  In this study, we propose a machine-learning-based approach to identify the
modal parameters of the output-only data for structural health monitoring (SHM)
that makes full use of the characteristic of independence of modal responses
and the principle of machine learning. By taking advantage of the independence
feature of each mode, we use the principle of unsupervised learning, making the
training process of the deep neural network becomes the process of modal
separation. A self-coding deep neural network is designed to identify the
structural modal parameters from the vibration data of structures. The mixture
signals, that is, the structural response data, are used as the input of the
neural network. Then we use a complex loss function to restrict the training
process of the neural network, making the output of the third layer the modal
responses we want, and the weights of the last two layers are mode shapes. The
deep neural network is essentially a nonlinear objective function optimization
problem. A novel loss function is proposed to constrain the independent feature
with consideration of uncorrelation and non-Gaussianity to restrict the
designed neural network to obtain the structural modal parameters. A numerical
example of a simple structure and an example of actual SHM data from a
cable-stayed bridge are presented to illustrate the modal parameter
identification ability of the proposed approach. The results show the
approach's good capability in blindly extracting modal information from system
responses.
