Aerodynamic response of structures with parametric uncertainties

Effect of parametric uncertainties on wind excited structural response

This paper presents a framework for assessing the contribution of different sources of parametric uncertainty in sediment runoff simulations. The proposed uncertainty assessment is comprised in the three procedures. First, global parametric sensitivity and uncertainty analysis based on a Monte Carlo Simulation technique was applied to identify the dominant uncertainty sources. The analysis revealed a few parameters significantly affecting the model behaviours. Second, the propagation of parametric uncertainties through sediment runoff simulations was investigated, which identified that sediment simulations tend to involve more uncertainty than only streamflow simulations. Third, by conducting scenario simulations considering different uncertainty sources, it explores a strategy for reducing the parametric uncertainty considering its propagation effect. The proposed framework can provide useful information for improving sediment runoff modelling and its application to river basin management recognizing predictive uncertainty.

Abstract. The future of the Antarctic Ice Sheet in response to climate warming is one of the largest sources of uncertainty in estimates of future changes in global mean sea level (ΔGMSL). Mass loss is currently concentrated in regions of warm circumpolar deep water, but it is unclear how ice shelves currently surrounded by relatively cold ocean waters will respond to climatic changes in the future. Studies suggest that warm water could flush the Filchner–Ronne (FR) ice shelf cavity during the 21st century, but the inland ice sheet response to a drastic increase in ice shelf melt rates is poorly known. Here, we use an ice flow model and uncertainty quantification approach to project the GMSL contribution of the FR basin under RCP emissions scenarios, and we assess the forward propagation and proportional contribution of uncertainties in model parameters (related to ice dynamics and atmospheric/oceanic forcing) on these projections. Our probabilistic projections, derived from an extensive sample of the parameter space using a surrogate model, reveal that the FR basin is unlikely to contribute positively to sea level rise by the 23rd century. This is primarily due to the mitigating effect of increased accumulation with warming, which is capable of suppressing ice loss associated with ocean-driven increases in sub-shelf melt. Mass gain (negative ΔGMSL) from the FR basin increases with warming, but uncertainties in these projections also become larger. In the highest emission scenario RCP8.5, ΔGMSL is likely to range from −103 to 26 mm, and this large spread can be apportioned predominantly to uncertainties in parameters driving increases in precipitation (30 %) and sub-shelf melting (44 %). There is potential, within the bounds of our input parameter space, for major collapse and retreat of ice streams feeding the FR ice shelf, and a substantial positive contribution to GMSL (up to approx. 300 mm), but we consider such a scenario to be very unlikely. Adopting uncertainty quantification techniques in future studies will help to provide robust estimates of potential sea level rise and further identify target areas for constraining projections.

Parameter uncertainty in hydrologic modeling is commonly evaluated, but assessing the impact of spatial input data uncertainty in spatially descriptive ‘distributed’ models is not common. This study compares the significance of uncertainty in spatial input data and model parameters on the output uncertainty of a distributed hydrology and sediment transport model, HYdrology Simulation using Time-ARea method (HYSTAR). The Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm was used to quantify parameter uncertainty of the model. Errors in elevation and land cover layers were simulated using the Sequential Gaussian/Indicator Simulation (SGS/SIS) techniques and then incorporated into the model to evaluate their impact on the outputs relative to those of the parameter uncertainty. This study demonstrated that parameter uncertainty had a greater impact on model output than did errors in the spatial input data. In addition, errors in elevation data had a greater impact on model output than did errors in land cover data. Thus, for the HYSTAR distributed hydrologic model, accuracy and reliability can be improved more effectively by refining parameters rather than further improving the accuracy of spatial input data and by emphasizing the topographic data over the land cover data.

Water resources modelers face the challenge of dealing with numerous uncertainties due to the lack of knowledge of the natural systems, numerical approaches used in modeling (equations, parameters, structures, solutions), and field data collected to set up and evaluate models. Propagation of parameter uncertainty into model results is a relevant topic in environmental hydrology. Uncertainty analyses improve assessment of hydrological modeling. There is a need in modern hydrology of developing and testing uncertainty analysis methods that support hydrological model evaluation. In this research the propagation of model parameter uncertainty into streamflow model results is evaluated. The Hydrological Simulation Program – FORTRAN (HSPF) supported by the US Environmental Protection Agency was evaluated using hydroenvironmental data from the Luxapallila Creek watershed located in Mississippi and Alabama, USA. The uncertainty bounds of model outputs were computed using the Monte Carlo simulation and Harr’s point estimation methods. Analysis of parameter uncertainty propagation on streamflow simulations from 12 HSPF parameters was accomplished using 5,000 Monte Carlo random samples and 24 Harr selected points for each selected parameter. The comparison showed that Harr’s method could be an appropriate initial indicator of parameter uncertainty propagation on streamflow simulations, particularly for hydrology models with several parameters.

