Adaptive Short-time Fourier Transform Research Articles

Adaptive window rotated second-order synchroextracting transform and its application in fault diagnosis of wind turbine gearbox

Time frequency (TF) analysis (TFA) based on vibration signals is a vital method for the health monitoring of wind turbine gearboxes. Based on classical synchrosqueezing transform and short-time Fourier transform (STFT), synchroextracting transform (SET) abstractly retains primary TF energy around the interested frequency components by reassigning the TF transformation coefficient. However, as the fixed window of these traditional TFA methods, they have poor matching effects on multi-component signals with fast-varying frequencies. To address this problem, this paper first optimizes the width of the short-term window based on STFT, and then proposes adaptive short-time Fourier transform (ASTFT). That is, the direction of the window function in the STFT is changed by automatically matching a series of rotation operators. Then, based on ASTFT and SET, the second-order partial derivatives of time and frequency are used to modify the formula of instantaneous frequency estimation. Therefore, adaptive window rotated second-order synchroextracting transform (AWRSSET) is put forward to obtain and sharpen TF representations of multi-component vibration signals of wind turbines in this paper. In order to accurately diagnose faults in wind turbines, this paper extracts the rotation speed curve from the TF plane, which is generated through AWRSSET, and then makes subsequent order-frequency analyses without a tachometer. AWRSSET can be applied to diagnosing faulty wind turbine gearboxes and gears with broken teeth under time-varying speed, both of which testify to the advantages of this method.

A Heavy-Haul Railway Corrugation Diagnosis Method Based on WPD-ASTFT and SVM

Rail corrugation in heavy-haul railway increases the contact forces between the wheel and the rail and deteriorates the rail condition. Severe corrugation affects railway operational safety. Fast diagnosis techniques allow technical personnel to perform timely maintenance and repair, preventing the quick deterioration of rail corrugation. This paper presents a heavy-haul railway corrugation diagnosis method incorporating the time-frequency analysis with machine learning methods. First, the signal is decomposed into several subsignals by wavelet packet decomposition (WPD). The paper proposes an adaptive short-time Fourier transform (ASTFT) and performs the ASTFT on the subsignals to obtain the optimal resolution time-frequency distribution and compute the corresponding entropy. The dimensionality reduction based on mean entropy is then performed for the high-dimensional data. The training and testing samples are classified using Support Vector Machine (SVM). The adaptive short-time Fourier transform (ASTFT) is incorporated with the Renyi entropy and the particle swarm optimization algorithm, which achieves a better aggregation of the time-frequency distribution and reduces the computation cost. Finally, to assist the repair work and estimate the severity of the corrugation section, the corrugation index is proposed. The corrugation indices for the determined corrugation sections are calculated to measure the severity of the corrugation. Experimental studies performed on the axle-box vertical acceleration data collected from the heavy-haul comprehensive inspection train show that the method presented by this paper achieves higher accuracy when compared with conventional feature classification methods for time-frequency analysis. The accuracy of corrugation recognition for the presented method is 93%.

A Concentrated Time-Frequency Method for Reservoir Detection Using Adaptive Synchrosqueezing Transform

The synchrosqueezing transform (SST) is an effective technique to concentrate the time-frequency (TF) energy and to retrieve the components of a non-stationary multicomponent signal. Therefore, it has been widely used to process and interpret seismic data. However, due to the fixed window width of the short-time Fourier transform (STFT), the STFT-based SST (FSST) is not well suitable for the characterization of the oil and gas reservoirs with varying layer thickness. Here, an adaptive SST is employed to characterize the features of the seismic signals for identifying the oil reservoirs with varying thickness. Overall, the proposed method is based on STFT with time-varying windows. For the local harmonic wave approximation and well-separated condition of a non-stationary multicomponent signal, the adaptive STFT is windowed with the Gaussian function. Compared with the conventional FSST, the adaptive FSST (AFSST) provides the TF concentration with better concentration and separates the components more accurately. In this work, both synthetic model and field seismic data are applied to validate the AFSST method, demonstrating that the AFSST method can precisely distinguish the stratigraphic characteristics.

