Nowadays, optimal control and optimal design are two of the most interesting problems in the field of mechanical engineering, and most of the approaches include, in one way or other, a sensitivity analysis.

 

The sensitivity analysis of the dynamics of multibody systems constitutes an important effort in the optimization process and an important amount of the CPU time is consumed in the forward dynamic calculations. Therefore, it is convenient to use the fastest available formulations to solve the dynamics.

 

Several approaches for the sensitivity of the dynamics of multibody systems have been developed, from the basic numerical calculation through real or complex finite differences to fast and complex analytical solutions, or automatic differentiation techniques. Accuracy plays an important role, since poor sensitivity accuracy will usually lead to slow convergence in the optimization process or even to non-optimal solutions.

 

Numerical perturbations constitute a simple method to compute the sensitivity of the dynamics of a mechanism, but it is an expensive technique in terms of computational time, and it can lead to inaccurate results. In general, the analytical calculations are faster and have a higher accuracy, but they are particular for each formulation and a generalization is not always easy to implement. Two analytical sensitivity approaches can be used: the direct differentiation method and the adjoint variable method.

 

With the continuous improvement in the capability of computers, the dynamics of complex mechanisms can be executed very fast, even in real time for relatively large multibody systems. However, the optimization of the dynamics is a more complicated and time demanding problem and two aspects must be considered: the time consumed by the sensitivity analysis and the accuracy of this sensitivity. The analytical calculations for the sensitivity analysis offer the best results in these two aspects, since these calculations are usually the fastest and have the best possible accuracy for a given dynamics.

 

Some years ago, the analytical sensitivity analysis of multibody systems solved with a global index-3 augmented Lagrangian formulation with projections of velocities and accelerations (ALI3-P) in natural coordinates, was presented with very good results in terms of computational time and accuracy. In this work, the analytical direct sensitivity for topological semi-recursive ALI3-P formulations is derived and the resulting sensitivity formulations are validated by means of a set of examples, including a five-bar linkage and a spatial slider-crank with springs. The approaches described in this work are implemented as general sensitivity formulations in the multibody simulation library MBSLIM.


Direct Sensitivity Analysis of Multibody Systems Modeled With Relative Coordinates Using an Augmented Lagrangian Formulation With Projections.

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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