HbMoM: a library for stochastic simulations in engineering using statistical moments

摘要

Stochastic simulations are becoming increasingly important in numerous engineering applications. The solution to the governing equations are complicated due to the high-dimensional spaces and the presence of randomness. In this paper we present HbMoM (http://libmom. sourceforge.net), a software library to solve various types of Stochastic Differential Equations (SDE) as well as estimate statistical distributions from the moments. The library provides a suite of tools to solve various SDEs using the method of moments (MoM) as well as estimate statistical distributions from the moments using moment matching algorithms. For a large class of problems, MoM provide efficient solutions compared with other stochastic simulation techniques such as Monte Carlo (MC). In the physical sciences, the moments of the distribution are usually the primary quantities of interest. The library enables the solution of moment equations derived from a variety of SDEs, with closure using non-standard Gaussian quadrature. In engineering risk assessment and decision making, statistical distributions are required. The library implements tools for fitting the Generalized Lambda Distribution (GLD) with the given moments. The objectives of this paper are (1) to briefly outline the theory behind moment methods for solving SDEs/estimation of statistical distributions; (2) describe the organization of the software and user interfaces; (3) discuss use of standard software engineering tools for regression testing, aid collaboration, distribution and further development. A number of representative examples of the use of HbMoM in various engineering applications are presented and future areas of research are discussed.