Uncertainty Propagation for Compositional Flow Using a Probability Distribution Method

We present a new variable-step Gauss–Legendre implicit-Runge–Kutta-based approach for orbit and uncertainty propagation, VGL-IRK, which includes adaptive step-size error control and which collectively, rather than individually, propagates nearby sigma points or states. The performance of VGL-IRK is compared to a professional (variable-step) implementation of Dormand–Prince 8(7) (DP8) and to a fixed-step, optimally-tuned, implementation of modified Chebyshev–Picard iteration (MCPI). Both nearly-circular and highly-elliptic orbits are considered using high-fidelity gravity models and realistic integration tolerances. VGL-IRK is shown to be up to eleven times faster than DP8 and up to 45 times faster than MCPI (for the same accuracy), in a serial computing environment. Parallelization of VGL-IRK and MCPI is also discussed.

Uncertainty propagation: Avoiding the expensive sampling process for real-time image-based measurements

We present a statistical framework for model calibration and uncertainty estimation for complex deterministic models. A Bayesian approach is used to combine data from observations, the deterministic model, and prior parameter distributions to obtain forecast distributions. A case study is presented in which the statistical framework is applied using the hydrogeochemical model (MAGIC) for an assessment of recovery from acidification of soils and surface waters at a long-term study site in Norway under different future acid deposition conditions. The water quality parameters are coupled with a simple dose-response model for trout population health. Uncertainties in model output parameters are estimated and forecast results are presented as probability distributions for future water chemistry and as probability distributions of future healthy trout populations. The forecast results are examined for three different scenarios of future acid deposition corresponding to three different emissions control strategies for Europe. Despite the explicit consideration of uncertainties propagated into the future forecasts, there are clear differences among the scenarios. The case study illustrates how inclusion of uncertainties in model predictions can strengthen the inferences drawn from model results in support of decision making and assessments.

Collision Probability with Gaussian Mixture Orbit Uncertainty

System dependability or performance is often studied using stochastic models. These models capture the natural uncertainty in the system being studied, known as aleatory uncertainty. Randomness in events of interest like times to failure/recovery of components, ability to detect failures, ability to perform recovery action, inter-arrival time, service time, etc., are taken into account in the models, by means of their distributions. The models are usually solved at fixed parameter values. However, the model input parameter values have uncertainty associated with them as they are derived either from a finite number of observations (from lifetime determining experiments or field data) or are based upon expert guesses. This uncertainty in model input parameter values, known as epistemic uncertainty, is not normally taken into account by the stochastic aleatory model.KeywordsEpistemic UncertaintyUncertainty PropagationModel Input Parameter ValuesPerform Recovery ActionsExpert GuessesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper introduces an uncertainty model being developed for the National Transonic Facility (NTF). The model uses a Monte Carlo technique to propagate standard uncertainties of measured values through the NTF data reduction equations to calculate the combined uncertainties of the key aerodynamic force and moment coefficients and freestream properties. The uncertainty propagation approach to assessing data variability is compared with ongoing data quality assessment activities at the NTF, notably check standard testing using statistical process control (SPC) techniques. It is shown that the two approaches are complementary and both are necessary tools for data quality assessment and improvement activities. The SPC approach is the final arbiter of variability in a facility. Its result encompasses variation due to people, processes, test equipment, and test article. The uncertainty propagation approach is limited mainly to the data reduction process. However, it is useful because it helps to assess the causes of variability seen in the data and consequently provides a basis for improvement. For example, it is shown that Mach number random uncertainty is dominated by static pressure variation over most of the dynamic pressure range tested. However, the random uncertainty in the drag coefficient is generally dominated by axial and normal force uncertainty with much less contribution from freestream conditions.

Uncertainty propagation in risk and resilience analysis of hierarchical systems

The successful electrification of the transportation and stationary power markets requires batteries with 10–30 years of lifetime. Validations of such long time scales can take several years and require significant confidence in future life predictions. Battery life predictions across such timescales can be highly sensitive to uncertainty in the collection of primary parameters such as current, voltage and time. A methodology to quantify how these primary parameters propagate into the derived parameters of interest such as capacity and coulombic efficiency is presented. The recent development of high precision battery testing and equipment has met the need for accurate and precise assessment of measurement errors. As an example of the derived quantity uncertainty propagation methodology and approach developed in this paper, a prototype high current, high precision tester is also evaluated. The aim of this paper is to describe a standardized method for the precise quantification of battery derived parameter uncertainty, apply the method to the performance of a prototype high current, high precision tester (HPT) as a case study, and then to model the sensitivity of these precision results across a population of possible test conditions.

