A Symbolic Approach to Compute a Null-Space Basis in the Projection Method
A Symbolic Approach to Compute a Null-Space Basis in the Projection Method
复制标题
投影法中计算零空间基的符号方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
N. Pham
中科院分区：
文献类型：
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作者：
M. Giesbrecht;N. Pham
本文提出了一种符号-数值混合方法，用于求解与多体力学系统相关的参数化微分-代数约束方程的所谓投影法。这种方法的一个主要问题是计算多元有理函数矩阵的零空间基，即符号约束矩阵的雅可比矩阵。就输出的绝对大小而言，纯粹的符号方法是站不住脚的，而纯粹的数字方法不能提供不指定某些或所有参数的灵活性。相反，我们提出了一种混合方法，即进行符号预条件，然后用直线C代码表示零空间基，即黑盒零空间基。我们以一种数值敏感的方式来实现这一点，并展示了我们的黑盒在几乎所有参数设置下都是数值稳健的。对典型多体模型输入的实验结果验证了这一点。
We present a hybrid symbolic-numeric approach for the so-called projection method for solving the parameterized differential-algebraic constraint equations associated with multibody mechanical systems. A primary problem in this approach is computing a null-space basis of a matrix of multivariate rational functions, the Jacobian of the symbolic constraint matrix. A purely symbolic approach is untenable in terms of the sheer size of the output, whereas a purely numerical approach does not offer the flexibility of leaving some or all parameters unspecified. Instead we propose a hybrid approach, which does a symbolic preconditioning, followed by representing the null-space basis by straight-line C code, i.e., a black-box null-space basis. We do this in a numerically sensitive way, and show that our black box is numerically robust at almost all parameter settings. This is verified by experimental results on inputs from typical multibody models.