Aleatory Uncertainty Research Articles

Spatially variant biases considered self-supervised depth estimation based on laparoscopic videos

ABSTRACT Depth estimation is an essential tool in obtaining depth information for robotic surgery and augmented reality technology in the current laparoscopic surgery robot system. Since there is a lack of ground-truth for depth values and laparoscope motions during operation, depth estimation networks have difficulties in predicting depth maps from laparoscopic images under the supervised strategy. It is challenging to generate the correct depth maps for the different environments from abdominal images. To tackle these problems, we propose a novel monocular self-supervised depth estimation network with sparse nest architecture. We design a non-local block to capture broader and deeper context features that can further enhance the scene-variant generalisation capacity of the network for the differences in datasets. Moreover, we introduce an improved multi-mask feature in the loss function to tackle the classical occlusion problem based on the time-series information from stereo videos. We also use heteroscedastic aleatoric uncertainty to reduce the effect of noisy data for depth estimation. We compared our proposed method with other existing methods for different scenes in datasets. The experimental results show that the proposed model outperformed the state-of-the-art models qualitatively and quantitatively.

Reliability Assessment of RC Bridges Subjected to Seismic Loadings

An approach to estimate both the reliability index β and its complement, the probability of failure, through closed-form expressions that consider aleatory and epistemic uncertainties, is proposed. Alternatively, exceedance demand rates are obtained based on simplified expressions and numerical integration. Reliability indicators are calculated, considering the uncertainties in the compressive strength of concrete, steel yield, and section geometry, together with the aleatory uncertainties related to seismic loadings. Such indicators are estimated in a continuous RC bridge located in Acapulco, Guerrero, Mexico. The bridge was designed to comply with a drift of 0.004. Exceedance demand rates for drift thresholds from 0.001 to 0.012 are estimated, and maximum differences of 5.5% are found between the closed-form expression and numerical integration. The exceedance demand rate expressed by means of its inverse, the return period, indicates that the serviceability limit state is exceeded after 58 years of the bridge construction. The reliability index decreases by about 1.66%, and the probability of failure increases by about 16.1% when the epistemic uncertainties are considered. The approach shows the importance of epistemic uncertainties in the estimation of reliability indicators.

Seismic response and collapse analysis of a transmission tower-line system considering uncertainty factors

People's cognitive limitations and the unpredictability of structures introduce uncertainties into seismic performance analyses of structures in which transmission tower-line systems are essential components that may exhibit highly uncertain behavior. Nevertheless, it is important to have a clear understanding of the procedure required to manage the uncertainties surrounding structural seismic demand estimations. A practical method used to solve uncertainty problems is sensitivity and uncertainty analysis based on randomness and probability. To propagate all pertinent sources in aleatory uncertainty (input loading) in conjunction with epistemic randomness (modeling assumption errors) to actual structural seismic response and failure quantitative analysis, an uncertainty analysis method developed especially for transmission tower-line systems under seismic excitation is constructed based on sensitivity analysis and the Latin hypercube sampling method combined with incremental dynamic analysis. Sensitivity analysis reveals the relative importance of each parameter independently, while uncertainty analysis indicates the variation in the structural seismic performance under the combined actions of different uncertainty parameters. The final results demonstrate the need to consider the effects of both ground motion and structural modeling parameter uncertainties in seismic performance analyses of transmission tower-line systems.

An Interval Approach for the Availability Optimization of Multi-State Systems in the Presence of Aleatory and Epistemic Uncertainties

Abstract An essential step in the safe design of systems is choosing the system configuration that will maximize the overall availability of the system and minimize its overall cost. The main objective of this paper is to propose an optimization method of multistate system availability in the presence of both aleatory and epistemic uncertainties, to choose the best configuration for the system in terms of availability, cost, and imprecision. The problem is formulated as follows: let us consider several configurations of a system, with each configuration consisting of components with different working states, and imprecise failure and repair rates provided in the form of intervals. The aim is to find the best configuration regarding the system's imprecise availability, cost, and imprecision. First, the imprecise steady availability of each configuration is computed by using an original method based on Markovian approaches combined with interval contraction techniques. Then an objective function incorporating cost, the lower and upper bounds of availability, and imprecision is defined and computed to provide the best configuration. To illustrate the proposed method, a use case is discussed.