Multiple Source of Microseismic Signal Classification by Adaptive Short-time Fourier Transform Method

Multiple Source of Microseismic Signal Classification by Adaptive Short-time Fourier Transform Method

Adaptive short-time Fourier transform and synchrosqueezing transform for non-stationary signal separation

The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier transform (STFT) with a time-varying parameter, called the adaptive STFT. Based on the local approximation of linear frequency modulation mode, we analyze the well-separated condition of non-stationary multicomponent signals using the adaptive STFT with the Gaussian window function. We propose the STFT-based synchrosqueezing transform (FSST) with a time-varying parameter, named the adaptive FSST, to enhance the time-frequency concentration and resolution of a multicomponent signal, and to separate its components more accurately. In addition, we also propose the 2nd-order adaptive FSST to further improve the adaptive FSST for the non-stationary signals with fast-varying frequencies. Furthermore, we present a localized optimization algorithm based on our well-separated condition to estimate the time-varying parameter adaptively and automatically. Simulation results on synthetic signals and the bat echolocation signal are provided to demonstrate the effectiveness and robustness of the proposed method.

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.

Short-time Fourier transform with the window size fixed in the frequency domain

The Short-Time Fourier Transform (STFT) is widely used to convert signals from the time domain into a time–frequency representation. This representation has well-known limitations regarding time–frequency resolution. In this paper we use the basic concept of the Short-Time Fourier Transform, but fix the window size in the frequency domain instead of in the time domain. This approach is simpler than similar existing methods, such as adaptive STFT and multi-resolution STFT, and in particular it requires neither the band-pass filter banks of multi-resolution techniques, nor the evaluation of local signal characteristics of adaptive techniques. Three case studies are analyzed and the results show that the proposed method allows better identification of signal components compared to standard STFT, multi-resolution STFT and Adaptive Optimal-Kernel Time Frequency Representation, although the method is not computationally efficient in its present form. Some synthetic and real world signals are used to demonstrate the effectiveness of the proposed technique.

Low Computational Enhancement of STFT-Based Parameter Estimation

Short-time Fourier transform (STFT) is one of the most widely used tools to analyze frequency and phase of local sections of time-varying signals using a time window function. Since the fixed window size of STFT causes limitation in time-frequency representation (TFR), adaptive STFT (ASTFT) techniques have been studied to adjust the window size depending on the local signal characteristics. However, ASTFT techniques suffer from heavy computational complexity in general. In this paper, we propose low computational enhanced temporal and spectral parameter estimation techniques for STFT output of radar signals; forward and backward STFT enhancement techniques. The proposed forward STFT enhancement technique is to enhance the spectral resolution of a received radar signal by multiple times using a number of successive STFT outputs without applying additional STFT with wider time window. On the other hand, the proposed backward STFT enhancement technique is to improve the temporal resolution of a received radar signal using an STFT output with a wide time window, without applying multiple STFTs with smaller time window. The performance of the proposed techniques are theoretically analyzed, and the advantage of the proposed techniques to the conventional techniques in terms of computational complexity is demonstrated with numerous simulations.

STFT With Adaptive Window Width Based on the Chirp Rate

An adaptive time-frequency representation (TFR) with higher energy concentration usually requires higher complexity. Recently, a low-complexity adaptive short-time Fourier transform (ASTFT) based on the chirp rate has been proposed. To enhance the performance, this method is substantially modified in this paper: i) because the wavelet transform used for instantaneous frequency (IF) estimation is not signal-dependent, a low-complexity ASTFT based on a novel concentration measure is addressed; ii) in order to increase robustness to IF estimation error, the principal component analysis (PCA) replaces the difference operator for calculating the chirp rate; and iii) a more robust Gaussian kernel with time-frequency-varying window width is proposed. Simulation results show that our method has higher energy concentration than the other ASTFTs, especially for multicomponent signals and nonlinear FM signals. Also, for IF estimation, our method is superior to many other adaptive TFRs in low signal-to-noise ratio (SNR) environments.

