Uncertainty Propagation Research Articles

Probabilistic projections of the Amery Ice Shelf catchment, Antarctica, under conditions of high ice-shelf basal melt

Abstract. Antarctica's Lambert Glacier drains about one-sixth of the ice from the East Antarctic Ice Sheet and is considered stable due to the strong buttressing provided by the Amery Ice Shelf. While previous projections of the sea-level contribution from this sector of the ice sheet have predicted significant mass loss only with near-complete removal of the ice shelf, the ocean warming necessary for this was deemed unlikely. Recent climate projections through 2300 indicate that sufficient ocean warming is a distinct possibility after 2100. This work explores the impact of parametric uncertainty on projections of the response of the Lambert–Amery system (hereafter “the Amery sector”) to abrupt ocean warming through Bayesian calibration of a perturbed-parameter ice-sheet model ensemble. We address the computational cost of uncertainty quantification for ice-sheet model projections via statistical emulation, which employs surrogate models for fast and inexpensive parameter space exploration while retaining critical features of the high-fidelity simulations. To this end, we build Gaussian process (GP) emulators from simulations of the Amery sector at a medium resolution (4–20 km mesh) using the Model for Prediction Across Scales (MPAS)-Albany Land Ice (MALI) model. We consider six input parameters that control basal friction, ice stiffness, calving, and ice-shelf basal melting. From these, we generate 200 perturbed input parameter initializations using space filling Sobol sampling. For our end-to-end probabilistic modeling workflow, we first train emulators on the simulation ensemble and then calibrate the input parameters using observations of the mass balance, grounding line movement, and calving front movement with priors assigned via expert knowledge. Next, we use MALI to project a subset of simulations to 2300 using ocean and atmosphere forcings from a climate model for both low- and high-greenhouse-gas-emission scenarios. From these simulation outputs, we build multivariate emulators by combining GP regression with principal component dimension reduction to emulate multivariate sea-level contribution time series data from the MALI simulations. We then use these emulators to propagate uncertainty from model input parameters to predictions of glacier mass loss through 2300, demonstrating that the calibrated posterior distributions have both greater mass loss and reduced variance compared to the uncalibrated prior distributions. Parametric uncertainty is large enough through about 2130 that the two projections under different emission scenarios are indistinguishable from one another. However, after rapid ocean warming in the first half of the 22nd century, the projections become statistically distinct within decades. Overall, this study demonstrates an efficient Bayesian calibration and uncertainty propagation workflow for ice-sheet model projections and identifies the potential for large sea-level rise contributions from the Amery sector of the Antarctic Ice Sheet after 2100 under high-greenhouse-gas-emission scenarios.

Uncertainty-Aware Prediction of Remaining Useful Life in Complex Systems

Accurate prediction of the remaining useful life (RUL) of industrial systems is critical to ensuring smooth operation and safety. Various prognostic methods have been developed, but significant challenges remain for field applications. While many methods may achieve high accuracy, they often fall short in quantifying the uncertainty of their predictions. Without uncertainty quantification, it is difficult to assess the confidence level of the prognostic results. Therefore, it is essential to transparently present the uncertainty levels in the predicted results. This Ph.D. project aims to develop novel uncertainty-aware methods for RUL prediction of complex systems. The project will address the following situations where it is more and more uncertain: (a) propose a general framework for data-driven RUL methods to quantify uncertainty and generate adaptive confidence intervals under a single fault mode and a single operating condition; (b) consider both epistemic and aleatoric uncertainties in scenarios with multiple fault modes and multiple operating conditions and then calibrate uncertainty to enhance their accuracy; (c) explore how to predict RUL and quantify uncertainty when there are no run-to-failure data and RUL labels in practice; (d) handle uncertainty propagation from the component level to the system level. Through this research, the project will provide more reliable and comprehensive solutions for RUL prediction in complex systems.

Uncertainty Quantification of Microstructures: A Perspective on Forward and Inverse Problems for Mechanical Properties of Aerospace Materials

In this review, state‐of‐the‐art studies on the uncertainty quantification (UQ) of microstructures in aerospace materials is examined, addressing both forward and inverse problems. Initially, it introduces the types of uncertainties and UQ algorithms. In the review, the forward problem of uncertainty propagation in process–structure and structure–property relationships is then explored. Subsequently, the inverse UQ problem, also known as the design under uncertainty problem, is discussed focusing on structure–process and property–structure linkages. Herein, the review concludes by identifying gaps in the current literature and suggesting key areas for future research, including multiscale topology optimization under uncertainty, implementing physics‐informed neural networks to UQ problems, investigating the effects of uncertainty on extreme mechanical behavior, reliability‐based design, and UQ in additive manufacturing.

