Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations

Varela, Álvaro López; Sandu, Corina; Sandu, Adrian; Dopico, Domingo Calvo

doi:10.1007/s11044-023-09911-x

Multibody Syst Dyn

2023

DOI: 10.1007/s11044-023-09911-x

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Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations

Álvaro López Varela

Corina Sandu

Adrian Sandu

et al.

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2024

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Cited by 2 publications

References 29 publications

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

Lichtenecker,

Nachbagauer

2024

Multibody Syst Dyn

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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.

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

Lichtenecker,

Nachbagauer

2024

Multibody Syst Dyn

View full text Add to dashboard Cite

show abstract

Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

Verulkar,

Sandu,

Sandu

et al. 2024

Multibody Syst Dyn

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Real-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the gradient-based optimization methodology for multibody dynamic systems with joint friction using a direct sensitivity approach. The Brown–McPhee model has been used to characterize the joint friction in the system. This model is suitable for the study due to its accuracy for dynamic simulation and its compatibility with sensitivity analysis. This novel methodology supports codesign of the multibody system and its controller, which is especially relevant for applications like robotics and servo-mechanical systems, where the actuation and design are highly dependent on each other. Numerical results are obtained using a software package written in Julia with state-of-the-art libraries for automatic differentiation and differential equations. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applications.

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Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations

Cited by 2 publications

References 29 publications

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

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

Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

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