Presence Of Epistemic Uncertainties Research Articles

Learning Generative Models for Climbing Aircraft from Radar Data

Accurate trajectory prediction for climbing aircraft is hampered by the presence of epistemic uncertainties concerning aircraft operation, which can lead to significant misspecification between predicted and observed trajectories. This paper proposes a generative model for climbing aircraft in which the standard Base of Aircraft Data (BADA) model is enriched by a functional correction to the thrust that is learned from the data. The method offers three features: predictions of the arrival time with 66.3% less error when compared to BADA; generated trajectories that are realistic when compared to test data; and a means of computing confidence bounds for minimal computational cost.

Seismic vulnerability of industrial steel structures with masonry infills using a numerical approach

Recent earthquakes have highlighted the high vulnerability of the industrial structures that are not specifically designed for accounting seismic forces. Among them, a widespread typology is characterised by steel structures without bracing or other anti-seismic details and with masonry infills. With the aim of increasing the knowledge on the seismic behaviour of these structures, this work focuses on a mechanical-based approach for the evaluation of fragility curves for industrial areas. The exposure data are obtained by in-situ survey and acquiring information available in existing databases, like the Italian Cartis-GL one that is specifically devised for industrial structures. The variability of geometrical and mechanical data and the presence of epistemic uncertainties are considered by constructing a population of structures using the Monte Carlo method. Each structure is analysed through static-nonlinear simulations adopting mixed finite elements accounting for geometrical and constitutive nonlinearities. The approach is tested for infilled steel structures in the industrial area of the municipality of Spezzano Albanese (Italy). Results show that the presence of masonry infill drastically modifies the seismic behaviour of this structural typology. In particular, it turns out that if the mechanical contribution of the infill is neglected, the structures exhibit high damages even for low intensities of the seismic action.

Inference and Learning with Model Uncertainty in Probabilistic Logic Programs

An issue that has so far received only limited attention in probabilistic logic programming (PLP) is the modelling of so-called epistemic uncertainty, the uncertainty about the model itself. Accurately quantifying this model uncertainty is paramount to robust inference, learning and ultimately decision making. We introduce BetaProbLog, a PLP language that can model epistemic uncertainty. BetaProbLog has sound semantics, an effective inference algorithm that combines Monte Carlo techniques with knowledge compilation, and a parameter learning algorithm. We empirically outperform state-of-the-art methods on probabilistic inference tasks in second-order Bayesian networks, digit classification and discriminative learning in the presence of epistemic uncertainty.

Effective sensor placement based on a VIKOR method considering common cause failure in the presence of epistemic uncertainty

Owing to expensive cost and restricted structure, limited sensors are allowed to install in modern systems to monitor the working state, which can improve their availability. Therefore, an effective sensor placement method is presented based on a VIKOR algorithm considering common cause failure (CCF) under epistemic uncertainty in this paper. Specifically, a dynamic fault tree (DFT) is developed to build a fault model to simulate dynamic fault behaviors and some reliability indices are calculated using a dynamic evidence network (DEN). Furthermore, a VIKOR method is proposed to choose the possible sensor locations based on these indices. Besides, a sensor model is introduced by using a priority AND gate (PAND) to describe the failure sequence between a sensor and a component. All placement schemes can be enumerated when the number of sensors is given, and the largest system reliability is the best alternative among the placement schemes. Finally, a case study shows that CCF has some influence on sensor placement and cannot be neglected in the reliabilitybased sensor placement.

A Reliable Fracture Mechanics

A branch of human knowledge, which treats the behavior of cracked structures, is called fracture mechanics. Since there is no intact structure in the world, then the paramount importance of fracture mechanics in human life is accentuated. The main parameter of fracture mechanics is called crack compliance, which is the amount of flexibility added to the flexibility of the intact structure due to the presence of a crack with specified size. The compliance, similar to flexibility, is the sole characteristics of the cracked structure. In this way for a given structure with a specified crack, there should be a single compliance. Unfortunately, in classical fracture mechanics that is not the case! The number of crack compliances for a clacked structure is equal to the number of researchers who treated the case! This diversity in the results stems from the presence of epistemic uncertainty in the mathematical basis of classical fracture mechanics. In view of the need for remedy, the Abdolrasoul Ranjbaran Team (ART), investigated the case and proposed a reliable fracture mechanics, which is based on sound logical reasoning. The proposed reliable fracture mechanics is described in the presented paper. The paper is managed via fourteen titles as, introduction, the mathematical basis of the classical fracture mechanics, birthplace of the state based philosophy, strong form of governing equation, analytical solution by Laplace transform, the weak form equation, the finite element equation, logical basis of the state based philosophy, state functions, Persian curves, reliable crack compliance, energy release rate, stress intensity factor, and weight function for the stress intensity factor in sections one to fourteen respectively. The paper concludes with a list of cited references.

