Predictive modeling of nonlinear system responses using the Residual Improvement Deep Learning Algorithm (RIDLA)

Predicting specific location responses in nonlinear systems under random excitations is crucial for structural health monitoring, optimization design, and safety assessment. Traditional sensor-based response measurements face challenges due to limitations in quantity and installation positions, while nonlinear time history analysis suffers from high computational costs and modeling time. Simplified regression equations used in engineering often lack accuracy. This study introduces a novel Residual Improvement Deep Learning Algorithm (RIDLA) to construct high-precision prediction models for nonlinear systems subjected to random excitations. RIDLA leverages Long Short-Term Memory (LSTM) neural networks to capture nonlinear relationships in time series and iteratively improve model accuracy through interactive training with measured responses and computed residuals. This approach effectively predicts time history responses of nonlinear systems under random excitations. RIDLA’s performance is validated by predicting responses in two typical nonlinear systems: a 6-DOF nonlinear oscillator system and the interface force of a satellite–rocket connection subjected to random excitations. The results demonstrate that RIDLA provides highly accurate predictions and can be applied to other complex nonlinear systems.