Abstract
In order to improve the reliability analysis accuracy of the aircraft high-lift, an approach based on the Copula function theory and Bayesian updating is proposed. Considering the influence of the random variables’ correlation in the process of updating, choosing the reasonable prior joint distribution and likelihood function is crucial. Under the condition of the incomplete probability information, the analytic expressions of the prior joint distribution and likelihood function of the correlated random variables are derived through the Copula function. Then, the posterior joint distribution is obtained by Bayesian updating. The reliability of the lifting device is calculated based on the posterior distribution. The case analysis shows that the reliability results based on the proposed approach are more accurate and more coincident with the factual situation than the reliability analysis results based on the independence assumption of random variables.
Highlights
The high-lift device is used to improve take-off weight and add lift for take-off and landing of civil airplanes.1 The safety of airplanes has close relationship with the reliability of the high-lift device
With the prior joint probability density function (PDF) and the likelihood function, the posterior samples of E1 and G1 can be obtained based on the Markov chain Monte Carlo (MCMC) method, as plotted in Figures 5 and 6
Under the condition of the incomplete probability information, this article presents an approach for improving the reliability analysis accuracy of the aircraft high-lift by introducing the Copula function theory into Bayesian updating
Summary
The high-lift device is used to improve take-off weight and add lift for take-off and landing of civil airplanes. The safety of airplanes has close relationship with the reliability of the high-lift device. For the correlated random variables, the Copula function is introduced to construct the prior joint distribution and the likelihood function before Bayesian updating of the aircraft lift device. With the Copula function, we can build the prior joint PDF and likelihood function of correlated random variables using only the marginal probability distributions and correlation coefficient. Based on the definition of Sklar’s theorem, we can get the prior joint PDF and likelihood function of the correlated random variables by knowing a Copula function and their marginal distributions. This is especially significant in the practical engineering application. The function relationship between the Pearson correlation coefficient rP and the Copula parameter u is given by
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