Uncertainty Propagation Research Articles

Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory.

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.

A dimension reduction-based Kriging modeling method for high-dimensional time-variant uncertainty propagation and global sensitivity analysis

Surrogate models have been widely used in the uncertainty propagation and global sensitivity analysis of complex evaluation-expensive engineering problems. However, the construction of high-accuracy surrogate models for time-variant problems with high-dimensional inputs and outputs using a small number of training samples remains a challenge. To address this challenge, we propose a dimension reduction-based Kriging modeling (KMDR) method for high-dimensional time-variant uncertainty propagation and global sensitivity analysis. Singular value decomposition is performed on the original time-variant response to extract principal components from high-dimensional outputs. And the improved sufficient dimension reduction (ISDR) is performed on high-dimensional inputs to identify the latent input space with respect to each principal component of outputs. A ladle estimator with a rigorous mathematical definition is then employed to determine the number of principal components of the outputs and the dimensionalities of the latent input spaces. The ladle estimator considers variabilities in both eigenvalues and eigenvectors of a matrix and can determine the latent dimensionality more accurately and efficiently than existing approaches. Subsequently, Kriging models between high-dimensional inputs and each principal component of the outputs are constructed based on a newly devised Kriging kernel, which embeds the information of the ISDR into the kernel function and can achieve higher accuracy than directly constructing Kriging models between latent inputs and outputs. In addition, a generalized variance-based sensitivity index, which can quantify the effects of the inputs on the overall time-variant response, is defined and computed directly from Sobol’ sensitivity indices of the inputs at each time node. Finally, the surrogate model of the time-variant system constructed by the KMDR is directly adopted for efficient time-variant uncertainty propagation and global sensitivity analysis. Several examples demonstrate that the proposed approach can construct more accurate surrogate models and obtain more accurate time-variant uncertainty propagation and global sensitivity analysis results than existing methods with a small training set.

A Projection Approach to Local Regression with Variable-Dimension Covariates

Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random partition model admitting variable-dimension covariates. Cluster-specific response models further incorporate covariates via linear predictors, facilitating estimation of smooth prediction surfaces with relatively few clusters. We exploit marginalization techniques of Gaussian kernels to analytically project response distributions according to any pattern of missing covariates, yielding a local regression with internally consistent uncertainty propagation that uses only one set of coefficients per cluster. Aggressive shrinkage of these coefficients regulates uncertainty due to missing covariates. The method allows in- and out-of-sample prediction for any missingness pattern, even if the pattern in a new subject’s incomplete covariate vector was not seen in the training data. We develop an MCMC algorithm for posterior sampling that improves a computationally expensive update for latent cluster allocation. Finally, we demonstrate the model’s effectiveness for nonlinear point and density prediction under various circumstances by comparing with other recent methods for regression of variable dimensions on synthetic and real data. Supplemental materials for this article are available online.

Large group decision-making with a rough integrated asymmetric cloud model under multi-granularity linguistic environment

Large group decision-making often contains strong uncertainty and randomness due to the complexity of decision-making problems. Moreover, existing methods about large group decision-making usually assume that the relationships among decision-makers are mutually independent, which will neglect the relevance of decision information to some extent. To address these limitations, this paper proposes a novel rough integrated asymmetric cloud model to tackle large group decision-making under multi-granularity linguistic environment. This model can not only flexibly portray decision-makers’ preferences, but also objectively handle the uncertainty and randomness in large group decision-making through the relevance of preferences. Firstly, a trust propagation model based on rough integrated asymmetric cloud is raised to consider the impact of uncertainty and randomness in the trust propagation on large group decision-making. Secondly, a new asymmetric cloud distance and similarity are proposed to overcome some defects of existing methods. Thirdly, a decision-maker weight calculation method based on the Shapley function is advanced to enhance the decision-making reasonableness. Next, an investment problem is solved by the proposed method. Finally, the effectiveness and superiority of the proposed method are demonstrated by the sensitivity and comparison analyses.