Efficient non-probabilistic parallel model updating based on analytical correlation propagation formula and derivative-aware deep neural network metamodel

Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse parameter updating, present challenges in efficiency and convergence. In response to these challenges, a novel and flexible NPMU scheme is introduced, integrating analytical correlation propagation and parallel interval bounds prediction to enable automatic detection of parameter correlations. In the forward uncertainty propagation phase, a linear coordinate transformation is applied to map the original parameter space to a standard hypercube space, simplifying correlation-involved bounds prediction into conventional interval bounds prediction. Moreover, an analytical correlation propagation formula is derived using a second-order response approximation to sidestep the complexities of geometry-based correlation calculations. To expedite forward propagation, a derivative-aware neural network model is employed to replace the physical solver, facilitating improved fitting capabilities and automatic differentiation, including the calculation of Jacobian and Hessian matrices essential for correlation propagation. The neural network's inherent parallelism accelerates interval bounds prediction through parallel computation of samples. In the inverse parameter updating phase, the block coordinate descent algorithm is embraced to narrow the search space and boost convergence capabilities, while the perturbation method is utilized to determine the optimal starting point for optimization. Two numerical examples illustrate the efficacy of the proposed method in updating structural models while considering correlations.

Tropospheric links to uncertainty in stratospheric subseasonal predictions

Abstract. Variability in the stratosphere, especially extreme events such as sudden stratospheric warmings (SSWs), can impact surface weather. Understanding stratospheric prediction uncertainty is therefore crucial for skillful surface weather forecasts on weekly to monthly timescales. Using ECMWF subseasonal hindcasts, this study finds that stratospheric uncertainty is most strongly linked to tropospheric uncertainty over the North Pacific and Northern Europe, regions that can modulate but also respond to stratospheric variability, suggesting a two-way propagation of uncertainty. A case study of the 2018 SSW event shows an initial poleward and upward propagation of uncertainty from tropical convection, followed by a downward propagation where ensemble members that accurately predict the SSW are also better at predicting its downward impacts. These findings highlight the locations in the troposphere that are linked to stratospheric uncertainty and suggest that improved model representation of tropospheric mechanisms linked to polar vortex variability could enhance both stratospheric and extratropical surface prediction.

A re-sampling statistics based imprecise moment independent global sensitivity analysis methodology with limited data of uncorrelated and correlated geotechnical properties

Traditional Global Sensitivity Analysis (GSA) is often performed using variance-based Sobol’s GSA, considering statistics of inputs estimated from limited data to be precise. This can lead to inaccuracies in the importance ranking of inputs due to negligence of – i) epistemic uncertainties in their statistics, and ii) role of other moments of outputs in Sensitivity Indices (SIs). This study overcomes these limitations by proposing an imprecise moment independent GSA methodology. The methodology couples re-sampling statistical techniques, i.e., Jackknifing and Bootstrapping with Monte-Carlo Simulations based Borgonovo’s moment independent GSA to estimate distributions of SIs. The re-sampling techniques estimate epistemic uncertainties in the statistics of inputs by generating re-constituted samples. These epistemic uncertainties are then propagated via Borgonovo’s GSA to estimate their imprecise moment independent SIs. The methodology is further coupled with Nataf’s transformation and Moving Least Square-Response Surface Methods to deal with problems of correlated inputs and lack of explicit input-output relationships. The generalized nature of methodology is demonstrated for three real case studies (one tunnel and two slopes), with different correlation structures between inputs, input-outputs relationships (explicit/implicit), and failure mechanisms. The methodology estimated the distributions of SIs of inputs instead of their point estimates, indicating the propagation of epistemic uncertainties truthfully. The Jackknife-GSA was significantly efficient (∼99 %) with negligible differences in statistics of SIs as compared to Bootstrap-GSA. The correlation between inputs significantly affects the statistics of SIs. Further, a reduction in the imprecision of SIs of inputs with their increasing sample sizes was observed, which is consistent with the general understanding.

A validated simulation methodology for determining single lap shear allowable strength in thermoplastic polymer composites

While several modeling approaches exist to simulate the strength of single lap shear configurations, their application to obtaining design allowables for thermoplastic composites remains underexplored. This paper addresses this gap by presenting a novel methodology for the forward propagation of parameter uncertainty using advanced finite element models specifically tailored for thermoplastic carbon fiber composites. The proposed approach goes beyond traditional methods by integrating advanced damage models and a structured validation process, supported by an extensive experimental test campaign.We demonstrate the feasibility of determining design allowables through simulation by examining the influence of batch size on both the validation process and the prediction of allowable strength. Our findings provide new insights into the propagation of uncertainties in the context of composite material design, showing that it is possible to achieve reliable design allowables through simulation, which can significantly accelerate the development of new components while maintaining high safety standards.

