Aleatory Uncertainty Research Articles

Seismic Failure Risk Assessment of Post Electrical Equipment on Supporting Structures

To assess the seismic failure risk of post electrical equipment, an assessment method considering different sorts of uncertainty of the post electrical equipment was proposed. The aleatory and epistemic uncertainties were considered in the assessment, and the parameters in seismic hazard function of different sites were fitted. To investigate the effects of the supporting structure on the seismic fragility and risk of post electrical equipment, case studies on ultra-high-voltage gas insulated switchgear bushings mounted on two different supporting frames were conducted. The results indicated that both the maximum tensile stress of the bushing and the maximum displacement of the supporting frames should be considered as the limit statuses of the post electrical equipment. The different sorts of uncertainty increase the seismic failure risk of the post electrical equipment, and should be considered in the assessment. Besides, for the pillar-type porcelain element equipment, the supporting frames with lower lateral stiffness generated higher seismic failure risk. In constrast to the case of retrofitting the supporting frame to increase the lateral stiffness, the annual seismic failure risk of the GIS bushing mounted on the retrofitted supporting frame decreased 101%. Besides, the seismic failure risk of the post electrical equipment is not positive correlated with the peak ground acceleration. In the performance-based seismic design of the electrical substation, the seismic failure risk of the electrical equipment should be considered.

Seismic Risk Analysis of Subway Station Structures Combining the Epistemic Uncertainties from Both Seismic Hazard and Numerical Simulation

ABSTRACT To consider the influence of epistemic uncertainties in both seismic hazard and numerical simulation on seismic risk of subway station structures, the uncertainties mentioned above are uniformly characterized as the epistemic uncertainty of seismic demand of subway station structures from the perspective of uncertainty propagation in this paper. On this basis, the analytical formulations of seismic risk considering simultaneous aleatory and epistemic uncertainties are derived. The validity of the derived analytical formulations is verified by the Monte Carlo simulation and the influences of epistemic uncertainty on the seismic risk of subway station structure are further discussed.

Towards trustworthy rotating machinery fault diagnosis via attention uncertainty in transformer

To enable researchers to fully trust the decisions made by deep diagnostic models, interpretable rotating machinery fault diagnosis (RMFD) research has emerged. Existing interpretable RMFD research focuses on developing interpretable modules embedded in deep models to assign physical meaning to results, or on inferring the logic of the model to make decisions based on results. However, there is limited work on how to quantify uncertainty in results and explain its sources and composition. Uncertainty quantification and decomposition not only provide the confidence of the results, but also identify the source of unknown factors in the data, and consequently guide to enhance the interpretability and trustworthiness of models. Therefore, this paper proposes to use Bayesian variational learning to introduce uncertainty into the attention weights of Transformer to construct a probabilistic Bayesian Transformer for trustworthy RMFD. A probabilistic attention is designed and the corresponding optimization objective is defined, which can infer the prior and variational posterior distributions of attention weights, thus empowering the model to perceive uncertainty. An uncertainty quantification and decomposition scheme is developed to achieve confidence characterization of results and separation of epistemic and aleatoric uncertainty. The effectiveness of the proposed method is fully verified in three out-of-distribution generalization scenarios.

Robust optimization of the design of monopropellant propulsion control systems using an advanced teaching-learning-based optimization method

This research proposes a novel approach for the robust optimization of the design of hydrogen peroxide propulsion control systems using the efficient and advanced Teaching-Learning-Based Optimization (TLBO) method. This study adopts a robust design optimization (RDO) formulation that considers both epistemic and aleatory uncertainties, including sparse points and interval data, and uses the Johnson distribution family for uncertainty representation. The maximum likelihood estimation method is applied to determine the distribution parameters, also considering interval data with a nested optimization technique. A novel advanced TLBO method with high accuracy and convergence rate is employed to optimization of this robust design approach. The method’s originality and advancement come from two categories of modifications to the original framework: the structure of the teaching and learning phases and the initialization and search approach. The efficacy and applicability of the proposed Ad-TLBO, respectively, were evaluated using benchmark problems from the CEC2020 competition and three real-world engineering problems, with a comparison to some recently published and the CEC competition’s top-ranked algorithms. The results and statistical analyses of the Quade test, Wilcoxon signed-rank test, and Friedman test show that the proposed Ad-TLBO method outperforms the other algorithms. The proposed optimization method is eventually applied to design a monopropellant propulsion system as the control actuator of a satellite orbital transfer system. It is found that the proposed advanced TLBO is effective in handling uncertainty in real design problems and improves both the convergence rate and accuracy of the optimization process.

