标题： 约束机械系统的算子推理在降阶建模中的应用 显示英文标题

标题： Application of operator inference to reduced-order modeling of constrained mechanical systems

摘要： 受约束的机械系统出现在许多应用中，例如机器人和其他多体系统的建模。 在这种情况下，运动由微分代数方程（DAE）系统控制，通常具有大型稀疏的系统矩阵。 在计算资源有限的情况下，问题的维度强烈影响系统分析、优化和控制的仿真效果。 因此，我们旨在获得一个简化代理模型，该模型具有少量自由度，能够准确表示原始高维DAE模型的运动和其他重要特性。 经典模型降阶方法通过利用系统矩阵来构建高保真模型到低维子空间的投影。 实际上，动力学方程通常是专有软件产品中不可访问的部分。 在本工作中，我们展示了非侵入式算子推断（OpInf）方法在索引2和3的DAE系统中的应用。 考虑到对于适当的DAE，存在所谓的隐藏流形上的ODE实现，OpInf优化问题直接在降维子空间中提供了给定DAE系统的底层ODE表示。 一个显著的优势是，仅需要压缩形式的DAE解快照即可识别降阶系统矩阵。 通过使用半定规划强制系统算子的对称正定结构，保证了降阶模型的稳定性和可解释性。 数值结果展示了所提出方法在不同受约束机械系统示例中的实现，并针对各种载荷条件进行了测试。 显示英文摘要

摘要： Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse system matrices. The problem dimension strongly influences the effectiveness of simulations for system analysis, optimization, and control, given limited computational resources. Therefore, we aim to obtain a simplified surrogate model with a few degrees of freedom that is able to accurately represent the motion and other important properties of the original high-dimensional DAE model. Classical model reduction methods intrusively exploit the system matrices to construct the projection of the high-fidelity model onto a low-dimensional subspace. In practice, the dynamical equations are frequently an inaccessible part of proprietary software products. In this work, we show an application of the non-intrusive operator inference (OpInf) method to DAE systems of index 2 and 3. Considering the fact that for proper DAEs there exists an ODE realization on the so-called hidden manifold, the OpInf optimization problem directly provides the underlying ODE representation of the given DAE system in the reduced subspace. A significant advantage is that only the DAE solution snapshots in a compressed form are required for identification of the reduced system matrices. Stability and interpretability of the reduced-order model is guaranteed by enforcing the symmetric positive definite structure of the system operators using semidefinite programming. The numerical results demonstrate the implementation of the proposed methodology for different examples of constrained mechanical systems, tested for various loading conditions.