Local Instantaneous Frequency Research Articles

Structural Damage Diagnosis of Aerospace CFRP Components: Leveraging Transfer Learning in the Matching Networks Framework

This paper introduces a damage diagnosis method based on the reassignment method and matching networks (MNs) to study the structural health monitoring of aerospace composite material components. This aims to facilitate the mapping of signal features to complex failure modes. We introduce a signal processing technique based on the reassignment method, employing a sliding analysis window to re‐estimate local instantaneous frequency and group delay. By utilizing the short‐time phase spectrum of the signal, we correct the nominal time and frequency coordinates of the spectrum data, aligning them more accurately with the true support region of the analyzed signal. Subsequently, this paper developed a deep matching network (DMN) damage diagnosis model based on MNs. This model utilizes a convolutional neural network (CNN) to extract damage‐related features from the signal and introduces the full context embedding (FCE) method to enhance the compatibility of sample embeddings. In this process, the embeddings of each sample in the training set should be mutually independent, while the embeddings of test samples should be regulated by the distribution of training set sample data. Ultimately, the damage category of test samples is determined based on cosine similarity. We validate our model using damage sample data collected from experiments and simulations conducted under varying components and operating conditions. Comparative assessments with five mainstream methods reveal an average accuracy exceeding 96%. This underscores the exceptional recognition accuracy and generalization performance of our proposed method in cross‐operating condition fault diagnosis experiments concerning aircraft composite material components.

Inferring Topology of Networks With Hidden Dynamic Variables

Inferring the network topology from the dynamics of interacting units constitutes a topical challenge that drives research on its theory and applications across physics, mathematics, biology, and engineering. Most current inference methods rely on time series data recorded from all dynamical variables in the system. In applications, often only some of these time series are accessible, while other units or variables of all units are hidden, i.e. inaccessible or unobserved. For instance, in AC power grids, frequency measurements often are easily available whereas determining the phase relations among the oscillatory units requires much more effort. Here, we propose a network inference method that allows to reconstruct the full network topology even if all units exhibit hidden variables.We illustrate the approach in terms of a basic AC power grid model with two variables per node, the local phase angle and the local instantaneous frequency. Based solely on frequency measurements, we infer the underlying network topology as well as the relative phases that are inaccessible to measurement. The presented method may be enhanced to include systems with more complex coupling functions and additional parameters such as losses in power grid models. These results may thus contribute towards developing and applying novel network inference approaches in engineering, biology and beyond.

A Comprehensive Overview on Modified Versions of Stockwell Transform For Power Quality Monitoring

The increasing trends toward the accurate identification of power quality disturbances (PQD) via power quality (PQ) monitoring require an appropriate digital signal processing (DSP) technique and a robust classifier. To this end, Stockwell transform (ST), one of the most efficient feature extraction DSP tools, and its several variants play an utmost role in PQ assessment framework. Its time-varying spectral characteristics generally extract the local instantaneous frequency spectrum from the global temporary behavior of PQD signal. However, the Standard ST suffers from thepoor time-frequency resolution because of its frequency-dependent Gaussian window (GW). While the analysis of the statistically time-varying signals requires a suitable balance between time and frequency resolution. To this end, this paper provides a comprehensive literature review on several modified versions of Standard ST for the first time to reduce the computational complexity of the algorithm as well as maximize the energy concentration of the time-frequency plane. A comparative analysis of all the modified STs has been presented in tabular form to provide the key characteristics of each technique. Additionally, a case study has been presented to substantiate the highest accuracy of the proposed algorithm over the other ST variants. Apart from the PQD classification, miscellaneous applications of Standard ST and its modified variants have been indicated. This review paper may provide a valuable resource to the researchers for further improvement of the time-frequency resolution of ST not only in classifying PQD but also for its other wide applications.