Epistemic uncertainty quantification in structural systems using improved universal grey theory

It is important to account for uncertainties in structures during the analysis and design. Based on the source and nature, the uncertainties can be classified as aleatory and epistemic. Aleatory uncertainties arise due to the intrinsic randomness nature of physical system, whereas epistemic uncertainties realize on account of insufficient knowledge. When the information about the system is grey (i.e., partially available as range or interval), methods such as combinatorial approach, interval methods (IM) and universal grey theory (UGT) are generally adopted. The combinatorial optimization becomes computationally expensive when the dimension of uncertain system is large. Interval analysis leads to overestimation due to violations of the physical law and dependency problem. The satisfaction of the physical law (distributive law) that arises out of defining the arithmetic relations, contributes to the UGT free from dependency problem, and makes the approach more efficient. The traditional UGT is ineffective in certain conditions, wheneither one or both the bounds are negative with the absolute value of the upper bound being smaller i.e.,x¯⩽x̲. Therefore, this paper proposes a necessary modification in arithmetic operations to overcome the incapability of traditional UGT. The efficiency of proposed method is demonstrated through three numerical examples. Comparisons have been made with the conventional techniques to substantiate the proposed methodology, and the results obtained show that the proposed method is computationally efficient in terms of efforts and accuracy.

Thermal modelling of a small satellite data processing unit aided by sensitivity analysis and uncertainty quantification

Sensitivity analysis (SA) and uncertainty quantification (UQ) were used to verify the thermal design of the Intuition-1 nanosatellite data processing unit (DPU). For that purpose, a numerical model of the satellite was developed and validated against experimental data, which were obtained in thermal-vacuum chamber experiments. First, a simplified approach was applied to identify and eliminate less important parameters from further analysis. In the second step, a second-order probability approach was utilized to take into account the epistemic and aleatory uncertainties in the UQ study. The results identified crucial design parameters and the separate influence of aleatory and epistemic input uncertainty on the output variables. The results showed that the design of the nanosatellite DPU does not require modification and that minimizing the uncertainty of the input could considerably reduce the output uncertainty. The presented methodology can be applied to other systems to identify the importance of individual design parameters and predict the uncertainty of key responses under mixed aleatory and epistemic uncertainty. This process is crucial for the robustness of thermal design and provides valuable information supporting project decisions.

Local sensitivity informed anisotropic sparse grid method for uncertainty quantification of chemical kinetics

The determination of rate coefficient parameters in detailed chemical kinetic mechanisms through experiments often suffers from avoidable aleatory uncertainty, while the use of reduced mechanisms, based on various reduction methods, introduces epistemic uncertainty. Both sources of uncertainty pose significant challenges for modeling and numerical simulation, highlighting the need for calibrating these uncertain parameters to achieve robust chemical mechanisms in the next generation. However, the high-dimensional parameter space of chemical kinetic mechanisms remains a significant obstacle in uncertainty computing. The Anisotropic Sparse Grid (ASG) technique has been successful in dealing with high-dimensional uncertainty problems, but it lacks prior knowledge of anisotropy. To address this issue, we propose the Local Sensitivity-Informed Anisotropic Sparse Grid (LSIASG) method, which utilizes local sensitivity as prior information for the ASG method, thereby accelerating the entire uncertainty quantification process. We test the LSIASG method on a theoretical model, a detailed hydrogen kinetic mechanism, and a methane mechanism and demonstrate that it can capture high-dimensional uncertainty characteristics, including expectation and deviation.