Developing a probabilistic compaction model for the Northern Carnarvon Basin using Bayesian inference

AbstractExhumation affects sedimentary basin evolution by influencing structural, pressure and temperature dynamics, thereby impacting energy resource formation. Compaction‐based methods are widely used to quantify exhumation, utilising sonic and porosity data to track sediment uplift from its maximum burial depths. However, uncertainties arise from applying empirical compaction models developed for specific geological regions, highlighting the need for region‐specific models. Even such region‐specific models contain uncertainties, which can compromise exhumation estimates. We, therefore, develop a probabilistic compaction model for the Northwest Shelf Basins using sonic data from normally compacted and unexhumed shales from the Northern Carnarvon Basin (NCB). The model's robustness is estimated using MCMC, and uncertainty propagation analysis is employed to assess the impact of model uncertainty on the model's predictive applications. The model shows exponential porosity reduction with depth, demonstrating rapid compaction from the surface to ca. 2 km and slower compaction thereafter. The model is then applied to interpret new datasets from the Canning, Gippsland and NCB regions. The results reveal that while some parts of the NCB exhibit normal compaction without exhumation, others were significantly exhumed. Conversely, Canning and Gippsland Basin data indicate signs of significant exhumation, as suggested by previous studies, thereby confirming the model's effectiveness outside the Northwest Shelf. Since the model could not explain data from exhumed regions, we inferred new models incorporating “exhumation” parameters to interpret the complex compaction histories of these areas, and the best‐fitting models were selected using the Bayes Factor method. Uncertainty analysis revealed that the impacts of model uncertainty on exhumation estimates are consistent across wide depth ranges. Our findings highlight the need to refine compaction models for better predictive reliability and informed resource exploration in sedimentary basins.

A comprehensive framework to assess multi‐species landscape connectivity

Abstract Due to the central role of landscape connectivity in many ecological processes, evaluating and accounting for it has gained attention in both theoretical and applied ecological sciences. To address this challenge, researchers often use generic species to simplify multi‐species connectivity assessments. Yet, this approach tends to oversimplify movement behaviour, likely reducing realism and precision of connectivity model outputs. Also, the most widely used methods and theories for assessing landscape connectivity, namely circuit and network theories, have strong limitations. Finally, uncertainty or robustness estimates are rarely integrated in connectivity assessments. Here, we propose a versatile framework, which, instead of using arbitrary defined generic species, first identifies species groups based on species' environmental niches and morphological, biological, and ecological traits. Second, it combines circuit and network theories to take the best of the two methods to assess landscape connectivity for those groups, while integrating uncertainties in modelling choices. Specifically, ecological continuities (i.e. landscape elements contributing to connectivity) are calculated for these groups and used together with group dispersal capacities to derive network‐based connectivity metrics for conservation areas. We detailed our framework through a case study where we assess the connectivity of 1619 protected areas in metropolitan France for 193 vertebrate species. Our study revealed that both the protection of ecological continuities and the connectivity of protected areas for 11 mammal and 19 bird groups, respectively, were quite low, with variations among groups. Different protection types (i.e. national parks, reserves or prefectural orders) contributed unequally to the overall connectivity of group‐specific suitable habitats. Considering uncertainty propagation was crucial, as many connectivity metrics varied among repetitions. The proposed framework combines different connectivity tools to provide a more relevant and comprehensive assessment of landscape connectivity. It can be used to inform the decision‐making process for spatial planning, particularly in the context of connectivity conservation and management, or support theoretical studies to better understand the ecological role of landscape connectivity. Its flexibility allows easy application under various environmental conditions, including future scenarios.

Best Practices in Developing a Workflow for Uncertainty Quantification for Modeling the Biodegradation of Mg-Based Implants.

Computational models of electrochemical biodegradation of magnesium (Mg)-based implants are uncertain. To quantify the model uncertainty, iterative evaluations are needed. This presents a challenge, especially for complex, multiscale models as is the case here. Approximating high-cost and complex models with easy-to-evaluate surrogate models can reduce the computational burden. However, the application of this approach to complex degradation models remains limited and understudied. This work provides a workflow to quantify different types of uncertainty within biodegradation models. Three surrogate models-Kriging, polynomial chaos expansion, and polynomial chaos Kriging-are compared based on the minimum number of samples required for surrogate model construction, surrogate model accuracy, and computational time. The surrogate models are tested for three computational models representing Mg-based implant biodegradation. Global sensitivity analysis and uncertainty propagation are used to analyze the uncertainties associated with the different models. The findings indicate that Kriging proves effective for calibrating diverse computational models with minimal computational time and cost, while polynomial chaos expansion and polynomial chaos Kriging exhibit greater capability in predicting propagated uncertainties within the computationalmodels.

