Dual state-parameter estimation of continuous structural systems with physics-informed parallel neural networks

Abstract

Vibration-based structural identification is a common approach to infer structural integrity by, for example, estimating the state of the structural system and the associated model parameters that can then be used to predict performance. To this end, finite element (FE) model updating approaches have been widely employed. However, in the context of continuous systems, FE model updating can be computationally intensive and prone to truncation and numerical quadrature errors in the variational forms. Alternatively, purely data-based identification approaches, for example, artificial neural networks (NNs), have been suggested, yet such methods have been shown to be susceptible to overfitting. To overcome these challenges, this paper develops and demonstrates a physics-informed parallel neural networks (PIPNNs) framework for the purpose of solving dual state-parameter estimation problems of continuous structural systems that can be represented by a system of partial differential equations (PDEs). Specifically, the governing PDEs and associated continuity and equilibrium conditions of the system are embedded as soft constraints into the loss function of the NNs. The PIPNNs learn to approximate the PDEs and the unknown structural parameters by minimizing the physics-informed loss function. In the context of continuous systems, the PIPNNs are used to estimate the unknown structural parameters and then be used to estimate the full state of the system, for example, displacement along a multi-span bridge or a floor system. For general applicability, the supports and boundary conditions that produce discontinuities must be considered in the computational domain. To accomplish this, the computational domain is divided into subdomains, and each subdomain is represented as an individual governing PDE adjoining adjacent subdomains by means of compatibility and equilibrium conditions and solved synchronously by the PIPNNs. As such, each NN provides a unique representation in each subdomain while also satisfying additional constraints of continuity and differentiability at the interface between two subdomains. The framework is verified and validated against an alternative independent model, and its accuracy is assessed through the application to several illustrative examples.