The present work concerns the estimation of the probability density function (p.d.f.) of measured data in the Lamb wave-based damage detection. Although there was a number of research work which focused on the consensus algorithm of combining all the results of individual sensors, the p.d.f. of measured data, which was the fundamental part of the probability-based method, was still given by experience in existing work. Based on the analysis about the noise-induced errors in measured data, it was learned that the type of distribution was related with the level of noise. In the case of weak noise, the p.d.f. of measured data could be considered as the normal distribution. The empirical methods could give satisfied estimating results. However, in the case of strong noise, the p.d.f. was complex and did not belong to any type of common distribution function. Nonparametric methods, therefore, were needed. As the most popular nonparametric method, kernel density estimation was introduced. In order to demonstrate the performance of the kernel density estimation methods, a numerical model was built to generate the signals of Lamb waves. Three levels of white Gaussian noise were intentionally added into the simulated signals. The estimation results showed that the nonparametric methods outperformed the empirical methods in terms of accuracy.
Log-Transform Kernel Density Estimation of Income Distribution
