Uncertainty Propagation Research Articles

A stochastic Galerkin lattice Boltzmann method for incompressible fluid flows with uncertainties

Efficient modeling and simulation of uncertainties in computational fluid dynamics (CFD) remains a crucial challenge. In this paper, we present the first stochastic Galerkin (SG) lattice Boltzmann method (LBM) built upon the generalized polynomial chaos (gPC). The proposed method offers an efficient and accurate approach that depicts the propagation of uncertainties in stochastic incompressible flows. Formal analysis shows that the SG LBM preserves the correct Chapman–Enskog asymptotics and recovers the corresponding macroscopic fluid equations. Numerical experiments, including the Taylor–Green vortex flow, lid-driven cavity flow, and isentropic vortex convection, are presented to validate the solution algorithm. The results demonstrate that the SG LBM achieves the expected spectral convergence and the computational cost is significantly reduced compared to the sampling-based non-intrusive approaches, e.g., the routinely used Monte Carlo method. We obtain a speedup factor of 5.72 compared to Monte Carlo sampling in a randomized two-dimensional Taylor–Green vortex flow test case. By leveraging the accuracy and flexibility of LBM and the efficiency of gPC-based SG, the proposed SG LBM provides a powerful framework for uncertainty quantification in CFD practice.

SepsisLab: Early Sepsis Prediction with Uncertainty Quantification and Active Sensing.

Sepsis is the leading cause of in-hospital mortality in the USA. Early sepsis onset prediction and diagnosis could significantly improve the survival of sepsis patients. Existing predictive models are usually trained on high-quality data with few missing information, while missing values widely exist in real-world clinical scenarios (especially in the first hours of admissions to the hospital), which causes a significant decrease in accuracy and an increase in uncertainty for the predictive models. The common method to handle missing values is imputation, which replaces the unavailable variables with estimates from the observed data. The uncertainty of imputation results can be propagated to the sepsis prediction outputs, which have not been studied in existing works on either sepsis prediction or uncertainty quantification. In this study, we first define such propagated uncertainty as the variance of prediction output and then introduce uncertainty propagation methods to quantify the propagated uncertainty. Moreover, for the potential high-risk patients with low confidence due to limited observations, we propose a robust active sensing algorithm to increase confidence by actively recommending clinicians to observe the most informative variables. We validate the proposed models in both publicly available data (i.e., MIMIC-III and AmsterdamUMCdb) and proprietary data in The Ohio State University Wexner Medical Center (OSUWMC). The experimental results show that the propagated uncertainty is dominant at the beginning of admissions to hospitals and the proposed algorithm outperforms state-of-the-art active sensing methods. Finally, we implement a SepsisLab system for early sepsis prediction and active sensing based on our pre-trained models. Clinicians and potential sepsis patients can benefit from the system in early prediction and diagnosis of sepsis.

Composite Pressure Vessel Failure Simulation Considering Spatial Variability

Carbon fiber-reinforced polymers offer lightweight solutions for demanding applications, but material imperfections affect structural reliability. In this study, an efficient uncertainty propagation framework is applied to predict composite behavior. The framework accounts for spatial variability of fiber misalignment, uneven fiber distribution, and single-fiber strength. Spatial variability is represented at both the micro- and mesoscale. Macroscale simulations incorporate this spatial variability indirectly using homogenized material properties. The framework was applied to composite pressure vessels, whose stochastic burst pressure was predicted. The predictions were validated by experimental measurements. These measurements show that the actual burst pressure was underpredicted by an average of 5.8%. Several hypotheses were investigated to explain this discrepancy.

