Estimation of the parameters of the Normal flutter derivatives distribution

Abstract

Flutter derivatives are the most important parameters in flutter analysis of long-span cable-supported bridges. In recent years, Normal distribution has been commonly used, accepted and recommended distribution in literature to express the flutter derivatives probability distribution. However, it is well known that estimation of Normal distribution parameters is vital because imprecise and biased estimates can be misleading. Thus, in this paper, two new methods such as, Least Squares method and Bayesian Estimation method, are introduced for estimating Normal distribution parameters. Their performance is compared with Maximum Likelihood method by a simulation study and actual flutter derivatives. The results show that, in simulation test of random variables, the Least Squares method is highly competitive with the Bayesian Estimation method and the Maximum Likelihood method for all sample size and parameter settings. The performance of the Bayesian Estimation method behave in a very similar manner to the Maximum Likelihood method when non-informative priors are used. From analysis of actual flutter derivatives data, it is found that the Least Squares method is an adequate method to estimate Normal distribution parameters and it might have better suitability than the Bayesian Estimation method and the Maximum Likelihood method. As a result, the Least Squares method is very suitable and efficient in estimating Normal distribution parameters for flutter derivatives applications.