Variations in Aquatic Vegetation Diversity Responses to Water Level Sequences during Drought in Lakes under Uncertain Conditions

Water level variability and temporal change are critical for shaping the structure of aquatic vegetation. Much research has examined the response of aquatic vegetation to hydrological metrics. However, the hydrological sequence is a fundamental driver of aquatic ecosystem structure and function. Given the aleatory uncertainty of future water levels under an unstable climate, how aquatic vegetation responds to changing dynamics in hydrological processes, especially shifting water level sequences, remains insufficiently explored. In this paper, we establish an evaluation framework to study the response of vegetation diversity to variation in water level sequences during a drought event. To do this, the uncertainty and variability of water level processes are both considered. Altering water level processes was achieved using two types of scenarios in order to explore the effects of differing water level sequences (i.e., changing the order of high vs. low water levels) on the probability distribution of four indexes of aquatic plant diversity (e.g., Margalef’s, Simpson’s, Shannon’s, and Pielou’s evenness index). Our results show that altering the order of water level state can lead to differences in the diversity of aquatic vegetation, with a pronounced impact on vegetation complexity. This suggests that the specific sequence of water level events is critical for shaping aquatic vegetation structure. In addition, we found that a uniform distribution of water level state is beneficial for enhancing a species’ dominance in aquatic vegetation. Our findings provide guidance for improving the future development of freshwater ecosystem protection and lake management.

Wasserstein Actor-Critic: Directed Exploration via Optimism for Continuous-Actions Control

Uncertainty quantification has been extensively used as a means to achieve efficient directed exploration in Reinforcement Learning (RL). However, state-of-the-art methods for continuous actions still suffer from high sample complexity requirements. Indeed, they either completely lack strategies for propagating the epistemic uncertainty throughout the updates, or they mix it with aleatoric uncertainty while learning the full return distribution (e.g., distributional RL). In this paper, we propose Wasserstein Actor-Critic (WAC), an actor-critic architecture inspired by the recent Wasserstein Q-Learning (WQL), that employs approximate Q-posteriors to represent the epistemic uncertainty and Wasserstein barycenters for uncertainty propagation across the state-action space. WAC enforces exploration in a principled way by guiding the policy learning process with the optimization of an upper bound of the Q-value estimates. Furthermore, we study some peculiar issues that arise when using function approximation, coupled with the uncertainty estimation, and propose a regularized loss for the uncertainty estimation. Finally, we evaluate our algorithm on standard MujoCo tasks as well as suite of continuous-actions domains, where exploration is crucial, in comparison with state-of-the-art baselines. Additional details and results can be found in the supplementary material with our Arxiv preprint.

Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty

Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based controller synthesis method for continuous-state models with stochastic noise and uncertain parameters. By sampling techniques and robust analysis, we capture both aleatoric and epistemic uncertainty, with a user-specified confidence level, in the transition probability intervals of a so-called interval Markov decision process (iMDP). We synthesize an optimal policy on this iMDP, which translates (with the specified confidence level) to a feedback controller for the continuous model with the same performance guarantees. Our experimental benchmarks confirm that accounting for epistemic uncertainty leads to controllers that are more robust against variations in parameter values.

Semi-Supervised Deep Regression with Uncertainty Consistency and Variational Model Ensembling via Bayesian Neural Networks

Deep regression is an important problem with numerous applications. These range from computer vision tasks such as age estimation from photographs, to medical tasks such as ejection fraction estimation from echocardiograms for disease tracking. Semi-supervised approaches for deep regression are notably under-explored compared to classification and segmentation tasks, however. Unlike classification tasks, which rely on thresholding functions for generating class pseudo-labels, regression tasks use real number target predictions directly as pseudo-labels, making them more sensitive to prediction quality. In this work, we propose a novel approach to semi-supervised regression, namely Uncertainty-Consistent Variational Model Ensembling (UCVME), which improves training by generating high-quality pseudo-labels and uncertainty estimates for heteroscedastic regression. Given that aleatoric uncertainty is only dependent on input data by definition and should be equal for the same inputs, we present a novel uncertainty consistency loss for co-trained models. Our consistency loss significantly improves uncertainty estimates and allows higher quality pseudo-labels to be assigned greater importance under heteroscedastic regression. Furthermore, we introduce a novel variational model ensembling approach to reduce prediction noise and generate more robust pseudo-labels. We analytically show our method generates higher quality targets for unlabeled data and further improves training. Experiments show that our method outperforms state-of-the-art alternatives on different tasks and can be competitive with supervised methods that use full labels. Code is available at https://github.com/xmed-lab/UCVME.