Active learning-based metamodeling for hybrid uncertainty quantification of hydro-mechatronic-control systems: A case study of EHA systems

The Electro-Hydrostatic Actuator (EHA) is a typical hydro-mechatronic control system. Due to the limited accuracy of measurement, inadequate knowledge, and vague judgments, hybrid uncertainties, including aleatory or epistemic uncertainty, inevitably exist in the performance assessment of EHA systems. Existing methods ignored the hybrid uncertainties which can hardly obtain a satisfactory result while wasting a lot of time on the experimental design. To overcome this drawback, a metamodeling method for hybrid uncertainty propagation of EHA systems is developed via an active learning Gaussian Process (GP) model. The proposed method is bifurcated into three pillars: (A) Initializing the GP model and generating the optimum candidate sampling set by an Optimized Max-Minimize Distance (OMMD) algorithm, which aims to maximize the minimum distance between the added samples and original samples, (B) maximizing the learning function and generating new samples by a developed farthest or nearest judgment strategy, while updating the original GP model, and (C) judging the convergence by three uncertainty metrics, i.e., area metric, maximum variance metric, and mean value metric. A numerical example is exemplified to evaluate the effectiveness and efficiency of the proposed method. Meanwhile, the EHA system of aircrafts is examined to show the application of the proposed method for high-dimensional problems. The effects of the uncertainties in the Proportional-Integral-Differential (PID) of the EHA system are also examined.

Polypharmacy side effect prediction based on semi-implicit graph variational auto-encoder.

Polypharmacy, the use of drug combinations, is an effective approach for treating complex diseases, but it increases the risk of adverse effects. To predict novel polypharmacy side effects based on known ones, many computational methods have been proposed. However, most of them generate deterministic low-dimensional embeddings when modeling the latent space of drugs, which cannot effectively capture potential side effect associations between drugs. In this study, we present SIPSE, a novel approach for predicting polypharmacy side effects. SIPSE integrates single-drug side effect information and drug-target protein data to construct novel drug feature vectors. Leveraging a semi-implicit graph variational auto-encoder, SIPSE models known polypharmacy side effects and generates flexible latent distributions for drug nodes. SIPSE infers the current node distribution by combining the distributions of neighboring nodes with embedding noise. By sampling node embeddings from these distributions, SIPSE effectively predicts polypharmacy side effects between drugs. One key innovation of SIPSE is its incorporation of uncertainty propagation through noise embedding and neighborhood sharing, enhancing its graph analysis capabilities. Extensive experiments on a benchmark dataset of polypharmacy side effects demonstrated that SIPSE significantly outperformed five state-of-the-art methods in predicting polypharmacy side effects.

Bayesian hierarchical model for bias-correcting climate models

Abstract. Climate models, derived from process understanding, are essential tools in the study of climate change and its wide-ranging impacts. Hindcast and future simulations provide comprehensive spatiotemporal estimates of climatology that are frequently employed within the environmental sciences community, although the output can be afflicted with bias that impedes direct interpretation. Post-processing bias correction approaches utilise observational data to address this challenge, although they are typically criticised for not being physically justified and not considering uncertainty in the correction. This paper proposes a novel Bayesian bias correction framework that robustly propagates uncertainty and models underlying spatial covariance patterns. Shared latent Gaussian processes are assumed between the in situ observations and climate model output, with the aim of partially preserving the covariance structure from the climate model after bias correction, which is based on well-established physical laws. Results demonstrate added value in modelling shared generating processes under several simulated scenarios, with the most value added for the case of sparse in situ observations and smooth underlying bias. Additionally, the propagation of uncertainty to a simulated final bias-corrected time series is illustrated, which is of key importance to a range of stakeholders, such as climate scientists engaged in impact studies, decision-makers trying to understand the likelihood of particular scenarios and individuals involved in climate change adaption strategies where accurate risk assessment is required for optimal resource allocation. This paper focuses on one-dimensional simulated examples for clarity, although the code implementation is developed to also work on multi-dimensional input data, encouraging follow-on real-world application studies that will further validate performance and remaining limitations. The Bayesian framework supports uncertainty propagation under model adaptations required for specific applications, providing a flexible approach that increases the scope of data assimilation tasks more generally.

