Aleatory Uncertainty Research Articles

Diversity entropy-based Bayesian deep learning method for uncertainty quantification of remaining useful life prediction in rolling bearings

Remaining useful life (RUL) prediction of rolling bearings plays a critical role in reducing unplanned downtime and improving machine productivity. The existing prediction methods primarily provide point estimates of RUL without quantifying uncertainty. However, uncertainty quantification of RUL is crucial to conduct reliable risk analysis and make maintenance decision, which can significantly decrease the maintenance costs. To solve the uncertainty quantification problem and improve prediction accuracy at the same time, a novel diversity entropy-based Bayesian deep learning (DE-BDL) method is proposed. First, start degradation time (SDT) of bearings is adaptively determined using diversity entropy, which can extract early degradation information. Then, multi-scale diversity entropy (MDE) is developed to extract dynamic characteristics over multiple scales. Third, the obtained features using MDE are fed into the BDL model for degradation tracking and prediction. By doing this, the proposed DE-BDL method has merits in subsequent decision making, which can not only provide point estimation but also offer uncertainty quantification with epistemic uncertainty and aleatoric uncertainty. The superiority of the proposed method is validated using run-to-failure data. The experimental results and comparison with state-of-art prediction methods have demonstrated that the proposed DE-BDL method is promising for RUL of rolling bearings.

Epistemic uncertainty in poorly detailed existing frames accounting for masonry infill variability and RC shear failure

AbstractRobust performance‐based earthquake assessment should consider the effects of both aleatory and epistemic uncertainty on seismic response parameters. While the effects of modelling uncertainty on specific engineering demand parameters and collapse fragility curves have been widely investigated to date on bare frame structural typologies, little attention has been paid to the impact of masonry infill properties variability on the uncertainty estimation in existing infilled RC frames. Previous studies available in the literature are mainly related to seismically designed RC buildings and the suggestions provided in international guidelines cannot be reasonably adopted for poorly detailed RC existing frames. As regards the uncertainty in existing RC frames, the role of masonry infills was often neglected or their interaction with the surrounding frames was not rigorously accounted for in the uncertainty estimation. With such limitations in mind, the aim of this study is to provide more realistic modelling uncertainty quantities to be adopted in seismic assessment of existing infilled RC frames, including, in a thorough manner, the impact of the variability of the masonry infill typologies and the occurrence of RC frame shear failure. Both the aleatory and epistemic uncertainties are estimated, in terms of the overall dispersion on specific engineering demand parameters and collapse fragility curves. Finally, the impact of such uncertainties on seismic risk estimates, quantified through expected annual losses, is also thoroughly investigated. The inclusion of additional random variables, not considered so far, in the uncertainty estimation framework, led to importantly higher modelling uncertainty quantities than those currently available from previous studies.

A Bayesian Deep Learning Framework for RUL Prediction Incorporating Uncertainty Quantification and Calibration

In this article, deep learning (DL) has attracted increasing attention for remaining useful life (RUL) prediction. However, most DL-based prognostics methods only provide deterministic RUL values while ignoring the associated epistemic and aleatoric uncertainties. In practice, it is important to know the exact confidence in model predictions for decision making. In this article, a Bayesian deep learning (BDL) framework for RUL prediction incorporating uncertainty quantification and calibration is proposed. First, the epistemic and aleatoric uncertainties, which account for the ignorance about the model and the noise inherent in the observations, respectively, are characterized by integrating both types of uncertainties into a BDL framework. Second, to avoid under- and over-confident predictions, a novel iterative calibration method is proposed to jointly calibrate epistemic, aleatoric, and predictive uncertainties by combining isotonic regression with standard deviation scaling. The effectiveness of the proposed method is demonstrated by the case study of turbofan engines and lithium-ion batteries datasets.