Uncertainty Quantification Across Design Space Using Spatially Accurate Polynomial Chaos

In the last decade, the demand for stochastic engineering results has increased substantially. Concurrently, improvements in computing hardware, access to large computing clusters, and efficient statistical methods have made uncertainty quantification studies feasible for complex, computationally expensive simulations such as computational fluid dynamics or finite element methods. In current practice, uncertainty may be quantified at particular locations within a flight envelope or design space, but an ongoing challenge remains to interpolate or extrapolate this information to predict the uncertainty at untested or unsimulated locations. The goal of this paper is to introduce a spatially accurate polynomial chaos method, which can interpolate both aleatory and epistemic uncertainty throughout a flight envelope or design space. An additive correction is also presented, which improves accuracy at a small additional sample cost. Interpolation of polynomial chaos expansion coefficients is achieved using established regression techniques, allowing for a spatially accurate uncertainty propagation method which is agnostic to the characterization of parametric input uncertainties. As a demonstration of the method, results are shown for an analytic test function and for simulations of the NASA Common Research Model. The results indicate that Spatially Accurate Polynomial Chaos and its additive correction can provide accurate interpolated estimates of uncertainty.

Modeling Epistemic Uncertainty in Offshore Wind Farm Production Capacity to Reduce Risk.

Financial stakeholders in offshore wind farm projects require predictions of energy production capacity to better manage the risk associated with investment decisions prior to construction. Predictions for early operating life are particularly important due to the dual effects of cash flow discounting and the anticipated performance growth due to experiential learning. We develop a general marked point process model for the times to failure and restoration events of farm subassemblies to capture key uncertainties affecting performance. Sources of epistemic uncertainty are identified in design and manufacturing effectiveness. The model then captures the temporal effects of epistemic and aleatory uncertainties across subassemblies to predict the farm availability-informed relative capacity (maximum generating capacity given the technical state of the equipment). This performance measure enables technical performance uncertainties to be linked to the cost of energy generation. The general modeling approach is contextualized and illustrated for a prospective offshore wind farm. The production capacity uncertainties can be decomposed to assess the contribution of epistemic uncertainty allowing the value of gathering information to reduce risk to beexamined.

Bayesian Uncertainty Identification of Model Parameters for the Jointed Structures with Nonlinearity

Jointed structures in engineering naturally perform with some of nonlinearity and uncertainty, which significantly affect the dynamic characteristics of the structural system. In this paper, the method of Bayesian uncertainty identification of model parameters for the jointed structures with local nonlinearity is proposed. Firstly, the nonlinear stiffness and damping of the joints under the random excitation are represented with functions of excitation magnitude in terms of the equivalent linearization. The process of uncertainty identification is separated from the representation of local nonlinearity. In this way, the dynamic behavior of the joints is penetratingly characterized instead of ascribing the nonlinearity to uncertainty. Secondly, a variable-expanded Bayesian (VEB) method is originally proposed to identify the mixed of aleatory and epistemic uncertainties of model parameters. Different from traditional Bayesian identification, the aleatory uncertainties of model parameters are identified as one of the most important parts rather than only measurement noise of output. Notablely, a series of intermediate variables are introduced to expand the parameter with aleatory uncertainty in order to overcome the difficulty of establishing the likelihood function. Moreover, a 3-DOF numerical example is illustrated with case studies to verify the proposed method. The influence of observed sample size and prior distribution selection on the identification results is tested. Furthermore, an engineering example of the jointed structure with rubber isolators is performed to show the practicability of the proposed method. It is indicated that the computational model updated with the accurately identified parameters with both nonlinearity and uncertainty has shown the excellent predictive capability.

