当前位置: X-MOL 学术arXiv.cs.SY › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Non-intrusive Balancing Transformation of Highly Stiff Systems with Lightly-damped Impulse Response
arXiv - CS - Systems and Control Pub Date : 2021-09-21 , DOI: arxiv-2109.10408
Elnaz Rezaian, Cheng Huang, Karthik Duraisamy

Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and lightly-damped systems, a non-intrusive data-driven method is developed for balancing discrete-time systems via the eigensystem realization algorithm (ERA). The advantage of ERA for balancing transformation makes full-state outputs tractable. Further, ERA enables balancing despite stiffness, by eliminating computation of balancing modes and adjoint simulations. As a demonstrative example, we create balanced ROMs for a one-dimensional reactive flow with pressure forcing, where the stiffness introduced by the chemical source term is extreme (condition number $10^{13}$), preventing analytical implementation of BT. We investigate the performance of ROMs in prediction of dynamics with unseen forcing inputs and demonstrate stability and accuracy of balanced ROMs in truly predictive scenarios whereas without ERA, POD-Galerkin and Least-squares Petrov-Galerkin projections fail to represent the true dynamics. We show that after the initial transients under unit impulse forcing, the system undergoes lightly-damped oscillations, which magnifies the influence of sampling properties on predictive performance of the balanced ROMs. The importance of proper sampling is established via sensitivity analysis in a predictive setting.

中文翻译:

具有轻阻尼脉冲响应的高刚度系统的非侵入式平衡变换

平衡截断 (BT) 是一种模型简化方法,它利用坐标变换来保留高度可观察和可到达的特征方向。为了解决应用于高刚性和轻阻尼系统的 BT 的可实现性和可扩展性,开发了一种非侵入式数据驱动方法,用于通过本征系统实现算法 (ERA) 平衡离散时间系统。ERA 在平衡转换方面的优势使全状态输出易于处理。此外,通过消除平衡模式和伴随模拟的计算,ERA 能够实现平衡,而无需考虑刚度。作为示范示例,我们为具有压力强迫的一维反应流创建平衡 ROM,其中化学源项引入的刚度非常大(条件数 $10^{13}$),从而阻止了 BT 的分析实现。我们研究了 ROM 在具有看不见的强制输入的动态预测中的性能,并证明了平衡 ROM 在真正预测场景中的稳定性和准确性,而没有 ERA,POD-Galerkin 和最小二乘法 Petrov-Galerkin 投影无法代表真实的动态。我们表明,在单位脉冲强迫下的初始瞬变之后,系统会经历轻阻尼振荡,这放大了采样特性对平衡 ROM 预测性能的影响。适当抽样的重要性是通过预测设置中的敏感性分析来确定的。POD-Galerkin 和最小二乘 Petrov-Galerkin 投影不能代表真实的动态。我们表明,在单位脉冲强迫下的初始瞬变之后,系统会经历轻阻尼振荡,这放大了采样特性对平衡 ROM 预测性能的影响。适当抽样的重要性是通过预测设置中的敏感性分析来确定的。POD-Galerkin 和最小二乘 Petrov-Galerkin 投影不能代表真实的动态。我们表明,在单位脉冲强迫下的初始瞬变之后,系统会经历轻阻尼振荡,这放大了采样特性对平衡 ROM 预测性能的影响。适当抽样的重要性是通过预测设置中的敏感性分析来确定的。
更新日期:2021-09-23
down
wechat
bug