Selection of Ground Motion Intensity Measures in Fragility Analysis of a Mega-Scale Steel Frame Structure at Separate Limit States: A Case Study

Selecting an appropriate ground motion intensity measure (IM) to estimate the aleatory uncertainty produced by ground motion variability is the first and crucial step in fragility analysis. The choice of IM is influenced not only by the structural system type itself but also by the limit state of the structural damage. In this study, an investigation of the selection of IM in fragility analysis with respect to different limit states is developed for a 48-story mega-scale steel frame structure with buckling restrained braces. A comparative study of the efficiency of 27 IMs is conducted at four structural damage limit states, i.e., negligible, light, moderate, and severe, through the lognormal standard deviation estimated in fragility equations. In addition, for the purpose of considering the influence of different earthquake characteristics, two completely different sets of ground motions are selected, namely near-field pulse-like and far-field earthquakes. The research shows that the ground motion characteristics and structural damage limit states have nonnegligible effects on the flexibility of intensity measures. For combination-type IMs, the number of combined terms and the combined power index have a significant impact on their performance; thus, an optimized dual-parameter combination-type intensity measure is recommended.

Comprehensive treatment of uncertainties in risk‐targeted performance‐based seismic design and assessment of bridges

AbstractThis study complements and extends a recent work on the development of a rigorous framework for risk‐targeted performance‐based seismic design/assessment of ordinary standard bridges (OSBs) in California. Rooted in the formulation of this framework is an updated fully probabilistic performance‐based earthquake engineering (PBEE) assessment methodology wherein metrics of structural performance are formulated in terms of the mean return periods of exceedances for several strain‐based limit‐states (LSs). The originally proposed framework explicitly considering: (1) the uncertainty in the seismic input, and (2) the uncertainty in the capacity of the various LSs, is extended in this study to account for the following additional pertinent sources of uncertainty: (i) the aleatory uncertainty associated with finite element (FE) model parameters, and (ii) the epistemic parameter estimation uncertainty associated with using finite datasets to estimate the parameters of the probability distributions characterizing the FE model parameters and LS fragilities. These additional sources of uncertainty are commonly omitted or neglected in PBEE often by invoking that the earthquake ground motion uncertainty is the predominant source of uncertainty. However, their inclusion and consistent propagation in seismic performance‐based assessment of OSBs is imperative to obtain a more complete picture of seismic performance, thereby leading to a more comprehensive, transparent, and reliable design of these simple, yet essential bridges which represent an integral part of lifeline infrastructure systems especially in earthquake‐prone regions. The analytical and computational framework previously assembled is extended via modular incorporation of these additional sources of uncertainty. Four OSB testbeds and their risk‐targeted re‐designed versions are analyzed with and without these additional sources of uncertainty to evaluate their significance.

Intelligent decision support for collision avoidance manoeuvre planning under uncertainty

This paper presents a decision support system that can automatically allocate collision avoidance manoeuvres in the event of a high risk close encounter between two space objects. Decisions are supported by an Intelligent Classification System that combines Dempster-Shafer theory of evidence with Machine Learning to automatically classify conjunctions according to the probability of collision, the uncertainty on the probability of collision, the time to close approach and the cost of a collision avoidance manoeuvre. We propose a simple analytical model that allows for the fast and robust computation of both impulsive and low-thrust manoeuvres under a mix of aleatory and epistemic uncertainty. Aleatory uncertainty is the non-reducible randomness in observation data, dynamic model and parameters, while epistemic uncertainty is the lack of knowledge on system dynamics and observation data, including the model of aleatory uncertainty itself. Dempster-Shafer theory of evidence is used to model the epistemic uncertainty in the calculation of the probability of collision. Some numerical examples are included to show the performance of the collision avoidance manoeuvre optimisation strategy and of the intelligent decision support system.

Multifidelity Model Calibration in Structural Dynamics Using Stochastic Variational Inference on Manifolds.

Bayesian techniques for engineering problems, which rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian process based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data.

