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The aim of this study is to provide a fast and reliable approach to detect weak arc faults that do not noticeably distort the bus current, with the minimum possible arc duration required to respond in low-voltage AC systems. Progressive singular-value decomposition is utilized to filter interference components, primarily AC/DC components. Then, the signals are thoroughly decomposed by empirical analytic tools in the time-frequency domain, combined with the fast Fourier transform to enhance feature extraction in the frequency domain. The features are passed to the neural networks, where the networks are trained and validated repetitively by datasets that are randomly selected from the data sampling. The comparison experiments demonstrate the excellent performance of the proposed method under all crucial evaluation criteria of arc-fault detection.