The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Sankaran Mahadevan - One of the best experts on this subject based on the ideXlab platform.

  • Reliability-based design optimization of multidisciplinary system under aleatory and Epistemic Uncertainty
    Structural and Multidisciplinary Optimization, 2017
    Co-Authors: Kais Zaman, Sankaran Mahadevan
    Abstract:

    This paper proposes formulations and algorithms for reliability-based design optimization (RBDO) of both single and multidisciplinary systems under both aleatory Uncertainty (i.e., natural or physical variability) and Epistemic Uncertainty (i.e., imprecise probabilistic information). The proposed formulations specifically deal with Epistemic Uncertainty arising from interval data. When the only information available for an input variable is in the form of interval data, it is likely that the distribution type for the input variable is not known or cannot be specified accurately. This paper uses a four-parameter flexible Johnson family of distributions to represent the Uncertainty described by interval data. An efficient approach is proposed to decouple the design analysis from the Uncertainty analysis. The proposed methodology for multidisciplinary system optimization does not require any coupled system level analysis. The proposed methods are illustrated through several example problems.

  • reliability analysis under Epistemic Uncertainty
    Reliability Engineering & System Safety, 2016
    Co-Authors: Saideep Nannapaneni, Sankaran Mahadevan
    Abstract:

    Abstract This paper proposes a probabilistic framework to include both aleatory and Epistemic Uncertainty within model-based reliability estimation of engineering systems for individual limit states. Epistemic Uncertainty is considered due to both data and model sources. Sparse point and/or interval data regarding the input random variables leads to Uncertainty regarding their distribution types, distribution parameters, and correlations; this statistical Uncertainty is included in the reliability analysis through a combination of likelihood-based representation, Bayesian hypothesis testing, and Bayesian model averaging techniques. Model errors, which include numerical solution errors and model form errors, are quantified through Gaussian process models and included in the reliability analysis. The probability integral transform is used to develop an auxiliary variable approach that facilitates a single-level representation of both aleatory and Epistemic Uncertainty. This strategy results in an efficient single-loop implementation of Monte Carlo simulation (MCS) and FORM/SORM techniques for reliability estimation under both aleatory and Epistemic Uncertainty. Two engineering examples are used to demonstrate the proposed methodology.

  • separation of aleatory and Epistemic Uncertainty in probabilistic model validation
    Reliability Engineering & System Safety, 2016
    Co-Authors: Joshua Mullins, Sankaran Mahadevan, You Ling, Lin Sun, Alejandro Strachan
    Abstract:

    This paper investigates model validation under a variety of different data scenarios and clarifies how different validation metrics may be appropriate for different scenarios. In the presence of multiple Uncertainty sources, model validation metrics that compare the distributions of model prediction and observation are considered. Both ensemble validation and point-by-point approaches are discussed, and it is shown how applying the model reliability metric point-by-point enables the separation of contributions from aleatory and Epistemic Uncertainty sources. After individual validation assessments are made at different input conditions, it may be desirable to obtain an overall measure of model validity across the entire domain. This paper proposes an integration approach that assigns weights to the validation results according to the relevance of each validation test condition to the overall intended use of the model in prediction. Since Uncertainty propagation for probabilistic validation is often unaffordable for complex computational models, surrogate models are often used; this paper proposes an approach to account for the additional Uncertainty introduced in validation by the uncertain fit of the surrogate model. The proposed methods are demonstrated with a microelectromechanical system (MEMS) example.

  • relative contributions of aleatory and Epistemic Uncertainty sources in time series prediction
    International Journal of Fatigue, 2016
    Co-Authors: Sankaran Mahadevan
    Abstract:

