Sensitivity Analysis And Design Optimization Of Multibody Systems

Sensitivity analysis and dynamic optimization of multibody systems are very important parts of Computer-Aided Engineering (CAE). The sensitivity analysis provides the dependence of state variables and objective function on design parameters, and acts as the bridge between dynamics analysis and design optimization of multibody systems. Investigations on sensitivity analysis and dynamic optimization can not only enrich the contents of traditional kinematics, dynamics and design optimization of mutltibody systems, but also provide efficient analysis tools for the CAE.The kinematics and dynamics of multibody systems are generally described by a set of non-linear algebraic equations, ordinary differential equations or differential-algebraic equations with high dimensions. The dimensions and complexity of the state sensitivity equations will increase rapidly with increasing of design parameters, which makes sensitivity analysis to be more difficult than traditional multibody system dynamics. Systematic studies on the theories and computational algorithms of sensitivity analysis and dynamic optimization of multibody systems are presented in this paper based on general models of multibody systems and definitions of initial and final time conditions, design objective functions in general forms.For the investigations on sensitivity analysis, we derive the formulations of first and second order sensitivity analysis using direct differentiation method and adjoint variable method based on non-linear algebraic equations of mutibody system kinematics, ordinary differential equations and differential-algebraic equations of mutibody system dynamics firstly. Based on the previous results of first order sensitivity analysis formulations of the direct differentiation method and the adjoint variable method, a novel hybrid method is proposed to second order sensitivity analysis with low complexity and high computation efficiency. Several numerical examples are presented to validate and compare the formulations given in this paper.For the investigations on optimization based on multibody systems, the augmented Lagrange method (ALM) with excellent performance of convergence and stability is modified to optimization task of this paper integrating the first order sensitivity analysis and the second order sensitivity analysis. Steepest descent method, conjugate gradient method and quasi-Newton method based on first order sensitivity analysis and improved Newton method, Greenstadt eigenvalue method, Gill-Murray method and trust region method based on second order sensitivity analysis are used to optimize unconstrained problems during the iterative process of ALM. Algorithm design and analysis of each method are given and compared. For the non-differentiable objective function, maximum entropy method is used to transform it into differentiable objective function, then augmented Lagrange method is use to transform constraint optimization problems into unconstraint optimization problems. Different mathematical models of multibody systems are used to validate and compare the optimization algorithms proposed in this paper through several numerical examples.