstrømnings model, NAM) combined with generalized likelihood uncertainty estimation (GLUE). The central conclusions are: (1) the subjective aspects of GLUE (e.g., the cutoff threshold values of likelihood function) are investigated for 8 flood events that occurred in the Thu bon river watershed in Vietnam, resulting that the values of 0.82 for Nash–Sutcliffe efficiency, 4.05% for peak error, and 4.35% for volume error are determined as the acceptance thresholds. Moreover, the number of ensemble behavioral sets required to maintain the sufficient range of uncertainty but to avoid any unnecessary computation was set to 500. (2) The number of experiment designs (N) and degree of polynomial (p) are key factors in estimating PCE coefficients, and values of N = 50 and p = 4 are preferred. (3) The results computed using a PCE model consisting of polynomial bases are as good as those given by the NAM, while the total times required for making an ensemble in the PCE model are approximately seventeen times faster. (4) Two parameters ("CQOF" and "CK12") turned out to be most dominant based on a visual inspection of the posterior distribution and the mathematical computations of the Sobol' and Morris sensitivity analysis. Identification of the posterior parameter distributions from the calibration process helps to find the behavioral sets even faster. The unified framework that presents the most efficient ways of predicting flow regime and quantifying the uncertainty without deteriorating accuracy will ultimately be helpful for providing warnings and mitigating flood risk in a timely manner. [ABSTRACT FROM AUTHOR]

A major transition in the history of the Pancrustacea was the invasion of several lineages of these animals onto land. We investigated the functional performance of odor-capture organs, antennae with olfactory sensilla arrays, through the use of a computational model of advection and diffusion of odorants to olfactory sensilla while varying three parameters thought to be important to odor capture (Reynolds number, gap-width-to-sensillum-diameter ratio, and angle of the sensilla array with respect to oncoming flow). We also performed a sensitivity analysis on these parameters using uncertainty quantification to analyze their relative contributions to odor-capture performance. The results of this analysis indicate that odor capture in water and in air are fundamentally different. Odor capture in water and leakiness of the array are highly sensitive to Reynolds number and moderately sensitive to angle, whereas odor capture in air is highly sensitive to gap widths between sensilla and moderately sensitive to angle. Leakiness is not a good predictor of odor capture in air, likely due to the relative importance of diffusion to odor transport in air compared to water. We also used the sensitivity analysis to make predictions about morphological and kinematic diversity in extant groups of aquatic and terrestrial crustaceans. Aquatic crustaceans will likely exhibit denser arrays and induce flow within the arrays, whereas terrestrial crustaceans will rely on more sparse arrays with wider gaps and little-to-no animal-induced currents. [ABSTRACT FROM AUTHOR]

Assessing epistemic uncertainties is considered as a milestone for improving numerical predictions of a dynamical system. In hydrodynamics, uncertainties in input parameters translate into uncertainties in simulated water levels through the shallow water equations. We investigate the ability of generalized polynomial chaos (gPC) surrogate to evaluate the probabilistic features of water level simulated by a 1-D hydraulic model (MASCARET) with the same accuracy as a classical Monte Carlo method but at a reduced computational cost. This study highlights that the water level probability density function and covariance matrix are better estimated with the polynomial surrogate model than with a Monte Carlo approach on the forward model given a limited budget of MASCARET evaluations. The gPC-surrogate performance is first assessed on an idealized channel with uniform geometry and then applied on the more realistic case of the Garonne River (France) for which a global sensitivity analysis using sparse least-angle regression was performed to reduce the size of the stochastic problem. For both cases, Galerkin projection approximation coupled to Gaussian quadrature that involves a limited number of forward model evaluations is compared with least-square regression for computing the coefficients when the surrogate is parameterized with respect to the local friction coefficient and the upstream discharge. The results showed that a gPC-surrogate with total polynomial degree equal to 6 requiring 49 forward model evaluations is sufficient to represent the water level distribution (in the sense of the ℓ2 norm), the probability density function and the water level covariance matrix for further use in the framework of data assimilation. In locations where the flow dynamics is more complex due to bathymetry, a higher polynomial degree is needed to retrieve the water level distribution. The use of a surrogate is thus a promising strategy for uncertainty quantification studies in open-channel flows and should be extended to unsteady flows. It also paves the way toward cost-effective ensemble-based data assimilation for flood forecasting and water resource management. [ABSTRACT FROM AUTHOR]