    Abstract This paper develops a novel computational framework to compute the Sobol indices that quantify the relative contributions of various Uncertainty sources towards the system response prediction Uncertainty. In the presence of both aleatory and Epistemic Uncertainty, two challenges are addressed in this paper for the model-based computation of the Sobol indices: due to data Uncertainty, input distributions are not precisely known; and due to model Uncertainty, the model output is uncertain even for a fixed realization of the input. An auxiliary variable method based on the probability integral transform is introduced to distinguish and represent each Uncertainty source explicitly, whether aleatory or Epistemic. The auxiliary variables facilitate building a deterministic relationship between the Uncertainty sources and the output, which is needed in the Sobol indices computation. The proposed framework is developed for two types of model inputs: random variable input and time series input. A Bayesian autoregressive moving average (ARMA) approach is chosen to model the time series input due to its capability to represent both natural variability and Epistemic Uncertainty due to limited data. A novel controlled-seed computational technique based on pseudo-random number generation is proposed to efficiently represent the natural variability in the time series input. This controlled-seed method significantly accelerates the Sobol indices computation under time series input, and makes it computationally affordable.

  • robustness based design optimization of multidisciplinary system under Epistemic Uncertainty
    AIAA Journal, 2013
    Co-Authors: Kais Zaman, Sankaran Mahadevan
    Abstract:

    This paper proposes formulations and algorithms for design optimization of multidisciplinary systems under both aleatory Uncertainty (i.e., natural or physical variability) and Epistemic Uncertainty (due to sparse or imprecise information) from the perspective of system robustness. The availability of sparse and interval data regarding input or design random variables introduces Uncertainty about their probability distribution type and distribution parameters. A single-loop approach is developed for the design optimization, which does not require any coupled multidisciplinary Uncertainty propagation analysis. Thus, the computational complexity and cost involved in estimating the mean and variation of the objective and constraints are greatly reduced. A decoupled approach is used to unnest the robustness-based design from the analysis of nondesign Epistemic variables to achieve further computational efficiency. The proposed methods are illustrated for a mathematical problem and a practical engineering prob...

Jon C Helton - One of the best experts on this subject based on the ideXlab platform.

  • probability of loss of assured safety in systems with multiple time dependent failure modes representations with aleatory and Epistemic Uncertainty
    Reliability Engineering & System Safety, 2014
    Co-Authors: Jon C Helton, Martin Pilch, Ca Dric J Sallaberry
    Abstract:

    Weak link (WL)/strong link (SL) systems are important parts of the overall operational design of high-consequence systems. In such designs, the SL system is very robust and is intended to permit operation of the entire system under, and only under, intended conditions. In contrast, the WL system is intended to fail in a predictable and irreversible manner under accident conditions and render the entire system inoperable before an accidental operation of the SL system. The likelihood that the WL system will fail to deactivate the entire system before the SL system fails (i.e., degrades into a configuration that could allow an accidental operation of the entire system) is referred to as probability of loss of assured safety (PLOAS). Representations for PLOAS for situations in which both link physical properties and link failure properties are time-dependent are derived and numerically evaluated for a variety of WL/SL configurations, including PLOAS defined by (i) failure of all SLs before failure of any WL, (ii) failure of any SL before failure of any WL, (iii) failure of all SLs before failure of all WLs, and (iv) failure of any SL before failure of all WLs. The indicated formal representations and associated numerical procedures for the evaluation of PLOAS are illustrated with example analyses involving (i) only aleatory Uncertainty, (ii) aleatory Uncertainty and Epistemic Uncertainty, and (iii) mixtures of aleatory Uncertainty and Epistemic Uncertainty.

  • quantification of margins and uncertainties alternative representations of Epistemic Uncertainty
    Reliability Engineering & System Safety, 2011
    Co-Authors: Jon C Helton, Jay D Johnson
    Abstract:

    Abstract In 2001, the National Nuclear Security Administration of the U.S. Department of Energy in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory and Sandia National Laboratories) initiated development of a process designated Quantification of Margins and Uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. A previous presentation, “Quantification of Margins and Uncertainties: Conceptual and Computational Basis,” describes the basic ideas that underlie QMU and illustrates these ideas with two notional examples that employ probability for the representation of aleatory and Epistemic Uncertainty. The current presentation introduces and illustrates the use of interval analysis, possibility theory and evidence theory as alternatives to the use of probability theory for the representation of Epistemic Uncertainty in QMU-type analyses. The following topics are considered: the mathematical structure of alternative representations of Uncertainty, alternative representations of Epistemic Uncertainty in QMU analyses involving only Epistemic Uncertainty, and alternative representations of Epistemic Uncertainty in QMU analyses involving a separation of aleatory and Epistemic Uncertainty. Analyses involving interval analysis, possibility theory and evidence theory are illustrated with the same two notional examples used in the presentation indicated above to illustrate the use of probability to represent aleatory and Epistemic Uncertainty in QMU analyses.