In order to maximise the impact automotive energy-absorbing capacity considering uncertainties in the parameters of the design, it is desired to perform a robust optimum design process. Moreover, the optimum design of such absorption system is inherently a multi-objective optimisation problem. In this paper, a multi-objective optimisation approach is thus proposed to consider the robustness issue of those objective functions in the presence of parameter uncertainties. First, the axial impact crushing behaviour of the S-shaped box beams, as a highly simplified model of the front member of a vehicle body, is studied by the finite-element method using the software ABAQUS. Two polynomial meta-models based on the evolved group method of data handling (GMDH) neural networks are then obtained to simply represent both the absorbed energy (E) and the peak crushing force (F max) with respect to geometrical and material design variables using the training and testing data obtained from the finite-element study. Using such obtained polynomial neural network models and the Monte Carlo simulation, a multi-objective genetic algorithm is then used for the reliability-based robust Pareto design of the S-shaped box beams having probabilistic uncertainties in material and geometrical parameters. In this way, the statistical moments of mean and variances of the important crashworthiness criteria functions, namely the specific energy absorption (SEA) and the peak crushing force (F max), are considered as the conflicting objectives. It is shown that some useful optimal design principles involved in the performance of the S-shaped box beams can be discovered by the reliability-based robust Pareto optimisation.

A probabilistic framework and the supporting tools are developed and demonstrated to investigate the out-of-plane properties of a composite lamina. The framework methodology consists of a sensitivity analysis to determine the most influential input parameters followed by a probabilistic analysis to quantify the effects of the uncertainty in these parameters on lamina properties. To demonstrate the framework, sensitivity analysis is performed through finite element analysis of unit cell models to identify the most influential constituent and configuration parameters on lamina behavior, specifically on out-of-plane lamina properties. The effects of uncertainty in these input parameters are then quantified through Monte Carlo simulation using probabilistic distributions to represent each input under consideration. One of three distribution types (Normal, Lognormal, and Weibull) can be assigned, and a different distribution type can represent each input parameter. To study configuration effects, a representative volume element (RVE) consisting of two different fiber materials is investigated. The location and percent composition of the two different fiber materials are varied to analyze their effects on out-of-plane lamina properties.

<strong class="journal-contentHeaderColor">Abstract.</strong> Due to the remote location of many volcanoes, there is substantial uncertainty about the timing, amount and vertical distribution of volcanic ash released when they erupt. One approach to determine these properties is to combine prior estimates with satellite retrievals and simulations from atmospheric dispersion models to create posterior emission estimates, constrained by both the observations and the prior estimates, using a technique known as source inversion. However, the results are dependent not only on the accuracy of the prior assumptions, the atmospheric dispersion model and the observations used, but also on the accuracy of the meteorological data used in the dispersion simulations. In this study, we advance the source inversion approach by using an ensemble of meteorological data from the Met Office Global and Regional Ensemble Prediction System to represent the uncertainty in the meteorological data and apply it to the 2019 eruption of Raikoke. Retrievals from the Himawari-8 satellite are combined with NAME dispersion model simulations to create posterior emission estimates. The use of ensemble meteorology provides confidence in the posterior emission estimates and associated dispersion simulations that are used to produce ash forecasts. Prior mean estimates of fine volcanic ash emissions for the Raikoke eruption based on plume height observations are more than 15 times higher than any of the mean posterior ensemble estimates. In addition, the posterior estimates have a different vertical distribution, with 27 %–44 % of ash being emitted into the stratosphere compared to 8 % in the mean prior estimate. This has consequences for the long-range transport of ash, as deposition to the surface from this region of the atmosphere happens over long timescales. The posterior ensemble spread represents uncertainty in the inversion estimate of the ash emissions. For the first 48 h following the eruption, the prior ash column loadings lie outside an estimate of the error associated with a set of independent satellite retrievals, whereas the posterior ensemble column loadings do not. Applying a risk-based methodology to an ensemble of dispersion simulations using the posterior emissions shows that the area deemed to be of the highest risk to aviation, based on the fraction of ensemble members exceeding predefined ash concentration thresholds, is reduced by 49 %. This is compared to estimates using an ensemble of dispersion simulations using the prior emissions with ensemble meteorology. If source inversion had been used following the eruption of Raikoke, it would have had the potential to significantly reduce disruptions to aviation operations. The posterior inversion emission estimates are also sensitive to uncertainty in other eruption source parameters and internal dispersion model parameters. Extending the ensemble inversion methodology to account for uncertainty in these parameters would give a more complete picture of the emission uncertainty, further increasing confidence in these estimates.