Seismic Local Instantaneous Frequency Extraction for Describing Superposed Sands

Seismic instantaneous frequency (IF), as one of the instantaneous attributes, is widely used for seismic interpretation and stratigraphy analysis. The Hilbert transform (HT)-based complex analysis approaches are commonly used to extract seismic IF, which are sensitive to kinds of noise contained in field data. Although the normalized HT (NHT) improves the antinoise property of HT by normalizing the original trace, the HT-based methods are a global operator that is not suitable for the local analysis. For example, IF calculated by using the HT-based method is unstable when meeting strong seismic events. In this letter, we propose a workflow to extract local IF (LIF) and then apply it to describe superposed sands. Note that the proposed workflow extracts a stable IF result even when processing a seismic trace with strong events. To demonstrate the effectiveness of the proposed workflow, we apply it to both synthetic and field data. Compared with results from HT and NHT, the proposed workflow provides a stable IF extraction and offers potentials in precisely highlighting superposed sands.

Seismic time–frequency spectrum analysis based on local polynomial Fourier transform

Time–frequency analysis technology is widely used in non-stationary seismic data analysis. The energy concentration of the spectrum depends on the consistency of the kernel function of the time–frequency analysis method and the instantaneous frequency variation of the signals. The conventional time–frequency analysis methods usually require that the local instantaneous frequency of the signals remains unchanged or linearly changed. So it is difficult to accurately characterize the instantaneous frequency nonlinear variation of the non-stationary signal. The local polynomial Fourier transform (LPFT) method can effectively describe the instantaneous frequency variation by local high-order polynomial fitting and obtain the results with high spectral and energy concentration. The numerical simulations and field seismic data applications show that the time–frequency spectrum results obtained by LPFT can reflect the instantaneous frequency variation characteristics of the seismic data, while ensuring the concentration of time–frequency energy.

Prospects of FMCW‐based frequency diverse array radar

The linear frequency modulated (LFM) frequency modulated continuous wave (FMCW)-based frequency diverse array (FDA) radar concept is investigated in detail. The radar operates as a linear pulsed FMCW/FDA in the transmission (TX) mode while it operates as a pulsed FMCW/phased array (PA) in the receiving mode. The issues such as low signal-to-noise ratio (SNR) of FDA, the time-angle scanning and time-range ambiguities are studied. It is shown that the local instantaneous frequency bandwidth is much smaller than the radio frequency (RF) deviation of LFM. Positive and negative slope TX/RF locations offer frequency diversity. Time domain and frequency domain signal processings are described. A Ku band direct digital synthesis-based FMCW/FDA radar example based on the cumulative detection scheme is given and compared with an equivalent FMCW/PA radar.

An ameliorated synchroextracting transform based on upgraded local instantaneous frequency approximation

This paper introduces an upgraded synchroextracting transform (SET), namely ameliorated synchroextracting transform (ASET), to deal with fast time-varying and strong frequency modulated signals for time and frequency analysis (TFA). SET is a recently developed time-frequency representation (TFR) method with an exceptional capability to enhance the readability of TFR, yet the kernel of SET is based upon the assumption of purely harmonic signal, therefore, it is more applicable to slow time-varying and weekly frequency modulated signals. However, for rotating machines in real practice, fluctuation loads and varying rotational speeds are always inevitable, the resultant vibrations will exhibit non-stationary frequency-modulated nature. To tackle this problem, in this paper, the synchroextracted operator in SET is upgraded in terms of second-order Taylor expansion to estimate the fast and strong frequency modulated signals so that a better TFR can be achieved. The advantages of ASET is demonstrated with simulated and experimental studies by comparing the existing time and frequency analysis methods. The sharpness of TFR, the ability of signal reconstruction and the robustness to noise pollution are also demonstrated.

Space scanning FMCW‐based two‐dimensional frequency diverse array radar

The frequency-modulated continuous wave (FMCW)-based frequency diverse array (FDA) radar concept is extended to two dimensions (2D). The radar operates as a linear pulsed FMCW/FDA in the transmission (TX) mode while it operates as a pulsed FMCW/phased array (PA) in the receiving mode. It is shown that the FDA has the capability of scanning a 2D angular sector in a single pulse TX. It is shown that local instantaneous frequency bandwidth is much smaller than the radiofrequency (RF) frequency deviation of linear frequency modulation. Positive and negative slope TX/RF locations offer frequency diversity. The low signal-to-noise ratio of FDA is well compensated due to target temporal decorrelation diversity in the observation time and by the cumulative detection scheme used. Time domain and frequency domain signal processings are described. A Ku-band direct digital synthesis-based FDA radar design is compared by a corresponding equivalent PA radar.