Cardiac resynchronization therapy is not effective in a variable proportion of heart failure patients. An accurate knowledge of each patient's electroanatomical features could be helpful to determine the most appropriate treatment. The goal of this study was to analyze and quantify the sensitivity of left ventricular (LV) activation and the electrocardiogram (ECG) to changes in 39 parameters used to tune realistic anatomical-electrophysiological models of the heart. Electrical activity in the ventricles was simulated using a reaction-diffusion equation. To simulate cellular electrophysiology, the Ten Tusscher-Panfilov 2006 model was used. Intracardiac electrograms and 12-lead ECGs were computed by solving the bidomain equation. Parameters showing the highest sensitivity values were similar in the six patients studied. QRS complex and LV activation times were modulated by the sodium current, the cell surface-to-volume ratio in the LV, and tissue conductivities. The T-wave was modulated by the calcium and rectifier-potassium currents, and the cell surface-to-volume ratio in both ventricles. We conclude that homogeneous changes in ionic currents entail similar effects in all ECG leads, whereas the effects of changes in tissue properties show larger inter-lead variability. The effects of parameter variations are highly consistent between patients and most of the model tuning could be performed with only ~10 parameters. [ABSTRACT FROM AUTHOR]

Most approximations for stochastic differential equations with high-dimensional, non-Gaussian inputs suffer from a rapid (e.g., exponential) increase of computational cost, an issue known as the curse of dimensionality. In astrodynamics, this results in reduced accuracy when propagating an orbit-state probability density function. This paper considers the application of separated representations for orbit uncertainty propagation, where future states are expanded into a sum of products of univariate functions of initial states and other uncertain parameters. An accurate generation of separated representation requires a number of state samples that is linear in the dimension of input uncertainties. The computation cost of a separated representation scales linearly with respect to the sample count, thereby improving tractability when compared to methods that suffer from the curse of dimensionality. In addition to detailed discussions on their construction and use in sensitivity analysis, this paper presents results for three test cases of an Earth orbiting satellite. The first two cases demonstrate that approximation via separated representations produces a tractable solution for propagating the Cartesian orbit-state uncertainty with up to 20 uncertain inputs. The third case, which instead uses Equinoctial elements, reexamines a scenario presented in the literature and employs the proposed method for sensitivity analysis to more thoroughly characterize the relative effects of uncertain inputs on the propagated state. [ABSTRACT FROM AUTHOR]

The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young's modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young's modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young's modulus of the epoxy matrix. [ABSTRACT FROM AUTHOR]

Surrogate models are usually used to perform global sensitivity analysis (GSA) by avoiding a large ensemble of deterministic simulations of the Monte Carlo method to provide a reliable estimate of GSA indices. However, most surrogate models such as polynomial chaos (PC) expansions suffer from the curse of dimensionality due to the high-dimensional input space. Thus, sparse surrogate models have been proposed to alleviate the curse of dimensionality. In this paper, three techniques of sparse reconstruction are used to construct sparse PC expansions that are easily applicable to computing variance-based sensitivity indices (Sobol indices). These are orthogonal matching pursuit (OMP), spectral projected gradient for L minimization (SPGL1), and Bayesian compressive sensing with Laplace priors. By computing Sobol indices for several benchmark response models including the Sobol function, the Morris function, and the Sod shock tube problem, effective implementations of high-dimensional sparse surrogate construction are exhibited for GSA. [ABSTRACT FROM AUTHOR]

In this paper we present a stochastic model reduction method for efficiently solving nonlinear unconfined flow problems in heterogeneous random porous media. The input random fields of flow model are parameterized in a stochastic space for simulation. This often results in high stochastic dimensionality due to small correlation length of the covariance functions of the input fields. To efficiently treat the high-dimensional stochastic problem, we extend a recently proposed hybrid high-dimensional model representation (HDMR) technique to high-dimensional problems with multiple random input fields and integrate it with a sparse grid stochastic collocation method (SGSCM). Hybrid HDMR can decompose the high-dimensional model into a moderate M-dimensional model and a few one-dimensional models. The moderate dimensional model only depends on the most M important random dimensions, which are identified from the full stochastic space by sensitivity analysis. To extend the hybrid HDMR, we consider two different criteria for sensitivity test. Each of the derived low-dimensional stochastic models is solved by the SGSCM. This leads to a set of uncoupled deterministic problems at the collocation points, which can be solved by a deterministic solver. To demonstrate the efficiency and accuracy of the proposed method, a few numerical experiments are carried out for the unconfined flow problems in heterogeneous porous media with different correlation lengths. The results show that a good trade-off between computational complexity and approximation accuracy can be achieved for stochastic unconfined flow problems by selecting a suitable number of the most important dimensions in the M-dimensional model of hybrid HDMR. [ABSTRACT FROM AUTHOR]

In this work, we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example, we calibrate the model against experimental data that are subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model. [ABSTRACT FROM AUTHOR]