A review on uncertainty quantification of shadowing reconstruction and signal measurements in Radio Tomographic Imaging

Radio Tomographic Imaging (RTI) is a novel technology to reconstruct the target-induced shadowing effect of signal propagation in the Radio-Frequency (RF) sensing network, through the Received Signal Strength (RSS) measurements in the RF propagation links. As a novel wireless-signal reconstruction technology, RTI is widely utilized in the Device-Free Localization (DFL) and Location-Based Services (LBS) applications. However, the multipath interference in RF sensing network often induces serious uncertainty in RTI system, including the RSS measurement noise and the RTI reconstruction degradation. Addressing this problem, as the RTI system is to reconstruct the probability image of shadowing by using the RSS measurements, from the perspective of probabilistic modeling, the RTI reconstruction issue is modeled as the Maximum a Posterior Probability (MAP) of the reconstructed shadowing image from the RSS measurements. Then lots of RTI reconstruction methods for uncertainty quantification, have been developed to improve the RSS measurement accuracy and the RTI reconstruction quality. Therefore, for the first time, this article conducts a comprehensive survey of the recent RTI methods from the viewpoint of uncertainty quantification. At first, the uncertainty quantification in these RTI methods of the shadowing image and RSS measurements are united into the Epistemic uncertainty and Aleatoric uncertainty respectively. Besides, these methods are further classified into different categories based on their technical commonalities. Moreover, the presenting challenges of uncertainty quantification in the actual RTI applications are also discussed, and based on that, the potential development directions of these methods for improving the RSS measurement accuracy and RTI reconstruction performance in future are reasonably predicted.

Intelligent selection of NEO deflection strategies under uncertainty

This paper presents an Intelligent Decision Support System (IDSS) that can automatically assess the suitable robust deflection strategies to respond to a Near Earth Objects (NEO) impact scenario. The input to the IDSS is the warning time, the orbital parameters and mass of the NEO and the corresponding uncertainties. The output is the deflection strategies that are more likely to offer a successful deflection. Both aleatory and epistemic uncertainties on ephemerides and physical properties of the NEO are considered.The training data set is produced by generating thousands of virtual impactors, sampled from the current distribution of NEO. For each virtual impactor we perform a robust optimisation, under mixed aleatory/epistemic uncertainties, of the deflection scenario with different deflection strategies. The robust performance indices is considered by the deflection effectiveness, which is quantified by Probability of Collision post deflection. The IDSS is based on a combination Dempster-Shafer theory of evidence and a Random Forest classifier that is trained on the data set of virtual impactors and deflection scenarios. Five deflection strategies are modelled and included in the IDSS: Nuclear Explosion, Kinetic Impactor, Laser Ablation, Gravity Tractor and Ion Beam Shepherd. Simulation results suggest that the proposed decision support system can quickly provide robust decisions on which deflection strategies are to be chosen to respond to a NEO impact scenario. Once trained the IDSS does not require re-running expensive simulations to make decisions on which deflection strategies are to be used and is, therefore, suitable for the rapid pre-screening or reassessment of deflection options.

Hybrid uncertainty propagation and reliability analysis using direct probability integral method and exponential convex model

Uncertainty propagation and reliability evaluation, being the crucial parts of engineering system analysis, play vital roles in safety assessment. How to reasonably consider the complex multisource uncertainty behavior in both static and dynamic systems is paramount to ensuring their safe operation. However, there is a significant lack of research on aleatory and epistemic uncertainties for both static and dynamic systems. To this end, a new hybrid exponential model is proposed by combining probabilistic and non-probabilistic exponential models, which aims to accurately measure the uncertainty propagation and reliability evaluation problem with aleatory and epistemic uncertainties for static and dynamic systems. The proposed hybrid exponential model consists of nested double optimization loops. The outer loop performs a probabilistic analysis based on the direct probability integral method, and the inner loop performs a non-probabilistic computation. Then, a new hybrid exponential probability integral method is developed to effectively perform uncertainty propagation and reliability analysis. Finally, four examples, including two static and two dynamic examples with complex performance functions, are tested. The results indicate that the proposed hybrid exponential model offers a universal tool for uncertainty quantification in static and dynamic systems. Moreover, the hybrid exponential probability integral method can accurately and efficiently obtain the upper and lower bounds of the probability density function and cumulative distribution function.