An adaptive non-parametric short-time Fourier transform: Application to echolocation

This paper studies a novel time–frequency representation method—adaptive non-parametric short-time Fourier transform (ANSTFT), together with its application to the echolocation signal analysis. By rotating the signal in the analysis window, the local instantaneous frequency has been reset to parallel to the time axis. Then the high frequency and time resolution have been achieved with the mono-frequency signal simultaneously. To find the optimal rotating angle of the local signal, an iterative approximation algorithm has been utilized, which makes the ANSTFT a non-parametric data driving method and have the better generalization ability than the conventional adaptive STFT. Moreover, several numerical examples are presented to illustrate the aforementioned characteristics and the application of ANSTFT to echolocation signal analysis demonstrates its validity.

Nonlinearity and non-stationarity analysis of dynamic response of vehicle–track coupling system enhanced by Huang transform

A method is proposed to analysis the nonlinearity and non-stationarity of dynamic response of high speed vehicle–track coupling system, to understand the properties of signal and its underlying physical meaning. First, a space coupling model of high speed vehicle–track system is built according to the theory of coupling dynamics of vehicle–track system. Then, the dynamic response of vehicle–track system is processed by Ensemble Empirical Mode Decomposition (EEMD) to generate the intrinsic mode functions (IMFs). Next, the “Direct Quadrature” (DQ) method is used to calculate the local instantaneous frequency and instantaneous amplitude of the IMFs, the generalized zero-crossing method and the full wave zero-crossing method are applied to calculate the mean local frequency of the IMFs. Finally, the index and degree of nonlinearity and non-stationarity based on intra-wave frequency modulation (the deviation of the instantaneous frequency from the generalized zero-crossing frequency) and inter-wave frequency modulation (the deviation of the instantaneous frequency from the full wave zero-crossing frequency), are defined to quantify the nonlinearity and non-stationarity of dynamic response. The usefulness and capability of the proposed method are displayed through two cases, which are considered general enough to be the representatives of nonlinear and non-stationary dynamic response of vehicle–track coupling system.

Method for Exact Compensation of Voltage and Current Phasors Computed by Orthogonal Finite Impulse Response Filters During Frequency Variations

This article presents a generic method that fully compensates for the errors introduced by orthogonal finite impulse response filters (full-cycle discrete Fourier transform, half-cycle discrete Fourier transform, Cosine filter) in phasor computation during frequency variations in power systems. To accomplish this, the proposed method uses an accurate and easily calculated estimate of the local instantaneous frequency. The method is robust and precise and can be extended to deal satisfactorily with the effect of harmonics. Also, its implementation simplicity makes it attractive for real-time applications. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Local instantaneous frequency estimation of multi-component signals

We present a method for estimating the instantaneous frequency (IF) of multi-component signals. This method involves the calculation of a time–frequency energy density of the signal, then obtaining a local IF estimate from this joint density. Time–frequency energy density is calculated as a least squares optimal combination of multi-window Gabor based evolutionary spectra. The optimal weights are obtained by minimizing an error criterion that is the difference between a reference time–frequency distribution and the combination of evolutionary spectra. IF of the signal components is estimated from the final evolutionary spectrum at small time–frequency regions as the average of frequencies at each time. As such, local IF information of a multi-component signal can be estimated in the time–frequency plane.

Vertical and horizontal disparities from phase

We apply the notion that phase differences can be used to interpret disparity between a pair of stereoscopic images. Indeed, phase relationships can also be used to obtain both orientation and probabilistic measures towards the computation of edges and corners, as well as the directional instantaneous frequency of an image field. The method of phase differences is shown to be equivalent to a Newton-Raphson root finding iteration through the resolutions of band-pass filtering. The method does, however, suffer from stability problems, and in particular stationary phase and interference. The stability problems associated with this technique are implicitly derived from the mechanism used to interpret disparity, which in general requires an assumption of linear phase and the local instantaneous frequency. We present two techniques. First, we use the centre frequency of the applied band-pass filter to interpret disparity. This interpretation, however, suffers heavily from phase error, and requires considerable damping prior to convergence. Second, we use the derivative of phase to obtain the instantaneous frequency from an image, which is then used to improve the disparity estimate. These ideas are extended into 2D where it is possible to extract both vertical and horizontal disparities.