Research on consumption prediction of spare parts based on fuzzy C-means clustering algorithm and fractional order model

In order to achieve the non-stationary de-noising signal effectively, and to solve the prediction of less sample, a hybrid model composed of FCCA (Fuzzy C-means clustering algorithm) and FOM (Fractional Order Model) was constructed. The degree of each data point was determined by FCCA to de-noise and the p order cumulative matrix was extended to r fractional cumulative matrix, so that the fractional order cumulative grey model was established to make forecasting. The results of numerical example showed that the hybrid model can obtain better prediction accuracy

Radon spectrogram-based approach for automatic IFs separation

The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper domain. Unfortunately, if signal modes supports overlap both in time and frequency, separation is only possible through a parametric approach whenever the signal class is a priori fixed. In this work, time-frequency analysis and Radon transform are jointly used for the unsupervised separation of modes of a generic frequency modulated signal in noisy environment. The proposed method takes advantage of the ability of the Radon transform of a proper time-frequency distribution in separating overlapping modes. It consists of a blind segmentation of signal components in Radon domain by means of a near-to-optimal threshold operation. The inversion of the Radon transform on each detected region allows us to isolate the instantaneous frequency curves of each single mode in the time-frequency domain. Experimental results performed on constant amplitudes chirp signals confirm the effectiveness of the proposed method, opening the way for its extension to more complex frequency modulated signals

Signal reconstruction from two close fractional Fourier power spectra

Based on the definition of the instantaneous frequency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fractional power spectrum can be found from the knowledge of two close fractional power spectra. It permits to find the instantaneous frequency and to solve the phase retrieval problem up to a constant phase term, if only two close fractional power spectra are known. The proposed technique is noniterative and noninterferometric. The efficiency of the method is demonstrated on several examples including monocomponent, multicomponent, and noisy signals. It is shown that the proposed method works well for signal-to-noise ratios higher than about 3 dB. The appropriate angular difference of the fractional power spectra used for phase retrieval depends on the complexity of the signal and can usually reach several degrees. Other applications of the angular derivative of the fractional power spectra for signal analysis are discussed briefly. The proposed technique can be applied for phase retrieval in optics, where only the fractional power spectra associated with intensity distributions can be easily measured

Signal reconstruction from two close fractional Fourier power spectra

Based on the definition of the instantaneous fre quency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fractional power spectrum can be found from the knowledge of two close fractional power spectra. It per mits us to find the instantaneous frequency and to solve the phase retrieval problem up to a constant phase term, if only two close fractional power spectra are known. The proposed technique is noniterative and noninterferometric. The efficiency of the method is demonstrated on several examples including monocomponent, multicomponent, and noisy signals. It is shown that the proposed method works well for signal-to-noise ratios (SNRs) higher than about 3 dB. The appropriate angular difference of the fractional power spectra used for phase retrieval depends on the complexity of the signal and can usually reach several degrees. Other applica tions of the angular derivative of the fractional power spectra for signal analysis are discussed briefly. The proposed technique can be applied for phase retrieval in optics, where only the fractional power spectra associated with intensity distributions can be easily measured

Signal reconstruction from two close fractional Fourier power spectra

Based on the definition of the instantaneous frequency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fractional power spectrum can be found from the knowledge of two close fractional power spectra. It permits to find the instantaneous frequency and to solve the phase retrieval problem up to a constant phase term, if only two close fractional power spectra are known. The proposed technique is noniterative and noninterferometric. The efficiency of the method is demonstrated on several examples including monocomponent, multicomponent, and noisy signals. It is shown that the proposed method works well for signal-to-noise ratios higher than about 3 dB. The appropriate angular difference of the fractional power spectra used for phase retrieval depends on the complexity of the signal and can usually reach several degrees. Other applications of the angular derivative of the fractional power spectra for signal analysis are discussed briefly. The proposed technique can be applied for phase retrieval in optics, where only the fractional power spectra associated with intensity distributions can be easily measured

Phase retrieval from intensity measurements in one-parameter canonical-transform systems

Phase retrieval and local frequency estimation of a signal from intensity profiles are important problems in radio location, optical signal processing, quantum mechanics, and other fields. Several successful iterative algorithms for phase reconstruction from the squared modulus of the signal and its power spectrum, or its Fresnel spectrum, have been proposed recently, and related techniques are applied in various regions of the electromagnetic spectrum and in quantum mechanics. The development of non-iterative procedures for generic systems remains an attractive research topic. A non-iterative approach for phase retrieval, based on the so-called transport-of-intensity equation in optics, was proposed by Teague [1] and then further developed by others. It was shown that the longitudinal derivative of the Fresnel spectrum is proportional to the transversal derivative of the product of the instantaneous power and the instantaneous frequency of the signal. A similar procedure was proposed for the fractional Fourier transform [2]. In this paper we show that a non-iterative formulation applies for general one-parameter canonical transforms [3]. We show that the local frequency (the first derivative of the phase of the signal) is directly related to the derivative of the squared modulus of the one-parameter canonical transform with respect to the parameter, and given by the evolution Hamiltonian of the optical medium. From this relationship we conclude that the phase of the signal can be reconstructed by letting it propagate in such systems, and measuring the intensity profiles of the signal for two close values of the parameter. [1] M. R. Teague, "Deterministic phase retrieval: a Green function solution," J. Opt. Soc. Am., vol. 73, pp. 1434-1441, 1983. [2] T. Alieva, M. J. Bastiaans, and LJ. Stankovic, "Signal reconstruction from two close fractional Fourier power spectra," IEEE Trans. Signal Process., vol. 51, pp. 112-123, 2003. [3] K. B. Wolf, Integral Transforms in Science and Engineering, Chap. 9, Plenum Press, New York, 1979