Non-stationary Transient Signals Research Articles

Horizontal rearrangement frequency domain chirplet transform: algorithm and applications

Abstract Based on the idea of optimal time–frequency analysis (TFA) theory, a time–frequency post-processing method called horizontal rearrangement frequency domain chirplet transform (HRFCT) is proposed. The proposed method is designed to analyze non-stationary transient signals with nonlinear group delay (GD), aiming at obtaining energy-concentrated and accurate time–frequency representation (TFR). First, based on the image characteristics of the constructed amplitude function, the selection criteria of GD are defined, that is, the local maximum of amplitude function and the local minimum of absolute value of derivative of amplitude function are calculated. Next, according to the calculated GD, the coefficients on the GD trajectory are adaptively extracted, and the coefficients that cause the TFR to be blurred are discarded. Finally, the analysis result of a two-component simulation signal demonstrates the satisfactory performance of the HRFCT, and compared with four advanced TFA methods, the competitiveness of the HRFCT is verified. Additionally, the application of the HRFCT in the processing of constant and variable speed bearing signals highlights its prospects in transient signal analysis and rotating machinery condition monitoring.

Multi-Scale Stochastic Resonance Spectrogram for fault diagnosis of rolling element bearings

It is not easy to identify incipient defect of a rolling element bearing by analyzing the vibration data because of the disturbance of background noise. The weak and unrecognizable transient fault signal of a mechanical system can be enhanced by the stochastic resonance (SR) technique that utilizes the noise in the system. However, it is challenging for the SR technique to identify sensitive fault information in non-stationary signals. This paper proposes a new method called multi-scale SR spectrogram (MSSRS) for bearing defect diagnosis. The new method considers the non-stationary property of the defective bearing vibration signals, and treats every scale of the time-frequency distribution (TFD) as a modulation system. Then the SR technique is utilized on each modulation system according to each frequencies in the TFD. The SR results are sensitive to the defect information because the energy of transient vibration is distributed in a limited frequency band in the TFD. Collecting the spectra of the SR outputs at all frequency scales then generates the MSSRS. The proposed MSSRS is able to well deal with the non-stationary transient signal, and can highlight the defect-induced frequency component corresponding to the impulse information. Experimental results with practical defective bearing vibration data have shown that the proposed method outperforms the former SR methods and exhibits a good application prospect in rolling element bearing fault diagnosis.

Seamless measurement technology of transient signals based on approximate entropy.

The acquisition of waveforms and the analysis of transient characteristics of signals are the fundamental tasks for time-domain measurement, while the reduction of the measuring gap till seamless measurement is extremely important to the acquisition, measurement, and analysis of transient signals. This paper, aimed at the seamless time-domain measurement of non-stationary transient signals, proposes an approximate entropy-based characteristic signal extraction algorithm on the basis of information entropy theories. The algorithm quantitatively describes the complexity (amount of information) of sampled signals using the approximate entropy value, self-adaptively captures characteristic signals under the control of the approximate entropy in real time, extracts the critical or useful information, and removes redundant or useless information so as to reduce the time consumption of processing data and displaying waveforms and realize the seamless time-domain measurement of transient signals finally. Experimental results show that the study could provide a new method for the design of electronic measuring instrument with seamless measurement capability.

Cross-correlation analysis and time delay estimation of a homologous micro-seismic signal based on the Hilbert–Huang transform

A micro-seismic signal's transient features are non-stationary. The traditional weighted generalized cross-correlation (GCC) algorithm is based on the cross-power spectrum density. This algorithm diminishes the performance of the time delay estimation for homologous micro-seismic signals. This paper analyzed the influence of calculation error on the cross-power spectrum density of a non-stationary signal and proposed a new cross-correlation analysis and time delay estimation method for homologous micro-seismic signals based on the Hilbert–Huang transform (HHT). First, the original signals are decomposed into intrinsic mode function (IMF) components using empirical mode decomposition (EMD) for de-noising. Subsequently, the IMF components and the original signals are analyzed using a cross-correlation analysis. The IMF components are subsequently remodeled at different scales using the Hilbert transform. The marginal spectrum density is obtained via a time integration of the remodeled components. The cross-marginal spectrum density of the two signals can also be obtained. Finally, the cross-marginal spectrum density is used in the weighted GCC algorithm for time delay estimation instead of the cross-power spectrum density. The time delay estimation is determined by searching for the weighted GCC function peak. The experiments demonstrated the superior time delay estimation performance of the new method for non-stationary transient signals. Therefore, a new time delay estimation method for non-stationary random signals is presented in this paper.