State uncertainty propagation and sensitivity analysis of the post-impact binary asteroid system

State uncertainty propagation and sensitivity analysis of the post-impact binary asteroid system

Uncertainty propagation of initial conditions in thermal models

The operation of machine tools often demands a highly accurate knowledge of the tool center point’s (TCP) position. The displacement of the TCP over time can be inferred from coupled thermal models, which comprise a set of geometrically coupled heat equations. Each of these equations represents the temperature in part of the machine, and they are often formulated on complicated geometries. The accuracy of the TCP prediction depends highly on the accuracy of the model parameters, such as heat exchange parameters, and the initial temperature. Thus it is of utmost interest to determine the influence of these parameters on the TCP displacement prediction. In turn, the accuracy of the parameter estimate is essentially determined by the measurement accuracy and the sensor placement. Determining the accuracy of a given sensor configuration is a key prerequisite of optimal sensor placement. In this paper, we develop a thermal model for the discretization of realistic machine tool. On top of this model we propose two numerical algorithms to evaluate any given thermal sensor configuration with respect to its accuracy. We compute the posterior variances from the posterior covariance matrix with respect to an uncertain initial temperature field. The full matrix is dense and potentially very large, depending on the size of the discretized model. We first present a way to compute this approximation, which relies on the computation of the model sensitivities with respect to the initial values. Additionally, we present a low-rank tensor method which exploits the underlying system structure. We compare the efficiency of both algorithms with respect to runtime and memory requirements and discuss their respective advantages with regard to optimal sensor placement problems.

Thermodynamically informed priors for uncertainty propagation in first-principles statistical mechanics

Thermodynamically informed priors for uncertainty propagation in first-principles statistical mechanics

Capturing the random mechanical behaviour of granular materials: a comprehensive stochastic discrete-element method study

This research pioneers a stochastic discrete-element method (DEM) by integrating the probability density evolution method (PDEM), offering a novel approach to connect particle-scale property uncertainties, specifically inter-particle friction coefficient (μ) and particle shear modulus (Gp), with macro-scale soil behaviour. Through 1100 DEM simulations, this study reveals that, for uniform particle size distribution, the uncertainty in μ substantially affects large-strain soil behaviour, with its effect being associated with packing density and soil state. The uncertainty effect of μ remains pronounced at the critical state, while the packing density effect diminishes. Stress distribution appears insensitive to uncertainty of μ, rather suggesting a predominant influence of particle size distributions. In contrast, the uncertainty effect of μ becomes negligible on small-strain behaviour, demonstrating a limited effect on small-strain stiffness. Uncertainty in Gp presents limited effects on large-strain behaviour, including stress ratios and dilatancy. At small strains, Gp shows a significant impact on stiffness, diverging from minimal influence identified for μ. This study presents a framework that integrates experimental techniques to study particle-scale uncertainty propagation, enhancing predictions of macro-scale soil behaviour. This approach could be beneficial for precise multi-scale simulations, incorporating particle-level uncertainties in engineering-scale models, thereby improving geotechnical practice predictability.

Statistical estimation of full-sky radio maps from 21cm array visibility data using Gaussian Constrained Realisations

Abstract An important application of next-generation wide-field radio interferometers is making high dynamic range maps of radio emission. Traditional deconvolution methods like CLEAN can give poor recovery of diffuse structure, prompting the development of wide-field alternatives like Direct Optimal Mapping and m-mode analysis. In this paper, we propose an alternative Bayesian method to infer the coefficients of a full-sky spherical harmonic basis for a drift-scan telescope with potentially thousands of baselines, that can precisely encode the uncertainties and correlations between the parameters used to build the recovered image. We use Gaussian Constrained Realisations (GCR) to efficiently draw samples of the spherical harmonic coefficients, despite the very large parameter space and extensive sky-regions of missing data. Each GCR solution provides a complete, statistically-consistent gap-free realisation of a full-sky map conditioned on the available data, even when the interferometer’s field of view is small. Many realisations can be generated and used for further analysis and robust propagation of statistical uncertainties. In this paper, we present the mathematical formalism of the spherical harmonic GCR-method for radio interferometers. We focus on the recovery of diffuse emission as a use case, along with validation of the method against simulations with a known diffuse emission component.