Reliability analysis of deep tunnels in spatially varying brittle rocks using interval and random field modelling

Rock properties are estimated using objective lab/in-situ testing and subjective judgements invoking different types of uncertainties, i.e., aleatory, and epistemic, along them, often indicated by varying information levels. This study presents a unified reliability method to integrate the spatial variability of inputs modelled via alternate uncertainty models (intervals and probability-boxes (p-boxes)) with those modelled as stochastic variables via probability distributions. The methodology employs advanced Karhunen–Loève decomposition to generate interval and random fields of inputs modelled via alternate and stochastic models, respectively. Input properties are allocated to the zones of the numerical model in Fast Lagrangian Analysis of Continua-2D (FLAC-2D) based on their spatial dependency and correlation functions through a developed MATLAB-FLAC coupled code. The methodology is demonstrated for a deep tunnel in Canada to be constructed along a massive rock prone to brittle failures. Intact rock properties are modelled as stochastic variables due to objective estimation, while Geological Strength Index (GSI) and deformation modulus are modelled using alternate models (interval and p-box, respectively) due to subjective and hybrid estimation (double uncertainty propagation algorithm). The results of the methodology are compared with those of traditional deterministic and random field methods. The methodology reduces the subjectivity invoked by including unavailable additional information (e.g., assuming probability distributions of inputs based on literature) and propagates the originally available information of inputs accurately. The final outputs are the p-boxes of response parameters (i.e., displacements and damage zone) instead of their fixed values (deterministic analysis) and probability distributions (traditional reliability analysis), indicating the propagation of both impreciseness and variability of inputs by the method. For this case study, the p-boxes of outputs were bounding their values/distributions estimated via traditional analyses, verifying the accuracy of the methodology. Further, the impreciseness in the outputs, highest in the damage zone extent, was due to imprecision in the estimated GSI.

Building reliability of risk assessment of domino effects in chemical tank farm through an improved uncertainty analysis method

The severity and complexity of fire-induced domino effects have received widespread attention. The spatial and temporal evolution process modeling of domino accidents is still stuck in single crisp value, in which the uncertainty will affect the reliability of the results. In this paper, we propose a computational method for uncertainty propagation of the evolution process modeling of the domino effect called Uncertainty Propagation of Domino Evolution Model (UPDEM), aiming to increase the reliability of risk assessment results. The method is capable of obtaining ranges and corresponding probability envelopes for tiame to failure and escalation probabilities, and quantifying uncertainty for all computational models that require input parameters. The uncertainty is quantified based on the evidence theory and a parameter cropping method based on the stress-strength interference model is proposed to optimize the evidence theory. The proposed method is applied to a case study and compared with previous studies. The comparison confirms that the results are more reliable after considering uncertainty and can produce the worst possible scenario consequence. Conducting the sensitivity analysis to prioritize the treatment of parameters and identify effective measures in risk control. The methodology can provide an important reference for decision-makers to prevent and control domino effects.

Uncertainty in the embodied energy assessment of buildings: a case of EWS type low-cost house in India

Studies on embodied energy of buildings often present results as a single-point estimate without considering the variability in input parameters and the uncertainty it poses on results. Uncertainty analysis is useful to improve the reliability of results. This study examines uncertainty in the embodied energy of a single-storey EWS type residential building due to variability in the embodied energy intensity of materials and material wastage factors. Data quality indicator (DQI) based semi-qualitative method is used for modelling the variability in input parameters. Monte Carlo Simulation is used for uncertainty propagation. The building embodied energy is found to vary from 4 to 9 GJ/m2 based on variation in input data. The mean building embodied energy is found to be 6.3 GJ/m2. The embodied energy intensity of materials is found to cause more variation in building embodied energy in comparison with mass of materials. 'Brick’ is identified as the significant key parameter based on the relative contribution to uncertainty and embodied energy at the building level. Cement and rebar are identified as key parameters. The DQI based methodology presented in this study is useful for Life Cycle Assessment practitioners to evaluate uncertainty in the embodied energy assessment of residential buildings.

Stochastic mesoscale characterization of ablative materials for atmospheric entry

This study addresses the estimation of material properties at a mesoscopic level using the PuMA software from an uncertainty quantification perspective. Stochastic simulation with PuMA is primarily related to the random distribution of fibers, which is an intrinsic source of uncertainty. Additionally, the selection of certain physical parameters, such as the fiber's thermal conductivity, introduces further uncertainties. The first contribution of this study is to propose a low-cost surrogate-based methodology with an unequal allocation scheme, applied for the first time to the stochastic mesoscale characterization of ablative materials. The second contribution is a study on uncertainty propagation and sensitivity analysis of material properties, providing a systematic assessment of the choice of voxel resolution for both the fibers and the domain. Specifically, the convergence of quantities of interest can be monitored, thus identifying the minimal reference elementary volume.

