Probability Density Evolution for Time-Varying Reliability Assessment of Wing Structures

Abstract

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.

Time‐varying reliability analysis based on hybrid Kalman filtering and probability density evolution

“…They presented the PDEM formula according to the principle of probability preservation, which allowed for randomness propagations in dynamic structures. The PDEM has received increasing attention during the recent decade and has been verified via several theoretical and experimental investigations 41,42 . The applicability of the PDEM has also been validated through comparisons with other methods, such as the Monte Carlo simulation of the reliability assessment of complex structures 43 .…”

“…The PDEM has received increasing attention during the recent decade and has been verified via several theoretical and experimental investigations. 41,42 The applicability of the PDEM has also been validated through comparisons with other methods, such as the Monte Carlo simulation of the reliability assessment of complex structures. 43 Although the PDEM has facilitated the analysis of complex and nonlinear stochastic structures, it still requires an efficient method to solve the equations of motion of structural systems to predict the time-varying derivative of the structural response, which is the PDEM input.…”

A full‐probabilistic cloud analysis for structural seismic fragility via decoupled M‐PDEM

“…The accuracy and effectiveness of PDEM have been rigorously examined through theoretical investigations and numerical validations, 41–43 demonstrating its capability to capture intricate probabilistic behaviors of complex systems. Furthermore, PDEM has found wide applications in various engineering domains, facilitating studies on uncertainty propagation 44–46 and reliability analysis 47–49 . Recent advancements 50 suggest that joint PDFs of multiple response quantities can be realized through the solution of decoupled one‐dimensional Li‐Chen equations, further reducing the computational complexity of time‐variant joint PDF analysis.…”

“…Furthermore, PDEM has found wide applications in various engineering domains, facilitating studies on uncertainty propagation [44][45][46] and reliability analysis. [47][48][49] Recent advancements 50 suggest that joint PDFs of multiple response quantities can be realized through the solution of decoupled one-dimensional Li-Chen equations, further reducing the computational complexity of time-variant joint PDF analysis.…”

A deep learning approach for the solution of probability density evolution of stochastic systems

“…In addition, by deriving the General Density Evolution Equation (GDEE) they proved that in stochastic structural systems, the equations governing the evolution of the probability density can be decoupled by introducing the physical solution of the system [3]. Over the past decade, PDEM has been used successfully in many numerical studies on the stochastic behavior of the structures [4][5][6] and has been validated in experimental studies [7,8]. Although PDEM decouples the probability density evolution PDE in the probability space [9], numerical treatment of the governing equations is still stringent and impractical for real-time applications.…”