Amplitude-modulated And Frequency-modulated Research Articles

WVDNet: Time-Frequency Analysis via Semi-Supervised Learning

The bilinear based method is one of the commonly used tools in time-frequency analysis (TFA) fields. However, it suffers from the trade-off of high resolution and cross-term interference. We propose WVDNet, a semi-supervised learning model for time-frequency analysis based on the Wigner-Ville distribution (WVD), to reduce the cross-term existing in WVD and relax the requirements of the training data set. The proposed WVDNet is based on the Mean-Teacher model to enable the task model to exploit the unlabeled training data. We first build a synthetic data set for model training, that contains different kinds of amplitude-modulated and frequency-modulated (AM-FM) signals. Next, a task model of WVDNet is designed and the consistency regularization based method is utilized to promote model training. Finally, experiments are conducted on both synthetic and real-world data, showing the effectiveness of suppressing cross-term and strong generalization ability.

Accurate AM-FM signal demodulation and separation using nonparametric regularization method

In this paper we propose a novel adaptive nonparametric regularization (NPR) method for solving optimization problems with linear constraint. The regular parameter in NPR algorithm is adaptively updated. We prove that the NPR is convergent and provide an early stop method (ESM) with a termination criterion to handle the perturbation problem which is unsolved in other methods such as the augmented Lagrange method (ALM). We then introduce a new differential operator which can absolutely annihilate the amplitude-modulated and frequency-modulated (AM-FM) signals (AM-FM operator, AFO). The proposed operator is a precise operator and thus can obtain a more accurate solution in operator based signal demodulation and separation problems. We apply the NPR algorithm in signal demodulation and separation based on the AFO and propose signal demodulation (NPR-AFOSD) and separation (NPR-AFOSS) algorithms. The experimental results on both synthetic AM-FM signals and the real-life data demonstrate that the proposed demodulation and separation methods are more effective and robust than the state-of-the-art methods.

A signal decomposition algorithm based on complex AM-FM model

Model-based adaptive signal decomposition algorithm is an important research topic in the field of signal analysis. The amplitude modulated and frequency modulated (AM-FM) model is the most common model in the signal. In this paper, an adaptive signal decomposition algorithm based on the complex AM-FM model is proposed. This algorithm first obtains the analytical expression of the analyzed signal; and then the optimal equation of the analytic signal based on the model is realized by initializing the instantaneous frequency (IF) of the model. Finally, the partial differential equation and the alternating direction method of multipliers technique are used to solve the optimization equation to achieve a high precision estimation of the model. Experiments on simulated and real-life data verify that the proposed algorithm can accurately estimate the instantaneous amplitude (IA) and IF of each component in the signal, and has strong robustness and high efficiency.

Damage Detection in Initially Nonlinear Structures Based on Variational Mode Decomposition

Nonlinear characteristics in the dynamic behaviors of civil structures degrade the performance of damage detection of the linear theory based traditional time- and frequency-domain methods. To overcome this challenge, this paper proposes a damage detection approach for nonlinear structures based on Variational Mode Decomposition (VMD). In this approach, the measured dynamic responses from nonlinear structures under earthquake excitations are adaptively decomposed into a finite number of monocomponents by using VMD. Each decomposed mono-component represents an amplitude modulated and frequency modulated (AMFM) signal with a limited frequency bandwidth. Hilbert transform is then employed to identify the instantaneous modal parameters of the decomposed monomodes, including instantaneous frequencies and mode shapes. Based on the identified modal parameters from the decomposed structural dynamic responses, two damage indices are defined to identify the location and severity of structural damage, respectively. To validate the effectiveness and accuracy of the proposed approach, a nonlinear seven-storey shear building model with four different damage cases under earthquake excitations is used in the numerical studies. In experimental verifications, data from shake table tests on a 12-storey scaled reinforced concrete frame structure with different earthquake excitations are analyzed with the proposed approach. The results in both numerical studies and experimental validations demonstrate that the proposed approach can be successfully applied for nonlinear structural damage identification.

