Uncertainty Propagation Analysis Research Articles

Addressing uncertainty in modelling cumulative impacts within maritime spatial planning in the Adriatic and Ionian region.

Maritime spatial planning (MSP) is envisaged as a tool to apply an ecosystem-based approach to the marine and coastal realms, aiming at ensuring that the collective pressure of human activities is kept within acceptable limits. Cumulative impacts (CI) assessment can support science-based MSP, in order to understand the existing and potential impacts of human uses on the marine environment. A CI assessment includes several sources of uncertainty that can hinder the correct interpretation of its results if not explicitly incorporated in the decision-making process. This study proposes a three-level methodology to perform a general uncertainty analysis integrated with the CI assessment for MSP, applied to the Adriatic and Ionian Region (AIR). We describe the nature and level of uncertainty with the help of expert judgement and elicitation to include all of the possible sources of uncertainty related to the CI model with assumptions and gaps related to the case-based MSP process in the AIR. Next, we use the results to tailor the global uncertainty analysis to spatially describe the uncertainty distribution and variations of the CI scores dependent on the CI model factors. The results show the variability of the uncertainty in the AIR, with only limited portions robustly identified as the most or the least impacted areas under multiple model factors hypothesis. The results are discussed for the level and type of reliable information and insights they provide to decision-making. The most significant uncertainty factors are identified to facilitate the adaptive MSP process and to establish research priorities to fill knowledge gaps for subsequent planning cycles. The method aims to depict the potential CI effects, as well as the extent and spatial variation of the data and scientific uncertainty; therefore, this method constitutes a suitable tool to inform the potential establishment of the precautionary principle in MSP.

Uncertainties in the estimation of in situ stresses: effects of heterogeneity and thermal perturbation

In situ stress directions and magnitudes in subsurface are commonly estimated using two different methods: (1) borehole break-out—drilling-induced fracture interpretation complemented by extended leak-off tests; (2) stress estimation from acoustic measurements using advanced wireline tools. Both methods use stress perturbations around boreholes to estimate far field stresses employing Kirsch’s equations, which are only valid for boreholes aligned with one of the principal stresses, linear elastic deformation and homogeneous isotropic materials. Furthermore, the original stress state may have been altered by drilling-mud-circulation induced temperature changes. Using heuristic models including heterogeneity, this study investigates potential errors in the estimation of far-field stress due to (a) the generalisation of Kirsch’s equations to heterogeneous media and (b) plausible temperature perturbations. First, errors due to uncertainties in measuring wave slowness are analysed for an idealised homogeneous material. Second, errors due to application of Kirsch’s equations are investigated considering potential effects of frictional interfaces between layers, pore pressure in the rock matrix and thermal perturbations induced by drilling for example cases. To analyse stress in these complex scenarios finite element analysis was used, revealing strong effects of lithological and thermal variations. Stress magnitude was amplified by stiff layers and was attenuated by soft ones. At layer interfaces, substantial changes in stress orientation occurred. Kirsch’s equations for the considered cases resulted in errors in far field stresses as large as 44% in the magnitude and 90° in orientations. An uncertainty propagation analysis indicated a high accuracy of acoustic estimates for homogenous materials. However, a dramatic impact of small-scale heterogeneity may not be resolved by the logging process.

The uncertainty propagation analysis of the projectile-barrel coupling problem

Abstract Based on the model which couples the projectile and gun barrel during an interior ballistic cycle, the uncertainty propagation analysis of the model is presented caused by the uncertainty of the input parameters. The Bootstrap method is employed to calculate the statistical moments (i.e. the mean, variance, skewness coefficient and kurtosis coefficient) of the parameters of the projectile. Meanwhile, the maximum entropy method is used to estimate the probability density function (PDF) and the cumulative density function (CDF), the interval of the parameters of the projectile are also given. Moreover, the results obtained are compared to the results calculated by Monte Carlo (MC) method to verify the effectiveness of the presented method. Finally, the rule and the uncertainty propagation model of the projectile-barrel coupling system are given with the variation of the uncertainties of the input parameters.