A physics-informed Bayesian data assimilation approach for real-time drilling tool lateral motion prediction

In this study, a Bayesian data assimilation method that fuses physics with motion sensor data is demonstrated to infer the dynamic states at points of interest on the bottomhole assembly (BHA) with proper uncertainty quantification. A 4.75 inch-LWD (Logging-while-drilling) tool has been used as a use case, where the dynamic states at the formation evaluation sensor can be predicted in real time with the measurements at the motion sensor as the required inputs. This was achieved with a developed transfer function that utilizes unscented Kalman filtering technique. The robustness of the transfer function was evaluated with synthetic data obtained from finite element analysis (FEA) simulations for various BHA configurations and drilling conditions. It was found that the prediction by the transfer function agrees favorably well with the true states of motion at the formation evaluation sensor. Specifically, using the developed transfer function can help reduce the relative errors for the motion trajectories at the formation evaluation sensor by a factor of 3, and can significantly enhance measurement quality risk classification. The developed transfer function method was further assessed with experimental roll test data, which is considered as close to drilling conditions. The prediction by the transfer function was found consistently close to the ground truth in the presence of backward whirl. The developed modeling method can potentially have broader impacts by enabling fit-for-basin virtual V&V (Verification and Validation) to accelerate LWD tool development, or enabling future drilling optimization.

A novel stochastic approach to investigate the probabilistic characteristics of the ship roll system with sinusoidal restoring force

A novel constrained optimization-oriented exponential–polynomial–closure (CO-EPC) method is developed to investigate the ship roll-motion with non-smooth damping and sinusoidal restoring moments under stochastic wave excitations. The ’non-smooth damping’ and ’sinusoidal restoring moments’ refer to the damping force and restoring force of the system, respectively, which are mathematically expressed using non-smooth and sinusoidal functions. The propagation of uncertainty in the system is governed by the Fokker–Plank–Kolmogorov (FPK) equation, as the presence of stochastic wave excitation induces Markovian behavior in the system responses. The solution of FPK must meet the non-negativity, normalization, and limitation attributes. To fulfill these essential requirements, a novel method has been developed. By deriving the moment functions of the non-smooth terms (for the damping moment part) and the sine terms (for the restoring moment part), the complicated FPK equation is solved. Through two case studies, it is found that the CO-EPC approach demonstrates superior efficiency compared to Monte Carlo simulation and produces more accurate solutions in contrast to the Gaussian closure method. These findings support the effectiveness of CO-EPC in studying the ship roll motion problem under stochastic wave excitations.

Reliability Analysis for RV Reducer by Combining PCE and Saddlepoint Approximation Considering Multi-Failure Modes

Abstract RV (Rotate Vector) reducer is an essential mechanical transmission device extensively used in industrial machinery, robotics, aerospace and other fields. The dynamic transmission characteristics and strength of the cycloidal pin gear, turning arm bearing of RV reducer significantly affect the motion accuracy and reliability of the whole equipment. Uncertainties from manufacturing and assembly error, working loads add complexity to these effects. Developing effective methods for uncertainty propagation and reliability analysis for the RV reducer is crucial. In this work, the mail failure modes of RV reducer are studied, and an effective reliability analysis method for RV reducer considering the correlation between multi-failure modes by combining polynomial chaos expansions (PCE) and saddlepoint approximation method (SPA) is proposed. This paper develops an uncertainty propagation strategy for RV reducer based on dynamic simulation and PCE method with high accuracy. On this basis, a surrogated cumulant generating function (CGF) and SPA are combined to analyze the stochastic characteristic for the failure behavior. Based on the probability density function (PDF) and cumulative distribution function (CDF) calculated by SPA, copula function is employed to quantify the correlations between the multi-failure modes. Then, the system reliability with multi-failure modes is estimated by SPA and optimal copula function. The proposed method provides an effective reliability assessment technology with high-accuracy for complex system under unknown physical model and distribution characteristics. The validity of the proposed approach is illustrated RV-320E reducer reliability estimation, offering a basis to improve the performance of complex dynamic system. .

Assessment of Measurement Uncertainty for S-Parameter Measurement Based on Covariance Matrix.

