Deep learning-based position detection for hydraulic cylinders using scattering parameters

Position detection of hydraulic cylinder pistons is crucial for numerous industrial automation applications. A typical traditional method is to excite electromagnetic waves in the cylinder structure and analytically solve the piston position based on the scattering parameters measured by a sensor. The core of this approach is a physical model that outlines the relationship between the measured scattering parameters and the targeted piston position. However, this physical model has shortcomings in accuracy and adaptability, especially in extreme conditions. To address these limitations, we propose machine learning and deep learning-based methods to learn the relationship directly in a data-driven manner. As a result, all deep learning models in this paper consistently outperform the physical one by a large margin. We further deliberate on the choice of models based on domain knowledge and provide in-depth analyses combining model performance with real-world physical characteristics. Specifically, we use Convolutional Neural Network (CNN) to discover local interactions of input among adjacent frequencies, apply Complex-Valued Neural Network (CVNN) to exploit the complex-valued nature of electromagnetic scattering parameters, and introduce a novel technique named Frequency Encoding to add weighted frequency information to the model input. The combination of these techniques results in our best-performing model, a complex-valued CNN with Frequency Encoding, which exhibits substantial improvement in accuracy with an error reduction of 1/12 compared to the traditional physical model.