基于时域误差限的大规模系统自适应模型降阶

为满足解大规模动态系统常微分方程组对精度和速度权衡的要求,提出了一种基于误差限的大规模系统自适应模型降阶方法,其中方法的误差分析基于时域最大误差限,降阶方法基于SVD-Krylov子空间的方法.方法既考虑了算法的复杂性,又保证了算法的精度.通过对典型实例分析,结果表明该方法在给定相对误差限10~(-4)下得出的降阶阶数在不同频率下都能给出很好的近似精度,低频1~10Hz平均相对误差为1.1812×10~(-5),高频1~10GHz平均相对误差为5.6408×10~(-5),即在很宽的频率范围内都能满足精度要求.

Large-Scale System Adaptive Model Order Reduction Based on the Time Domain Error Bound

To meet the demand of the solution in large-scale dynamic system of ordinary differential equation for speed and accuracy,we put forward an adaptive model order reduction method based on the error bound.The method uses time domain error bound and SVD-Krylov model order reduction method.This method takes into account both of the complexity and the accuracy of the algorithm.By the analysis of the typical example,the results show that the reduced system generated by this method can be good approximation to the original system in wide frequency range in given relative error bound 10-4.The approximation results also meet accuracy requirements in a wide frequency range,such as the average relative error is 1.1812 ×10-5 in 1～10Hz and 5.6408 ×10-5 in 1～10GHz.