Joint Time-frequency Research Articles

Damage detection of wind turbine system based on signal processing approach: a critical review

Numerous damage detection methods have been discovered to provide an early warning at the earliest possible stage against structural damage or any type of abnormality in the wind turbine system. In this paper, a comprehensive literature review is carried out in the field of damage detection for wind turbine systems. Several modern signal processing techniques including time-domain and frequency-domain analysis, joint time–frequency methods, entropy-based damage detection, supervisory control and data acquisition (SCADA), and machine learning approaches are all emphasized, and how to estimate the damage in wind turbine system by utilizing these various approaches is discussed. It is concluded that each of these methods offers its own unique merits and shortcomings in detecting certain types of damage with various levels of complexity. This research paper is aimed to inform the readers and experts about the damage detection techniques of the wind turbine system and fault diagnosis with various advanced signal processing methods.

Joint time–frequency mask and convolutional neural network for real-time separation of multipath in GNSS deformation monitoring

As one of the leading technologies of real-time dynamic deformation monitoring, global navigation satellite system (GNSS) has been widely used in deformation monitoring. Multipath error is the primary error source that limits the application of GNSS high-precision deformation monitoring, which cannot be eliminated by the double-differenced technique. It is a problem to separate and mitigate multipath in the GNSS deformation monitoring series in real-time. Therefore, we propose an approach to solve this problem, named time–frequency mask and convolutional neural network (TFM–CNN). The specific processes are as follows: (1) TFM–CNN network construction. We add a full-band deformation to the multipath and obtain the spectrogram of the signal by the short-time Fourier transform (STFT); meanwhile, the ideal ratio mask (IRM) is used to obtain the corresponding time–frequency mask matrix based on the spectrogram; furthermore, one-dimensional CNN mines the mapping relationship between the spectrogram and the time–frequency mask matrix. (2) Multipath separation. We obtain the spectrogram of the GNSS real-time deformation monitoring series by STFT. Then, we estimate its time–frequency mask matrix by the network. The matrix is multiplied by the spectrogram of the monitoring series to obtain the spectrogram of the multipath. Finally, we perform the inverse STFT to obtain the multipath in the GNSS monitoring series. The experimental results show that by training GNSS data in only a specific direction (such as the north direction), the mapping relationship between the spectrogram of multipath and the time–frequency mask matrix can be obtained, which can effectively separate multipath of the GNSS monitoring series in different observation environment in real-time. TFM-CNN significantly improves the monitoring accuracy and achieves millimeter level dynamic deformation monitoring.

Dynamic Electrochemical Impedance Spectroscopy of Lithium-ion Batteries: Revealing Underlying Physics through Efficient Joint Time-Frequency Modeling

The value and interpretation of dynamic electrochemical impedance spectroscopy (DEIS) during the charging and discharging of lithium-ion batteries is examined using the Doyle-Fuller-Newman pseudo-two-dimensional (P2D) lithium-ion battery model with parameters for a lithium-cobalt-oxide/graphite cell. Two computational approaches are explored to balance accuracy, speed, and interpretability: (i) A brute force time domain calculation of the full nonlinear equation set subject to direct current (DC) plus superimposed sinusoidal modulation of frequency ω 1, followed by post-processing with short-time Fourier transforms to track the dynamic impedance signal at the modulation frequency during charge and discharge; (ii) A fast-computing time-separated method that solves the C-rate dependent P2D equations for the DC charge/discharge transients occurring on the slow time-scales, t b ∼ O(3600 s/C), followed by solutions to linearized frequency domain equations derived for direct computation of the dynamic impedance signal. The time-separated method is rigorously correct in the limit 1/(t b ω 1) → 0. Key physics that drives differences between stationary and dynamic EIS signals is easily explored with the time-separated method. C-rate dependent studies show that DEIS signals are selectively sensitive to interfacial processes in ways that may be promising for real-time diagnostics and control of the negative electrode at high states-of-charge (SOC) and the positive electrode at low SOCs.