On revision of the Guide to the Expression of Uncertainty in Measurement: Proofs of fundamental errors in Bayesian approaches

The process of revising the Guide to the Expression of Uncertainty in Measurement (GUM) is ongoing. A successful revision must be theoretically sound, so it must be based on a recognized paradigm for scientific data analysis. The major candidate paradigms of statistical inference are the frequentist paradigm — where probability statements are only used to describe the frequency behaviour of processes — and the Bayesian paradigm — where probability statements are also used to describe the degree of belief of the speaker and where the subject of that belief may be the unknown value of a constant. These paradigms are incompatible, and there remains disagreement about which should form the basis of the practical procedures advocated in a revised GUM. This paper uses published results to examine foundational ideas in two different Bayesian approaches, which themselves are inconsistent at a basic, conceptual, level. So-called ‘objective’ Bayesian statistics is based on the premise that a probability distribution can accurately represent a set of information about a constant, which is a premise of the system of analysis currently favoured by the BIPM. This premise is proven to lead to a logical contradiction, which renders the theory untenable. In contrast, subjective Bayesian methods are theoretically satisfactory if they are used in their proper context, which is the context of personal decision-making. But simple examples show that the use of subjective probability in a client-centred measurement can lead to unacceptable results. These examples involve the mixing of epistemic uncertainty (the uncertainty of personal doubt) with aleatory uncertainty (the uncertainty of an unpredictable physical process). They show that these two types of uncertainty cannot always be treated as one, which is a conclusion with profound implications for the role of Bayesian statistics in science. The analysis in this paper also involves a discussion of the ‘meaning’ of probability, which has been a divisive subject for many years. It is argued here that the implied question is inappropriate: the relevant question is not “what does probability mean?” but “what role can probability meaningfully and accurately play?” The results about objective and subjective Bayesian statistics discussed in this paper support the conclusion that a sound and practical system of analysis must be based on the frequency role of probability.

The desirability bias in predictions under aleatory and epistemic uncertainty

The desirability bias (or wishful thinking effect) refers to when a person's desire regarding an event's occurrence has an unwarranted, optimistic influence on expectations about that event. Past experimental tests of this effect have been dominated by paradigms in which uncertainty about the target event is purely stochastic—i.e., involving only aleatory uncertainty. In six studies, we detected desirability biases using two new paradigms in which people made predictions about events for which their uncertainty was both aleatory and epistemic. We tested and meta-analyzed the impact of two potential moderators: the strength of evidence and the level of stochasticity. In support of the first moderator hypothesis, desirability biases were larger when people were making predictions about events for which the evidence for the possible outcomes was of similar strength (vs. not of similar strength). Regarding the second moderator hypothesis, the overall results did not support the notion that the desirability bias would be larger when the target event was higher vs. lower in stochasticity, although there was some significant evidence for moderation in one of the two paradigms. The findings broaden the generalizability of the desirability bias in predictions, yet they also reveal boundaries to an account of how stochasticity might provide affordances for optimistically biased predictions.

Reliability-based optimization of structural topologies using artificial neural networks

In this paper, a topology optimization approach is presented, where uncertain load and uncertain material parameters are considered. The concept of compliance minimization, i.e., stiffness maximization, is applied based on a plane stress finite element formulation. In order to take uncertain structural load parameters and uncertain material behavior into account, the topology optimization is embedded into a reliability-based design optimization approach. Uncertain structural parameters and design variables are quantified as random variables, intervals and probability boxes (p-boxes). This allows to consider aleatory and epistemic uncertainties by means of polymorphic uncertainty models within the topology optimization. Solving optimization problems with random variables, intervals and p-boxes leads to a high computational effort, because the objective functions and constraints have to evaluated millions of times. To speed up the optimization process, the finite element simulation of the topology optimization is replaced by artificial neural networks. This includes the topology dependent maximal stresses and displacements of the structure, which are used as constraints, and also the material density distribution inside the design domain. The reliability-based optimization of structural topologies approach is applied to a cantilever structure and a single span girder.