A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed using random sampling techniques and nonintrusive methods based on generalized polynomial chaos (PC). These methods allow us to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution at different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained by the variability in the model input. Finally, we present a synthetic experiment studying the variance-based sensitivity of the wave load on an offshore structure to a number of input uncertainties. In the numerical examples presented the PC methods exhibit fast convergence, suggesting that the problem is amenable to analysis using such methods. [ABSTRACT FROM AUTHOR]

This study aims at analyzing the combined impact of uncertainties in initial conditions and wind forcing fields in ocean general circulation models (OGCM) using polynomial chaos (PC) expansions. Empirical orthogonal functions (EOF) are used to formulate both spatial perturbations to initial conditions and space-time wind forcing perturbations, namely in the form of a superposition of modal components with uniformly distributed random amplitudes. The forward deterministic HYbrid Coordinate Ocean Model (HYCOM) is used to propagate input uncertainties in the Gulf of Mexico (GoM) in spring 2010, during the Deepwater Horizon oil spill, and to generate the ensemble of model realizations based on which PC surrogate models are constructed for both localized and field quantities of interest (QoIs), focusing specifically on sea surface height (SSH) and mixed layer depth (MLD). These PC surrogate models are constructed using basis pursuit denoising methodology, and their performance is assessed through various statistical measures. A global sensitivity analysis is then performed to quantify the impact of individual modes as well as their interactions. It shows that the local SSH at the edge of the GoM main current-the Loop Current-is mostly sensitive to perturbations of the initial conditions affecting the current front, whereas the local MLD in the area of the Deepwater Horizon oil spill is more sensitive to wind forcing perturbations. At the basin scale, the SSH in the deep GoM is mostly sensitive to initial condition perturbations, while over the shelf it is sensitive to wind forcing perturbations. On the other hand, the basin MLD is almost exclusively sensitive to wind perturbations. For both quantities, the two sources of uncertainty have limited interactions. Finally, the computations indicate that whereas local quantities can exhibit complex behavior that necessitates a large number of realizations, the modal analysis of field sensitivities can be suitably achieved with a moderate size ensemble. [ABSTRACT FROM AUTHOR]

We perform global sensitivity analysis (GSA) through polynomial chaos expansion (PCE) on a contaminant transport model for the assessment of radionuclide concentration at a given control location in a heterogeneous aquifer, following a release from a near surface repository of radioactive waste. The aquifer hydraulic conductivity is modeled as a stationary stochastic process in space. We examine the uncertainty in the first two (ensemble) moments of the peak concentration, as a consequence of incomplete knowledge of (a) the parameters characterizing the variogram of hydraulic conductivity, (b) the partition coefficient associated with the migrating radionuclide, and (c) dispersivity parameters at the scale of interest. These quantities are treated as random variables and a variance-based GSA is performed in a numerical Monte Carlo framework. This entails solving groundwater flow and transport processes within an ensemble of hydraulic conductivity realizations generated upon sampling the space of the considered random variables. The Sobol indices are adopted as sensitivity measures to provide an estimate of the role of uncertain parameters on the (ensemble) target moments. Calculation of the indices is performed by employing PCE as a surrogate model of the migration process to reduce the computational burden. We show that the proposed methodology (a) allows identifying the influence of uncertain parameters on key statistical moments of the peak concentration (b) enables extending the number of Monte Carlo iterations to attain convergence of the (ensemble) target moments, and (c) leads to considerable saving of computational time while keeping acceptable accuracy. [ABSTRACT FROM AUTHOR]

Polynomial chaos (PC) expansions are used to propagate parametric uncertainties in ocean global circulation model. The computations focus on short-time, high-resolution simulations of the Gulf of Mexico, using the hybrid coordinate ocean model, with wind stresses corresponding to hurricane Ivan. A sparse quadrature approach is used to determine the PC coefficients which provides a detailed representation of the stochastic model response. The quality of the PC representation is first examined through a systematic refinement of the number of resolution levels. The PC representation of the stochastic model response is then utilized to compute distributions of quantities of interest (QoIs) and to analyze the local and global sensitivity of these QoIs to uncertain parameters. Conclusions are finally drawn regarding limitations of local perturbations and variance-based assessment and concerning potential application of the present methodology to inverse problems and to uncertainty management. [ABSTRACT FROM AUTHOR]

A multidisciplinary approach is implemented to model and analyse the performance of Olympic rowing boats. A reduced-order model that couples rowers motions with the hull, oars and hydrodynamic and hydrostatic forces is detailed. This model is complemented with a sensitivity analysis carried out by means of a non-intrusive polynomial chaos expansion. Sensitivity analysis results for two different boat classes, namely, a lightweight single scull and a coxless four are presented and discussed. This analysis contrasts, for both classes, the effects of varying forces exerted by the rowers, weights of rowers and cadence of motions on the boat performance. [ABSTRACT FROM AUTHOR]