In this study we investigate signal transformation using Polynomial Artificial Neural Networks and their challenges in training. Measuring technologies basing on Guided Ultrasonic Waves (GUW) can be used for Structural Health Monitoring (SHM), e.g., in plate like composite structures. Feature extraction from such signals can be difficult due to missing closed analytic models. In recent years Machine learning (ML) algorithms are increasingly applied to GUW technologies to predict the presence and location of damage.
A major challenge is providing sufficient training data, as experimental recording of measuring data with a broad parameter space is a time-intensive operation with surface bonded transducers, since the transducer have to be attached and detached at different positions.  
A possible solution to this challenge is the use of scanning methods like air-coupled measured GUWs, which allow a fast measurement at different sensing positions. In SHM bonded transducers are typically used, so that a transformation between both methods is necessary. So far, it was shown in previous work [1] that the transformation is generally possible, but that due to the complexity of GUW signals, also prone to signal generation errors.
These errors can probably be attributed to the fact that the GUW signals consists of a superposition of cosine functions, which cannot be well approximated with classic activation functions like exponential-sigmoid and hyperbolic tangent functions.
In the present work the class of Polynomial Artificial Neural Networks (PANN) [2] is introduced to optimize the transformation process, were the polynomial coefficients are trainable parameters. Sigmoid and tanh functions are widely used due to their bound gradient, essential for stability in gradient-based training methods. Polynomial functions do not have a bound gradient. For that the coefficients are set before the model training in a way that the polynomials fit a GUW partially, e.g. ascending and descending flank of the wave. This facilitates the training of the model and minimizes the problem of a not bound gradient. We assume (but to be proven) that the signals of both measurement techniques should have a common feature vector, which can be approximated with an encoder-decoder architecture providing the transformation function between air coupled and surface bond GUW signals.   

[1]    Polle, C.; Bosse, S.; May, D. Transformation of Guided Ultrasonic Wave Signals from Air Coupled to Surface Bounded Measurement Systems with Machine Learning Algorithms for Training Data Augmentation., in Proceedings of the 11th International Electronic Conference on Sensors and Applications, 26–28 November 2024, MDPI: Basel, Switzerland, doi:10.3390/ecsa-11-20448
[2]    Jun Zhou, Huimin Qian, Xinbiao Lu, Zhaoxia Duan, Haoqian Huang, Zhen Shao, Polynomial    activation neural networks: Modeling, stability analysis and coverage BP-training, Neurocomputing, Volume 359, 2019, Pages 227-240, ISSN 0925-2312, https://doi.org/10.1016/j.neucom.2019.06.004.