Seismic reliability of structures equipped with LIR‐DCFP bearings in terms of superstructure ductility and isolator displacement

AbstractThis research deals with the seismic reliability of non‐linear base‐isolated structures equipped with Lateral Impact Resilient Double Concave Friction Pendulum (LIR‐DCFP) devices. Specifically, exceeding probabilities within the reference lifetime are assessed with respect to both superstructure ductility and isolator displacement demand. The innovative LIR‐DCFP bearing has an improved inner slider with an internal gap and is capable to reduce adverse effects of the lateral impact between the inner slider and the restraining rims. The dynamic behavior of the superstructure is represented by a simplified one‐degree‐of‐freedom model describing its lateral response. The isolation system is characterized by a model based on rigid body dynamics also including the lateral impact behavior. A wide parametric analysis is developed for several system properties considering the friction coefficients as relevant random variables. Different sets of natural seismic records able to match conditional spectra for a site in Riverside (California) were selected to consider the aleatory uncertainties of the seismic input. Incremental dynamic analyses were performed to determine the statistics of significant engineering demand parameters and compute probabilities exceeding specific limit states to define fragility curves. Finally, employing seismic hazard curves, the seismic reliability of isolated structures was evaluated. For increasing values of the internal gap, structures equipped with LIR‐DCFP devices exhibit better seismic performance with respect to classical DCFP bearings with same size, especially, if the superstructure is designed to behave essentially elastic when the lateral capacity of the isolation level is not reached, or the hardening post‐yield stiffness of the superstructure is relatively high. Reductions up to 20% in the exceeding probabilities within 50 years related to the ductility demand are achievable using the suggested LIR‐DCFP isolator.

Quantifying uncertainty in high resolution biophysical variable retrieval with machine learning

The estimation of biophysical variables is at the core of remote sensing science, allowing a close monitoring of crops and forests. Deriving temporally resolved and spatially explicit maps of parameters of interest has been the subject of intense research. However, deriving products from optical sensors is typically hampered by cloud contamination and the trade-off between spatial and temporal resolutions. In this work we rely on the HIghly Scalable Temporal Adaptive Reflectance Fusion Model (HISTARFM) algorithm to generate long gap-free time series of Landsat surface reflectance data by fusing MODIS and Landsat reflectances. An artificial neural network is trained on PROSAIL inversion to predict monthly biophysical variables at 30 m spatial resolution with associated, realistic uncertainty bars. We emphasize the need for a more thorough analysis of uncertainty, and propose a general and scalable approach to combine both epistemic and aleatoric uncertainties by exploiting Monte Carlo (MC) dropout techniques from the trained artificial network and the propagation of HISTARFM uncertainties through the model, respectively. A model recalibration was performed in order to provide reliable uncertainties. We provide new high resolution products of several key variables to quantify the terrestrial biosphere: Leaf Area Index (LAI), Fraction of Absorbed Photosynthetically Active Radiation (FAPAR), Canopy Water Content (CWC) and Fractional Vegetation Cover (FVC) are at 30 m Landsat spatial resolution and over large continental areas. Two study areas are considered: the large heterogeneous but moderately cloud covered contiguous United States, and the homogeneous but largely cloud covered Amazonia. The produced vegetation products largely agree with the test dataset (R = 0.90, RMSE = 0.80 m2/m2 and ME = 0.12 m2/m2 for LAI, and R = 0.98, RMSE = 0.07 and ME = 0.01 for FAPAR) providing low error and high accuracy. Additionally, the validation considers a thorough comparison with operational and largely validated medium resolution products, such as the Moderate-Resolution Imaging Spectroradiometer (MODIS) and Copernicus Global Land Service. Our products presented a good agreement and consistency with both MODIS (R = 0.84 and R = 0.85 for LAI and FAPAR, respectively) and Copernicus (R = 0.92 and R = 0.91 for LAI and FAPAR, respectively). To foster a wider adoption and reproducibility of the methodology we provide an application in GEE and source code at:https://github.com/IPL-UV/ee_BioNet/