Bayesian model identification through harmonic balance method for hysteresis prediction in bolted joints

Hysteresis is a nonlinear phenomenon present in many structures, such as those assembled by bolted joints. Despite a large number of recent findings related to identification techniques for these systems, the problem is still challenging and open to contributions. To fill the gap concerning the proposition of identification algorithms based on closed-form solutions, this work introduces the use of the harmonic balance method to identify a stochastic Bouc–Wen model for predicting the nonlinear behavior of bolted structures. A piecewise smooth procedure is applied on the hysteretic restoring force to become possible to derive an analytical approximation of the response based on the Fourier series. Firstly, the analytical approximation is used to calibrate deterministic Bouc–Wen parameters by minimizing the error between the Fourier amplitudes of the numerical model and those extracted from experimental data using the cross-entropy optimization method. Since the experimental data investigated here contain variability due to the measurement process (aleatoric uncertainties), the deterministic parameters are then used as a priori conditions to update their probability density functions via the Bayesian inference. Having the model parameters as random variables, the stochastic Bouc–Wen model is obtained. This methodology was illustrated in a bolted structure benchmark. The results indicate that the method proposed can identify an accurate stochastic Bouc–Wen model for predicting the dynamics of bolted structures, even taking into account data variability.

Uncertainty-aware learning for improvements in image quality of the Canada–France–Hawaii Telescope

ABSTRACTWe leverage state-of-the-art machine learning methods and a decade’s worth of archival data from Canada–France–Hawaii Telescope (CFHT) to predict observatory image quality (IQ) from environmental conditions and observatory operating parameters. Specifically, we develop accurate and interpretable models of the complex dependence between data features and observed IQ for CFHT’s wide-field camera, MegaCam. Our contributions are several-fold. First, we collect, collate, and reprocess several disparate data sets gathered by CFHT scientists. Second, we predict probability distribution functions of IQ and achieve a mean absolute error of ∼0.07 arcsec for the predicted medians. Third, we explore the data-driven actuation of the 12 dome ‘vents’ installed in 2013–14 to accelerate the flushing of hot air from the dome. We leverage epistemic and aleatoric uncertainties in conjunction with probabilistic generative modelling to identify candidate vent adjustments that are in-distribution (ID); for the optimal configuration for each ID sample, we predict the reduction in required observing time to achieve a fixed signal-to-noise ratio. On average, the reduction is $\sim 12{{\ \rm per\ cent}}$. Finally, we rank input features by their Shapley values to identify the most predictive variables for each observation. Our long-term goal is to construct reliable and real-time models that can forecast optimal observatory operating parameters to optimize IQ. We can then feed such forecasts into scheduling protocols and predictive maintenance routines. We anticipate that such approaches will become standard in automating observatory operations and maintenance by the time CFHT’s successor, the Maunakea Spectroscopic Explorer, is installed in the next decade.

Robust Bayesian Particle Filter for Space Object Tracking Under Severe Uncertainty

This paper introduces a robust Bayesian particle filter that can handle epistemic uncertainty in the measurements, dynamics, and initial conditions. The robust filter returns robust bounds on the output quantity of interest, rather than a crisp value. Particles are generated with an importance sampling technique and propagated only one time during the estimation process. The proposal distribution is constructed by running a parallel unscented Kalman filter to drive particles in regions of high expected likelihood and achieve a high effective sample size. The bounds are then computed by an inexpensive tuning of the importance weights via numerical optimization. A Branch & Bound algorithm over simplexes with a Lipschitz bounding function is employed to achieve guaranteed convergence to the lower and upper bounds in a finite number of steps. The filter is applied to the robust computation of the collision probability of SENTINEL 2B with a FENGYUN 1C debris in different operational instances, all characterized by a mix of aleatory and epistemic uncertainty on initial conditions and observation likelihoods.