Introducing uncertainties in acoustic engineering studies

PIBE (Prévoir l'Impact du Bruit des Éoliennes - Predicting the impact of wind-turbine noise) is a research project funded by ANR (French National Research Agency) which main objectives are to better understand the sound level created by wind-turbines and assess noise-reduction solutions. One topic of this project focuses on the propagation of uncertainties. Code_TYMPAN(tm) is an open-source software for calculating industrial noise in the environment. Its open architecture, implemented by a Python API, allows advanced users to build and solve models programmatically. This open architecture made possible the implementation of a parametrical computational tool. This tool generates input data, launches the calculations with Code_TYMPAN(tm), generates and post-processes output data. Thus, sensitivity analysis and propagation of uncertainties were performed on an industrial test case. This development demonstrates the feasibility of introducing uncertainties in acoustic engineering studies.

Bayesian uncertainty quantification for synthesizing superheavy elements

To improve the theoretical prediction power for synthesizing superheavy elements beyond Og, a Bayesian uncertainty quantification method is employed to evaluate the uncertainty of the calculated evaporation residue cross sections (ERCS) for the first time. The key parameters of the dinuclear system model (DNS-sysu), such as the diffusion parameter a, the damping factor Ed, and the level-density parameter ratio af/an are systematically constrained by the Bayesian analysis of recent ERCS data. One intriguing behaviour is shown that the optimal incident energies (OIE) corresponding to the largest ERCS weakly depend on the fission process. We also find that these parameters are strongly correlated and the uncertainty propagation considering the parameters independently is not reasonable. The 2σ confidence level of posterior distributions for a=0.586−0.002+0.002 fm, Ed=25.65−3.41+3.43 MeV, and af/an=1.081−0.021+0.021 are obtained. Furthermore, the confidence levels of the ERCS and OIE for synthesizing Z = 119 via the reactions Cr54+243Am, Ti50+249Bk, and V51+248Cm are predicted. This work sets the stage for future analyses to explore the OIE and reaction systems for the synthesis of superheavy elements.

Uncertainty propagation analysis for an aviation accelerometer using an improved saddlepoint approximation method

Uncertainty propagation analysis for an aviation accelerometer using an improved saddlepoint approximation method

A multi-scale uncertainty quantification model encompassing minimum-size unit cells for effective properties of plain woven composites

The uncertainty quantification is crucial to the high-precision prediction of composites’ effective properties. However, the unclear input uncertainties of multiscale parameters, complex uncertainty propagations of inter-scale correlations, and unaffordable computational cost of massive simulations are three primary problems at present. In this work, an innovative model with high accuracy and feasible cost for the mechanical property prediction of plain woven composites is developed encompassing minimum-size unit cells and multi-scale uncertainty quantification. For the accuracy holding, an uncertainty analysis process consists of the traceability description, inter-scale propagation and quantification is established. The uncertainties of geometry are described by uniform distributions for fiber, fiber bundle and composite scales, respectively; that of constituent properties is described by normal distributions for fiber and matrix, and its propagations to bundle and composite scales are realized by Nataf transformation methods with the consideration of parameter correlations. For the cost control, minimum-size unit cells are formulated by exhaustive analysis of structural symmetries to reduce the computational cost without accuracy compromising for the single simulation, and 1/8 and 1/16 unit cells compared with traditional full-size ones are obtained. The evolution convergence for statistical uncertainties of effective properties is finally obtained with totally reduced computational cost of 89%.

Too-Short-Arc Association and Clustering Method for Space-Based Optical Observations

Space-based optical observation is assuming an increasingly significant role in space surveillance and tracking. However, it often yields tracks that are too short, which are known as too short arcs (TSAs). A single TSA lacks sufficient information for reliable initial orbit determination of a resident space object. Therefore, it is typically necessary to perform tracklet association during catalog building and maintenance. This study presents a novel tracklet association method that improves upon existing techniques by combining admissible regions and nonlinear orbital uncertainty propagation. Proceeding by constructing TSA association matrices and TSA clustering matrices, the bond energy algorithm, traditionally employed in the design of distributed database systems, is applied to cluster TSAs based on the association results between two arbitrary TSAs. Furthermore, the proposed splitting algorithm reduces the computational load associated with clustering multiple tracklets and effectively handles erroneous association results. To assess the effectiveness of this approach, it was tested in a space-based optical-survey scenario, accounting for practical observation uncertainties. The simulation results demonstrate that the method achieves a high level of accuracy in both TSA association and clustering.