Efficient Bridging of Temporal Scales for Fatigue Simulations via a Compressive Sensing Approach

Fatigue damage simulations are computationally demanding due to the high number of simulated load cycles (up to 10^9 for high-cycle fatigue, HCF) and the non-linear nature of the system of equations in the context of finite element analysis (FEA). For conventional approaches, the Shannon–Nyquist theorem, established in the signal-processing community, prescribes the treatment of damage evolution for cyclic load sequences according to the highest excitation frequency. This results in expensive demands in terms of computation time and data storage.

The compressive sensing (CS) paradigm is widely applied in signal processing for the recovery of full time trajectories from sparse measurements in time. For engineering problems, CS approaches and ℓ1-norm minimization techniques for underdetermined systems of equations have emerged for a variety of applications in structural health monitoring, uncertainty modeling under incomplete data, and efficient uncertainty propagation in engineering mechanics.

The objective of this project is to reduce computational costs for fatigue damage simulations by developing a reduced-order model in both space and time. Established non-intrusive POD reduced-basis methods are investigated and applied for spatial model-order reduction. The compressive sensing approach is thoroughly investigated for its ability to circumvent the Shannon–Nyquist theorem and thereby significantly reduce the required number of simulated load cycles. Only individual load cycles are simulated with sparse temporal sampling, and the full damage evolution is recovered by constructing an inverse compressive sensing approach.

This project builds upon prior work in reduced-order modeling for fatigue damage simulations that employed cycle-jumping and intrusive LATIN–PGD methods. In contrast, the current research utilizes non-intrusive ROM techniques combined with compressive sensing for sparse recovery to enable fast time-domain predictions of damage evolution under cyclic loading.