The analysis of sensor data in nonlinear dynamical systems plays a fundamental role in a variety of modern engineering problems like Fatigue Analysis and Predictive Maintenance. In many applications, the accurate approximation of sensor signals supports and complements experimental efforts in order to accelerate the development process and conserve resources. Virtual sensing techniques aim to replace physical sensors in a system by using the data from available sensors to estimate additional unknown quantities of interest. Forward prediction estimates the system response for a given drive signal during the commission of component test rigs. Data-driven approaches can be convenient tools for forward prediction and virtual sensing, as they only require a sufficiently large dataset of the desired input and output quantities for the purpose of model parametrization. The presented approach explores two hybrid modeling strategies, which combine Frequency Response Function models with Long Short-Term Memory networks to approximate the behavior of non-linear dynamic systems with multiple input and output channels. The proposed method utilizes short subsequences of signals to carry out model training and prediction. Long sequence estimations are generated by combining the individual subsequence predictions using a windowing technique. Our approach is tested on a large, non-linear experimental dataset, obtained from a servo hydraulic fatigue test bench. To enable a comprehensive evaluation of the model quality, both hybrid modeling approaches are compared on virtual sensing and forward prediction tasks using multiple error metrics relevant to fatigue analysis.