Assessment of remaining service life of deteriorated concrete bridges under imprecise probabilistic information

This paper proposes a framework for the reliability-based remaining service life prediction of existing deteriorated structures considering both aleatory and epistemic uncertainties separately. A Bayesian probability box (p-box) is developed for modelling the epistemic uncertainty by considering the bounds of the distribution parameter, whereas the aleatory uncertainty is modelled as a precise distribution function. The framework allows to automatically update results and the bounds of estimation of remaining service life (RSL) by deploying data from regular and recurrent inspections of bridges, which are typically available in practice. The framework is applied to a real reinforced concrete bridge that has deteriorated due to corrosion of steel reinforcements to assess the capabilities of the proposed method. Results show a notable dispersion of the prediction of the RSL considering the imprecision of data which strongly highlights that the epistemic uncertainty should be considered when making decisions related to existing bridges. In fact, for the example presented, considering the epistemic uncertainty on corrosion of reinforcements could impact the probability of failure by a factor of nearly two. In addition, the updated Bayesian p-box can efficiently quantify significant reductions of epistemic uncertainty if additional information becomes available.

Stochastic Crashworthiness Optimization Accounting for Simulation Noise

Abstract Finite element-based crashworthiness optimization is extensively used to improve the safety of motor vehicles. However, the responses of crash simulations are characterized by a high level of numerical noise, which can hamper the blind use of surrogate-based design optimization methods. It is therefore essential to account for the noise-induced uncertainty when performing optimization. For this purpose, a surrogate, referred to as Non-Deterministic Kriging (NDK), can be used. It models the noise as a non-stationary stochastic process, which is added to a traditional deterministic kriging surrogate. Based on the NDK surrogate, this study proposes an optimization algorithm tailored to account for both epistemic uncertainty, due to the lack of data, and irreducible aleatory uncertainty, due to the simulation noise. The variances are included within an extension of the well-known expected improvement infill criterion referred to as Modified Augmented Expected Improvement (MAEI). Because the proposed optimization scheme requires an estimate of the aleatory variance, it is approximated through a regression kriging, which is iteratively refined. The proposed algorithm is tested on a set of analytical functions and applied to the optimization of an Occupant Restraint System (ORS) during a crash.

Utilization of Risk Analysis of Hydraulic Structures for Efficient Allocation of Means

Efficient allocation of available means presuppose detailed knowledge about risks, costs and benefits within the area of interest. The societal demand for increased safety of hydraulic structures, as components of the critical infrastructure, requires considerable investment. To evaluate the effectiveness of potential measures in an environment influenced by epistemic and aleatory uncertainties, risk analysis and cost-benefit analysis are used in practice. The above described approach is now fully implemented when considering natural floods and structural flood protection measures, and also presented in the paper. For potential failures of dams and other important hydraulic structures however the procedure becomes rather more complex to comprehend the effect of designed measures on different failure modes. After introducing governing theoretical principles used for the natural flood vs structural measures analysis, the paper presents examples of application of combination of cost-benefit and risk analysis in the framework of the authors’ work as Strategic Expert of the Ministry of Agriculture of the Czech Republic for the different stages of the flood prevention program. The last part of the paper focuses on dam safety and the application of risk analysis as a support tool for decision making processes. It describes the practice applied in the Czech Republic and comments on the advantages and disadvantages of the current approach while suggesting further possible improvement.

Uncertainty quantification and propagation of crowd behaviour effects on pedestrian-induced vibrations of footbridges

