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In this work, the signal recovery problem regarding incomplete and noisy spatio-temporal signals is studied. A spatio-temporal signal is considered as a time-varying graph signal and a diffusion-induced first-order Markov signal model is developed to incorporate both the spatial structure and temporal correlation into the underlying graph. With this model, prior knowledge on spatial smoothness and temporal correlation is revisited, and the connections between the graph structure and differential temporal smoothness are revealed. The authors then accordingly formulate a spatio-temporal signal recovery method by jointly exploiting the spatial smoothness, low rank and refined differential temporal smoothness. The formulated recovery problem is solved by a block coordinate descent-based algorithm, which iteratively optimises the recovery accuracy and temporal correlation matrix. The experiments on three real-world datasets reveal the high signal recovery accuracy of the proposed algorithm.

Custom power devices are used currently to deal with voltage sag and interruptions. Study on detection algorithm become urgent. In order to master sampling value product curve fitting detection algorithm, in theory, comparied it with others detection algorithm, studied on DSP emulate system, achieved it's many merits ; in practice, used it in 10kV SSTS, and validated it's quick utility chracteristic. Study it's localization, three results those larger calculation deviation brought by higher order harmonic component with identical amplitude, calculation result influenced little by allowable frequency deviation and less calculation deviation brought by more digit capacity of A/D transfer were achieved. From synthesis research, the final conclusions that, sampling value product curve fitting detection algorithm was more suitable to dispose voltage signal with better stability and less harmonic component in medium power system and special low-tension power system, and low-pass filter technology was used to detect voltage sag in low-tension power system with larger harmonic component by sampling value product curve fitting detection algorithm, were achieved.Index Terms--allowable frequency deviation; curve fitting algorithm; custom power; detection algorithm; interruptions; low-tension power system; medium power system; SSTS; transient power quality; voltage sag