Time-Frequency Representation Based on an Adaptive Short-Time Fourier Transform

In this paper, a new concise algorithm about time-frequency representation (TFR) based on an adaptive short-time Fourier transform (ASTFT) is presented. In this algorithm, the analysis window width is equal to the local stationary length which is measured by the instantaneous frequency gradient (IFG) of the signal. And the instantaneous frequency (IF) of the signal is obtained by detecting the ridge of wavelet transform (WT). The ASTFT provides much better performance than conventional TFR algorithms. Furthermore, the algorithm is simpler and more computational efficient than some of other adaptive TFR algorithms proposed previously. Several examples are presented to illustrate its behavior on different kinds of signals and demonstrate its validity.

FM interference suppression for PRC-CW radar based on adaptive STFT and time-varying filtering

The influence of frequency modulation (FM) interference on correlation detection performance of the pseudo random code continuous wave (PRC-CW) radar is analyzed. It is found that the correlation output deteriorates greatly when the FM interference power exceeds the anti-jamming limit of the radar. According to the fact that the PRC-CW radar echo is a wideband pseudo random signal occupying the whole TF plane, while the FM interference only concentrates in a small portion, a new method is proposed based on adaptive short-time Fourier transform (STFT) and time-varying filtering for FM interference suppression. This method filters the received signal by using a binary mask to excise only the portion of the TF plane corrupted by the interference. Two types of interference, linear FM (LFM) and sinusoidal FM (SFM), under different signal-to-jamming ratio (SJR) are studied. It is shown that the proposed method can effectively suppress the FM interference and improve the performance of target detection.

Using ASTFT Spectrum to Suppress Cross Terms in WVD and its Application in Fault Diagnosis

A new fault diagnosis method to suppress cross terms of Wigner-Ville distribution (WVD) using Adaptive Short-time Fourier Transform (ASTFT) spectrum is put forward. The relationships of correlation between auto terms and cross terms of WVD are obtained theoretically by analyzing the WVD. Firstly, the signal ASTFT spectrum which can determine the signal component positions in the time-frequency plane is obtained. Then, the ASTFT spectrum as a window function is selected to process the signal WVD. Thus the cross terms can be effectively restrained. The simulation results show that a better resolution and more effective suppression of cross terms can be obtained. At last, the proposed method is applied to the fault diagnosis of bearing. The simulation and the experiment results indicate that the proposed method is effective in feature extraction.

Improved instantaneous frequency estimation using an adaptive short-time Fourier transform

Instantaneous frequency estimation (IFE) arises in a variety of important applications, including FM demodulation. We present here a new time-frequency representation (TFR)-based approach to IFE based on an adaptive short-time Fourier transform (ASTFT). This TFR leads naturally to a type of short-term ML estimator of the IF. To further improve the performance, we apply a multistate hidden Markov model (HMM)-based post-estimation tracker. The end result is up to a 16-dB reduction in the threshold SNR over the frequency discriminator (FD) and an 8-dB improvement over the phase-locked loop (PLL) for a Rayleigh fading channel.

Adaptive short-time Fourier analysis

This article presents a method of adaptively adjusting the window length used in short-time Fourier analysis, related to our earlier work in which we developed a means of adaptively optimizing the performance of the cone kernel distribution (CKD). The optimal CKD cone length is, by definition, a measure of the interval over which the signal has constant or slowly changing frequency structure. The article shows that this length can also be used to compute a time-varying short-time Fourier transform (STFT). The resulting adaptive STFT shares many desirable properties with the adaptive CKD, such as the ability to adapt to transient as well as long-term signal components. The optimization requires O(N) operations per step, less than the fast Fourier transform (FFT) used in computing each time slice, making it competitive in complexity with nonadaptive time-frequency algorithms.