Towards predicting liquid fuel physicochemical properties using molecular dynamics guided machine learning models

Accurate determination of fuel properties of complex mixtures over a wide range of pressure and temperature conditions is essential to utilizing alternative fuels. The present work aims to construct cheap-to-compute machine learning (ML) models to act as closure equations for predicting the physical properties of alternative fuels. Those models can be trained using the database from MD simulations and/or experimental measurements in a data-fusion-fidelity approach. Here, Gaussian Process (GP) and probabilistic generative models are adopted. GP is a popular non-parametric Bayesian approach to build surrogate models mainly due to its capacity to handle the aleatory and epistemic uncertainties. Generative models have shown the ability of deep neural networks employed with the same intent. In this work, ML analysis is focused on two particular properties, the fuel density and diffusion, but it can also be extended to other physicochemical properties. This study explores the versatility of the ML models to handle multi-fidelity data. The results show that ML models can predict accurately the fuel properties of a wide range of pressure and temperature conditions.

A probabilistic model for quantifying uncertainty in the failure assessment diagram

Failure assessment diagrams are an integral component of asset integrity management in a variety of industrial sectors. They allow for the assessment of the significance of cracks in structures, between the domains of brittle fracture and plastic collapse. Numerical modelling, or empirically determined assessment lines across this continuum, are the basis of the guidance in current industrial standards. However, as the requirement of such assessments progresses from demonstrating safety to optimising resilience and resource allocation, it will become necessary to compute more informative (probabilistic) estimates, which are compatible with decision analysis.In this paper, Bayesian regression models are proposed as a suitable method of quantifying (aleatory and epistemic) uncertainty in the limit state on a failure assessment diagram. The data considered in this study consists of laboratory tests completed on wide plate fracture specimens. This work is intended to address the inconsistencies in current editions of industrial standards, and limitations (regarding flexibility and application) of existing scientific literature on the topic.Potential applications are discussed, including the use of fracture mechanics in meaningful reliability analysis, quantitative risk management, and optimising experimental design for future material tests.

A new chance reliability-based design optimization approach considering aleatory and epistemic uncertainties

A new chance reliability-based design optimization approach considering aleatory and epistemic uncertainties

Uncertainty Theory-Based Resilience Analysis for LEO Satellite Communication Systems

Resilience, the ability of a system to withstand disruptions and quickly return to a normal state, is essential for a low-Earth-orbit satellite communication system (LEO-SCS), as its large number of satellites, may encounter various disturbances. As a developing system with asymmetrical and insufficient data, it is with both aleatory and epistemic uncertainties, which renders existing resilience measures inapplicable. This paper utilizes uncertainty theory to define belief instantaneous availability, based on which a new resilience measure for the LEO-SCS is proposed. As the resilience is mainly determined by the dynamic and uncertain characteristics of an LEO-SCS, an uncertain satellite network evolution model is developed to describe its operating patterns, and an evaluation method is proposed to estimate its resilience. To illustrate our proposed uncertain theory-based resilience evaluation method, an LEO-SCS case with 48 satellites is studied, and its resilience values under different backup strategies are compared to assist in system design decisions.

Bayesian autoencoders with uncertainty quantification: Towards trustworthy anomaly detection

Despite numerous studies of deep autoencoders (AEs) for unsupervised anomaly detection, AEs still lack a way to express uncertainty in their predictions, crucial for ensuring safe and trustworthy machine learning systems in high-stake applications. Therefore, in this work, the formulation of Bayesian autoencoders (BAEs) is adopted to quantify the total anomaly uncertainty, comprising epistemic and aleatoric uncertainties. To evaluate the quality of uncertainty, we consider the task of classifying anomalies with the additional option of rejecting predictions of high uncertainty. In addition, we use the accuracy-rejection curve and propose the weighted average accuracy as a performance metric. Our experiments demonstrate the effectiveness of the BAE and total anomaly uncertainty on a set of benchmark datasets and two real datasets for manufacturing: one for condition monitoring, the other for quality inspection.