Towards an automatic uncertainty compiler

An uncertainty compiler is a tool that automatically translates original computer source code lacking explicit uncertainty quantification into code containing appropriate uncertainty representations and uncertainty propagation algorithms. It handles the specifications of input uncertainties, and inserts calls to intrusive uncertainty quantification algorithms. In theory, one could create an uncertainty compiler for any scientific programming language. The uncertainty compiler can apply intrusive uncertainty propagation methods to codes or parts of codes and, therefore, more comprehensively and flexibly address epistemic and aleatory uncertainties. This paper explores the concept and the practicalities of creating such a compiler.

Predictive uncertainty on astrophysics recovery from multifield cosmology

We investigate how the constraints on the density parameter (Ωm), the power spectrum amplitude (σ 8) and the supernova feedback parameters (A SN1 and A SN2) vary when exploiting information from multiple fields in cosmology. We make use of a convolutional neural network to retrieve the salient features from different combinations of field maps from IllustrisTNG in the CAMELS project. The fields considered are neutral hydrogen (HI), gas density (Mgas), magnetic fields (B) and gas metallicity (Z). We estimate the predictive uncertainty — sum of the squares of aleatoric and epistemic uncertainties — of the parameters inferred by our model by using Monte Carlo dropout, a Bayesian approximation. Results show that in general, the performance of the model improves as the number of channels of its input is increased. In the best setup which includes all fields (four channel input, Mgas-HI-B-Z) the model achieves R 2 > 0.96 on all parameters. Similarly, we find that the predictive uncertainty, which is dominated by the aleatoric uncertainty, decreases as more fields are used to train the model in general. The uncertainties obtained by dropout variational inference are overestimated on all parameters in our case, in that the predictive uncertainty is much larger than the actual squared error, which is the square of the difference between the ground truth and prediction. After calibration, which consists of a simple σ scaling method, the average deviation of the predictive uncertainty from the actual error goes down to 25% at most (on A SN1).

Likelihood of Primary Surface Faulting: Updating of Empirical Regressions

Abstract Surface faulting is a common phenomenon for crustal earthquakes and is an important source of localized hazard to buildings and infrastructure. Nevertheless, not all earthquakes of a given magnitude generate surface faulting. To correctly assess the hazard posed by surface fault displacement, it is critical to use reliable regressions of the likelihood of surface faulting. Such regressions are derived from empirical data and the ones currently used in engineering practice are based on datasets acquired several years ago. The aim of this work is to update the regressions characterizing the likelihood of primary surface faulting (i.e., P(Slip|m)). We systematically analyze Mw≥5.5 earthquakes that occurred in 1992–2018, with hypocentral depths lower than 20 km and epicenter onshore. We obtain information on the occurrence or non-occurrence of primary surface faulting for 363 earthquakes (87 with primary surface faulting and 276 without). We derive empirical regressions of P(Slip|m) from the entire dataset as well as for normal, strike-slip, and reverse earthquakes, and discuss the potential sources of aleatory and epistemic uncertainty. A sensitivity analysis shows that the P(Slip|m) term has a significant impact on the hazard curve expressed as the annual frequency of exceeding a given displacement value. We argue that the regressions presented in this work can be incorporated in models for probabilistic fault displacement hazard assessment, ultimately providing a better evaluation of the hazard.

Bayesian uncertainty quantification framework for wake model calibration and validation with historical wind farm power data

AbstractThe expected growth in wind energy capacity requires efficient and accurate models for wind farm layout optimization, control, and annual energy predictions. Although analytical wake models are widely used for these applications, several model components must be better understood to improve their accuracy. To this end, we propose a Bayesian uncertainty quantification framework for physics‐guided data‐driven model enhancement. The framework incorporates turbulence‐related aleatoric uncertainty in historical wind farm data, epistemic uncertainty in the empirical parameters, and systematic uncertainty due to unmodeled physics. We apply the framework to the wake expansion parametrization in the Gaussian wake model and employ historical power data of the Westermost Rough Offshore Wind Farm. We find that the framework successfully distinguishes the three sources of uncertainty in the joint posterior distribution of the parameters. On the one hand, the framework allows for wake model calibration by selecting the maximum a posteriori estimators for the empirical parameters. On the other hand, it facilitates model validation by separating the measurement error and the model error distribution. In addition, the model adequacy and the effect of unmodeled physics are assessable via the posterior parameter uncertainty and correlations. Consequently, we believe that the Bayesian uncertainty quantification framework can be used to calibrate and validate existing and upcoming physics‐guided models.

