In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses possible, certain use cases such as uncertainty quantification and real time high-precision simulation remain computationally challenging. This motivates the development of reduced order modelling methods, which can reduce the computational toll of simulations relying on mechanistic principles. The majority of existing reduced order modelling techniques involve projection onto linear bases. Such methods are well established for linear systems but when considering nonlinear systems their application becomes more difficult. Targeted schemes for nonlinear systems are available, which involve the use of multiple linear reduction bases or the enrichment of traditional bases. These methods are however generally limited to weakly nonlinear systems. In this work, nonlinear normal modes (NNMs) are demonstrated as a possible invertible reduction basis for nonlinear systems. The extraction of NNMs from output only data using machine learning methods is demonstrated and a novel NNM-based reduced order modelling scheme introduced. The method is demonstrated on a simulated example of a nonlinear 20 degree-of-freedom (DOF) system.

中文翻译：

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在非线性降阶建模中使用非线性正态模式

在许多工程领域，非线性数值分析在支持结构设计和监测方面发挥着越来越重要的作用。虽然不断增加的计算机资源使这种以前令人望而却步的分析成为可能，但某些用例（例如不确定性量化和实时高精度模拟）在计算上仍然具有挑战性。这推动了降阶建模方法的发展，这可以减少依赖于机械原理的模拟的计算成本。大多数现有的降阶建模技术都涉及到线性基的投影。这种方法对于线性系统已经很好地建立了，但是当考虑非线性系统时，它们的应用变得更加困难。非线性系统的目标方案可用，其中涉及使用多个线性还原碱基或传统碱基的富集。然而，这些方法通常限于弱非线性系统。在这项工作中，非线性正态模式 (NNM) 被证明是非线性系统可能的可逆约简基础。演示了使用机器学习方法从仅输出数据中提取 NNM，并介绍了一种新的基于 NNM 的降阶建模方案。该方法在非线性 20 自由度 (DOF) 系统的模拟示例中得到演示。演示了使用机器学习方法从仅输出数据中提取 NNM，并介绍了一种新的基于 NNM 的降阶建模方案。该方法在非线性 20 自由度 (DOF) 系统的模拟示例中得到演示。演示了使用机器学习方法从仅输出数据中提取 NNM，并介绍了一种新的基于 NNM 的降阶建模方案。该方法在非线性 20 自由度 (DOF) 系统的模拟示例中得到演示。