Synchroextracting chirplet transform for accurate IF estimate and perfect signal reconstruction

Synchroextracting transform (SET) is a recently developed time-frequency analysis (TFA) method aiming to achieve a highly concentrated TF representation. However, SET suffers from two drawbacks. The one is that SET is based upon the assumption of constant amplitude and linear frequency modulation signals, therefore it is unsatisfactory for strongly amplitude-modulated and frequency-modulated (AM-FM) signals. The other is that SET does not allow for perfect signal reconstruction, which leads to large reconstruction errors when addressing fast-varying signals. To tackle these problems, in this paper, we first present some theoretical analysis for the SET method, including the existence of the fixed squeeze frequency, the performances of the instantaneous frequency (IF) estimator and the SET reconstruction. Then, a new TFA method, named synchroextracting chirplet transform (SECT), is proposed, which sharpens the TF representation by extracting the TF points satisfying IF equation, and retains an excellent signal reconstruction ability. Numerical experiments on simulated and real signals demonstrate the effectiveness of the SECT method.

High‐order ridge reconstruction for more accurate signal estimate from time‐frequency representations

Ridge reconstruction (RR) method is one of the most commonly used ways for non-stationary signal reconstruction from time-frequency representations. However, this method leads to a large reconstruction error when dealing with strongly amplitude-modulated and frequency-modulated (AM-FM) signals. To tackle this problem, in this Letter the authors propose a new and powerful reconstruction approach, named high-order RR, by considering the high-order derivative information of amplitude and phase of the signal. In particular, an explicit reconstruction formula for second-order RR is derived. Simulation results demonstrate the superiority of the proposed approach in reconstruction accuracy when addressing AM-FM signals, as well as the stability for the selection of window width.

High-order synchrosqueezing wavelet transform and application to planetary gearbox fault diagnosis

The synchrosqueezing transform (SST) is a powerful tool for time-frequency analysis of signals with slowly varying instantaneous frequency (IF). However, the SST and its extensions provide poor time-frequency resolution for signals with wide frequency range and fast varying IF. In this paper, a new SST method called high-order synchrosqueezing wavelet transform is proposed to achieve a highly energy-concentrated time-frequency representation (TFR) for nonstationary signals with wide frequency range and fast varying IF. This method uses high-order group delay and chirp rate operators to obtain the accurate estimation of instantaneous frequency. The proposed method can effectively improve the energy concentration of the TFR and remain invertible simultaneously. The numerical simulations investigate the performance and noise robustness of the proposed method when analyzing a typical amplitude-modulated and frequency-modulated (AM-FM) multicomponent signal. Finally, the application of planetary gearbox fault diagnosis in the variable operating condition verifies the effectiveness of the proposed method.

Wind Turbine Diagnosis under Variable Speed Conditions Using a Single Sensor Based on the Synchrosqueezing Transform Method.

The gearbox is one of the key components in wind turbines. Gearbox fault signals are usually nonstationary and highly contaminated with noise. The presence of amplitude-modulated and frequency-modulated (AM-FM) characteristics compound the difficulty of precise fault diagnosis of wind turbines, therefore, it is crucial to develop an effective fault diagnosis method for such equipment. This paper presents an improved diagnosis method for wind turbines via the combination of synchrosqueezing transform and local mean decomposition. Compared to the conventional time-frequency analysis techniques, the improved method which is performed in non-real-time can effectively reduce the noise pollution of the signals and preserve the signal characteristics, and hence is suitable for the analysis of nonstationary signals with high noise. This method is further validated by simulated signals and practical vibration data measured from a 1.5 MW wind turbine. The results confirm that the proposed method can simultaneously control the noise and increase the accuracy of time-frequency representation.

Automatic sleep stages classification based on iterative filtering of electroencephalogram signals

Computer-aided sleep monitoring system can effectively reduce the burden of experts in analyzing the large volume of electroencephalogram (EEG) recordings corresponding to sleep stages. In this paper, a new technique for automated classification of sleep stages based on iterative filtering of EEG signals is presented. In order to perform sleep stages classification, the EEG signals are decomposed using iterative filtering method. The modes obtained from iterative filtering of EEG signal can be considered as amplitude-modulated and frequency-modulated (AM-FM) components. The discrete energy separation algorithm (DESA) is applied to the modes to determine amplitude envelope and instantaneous frequency functions. The extracted amplitude envelope and instantaneous frequency functions have been used to compute Poincare plot descriptors and statistical measures. The Poincare plot descriptors and statistical measures are applied as input features for different classifiers in order to classify sleep stages. The classifiers namely, naive Bayes, k-nearest neighbor, multilayer perceptron, C4.5 decision tree, and random forest are applied in order to classify the EEG epochs corresponding to various sleep stages. The experimental study has been performed on online available Sleep-EDF database for two-class to six-class classification of sleep stages based on EEG signals. The two-class to six-class classification problems are formulated by taking different combinations of EEG signals corresponding to various sleep stages. The comparison of the results is presented for different multi-class classification problems with the other recently proposed methods. The results show that the proposed method has provided better tenfold cross-validation classification accuracy than other existing methods.

