Accurate Instantaneous Frequency Research Articles

Parameter estimation of underwater moving sources by using matched Wigner transform

According to the acoustical Doppler effect, an improved narrow-band technique is proposed to estimate underwater source’s motion parameters including speed, closest distance, rest frequency, and closest point of approach (CPA) time, by using a single receiving sensor. First, the matched Wigner transform (MWT), which produces a time–frequency distribution (TFD) with optimal energy concentration and without inner artifacts for a high-order polynomial phase signal, is defined. On the basis of the MWT, a method is developed for the accurate instantaneous frequency (IF) estimation of Doppler signal. Moreover, we deduce that the Wigner–Ville distribution of the Doppler signal has a peak at the center of the TFD. Thereafter, the CPA time is directly estimated. When the CPA time is obtained, the other motion parameters can be easily estimated by using a simplified amplitude weighted nonlinear least-squares method, which fits the IF estimates to the predicted Doppler shift. Finally, the effectiveness of the proposed scheme is validated by using underwater acoustic data.

Damage Modes Recognition and Hilbert-Huang Transform Analyses of CFRP Laminates Utilizing Acoustic Emission Technique

Discrimination of acoustic emission (AE) signals related to different damage modes is of great importance in carbon fiber-reinforced plastic (CFRP) composite materials. To gain a deeper understanding of the initiation, growth and evolution of the different types of damage, four types of specimens for different lay-ups and orientations and three types of specimens for interlaminar toughness tests are subjected to tensile test along with acoustic emission monitoring. AE signals have been collected and post-processed, the statistical results show that the peak frequency of AE signal can distinguish various damage modes effectively. After a AE signal were decomposed by Empirical Mode Decomposition (EMD) method, it may separate and extract all damage modes included in this AE signal apart from damage mode corresponding to the peak frequency. Hilbert-Huang Transform (HHT) of AE signals can clearly illustrate the frequency distribution of Intrinsic Mode Functions (IMF) components in time-scale in different damage stages, and can calculate accurate instantaneous frequency for damage modes recognition to help understanding the damage process.

Random denoising and signal nonlinearity approach by time-frequency peak filtering using weighted frequency reassignment

Time-frequency peak filtering (TFPF) may efficiently suppress random noise and hence improve the signal-to-noise ratio. However, the errors are not always satisfactory when applying the TFPF to fast-varying seismic signals. We begin with an error analysis for the TFPF by using the spread factor of the phase and cumulants of noise. This analysis shows that the nonlinear signal component and non-Gaussian random noise lead to the deviation of the pseudo-Wigner-Ville distribution (PWVD) peaks from the instantaneous frequency. The deviation introduces the signal distortion and random oscillations in the result of the TFPF. We propose a weighted reassigned smoothed PWVD with less deviation than PWVD. The proposed method adopts a frequency window to smooth away the residual oscillations in the PWVD, and incorporates a weight function in the reassignment which sharpens the time-frequency distribution for reducing the deviation. Because the weight function is determined by the lateral coherence of seismic data, the smoothed PWVD is assigned to the accurate instantaneous frequency for desired signal components by weighted frequency reassignment. As a result, the TFPF based on the weighted reassigned PWVD (TFPF_WR) can be more effective in suppressing random noise and preserving signal as compared with the TFPF using the PWVD. We test the proposed method on synthetic and field seismic data, and compare it with a wavelet-transform method and [Formula: see text] prediction filter. The results show that the proposed method provides better performance over the other methods in signal preserving under low signal-to-noise ratio.

Acoustic emission characterization methods of damage modes identification on carbon fiber twill weave laminate

In order to get a deep understanding of composite failure mechanisms, the new advanced signal processing methodologies are established for the analysis of the large number of acoustic emission (AE) data obtained from the quasi-static tension test of carbon fiber twill weave composite. For this purpose, AE signals have been collected and post-processed for tension test, and are analyzed with three signal processing methods: Empirical Mode Decomposition (EMD), Hilbert-Huang Transform (HHT) and modified energy entropy algorithm. AE signals can be decomposed into a set of Intrinsic Mode Functions (IMF) components, results from this study reveal that the peak frequency of IMF components based on Fast Fourier Transform (FFT) corresponds to different damage mechanisms of composite. HHT of AE signals can clearly express the frequency distribution of IMF component in time-scale in different damage stages, and can calculate accurate instantaneous frequency for damage modes recognition. The energy entropy based on EMD is introduced to act as a new relevant descriptor of composite damage modes in order to improve the characterization and the discrimination of the damage mechanisms.

