A Bayesian method for establishing fatigue design curves

Edwards, G.R.; Pacheco, Luis Alfonso Moreno

doi:10.1016/0167-4730(84)90005-5

Cited by 16 publications

(3 citation statements)

References 3 publications

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“…The notional fatigue reliability on the design curve only reflects the observed physical uncertainty associated with the fatigue process itself, but for the small fatigue data set the statistical uncertainties concerning the point parameter estimates could be equally significant. Bayesian analysis has been presented for establishing design S-N curves from small censored data sets to solve underlying statistical uncertainties [14]. Although a number of papers have appeared which exploited Bayesian inference in the analysis of the propagation of fatigue cracks, very few attempts have been made in the past to use the Bayesian approach in the context of S-N fatigue tests [12].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Bayesian fatigue data analysis

Liu

Lü

Hoogenboom

2017

International Journal of Fatigue

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The problem minimizing the number of specimens required for fatigue data analysis is considered in this research. Assuming unknown hyperparameters described via prior distributions, a hierarchical Bayesian model with accumulated prior information was proposed to deal with this issue. One of the main advantages of hierarchical Bayesian model over the empirical Bayesian model is that the prior distributions with hierarchical structure can incorporate structural prior and subjective prior simultaneously. The probabilistic stress-cycle (P-S-N) curves are generated from the predictive distributions, involving both the randomness of parameters and the scatter of observations, and calculated by an identical hierarchical structure. The numerical calculation is done via the Gibbs sampler, which makes the whole process simple and intuitive.

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Section: Introductionmentioning

confidence: 99%

Hierarchical Bayesian fatigue data analysis

Liu

Lü

Hoogenboom

2017

International Journal of Fatigue

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“…Evaluating fatigue test results with Bayesian analysis has already been broadly investigated. [15][16][17][18] Thus, applying Bayes' theorem can require less data than standard evaluation to infer the correct S-N curve parameters faster and more robustly with little data. It is, therefore, predestined for evaluating fatigue tests.…”

Section: Related Workmentioning

confidence: 99%

“…Robert et al 14 shows that Bayesian analysis is a robust evaluation approach for small sample sizes and censored data when considering survived and failed specimens. Evaluating fatigue test results with Bayesian analysis has already been broadly investigated 15–18 . Thus, applying Bayes' theorem can require less data than standard evaluation to infer the correct S‐N curve parameters faster and more robustly with little data.…”

Section: Introductionmentioning

confidence: 99%

Reduction of testing effort for fatigue tests: Application of Bayesian optimal experimental design

Frie,

Kolyshkin,

Mordeja

et al. 2023

Fatigue Fract Eng Mat Struct

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S‐N curve parameter determination is a time‐ and cost‐intensive procedure. A standardized method for simultaneously determining all S‐N curve parameters with minimum testing effort is still missing. The Bayesian optimal experimental design (BOED) approach can reduce testing effort and accelerates uncertainty reduction during fatigue testing for S‐N curve parameters. The concept is applicable to all S‐N curve models and is exemplary illustrated for a bilinear S‐N curve model. We demonstrate the fatigue testing workflow for the bilinear S‐N curve in detail while discussing steps and challenges when generalizing to other S‐N curve models. Applying the BOED to the bilinear S‐N curve models, minor errors and uncertainties for all S‐N curve parameters are obtained after only 10 experiments for data scatter values below 1.1. For such, the relative error in fatigue limit estimation was less than 1% after five tests. When S‐N data scatter higher than 1.2 is concerned, 17 tests were required for robust analysis. The BOED methodology should be applied to other S‐N curve models in the future. The high computational effort and the approximation of the posterior distribution with a normal distribution are the limitations of the presented BOED approach.

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A Bayesian procedure for drawing inferences from random data

Edwards

1984

Reliability Engineering

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A Bayesian method for establishing fatigue design curves

Cited by 16 publications

References 3 publications

Hierarchical Bayesian fatigue data analysis

Hierarchical Bayesian fatigue data analysis

Reduction of testing effort for fatigue tests: Application of Bayesian optimal experimental design

A Bayesian procedure for drawing inferences from random data

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