Neural ordinary differential equation for sequential optimal design of fatigue test under accelerated life test analysis

The literature on fatigue analysis can be classified into parametric or analytic approaches that try to model the fatigue data with a specific distribution, such as the optimal sequential Accelerated Life Test (ALT), considering the fatigue life cycle and stress amplitude. To the best of our knowledge, no work incorporates the accelerated lifecycle distribution of fatigue data into the parametric approach, nor does it incorporate the complex relationships in the elastic–plastic behavior of the material in the ALT models using the sequential optimal test design. In this work, we define an optimization model that takes both parametric and analytic solutions into account and minimizes the negative log-likelihood of the ALT model when the fatigue lifecycle follows a lognormal distribution for several constraints extracted from physical attributes of elastic–plastic models and assumptions of the ALT approach, where model-based optimization is sequentially updated. We utilized a model-based deep neural network solution based on the differential equation of the analytical model to solve the optimization problem. Our simulation results based on empirical data prove the practical implementation of our approach and validate the result for obtaining the optimal test plan and estimated parameters of the ALT and elastic–plastic model.