Windowed Fourier transform profilometry based on improved S-transform

A novel method for windowed Fourier transform (WFT) profilometry is presented. This method is based on improved S-transform. The impact of the second order derivative of the phase (φ''(b)) to the ridge of S-transform is derived, and how to estimate this deviation is discussed. An important conclusion that more accurate instantaneous frequency can be obtained after removing this deviation is shown. Thus, an accurate phase map of the fringe pattern is obtained by using the WFT based on the window size map, and this map is related to the instantaneous frequency. The method is compared with the WFT based on the wavelet transform. A numerical simulation and experimental example have shown its validity in practical applications.

OVERCOMING THE NEGATIVE FREQUENCIES - INSTANTANEOUS FREQUENCY AND AMPLITUDE ESTIMATION USING OSCULATING CIRCLE METHOD

There are many methods able to extract the instantaneous frequencies from a time series for practical applications. Gabor's method is one of the most popular and simple methods. For wide band time series, Gabor's method may produce negative frequencies. The limitation of Gabor's method is that, in order to avoid resulting with negative frequencies, it can only be applied to time series with mono component and near zero mean. In this paper, a new method that does not generate negative frequencies, the Osculating Circle (OC) Method, is presented. The OC method is based on Gabor's method but with modified unwrapped phase calculation. This new method can provide accurate instantaneous frequency (IF) and instantaneous amplitude (IA) calculation with only positive frequency results. This paper is focused on overcoming the negative frequency encountered in traditional Garbo's method. Although, other important topics such as the noise are not discussed in detail in this paper.

Fault Feature Extraction Based on Improved EEMD and Hilbert Transform

Ensemble Empirical Mode Decomposition (EEMD) can overcome the mode mixing problem in Empirical Mode Decomposition (EMD) effectively. The Hilbert-Huang transform still exists end effect in applications, in order to improve the end effect, this paper put forward a method of fault feature extraction based on improved EEMD and Hilbert transform which combines support vector regression (SVR) machine with mirror extension to continue the signal. The analysis on simulation experiments results show that the method can restrain the end effect effectively, get a more accurate instantaneous frequency and instantaneous amplitude.

A Comparative Study on the Local Mean Decomposition and Empirical Mode Decomposition and Their Applications to Rotating Machinery Health Diagnosis

Health diagnosis of the rotating machinery can identify potential failure at its early stage and reduce severe machine damage and costly machine downtime. In recent years, the adaptive decomposition methods have attracted many researchers’ attention, due to less influences of human operators in the practical application. This paper compares two adaptive methods: local mean decomposition (LMD) and empirical mode decomposition (EMD) from four aspects, i.e., local mean, decomposed components, instantaneous frequency, and the waveletlike filtering characteristic through numerical simulation. The comparative results manifest that more accurate instantaneous frequency and more meaningful interpretation of the signals can be acquired by LMD than by EMD. Then LMD and EMD are both exploited in the health diagnosis of two actual industrial rotating machines with rub-impact and steam-excited vibration faults, respectively. The results reveal that LMD seems to be more suitable and have better performance than EMD for the incipient fault detection. LMD is thus proved to have potential to become a powerful tool for the surveillance and diagnosis of rotating machinery.