Bayesian neural networks with physics‐aware regularization for probabilistic travel time modeling

AbstractThe integration of data‐driven models such as neural networks for high‐consequence decision making has been largely hindered by their lack of predictive power away from training data and their inability to quantify uncertainties often prevalent in engineering applications. This article presents an ensembling method with function‐space regularization, which allows to integrate prior information about the function of interest, thus improving generalization performance, while enabling quantification of aleatory and epistemic uncertainties. This framework is applied to build a probabilistic ambulance travel time predictor, leveraging historical ambulance data provided by the Fire Department of New York City. Results show that the integration of a non‐Gaussian likelihood and prior information from a road network analysis yields appropriate probabilistic predictions of travel times, which could be further leveraged for emergency medical service (EMS) decision making.

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.

Seismic resilience assessment of Small Modular Reactors by a Three-loop Monte Carlo Simulation

We develop a three-loop Monte Carlo Simulation (MCS) framework for the seismic resilience assessment of Small Modular Reactors (SMRs), embedding Probabilistic Seismic Hazard Analysis (PSHA), seismic fragility evaluation and multiple SMR units accident sequence analysis. A set of metrics are computed to capture different aspects of SMR resilience to earthquakes, specifically the ability to withstand seismic disruption, mitigate consequences and restore normal operation. The MCS framework allows accounting for the aleatory and epistemic uncertainties of the PSHA and fragility parameters. An application is given with regards to an advanced Nuclear Power Plant (aNPP) consisting of four reactor units of NuScale SMR design. A comparison is made to a conventional NPP (cNPP), i.e., a typical large reactor of equivalent generation capacity. Both plants are fictitiously located on the Garigliano nuclear site (southern Italy). The results show that resilient features of SMRs overcome cNPPs in terms of post-accident scenario mitigation and restoration capabilities.

Probabilistic safety risk assessment in large-diameter tunnel construction using an interactive and explainable tree-based pipeline optimization method

Due to knowledge alienation, the application of artificial intelligence (AI) techniques in tunnel construction has been greatly stunted in recent years. In order to motivate the development of techniques in tunneling works, we propose an approach that combines automated machine learning, explainable AI, and building information modeling in this paper. Considering geotechnical uncertainties from soil properties and aleatoric uncertainties from the predicting model, this approach is used to evaluate the system risk during a large-diameter tunnel excavation taking into account the two sources of uncertainties simultaneously. The geotechnical uncertainties are evaluated by the confidence interval of the mean of samples in the Monte-Carlo simulation, and the aleatoric uncertainties are evaluated by computing the prediction interval of the machine learning models. It is found that the number of Monte-Carlo samples significantly affects the evaluation of the system’s reliability. Based on our results, a generalized setup with 1000 samples performs the best and is recommended considering the efficiency of computation, as well as the reliability and conservativeness of the result. This paper effectively assists with system reliability evaluation in large-diameter tunnel constructions, where the interactive and explainable AI approach largely motivates the application of AI techniques in the field of tunnel construction.

Quantification of Equivalent Strut Modeling Uncertainty and Its Effects on the Seismic Performance of Masonry Infilled Reinforced Concrete Frames

ABSTRACT Quantifying aleatory and epistemic uncertainty in nonlinear structural response simulation is key to robust performance-based seismic assessments. This paper focuses on the modeling parameters that are used to describe the nonlinear force-deformation response of the equivalent infill struts used in models of reinforced concrete frames with infills. The variability in several parameters is characterized by developing empirical and theoretical multivariate probability distributions based on the deduced-to-predicted ratios derived using data from 113 physical experiments. The effect of the uncertainty in the infill strut modeling parameters on maximum story drift ratios and associated limit state fragility functions is investigated for a 3-story reinforced concrete frame building with infills. Multiple stripe analysis is performed using hazard-consistent ground motions. Relative to when only record-to-record variability is considered, modeling parameter uncertainty has a non-negligible effect on the dispersion of the maximum story drift ratios, and affects both the median and dispersion of the limit state fragilities.