The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the particular case of material nonlinearity. A physics-based parametric representation is developed, incorporating dependencies on system properties and/or excitation characteristics. The pMOR formulation relies on use of a Proper Orthogonal Decomposition applied to a series of snapshots of the nonlinear dynamic response. A new approach to manifold interpolation is proposed, with interpolation taking place on the reduced coefficient matrix mapping local bases to a global one. We demonstrate the performance of this approach firstly on the simple example of a shear-frame structure, and secondly on the more complex 3D numerical case study of an earthquake-excited wind turbine tower. Parametric dependence pertains to structural properties, as well as the temporal and spectral characteristics of the applied excitation. The developed parametric Reduced Order Model (pROM) can be exploited for a number of tasks including monitoring and diagnostics, control of vibrating structures, and residual life estimation of critical components.

中文翻译：

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非线性参数模型降阶的局部基逼近方法

工程系统的有效状态评估需要将高保真模型与从系统“原样”状态提取的数据相结合。为了完成这项任务，本文为非线性结构动力学和材料非线性的特殊情况实施了参数化模型降阶 (pMOR) 方案。开发了基于物理的参数表示，结合了对系统属性和/或激励特性的依赖。pMOR 公式依赖于对一系列非线性动态响应快照应用的适当正交分解的使用。提出了一种流形插值的新方法，插值发生在将局部基映射到全局基的约简系数矩阵上。我们首先在剪切框架结构的简单示例上展示了这种方法的性能，其次在地震激发的风力涡轮机塔架的更复杂的 3D 数值案例研究中展示了这种方法的性能。参数依赖性与结构特性以及所施加激励的时间和光谱特性有关。开发的参数化降阶模型 (pROM) 可用于许多任务，包括监测和诊断、振动结构的控制以及关键部件的剩余寿命估计。