An oblique-extrema-based approach for empirical mode decomposition

It has been found that envelopes established by extrema in the empirical mode decomposition cannot always depict the local characteristics of a signal very well. This is due in part to the slight oscillations characterized as hidden scales which are almost left untreated during the sifting process. When involving hidden scales, the intrinsic mode function usually contains at a given instance multiple oscillation modes. In view of this, based on inflection points this paper presents a new decomposition algorithm called ‘oblique-extrema empirical mode decomposition’ to settle these problems. With this algorithm, any signal can be decomposed into a finite number of ‘oblique-extrema intrinsic mode functions’ which may possess better-behaved Hilbert transforms and produce more accurate instantaneous frequencies. It can suppress the effect of hidden scales and gets one step further in extracting finer scales. Experimental results demonstrate good performances of this new method.

New process method for end effects of HILBERT-HUANG transform

The HILBERT-HUANG transform consists of two steps:empirical mode decomposition (EMD) and HILBERT tr- ansform.The end effects produce both in the decomposition process of EMD and H1LBERT transforms applied to the intrinsic mode functions (IMFs).A novel wave characteristic matching extending method is proposed to overcome the end effects of EMD and HILBERT transform.Therefore,the decomposition precision is improved,the accurate instantaneous frequencies and instantaneous amplitudes could be obtained.The extending data derived from the original signal by the simple algorithm,only once extending needed in HILBERT-HUANG transform processing.The simulation and fault test analysis demonstrate the effectiveness of the method.

PROCESS METHOD FOR END EFFECTS OF HILBERT-HUANG TRANSFORM BASED ON SUPPORT VECTOR REGRESSION MACHINES

The end effects of Hilbert-Huang transform are shown in two aspects. On one hand, the end effects are produced when the signal is decomposed by empirical mode de- composition (EMD) method; on the other hand, the end effects are produced too when the Hilbert transforms are applied to the intrinsic mode functions (IMFs). To overcome the end effects of Hilbert-Huang transform, the support vector regression machines are used to predict the signal before the signal is decomposed by EMD (Empirical Mode Decomposition), thus the end effects could be overcome effectively and the IMFs (Intrinsic Mode Functions) with physical sense could be obtained. After that, to restrain the end effects of Hilbert transform, the support vector regression machines are used again to predict the IMFs before the Hilbert transform of the IMFs, therefore, the accurate instantaneous frequencies and instantaneous amplitudes could be obtained and the Hilbert spectrum with physical sense could be acquired. The analysis results from the simulated and practical signals demonstrate that the end effects of Hilbert-Huang transform could be resolved effectively by the time series forecasting method based on support vector regression machines which is superior to the time series forecasting method based on neural networks.

Application of support vector regression machines to the processing of end effects of Hilbert–Huang transform

The end effects of Hilbert–Huang transform are represented in two aspects. On the one hand, the end effects occur when the signal is decomposed by empirical mode decomposition (EMD) method. On the other hand, the end effects occur again while the Hilbert transforms are applied to the intrinsic mode functions (IMFs). To restrain the end effects of Hilbert–Huang transform, the support vector regression machines are used to predict the signals before the signal is decomposed by EMD method, thus the end effects could be restrained effectively and the IMFs with certain physical sense could be obtained. For the same purpose, the support vector regression machines are used again to predict the IMFs before the Hilbert transform of the IMFs, thus the accurate instantaneous frequencies and amplitudes could be obtained and the corresponding Hilbert spectrum with physical sense could be acquired. The analysis results from the simulation and experimental signals demonstrate that the end effects of Hilbert–Huang transform could be resolved effectively by the time series forecasting method based on support vector regression machines which is superior to that based on neural networks.

Analysis of polynomial FM signals corrupted by heavy-tailed noise

In this paper, we consider the analysis of polynomial FM signals corrupted by additive heavy-tailed noise. Standard time–frequency techniques fail to analyze such signals. For that, we propose here a new technique, named the robust polynomial Wigner-Ville distribution (r-PWVD) to handle this case. We show that this representation outperforms the robust Wigner-Ville distribution (r-WVD) and the robust spectrogram in terms of artifacts suppression and high time–frequency resolution for this class of signals. Also, we show that the peak of the r-PWVD is an accurate instantaneous frequency estimator. Examples and Monte-Carlo simulations are presented in order to validate and prove the performance of the proposed algorithm.