A multiresolution approach is presented to study the uncertainty propagation problem in dynamic systems. The proposed approach is an extension of the generalized polynomial chaos and involves a separation of random variables from deterministic ones in the solution algorithm for a stochastic dierential equation. The random variables are expanded in various local polynomial expansions which are further blended together to obtain a global approximation for the random state variables. These polynomials are associated with the assumed probability density functions for the input variables. Galerkin projection is used to generate a system of deterministic dierential equations for the expansion coecients. We rst present this method to linear systems with parametric uncertainties, and subsequently we generalize it to nonlinear systems with parametric and initial condition uncertainties. The eectiveness of the proposed method is demonstrated by considering dierent numerical examples.

Understanding uncertainty in crop modeling is essential for improving prediction accuracy and decision-making in agricultural management. Monte Carlo simulations are widely used for uncertainty and sensitivity analysis, but their application to closed-source models like AquaCrop presents significant challenges due to the lack of direct access to source code. This study introduces Aqua-MC, an automated framework designed to facilitate Monte Carlo simulations in AquaCrop by integrating probabilistic parameter selection, iterative execution, and uncertainty quantification within a structured workflow. To demonstrate its effectiveness, Aqua-MC was applied to wheat yield modeling in Qazvin, Iran, where parameter uncertainty was assessed using 3000 Monte Carlo simulations. The DYNIA (Dynamic Identifiability Analysis) method was employed to evaluate the time-dependent sensitivity of 47 model parameters, providing insights into the temporal evolution of parameter influence. The results revealed that soil evaporation and yield predictions exhibited the highest uncertainty, while transpiration and biomass outputs were more stable. The study also highlighted that many parameters had low impact, suggesting that reducing the number of free parameters could enhance model efficiency. Despite its advantages, Aqua-MC has some limitations, including its computational intensity and reliance on the GLUE method, which may overestimate uncertainty bounds. To improve applicability, future research should focus on parallel computing, cloud-based execution, integration with machine learning techniques, and expanding Aqua-MC to multi-crop studies. By overcoming the limitations of closed-source models, Aqua-MC provides a scalable and efficient solution for performing large-scale uncertainty analysis in crop modeling.

