A discrete adjoint gradient approach for equality and inequality constraints in dynamics

IF 2.6 2区 工程技术 Q2 MECHANICS
Daniel Lichtenecker, Karin Nachbagauer
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引用次数: 0

Abstract

The optimization of multibody systems requires accurate and efficient methods for sensitivity analysis. The adjoint method is probably the most efficient way to analyze sensitivities, especially for optimization problems with numerous optimization variables. This paper discusses sensitivity analysis for dynamic systems in gradient-based optimization problems. A discrete adjoint gradient approach is presented to compute sensitivities of equality and inequality constraints in dynamic simulations. The constraints are combined with the dynamic system equations, and the sensitivities are computed straightforwardly by solving discrete adjoint algebraic equations. The computation of these discrete adjoint gradients can be easily adapted to deal with different time integrators. This paper demonstrates discrete adjoint gradients for two different time-integration schemes and highlights efficiency and easy applicability. The proposed approach is particularly suitable for problems involving large-scale models or high-dimensional optimization spaces, where the computational effort of computing gradients by finite differences can be enormous. Three examples are investigated to validate the proposed discrete adjoint gradient approach. The sensitivity analysis of an academic example discusses the role of discrete adjoint variables. The energy optimal control problem of a nonlinear spring pendulum is analyzed to discuss the efficiency of the proposed approach. In addition, a flexible multibody system is investigated in a combined optimal control and design optimization problem. The combined optimization provides the best possible mechanical structure regarding an optimal control problem within one optimization.

Abstract Image

动力学中平等和不平等约束的离散邻接梯度法
多体系统的优化需要精确高效的敏感性分析方法。邻接法可能是分析灵敏度的最有效方法,尤其是对于优化变量众多的优化问题。本文讨论了基于梯度的优化问题中动态系统的灵敏度分析。本文提出了一种离散的邻接梯度法,用于计算动态模拟中的等式和不等式约束的敏感性。该方法将约束条件与动态系统方程相结合,通过求解离散邻接代数方程直接计算敏感性。这些离散邻接梯度的计算方法可以很容易地适应不同的时间积分器。本文演示了两种不同时间积分方案的离散邻接梯度,突出了其高效性和易用性。所提出的方法尤其适用于涉及大规模模型或高维优化空间的问题,在这些问题中,通过有限差分计算梯度的计算量可能非常大。研究了三个例子来验证所提出的离散邻接梯度方法。对一个学术实例的敏感性分析讨论了离散临界变量的作用。分析了非线性弹簧摆的能量优化控制问题,讨论了所提方法的效率。此外,还研究了柔性多体系统的优化控制和设计组合优化问题。在一次优化中,结合优化为最优控制问题提供了最佳的机械结构。
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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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