The data-driven polynomial chaos expansion (DD-PCE) method is claimed to be a more general approach of uncertainty propagation (UP). However, as a common problem of all the full PCE approaches, the size of polynomial terms in the full DD-PCE model is significantly increased with the dimension of random inputs and the order of PCE model, which would greatly increase the computational cost especially for high-dimensional and highly non-linear problems. Therefore, a sparse DD-PCE is developed by employing the least angle regression technique and a stepwise regression strategy to adaptively remove some insignificant terms. Through comparative studies between sparse DD-PCE and the full DD-PCE on three mathematical examples with random input of raw data, common and nontrivial distributions, and a ten-bar structure problem for UP, it is observed that generally both methods yield comparably accurate results, while the computational cost is significantly reduced by sDD-PCE especially for high-dimensional problems, which demonstrates the effectiveness and advantage of the proposed method.

This paper presents a novel uncertainty propagation approach for multidisciplinary systems with feedback couplings, model discrepancy, and parametric uncertainty. The proposed method incorporates aspects of Gibbs sampling, importance resampling, and density estimation to ensure that, under mild assumptions, the current method is provably convergent in distribution. The method uses the samples available from previously simulating the disciplines by applying sequential importance resampling. The absence or lack of samples in each discipline is addressed by introducing an adaptive greedy sample increment process to improve the efficiency of uncertainty analysis with minimum possible computational cost. A key feature of the approach is that disciplinary models are all synthesized independently based on their available data, and it does not require any full coupled system-level evaluations. The proposed approach is illustrated on the propagation of uncertainty for an aerodynamics–structures system and is compared to a system-level Monte Carlo uncertainty analysis approach.

Quantification of Margins and Uncertainties (QMU) is a decision-support methodology for complex technical decisions centering on performance thresholds and associated margins for engineering systems. Uncertainty propagation is a key element in QMU process for structure reliability analysis at the presence of both aleatory uncertainty and epistemic uncertainty. In order to reduce the computational cost of Monte Carlo method, a mixed uncertainty propagation approach is proposed by integrated Kriging surrogate model under the framework of evidence theory for QMU analysis in this paper. The approach is demonstrated by a numerical example to show the effectiveness of the mixed uncertainty propagation method.

Metamaterials have recently emerged in the search for lightweight noise and vibration solutions. One of their appealing properties for noise control engineering is the ability to create stop bands, which are frequency ranges without free wave propagation. These stop bands arise from the sub-wavelength addition of identically tuned resonators in or on a host structure. However, when manufacturing metamaterials, variability in material properties and geometry is inevitably introduced. On the one hand, the metamaterial attenuation performance can deteriorate due to variability, while on the other hand, variability can even broaden their typically narrowband performance. During the early phases in the design, when often little information concerning the inherent variability is available, it would be desirable to be able to assess the input uncertainty effects on the performance of metamaterials. This work focuses on the numerical assessment of the impact of uncertainties in resonator properties on the vibration attenuation performance of metamaterial beams. To this end, a machine learning based optimization strategy, the so-called Bayesian optimization, is employed in a recently developed non-intrusive uncertainty propagation approach. This enables a very efficient evaluation of the upper and lower bounds on the metamaterial performance, with the uncertain resonator parameters defined as interval variables.

This systematic review examines how uncertainty is sampled and propagated through interconnected model chains in climate‐induced flood risk assessments. We focus on top‐down modeling frameworks, where greenhouse gas scenarios drive global and regional climate models, followed by downscaling, bias adjustment, and impact modeling. This sequential approach leads to cumulative uncertainty, also known as uncertainty cascades, that complicate decision‐making in disaster risk management and climate change adaptation. Our review of 143 studies reveals significant variation in model selection and propagation approaches, with no consensus on best practices. While climate model uncertainty is widely sampled, uncertainty in impact, damage, and adaptation models is often less explored. We find that selective sampling and propagation choices can unintentionally increase deep uncertainty, particularly when low‐probability, high‐impact events are excluded. Disciplinary differences in uncertainty treatment further hinder transparency and comparability of model results. We argue that without improved transparency of modeling decisions, ensemble‐based studies risk amplifying uncertainty rather than reducing it. To support robust adaptation planning and improve traceability and confidence in climate impact assessments, we propose a checklist to guide the modeling process. This article is categorized under: Assessing Impacts of Climate Change > Representing Uncertainty Assessing Impacts of Climate Change > Evaluating Future Impacts of Climate Change Climate Models and Modeling > Knowledge Generation with Models

Large eddy simulation of autoignition with a subgrid probability density function method

Bivariate distribution of chain length and composition in multicomponent polymerization