Multicomponent AM-FM Signals Research Articles

Research on the composite fault diagnosis of gearbox based on local mean decomposition and Hilbert demodulation

For the sake of deriving the signature frequencies of the composite malfunctions of broken and worn teeth of gearbox, the essay raised a method on account of local mean decomposition and Hilbert demodulation to diagnose gearbox composite fault. The local mean decomposition translates a complicated multi-component AM-FM signal into several PF elements with certain physical significance. Every PF component can be approximately regarded as a simplex component AM-FM signal. Using correlation coefficient method, the Hilbert envelope demodulation spectrum is analyzed by selecting the PF component which is strongly relevant to the incipient composite malfunction signal, and the malfunction signature frequency is identified from the demodulation spectrum. Through analyzing the emulation signal and the vibration signal of the actual gear box broken-wear complex fault, and compared with EMD, it is shown that the means can effectually discern the malfunction characteristic frequency in the composite fault signal.

Pre-filtered Phase-Locking Scheme for Multi-component AM–FM Signal Decomposition

An online multi-component AM–FM signal decomposition method is proposed based on pre-filtered phase-locking scheme. A second-order generalized integrator (SOGI) and cascaded delayed signal cancelation technique (CDSC) are employed as pre-filters for the phase-locking scheme (PLL). The CDSC technique separates the AM–FM signals from the multi-component signal as a mono-component AM–FM, and a PLL structure demodulates the instantaneous amplitude (IA) and instantaneous frequency (IF) from the individual AM–FM signals. The IF estimated from PLL is fed back to SOGI and CDSC blocks in order to adaptively adjust the number of samples. PLL structures are augmented in parallel to extract IA and IF of multi-component AM–FM signals. The proposed scheme is implemented in field programmable gate array and tested for sinusoidal multi-component AM–FM model. It is evident from the simulation and experimental investigation that the algorithm could efficiently track IF and IA and offers good dynamic response and operating range.

Time-frequency representation based on robust local mean decomposition for multicomponent AM-FM signal analysis

Local mean decomposition (LMD) is a promising approach to implement time-frequency representation (TFR) for multicomponent amplitude-modulated (AM) and frequency-modulated (FM) signal analysis; however, its performance usually suffers from end effect and mode mixing problems. To address this issue, this paper proposes a novel comprehensive scheme to improve LMD performance. The novel scheme can automatically determine the fix subset size of the moving average algorithm and the optimal number of sifting iterations in a sifting process. Extensive simulations have been explored for multicomponent AM-FM signal analysis by means of TFR with the improved LMD. Moreover, the improved LMD shows potential application in bearing fault diagnosis in conjunction with the well-known fast kurtogram.

Demodulation analysis based on adaptive local iterative filtering for bearing fault diagnosis

Abstract The vibration signals from defective rolling bearings are multi-component amplitude modulation (AM)-frequency modulation (FM) signals. Traditional envelope analysis method is based on a filter. The centre frequency and bandwidth of the filter are set according to experience. So the filter method will induce a demodulation error. This research proposes a rolling bearing fault diagnosis method based on adaptive local iterative filtering (ALIF) and envelope spectrum. The ALIF method is a new method for the analysis of non-stationary signals. It uses an iterative filters strategy together with an adaptive, data-driven filter length selection to achieve the necessary decomposition. Smooth filters with compact support from the solutions of the Fokker–Planck equations are used within the ALIF method. The ALIF method offers good performance in obtaining more accurate components of non-stationary signals and in suppressing mode mixing. The ALIF method can decompose a multi-component AM-FM signal into a number of stationary components. The envelope demodulation method is used to analyse those components containing fault information which, in turn, can reveal bearing fault features. The vibration signals from a rolling bearing with an outer race fault and an inner race fault are used to verify the proposed method. The results show that this method can effectively extract bearing fault features.

Adaptive multimode signal reconstruction from time-frequency representations.

This paper discusses methods for the adaptive reconstruction of the modes of multicomponent AM–FM signals by their time–frequency (TF) representation derived from their short-time Fourier transform (STFT). The STFT of an AM–FM component or mode spreads the information relative to that mode in the TF plane around curves commonly called ridges. An alternative view is to consider a mode as a particular TF domain termed a basin of attraction. Here we discuss two new approaches to mode reconstruction. The first determines the ridge associated with a mode by considering the location where the direction of the reassignment vector sharply changes, the technique used to determine the basin of attraction being directly derived from that used for ridge extraction. A second uses the fact that the STFT of a signal is fully characterized by its zeros (and then the particular distribution of these zeros for Gaussian noise) to deduce an algorithm to compute the mode domains. For both techniques, mode reconstruction is then carried out by simply integrating the information inside these basins of attraction or domains.

