论文标题
在应用生成对抗网络中用于非线性模态分析
On the application of generative adversarial networks for nonlinear modal analysis
论文作者
论文摘要
线性模态分析是设计和分析结构的有用工具。但是，非线性模态分析的综合基础尚待开发。在当前的工作中，提出了机器学习方案，以进行非线性模态分析。该方案的重点是定义从潜在的“模态”空间到自然坐标空间的一对一映射，同时还施加了模式形状的正交性。该映射是通过使用最近开发的周期符合的生成对抗网络（Cycle-GAN）以及针对维持所需正交性的神经网络组装来实现的。该方法对来自具有立方非线性和不同数量的自由度的结构的模拟数据进行了测试，并从具有柱状非线性的实验性三级自由度设置的数据中进行了测试。结果揭示了该方法在分离“模式”方面的效率。该方法还提供了非线性叠加函数，在大多数情况下，该函数的精度非常好。
Linear modal analysis is a useful and effective tool for the design and analysis of structures. However, a comprehensive basis for nonlinear modal analysis remains to be developed. In the current work, a machine learning scheme is proposed with a view to performing nonlinear modal analysis. The scheme is focussed on defining a one-to-one mapping from a latent `modal' space to the natural coordinate space, whilst also imposing orthogonality of the mode shapes. The mapping is achieved via the use of the recently-developed cycle-consistent generative adversarial network (cycle-GAN) and an assembly of neural networks targeted on maintaining the desired orthogonality. The method is tested on simulated data from structures with cubic nonlinearities and different numbers of degrees of freedom, and also on data from an experimental three-degree-of-freedom set-up with a column-bumper nonlinearity. The results reveal the method's efficiency in separating the `modes'. The method also provides a nonlinear superposition function, which in most cases has very good accuracy.