S-parameters are widely used to detail the scattering parameters of radio frequency (RF) components and microwave circuit modules. The vector network analyzer (VNA) is the most commonly used device for measuring S-parameters. Given the multiple frequency points, complex values, and intricate uncertainty propagation involved, accurately assessing the uncertainty of S-parameter measurements is difficult. In this study, we proposed a new method for assessing S-parameter uncertainty based on the covariance matrices, tracing back to the nominal uncertainty of calibration standards. First, we analyzed the relevant theory of uncertainty assessment using covariance matrices and subsequently deduced the mechanism of Type B uncertainty propagating from calibration standards to error model coefficients and S-parameter measurements to evaluate Type B measurement uncertainty. In this study, a novel measurement system was constructed for measuring grounded coplanar waveguides by using a VNA and calibration standards with 8- and 12-error models. Initially, the model assessed the Type B uncertainty of measuring four S-parameters of a grounded coplanar waveguide. Next, the VNA calibrated with the 12-error model was used to conduct multiple repeated measurements to assess the Type A uncertainty of the grounded coplanar waveguide. Finally, the composite uncertainty was constructed, which demonstrated that the proposed method can be used for assessing the uncertainty of S-parameters.

Measurement of respiratory rate with cardiac belt: Metrological characterization

The rapid growth of available wearable technologies, particularly in the healthcare sector, has ushered in a new era of digital health. This progress has introduced new possibilities for the monitoring of vital signs, including breathing rate (BR). BR is a crucial health parameter used to assess an individual's overall well-being; specifically, it can be considered a precise indicator of pathological conditions and stressors. The aim of this study is to conduct a metrological characterization of one of the most widely used BR sensors for the measurement of BR (i.e., Zephyr BioHarness 3.0), comparing it to a BR gold standard monitor (i.e., a spirometer), in determined test conditions, including both natural and defined BR patterns. Additionally, the Monte Carlo method (MCM) was applied to evaluate the propagation of the measurement uncertainty in the identification of the peaks of respiratory signal, used to calculate BR. Results reveal that the Zephyr BioHarness 3.0 sensor provides highly accurate BR measurements, with a precision of ±1 bpm. Bland-Altman analysis indicates a 95 % confidence interval of [-2; 3] bpm, demonstrating a close agreement with the reference instrument. The Pearson's correlation coefficient of 0.95 further validates the linear correlation between the reference/test measurements. The simulation based on MCM provides an expanded uncertainty of ±2 bpm (coverage factor k = 2) in BR estimation due to the uncertainty in the peaks identification (compatible with the accuracy provided by the manufacturer). These results highlight the Zephyr BioHarness 3.0 sensor reliability for BR monitoring while emphasizing the significance of accounting for different disturbing factors, e.g., uncertainty in peak detection during data analysis, also to provide a rigorous level of confidence in the measurement results, hence being able to properly interpret them in biomedical applications.

Hybrid Method of Uncertainty Propagation for Near-Earth Conjunction Analysis

In this research, several existing semi-analytical dynamics and uncertainty propagation techniques are combined with conjunction models to achieve fast and accurate probability of collision results. Initial Gaussian uncertainty associated with two objects is split into smaller Gaussian distributions using Gaussian mixture models to achieve mixture components that will maintain linearity over longer propagation times. These mixture components are propagated forward using second-order state transition tensors that can capture the nonlinearity in the propagation accurately by taking into account the desired dynamics. The dynamic solution and these tensors are computed using the Deprit–Lie averaging approach, including transformations between mean and osculating states, which accounts for perturbations due to solar radiation pressure and J2. This simplified dynamic system allows fast and accurate propagation by combining the speed of propagation with averaged dynamics and the accuracy of short-period variation addition. Combined, these mathematical tools are used to propagate the object’s uncertainties forward. The final distributions are compared using analytical conjunction methods to compute the probability of collision, which is then compared to the Monte Carlo result to confirm the method’s validity.

