The frequency division multiplexing (FDM) is an effective method to improve the detection ability of high-frequency disturbance in phase-sensitive optical time domain reflectometer (ϕ-OTDR). However, as the probe channels increase, crosstalk between channels will be generated. As a result, the recovery phase signal-to-noise ratio (SNR) will be deteriorated, which will reduce the detection capability of ϕ-OTDR. Therefore, a novel method for suppressing crosstalk noise by compressed sensing under multi-frequency ϕ-OTDR is proposed in this paper. The band-limited characteristics of vibration are deeply analyzed, and the frequency domain is chosen as the sparse domain. Noise without sparsity is discarded in the compression process. Furthermore, the noise cannot be recovered in the reconstruction process which uses the critical information containing the global property of phase signal. Consequently, the influence of crosstalk noise is reduced effectively. In experiments, compared with the restored signals without the proposed method, the average SNRs of the reconstructed 12 kHz sinusoidal vibration are respectively enhanced by 18.57 dB, 40.47 dB, and 41.67 dB in the sensing system with 6, 7, and 8 channels. In addition, the 24 kHz triangular wave signal and the disturbance composed of several different frequencies with random amplitudes can be detected and reconstructed. The proposed crosstalk noise suppression method provides a potential choice for ϕ-OTDR performance enhancement.

In order to suppress the phase distortion caused by fading in phase-sensitive optical time-domain reflectometer ( $\varphi $ -OTDR) system, a new multi-resolution phase compensation algorithm is proposed in this paper. When the intensity of the beat signal approaches the system floor noise, the phase variation will gradually follow the uniform distribution, and fading occurs. The fading region in the spatiotemporal phase plane would be determined subsequently by synthesizing the differential section intensity. The redundancy and local correlation of the phase plane is thoroughly utilized by the patch searching algorithm in multi-resolution. Hence, the marked fading region would be compensated by the fading free region in the phase plane. The proposed method has been proved and analyzed that the fading can be effectively suppressed in the $\varphi $ -OTDR system in the experiment. The fading region can be accurately compensated whether the disturbance exists. The disturbance can be restructured effectively with SNR of 31.2 dB. Furthermore, the strain resolution was achieved to 7.685 $\text{p}\varepsilon /\surd $ Hz. Therefore, the proposed method provides a promising approach to realizing fading elimination without additional structure in the $\varphi $ -OTDR system.

In order to explore the correlation between meteorological factors and power load changes, as well as the role of these factors in load forecasting, a hybrid load forecasting modeling framework based on quantile Granger causality test and bidirectional long short-term memory (QGCT-BiLSTM) is proposed. The Augmented Dickey–Fuller test (ADF) is used to test the smoothness of the influencing factor series and the load series, and the variables that passed the smoothness test are subjected to QGCT for identification of the characteristic variables with significant causal associations. Furthermore, the BiLSTM model is then constructed using the selected factors to generate load forecasts. Using real data from Fujian, China, we demonstrate that QGCT-based feature screening reduces forecasting errors by an average of 34.96%, where the RMSE, MAE and MAPE are 29.19%, 30.06% and 45.63%, respectively, thereby validating the necessity of causal factor selection. Additionally, single-factor perturbation analysis at seasonal scales quantifies load sensitivity to environmental changes, while geographic–climatic coupling mechanisms explain observed load variation patterns. The results confirm that QGCT-BiLSTM effectively isolates critical meteorological drivers and significantly enhances prediction accuracy compared to conventional approaches, achieving 20.3% lower RMSE and 16.8% lower MAE than LSTM.