Mechanisms and timing of injury to the thoracic, lumbar and sacral spine in simulated underbody blast PMHS impact tests

During an underbody blast (UBB) event, mounted occupants are exposed to high rate loading of the spine via the pelvis. The objective of this study was to simulate UBB loading conditions and examine mechanisms of injury in the thoracic, lumbar and sacral spine. Fourteen instrumented, whole-body, postmortem human subject (PMHS) experiments were performed using the WSU-decelerative horizontal sled system. The specimens were positioned supine on a decelerative sled, which then impacted an energy absorbing system mounted to a concrete barrier. Variables included the peak velocity and time-to-peak velocity for seat and floor, and the presence or absence of personal protective equipment (PPE) and seat padding. Post-test CT scans and autopsies were performed to identify the presence and severity of injuries. Acceleration and angular rate data collected at vertebra T1, T5, T8, T12, and S1 were used to assess injury timing and mechanisms. Additionally, joint time-frequency analysis (JTFA) of the spinal Z acceleration of the sacrum and vertebrae was developed with the aim of verifying spinal fracture timing. Injuries observed in the spine were attributed to axial compression applied through the pelvis, together with flexion moment due to the offset in the center of gravity of the torso, and are consistent with UBB-induced combat injuries reported in the literature. The injury timing estimation techniques discussed in this study provide a time interval when the fractures are predicted to have occurred. Furthermore, this approach serves as an alternative to the estimation methods using acoustic sensors, force and acceleration traces, and strain gauges.

STFT Based on Bandwidth-Scaled Microwave Photonics

Short-time Fourier transform (STFT) is a fundamental concept that enables the observation of dynamic spectral evolution for non-stationary signals. Broadband STFT based on digital signal processing (DSP) usually has limited acquisition frame rate, which is inherently constrained by the performance limitations of present DSP engine. The further extended acquisition frame rate can be achieved by all-optical spectrum analysis approaches, while the frequency resolution is usually worse than 1 GHz. In this article, STFT based on bandwidth-scaled microwave photonics is proposed, where the requirement for dispersion is relaxed and the attendant transmission delay in dispersive media is greatly reduced. Moreover, the frequency resolution towards MHz level could be expected in the proposed STFT. We prove that “bandwidth scaling” combined with periodic wavelength-to-time mapping (WTM) mathematically agrees with the definition of STFT. The method of customizing system parameters according to the requirements of ultrafast spectrum measurement is carefully clarified. Experimentally, joint time-frequency analysis for a variety of ultrafast non-stationary RF signals is demonstrated, where dynamic frequency resolution of 60 MHz, dynamic observation bandwidth of 1.98 GHz and acquisition frame rate of 160 MHz are simultaneously realized. The scheme we proposed is promising for the dynamic spectrum monitoring of broadband non-stationary RF signals.

Time-varying fault feature extraction of rolling bearing via time–frequency sparsity

The joint time–frequency (TF) distribution is a critical method of describing the instantaneous frequency that changes with time. To eliminate the errors caused by strong modulation and noise interference in the process of time-varying fault feature extraction, this paper proposes a novel approach called second-order time–frequency sparse representation (SOTFSR), which is based on convex optimization in the domain of second-order short-time Fourier transform (SOSTFT) where the TF feature manifests itself as a relative sparsity. According to the second-order local estimation of the phase function, SOSTFT can provide a sparse TF coefficient in the short-time Fourier transform (STFT) domain. To obtain the optimal TF coefficient matrix from noisy observations, it is innovatively formulated as a typical convex optimization problem. Subsequently, a multivariate generalized minimax concave penalty is employed to maintain the convexity of the least-squares cost function to be minimized. The aim of the proposed SOTFSR is to obtain the optimal STFT coefficient in the TF domain for extraction of time-varying features and for perfect signal reconstruction. To verify the superiority of the proposed method, we collect the multi-component simulation signals and the signals under variable speed from a rolling bearing with an inner ring fault. The experimental results show that the proposed method can effectively extract the time-varying fault characteristics.

