A hybrid virtual sensing approach for approximating non-linear dynamic system behavior using LSTM networks

Modern Internet of Things solutions are used in a variety of different areas, ranging from connected vehicles and healthcare to industrial applications. They rely on a large amount of interconnected sensors, which can lead to both technical and economical challenges. Virtual sensing techniques aim to reduce the number of physical sensors in a system by using data from available measurements to estimate additional unknown quantities of interest. Successful model-based solutions include Kalman filters or the combination of finite element models and modal analysis, while many data-driven methods rely on machine learning algorithms. The presented hybrid virtual sensing approach combines Long Short-Term Memory networks with frequency response function models in order to estimate the behavior of non-linear dynamic systems with multiple input and output channels. Network training and prediction make use of short signal subsequences, which are later recombined by applying a windowing technique. The frequency response function model acts as a baseline estimate which perfectly captures linear dynamic systems and is augmented by the non-linear Long Short-Term Memory network following two different hybrid modeling strategies. The approach is tested using a non-linear experimental dataset, which results from measurements of a three-component servo-hydraulic fatigue test bench. A variety of metrics in time and frequency domains, as well as fatigue strength under variable amplitudes are used to evaluate the approximation quality of the proposed method. In addition to virtual sensing, the algorithm is also applied to a forward prediction task. Synthetic data are used in a separate study to estimate the prediction quality on datasets of different size.