PARAFAC Decomposition for Ultrasonic Wave Sensing of Fiber Bragg Grating Sensors: Procedure and Evaluation

Ultrasonic wave-sensing technology has been applied for the health monitoring of composite structures, using normal fiber Bragg grating (FBG) sensors with a high-speed wavelength interrogation system of arrayed waveguide grating (AWG) filters; however, researchers are required to average thousands of repeated measurements to distinguish significant signals. To resolve this bottleneck problem, this study established a signal-processing strategy that improves the signal-to-noise ratio for the one-time measured signal of ultrasonic waves, by application of parallel factor analysis (PARAFAC) technology that produces unique multiway decomposition without additional orthogonal or independent constraints. Through bandpass processing of the AWG filter and complex wavelet transforms, ultrasonic wave signals are preprocessed as time, phase, and frequency profiles, and then decomposed into a series of conceptual three-way atoms by PARAFAC. While an ultrasonic wave results in a Bragg wavelength shift, antiphase fluctuations can be observed at two adjacent AWG ports. Thereby, concentrating on antiphase features among the three-way atoms, a fitting atom can be chosen and then restored to three-way profiles as a final result. An experimental study has revealed that the final result is consistent with the conventional 1024-data averaging signal, and relative error evaluation has indicated that the signal-to-noise ratio of ultrasonic waves can be significantly improved.