A new methodology for experimental analysis of single-cavity bubble’s nucleation, growth and detachment in saturated HFE-7100

The study of single bubble nucleation, growth and detachment processes has being carried out with remarkable relevance in the last fifty years. The complexity of the associated phenomena are still a challenge for the researchers in the field, yielding a lot of works trying to explain the enrolled mechanisms. These studies include experimental, numerical and even theoretical approaches. In particular but not exclusively for numerical approaches, it is of essential importance having a solid and detailed experimental description of the full event. It is in this context that this work emerges, proposing a methodology for characterizing the single bubble nucleation, growth and detachment process. This methodology is based in the determination of a “typical bubble” that represents the whole phenomena, providing the reconstruction of a main bubble life-cycle with its uncertainty (both in space and time). This reconstruction allows the determination of several important characteristics, such as bubble volume, apparent contact angle, dry radius, and the forces acting on the bubble. This work analyzes a set of bubbles growing from a cavity of 91μm diameter, under saturated conditions at 0,583 bar and superheating of 25,8 °C. All the outputs were obtained considering a carefully uncertainty determination and propagation from both systematic and random sources, which are not negligible as it is demonstrated in this work. The importance of considering a sufficient number of bubbles to characterize the phenomenon was also addressed, considering an analysis of uncertainties for different set of bubbles. The methodology was also confronted to previous approaches reported elsewhere, that ensured its performance, robustness, and validation.

Inter-laboratory reproduction and sensitivity study of a finite element model to quantify human femur failure load: Case of metastases

IntroductionMetastases increase the risk of fracture when affecting the femur. Consequently, clinicians need to know if the patient's femur can withstand the stress of daily activities. The current tools used in clinics are not sufficiently precise. A new method, the CT-scan-based finite element analysis, gives good predictive results. However, none of the existing models were tested for reproducibility. This is a critical issue to address in order to apply the technique on a large cohort around the world to help evaluate bone metastatic fracture risk in patients. The aim of this study is then to evaluate 1) the reproducibility 2) the transposition of the reproduced model to another dataset and 3) the global sensitivity of one of the most promising models of the literature (original model). MethodsThe model was reproduced based on the paper describing it and discussion with authors to avoid reproduction errors. The reproducibility was evaluated by comparing the results given in the original model by the original first team (Leuven, Belgium) and the reproduced model made by another team (Lyon, France) on the same dataset of CT-scans of ex vivo femurs. The transposition of the model was evaluated by comparing the results of the reproduced model on two different datasets. The global sensitivity analysis was done by using the Morris method and evaluates the influence of the density calibration coefficient, the segmentation, the orientations and the length of the femur. ResultsThe original and reproduced models are highly correlated (r2 = 0.95), even though the reproduced model gives systematically higher failure loads. When using the reproduced model on another dataset, predictions are less accurate (r2 with the experimental failure load decreases, errors increase). The global sensitivity analysis showed high influence of the density calibration coefficient (mean variation of failure load of 84 %) and non-negligible influence of the segmentation, orientation and length of the femur (mean variation of failure load between 7 and 10 %). ConclusionThis study showed that, although being validated, the reproduced model underperformed when using another dataset. The difference in performance depending on the dataset is commonly the cause of overfitting when creating the model. However, the dataset used in the original paper (Sas et al., 2020a) and the Leuven's dataset gave similar performance, which indicates a lesser probability for the overfitting cause. Also, the model is highly sensitive to density parameters and automation of measurement may minimize the uncertainty on failure load. An uncertainty propagation analysis would give the actual precision of such model and improve our understanding of its behavior and is part of future work.