  • conceptual and computational basis for the quantification of margins and Uncertainty
    2009
    Co-Authors: Jon C Helton
    Abstract:

    In 2001, the National Nuclear Security Administration of the U.S. Department of Energy in conjunction with the national security laboratories (i.e, Los Alamos National Laboratory, Lawrence Livermore National Laboratory and Sandia National Laboratories) initiated development of a process designated Quantification of Margins and Uncertainty (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. This presentation discusses and illustrates the conceptual and computational basis of QMU in analyses that use computational models to predict the behavior of complex systems. Topics considered include (1) the role of aleatory and Epistemic Uncertainty in QMU, (2) the representation of Uncertainty with probability, (3) the probabilistic representation of Uncertainty in QMU analyses involving only Epistemic Uncertainty, (4) the probabilistic representation of Uncertainty in QMU analyses involving aleatory and Epistemic Uncertainty, (5) procedures for sampling-based Uncertainty and sensitivity analysis, (6) the representation of Uncertainty with alternatives to probability such as interval analysis, possibility theory and evidence theory, (7) the representation of Uncertainty with alternatives to probability in QMU analyses involving only Epistemic Uncertainty, and (8) the representation of Uncertainty with alternatives to probability in QMU analyses involving aleatory and Epistemic Uncertainty. Concepts and computational procedures are illustrated with both notional examples and examples from reactor safety and radioactive waste disposal.

  • representation of analysis results involving aleatory and Epistemic Uncertainty
    International Journal of General Systems, 2008
    Co-Authors: Jon C Helton, Jay D Johnson, William L Oberkampf, Cedric J Sallaberry
    Abstract:

    Procedures are described for the representation of results in analyses that involve both aleatory Uncertainty and Epistemic Uncertainty, with aleatory Uncertainty deriving from an inherent randomness in the behaviour of the system under study and Epistemic Uncertainty deriving from a lack of knowledge about the appropriate values to use for quantities that are assumed to have fixed but poorly known values in the context of a specific study. Aleatory Uncertainty is usually represented with probability and leads to cumulative distribution functions (CDFs) or complementary CDFs (CCDFs) for analysis results of interest. Several mathematical structures are available for the representation of Epistemic Uncertainty, including interval analysis, possibility theory, evidence theory and probability theory. In the presence of Epistemic Uncertainty, there is not a single CDF or CCDF for a given analysis result. Rather, there is a family of CDFs and a corresponding family of CCDFs that derive from Epistemic uncertaint...

  • a sampling based computational strategy for the representation of Epistemic Uncertainty in model predictions with evidence theory
    Computer Methods in Applied Mechanics and Engineering, 2007
    Co-Authors: Jon C Helton, Jay D Johnson, William L Oberkampf, Curtis B Storlie
    Abstract:

    Evidence theory provides an alternative to probability theory for the representation of Epistemic Uncertainty in model predictions that derives from Epistemic Uncertainty in model inputs, where the descriptor Epistemic is used to indicate Uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model. The potential benefit, and hence appeal, of evidence theory is that it allows a less restrictive specification of Uncertainty than is possible within the axiomatic structure on which probability theory is based. Unfortunately, the propagation of an evidence theory representation for Uncertainty through a model is more computationally demanding than the propagation of a probabilistic representation for Uncertainty, with this difficulty constituting a serious obstacle to the use of evidence theory in the representation of Uncertainty in predictions obtained from computationally intensive models. This presentation describes and illustrates a sampling-based computational strategy for the representation of Epistemic Uncertainty in model predictions with evidence theory. Preliminary trials indicate that the presented strategy can be used to propagate Uncertainty representations based on evidence theory in analysis situations where naive sampling-based (i.e., unsophisticated Monte Carlo) procedures are impracticable due to computational cost.

