Low operational order analytic sensitivity analysis for tree-type multibody dynamic systems

Computing first-order sensitivity information is crucial for many gradient- based optimization strategies, where the algorithms employed play a key rol e in determining the computational efficiency of the optimization process. For complex multibody system optimization problems, the numerical accuracy, stability, convergence characteristics, and computational order of the und erlying formulations all contribute to the overall cost of the optimization process. The computational efficiency of the underlying forward problem an d the associated sensitivity analysis must each be considered if one is to properly manage these design problems under time and computational resource constraints. An algorithm is presented that determines the key state deriv atives, central to first-order sensitivity analysis, in a fully recursive m anner. The algorithm significantly reduces the cost of determining analytic first-order sensitivity information for large-scale, tree-type multi-rigid -body dynamic systems. Qualitative and quantitative validation on the opera tional requirement of the present method are made through analytical means and empirical studies.