A regularization method for solving dynamic problems with singular configuration

Abstract

In the simulation process for multi-body systems, the generated redundant constraints will result in ill-conditioned dynamic equations, which are not good for stable simulations when the system motion proceeds near a singular configuration. In order to overcome the singularity problems, the paper presents a regularization method with an explicit expression based on Gauss principle, which does not need to eliminate the constraint violation after each iteration step compared with the traditional methods. Then the effectiveness and stability are demonstrated through two numerical examples, a slider-crank mechanism and a planar four-bar linkage. Simulation results obtained with the proposed method are analyzed and compared with augmented Lagrangian formulation and the null space formulation in terms of constraints violation, drift mechanical energy and computational efficiency, which shows that the proposed method is suitable to perform efficient and stable dynamic simulations for multi-body systems with singular configurations.

An Electromagnetic Load Identification Method Based on the Polynomial Structure Selection Technique

“…Te regularization method [26,27] is usually used to eliminate ill-posed problem in identifying the coefcients a of Chebyshev orthogonal polynomials in equation ( 15) combined the known ratio λ together with the signifcant mode shape matrix ϕ * o and equivalent amplitude coefcients r * i . To examine the identifcation accuracy, the correlation degree CC and the total error RE between the real F r and identifed load 􏽥 F r are defned as shown in the following equation:…”