Article

Einsatz der Bayes'schen Statistik in der Zuverlässigkeitsbestimmung von zerstörungsfreien Prüfsystemen

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

The assessment of the Probability of Detection (POD) is used to evaluate the reliability of the non-destructive testing (NDT) system. The POD is required in industries, where a missed flaw might cause grave consequences. If only the artificial defects are evaluated, the POD could lead to wrong conclusion or even be invalid. The POD based on real flaws is needed. A small amount of real flaws can lead to a not statistically significant result or even to incorrect results. This work presents an approach to obtain to a significant result for the POD of the current dataset, despite the small amount of real defects. Two steps are necessary to assess a NDT system based on real flaws. First we evaluated the correlation between the NDT signal and the real size of the flaw. Second we use a statistical approach based on the Bayesian statistics to assess a POD in spite of the small amount of data. The approach allows including information of the POD evaluation of artificial defects in the assessment of the POD of real flaws.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

Article
Reliability evaluations of modern test systems under the Industry 4.0 technologies, play a vital role in the successful transformation to NDE 4.0. This is due to the fact that NDE 4.0 is mainly based on the interconnection between the cyber-physical systems. When the individual reliability of the various important technologies from the Industry 4.0 such as the digital twin, digital thread, Industrial Internet of Things (IIoT), artificial intelligence (AI), data fusion, digitization, etc. is high, then it is possible to obtain the reliability beyond the intrinsic capability of the test system. In this paper, the significance of the reliability evaluation is reviewed under the vision of NDE 4.0, including examples of data fusion concepts as well as the importance of algorithms (like explainable artificial intelligence), the practical use is discussed and elaborated accordingly.
Article
In an earlier article, a method of calculating two-sided confidence bands for cumulative distribution functions was suggested. In this article, the construction of one-sided confidence bands is described. The case of the genera1 location-scale parameter mode1 is discussed, and formulas for the normal and extreme-value models are given as illustrations. A simple numerical example is also included.
Article
In recent years, Bayesian model updating techniques based on measured data have been applied to system identification of structures and to structural health monitoring. A fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying structural system and to its exclusive foundation on the probability axioms. The plausibility of each structural model within a set of possible models, given the measured data, is quantified by the joint posterior probability density function of the model parameters. This Bayesian approach requires the evaluation of multidimensional integrals, and this usually cannot be done analytically. Recently, some Markov chain Monte Carlo simulation methods have been developed to solve the Bayesian model updating problem. However, in general, the efficiency of these proposed approaches is adversely affected by the dimension of the model parameter space. In this paper, the Hybrid Monte Carlo method is investigated (also known as Hamiltonian Markov chain method), and we show how it can be used to solve higher-dimensional Bayesian model updating problems. Practical issues for the feasibility of the Hybrid Monte Carlo method to such problems are addressed, and improvements are proposed to make it more effective and efficient for solving such model updating problems. New formulae for Markov chain convergence assessment are derived. The effectiveness of the proposed approach for Bayesian model updating of structural dynamic models with many uncertain parameters is illustrated with a simulated data example involving a ten-story building that has 31 model parameters to be updated.