Low Operational Order Analytic Sensitivity Analysis for Tree-Type Multibody Dynamic Systems

Abstract

Computing e rst-order sensitivity information is crucial for many gradient-based optimization strategies, where thealgorithmsemployedplayakeyroleindeterminingthecomputationalefe ciencyoftheoptimizationprocess.For complex multibody system optimization problems, the numerical accuracy, stability, convergence characteristics, and computational order of the underlying formulations all contribute to the overall cost of the optimization process. The computational efe ciency of the underlying forward problem and the associated sensitivity analysis musteach beconsideredifoneistoproperlymanagethesedesign problemsundertimeandcomputationalresource constraints. An algorithm is presented that determines the key state derivatives, central to e rst-order sensitivity analysis,inafullyrecursivemanner.Thealgorithmsignie cantlyreducesthecostofdetermininganalytice rst-order sensitivity information for large-scale, tree-type multi-rigid-body dynamic systems. Qualitative and quantitative validation on theoperational requirementofthepresentmethod are made through analytical means and empirical studies.