Low-dimensional dynamical models of structures with uncertain boundaries via a hybrid knowledge- and data-driven approach

Knowledge-driven modeling of structural dynamics relies heavily on the cognitive abilities of modelers and often struggles to address uncertain boundaries where multiple affecting factors generally exist, especially those currently not well understood. To address the issue, we present a new low-dimensional dynamical modeling approach, integrating data-driven technologies with traditional knowledge-driven methods to model uncertain boundaries and the other parts of the system accordingly. By modeling a flexible beam with one end uncertainly constrained and the other fixed, we fully demonstrate this methodology. The global mode method, an example of modal approaches, is employed to develop a low-dimensional model of the known part of the structure. Meanwhile, the artificial neural network, an example of data-driven methods, is employed to model the uncertain boundary whose effects on the natural characteristics of the system are considered. The simulation results demonstrate that the use of neural networks to develop a surrogate model with uncertain boundary conditions leads to a more accurate dynamical equivalent model when considering the effect of the uncertain boundary on the modal shape of the whole structure. Both theoretical and experimental validations are performed, which show good accuracy of the simulation results obtained from the developed models. Moreover, the models show good generalization capabilities in different excitations and achieve a 92% reduction in computation time compared to finite element models. This work not only lays a solid theoretical foundation but also paves a new way for developing future dynamical modeling techniques of complex and advanced systems.