Quantile Based Probabilistic Characterization of Geotechnical Variables Using Maximum Entropy Principle

Abstract

AbstractIn probabilistic reliability analysis and design, critical geotechnical variables such as soil shear strength are usually characterized as random variables in terms of probability density function or cumulative distribution function, of which the type is usually determined from histograms or simply from experience, and the parameters are estimated using the method of moments or the method of maximum likelihood. However, the difficulty in obtaining accurate moment estimates from small samples has been the main impediment to accurately determination of probabilistic models. The present paper proposes a novel probabilistic characterization of soil properties by using quantile functions based on the principle of maximum entropy and probability-weighted moments. Quantile functions are equivalent to the probability distribution of stochastic data since the quantile function is the inverse of the cumulative distribution function. The maximum entropy method is presented to generate a least unbiased quantile function for soil properties from observed soil samples. Due to the use of probability-weighted moments, the entropy-based quantile functions can quantify uncertainties more accurately from samples than probability density functions or cumulative distribution functions. A comparative study between maximum entropy quantile distributions and traditional quantile distributions is conducted to evaluate the performance of quantile distributions. The analytical entropy quantile distribution obtained can be readily used in probabilistic reliability analysis to enhance the accuracy of calculation.