Due to the inherent $\pi $ -phase constraint in phase unwrapping algorithms, the dynamic strain range of phase-sensitive optical time domain reflectometry ( $\Phi $ -OTDR) is significantly limited. $\Phi $ -OTDR with modified architectures have proven effective in expanding the dynamic strain range. However, such methods still subject to the $\pi $ -phase constraint, resulting in inconsistent enhancement of the dynamic strain range across the frequency response bandwidth. This work innovatively proposes a least squares linear programming phase unwrapping (ls-LPPU) algorithm, which determines the wrapping orders under large dynamic strains by minimizing the squared optical path difference between two wavelengths, thereby achieving temporally independent phase unwrapping. Experimental results demonstrate that the proposed method achieves precise restoration of large dynamic strains ranging from 13.8 to $44.6~\mu \varepsilon $ , representing an enhancement of at least 90-fold. Furthermore, under a pulse repetition frequency of 10 kHz, error-free recovery of large dynamic strains with frequencies spanning 0.9–4.5 kHz is realized. The ls-LPPU algorithm facilitates the restoration of large dynamic strains by directly obtaining the phase wrapped orders. Meanwhile, its temporally independent characteristic eliminates the $\pi $ -phase constraint, achieving the decoupling of dynamic strain extension and frequency response bandwidth.

A novel method for recognizing acoustic signals of partial discharge optical fiber sensors using the time-frequency phase composition property is proposed in this paper. The method involves obtaining the Wigner–Ville time-frequency distribution for acoustic signals from partial discharge optical fiber sensors through the Cohen bilinear time-frequency transformation, which provides a high time-frequency resolution. The Wigner–Ville distribution could reflect the insulation defect-related properties in detail, owing to the fact that the intensity distribution in the time domain and energy distribution in the frequency domain is seriously influenced by medium dispersion and acoustic propagation. The time-frequency phase composition property is implemented by combining the Wigner–Ville distributions at different phases in the power cycle, which comprehensively represent the characteristics of the acoustic signals from partial discharge optical fiber sensors. A Vision Transformer with an attention block is introduced to identify the acoustic signals of partial discharge sensors. The attention block ensures that the neural network assigns more weight to the energy concentration areas in the extracted acoustic features. To validate the proposed approach, experiments are conducted to identify the acoustic signals of partial discharge optical fiber sensors. The proposed method achieves an impressive accuracy of 99.56% on three group testing sets. This indicates that the proposed approach is a promising method for identifying acoustic signals of partial discharge sensors to detect various insulation defects using acoustic emission feature analysis.