The reliable prediction of pedestrian-induced vibration is essential for vibration serviceability assessment and further vibration mitigation design of footbridges. The response of the footbridge is governed by not only the structure dynamic model but also the crowd-induced load, which naturally involves randomness and uncertainty. It is consequently significant to appropriately characterize the uncertainties during the numerical modelling of the crowd behaviour effects on crowd-induced load. This work proposes a comprehensive approach to quantify the uncertainty from both the structure dynamic model and the crowd behaviour, and subsequently, to propagate the multiple sources of uncertainties from the input parameters to the response of the footbridge. The crowd behaviour is simulated using the social force model and translated to the crowd-induced load by combining with a single pedestrian induced walking force model. By decoupling the continuous model into several single degrees of freedom systems according to relevant modes in the vibration serviceability evaluation, the structure dynamic model of the footbridge is developed where the structural responses are calculated. In this paper, all the uncertain parameters are investigated together in a double-loop framework to perform uncertainty quantification and propagation in the form of probability-box (shortly termed as P-box). The uncertainty space of the peak structural responses is finally obtained by the Monte Carlo sampling and optimization in the outer loop and inner loop, respectively. Feasibility and performance of the overall approach are demonstrated by considering a real scale footbridge, and the failure probability of each comfort class regarding the peak acceleration response is also evaluated. Results show that, special attention should be paid on both the epistemic and aleatory uncertainties from the crowd behaviour in the vibration serviceability assessments of footbridges. The proposed uncertainty quantification framework may provide significant insights and improve the reliability for future vibration serviceability evaluations of footbridges by incorporating the crowd behaviour effects.

Context-Aware Sensor Uncertainty Estimation for Autonomous Vehicles

Sensor uncertainty significantly affects the performance of autonomous vehicles (AVs). Sensor uncertainty is predominantly linked to sensor specifications, and because sensor behaviors change dynamically, the machine learning approach is not suitable for learning them. This paper presents a novel learning approach for predicting sensor performance in challenging environments. The design of our approach incorporates both epistemic uncertainties, which are related to the lack of knowledge, and aleatoric uncertainties, which are related to the stochastic nature of the data acquisition process. The proposed approach combines a state-based model with a predictive model, where the former estimates the uncertainty in the current environment and the latter finds the correlations between the source of the uncertainty and its environmental characteristics. The proposed approach has been evaluated on real data to predict the uncertainties associated with global navigation satellite systems (GNSSs), showing that our approach can predict sensor uncertainty with high confidence.

A multi‐fidelity Bayesian framework for robust seismic fragility analysis

AbstractFragility analysis of structures via numerical methods involves a complex trade‐off between the desired accuracy, the explicit consideration of uncertainties (both epistemic and aleatory) related to the numerical structural model and the available computational performance. This paper introduces a framework for deriving numerical fragility relationships based on multi‐fidelity non‐linear models of the structure under investigation and response‐analysis types. The proposed framework aims to reduce the computational burden while achieving a desired accuracy of the fragility estimates without neglecting aleatory and epistemic uncertainties. The proposed approach is an extension of the well‐known robust fragility (RF) analysis framework. Different model classes, each characterised by increasing refinement, are used to define multi‐fidelity polynomial expansions of the fragility model parameters. Each analysis result is then considered as a ‘new observation’ in a Bayesian framework and used to update the coefficients of the polynomial expansions. An adaptive sampling algorithm is also proposed to futher improve the performance of the multi‐fidelity framework. Specifically, such an adaptive sampling algorithm relies on partitioning the sample space and the Kullback–Leibler divergence to find the optimal sampling path. The sample space partitioning allows an analyst to specify different criteria and parameters of the algorithm for different regions, thus further improving the performance of the procedure. The proposed approach is illustrated for an archetype reinforced concrete (RC) frame for which two model classes are developed/analysed: the simple lateral mechanism analysis (SLaMA), coupled with the capacity spectrum method, and non‐linear dynamic analysis. Both model classes involve a cloud‐based approach employing unscaled real (i.e. recorded) ground motions. The fragility relationships derived with the proposed procedure are finally compared to those calculated by using only the most advanced/high‐fidelity (HF) model class, thus quantifying the performance of the proposed approach and highlighting further research needs.

