Probability Distribution Modeling of Sparse Data for Geotechnical Reliability Analysis

Geotechnical parameters are often uncertain due to the spatial variability of geotechnical engineering materials. Additionally, it is difficult to obtain a large number of data because of the time, cost, and site limitations. As a result, it remains a great challenge to properly estimate the probability distributions of geotechnical parameters with sparse data, which may affect the subsequent geotechnical reliability analysis. This paper aims to address these issues using an adaptive method that combines the kernel density estimation (KDE) and the genetic algorithm (GA), namely, KDE-GA. The proposed KDE-GA method can model the probability distributions [e.g., probability density function (PDF) and cumulative distribution function (CDF)] of geotechnical parameters with sparse data in a rational manner. The key point of this method is to find the optimal bandwidth by minimizing the maximum absolute discrepancy between the empirical CDF and the estimated CDF. Once the bandwidth is determined, the approximated PDF and CDF can be conveniently obtained using the KDE with Gaussian kernel function. After that, the KDE-GA is incorporated with the Metropolis–Hastings (MH) algorithm to form the KDE-GA-MH method for geotechnical reliability analysis. The effectiveness of the KDE-GA and KDE-GA-MH methods are verified through several examples.