Detection and Classification of Nonstationary Transient Signals Using Sparse Approximations and Bayesian Networks

This paper considers sequential detection and classification of multiple transient signals from vector observations corrupted with additive noise and multiple types of structured interference. Sparse approximations of observations are found to facilitate computation of the likelihood of each signal model without relying on restrictive assumptions concerning the distribution of observations. Robustness to interference may be incorporated by virtue of the inherent separation capabilities of sparse coding. Each signal model is characterized by a Bayesian Network, which captures the temporal dependency structure among coefficients in successive sparse approximations under the associated hypothesis. Generalized likelihood ratios tests may then be used to perform signal detection and classification during quiescent periods, and quiescent detection whenever a signal is present. The results of applying the proposed method to a national park soundscape analysis problem demonstrate its practical utility for detecting and classifying real acoustical sources present in complex sonic environments.

Fault diagnosis of stamping process based on empirical mode decomposition and learning vector quantization

Sheet metal stamping process is widely used in industry due to its high accuracy and productivity. However, monitoring the process is a difficult task since the monitoring signals are typically non-stationary transient signals. In this paper, empirical mode decomposition (EMD) is applied to extract the main features of the strain signals. First, the signal is decomposed by EMD into intrinsic mode functions (IMF). Then the signal energy and the Hilbert marginal spectrum, which reflects the working condition and the fault pattern of the process, are computed. Finally, to identify the faulty conditions of process, the learning vector quantization (LVQ) network is used as a classifier with the Hilbert marginal spectrum as the input vectors. The performance of this method is tested by 107 experiments derived from different conditions in the sheet metal stamping process. The artificially created defects can be detected with a success rate of 96.3%. The method seems to be useful to monitor a sheet metal stamping process in practice.

Intensity analysis methods for transient signals

Conventionally, the Fourier transform is applied for sound intensity analysis of stationary signals, but this method can be applied for analyzing non-stationary transient signals. Instead of the Fourier transform analysis, instantaneous spectrum analysis methods such as the Wigner–Ville distribution and the wavelet transform are proposed. By using the mathematical example as a transient signal, advantages and disadvantages of these methods including the short-time Fourier transform are compared. From calculation results, it is considered that the STFT method is the most suitable for the accurate measurement of sound intensity levels, but the WT method is also recommended from its higher resolution of transient signals.

Wavelet-Based Enhancement of Lung and Bowel Sounds Using Fractal Dimension Thresholding— Part I: Methodology

An efficient method for the enhancement of lung sounds (LS) and bowel sounds (BS), based on wavelet transform (WT), and fractal dimension (FD) analysis is presented in this paper. The proposed method combines multiresolution analysis with FD-based thresholding to compose a WT-FD filter, for enhanced separation of explosive LS (ELS) and BS (EBS) from the background noise. In particular, the WT-FD filter incorporates the WT-based multiresolution decomposition to initially decompose the recorded bioacoustic signal into approximation and detail space in the WT domain. Next, the FD of the derived WT coefficients is estimated within a sliding window and used to infer where the thresholding of the WT coefficients has to happen. This is achieved through a self-adjusted procedure that iteratively "peels" the estimated FD signal and isolates its peaks produced by the WT coefficients corresponding to ELS or EBS. In this way, two new signals are constructed containing the useful and the undesired WT coefficients, respectively. By applying WT-based multiresolution reconstruction to these two signals, a first version of the desired signal and the background noise is provided, accordingly. This procedure is repeated until a stopping criterion is met, finally resulting in efficient separation of the ELS or EBS from the background noise. The proposed WT-FD filter introduces an alternative way to the enhancement of bioacoustic signals, applicable to any separation problem involving nonstationary transient signals mixed with uncorrelated stationary background noise. The results from the application of the WT-FD filter to real bioacoustic data are presented and discussed in an accompanying paper.

The Analysis of Under Water Vehicle Non-Stationary AcousticTransient Signals Using a New Fast Algorithm for ConstructingPositive Time-Frequency Distributions

It is well know that under water vehicles emit many types of acoustic signals, including stationary as well as non-stationary. The non-stationary transient signals are receiving considerable attention, especially from the standpoint of detection and tracking of under water vehicles. Thus, modern methods for processing these non-stationary acoustic transient signals are required. This paper presents a very powerful method for analyzing acoustic transient signals, the positive time-frequency distribution. A fast algorithm that implements the minimum cross-entropy positive time-frequency distribution makes practical the processing of ’’real world data‘‘, like under water vehicle acoustic transient signals. An example of such a signal is presented, which is a generic acoustic transient signal from a under water vehicle. The signal is only representative, as it is normalized in time, in frequency, and in amplitude. The positive time-frequency distribution constructed for this generic transient signal is contrasted with the one-third octave method, which is currently the primary method being used by the under water vehicle community to analyze under water vehicle transients. The positive distribution is also contrasted with broad band and narrow band spectrograms.