Bayesian methodology for reliability model acceptance

Zhang, Ruoxue; Mahadevan, Sankaran

doi:10.1016/s0951-8320(02)00269-7

Cited by 102 publications

(35 citation statements)

References 10 publications

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“…Moreover, in the model validation part, we also propose an evidential method; and the probability distribution of experimental evidence as well as that of the model prediction, which is derived from the uncertainty propagation technique, is involved. The proposed method borrows the idea of Bayesian hypothesis testing and the definition of Bayes factor in [20,31] as reference, inspired by which, groups of BPAs for the decision making of model acceptance are generated and obtained.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Evidential Model Validation under Epistemic Uncertainty

Deng

2018

Mathematical Problems in Engineering

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This paper proposes evidence theory based methods to both quantify the epistemic uncertainty and validate computational model. Three types of epistemic uncertainty concerning input model data, that is, sparse points, intervals, and probability distributions with uncertain parameters, are considered. Through the proposed methods, the given data will be described as corresponding probability distributions for uncertainty propagation in the computational model, thus, for the model validation. The proposed evidential model validation method is inspired by the idea of Bayesian hypothesis testing and Bayes factor, which compares the model predictions with the observed experimental data so as to assess the predictive capability of the model and help the decision making of model acceptance. Developed by the idea of Bayes factor, the frame of discernment of Dempster-Shafer evidence theory is constituted and the basic probability assignment (BPA) is determined. Because the proposed validation method is evidence based, the robustness of the result can be guaranteed, and the most evidence-supported hypothesis about the model testing will be favored by the BPA. The validity of proposed methods is illustrated through a numerical example.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Evidential Model Validation under Epistemic Uncertainty

Deng

2018

Mathematical Problems in Engineering

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“…The work of Zhang and Mahadevan (2003) initiated a large body of literature (Mahadevan and Rebba, 2005;Rebba and Mahadevan, 2006;Jiang and Mahadevan, 2008a;Jiang and Mahadevan, 2008b;Jiang and Mahadevan, 2009), which uses Bayesian hypothesis testing to accept or reject a design based on model validity. They investigated the effect of model inaccuracies on the reliability requirements of a design using Bayesian formulations to calculate the posterior probability of a design being valid or invalid.…”

Section: Background and Previous Researchmentioning

confidence: 99%

A Variable-Size Local Domain Approach to Computer Model Validation in Design Optimization

Drignei¹,

Mourelatos²,

Kokkolaras³

et al. 2011

SAE Int. J. Mater. Manuf.

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A common approach to the validation of simulation models focuses on validation throughout the entire design space. A more recent methodology validates designs as they are generated during a simulation-based optimization process. The latter method relies on validating the simulation model in a sequence of local domains. To improve its computational efficiency, this paper proposes an iterative process, where the size and shape of local domains at the current step are determined from a parametric bootstrap methodology involving maximum likelihood estimators of unknown model parameters from the previous step. Validation is carried out in the local domain at each step. The iterative process continues until the local domain does not change from iteration to iteration during the optimization process ensuring that a converged design optimum has been obtained. The proposed methodology is illustrated using a thermal, one-dimensional, linear heat conduction problem in a solid slab with heat flux boundary conditions.

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“…Standards pointing out clear and accepted procedures for model validation under uncertainty are yet to be developed (Thacker and Huyse, 2002;Thacker, 2003). A method to validate reliability prediction models based on Bayesian hypothesis testing has recently been proposed when reliability testing is feasible (Zhang and Mahadevan, 2003). A six-step procedure based upon a Bayesian statistical methodology was proposed (Bayyari et al, 2002) and applied to problems of interest in automotive industry.…”

Section: Motivationmentioning

confidence: 99%

Statistical validation of simulation models

Rebba¹,

Huang²,

Liu³

et al. 2006

IJMPT

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This paper investigates various statistical methodologies for validating simulation models in automotive design. Validation metrics to compare model prediction with experimental observation, when there is uncertainty in both, are developed. Two types of metrics based on Bayesian analysis and principal components analysis are proposed. The validation results are also compared with those obtained from classical hypothesis testing. A fatigue life prediction model for composite materials and a residual stress prediction model for a spot-welded joint are validated, using the proposed methodology.

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Bayesian methodology for reliability model acceptance

Cited by 102 publications

References 10 publications

Evidential Model Validation under Epistemic Uncertainty

Evidential Model Validation under Epistemic Uncertainty

A Variable-Size Local Domain Approach to Computer Model Validation in Design Optimization

Statistical validation of simulation models

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