Probability density evolution for time-varying reliability assessment of wing structures

Reliability evaluation is a key factor in serviceability and safety analysis of air vehicles. Structural health monitoring methods have grown to a degree of maturity in many industries. However, there is a challenging interest to tie in SHM with reliability assessment. In this respect, consideration of stochastic structural dynamics with SHM data and random loadings opens a new chapter in failure prevention. The current study focuses on the stochastic behavior of structures as a way to relate SHM data with reliability. In this respect, uncertain factors such as atmospheric turbulence, structural parameters, and sensor outputs are considered in the process of reliability assessment. Firstly, an experimental evaluation is conducted using a simple cantilevered beam. Subsequently, system identification is weaved in with a probability density evolution equation for calculating the reliability of a wing structural component. Numerical simulations demonstrate that structural reliability of a typical WSC can be effectively evaluated. The proposed scheme paves the way for new SHM research topics such as online life prediction and reliability based failure prevention

A Deep Learning Approach for the solution of Probability Density Evolution of Stochastic Systems

Derivation of the probability density evolution provides invaluable insight into the behavior of many stochastic systems and their performance. However, for most real-time applica-tions, numerical determination of the probability density evolution is a formidable task. The latter is due to the required temporal and spatial discretization schemes that render most computational solutions prohibitive and impractical. In this respect, the development of an efficient computational surrogate model is of paramount importance. Recent studies on the physics-constrained networks show that a suitable surrogate can be achieved by encoding the physical insight into a deep neural network. To this aim, the present work introduces DeepPDEM which utilizes the concept of physics-informed networks to solve the evolution of the probability density via proposing a deep learning method. DeepPDEM learns the General Density Evolution Equation (GDEE) of stochastic structures. This approach paves the way for a mesh-free learning method that can solve the density evolution problem with-out prior simulation data. Moreover, it can also serve as an efficient surrogate for the solu-tion at any other spatiotemporal points within optimization schemes or real-time applica-tions. To demonstrate the potential applicability of the proposed framework, two network architectures with different activation functions as well as two optimizers are investigated. Numerical implementation on three different problems verifies the accuracy and efficacy of the proposed method