Revision of Bearing Fault Characteristic Spectrum Using LMD and Interpolation Correction Algorithm

The fault spectral precision plays a significant role in the field of mechanical diagnosis. A bearing fault characteristic spectrum revised approach based on local mean decomposition (LMD) and interpolation correction theory is proposed. Bearing fault vibration signal belongs to multi-component modulated AM-FM signals, the LMD method can decompose this fault vibration signals into a number of different characteristic time scales product functions (PFs), then the spectrum analysis method is applied to the first PF1 component and the instantaneous frequencies and instantaneous amplitudes are obtained. However, in order to acquire accurate frequency and amplitude information and overcome the drawbacks such as energy leakage and fence effect, interpolation correction algorithm is introduced to the characteristic spectrum. The experimental results show that this method can effectively diagnose the bearing fault and accurately extract the characteristic spectrum information of bearing vibration signals and it has very high engineering application value.

Rolling Bearings Fault Diagnosis Based on Generalized Demodulation Time-Frequency Analysis Method

In view of the characteristics of the non-stationary and multi-component AM-FM signals of vibration signals in the rolling element bearing, the generalized demodulation time-frequency analysis method is used for its fault diagnosis, overcoming the problem that the maximal overlap discrete wavelet packet transform (MODWPT) has no adaptability. First of all, the original vibration signal is took preprocessing by generalized Fourier; Then, using MODWPT to decompose signals after pretreatment and obtaining weights; Once again, the weights are carried out the inverse generalized Fourier transform to get the weights of the original signal; Finally, reconstructing principal component of the original signal to get the Hilbert instantaneous energy spectrum, roller bearing fault diagnoses based on the Hilbert instantaneous energy spectrum. The experimental results show that the method can effectively diagnose rolling bearing fault.

Basis approach to estimate the instantaneous frequencies in multicomponent AM-FM signals

Abstract In this paper, an analytical approach to estimate the instantaneous frequencies of a multicomponent signal is presented. A non-stationary signal composed of oscillation modes or resonances is described by a multicomponent AM-FM model. The proposed method has two main stages. At first, the signal is decomposed into its oscillation components. Afterwards, the instantaneous frequency of each component is estimated. The decomposition stage is performed through the basis expansion exploiting orthogonal rational functions in the complex plane. Orthogonal rational bases are generalized to expand linear time-varying systems. To decompose the non-stationary signal, its equivalent time-varying system is sought. The time-varying poles of this system are required to construct appropriate basis functions. An adaptive data segmentation algorithm is provided for this purpose. The effect of noise is scrutinized analytically and evaluated experimentally to verify the robustness of the new method. The performance of this method in extraction of embedded instantaneous frequencies is asserted by simulations on both synthetic data and real-world audio signal.

Multicomponent AM-FM signal separation and demodulation with null space pursuit

The operator-based signal separation approach, which formulates signal separation as an optimization problem, uses an adaptive operator to separate a signal into additive subcomponents. Furthermore, it is possible to design different operators to fit different signal models. In this paper, we propose a new kind of differential operator to separate multicomponent AM-FM signals. We then use the estimated operators to calculate each sub-component’s envelope and instantaneous frequency. To demonstrate the efficacy of the proposed method, we compare the decomposition and AM-FM demodulation results of several signals, including real-life signals.

Multicomponent AM–FM signals analysis based on EMD–B-splines ESA

In this paper a signal analysis framework for estimating time-varying amplitude and frequency functions of multicomponent amplitude and frequency modulated (AM–FM) signals is introduced. This framework is based on local and non-linear approaches, namely Energy Separation Algorithm (ESA) and Empirical Mode Decomposition (EMD). Conjunction of Discrete ESA (DESA) and EMD is called EMD–DESA. A new modified version of EMD where smoothing instead of an interpolation to construct the upper and lower envelopes of the signal is introduced. Since extracted IMFs are represented in terms of B-spline (BS) expansions, a closed formula of ESA robust against noise is used. Instantaneous Frequency (IF) and Instantaneous Amplitude (IA) estimates of a multicomponent AM–FM signal, corrupted with additive white Gaussian noise of varying SNRs, are analyzed and results compared to ESA, DESA and Hilbert transform-based algorithms. SNR and MSE are used as figures of merit. Regularized BS version of EMD–ESA performs reasonably better in separating IA and IF components compared to the other methods from low to high SNR. Overall, obtained results illustrate the effectiveness of the proposed approach in terms of accuracy and robustness against noise to track IF and IA features of a multicomponent AM–FM signal.

EMD Revisited: A New Understanding of the Envelope and Resolving the Mode-Mixing Problem in AM-FM Signals

Empirical mode decomposition (EMD) is an adaptive and data-driven approach for analyzing multicomponent nonlinear and nonstationary signals. The stop criterion, envelope technique, and mode-mixing problem are the most important topics that need to be addressed in order to improve the EMD algorithm. In this paper, we study the envelope technique and the mode-mixing problem caused by separating multicomponent AM-FM signals with the EMD algorithm. We present a new necessary condition on the envelope that questions the current assumption that the envelope passes through the extreme points of an intrinsic mode function (IMF). Then, we present a solution to the mode-mixing problem that occurs when multicomponent AM-FM signals are separated. We experiment on several signals, including simulated signals and real-life signals, to demonstrate the efficacy of the proposed method in resolving the mode-mixing problem.

Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform Samples

We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu, and Wu [Appl. Comput. Harmonic Anal., 30 (2010), pp. 243–261] and consider a variant of Synchrosqueezing, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multicomponent AM-FM signal. We describe an algorithm to recover these instantaneous frequencies from the uniform or nonuniform samples of the signal and show that our method is robust to noise. We also consider an alternative approach based on the conventional, Hilbert transform-based notion of instantaneous frequency to compare to our new method. We use these methods on several test cases and apply our results to a signal analysis problem in electrocardiography.

Application of the improved generalized demodulation time–frequency analysis method to multi-component signal decomposition

The generalized demodulation time–frequency analysis approach is a novel signal processing method, which is suitable for processing non-stationary signals, especially for processing amplitude-modulated and frequency-modulated (AM–FM) signals. The novelty of this method is that the signal whose time–frequency distributions are curved paths can be transformed into that whose time–frequency distributions are linear paths paralleling time axis by using generalized demodulation. Furthermore, the generalized demodulated signal can be decomposed into a number of mono-component signals whose instantaneous frequencies have physical meaning through the use of the maximal overlap discrete wavelet packet transform (MODWPT). Therefore, the complete time–frequency distributions of the original signal can be obtained. However, the generalized demodulation time–frequency analysis method fails to provide the time domain waveform of each mono-component signal. In this paper, aiming at the multi-component AM–FM signal, each mono-component signal of which only has single-sided spectra, the improvement to the generalized demodulation time–frequency analysis approach has been made and the improved method is introduced into certain multi-component AM–FM signal decomposition. The analysis results demonstrate that the validity of the proposed approach. In addition, the estimation of the phase function that is key step in the generalized demodulation time–frequency analysis approach is also discussed.

Adaptive Maximum Windowed Likelihood Multicomponent AM-FM Signal Decomposition

Considering a real signal as the sum of a number of sinusoidal signals in the presence of additive noise, maximum windowed likelihood (MWL) criterion is introduced and applied to construct an adaptive algorithm in order to estimate the amplitude and frequency of these components. The amplitudes, phases and frequencies are assumed to be slowly time varying. Employing MWL an adaptive algorithm is obtained in two steps. First, assuming some initial values for the frequency of each component, a closed form is derived to estimate the amplitudes. Then, the gradient of MWL is used to adaptively track the frequencies, using the latter values of amplitudes. The proposed algorithm has a parallel structure in which each branch estimates parameters of one of the components. The proposed multicomponent phase locked loop (MPLL) algorithm is implemented employing low complexity blocks. It is adjustable to be used in different conditions. The mean squared error of the algorithm is studied to analyze the effect of the window length and type and the step size. Simulations have been conducted to illustrate the efficiency and the performance of the algorithm in different conditions including: the effect of the initialization, the frequency resolution, for chirp components, for components during frequency crossover and for speech signals. Simulations illustrate that the method efficiently tracks slowly time-varying components of the signals such as voiced speech segments.

Multicomponent AM-FM demodulation via periodicity-based algebraic separation and energy-based demodulation

Previously investigated multicomponent AM-FM demodulation techniques either assume that the individual component signals are spectrally isolated from each other or that the components can be isolated by linear time-invariant filtering techniques and, consequently, break down in the case where the components overlap spectrally or when one of the components is stronger than the other. In this paper, we present a nonlinear algorithm for the separation and demodulation of discrete-time multicomponent AM-FM signals. Our approach divides the demodulation problem into two independent tasks: algebraic separation of the components based on periodicity assumptions and then monocomponent demodulation of each component by instantaneously tracking and separating its source energy into its amplitude and frequency parts. The proposed new algorithm avoids the shortcomings of previous approaches and works well for extremely small spectral separations of the components and for a wide range of relative amplitude/power ratios. We present its theoretical analysis and experimental results and outline its application to demodulation of cochannel FM voice signals.

On the instantaneous frequencies of multicomponent AM-FM signals

We study the instantaneous frequencies (IFs) of multicomponent AM-FM signals by extending the work on the two-component case by Loughlin and Tacer (see ibid.,, vol. 4, no.5, p.123-25, 1997) to the more general M-component case. A novel necessary and sufficient condition for the valid interpretation of the IF as a nonnegatively weighted average of the IFs of the components is proposed, which we apply as a method of interpreting the IFs of signals having no more than three dominant components at each time. Our quantitative study shows that in general, the IF-based monocomponent AM-FM decomposition is not appropriate for the modeling and analysis of multicomponent AM-FM signals unless all the components are well separated in the time domain.