Surrogate-based worst-case analysis of a knee joint model using Genetic Algorithm

Verification, validation, and uncertainty quantification is generally recognized as a standard for assessing the credibility of mechanical models. This is especially evident in biomechanics, with intricate models, such as knee joint models, and highly subjective acquisition of parameters. Propagation of uncertainty is numerically expensive but required to evaluate the model reliability. An alternative to this is to analyze the worst-case models obtained within the specific bounds set on the parameters. The main idea of the paper is to search for two models with the greatest different response in terms of displacement-load curve. Real-Coded Genetic Algorithm is employed to effectively explore the high-dimensional space of uncertain parameters of a 2D dynamic knee model, while Radial Basis Function surrogates reduce the computation by orders of magnitude to near real-time, with negligible impact on the quality. It is expected that the studied knee joint model is very sensitive to uncertainty in the geometrical parameters. The obtained worst-case knee models showcase unrealistic behavior with one of them unable to fully extend, and the other largely overextending. Their relative difference in extension is up to 35% under ±1 mm bound set on the geometry. This unrealistic behavior of knee joint model is confirmed by the large standard deviation obtained from a classical sampling-based sensitivity analysis. The results confirm the viability of the method in assessing the reliability of biomechanical models. The proposed approach is general and could be applied to other mechanical systems as well.

Deep Learning-Based Multifidelity Surrogate Modeling for High-Dimensional Reliability Prediction

Abstract Multifidelity surrogate modeling offers a cost-effective approach to reducing extensive evaluations of expensive physics-based simulations for reliability prediction. However, considering spatial uncertainties in multifidelity surrogate modeling remains extremely challenging due to the curse of dimensionality. To address this challenge, this paper introduces a deep learning-based multifidelity surrogate modeling approach that fuses multifidelity datasets for high-dimensional reliability analysis of complex structures. It first involves a heterogeneous dimension transformation approach to bridge the gap in terms of input format between the low-fidelity and high-fidelity domains. Then, an explainable deep convolutional dimension-reduction network (ConvDR) is proposed to effectively reduce the dimensionality of the structural reliability problems. To obtain a meaningful low-dimensional space, a new knowledge reasoning-based loss regularization mechanism is integrated with the covariance matrix adaptation evolution strategy (CMA-ES) to encourage an unbiased linear pattern in the latent space for reliability prediction. Then, the high-fidelity data can be utilized for bias modeling using Gaussian process (GP) regression. Finally, Monte Carlo simulation (MCS) is employed for the propagation of high-dimensional spatial uncertainties. Two structural examples are utilized to validate the effectiveness of the proposed method.

Stochastic assessment of electric powertrain whining noise under early-stage design uncertainties

Despite the advantage of being quieter than traditional internal combustion engine vehicles, electric vehicles are often distinguished by high-frequency tonal components, which can be perceived as unpleasant to the occupants and the environment. To ensure optimal acoustic comfort in electric vehicles, it is important to analyze the NVH behavior of e-powertrains during the early stages of the design process which poses inherent uncertainties, such as varying operating conditions, partial knowledge of design parameters, dispersion in measurement-based data, etc. To effectively address these uncertainties, it is necessary to use fast and comprehensive stochastic models during the design phase. In this work, a probabilistic framework is presented to estimate the electric powertrain’s interior whining noises considering the structure-borne contribution. Hence, two different stochastic metamodels are developed for efficient quantification and propagation of uncertainties from electric motor stage to powertrain mounting system. Multivariate Bayesian regression models help to incorporate prior knowledge on the uncertain parameters and generate the respective posterior distributions using Markov chains Monte Carlo (MCMC) techniques. For this particular application, the data is generated through weakly-coupled multi-physical domains estimated using semi-analytical approaches and combined with measured vehicle transfer functions. Importantly, the validation of each domain is conducted separately to ensure accurate representation. The results obtained from the developed probabilistic framework will aid in the early design stages by guiding engineers in making informed decisions to optimize NVH performance.