A unified response surface framework for the interval and stochastic finite element analysis of structures with uncertain parameters

In this paper, finite element analysis of structures with uncertain properties is addressed within both a probabilistic and non-probabilistic framework. Specifically, uncertainties affecting structural parameters are modelled either as interval or random variables. In both cases, uncertainty propagation analysis is performed by applying a ratio of polynomial response surface which enables to derive approximate closed-form expressions of the main descriptors of interval and random response variability by requiring just a few deterministic analyses at selected sampling points. A unified response surface framework for interval and stochastic finite element analysis is thus developed which allows comparisons of structural response variability under different uncertainty models. Numerical results focusing on the comparison between the interval and stochastic response of structures with uncertain Young’s modulus are presented.

Uncertainty quantification of 2 models of cardiac electromechanics.

Computational models of the heart have reached a maturity level that render them useful for in silico studies of arrhythmia and other cardiac diseases. However, the translation to the clinic of cardiac simulations critically depends on demonstrating the accuracy, robustness, and reliability of the underlying computational models under the presence of uncertainties. In this work, we study for the first time the effect of parameter uncertainty on 2 state-of-the-art coupled models of excitation-contraction of cardiac tissue. To this end, we perform forward uncertainty propagation and sensitivity analyses to understand how variability in key maximal conductances affect selected quantities of interest, such as the action potential duration (APD90 ), maximum intracellular calcium concentration, cardiac stretch, and stress. Our results suggest a strong linear relationship between selected maximal conductances and quantities of interest for a variability in parameters up to 25%, which justifies the construction of linear response surfaces that are used to compute the empirical probability density functions of all the quantities of interest under study. For both electromechanical models analyzed, uncertainty in the material parameters associated to the passive mechanical response of cardiac tissue does not affect the duration of action potentials, neither the amplitude of intracellular calcium concentrations. Our results confirm the poor mechanoelectric feedback that classical models of cardiac electromechanics have, even under the presence of parameter uncertainty.

Orbit uncertainty propagation and sensitivity analysis with separated representations

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.

A vine-copula-function-based structural uncertainty propagation analysis method

Most of the existing uncertainty propagation analysis methods assume that the input variables are independent of each other. However, in practical engineering, there are a lot of correlations among variables. In order to solve this problem, this paper proposes a vine copula based structural uncertainty propagation analysis method which is an effective approach for performing an uncertainty propagation analysis on complex multidimensional correlation problems. First, a joint probability distribution function (PDF) among multidimensional input random variables is established using a vine copula function. Second, correlated variables are transferred to independent variables by Rosenblatt transformation and the first four original moments of the response are calculated by dimension reduction integration method. Third, PDF of response is calculated by maximum entropy principle. Three numerical examples indicate that this method produces small discrepancy compared with Monte Carlo Simulation and is satisfactory respect to computation accuracy and efficiency. This method can be used to analyze the uncertainty propagation of complex engineering problems with complex correlations.

Global sensitivity analysis as a support for the generation of simplified building stock energy models

Buildings are responsible for 40% of total final energy consumptions in Europe. Numerous bottom-up models were recently developed to support local authorities in assessing the energy consumption of large building stocks and reduction potentials. However, current models rarely consider uncertainty associated to building usage and characteristics within the stock, resulting in potentially biased results.This study presents a generic model simplification approach using uncertainty propagation and stochastic sensitivity analysis to derive fast simplified (surrogate) models to estimate the current building stock energy use for improved urban planning. The methodology includes an engineering-based energy model as input to global sensitivity analysis (GSA) using the elementary effects (EE) screening and Sobol’ method for key parameters identification and regression analysis to derive simplified models for entire building stocks.The application to the housing stock of Esch-sur-Alzette (Luxembourg) showed that the parameters explaining most of the variability in final energy use for heating and domestic hot water are floor area, set-point temperature, external walls U-values, windows and heating system type. Results of the simplified models were validated against measured data and confirmed the validity of the approach for a simple yet robust assessment of the building stock energy use considering uncertainty and variability.