The logic of uncertainty in law and life

Abstract My central interest is decision making in the presence of epistemic uncertainty. A method appropriate for both specialized inquiries and everyday reasoning is based on credal logic, which employs multivalent degrees of belief rather than traditional probability theory. It accounts for epistemic uncertainty as unallocated belief. It holds that, when facing real uncertainty, if a person believes a and believes b, then the person believes a and b together. This brand of multivalent logic underlies and justifies how legal decision makers and the rest of us find facts in a world infused with epistemic uncertainty. Indeed, this article closes by showing the equivalence of multivalent logic and inference to the best explanation. By demonstrating this similarity in reasoning, I aim to shore up our faith in the logic of traditional legal reasoning.

Reliability analysis of corrosion initiation in reinforced concrete structures subjected to chlorides in presence of epistemic uncertainties

This paper presents a methodology for assessing the corrosion initiation in reinforced concrete (RC) structures subjected to chlorides, with a focus on the influence of epistemic uncertainties inherent to input parameters. Epistemic uncertain parameters were modeled using fuzzy probability theory. The chloride penetration was modeled using a finite element solution of the coupled heat transfer, moisture and chloride transport in concrete. The environmental conditions were modeled using a stochastic process. The reliability analysis was undertaken using a hybrid fuzzy Monte Carlo simulation. As an illustration, the durability of concrete basins of a newly constructed waste water treatment plant, with respect to reinforcement corrosion, was examined. The time to corrosion initiation was found to approximately follow a generalized extreme value distribution with fuzzy parameters. The stochastic modeling of exposure conditions accelerated the corrosion initiation. The time to corrosion initiation is highly sensitive to the epistemic uncertainty in the threshold chloride level in concrete. Reducing this uncertainty will result in an important improvement in accuracy. The proposed method is suitable for durability assessment of recent RC structures with little or no available performance data.

Random-interval hybrid reliability analysis for fan performance in the presence of epistemic uncertainty

With the aim of reducing fan performance failure, an effective method of fan reliability analysis based on a hybrid uncertainty model was investigated using a combination of orthogonal test design, an approximation model, and computational fluid dynamics (CFD) simulation and analysis technology. By introducing interval uncertainty, this method can effectively solve the problem of quantifying model uncertainty owing to the lack of experimental samples and can greatly expand the applicability of reliability analysis technology in fluid machinery research. Random and interval uncertainty parameters were introduced to describe the fan system and a mixed random-interval reliability analysis model of fan performance was established based on the traditional first-order reliability analysis method. Using CFD analysis of the renormalization group (RNG) model, the flow, pressure, shaft power, efficiency, and other fan performance parameters were calculated, and the performance function was obtained. Owing to the low efficiency of the CFD calculation, the effective iterative algorithm of response surface to solve hybrid reliability model was studied, and the failure probability interval of fan performance was calculated. The method was used to study the fan performance of a rail transit train, and the failure probability, reliability index, and performance parameter sensitivity and uncertainty were analyzed. The influence of parameter uncertainty on system reliability was determined, and the engineering measures necessary to improve the fan’s performance reliability were proposed.

Logic in Law and Science

My central interest is decisionmaking in the presence of epistemic uncertainty. A method appropriate for both specialized inquiries and everyday reasoning is based on credal logic, which employs multivalent degrees of belief rather than traditional probability theory. It accounts for epistemic uncertainty as unallocated belief. It holds that, when facing real uncertainty, if a person believes a and believes b, then the person believes a and b together. This brand of multivalent logic underlies and justifies how legal decisionmakers and the rest of us find facts in a world infused with epistemic uncertainty. Indeed, this Article closes by showing the equivalence of multivalent logic and inference to the best explanation. By demonstrating this similarity in reasoning, I aim to shore up our faith in the logic of traditional legal reasoning.