High-Accuracy AM-FM Radar with an Active Reflector

An amplitude-modulated and frequency-modulated (AM-FM) radar with an active reflector to produce high-accuracy distance measurements is proposed and demonstrated in this paper. The proposed radar consists of an AM-FM base module and an active reflector. The combination of AM and FM modulations resolves ambiguity of the absolute distance in typical AM radars, while improving range accuracy in typical FM radars with narrow bandwidth. Also, the active reflector, which translates the frequency of the received signal, resolves the problem of phase detection interference due to the direct Tx-to-Rx leakage in AM radars. In this paper, the operating principle, experimental tests, and analysis are presented. The implemented AM-FM radar operates in X-band (Tx: 10.5 GHz, Rx: 8.5 GHz) with the 620 MHz bandwidth. The measured range accuracy of less than ±10 mm at a distance of 70 m is obtained.

Radar imaging of non-uniformly rotating targets via a novel approach for multi-component AM-FM signal parameter estimation.

A novel radar imaging approach for non-uniformly rotating targets is proposed in this study. It is assumed that the maneuverability of the non-cooperative target is severe, and the received signal in a range cell can be modeled as multi-component amplitude-modulated and frequency-modulated (AM-FM) signals after motion compensation. Then, the modified version of Chirplet decomposition (MCD) based on the integrated high order ambiguity function (IHAF) is presented for the parameter estimation of AM-FM signals, and the corresponding high quality instantaneous ISAR images can be obtained from the estimated parameters. Compared with the MCD algorithm based on the generalized cubic phase function (GCPF) in the authors’ previous paper, the novel algorithm presented in this paper is more accurate and efficient, and the results with simulated and real data demonstrate the superiority of the proposed method.

A rotating machinery fault diagnosis method based on local mean decomposition

Local mean decomposition (LMD) is a novel self-adaptive time-frequency analysis method, which is particularly suitable for the processing of multi-component amplitude-modulated and frequency-modulated (AM-FM) signals. By using LMD, any complicated signal can be decomposed into a number of product functions (PFs), each of which is the product of an envelope signal and a purely frequency modulated signal from which physically meaningful instantaneous frequencies can be obtained. In fact, each PF is just a mono-component AM-FM signal. Therefore, the procedure of LMD may be regarded as the process of demodulation. While fault occurs in gear or roller bearing, the vibration signals picked up would exactly display AM-FM characteristics. So it is possible to diagnose gear and roller bearing fault by LMD. Targeting the modulation features of the gear or roller bearing fault vibration signal, a rotating machinery fault diagnosis method based on LMD is proposed. In this paper, firstly the LMD method is introduced; secondly, the LMD method is compared with another competing time-frequency analysis approach, namely, empirical mode decomposition (EMD) method and the results show the superiority of the LMD method; finally, the LMD method is applied to the gear and roller bearing fault diagnosis. The analysis results from the practical gearbox vibration signal demonstrate that the diagnosis approach based on LMD could identify gear and roller bearing work condition accurately and effectively.

The application of energy operator demodulation approach based on EMD in machinery fault diagnosis

An energy operator demodulation approach based on EMD (Empirical Mode Decomposition) is proposed to extract the instantaneous frequencies and amplitudes of the multi-component amplitude-modulated and frequency-modulated (AM-FM) signals. Furthermore the proposed approach is applied to machinery fault diagnosis. Firstly, EMD method is used to decompose a multi-component AM-FM signal into a number of intrinsic mode functions (IFMs). Secondly, the energy operator demodulation method is applied to each IMF and the instantaneous amplitudes and frequencies of a multi-component AM-FM signal are extracted. Finally, the spectrum analysis is applied to each instantaneous amplitude in order to obtain envelope spectra from which the mechanical fault can be diagnosed. The analysis results show that the energy operator demodulation approach based on EMD can extract the characteristic of machinery fault vibration signals efficiently.