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This paper proposes a methodology for the diagnosis of electrical system conditions using fractional-order integral transforms for feature extraction. This work proposes three feature extraction algorithms using the Fractional Fourier Transform (FRFT), the Fourier Transform combined with the Mittag-Leffler function, and the Wavelet Transform (WT). Each algorithm extracts data from an electrical system to obtain a set of features that are classified by an Artificial Neural Network to determine the system's condition. The algorithms are utilized in diagnosing two types of electrical machine faults, one in a photovoltaic system, and another in classifying the power quality disturbances (PQDs). An optimization algorithm is suggested to find the optimal orders of integral transforms. The obtained results demonstrate the system's effective diagnosis, displaying superior performance in classifying the faults and PQDs with complex signals. [ABSTRACT FROM AUTHOR]

Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper, we establish some analysis for linear feature extraction by a deep multi-channel convolutional neural networks (CNNs), which demonstrates the power of deep learning over traditional linear transformations, like Fourier, wavelets, redundant dictionary coding methods. Moreover, we give an exact construction presenting how linear features extraction can be conducted efficiently with multi-channel CNNs. It can be applied to lower the essential dimension for approximating a high-dimensional function. Rates of function approximation by such deep networks implemented with channels and followed by fully connected layers are investigated as well. Harmonic analysis for factorizing linear features into multi-resolution convolutions plays an essential role in our work. Nevertheless, a dedicate vectorization of matrices is constructed, which bridges 1D CNN and 2D CNN and allows us to have corresponding 2D analysis. [ABSTRACT FROM AUTHOR]