Sensitivity and calibration of turbulence model in the presence of epistemic uncertainties

The solution of Reynolds-averaged Navier–Stokes equations employs an appropriate set of equations for the turbulence modelling. The closure coefficients of the turbulence model were calibrated using empiricism and arguments of dimensional analysis. These coefficients are considered universal, but there is no guarantee this property applies to test cases other than those used in the calibration process. This work aims at revisiting the calibration of the closure coefficients of the original Spalart–Allmaras turbulence model using machine learning, adaptive design of experiments and accessing a high-performance computing facility. The automated calibration procedure is carried out once for a transonic, wall-bounded flow around the RAE 2822 aerofoil. It was found that: (a) an optimal set of closure coefficients exists that minimises numerical deviations from experimental data; (b) the improved prediction accuracy of the calibrated turbulence model is consistent across different flow solvers; and (c) the calibrated turbulence model outperforms slightly the standard model in analysing complex flow features around additional test cases (ONERA M6 wing, axisymmetric transonic bump, forced sinusoidal motion of NACA 0012 aerofoil). A by-product of this study is a fully calibrated turbulence model that leverages on current state-of-the-art computational techniques, overcoming inherent limitations of the manual fine-tuning process.

Uncertainty analysis and risk‐based design of detention basin without damage function

AbstractRisk‐based analysis provides an economically defensible framework for determining the optimal design of hydrosystems with the minimum total cost including project cost (installation plus operation/maintenance/repair) and failure‐induced expected damage cost. However, failure‐related damage function with good quality may not be widely available in practical applications for assessing annual expected damage cost. In addition to aleatory uncertainty representing natural randomness of hydrologic events, there exists a variety of epistemic uncertainties due to knowledge deficiency from the use of inadequate models, inaccurate model parameters, etc. The presence of epistemic uncertainties could affect the loads and capacity of hydrosystem facilities which, in turn, would affect the value of failure‐induced physical performance indicators. Using detention basin design as an example, this paper presents a systematic framework to integrate aleatory and epistemic uncertainties for the risk‐based design under the condition of no monetary damage function. For illustration, aleatory uncertainty due to randomness of rainfall intensity and epistemic uncertainties caused by runoff coefficient and curve number are considered in risk‐based design of an example detention basin.

Assessing Impact of Epistemic and Technological Uncertainty on Aircraft Subsystem Architectures

The progressive transition from conventional to More Electric aircraft subsystem architectures occurring in the aerospace industry necessitates earlier consideration of subsystem impacts in the design process. Significant challenges arise in this regard due to the unavailability of historical information regarding unconventional subsystem architectures as well as the limited definition of the aircraft that exists during the early design phases. This paper assesses the impact of sources of uncertainty on subsystem architectures using the Integrated Subsystem Sizing and Architecture Assessment Capability, which links subsystem and aircraft sizing and analyses. Uncertainty may arise due to limitations, assumptions, or simplifications in the undertaken modeling approach or due to variations in the assumed or projected technological state-of-the-art. In this work, some of these major sources of uncertainty are identified and propagated into the performance analysis of a selected number of subsystem architectures. Both the gross effect of all identified sources of uncertainty and the relative impacts of individual ones are evaluated. More substantially electrified subsystem architectures are seen to retain a performance advantage even in the presence of epistemic uncertainty and show more significant improvement with improving technological state-of-the-art, most notably that of power electronics, electrical generators, and electric motors.