Configuration uncertainty propagation of gravitational-wave observatory using a directional state transition tensor

Configuration stability is essential for a space-based Gravitational-Wave (GW) observatory, which can be impacted by orbit insertion uncertainties. Configuration uncertainty propagation is vital for investigating the influences of uncertainties on configuration stability and can be potentially useful in the navigation and control of GW observatories. Current methods suffer from drawbacks related to high computational burden. To this end, a Radial-Tangential-Ddirectional State Transition Tensor (RT-DSTT)-based configuration uncertainty propagation method is proposed. First, two sensitive directions are found by capturing the dominant secular terms. Considering the orbit insertion errors along the two sensitive directions only, a reduced-order RT-DSTT model is developed for orbital uncertainty propagation. Then, the relationship between the uncertainties in the orbital states and the uncertainties in the configuration stability indexes is mapped using high-order derivatives. The result is a semi-analytical solution that can predict the deviations in the configuration stability indexes given orbit insertion errors. The potential application of the proposed RT-DSTT-based method in calculating the feasible domain is presented. The performance of the proposed method is validated on the Laser Interferometer Space Antenna (LISA) project. Simulations show that the proposed method can provide similar results to the STT-based method but requires only half of the computational time.

Uncertainty-Aware Trajectory Planning: Using Uncertainty Quantification and Propagation in Traversability Prediction of Planetary Rovers

Uncertainty-Aware Trajectory Planning: Using Uncertainty Quantification and Propagation in Traversability Prediction of Planetary Rovers

Reconstruction of Cenozoic δ11Bsw Using a Gaussian Process

AbstractThe boron isotope ratio of seawater (δ11Bsw) is a parameter which must be known to reconstruct palaeo pH and CO2 from boron isotope measurements of marine carbonates. Beyond a few million years ago, δ11Bsw is likely to have been different to modern. Palaeo δ11Bsw can be estimated by simultaneously constraining the vertical gradients in foraminiferal δ11B (Δδ11B) and pH (ΔpH). A number of subtly different techniques have been used to estimate ΔpH in the past, all broadly based on assumptions about vertical gradients in oxygen, and/or carbon, or other carbonate system constraints. In this work we pull together existing data from previous studies, alongside a constraint on the rate of change of δ11Bsw from modeling. We combine this information in an overarching statistical framework called a Gaussian Process. The Gaussian Process technique allows us to bring together data and constraints on the rate of change in δ11Bsw to generate random plausible evolutions of δ11Bsw. We reconstruct δ11Bsw, and by extension palaeo pH, across the last 65Myr using this novel methodology. Reconstructed δ11Bsw is compared to other seawater isotope ratios, namely , , and δ7Li, which we also reconstruct with Gaussian Processes. Our method provides a template for incorporation of future δ11Bsw constraints, and a mechanism for propagation of uncertainty in δ11Bsw into future studies.

Data-driven uncertainty propagation for stochastic predictive control of multi-energy systems

Stochastic predictive control schemes that account for epistemic and aleatoric uncertainties, i.e. lack of model knowledge and stochastic disturbances, are of major interest for multi-energy systems. However, there exists a trade-off between model complexity, computational effort, and accuracy of uncertainty quantification. This paper attempts to assess this trade-off by comparing a recently proposed approach combining Willems’ fundamental lemma with polynomial chaos expansion to a model-based scheme that first propagates uncertainty with PCE and then considers chance constraints in the optimization. The simulation results show that the data-driven scheme yields similar performance and computational efficiency compared to the model-based scheme, with the advantage of avoiding the construction of explicit models.

Uncertainty Quantification Analysis in the Blade Element Momentum Method

The blade element momentum (BEM) method is a widely used non-linear model for the efficient performance evaluation and design of wind turbines. The aim of this paper is to quantify the uncertainty related to BEM model inputs and sub-models, and investigate how these propagate through the model. Uncertainties related to viscous dissipation in the wake, aerofoil force coefficients, and tip-loss models are considered. Global sensitivity to these parameters is analysed using non-intrusive polynomial chaos expansion, which provides a structured method for uncertainty propagation and sensitivity quantification. Sobol indices are employed to rank the relative importance of each factor to the overall uncertainty in the system. By analysing the NREL 5 MW and DTU 10 MW reference wind turbines, we observe that the different rotors may exhibit different levels of sensitivity to input parameters. The effect of viscous mixing in the turbine wake is found to have a significant impact on predicted rotor performance. Uncertainty in tip-loss model coefficients is also found to generally be important, particularly when evaluating spanwise variations in rotor loads. Uncertainty quantification has the potential to improve understanding of BEM modelling, and provide guidance on the importance of sub-model improvements.

