Robust propagation of probability boxes by interval predictor models

Sadeghi, Jonathan; Angelis, Marco de; Patelli, Edoardo

doi:10.1016/j.strusafe.2019.101889

Cited by 25 publications

(8 citation statements)

References 24 publications

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“…In [33,37] they extend IPMs to Random Predictor Models (RPMs) by replacing the interval-valued map with a random-variable-valued map to obtain probabilities within the IPM boundaries. In addition, Sadeghi et al [158] describe how to propagate mixed uncertainties in the form of p-boxes by IPMs. In [157] they combine IPMs with a Frequentist probabilistic framework.…”

Section: Interval Predictor Modelsmentioning

confidence: 99%

Unified Framework and Survey for Model Verification, Validation and Uncertainty Quantification

Riedmaier

Danquah

Schick

et al. 2020

Arch Computat Methods Eng

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Simulation is becoming increasingly important in the development, testing and approval process in many areas of engineering, ranging from finite element models to highly complex cyber-physical systems such as autonomous cars. Simulation must be accompanied by model verification, validation and uncertainty quantification (VV&UQ) activities to assess the inherent errors and uncertainties of each simulation model. However, the VV&UQ methods differ greatly between the application areas. In general, a major challenge is the aggregation of uncertainties from calibration and validation experiments to the actual model predictions under new, untested conditions. This is especially relevant due to high extrapolation uncertainties, if the experimental conditions differ strongly from the prediction conditions, or if the output quantities required for prediction cannot be measured during the experiments. In this paper, both the heterogeneous VV&UQ landscape and the challenge of aggregation will be addressed with a novel modular and unified framework to enable credible decision making based on simulation models. This paper contains a comprehensive survey of over 200 literature sources from many application areas and embeds them into the unified framework. In addition, this paper analyzes and compares the VV&UQ methods and the application areas in order to identify strengths and weaknesses and to derive further research directions. The framework thus combines a variety of VV&UQ methods, so that different engineering areas can benefit from new methods and combinations. Finally, this paper presents a procedure to select a suitable method from the framework for the desired application.

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Section: Interval Predictor Modelsmentioning

confidence: 99%

Unified Framework and Survey for Model Verification, Validation and Uncertainty Quantification

Riedmaier

Danquah

Schick

et al. 2020

Arch Computat Methods Eng

View full text Add to dashboard Cite

show abstract

“…are assigned to the central moments of a type-III uncertain parameter. Recent advances in propagation algorithms include methods based on Polynomial Chaos Expansions [28,29], interval predictor models [30], methods based on importance sampling [31] potentially in combination with a high-dimensional model representation of the underlying numerical model [32,19], techniques based on affine arithmetic [33] or multi-level strategies [34]. Furthermore, also efficient interval Monte Carlo [35,36] or techniques based on linear programming [37] have been introduced in this context.…”

Section: Introductionmentioning

confidence: 99%

Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities

Faes

Valdebenito

Moens

et al. 2021

Mechanical Systems and Signal Processing

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This paper presents a highly efficient and effective approach to bound the responses and probability of failure of linear systems where the model parameters are subjected to combinations of epistemic and aleatory uncertainty. These combinations can take the form of imprecise probabilities or hybrid uncertainties. Typically, such computations involve solving a nested double loop problem, where the propagation of the aleatory uncertainty has to be performed for each realisation of the epistemic uncertainty. Apart from near-trivial cases, such computation is intractable without resorting to surrogate modeling schemes. In this paper, a method is presented to break this double loop by virtue of the operator norm theorem. Indeed, in case linear models are considered and under the restriction that the model definition cannot be subject to aleatory uncertainty, the paper shows that the computational efficiency, quantified by the required number of model evaluations, of propagating these parametric uncertainties can be improved by several orders of magnitude.Two case studies involving a finite element model of a clamped plate and a six-story building are included to illustrate the application of the developed technique, as well as its computational merit in comparison to existing double-loop approaches.

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“…In reference [14], a method is introduced to propagate imprecise probabilities by combining Improved Interval Analysis via Extra Unitary Interval in combination with classical probabilistic analysis. Also several surrogate modelling schemes for the propagation of imprecise probabilities have been introduced in literature, based on e.g., polynomial chaos expansions [15] or Interval Predictor Models [16].…”

Section: Introductionmentioning

confidence: 99%

“…Simulation 1: Two imprecise random fields containing a large epistemic uncertainty Within this study, two imprecise random fields [Y D ](z, θ) and [r](z, θ) are considered affecting the nonlinear damage evolution. Both random fields are imprecise due to an interval valued correlation length L I• =[2,16]m caused by a large epistemic uncertainty. The simulation is performed by Monte Carlo method using n MC = 40000 samples in case both imprecise random fields are considered and n MC = 20000 if there is only one imprecise random field input.5.1.1.…”

mentioning

confidence: 99%

Imprecise random field analysis for non-linear concrete damage analysis

Dannert

Faes

Fleury

et al. 2021

Mechanical Systems and Signal Processing

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Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a damage model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding random field is discretized by Karhunen-Loève expansion. In a first study, the effect of the series truncation is discussed as well as the resulting variance error on the probability box (p-box) that represents uncertainty on the damage in a concrete beam as a result of the imprecise random field. It is shown that a certain awareness for the influence of the truncation order on the local field variance is needed when the series is truncated according to a fixed mean variance error.In the following case study, the main investigation is on the propagation of imprecise random fields in the context of non-linear finite element problems, i.e. quasi-brittle damage of a four-point bended concrete beam. The global and local damage as the quantities of interest are described by a p-box. The influence of several imprecise random field input parameters to the resulting p-boxes is studied. Furthermore, it is examined whether correlation length values located within the interval, so-called intermediate values, affect the p-box bounds. It is shown that, from the engineering point of view, a pure vertex analysis of the correlation length intervals is sufficient to determine the p-box in this context.

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Robust propagation of probability boxes by interval predictor models

Cited by 25 publications

References 24 publications

Unified Framework and Survey for Model Verification, Validation and Uncertainty Quantification

Unified Framework and Survey for Model Verification, Validation and Uncertainty Quantification

Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities

Imprecise random field analysis for non-linear concrete damage analysis

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