Uncertainty analysis with double heterogeneity treatment based on the generalized perturbation theory

Two generalized adjoint solution modules, the generalized adjoint transport equation solver and the generalized adjoint B1 equation solver, were implemented into DeCART for the general response uncertainty analysis on the doubly heterogeneous system. The generalized adjoint transport equation solver for the doubly heterogeneous system was implemented based on the Sanchez-Pomraning method. Moreover, the generalized adjoint B1 equation solution scheme was newly set up using the adjoint B1 equation for an efficient calculation. From the benchmark analysis on the MHTGR-350 Ex. I-1, it was confirmed that the two generalized adjoint solver can provide reliable results for the doubly heterogeneous region. Then, the uncertainties for the kinf and the microscopic cross sections on the same problem were evaluated using DeCART/MUSAD code system. The results reveal that the double heterogeneity does not have a significant effect on the kinf uncertainty but slightly increases the uncertainty of 238U capture compared with the homogeneous case.

反应堆压力容器水位测量不确定度评定研究

压力容器水位是核电厂设计和运行关注的重点参数之一，本文利用标准不确定度评定方法，结合CPR1000核电厂RPVL测量方法及相关数据，建立了压力容器水位测量不确定度评定模型，为压力容器水位测量不确定度评定提出了具体的方法。为今后核电厂压力容器水位设计和运行，以及进行性能改进提供了理论依据和指导方向。 Pressure vessel water level is one of the key parameters in nuclear power plant design and opera-tion. This paper researched on general uncertainty analysis model of pressure vessel water level measurement, based on the standard uncertainty analysis method. And the CPR1000 nuclear power plant RPVL measurement system and data were used to elaborate the specific uncertainty analysis method of water level measurement. This uncertainty analysis method could be retained as reference and guidance to pressure vessel water level measurement design, maintenance and performance improvement.

The path for innovative severe accident neutronics studies in ZPRs. part I.2 - Interpretation of SNEAK-12A experiment for core disruption in LMFBRs impact of nuclear data uncertainties on reactivity coefficients

The present work details a further investigation of the SNEAK-12A experimental program, which aimed to study material relocation in Sodium Fast Reactors (SFRs) leading to core degradation. The further investigation include sensitivity and uncertainty propagation analysis. In this paper, a comparison is made using two codes, a Monte Carlo based code Serpent 2 and the deterministic system code ERANOS. A sensitivity analysis was made utilizing the two codes, with comparison of two nuclear data libraries (ENDF/B-VII.1 and JEFF-3.1.1). The code-to-code comparison resulted in a very good agreement, while the comparison of libraries showed large discrepancies, manly due to the differences in the sodium cross-section data. The sensitivity analysis, was followed by a complete propagated uncertainty analysis based on the covariance evaluated data available in the COMAC data evaluation. The results of the uncertainties show that there are still large discrepancies linked to the nuclear data. This work is done within the frame work of new core design capacities and new ways of conducting in Zero Power Reactors, such as the ZEPHYR project led independently by CEA.

A CONSISTENT DATA FUSION APPROACH FOR UNCERTAINTY QUANTIFICATION IN RIGID MUSCULOSKELETAL SIMULATION

Uncertainty quantification in rigid musculoskeletal modeling is essential to analyze the risks related to the simulation outcomes. Data fusion from multiple sources is a potential solution to reduce data uncertainties. This present study aimed at proposing a new data fusion rule leading to a more consistent and coherent data for uncertainty quantification. Moreover, a new uncertainty representation was developed using imprecise probability approach. A biggest maximal coherent subsets (BMCS) operator was defined to fuse interval-valued data ranges from multiple sources. Fusion-based probability-box structure was developed to represent the data uncertainty. Case studies were performed for uncertainty propagation through inverse dynamics and static optimization algorithms. Hip joint moment and muscle force estimation were computed under effect of the uncertainties of thigh mass and muscle properties. Respective p-boxes of these properties were generated. Regarding the uncertainty propagation analysis, correlation coefficients showed a very good value ([Formula: see text]) for the proposed fusion operator according to classical operators. Muscle force variation of the rectus femoris was computed. Peak-to-peak (i.e., difference between maximal values) rectus femoris forces showed deviations of 55[Formula: see text]N and 40[Formula: see text]N for the first and second peaks, respectively. The development of the new fusion operator and fusion-based probability-box leads to a more consistent uncertainty quantification. This allows the estimation of risks associated with the simulation outcomes under input data uncertainties for rigid musculoskeletal modeling and simulation.

A Statistical Direct Volume Rendering Framework for Visualization of Uncertain Data.