On the Challenges of Simulating Streamflow in Glacierized Catchments of the Himalayas Using Satellite and Reanalysis Forcing Data

Abstract Hydrologic assessment of climate change impacts on complex terrains and data-sparse regions like High Mountain Asia is a major challenge. Combining hydrological models with satellite and reanalysis data for evaluating changes in hydrological variables is often the only available approach. However, uncertainties associated with the forcing dataset, coupled with model parameter uncertainties, can have significant impacts on hydrologic simulations. This work aims to understand and quantify how the uncertainty in precipitation and its interaction with the model uncertainty affect streamflow estimation in glacierized catchments. Simulations for four precipitation datasets [Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG), Climate Hazards Group Infrared Precipitation with Station (CHIRPS), ERA5-Land, and Asian Precipitation–Highly Resolved Observational Data Integration Toward Evaluation (APHRODITE)] and two glacio-hydrological models [Glacio-Hydrological Degree-Day Model (GDM) and Hydrological Model for Distributed Systems (HYMOD_DS)] are evaluated for the Marsyangdi and Budhigandaki River basins in Nepal. Temperature sensitivity of streamflow simulations is also investigated. Relative to APHRODITE, which compared well with ground stations, ERA5-Land overestimates the catchment average precipitation for both basins by more than 70%; IMERG and CHIRPS overestimate by ∼20%. Precipitation uncertainty propagation to streamflow exhibits strong dependencies to model structure and streamflow components (snowmelt, ice melt, and rainfall-runoff), but overall uncertainty dampens through precipitation-to-streamflow transformation. Temperature exerts a significant additional source of uncertainty in hydrologic simulations of such environments. GDM was found to be more sensitive to temperature variations, with >50% increase in total flow for 20% increase in actual temperature, emphasizing that models that rely on lapse rates for the spatial distribution of temperature have much higher sensitivity. Results from this study provide critical insight into the challenges of utilizing satellite and reanalysis products for simulating streamflow in glacierized catchments. Significance Statement This work investigates the uncertainty of streamflow simulations due to climate forcing and model parameter/structure uncertainty and quantifies the relative importance of each source of uncertainty and its impact on simulating different streamflow components in glacierized catchments of High Mountain Asia. Results highlight that in high mountain regions, temperature uncertainty exerts a major control on hydrologic simulations and models that do not adequately represent the spatial variability of temperature are more sensitive to bias in the forcing data. These findings provide guidance on important aspects to be considered when modeling glacio-hydrological response of catchments in such areas and are thus expected to impact both research and operation practice related to hydrologic modeling of glacierized catchments.

Uncertainty estimation and evaluation of deformation image registration based convolutional neural networks

Objective. Fast and accurate deformable image registration (DIR), including DIR uncertainty estimation, is essential for safe and reliable clinical deployment. While recent deep learning models have shown promise in predicting DIR with its uncertainty, challenges persist in proper uncertainty evaluation and hyperparameter optimization for these methods. This work aims to develop and evaluate a model that can perform fast DIR and predict its uncertainty in seconds. Approach. This study introduces a novel probabilistic multi-resolution image registration model utilizing convolutional neural networks to estimate a multivariate normal distributed dense displacement field (DDF) in a multimodal image registration problem. To assess the quality of the DDF distribution predicted by the model, we propose a new metric based on the Kullback–Leibler divergence. The performance of our approach was evaluated against three other DIR algorithms (VoxelMorph, Monte Carlo dropout, and Monte Carlo B-spline) capable of predicting uncertainty. The evaluation of the models included not only the quality of the deformation but also the reliability of the estimated uncertainty. Our application investigated the registration of a treatment planning computed tomography (CT) to follow-up cone beam CT for daily adaptive radiotherapy. Main results. The hyperparameter tuning of the models showed a trade-off between the estimated uncertainty’s reliability and the deformation’s accuracy. In the optimal trade-off, our model excelled in contour propagation and uncertainty estimation (p <0.05) compared to existing uncertainty estimation models. We obtained an average dice similarity coefficient of 0.89 and a KL-divergence of 0.15. Significance. By addressing challenges in DIR uncertainty estimation and evaluation, our work showed that both the DIR and its uncertainty can be reliably predicted, paving the way for safe deployment in a clinical environment.

