微分代数系统中分块快速指标约简的启发式算法

A Heuristic Algorithm for Block Fast Index Reduction in Differential Algebraic Systems

为了高效地优化多领域统一建模仿真软件中稀疏微分代数方程的指标约简技术,提出了一种分块快速指标约简的启发式算法。它的主要思想是将微分代数方程的符号矩阵进行块状上三角化,然后沿每一独立块状上三角化的子符号矩阵对角线方向,由上往下依次对其每一对角子方阵运用含参数Pryce方法进行指标约简。大量数值实验结果表明,分块快速指标约简方法可以求出微分代数方程的最优偏移向量,其效率明显优于Pryce方法的效率,效率提高倍数与对角子方阵块数成正相关。进一步以数控冲床为例,对其微分代数方程采用分块快速指标约简算法进行指标约简,验证了该方法高效地解决了较大规模高指标微分代数方程的指标约简问题,便捷地获得了该系统的最优偏移向量等结构信息。

In order to optimize the index reduction technology of sparse differential algebraic equations(DAEs) from multi-domain unified modeling software,a heuristic algorithm for block fast index reduction method(BFIRM) was proposed.The main principle of BFIRM is to do block triangularization of DAEs' signature matrix,then to use Pryce method with parameters to process diagonal subsquare-matrix in block triangulated signature matrix from top to bottom in sequence.A large number of numerical experiment results showed that BFIRM can solve the canonical offsets vectors of sparse DAEs efficiently.And the reduction efficiency positively correlates with the number of the diagonal blocks.Moreover,to take CNC punch machine tool as an example,its DAEs was reduced by the BFIRM.This method was verified effectively in reducing the index of large-scale DAEs with high index and easily got DAEs' structural information,such as canonical offsets vectors.