Snap-Through Buckling Reliability Analysis Under Spatiotemporal Variability and Epistemic Uncertainty

Surrogate models often provide an effective tradeoff between accuracy and efficiency during reliability analysis with expensive physics models. In snap-through buckling reliability analysis, a surrogate model could be built for the critical buckling load, as a function of loading, material properties, geometry, and boundary conditions. However, in the presence of spatiotemporal variability, the response surface of the critical buckling load is often highly nonlinear and irregular, thus rendering commonly used response surface-type surrogate modeling strategies ineffective. This paper proposes a new buckling reliability analysis method based on support vector machines for structures subjected to spatiotemporal variability and in the presence of epistemic uncertainty regarding model inputs and parameters. Bayesian calibration is first used to quantify the epistemic uncertainty in the modeling of spatiotemporal variability under limited data. Upon the modeling of spatiotemporal variability and epistemic uncertainty, a time-dependent reliability analysis method is developed for the snap-through buckling failure by constructing a nonlinear support vector machine classifier. Considering that the computer simulation is computationally expensive and the support vector machine classifier may not be well trained due to limited computational resources, a method is also developed to quantify the uncertainty in the reliability estimate due to classification uncertainty. A curved beam with an uncertain boundary condition, spatially varying cross-section geometry, and spatiotemporally varying loading is used to demonstrate the effectiveness of the proposed method.

An Efficient Method for Reliability Analysis of Systems Under Epistemic Uncertainty Using Belief Function Theory

We present an efficient method based on the inclusion-exclusion principle to compute the reliability of systems in the presence of epistemic uncertainty. A known drawback of belief functions and other imprecise probabilistic theories is that their manipulation is computationally demanding. Therefore, we investigate some conditions under which the measures of belief function theory are additive. If this property is met, the application of belief functions is more computationally efficient. It is shown that these conditions hold for minimal cuts and paths in reliability theory. A direct implication of this result is that the credal state (state of beliefs) about the failing (working) behavior of components does not affect the credal state about the working (failing) behavior of the system. This result is proven using a reliability analysis approach based on belief function theory. This result implies that the bounding interval of the system's reliability can be obtained with two simple calculations using methods similar to those of classical probabilistic approaches. A discussion about the applicability of the discussed theorems for non-coherent systems is also proposed.

Analysis of the Robustness and Recovery of Critical Infrastructures by Goal Tree–Success Tree: Dynamic Master Logic Diagram, Within a Multistate System-of-Systems Framework, in the Presence of Epistemic Uncertainty

In this paper, we evaluate the robustness and recovery of connected critical infrastructures (CIs) under a system-of-systems (SoS) framework taking into account: (1) the dependencies among the components of an individual CI and the interdependencies among different CIs; (2) the variability in component performance, by a multistate model; and (3) the epistemic uncertainty in the probabilities of transitions between different components states and in the mean values of the holding-times distributions, by means of intervals. We adopt the goal tree success tree–dynamic master logic diagram (GTST–DMLD) for system modeling and perform the quantitative assessment by Monte Carlo simulation. We illustrate the approach by way of a simplified case study consisting of two interdependent infrastructures (electric power system and gas network) and a supervisory control and data acquisition (SCADA) system connected to the gas network.

The use of a credibility index in the life-cycle assessment of structures

The behaviour of structural systems can change during their service lives due to unexpected loadings, environmental effects and deterioration processes. In order to optimise maintenance interventions, the life cycle of a structure has to be properly assessed. Structural health monitoring (SHM) using collected experimental data provides a method for assessing structural behaviour over time. As the cost related to SHM is substantial, sometimes that monitoring is limited in space and time. However, the modelling of the structural behaviour using experimental data-sets is characterised by increased uncertainty both in the choice of the appropriate model (epistemic uncertainty) and in parameters estimation (aleatory uncertainty). This paper provides an original procedure to support decisions in the presence of epistemic uncertainty. The procedure provides the development of a credibility index able to catch, between two possible models, which is the most reliable to describe the evolution of parameters of interest. Considering as a case study the occurrence of a foundation settlement in an arch bridge, the efficacy of the model proposed is assessed. The approach can be applied to investigate the behaviour of other aspects of the life-cycle assessment: the evolution of structural resistance, the failure time of an element or of the whole system.