Yucca Mountain has been proposed by the U.S. Department of Energy as the nation’s long-term, permanent geologic repository for spent nuclear fuel or high-level radioactive waste. The potential repository would be located in Yucca Mountain’s unsaturated zone (UZ), which acts as a critical natural barrier delaying arrival of radionuclides to the water table. Since radionuclide transport in groundwater can pose serious threats to human health and the environment, it is important to understand how much and how fast water and radionuclides travel through the UZ to groundwater. The UZ system consists of multiple hydrogeologic units whose hydraulic and geochemical properties exhibit systematic and random spatial variation, or heterogeneity, at multiple scales. Predictions of radionuclide transport under such complicated conditions are uncertain, and the uncertainty complicates decision making and risk analysis. This project aims at using geostatistical and stochastic methods to assess uncertainty of unsaturated flow and radionuclide transport in the UZ at Yucca Mountain. Focus of this study is parameter uncertainty of hydraulic and transport properties of the UZ. The parametric uncertainty arises since limited parameter measurements are unable to deterministically describe spatial variability of the parameters. In this project, matrix porosity, permeability and sorption coefficient of the reactive tracer (neptunium) of the UZ are treated as random variables. Corresponding propagation of parametric uncertainty is quantitatively measured using mean, variance, 5th and 95th percentiles of simulated state variables (e.g., saturation, capillary pressure, percolation flux, and travel time). These statistics are evaluated using a Monte Carlo method, in which a three-dimensional flow and transport model implemented using the TOUGH2 code is executed with multiple parameter realizations of the random model parameters. The project specifically studies uncertainty of unsaturated flow and radionuclide transport caused by multi-scale heterogeneity at the layer and local scales. Typically, in studies of Yucca Mountain, the layer scale refers to hydrogeologic layers with layer-wise average properties, and the local scale refers to the spatial variation of hydraulic properties within a layer. While most studies of radionuclide transport in the UZ have been conducted at the layer scale, the uncertainty at the local scale within a layer is also important, since it affects flow path, velocity, and travel time of radionuclide. This report first presents the uncertainty caused by layer-scale heterogeneity of matrix permeability, porosity, and sorption coefficients of reactive tracers. Homogeneous fields of the parameters are generated at each hydrogeologic layer for Monte Carlo simulations. This study is referred to as the homogeneous case. To assess the uncertainty caused by local-scale heterogeneity, the sequential Gaussian simulator (SGSIM) of GSLIB (Deutsch and Journel, 1998) is used to generate heterogeneous parameter fields within each layer, and Monte Carlo simulations are conducted. This study is referred to as the heterogeneous cases. For the homogeneous and heterogeneous cases, the mean, variance, 5th and 95th percentiles of simulated state variables are estimated for uncertainty assessment. In addition, the statistics of the two cases are compared to investigate effect of local-scale heterogeneity on the unsaturated flow and radionuclide transport. It is found that the local-scale heterogeneity increased the predictive uncertainty of percolation flux and cumulative mass arrival for computational blocks below the footprint of proposed repository, whereas mean predictions are hardly affected. The local-scale heterogeneity significantly affects travel times to the water table for both conservative and reactive tracers. In the early simulation period, tracer mean travel times are delayed, whereas the influence of local-scale heterogeneity diminishes during the late simulation period. Simulated state variables in this project are more realistic than those of using one- or two dimensional models, due to a three-dimensional numerical model used in the project to characterize hydrological conditions at the UZ. Therefore, we expect that results of this project can be used directly to facilitate DOE site performance analysis and decision making.

This paper assesses the effects of (1) the gravity load‐resisting system (GLRS) modeling approach, (2) the seismic force‐resisting system (SFRS) modeling approach, and (3) the uncertainty of the model parameters of the constitutive law of the longitudinal reinforcing steel of the SFRS on the seismic responses of a 12‐story reinforced concrete wall building with force‐limiting connections. This is achieved by conducting nonlinear numerical earthquake simulations. The seismic responses of the building models with force‐limiting connections using two GLRS modeling approaches, (1) a moment frame system and (2) a pin‐base lean‐on‐column system, are compared. The seismic responses of the building models with conventional connections and force‐limiting connections, respectively, using two SFRS modeling approaches, (1) a distributed‐plasticity modeling approach and (2) a lumped‐plasticity modeling approach, are compared. A joint probability density function for the ASTM‐A615 Grade 60 steel available in the literature is used to conduct an uncertainty propagation analysis through Monte Carlo simulation. The uncertainty in the steel model parameters is propagated to the seismic responses of the building models with conventional connections and force‐limiting connections, respectively. The distributions of the mean values of the peak structural responses of the building models are studied. The effects of the GLRS modeling approach on the seismic responses are not significant in the context of seismic performance‐based design and assessment of buildings with force‐limiting connections. The effects of the SFRS modeling approach and the uncertainty in the steel model parameters on the floor total acceleration and force responses are reduced by including force‐limiting connections.

This thesis is concerned with the calibration of disease models in order to inform decisions about public health problems. These models are used to make predictions about the likely outcomes of disease spread (e.g. morbidity and mortality) in a population, given different interventions (e.g. vaccination, screening and treatment). These models necessitate simpli cations of the underlying mechanisms of disease progression, but have become essential tools in areas such as cost-effectiveness research. Although there are many types of models that can be used, all of them involve parameters, which affect the model's outputs, for example, the age of onset of illness, duration of particular health states or disease specifc mortality. Identifying areas of the model's parameter space that are consistent with data is referred to as model calibration. One of the areas of concern when searching a model's parameter space to get a prediction from the model (that best agrees with observed data) is the propagation of uncertainty. If one has a prediction about an outcome, the question of how uncertain we are about this prediction should be raised. In model calibration, the uncertainty we are interested in is uncertainty in parameters[5]. There are many approaches to model calibration with little consensus on the best practice. Additionally, within the current approaches, some signifi cant problems, that one could face when attempting calibration, merit further examination. We highlight this with a literature search. We believe, that many popular approaches have not yet addressed fundamental issues and more research may be needed to tackle these issues. The model calibrations in this thesis are carried out in a Bayesian framework, using Markov chain Monte Carlo (MCMC) techniques. Although the ultimate goal of calibration should be predictions about some quantities of interest, the emphasis of this work is on the techniques and methodology of model calibration in general. Many possible difficulties of using MCMC and some other sampling approaches are presented and discussed. Avenues for additional research are identified.

