Physics-informed neural network classification framework for reliability analysis

Reliability analysis is crucial for quantitatively evaluating structural safety amidst uncertainties, laying the foundation for reliability-based design optimization aimed at augmenting structural reliability and reducing economic expenditures, thereby offering substantial engineering benefits. However, performing reliability analysis on intricate structures, especially those requiring time-intensive finite element models, presents a formidable challenge. This study develops an innovative physics-informed neural network classification (PINNC) model to tackle this issue. In the PINNC model, the loss associated with the structural output state (i.e., safety or failed state) is defined as classification loss. Additionally, the structural output value (i.e., actual structural response) is treated as critical physical information, with its associated loss termed as physical loss. To facilitate a separate calculation of physical loss and classification loss, a parametric sigmoid activation function is used, establishing a link between the structural output value and the structural output state. The total loss is calculated as a weighted sum of both physical and classification losses. Unlike conventional neural network classification models that solely focus on classification loss, the PINNC model integrates both physical and classification losses, markedly improving the model's efficacy in structural reliability analysis. Moreover, an adaptive framework is developed to incrementally include samples proximal to the limit state surface as new training data, thereby reinforcing the PINNC model's computational precision. The effectiveness of the proposed PINNC framework in overcoming reliability analysis challenges is demonstrated through various applications.