Identification of Pareto‐fronts in the presence of epistemic uncertainty

AbstractNumerical design methods based on deterministic multi‐objective optimization provide — for conflicting objective functions — a Pareto‐optimal set including diverse trade‐off solutions. Based on the visualization of the set in the objective space — the Pareto‐front — the decision maker is able to choose a satisfying design. Though, the presence of uncertain input variables in the optimization task requires a new concept for the identification of the Pareto‐front and the projection of uncertainty within the front. In this contribution, an approach for considering the epistemic uncertainty within the evolutionary multi‐objective optimization method based on Nondominated Sorting Genetic Algorithm (NSGA‐II) is presented. The description of uncertainty occurs within the framework of the Fuzzy set theory. The proposed approach is coupled to the Finite Element Analysis and response surface approximations based on artificial neural networks. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Component Ranking by Birnbaum Importance in Presence of Epistemic Uncertainty in Failure Event Probabilities

Birnbaum Importance Measure (IM) allows ranking the components of a system with respect to the impact that their failures have on the system's performance, e.g., its reliability or availability. Such ranking is done in industry to efficiently manage Operation and Maintenance (O&M) activities, and to optimize plant design. In the computation of the Birnbaum IM of the components, uncertainty in the parameters of the system model is often neglected. This neglect may lead to erroneous, possibly non-conservative ranking. In this work, we develop a method based on Possibility Theory (PT) for giving due account to epistemic uncertainties in Birnbaum IMs. An example is given with reference to the components of the Auxiliary FeedWater System (AFWS) of a Nuclear Power Plant.

Structured elicitation of expert judgments for threatened species assessment: a case study on a continental scale using email

Summary1. Expert knowledge is used routinely to inform listing decisions under the IUCN Red List criteria. Differences in opinion arise between experts in the presence of epistemic uncertainty, as a result of different interpretations of incomplete information and differences in individual beliefs, values and experiences. Structured expert elicitation aims to anticipate and account for such differences to increase the accuracy of final estimates.2. A diverse panel of 16 experts independently evaluated up to 125 parameters per taxon to assess the IUCN Red List category of extinction risk for nine Australian bird taxa. Each panellist was provided with the same baseline data. Additional judgments and advice were sought from taxon specialists outside the panel. One question set elicited lowest and highest plausible estimates, best estimates and probabilities that the true values were contained within the upper and lower bounds. A second question set elicited yes/no answers and a degree of credibility in the answer provided.3. Once initial estimates were obtained, all panellists were shown each others’ values. They discussed differences and reassessed their original values. Most communication was carried out by email.4. The process took nearly 6 months overall to complete, and required an average of 1 h and up to 13 h per taxon for a panellist to complete the initial assessment.5. Panellists were mostly in agreement with one another about IUCN categorisations for each taxon. Where they differed, there was some evidence of convergence in the second round of assessments, although there was persistent non‐overlap for about 2% of estimates. The method exposed evidence of common subjective biases including overconfidence, anchoring to available data, definitional ambiguity and the conceptual difficulty of estimating percentages rather than natural numbers.6. This study demonstrates the value of structured elicitation techniques to identify and to reduce potential sources of bias and error among experts. The formal nature of the process meant that the consensus position reached carried greater weight in subsequent deliberations on status. The structured process is worthwhile for high profile or contentious taxa, but may be too time intensive for less divisive cases.

Risk-informed decision-making in the presence of epistemic uncertainty

An important issue in risk analysis is the distinction between epistemic and aleatory uncertainties. In this paper, the use of distinct representation formats for aleatory and epistemic uncertainties is advocated, the latter being modelled by sets of possible values. Modern uncertainty theories based on convex sets of probabilities are known to be instrumental for hybrid representations where aleatory and epistemic components of uncertainty remain distinct. Simple uncertainty representation techniques based on fuzzy intervals and p-boxes are used in practice. This paper outlines a risk analysis methodology from elicitation of knowledge about parameters to decision. It proposes an elicitation methodology where the chosen representation format depends on the nature and the amount of available information. Uncertainty propagation methods then blend Monte Carlo simulation and interval analysis techniques. Nevertheless, results provided by these techniques, often in terms of probability intervals, may be too complex to interpret for a decision-maker and we, therefore, propose to compute a unique indicator of the likelihood of risk, called confidence index. It explicitly accounts for the decision-maker's attitude in the face of ambiguity. This step takes place at the end of the risk analysis process, when no further collection of evidence is possible that might reduce the ambiguity due to epistemic uncertainty. This last feature stands in contrast with the Bayesian methodology, where epistemic uncertainties on input parameters are modelled by single subjective probabilities at the beginning of the risk analysis process.