Scientists and decision-makers globally confront systemic challenges posed by the intertwining issues of water scarcity and climate change. These challenges give rise to cascading impacts across ecological and socioeconomic systems, often exacerbated by feedback loops and unforeseeable consequences (UNDRR, 2021). As non-linear changes loom, the reliance on consolidative modeling becomes dangerous, risking the activation of disastrous tipping points with severe implications for both nature and humans (Kreibich et al., 2022). The costs associated with neglecting uncertainties in modeling and policy spans diverse domains, including ecosystems, income, employment, capital value, insurance, etc. (UNDRR, 2022; Parrado et al., 2019; Adamson and Loch, 2021). This aligns with the concept of Knightian or deep uncertainty, where the external context, system dynamics, and conflicting outcomes are not fully known or agreed upon (Knight, 1921; Marchau et al., 2019; Lempert et al., 2006). A growing scientific and policy consensus emphasizes the need to move beyond traditional notions of optimality and deterministic prediction in conditions of deep uncertainty. Resilience and robustness emerge as crucial concepts, requiring the development of socio-ecological system (SES) models that explicitly quantify uncertainties (Adamson and Loch, 2021; Di Baldassarre et al., 2016; IPCC, 2021; UNDRR, 2021).Recent research in SES, including coupled human and natural systems and socio-hydrology science, offers innovative modeling techniques integrating human and natural components. These techniques account for feedbacks and heterogeneity between systems, improving insight and the ability to predict tipping points (Gain et al., 2021). Recent studies demonstrate the potential of linking coupled models of human-water systems with sensitivity analysis and multi-system ensembles for robust water management policies (Basheer et al., 2023; Smith et al., 2021).This review initially identified 2160 papers, filtering them to 198 studies that account quantitatively modelling in, both human and water systems. The geographical focus spans the USA, Europe, Australia, the Middle East, South America, China, and East Africa. The models range from piecewise equations to full-fledged representations. However, structural uncertainties are seldom explored, with only 3.5% of studies conducting multi-model ensemble experiments. This highlights a significant oversight in recognizing biases from simplifications. Conversely, parameter uncertainties are more frequently addressed (20.2%), focusing on hydrology, groundwater, behavioral, infrastructure, climatic, economic, and agronomic variables. Input uncertainties, notably contemporary (discharge data) and future (climate change) inputs, are extensively studied (148 out of 198), employing methods like expert judgment and Monte Carlo simulations. Despite this, the review highlights a limited exploration of structural uncertainties and the potential inadequacy of linear piecewise equations, emphasizing the need for more nuanced and robust approaches to enhance the accuracy and reliability of socio-environmental systems modeling.Based on this study, we make the following recommendations to mainstream uncertainty quantification into SES modeling: (i) Quantify parameter and structural uncertainties within systems, (ii) Quantify structural uncertainties between models, (iii) Input uncertainties must be more thoroughly assessed and model assumptions systematically revised, (iv) Deliver actionable science that mainstreams uncertainty quantification into decision making, (v) Establish balanced stakeholder engagement and clear and transparent science-policy engagement rules, (vi) Balance complexity and usefulness to keep the model relevant.

Groundwater flow and mass transport predictions are subjected to uncertainty due to heterogeneity of hydraulic conductivity, whose variability in space is considerably higher than that of other hydraulic properties relevant to groundwater flow. To characterize the distribution of hydraulic conductivity, random space function (RSF) is often used. The Bayesian approach was applied to quantitatively study the effect of parameter uncertainty in RSF on a hypothetical two-dimensional uniform groundwater flow and mass transport. Specifically, the parameter uncertainty transmitted to macrodispersion in mass transport model was also inferred. The results showed that the posterior probability distributions of parameters were updated after Bayesian inference. The numerical experiments indicated that the overall predictive uncertainty was increased with simulating time along the flow direction. As to the relative contribution of the two types of uncertainty, it indicated that parametric uncertainty was a little more important than stochastic uncertainty for the predictive uncertainty of hydraulic head. When the uncertainty of hydraulic head as well as macrodispersion was transported to mass transport model, a much bigger contribution of stochastic uncertainty was observed. Therefore, parametric uncertainty should not be neglected during the process of subsurface simulation.