Using Collocation to Propagate Uncertainties Through “Black-Box” Vehicle Models 2010-01-1924

This study developed and implemented an efficient computational method to propagate uncertainties through “black-box” models of mechanical systems. The system of interest was a wheel loader, but the methodology developed can be applied to various multibody systems. The technique implemented focused on efficiently modeling stochastic systems for which the equations of motion (EOMs) are not available. The analysis targeted the reaction forces in joints of interest. To validate the stochastic method proposed, it was implemented on a simple linkage mechanism modeled in two different ways: i) using differential algebraic equations (DAEs) coded in Matlab, and ii) using computer aided design (CAD) in ProMechanica (the so-called “black-box” model). A stochastic model of the simple mechanism was developed using a Monte Carlo approach and a linear/quadratic transformation method, to serve for benchmarking purposes. A collocation method based on the polynomial chaos methodology was then developed for both Matlab and ProMechanica models. The method was validated on the simple linkage mechanism model using the results from the models obtained earlier using traditional stochastic techniques. It was next applied to a complex ProMechanica CAD model of a Cat Wheel Loader. The collocation method implemented proved to be reliable and easier to implement than traditional stochastic methods. Moreover, it has been shown that it can be successfully applied to “black-box” models.