With uncertainty present in almost all modalities of data acquisition, reduction, transformation, and representation, there is a growing demand for mathematical analysis of uncertainty propagation in data processing pipelines. In this paper, we present a statistical framework for quantification of uncertainty and its propagation in the main stages of the visualization pipeline. We propose a novel generalization of Irwin-Hall distributions from the statistical viewpoint of splines and box-splines, that enables interpolation of random variables. Moreover, we introduce a probabilistic transfer function classification model that allows for incorporating probability density functions into the volume rendering integral. Our statistical framework allows for incorporating distributions from various sources of uncertainty which makes it suitable in a wide range of visualization applications. We demonstrate effectiveness of our approach in visualization of ensemble data, visualizing large datasets at reduced scale, iso-surface extraction, and visualization of noisy data.

Ignoring correlation in uncertainty and sensitivity analysis in life cycle assessment: what is the risk?

Life cycle assessment (LCA) is an established tool to quantify the environmental impact of a product. A good assessment of uncertainty is important for making well-informed decisions in comparative LCA, as well as for correctly prioritising data collection efforts. Under- or overestimation of output uncertainty (e.g. output variance) will lead to incorrect decisions in such matters. The presence of correlations between input parameters during uncertainty propagation, can increase or decrease the the output variance. However, most LCA studies that include uncertainty analysis, ignore correlations between input parameters during uncertainty propagation, which may lead to incorrect conclusions. Two approaches to include correlations between input parameters during uncertainty propagation and global sensitivity analysis were studied: an analytical approach and a sampling approach. The use of both approaches is illustrated for an artificial case study of electricity production. Results demonstrate that both approaches yield approximately the same output variance and sensitivity indices for this specific case study.Furthermore, we demonstrate that the analytical approach can be used to quantify the risk of ignoring correlations between input parameters during uncertainty propagation in LCA. We demonstrate that: (1) we can predict if including correlations among input parameters in uncertainty propagation will increase or decrease output variance; (2) we can quantify the risk of ignoring correlations on the output variance and the global sensitivity indices. Moreover, this procedure requires only little data.

Validation of wax deposition models with recent laboratory scale flow loop experimental data

Experimental data at various conditions are important for improving wax deposition prediction and upscaling efforts. This study consolidates several single-phase wax deposition data acquired in recent years and validates several wax deposition models for a comprehensive range of experimental conditions. The film mass transfer (FMT), equilibrium (EM), Matzain (1999), and Venkatesan (2004) models were tested against 70 experimental data points (19 sets of initial operating conditions), obtained with four different oils and flow loop facilities. Uncertainty propagation analysis was performed to estimate reasonable ranges of error in the prediction that may be caused by fluid properties or standard correlations instead of the model formulation itself. The FMT model regularly over-predicts the deposition rate, which is consistent with previous theoretical, experimental, and visualization studies. It is observed that EM does not necessarily serves as the lower bound of deposition rate, suggesting that some form of flux reduction effects may exist. Sherwood number analysis was performed to validate conclusions from FMT and EM model assessment. A fix set of shear coefficient values in Venketasan's model is not sufficient to achieve acceptable accuracy in general, indicating that the shear coefficients are likely to be oil and flow conditions dependent. Matzain's model delivers relatively superior performance on deposit wax mass and flux predictions among the four models, although it is still unable to predict aging mechanistically and the deposition trends as a whole. In conclusion, more mechanistically rigorous wax deposition models and experimental data are still needed.

ITOUGH2: A multiphysics simulation-optimization framework for analyzing subsurface systems

iTOUGH2 is a simulation-optimization framework for the TOUGH suite of nonisothermal multiphase flow models and related simulators of geophysical, geochemical, and geomechanical processes. After appropriate parameterization of subsurface structures and their properties, iTOUGH2 runs simulations for multiple parameter sets and analyzes the resulting output for parameter estimation through automatic model calibration, local and global sensitivity analyses, data-worth analyses, and uncertainty propagation analyses. Development of iTOUGH2 is driven by scientific challenges and user needs, with new capabilities continually added to both the forward simulator and the optimization framework. This review article provides a summary description of methods and features implemented in iTOUGH2, and discusses the usefulness and limitations of an integrated simulation-optimization workflow in support of the characterization and analysis of complex multiphysics subsurface systems.

