Stability preservation for parametric model order reduction by matrix interpolation
Stability preservation for parametric model order reduction by matrix interpolation
复制标题
通过矩阵插值实现参数模型降阶的稳定性保持
DOI：
10.1109/ecc.2014.6862564
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
B. Lohmann
中科院分区：
文献类型：
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作者：
M. Geuß;H. Panzer;Thomas Wolf;B. Lohmann
针对高阶线性时不变系统，提出了一种在整个参数范围内通过矩阵插值来保持参数模型降阶稳定性的方法。第一步，针对一组离散参数向量计算高维参数相关系统的系统矩阵。通过基于投影的约简方法来约简局部高阶系统。其次，通过求解低维李亚普诺夫方程使简化模型收缩。第三，将它们转换为一组一致的广义坐标，以获得准确的插值结果。这三个步骤都是离线完成的，并存储本地系统的矩阵。最后，可以通过对局部低维模型的预先计算矩阵进行插值来在线计算新参数向量的稳定降阶模型。我们证明这种方法的工作原理没有任何关于大型模型结构的限制条件，并且适合实时应用。
A method to preserve stability in parametric model order reduction by matrix interpolation for the whole parameter range is proposed for high-order linear time-invariant systems. In the first step, system matrices of the high-dimensional parameter-dependent system are computed for a discrete set of parameter vectors. The local high-order systems are reduced by a projection-based reduction method. Secondly, the reduced models are made contractive by solving low-dimensional Lyapunov equations. Thirdly, they are transformed into a consistent set of generalized coordinates for accurate interpolation results. These three steps are done offline and the matrices of the local systems are stored. Finally, a stable reduced order model for a new parameter vector can be calculated online by interpolating the precomputed matrices of the local low-dimensional models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications.