Assessment of hybrid machine learning models for non-linear system identification of fatigue test rigs

TL;DR

This work tackles non-linear system identification for fatigue test rigs by augmenting traditional frequency response function (FRF) models with windowed Long Short-Term Memory (LSTM) networks to enable fast forward prediction and virtual sensing. Two hybrid schemes are proposed: hybrid 1 adds an LSTM-predicted non-linear correction to FRF predictions, while hybrid 2 feeds the FRF baseline into the LSTM as additional input, often yielding superior accuracy. Evaluations on a servo-hydraulic fatigue bench show that hybrid 2 consistently improves prediction accuracy and fatigue-damage estimation (e.g., Multi-Rain metrics) over FRF or pure LSTM models, especially under variable-amplitude service loads; boundary-region data remain challenging for neural networks. Overall, the hybrid FRF-LSTM approach enables accurate, data-efficient non-linear predictions and offers a pathway to reduce experimental campaigns and energy consumption in fatigue testing, with the dataset and methods reproducible for further research ($N = K \, S_a^{-k}$).

Abstract

The prediction of system responses for a given fatigue test bench drive signal is a challenging task, for which linear frequency response function models are commonly used. To account for non-linear phenomena, a novel hybrid model is suggested, which augments existing approaches using Long Short-Term Memory networks. Additional virtual sensing applications of this method are demonstrated. The approach is tested using non-linear experimental data from a servo-hydraulic test rig and this dataset is made publicly available. A variety of metrics in time and frequency domains, as well as fatigue strength under variable amplitudes, are employed in the evaluation.

Figures (11)

• Figure 1: LSTM networks are composed of memory blocks, which process information using the inner cell state $\underline{\boldsymbol c}$. This inner state can be updated, forgotten or used to create the block output $\underline{\boldsymbol h}$ depending on the block input at the current time step $\underline{\boldsymbol x} (t_i)$ and the previous output $\underline{\boldsymbol h} (t_{i-1})$. All operations related to the inner state are carried out by respective gates $G$ and the network $N$, whose parameters are learned from a dataset during training.
• Figure 2: Individual subsequence predictions (top) are combined as a weighted sum using corresponding window functions (center). As a consequence, predictions for long sequences (bottom) resulting from measurement data can be realized.
• Figure 3: The hybrid modelling scheme hybrid 1 uses an LSTM network to apply a nonlinear correction of the linear FRF model prediction. In hybrid 2, the LSTM network is instead provided with both the original input data and the corresponding FRF model output, so that the linear solution can be incorporated into the prediction.
• Figure 4: The proposed hybrid models can be applied to different signal estimation problems. In forward prediction (FP), the output sensor data is estimated based on the drive signal, which controls the system excitation. In a virtual sensing task (VS), one or more output sensors are estimated from the remaining measurements. The assignment of input and output data during model parameterization changes depending on the use case.
• Figure 5: A three-component servo-hydraulic test bench (a) for the fatigue assessment of suspension hydro-mounts (b) is used to generate an experimental dataset.