Integrated failure probability estimation based on structural integrity analysis and failure data: Natural gas pipeline case

In this paper, the authors present an approach as an overall framework for the estimation of the failure probability of pipelines based on: the results of the deterministic-probabilistic structural integrity analysis (taking into account loads, material properties, geometry, boundary conditions, crack size, and defected zone thickness), the corrosion rate, the number of defects and failure data (involved into the model via application of Bayesian method). The proposed approach is applied to estimate the failure probability of a selected part of the Lithuanian natural gas transmission network. The presented approach for the estimation of integrated failure probability is a combination of several different analyses allowing us to obtain: the critical crack's length and depth, the failure probability of the defected zone thickness, dependency of the failure probability on the age of the natural gas transmission pipeline. A model's uncertainty analysis and uncertainty propagation analysis are performed, as well.

Simulation-based robust design of complex product considering uncertainties of metamodel, design variables, and noise parameters

The uncertainties of design variables, noise parameters, and metamodel are important factors in simulation-based robust design optimization. Most conventional metamodel construction methods only consider one or two uncertainties. In this paper, a new surrogate modeling method simultaneously measuring all the uncertainties is proposed for simulation-based robust design optimization of complex product. The effect of metamodel uncertainty on product performance uncertainty is quantified through uncertainty propagation analysis among design variables uncertainty, noise parameters uncertainty, metamodel uncertainty, and performance uncertainty. Then, the sampling points are selected and the metamodel is constructed based on the predictive interval of product performance and mean square error of the Kriging metamodel. The constructed metamodel is applied to robust design optimization considering multiple uncertainties. Results of two mathematical examples show that the proposed metamodel considering multiple uncertainties increases the result accuracy of robust design optimization. Finally, the proposed algorithm is applied to robust design optimization of a heat exchanger, and the total heat transfer rate is enhanced under uncertainties of fin structural parameters, operation conditions parameters and simulation metamodel.

Robustness in network community detection under links weights uncertainties

In network analysis, a community can be defined as a group of nodes of a network (or clusters) that are densely interconnected with each other but only sparsely connected with the rest of the network. Several algorithms have been used to obtain a convenient partition allowing extracting the communities in a given network, based on their topology and, possibly, the weights of links. These weights usually represent specific characteristics for example: distance, reactance, reliability. Even if the optimum partitions could be derived, there are uncertainties associated to the network parameters that affect the network partition. In this paper, the authors extend a previous approach for assessing the effects of weight uncertainties on community structures and propose a global approach for (a) understanding the global similarity among the partitions; (b) analyzing the robustness of the communities derived without uncertainty; and (c) quantifying the robustness of the inter-community links. To this aim an uncertainty propagation analysis, based on the Monte Carlo technique is proposed. The approach is illustrated through analyzing the topology of an electric power system.

Nuclear data uncertainty propagation analysis for depletion calculation in PWR and FR pin-cells

In order to assess the nuclear data uncertainty propagation in the depletion calculation, a computational code named SUNDEW has been developed based on the home-developed lattice code NECP-CACTI. In the SUNDEW, Generalized Perturbation Theory (GPT) is applied to calculate sensitivity coefficients of response function with respect to the nuclear cross sections. Method of Characteristics (MOC) is employed to solve the transport equation, adjoint and generalized adjoint transport equations. Chebyshev Rational Approximation Method (CRAM) is implemented to solve the depletion equation and adjoint depletion equation. The sensitivity coefficients of Keff and nuclide density with respect to the nuclear cross sections are verified by comparing with the results of direct perturbation calculation. The uncertainties on Keff and the nuclide density at different depletions, which are induced by the nuclear cross sections uncertainties, are analyzed based on ENDF/B-VII.1 covariance data for LWR and fast reactor pin-cells. The numerical results show that there are significant differences between LWR and fast reactor pin-cells. The differences are mainly caused by the differences of the sensitivity coefficients between the LWR and fast reactor pin-cells. In addition, to identify the cross section improvement priority for nuclides, reactions and energy ranges, the dominant contributors to Keff and nuclide density uncertainties are analyzed at different depletions.