Robert M Kirby - One of the best experts on this subject based on the ideXlab platform.

  • mixed aleatory and Epistemic Uncertainty quantification using fuzzy set theory
    International Journal of Approximate Reasoning, 2015
    Co-Authors: Mahsa Mirzargar, Robert M Kirby
    Abstract:

    Abstract This paper proposes algorithms to construct fuzzy probabilities to represent or model the mixed aleatory and Epistemic Uncertainty in a limited-size ensemble. Specifically, we discuss the possible requirements for the fuzzy probabilities in order to model the mixed types of Uncertainty, and propose algorithms to construct fuzzy probabilities for both independent and dependent datasets. The effectiveness of the proposed algorithms is demonstrated using one-dimensional and high-dimensional examples. After that, we apply the proposed Uncertainty representation technique to isocontour extraction, and demonstrate its applicability using examples with both structured and unstructured meshes.

Hongzhong Huang - One of the best experts on this subject based on the ideXlab platform.

  • reliability assessment of complex electromechanical systems under Epistemic Uncertainty
    Reliability Engineering & System Safety, 2016
    Co-Authors: Yuanjian Yang, Weiwen Peng, Hongzhong Huang
    Abstract:

    The appearance of macro-engineering and mega-project have led to the increasing complexity of modern electromechanical systems (EMSs). The complexity of the system structure and failure mechanism makes it more difficult for reliability assessment of these systems. Uncertainty, dynamic and nonlinearity characteristics always exist in engineering systems due to the complexity introduced by the changing environments, lack of data and random interference. This paper presents a comprehensive study on the reliability assessment of complex systems. In view of the dynamic characteristics within the system, it makes use of the advantages of the dynamic fault tree (DFT) for characterizing system behaviors. The lifetime of system units can be expressed as bounded closed intervals by incorporating field failures, test data and design expertize. Then the coefficient of variation (COV) method is employed to estimate the parameters of life distributions. An extended probability-box (P-Box) is proposed to convey the present of Epistemic Uncertainty induced by the incomplete information about the data. By mapping the DFT into an equivalent Bayesian network (BN), relevant reliability parameters and indexes have been calculated. Furthermore, the Monte Carlo (MC) simulation method is utilized to compute the DFT model with consideration of system replacement policy. The results show that this integrated approach is more flexible and effective for assessing the reliability of complex dynamic systems.

  • belief universal generating function analysis of multi state systems under Epistemic Uncertainty and common cause failures
    IEEE Transactions on Reliability, 2015
    Co-Authors: Yu Liu, Yuanjian Yang, Hongzhong Huang
    Abstract:

    Because of the complexity of engineering systems, and the fact that insufficient data are only available to obtain the precise state probability of components, an extended universal generating function (UGF) based on belief function theory is introduced in this paper to conduct the reliability analysis of multi-state systems (MSSs) with Epistemic Uncertainty. The behavior of common cause failures (CCFs) is further incorporated, and the occurrence probability of CCFs is evaluated using a weighted impact vector method. A numerical example is used to illustrate how the proposed method works. In addition, a global optimization method is used to obtain the truth interval of the system reliability, and the results are compared with those obtained by using some existing methods. The case study shows that the belief UGF method can effectively avoid the interval expansion problem and the overestimation problem involved in the interval UGF method, and the proposed method can be used to provide a reliable way to evaluate the reliability of MSSs with interval data and CCFs.

Enrico Zio - One of the best experts on this subject based on the ideXlab platform.