Integrated probabilistic-fuzzy synthetic evaluation of drinking water quality in rural and remote communities

An integrated probabilistic-fuzzy synthetic evaluation (PFSE) approach was developed for assessing drinking water quality in rural and remote communities (RRCs) through the lens of health risks and aesthetic impacts. The probabilistic health risk assessment can handle aleatory uncertainty raised by the variation of contaminant concentrations, and fuzzy synthetic evaluation (FSE) can address vagueness and ambiguity in human perception of risks and aesthetic impacts. The PFSE approach was applied to five RRCs in British Columbia, Canada where different drinking water quality issues, including high metal(loids) concentrations, the presence of coliforms, and poor aesthetics were reported. Cancer, non-cancer, and microbial risks assessed, as well as both quantitative and qualitative aesthetic impact assessment outcomes, were aggregated into synthetic water quality indices for water quality ranking. The probabilistic health risk assessment results revealed significant health risks for a community with relatively high arsenic concentrations (mean value = 7.0 μg/L) in the water supply. The microbial risks were also found significant (disability-adjusted life years >1 × 10−6) for all communities because of the presence of coliforms in the water. The FSE results indicated that the drinking water quality of five RRCs was associated with high aggregated impacts, which concurred with the “poor” water quality ratings according to the Canadian Water Quality Index. The water quality of the five RRCs was ranked based on the synthetic water quality evaluation indices. The PFSE approach can help decision-makers prioritize RRCs in effective resource allocation for addressing drinking water quality issues.

Seismic fragility functions for a pervasive unique form of construction with very high potential for social losses in Trinidad and Tobago: Two-story houses

The twin-island republic of Trinidad and Tobago is fortunate to have a long history of abundance of natural resources resulting in its being a major source of economic support for the English-speaking sovereign states of the Caribbean. The economic stability of the Caribbean is threatened, via a domino effect, by the current prevalent form of residential structures in Trinidad and Tobago because of a lack of conformity with proper seismic design in an earthquake-prone region (SS of 1.1 g–1.8 g). Continuing from a previous study of single-story houses in Trinidad and Tobago, fragility functions for three types of typical two-story residential structures were derived using Incremental Dynamic Analysis considering both aleatory and epistemic uncertainties. The selected ground motion records are compatible with spectra derived for Trinidad and Tobago. Fragility functions for the structures are with respect to limit states of slight, moderate, extensive, and complete damage as well as out-of-plane dynamic instability. These fragility functions can be used for regional risk assessment hence the derivation of disaster mitigation and management plans thereby avoiding a major crisis in the Caribbean.

Rehabilitation of reinforced concrete building using the fuseis beam-link system

A methodology is introduced for applying the FUSEIS beam-link steel lateral-load-resisting system for strengthening existing reinforced-concrete buildings. The purpose is to take advantage of the easy replaceability and architectural versatility of the FUSEIS systems to strengthen a deficient structure, while minimizing the economic impact of the rehabilitation works due to suspension of the operation of the building. Additionally, a case study is presented, where an existing building is upgraded by introducing FUSEIS beam-link systems, first by performing response spectra analysis using an initial behaviour factor, then refining the results via the INNOSEIS performance-based methodology. This necessitates the use of nonlinear dynamic analyses to quantify a risk-consistent behaviour factor that incorporates the effect of aleatory and epistemic uncertainty on the actual systems’ performance. Finally, a pre-normative assessment for the q-factor of FUSEIS-beam link systems is achieved, for use in existing reinforced concrete buildings within Eurocode 8.

Analysis of Structural Systems with Imprecise Uncertainties using High Dimensional Model Representation

Uncertainties present in any structural system inherently affect the performance and design of the system. The sources of uncertainties serve the basis for delineating the types as aleatory or epistemic. The probabilistic models can be considered as the most valuable strategies to deal with aleatory uncertainties, while convex models, possibility theory, evidence theory and Bayesian probability theory can be used to deal with epistemic uncertainty. However, when only scarce datasets are available and knowledge is incomplete, a more general framework, such as probability-box, is more appropriate to describe the uncertainty. Furthermore, analysis of complex and multi-dimensional structures is expensive and time consuming when numerical techniques are used. Therefore, simulation of such structures for many realisation of uncertain input becomes a challenging task in the uncertainty analysis. In this paper, complex structural systems with imprecise uncertain input are studied and evaluated efficiently by High Dimensional Model Representation based uncertainty analysis.