Time-frequency analysis of acoustic waves in an integrated acousto-optical modulator based on LiNbO3

The work presents a method allowing calculating the input admittance of an acousto-optic modulator with XY-cut lithium niobate substrate for a specific interdigital transducer structure is presented. The method does not require complex numerical computations and is sufficiently accurate. The method is based on the information about the pole of a Green’s function for a given piezocrystal. A method of measuring parameters and finding the types of the excited acoustic waves based on joint time-frequency analysis using modern vector network analyzers is also presented. Good correlation between theoretical and experimental investigation is demonstrated.

Compressed-Sensing-Based Time–Frequency Representation for Disturbance Characterization of Maglev On-Board Distribution Systems

The frequency variating source, linear generator, and switching devices lead to dynamic characteristics of the low-frequency conducted emissions within maglev on-board distribution systems. To track the time-varying feature of these disturbances, a joint time–frequency representation combined adaptive optimal kernel with compressed sensing technique is proposed in this paper. The joint representation is based on Wigner–Ville distribution, and employs adaptive optimal kernel to remove undesirable cross terms. The compressed sensing technique is introduced to deal with the tradeoff between cross-component reduction and auto-component smearing faced by kernel-function-based bilinear time–frequency representation. The time–frequency aggregation and accuracy performance of joint time–frequency representation is quantified using Rényi entropy and l1-norm. To verify its performance in disturbance signature analysis for distribution systems and primarily characterize the low-frequency conducted emissions of maglev, a maglev on-board distribution system experimental platform is employed to extract the low-frequency disturbances which pose threats to the controlling system. Comparison with Wigner–Ville distribution demonstrates the joint time–frequency representation method outperforms in tracking time-varying and transient disturbances of maglev on-board distribution systems.

Novel Parameter Estimation Method for a Ballistic Warhead with Micromotion

This paper proposes a novel method to estimate the parameters of a ballistic warhead with micromotion. First, the independent component analysis decomposes the echo signals received from the ballistic warhead into individual signals corresponding to each scatterer. Second, the one-dimensional micro-Doppler frequency trajectories are extracted from two-dimensional joint time-frequency images of decomposed individual signals. Finally, the adaptive particle swarm optimization is used to estimate the parameters that best match the mathematical model composed of unknown parameters to the one-dimensional micro-Doppler frequency trajectories. In simulations using a conical warhead model, the parameters for a ballistic warhead with micromotion are accurately estimated.

Wavlet Decomposition based Diagnostic for Structural Health Monitoring on Metallic Aircrafts: Case of Crack Triangulation and Corrosion Detection

This work focus on the structural health monitoring of aircrafts parts specimen structures made of 2024 Aluminum alloys using a reliable Joint Time Frequency Analysis calculation (Joint Temporal Frequency Analysis). In this paper we demonstrate the feasibility of a new non destructive control method capable to probe very large structures within a short time. The method we developed is based through a wide piezoelectric sensors network on a smart comparison between two acoustic signatures: the healthy structure response captured before the commissioning of the plane and “an after flight” response. The sensors network exploits the capability of piezoelectric patches to generate/measure specific Lamb wave’s modes. The system is therefore dynamically configured to localize mechanicals flaws using a triangulation algorithm that operates using different techniques like pitch-catch and pulse-echo. The aim of this paper is to highlight a methodology that is currently being integrated into reconfigurable qualified and certified hardware architecture. The idea behind is to interface the airplane's structure to an integrated modular avionics calculator (IMA).An analytic study is performed and tests to prove the proposed method feasibility on corroded and damaged structures specimens are provided at the end of this paper.

JTF Analysis of Micromotion Targets Based on Single-Window Variational Inference

This article addresses the problem of joint time–frequency (JTF) analysis of micromotion targets in complex environments in an approximate Bayesian inference framework. First, the sparse observation model is constructed, which is then decomposed into a series of single-window-JTF (SW-JTF) analysis problems to tackle the high dimension of the over-complete dictionary. On this basis, the probabilistic graphical model is constructed by imposing the Gamma-complex Gaussian prior to the JTF distribution. Finally, the model parameters are solved effectively by single-window variational inference (SWVI). Compared with the available methods, the proposed method could obtain better-focused JTF signature for narrowband data and higher quality range-instantaneous Doppler (RID) image for wideband data, especially in low signal-to-noise ratio (SNR) and data corruption scenarios.