  • on the optimal redundancy allocation for multi state series parallel systems under Epistemic Uncertainty
    Reliability Engineering & System Safety, 2017
    Co-Authors: Muxia Sun, Enrico Zio
    Abstract:

    In this paper, we study the redundancy allocation problem (RAP) for multi-state series–parallel systems (MSSPSs). For each multi-state component, the exact values of its state probabilities are assumed to be unknown, due to Epistemic Uncertainty (EU), and only conservative lower and upper bounds of them are given. The objective of the RAP is to simultaneously maximize the supremum and infimum of the system's uncertain availability, under a cost constraint. The problem is two-stage and multi-objective. In this work, we: 1. provide a linear-time algorithm to obtain the component state distribution, under which the uncertain system availability will be at its supremum or infimum; 2. show that the problem is reducible to one-stage; 3. analyze the landscape of MSSPS RAP under EU and propose a modified NSGA-II, with targeted designs of repair and local search operation. The proposed algorithm is compared with standard NSGA-II on multiple benchmarks. The results show that the proposed algorithm significantly outperforms the standard NSGA-II in both optimality and time efficiency.

  • Probability box as a tool to model and control the effect of Epistemic Uncertainty in multiple dependent competing failure processes
    Applied Soft Computing, 2017
    Co-Authors: Qingyan Zhang, Zhiguo Zeng, Enrico Zio, Rui Kang
    Abstract:

    Engineering components and systems are often subject to multiple dependent competing failure processes (MDCFPs). MDCFPs have been well studied in literature and various models have been developed to predict the reliability of MDCFPs. In practice, however, due to the limited resource, it is often hard to estimate the precise values of the parameters in the MDCFP model. Hence, the predicted reliability is affected by Epistemic Uncertainty. Probability box (P-box) is applied in this paper to describe the effect of Epistemic Uncertainty on MDCFP models. A dimension-reduced sequential quadratic programming (DRSQP) method is developed for the construction of P-box. A comparison to the conventional construction method shows that DRSQP method reduces the computational costs required for P-box constructions. Since Epistemic Uncertainty reflects the unsureness in the predicted reliability, a decision maker might want to reduce it by investing resource to more accurately estimate the value of each model parameter. A two-stage optimization framework is developed to allocate the resource among the parameters and ensure that Epistemic Uncertainty is reduced in a most efficient way. Finally, the developed methods are applied on a real case study, a spool valve, to demonstrate their validity.

  • A Model-Based Reliability Metric Considering Aleatory and Epistemic Uncertainty
    IEEE Access, 2017
    Co-Authors: Zhiguo Zeng, Rui Kang, Meilin Wen, Enrico Zio
    Abstract:

    —Model-based reliability analysis and assessment methods rely on models, which are assumed to be precise, to predict reliability. In practice, however, the precision of the model cannot be guaranteed due to the presence of Epistemic Uncertainty. In this paper, a new reliability metric, called belief reliability, is defined to explicitly account for Epistemic Uncertainty in model-based reliability analysis and assessment. A new method is developed to explicitly quantify Epistemic Uncertainty by measuring the effectiveness of the engineering analysis and assessment activities related to reliability. To evaluate belief reliability, an integrated framework is presented, where the contributions of design margin, aleatory Uncertainty and epis-temic Uncertainty are integrated to yield a comprehensive and systematic description of reliability. The developed methods are demonstrated by two case studies.

  • Measuring reliability under Epistemic Uncertainty: Review on non-probabilistic reliability metrics
    Chinese Journal of Aeronautics, 2016
    Co-Authors: Rui Kang, Zhiguo Zeng, Qingyuan Zhang, Enrico Zio
    Abstract:

    Abstract In this paper, a systematic review of non-probabilistic reliability metrics is conducted to assist the selection of appropriate reliability metrics to model the influence of Epistemic Uncertainty. Five frequently used non-probabilistic reliability metrics are critically reviewed, i.e., evidence-theory-based reliability metrics, interval-analysis-based reliability metrics, fuzzy-interval-analysis-based reliability metrics, possibility-theory-based reliability metrics (posbist reliability) and Uncertainty-theory-based reliability metrics (belief reliability). It is pointed out that a qualified reliability metric that is able to consider the effect of Epistemic Uncertainty needs to (1) compensate the conservatism in the estimations of the component-level reliability metrics caused by Epistemic Uncertainty, and (2) satisfy the duality axiom, otherwise it might lead to paradoxical and confusing results in engineering applications. The five commonly used non-probabilistic reliability metrics are compared in terms of these two properties, and the comparison can serve as a basis for the selection of the appropriate reliability metrics.