Accurate Time-frequency Representation 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.

Very Accurate Time-Frequency Representation of Induction Motors Harmonics for Fault Diagnosis Under Load Variations

Very Accurate Time-Frequency Representation of Induction Motors Harmonics for Fault Diagnosis Under Load Variations

Composite signal detection using multisynchrosqueezing wavelet transform

It is important to study recognition and recovery of effective signal components for information extraction of composite signals. However, owing to the limitation of time-frequency (TF) resolution, composite signal detection has always been a difficult problem, particularly for signals with crossover frequencies, namely crossover signals. This study proposes a new approach to solve signal estimation based on optimization of TF distribution. Firstly, based on the theory of multisynchrosqueezing transform (MSST), a high-order multisynchrosqueezing wavelet transform (HMSWT) that can accurately estimate the nonlinear instantaneous frequency (IF) is studied. On this basis, wavelet coefficient reassignment is extended to two dimensions by introducing the chirp rate, and a high-order multisynchrosqueezing chirplet transform (HMSCT) is proposed to realize cross-component parameter estimation. This study realizes the theoretical expansion of MSST and performs multiple reassignments on a three-dimensional time-frequency-chirp rate (TFC) framework for the first time. Numerical experiments on typical multi-component FM signals show that the proposed method can provide a more accurate TF representation and high-precision component separation.

Synchro-Squeezed Adaptive Wavelet Transform-Based Optimized Multiple Analytical Mode Decomposition: Parameter Identification of Cable-Stayed Bridge under Earthquake Input

Deriving critical parametric information from recorded signals for system identification is critical in structural health monitoring and damage detection, while the time-varying nature of most signals often requires significant processing efforts due to structural nonlinearity. In this study, synchro-squeezed adaptive wavelet transform-based optimized multiple analytical mode decomposition (SSAWT-oMAMD) is proposed. The SSAWT algorithm acts as the preprocessing algorithm for clear signal component separation, high temporal and frequency resolution, and accurate time–frequency representation. Optimized MAMD is then utilized for signal denoising, decomposition, and identification, with the help of AWT for bisecting frequency determination. The SSAWT-oMAMD is first verified by the analytical model of two Duffing systems, where clear separation of the two signals is presented and identification of complex time-varying stiffness is achieved with errors less than 2.9%. The algorithm is then applied to system identification of a cable-stayed bridge model subjected to earthquake loading. Based on both numerical and experimental results, the proposed method is effective in identifying the structural state and viscous damping coefficient.

GNSS Code Multipath Time-Frequency Analysis Using Wavelet-Based Synchrosqueezing Transform in Urban Environments

Time–frequency (TF) analysis can be used as a useful tool to detect the global navigation satellite system (GNSS) code multipath (MP) and its frequency content. An accurate TF representation (TFR) is critical for highlighting the MP’s frequency signature and identifying its possible sources. The popular short-time Fourier transform (STFT) method has limitations in dealing with fast varying instantaneous frequencies, which are frequently observed in global navigation satellite system (GNSS) measurements due to MP. The wavelet-based synchrosqueezing transform (WSST) is a potential technique for providing a detailed high-resolution TFR. In this letter, we use WSST to perform TF analysis on both simulated and real-world data, demonstrating its utility in detecting code MP and its frequency content in urban environments. Based on the results, possible MP sources for the real datasets were identified. Furthermore, the proposed technique’s TF analysis results were validated using the ray-tracing method, demonstrating its effectiveness for MP detection.

An improved smooth-windowed Wigner-Ville distribution analysis for voltage variation signal

This paper outlines research conducted using bilinear time-frequency distribution (TFD), a smooth-windowed wigner-ville distribution (SWWVD) used to represent time-varying signals in time-frequency representation (TFR). Good time and frequency resolutions offer superiority in SWWVD to analyze voltage variation signals that consist of variations in magnitude. The separable kernel parameters are estimated from the signal in order to get an accurate TFR. The TFR for various kernel parameters is compared by a set of performance measures. The evaluation shows that different kernel settings are required for different signal parameters. Verification of the TFD that operated at optimal kernel parameters is then conducted. SWWVD exhibits a good performance of TFR which gives high peak-to-side lobe ratio (PSLR) and signal-to-cross-terms ratio (SCR) accompanied by low main-lobe width (MLW) and absolute percentage error (APE). This proved that the technique is appropriate for voltage variation signal analysis and it essential for development in an advanced embedded system.

Application of adaptive wavelet transform based multiple analytical mode decomposition for damage progression identification of Cable-Stayed bridge via shake table test

Extracting useful information (damage existence, location, identification, and quantification) from measured signals for damage identification is critical in structural health monitoring, while time-varying nature of most signals often require huge efforts. In this paper, adaptive wavelet analysis AWT is first introduced as a preprocessing approach of clearer, smoother and more accurate time–frequency representation. Optimized analytical mode decomposition (AMD) is then utilized for signal component extraction, with the help of AWT for bisecting frequency determination. Examples of time-varying signals of sinusoidal function and Duffing systems are used to illustrate the advantages of the algorithm, which proves to be successful in signal decomposition. Multiple AMD (MAMD) with the optimized algorithm is then utilized together with AWT for signal decomposition and system identification of the shake table test of a 1/20-scale cable-stayed bridge model. The extracted stiffness and damping coefficients retain a preliminary indication of the damage progression during the earthquake input.

Time-Frequency Represetation of Radar Signals Using Doppler-Lag Block Searching Wigner-Ville Distribution

Radar signals are time-varying signals where the signal parameters change over time. For these signals, Quadratic Time-Frequency Distribution (QTFD) offers advantages over classical spectrum estimation in terms of frequency and time resolution but it suffers heavily from cross-terms. In generating accurate Time-Frequency Representation (TFR), a kernel function must be able to suppress cross-terms while maintaining auto-terms energy especially in a non-cooperative environment where the parameters of the actual signal are unknown. Thus, a new signal-dependent QTFD is proposed that adaptively estimates the kernel parameters for a wide class of radar signals. The adaptive procedure, Doppler-Lag Block Searching (DLBS) kernel estimation was developed to serve this purpose. Accurate TFRs produced for all simulated radar signals with Instantaneous Frequency (IF) estimation performance are verified using Monte Carlo simulation meeting the requirements of the Cramer-Rao Lower Bound (CRLB) at SNR > 6 dB.

A synchroextracting-based method for early chatter identification of robotic drilling process

The robotic drilling process has shown its high industrial application potential for millions of holes in the aviation manufacturing. However, due to the relatively low stiffness of the serial robot manipulator, the robotic drilling system is more prone to chatter, leading to poor surface roughness, unbearable noise, and even causing severe damage to the end effector spindle. Consequently, it is of vital significance to identify and suppress this undesirable vibration. In this paper, a synchroextracting-based method is proposed for the early chatter detection of robotic drilling operations. The proposed algorithm is implemented through the following steps. First, the accurate time-frequency representation of the measured vibration signal is acquired by employing the synchroextracting transform (SET), which has high energy concentration and robustness to measurement noise. Second, the whole signal is divided into a finite number of frequency bands, and the corresponding sub-signal for each frequency band can be reconstructed by retaining the maximum coefficient of the SET. Finally, working as the chatter indicator, the statistical energy entropy is utilized to capture the inhomogeneous variation of energy distribution during the chatter transition process. Robotic drilling experiments with different cutting conditions were conducted to verify the effectiveness of the proposed chatter identification method. The results demonstrate that the presented synchroextracting-based algorithm can identify the chatter at an early stage, which is useful for the subsequent chatter suppression.

Time-Frequency Analysis of Seismic Data Using Synchrosqueezing Transform

Time-frequency analysis can provide useful information in seismic data processing and interpretation. An accurate time-frequency representation is important in highlighting subtle geologic structures and in detecting anomalies associated with hydrocarbon reservoirs. The popular methods, like short-time Fourier transform and wavelet analysis, have limitations in dealing with fast varying instantaneous frequencies, which is often the characteristic of seismic data. The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation. We apply the SST to seismic data and show its potential to seismic signal processing applications.

IF estimation of FSK signals using adaptive smoothed windowed cross Wigner–Ville distribution

Time-varying signals such as frequency shift-keying (FSK) signals can be characterized by the instantaneous frequency (IF). From the estimated IF, it is possible to derive the signal modulation parameters such as the subcarrier frequencies and the symbol duration. If accurate time–frequency representation (TFR) is obtained, the cross time–frequency distribution (XTFD) provides an optimum solution to IF estimation over quadratic time–frequency distribution (QTFD). Thus, an adaptive XTFD is proposed, the adaptive smoothed windowed cross Wigner–Ville distribution (ASW-XWVD), for which the kernel parameters are estimated according to the signal characteristics and the choice of reference signal. The IF is estimated from the peak of the TFR and comparison is performed using the S-transform. The variance in the IF estimation using the proposed ASW-XWVD meets the Cramer–Rao lower bound (CRLB) at minimum signal-to-noise ratio (SNR) of −3dB, while the S-transform never meets the CRLB, even at SNR of 12dB. For practical applications, the ASW-XWVD is applied to the FSK signal in the high frequency (HF) band and is able to provide accurate TFR and IF estimates at SNR of 14dB.

Bivariate Empirical Mode Decomposition for Unbalanced Real-World Signals

The bivariate empirical mode decomposition (BEMD) algorithm employs uniform sampling on a circle to perform projections in multiple directions, in order to calculate the local mean of a bivariate signal. However, this approach is adequate only for equal powers in both the data channels within a bivariate signal, and results in suboptimal performance for data channels exhibiting power imbalance, a typical case in practice. To that end, we exploit second-order bivariate statistical properties to introduce a nonuniform sampling scheme for data adaptive selection of the projection directions. In this way, the resulting nonuniformly sampled BEMD (NS-BEMD) algorithm provides a more accurate time-frequency representation of bivariate data than standard BEMD, for the same number of projections. The advantages of the proposed approach are demonstrated in case studies on BEMD for correlated data channels, selection of optimal noise power in noise-assisted BEMD, and for speed estimation using Doppler radar.

Detection and characterization of multiple power quality disturbances with a fast S-transform and decision tree based classifier

This paper proposes fast variants of the discrete S-transform (FDST) algorithm to accurately extract the time localized spectral characteristics of nonstationary signals. Novel frequency partitioning schemes along with band pass filtering are proposed to reduce the computational cost of S-transform significantly. A generalized window function is introduced to improve the energy concentration of the time-frequency (TF) distribution. An application of the proposed algorithms is extended for detection and classification of various nonstationary power quality (PQ) disturbances. The relevant features required for classification were extracted from the time-frequency distribution of the nonstationary power signal patterns. An automated decision tree (DT) construction algorithm was employed to select optimal set of features based on a specified optimality criterion for extraction of the decision rules. The set of decision rules thus obtained were used for identification of the PQ disturbance types. Various single as well as simultaneous power signal disturbances were considered in this paper to prove the efficiency of proposed classification scheme. A comparison of the classification accuracies with techniques proposed earlier, clearly demonstrates the improved performance. The major contributions of this manuscript are new FDST algorithms for fast and accurate time-frequency representation and an efficient classification algorithm for identifying PQ disturbances. The advantages of the classification algorithm are (i) accurate feature derivation from the TF distribution and optimum feature selection by the DT construction algorithm, (ii) robust performance at different signal-to-noise ratios, (iii) simple decision rules for classification, and (iv) recognition of simultaneous PQ events.

Adaptive Optimal Kernel Smooth-Windowed Wigner-Ville Distribution for Digital Communication Signal

Time-frequency distributions (TFDs) are powerful tools to represent the energy content of time-varying signal in both time and frequency domains simultaneously but they suffer from interference due to cross-terms. Various methods have been described to remove these cross-terms and they are typically signal-dependent. Thus, there is no single TFD with a fixed window or kernel that can produce accurate time-frequency representation (TFR) for all types of signals. In this paper, a globally adaptive optimal kernel smooth-windowed Wigner-Ville distribution (AOK-SWWVD) is designed for digital modulation signals such as ASK, FSK, and M-ary FSK, where its separable kernel is determined automatically from the input signal, without prior knowledge of the signal. This optimum kernel is capable of removing the cross-terms and maintaining accurate time-frequency representation at SNR as low as 0 dB. It is shown that this system is comparable to the system with prior knowledge of the signal.

Adaptive autoregressive modeling of non-stationary vibration signals under distinct gear states. Part 2: experimental analysis

Parametric time–frequency representation based on parametric models is more desirable for presenting highly precise time–frequency domain information due to its high-resolution property. However, the sensitivity and robustness of parametric models, in particular the parametric models on the basis of advanced adaptive filtering algorithms, has never been investigated for on-line condition monitoring of rotating machinery. Part 1 of this study proposed three adaptive parametric models based on three advanced adaptive filtering algorithms. Part 2 of this study is concerned with the effectiveness of the proposed models under distinct gear states, especially the highly non-stationary conditions accrued from advanced gear faults. Four gear states are considered: healthy state, adjacent gear tooth failure, non-adjacent gear tooth failure and distributed gear tooth failure. The vibration signals used in this study include the time-domain synchronous averaging signal and gear motion residual signal for each considered gear state. The test results demonstrate that the optimum filter behavior can readily be attained and the white Gaussian assumption of innovations can relatively be easily guaranteed for the NAKF-based model under distinct gear states and a wide variety of model initializations. On the other hand, the EKF- and MEKF-based models are capable of generating more accurate time–frequency representations than the NAKF-based model, but in general the optimality condition for white Gaussian assumption cannot be guaranteed for these two advanced models. Therefore, the NAKF-based model is preferred for automatic condition monitoring due to its appealing robustness to distinct gear states and arbitrary model initializations, whereas the EKF- and MEKF-based models are desirable when accurate time–frequency representation is concerned.