Grain size evaluation with time-frequency ultrasonic backscatter

The ultrasonic backscatter signal can be used to evaluate the grain size of polycrystalline media nondestructively. In this article, the joint time-frequency analysis is introduced into the ultrasonic backscatter model, with the independent scattering approximation. The time-frequency domain model is applied to predict the spatial variance surface (SVS) and fit the experimental results to evaluate the grain size with the approach giving a relative error of 2.26% in comparison with metallography. Moreover, it shows that the present method suppresses electrical noise better than either the time domain or the frequency domain models alone. Based on the global sensitivity analysis of Sobol's method, the sensitivities of transducer parameters and material parameters in the ultrasonic backscatter model are estimated. The sensitivity analysis shows that not all the transducer parameters in the model must be calibrated carefully. In addition, it is found that the grain size sensitivity index of the time-frequency backscatter model is higher than the time domain or the frequency-domain backscatter models. Overall, the backscatter model in the time-frequency domain can evaluate the microstructure more accurately.

Refocusing High-Resolution SAR Images of Complex Moving Vessels Using Co-Evolutionary Particle Swarm Optimization

To increase the global convergence and processing efficiency of particle swarm optimization (PSO) applied in the adaptive joint time-frequency, in this study an improved PSO is proposed to refocus the high-resolution SAR images of complex moving vessels in high sea states. According to the characteristics of the high-order multi-component polynomial phase signal, this algorithm provides parallel processing and co-evolution methods by setting the different permissions of the sub-population and sharing its search information. As a result, the multiple components can be extracted simultaneously. Experiments were conducted using the simulation data and Gaofen-3 (GF-3) SAR data. Results showed the processing speed increased by more than 40% and the global convergence was significantly improved. The imaging results verify the efficiency and robustness of this co-evolutionary PSO.

Hilbert Transform Analyzer for Mechanical Fault Detection of Vehicle Alternators

Checking the alternator with mechanical measurements of moving parts takes sufficient time, especially in compact design engines. Therefore, this article presents a new method for alternator fault detection using the Hilbert transform application. The instantaneous amplitude and frequency are used as input variables for fault detection. Joint time-frequency analysis based on the wavelet analysis is also applied to identify the nonlinear characteristics. Various wavelet functions are examined, and some recommendations regarding the most suitable ones and the interpretation of the results are discussed. As a result, the backbone curve obtained from the instantaneous amplitude and frequency demonstrates the presence of the nonlinear phenomena, which can help make decisions about an alternator in normal conditions or indicate fault detection. From the test results, this method is very promising to be applied as part of vehicle's preventive maintenance.

Seismic Reflection Coefficient Inversion Using Basis Pursuit Denoising in the Joint Time-Frequency Domain

Seismic reflection coefficient inversion in the joint time-frequency domain is a method for inverting reflection coefficients using time domain and frequency domain information simultaneously. It can effectively improve the time-frequency resolution of seismic data. However, existing research lacks an analysis of the factors that affect the resolution of inversion results. In this paper, we analyze the influence of parameters, such as the length of the time window, the size of the sliding step, the dominant frequency band, and the regularization factor of the objective function on inversion results. The SPGL1 algorithm for basis pursuit denoising was used to solve our proposed objective function. The applied geological model and experimental field results show that our method can obtain a high-resolution seismic reflection coefficient section, thus providing a potential avenue for high-resolution seismic data processing and seismic inversion, especially for thin reservoir inversion and prediction.

Scalar Feedback-Based Joint Time-Frequency Precoder Interpolation for MIMO-OFDM Systems

In MIMO-OFDM systems, knowledge of the precoding matrix enables effective resource allocation for high rates and low BER. However, feeding back precoders for all subcarriers introduces large overheads. Past work has shown that the orthonormal structure of the precoder enables effective parameterization and quantization using Givens rotations and Householder transformations. Also, the use of temporal and frequency correlations can further reduce the feedback requirements. We present a framework that utilizes adaptive feedback with joint time-frequency prediction for precoder construction at the transmitter. Simulations reveal that the proposed method achieves significantly lower BERs for various channel profiles compared to other approaches.

On the co-movement of crude, gold prices and stock index in the Indian market

The nonlinear relationship in the joint time-frequency domain has been studied for the Indian National Stock Exchange (NSE) with the international Gold price and WTI Crude Price being converted from Dollar to Indian National Rupee based on that week’s closing exchange rate. Though a good correlation was obtained during some period, but as a whole no such cointegration relation can be found out. Using the Discrete Wavelet Analysis, the data was decomposed and the presence of Granger Causal relations was tested. Unfortunately, no significant relationships are being found. We then studied the Wavelet Coherence of the two pairs, namely NSE-Nifty & Gold and NSE-Nifty & Crude. For different frequencies, the coherence between the pairs have been studied. At lower frequencies, some relatively good coherence have been found. In this paper, we report for the first time the co-movements between Crude Oil, Gold and Indian Stock Market Index using Wavelet Analysis (both Discrete and Continuous), a technique which is most sophisticated and recent in market analysis. Thus, for long-term traders they can include gold and/or crude in their portfolio along with NSE-Nifty index in order to decrease the risk (volatility) of the portfolio for the Indian Market. But for short-term traders, it will not be effective, not to include all the three in their portfolio.

Fringe double for self-mixing interference based on the narrow transmission spectrum mapping.

In this work, a novel fringe double scheme with a Fabry-Pérot (F-P) cavity is proposed for self-mixing interferometry based on the narrow transmission spectrum mapping. While the laser beam with self-mixing interference (SMI) propagates through the F-P cavity with the narrow transmission spectrum, the SMI fringe doubles as the optical frequency modulation caused by SMI sweeps the peak of the transmission spectrum of the F-P cavity completely. The doubled SMI signal is very suitable for displacement reconstruction with fringe counting and velocity monitoring with joint time-frequency analysis, since it inherits the merits of the transmission spectrum of the F-P cavity (sharp, neat, and stable). This method has the potential to simplify signal processing and improve the resolution of SMI measurement systems.

Harmonic wavelets based response evolutionary power spectrum determination of linear and nonlinear structural systems with singular matrices

A new approximate analytical technique is proposed for determining the response evolutionary power spectrum (EPS) of stochastically excited structural multi-degree-of-freedom (MDOF) linear and nonlinear systems with singular matrices. Such systems can appear, indicatively, when a redundant coordinates modeling is adopted for forming the equations of motion of complex multi-body systems. For this case, it can be argued that this modeling approach facilitates the system’s stochastic response analysis, since employment of redundant DOFs is associated with computational cost efficient solution frameworks, and potentially provides with enhanced modeling flexibility. In this context, aiming at the joint time–frequency response analysis of MDOF systems, recently developed wavelet-based solution frameworks, which generalize classic input–output relationships of random vibration, are adopted and further generalized in this paper to account for systems with singular matrices. Specifically, resorting to the theory of generalized inverses of singular matrices, as well as to the theory of harmonic wavelets, a Moore–Penrose generalized matrix inverse excitation-response relationship is derived herein for determining the response EPS of linear MDOF systems. Further, a recently developed harmonic-wavelet-based statistical linearization technique is also generalized to account for the case of nonlinear MDOF systems. The validity of the proposed technique is demonstrated by pertinent numerical examples.

Mechanism of low frequency high amplitude pressure fluctuation in a pump-turbine during the load rejection process

ABSTRACT Owing to the complexity of the load rejection process, the accompanied complex low frequency pressure fluctuations and their sources have not been determined. Herein, the load rejection transient process of a pump-turbine was simulated with a three-dimensional (3-D) large eddy simulation method and a dynamic mesh technology. The simulation results were validated against the experimental data. Through the joint time-frequency analysis of simulated pressure, the complex low frequency pressure fluctuation components were captured, which are generally lower than the rated rotational frequency of the runner. A comprehensive formation mechanism of these complex low frequency pressure fluctuation components was attributed to three transient hydraulic phenomena and their interactions: the water hammer in the pump-turbine, local reverse flow near the runner inlet, and 3-D blocking water ring in the vaneless space. These findings facilitate the elucidation and elimination of complex low frequency high amplitude pressure fluctuations during the load rejection transient process.