Taillefer—A Tool for Sensitivity Analysis and Uncertainty Propagation Studies for Steady-State Thermal-Hydraulic Simulations of Involute Fuel Element Research Reactors

Taillefer is a versatile Python tool for carrying out Sensitivity Analysis (SA) and uncertainty propagation (UP) studies based on Monte Carlo sampling. Developed with the primary goal of investigating sensitivities and uncertainties of steady-state thermal-hydraulic (SSTH) safety parameters of the high-performance research reactors Forschungs Neutronenquelle Heinz Maier-Leibnitz (FRM II) in Garching, Germany, and the Réacteur à Haut Flux (RHF) in Grenoble, France, it can also be used for a large variety of other modeling problems. The work presented here aims to explain the underlying mathematical background of SA and UP studies with Taillefer and to show some steps to verify these routines. Furthermore, a real-life application example is provided that demonstrates Taillefer’s use in SSTH analysis of the RHF. For this purpose, Taillefer is coupled to the external thermal-hydraulic software PLTEMP/ANL, which is one of the codes used at FRM II and RHF to access SSTH performance and safety parameters. Determining these crucial quantities is part of identifying possible low-enriched uranium (LEU) core designs that are suitable to replace the currently used highly enriched uranium fuels of the two reactors, supporting global nonproliferation efforts. Taillefer is a powerful tool in these conversion studies, as it increases the reliability of the LEU safety parameters by providing information about sensitivities and uncertainties in addition to the nominal values predicted by the thermal-hydraulic software.

Hybrid positioning algorithm based on least squares and LM for 3D cluster networks

This paper proposes a hybrid positioning algorithm, LS-LM, based on least squares (LS) and Levenberg–Marquardt (LM) for position estimation of low-cost and miniaturized unmanned cluster networks in the absence of GPS. The LS method is first used to obtain an initial solution of position estimation, and the LM algorithm to iteratively refine the solution. The LS-LM algorithm has the advantages of simple computation, no complicated communication, and full distribution. It has high accuracy in the coordinated positioning algorithm without coordinate matching. In evaluating its efficacy,we have compared the root mean square error of the LS-LM algorithm to that of the LS method, tetrahedron shape measurement (TSM) algorithm and improved trilateration localization method with minimum uncertainty propagation and optimized selection of anchor nodes (ITL-MEPOSA) method. The simulation results demonstrate a varying degree of reduction in error with the application of the LS-LM algorithm.

Uncertainty-Aware First-Principles Exploration of Chemical Reaction Networks.

Exploring large chemical reaction networks with automated exploration approaches and accurate quantum chemical methods can require prohibitively large computational resources. Here, we present an automated exploration approach that focuses on the kinetically relevant part of the reaction network by interweaving (i) large-scale exploration of chemical reactions, (ii) identification of kinetically relevant parts of the reaction network through microkinetic modeling, (iii) quantification and propagation of uncertainties, and (iv) reaction network refinement. Such an uncertainty-aware exploration of kinetically relevant parts of a reaction network with automated accuracy improvement has not been demonstrated before in a fully quantum mechanical approach. Uncertainties are identified by local or global sensitivity analysis. The network is refined in a rolling fashion during the exploration. Moreover, the uncertainties are considered during kinetically steering of a rolling reaction network exploration. We demonstrate our approach for Eschenmoser-Claisen rearrangement reactions. The sensitivity analysis identifies that only a small number of reactions and compounds are essential for describing the kinetics reliably, resulting in efficient explorations without sacrificing accuracy and without requiring prior knowledge about the chemistry unfolding.