Probabilistic Printability Maps for Laser Powder Bed Fusion Via Functional Calibration and Uncertainty Propagation

Abstract In this work, we develop an efficient computational framework for process space exploration in laser powder bed fusion (LPBF) based additive manufacturing technology. This framework aims to find suitable processing conditions by characterizing the probability of encountering common build defects. We employ a Bayesian approach toward inferring a functional relationship between LPBF processing conditions and the unobserved parameters of laser energy absorption and powder bed porosity. The relationship between processing conditions and inferred laser energy absorption is found to have good correspondence to the literature measurements of powder bed energy absorption using calorimetric methods. The Bayesian approach naturally enables uncertainty quantification and we demonstrate its utility by performing efficient forward propagation of uncertainties through the modified Eagar–Tsai model to obtain estimates of melt pool geometries, which we validate using out-of-sample experimental data from the literature. These melt pool predictions are then used to compute the probability of occurrence of keyhole and lack-of-fusion based defects using geometry-based criteria. This information is summarized in a probabilistic printability map. We find that the probabilistic printability map can describe the keyhole and lack-of-fusion behavior in experimental data used for calibration, and is capable of generalizing to wider regions of processing space. This analysis is conducted for SS316L, IN718, IN625, and Ti6Al4V using melt pool measurement data retrieved from the literature.

Multimodal uncertainty propagation analysis for the morphing wings of cross-domain variant aircraft

Multimodal uncertainty propagation analysis for the morphing wings of cross-domain variant aircraft

Data inaccuracy quantification and uncertainty propagation for bibliometric indicators

Abstract This study introduces an approach to estimate the uncertainty in bibliometric indicator values that is caused by data errors. This approach utilizes Bayesian regression models, estimated from empirical data samples, which are used to predict error-free data. Through direct Monte Carlo simulation—drawing many replicates of predicted data from the estimated regression models for the same input data—probability distributions for indicator values can be obtained which provide the information on their uncertainty due to data errors. It is demonstrated how uncertainty in base quantities, such as the number of publications of certain document types of a unit of analysis and the number of citations of a publication, can be propagated along a measurement model into final indicator values. Synthetic examples are used to illustrate the method and real bibliometric research evaluation data is used to show its application in practice. Though in this contribution we just use two out of a larger number of known bibliometric error categories and therefore can account for only some part of the total uncertainty due to inaccuracies, the latter example reveals that average values of citation impact scores of publications of research groups need to be used very cautiously as they often have large margins of error resulting from data inaccuracies.

Uncertainty propagation of flutter analysis for long-span bridges using probability density evolution method

Dynamic and aerodynamic uncertainties are inevitably involved in the wind-bridge system due to some unknown information or complicated environment conditions. The deterministic aeroelastic flutter study is unable to account for these uncertainties and fail to describe the fragility or risk of flutter instability of the bridge. To achieve the uncertainty propagation of flutter analysis for long-span bridges, the advanced probability density evolution method is introduced. The increase of wind speed is treated as a time-varying parameter incorporated into the generalized density evolution equation. The two-dimensional bimodal and three-dimensional multi-mode methods for bridge flutter analysis are utilized to track the probability density evolution of damping ratio and frequency of each mode. The probability of flutter critical wind speeds can then be readily determined. The probability density evolution process is applied to a simply supported beam bridge with quasi-flat box girder and a suspension bridge with closed-box girder by considering the uncertainties of the structural properties and flutter derivatives. The probability density evolution method is proved to produce a reasonable result which shows a good agreement with Monte Carlo method, but requires fewer sample points, which improves the computational efficiency.

Analysis of 115In(n,γ)116mIn reaction cross-section and covariance for 13.52MeV and 14.54MeV neutron induced energies.

Neutron induced reactions play a vital role in the field of nuclear and particle physics. An effort was made to study the neutron-induced reaction cross-section of 115In(n,γ)116mIn with 197Au(n,γ)198Au as monitor reaction and carried out the reaction for the neutron energies of 13.520±0.005 and 14.54±0.24MeV. The neutrons obtained from the D-T fusion reaction of Purnima neutron generator were used for the activation of the given reaction and the monitor. The covariance analysis and the partial uncertainties due to various attributes were utilised for estimating the uncertainty propagation and hence obtained the correlation for measured reaction cross-sections. The measured reaction cross-sections have been validated with earlier reported data from EXFOR, ENDF data of various libraries, and also theoretically calculated the values of the TALYS-1.9 code.