scholarly journals Instantaneous Frequency Identification Using Adaptive Linear Chirplet Transform and Matching Pursuit

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Chang Xu ◽  
Cong Wang ◽  
Jingbo Gao
Keyword(s):  
Instantaneous Frequency ◽  
Matching Pursuit ◽  
Vibration Signal ◽  
High Time Resolution ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Identification Method ◽  
Chirplet Transform ◽  
Comparison Results ◽  
Frequency Identification

An instantaneous frequency identification method of vibration signal based on linear chirplet transform and Wigner-Ville distribution is presented. This method has an obvious advantage in identifying closely spaced and time-varying frequencies. The matching pursuit algorithm is employed to select optimal chirplets, and a modified version of chirplet transform is presented to estimate nonlinear varying frequencies. Because of the high time resolution, the modified chirplet transform is superior to the original method. The proposed method is applied to time-varying systems with both linear and nonlinear varying stiffness and systems with closely spaced modes. A wavelet-based identification method is simulated to compare with the proposed method, with the comparison results showing that the chirplet-based method is effective and accurate in identifying both time-varying and closely spaced frequencies. A bat echolocation signal is used to verify the effectiveness of the modified chirplet transform. The result shows that it will significantly increase the accuracy of nonlinear frequency trajectory identification.

Time-Varying Frequency Formula for the Purely Nonlinear Damped Oscillator

2014 ◽  
Author(s):  
Mohammad A. AL-Shudeifat
Keyword(s):  
Instantaneous Frequency ◽  
Nonlinear Oscillator ◽  
Analytical Formula ◽  
Initial Energy ◽  
Physical Parameters ◽  
Frequency Change ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Time Varying Frequency ◽  
Damped Oscillator

The frequency of the purely nonlinear and non-conservative oscillator is a time-varying quantity due to the presence of damping. For the nonlinear oscillator addressed here, only cubic-power stiffness nonlinearity is considered. The nonlinear frequency of the conservative nonlinear oscillator is dependent on the initial energy induced into the system. However, for the non-conservative and purely nonlinear oscillator, the instantaneous frequency is dependent on the instantaneous energy of the system. Consequently, the exact amplitude decay formula obtained in a recent publication for such oscillator is accurately applied here to obtain an accurate analytical formula for the time-varying frequency of the considered system. Excellent agreement between the results obtained by the new time-varying frequency formula presented here and both numerical simulation and wavelet transform has been clearly observed. This analytical formula is found to be accurate in identifying the instantaneous frequency change of the system regardless of its physical parameters and the initial input energies.

Time-Varying Modal Analysis by SDOF Wavelets

2000 ◽  
Author(s):  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Matching Pursuit ◽  
Damping Ratio ◽  
Identification Problem ◽  
Mode Shapes ◽  
Time Varying ◽  
Identification Method ◽  
Time Varying Systems ◽  
Single Input ◽  
Expansion Coefficients ◽  
The Time Domain

Abstract The purpose of this paper is to provide a modal expression of a time-varying MDOF system and to develop an identification method for it. The single-input-multi-output relation of a time-varying N-DOF system is expressed as a superposition of N time-varying SDOF subsystems in the time domain, where the expansion coefficients represent the time-varying mode-shapes, and the natural frequency and the damping ratio of each subsystem represent the time-varying modal parameters of each mode. Then we define the SDOF wavelets, which correspond to the time-varying impulse responses of SDOF subsystems and show that the output of the entire system can be expressed by a superposition of SDOF wavelets. Then, the identification problem is reduced to an atomic decomposition problem of choosing the nearly best set of SDOF wavelets and determining the expansion coefficients. We develop a modified matching pursuit algorithm, called modal pursuit, to solve the problem. Basic examples are numerically examined to show that the proposed modal representation and the identification method are applicable to track the modal characteristics of time-varying systems.

A novel amplitude-independent crack identification method for rotating shaft

2018 ◽  
Vol 232 (22) ◽  
pp. 4098-4112 ◽  
Author(s):  
Laihao Yang ◽  
Xuefeng Chen ◽  
Shibin Wang
Keyword(s):  
Frequency Analysis ◽  
Instantaneous Frequency ◽  
Vibration Signal ◽  
Rotor System ◽  
Crack Identification ◽  
Fast Time ◽  
Time Varying ◽  
Cracked Rotor ◽  
Time Frequency ◽  
Cracked Rotor System

The shaft crack is one of the most common and serious malfunctions in rotating machines and may lead to catastrophic failure if undetected in time. However, the conventional crack identification methods are amplitude-dependent and thus can be only applied to the crack identification under some specific conditions. In this paper, a novel amplitude-independent crack identification method (AiCIM) is significantly proposed to eliminate the amplitude-dependent property and promote the effectiveness of the crack identification. First and foremost, a fast time-varying vibration phenomenon of the cracked-rotor system is newly found. Through the theoretical analysis, the fast time-varying vibration mechanism of the cracked-rotor system is revealed for the first time. It is indicated that the vibration signal of the cracked-rotor system is modulated by the fast-oscillated instantaneous frequency, which is independent of the amplitude of the vibration signal. AiCIM is then put forward on the basis of the fast time-varying vibration mechanism and matching time–frequency analysis theory. Specially, the amplitude-independent instantaneous frequency of the vibration signal is extracted via the matching time–frequency analysis theory, and the time–frequency representation energy-concentration is enhanced along the instantaneous frequency trajectory. Since instantaneous frequency of the vibration signal carrying the critical fault information is employed to identify the shaft crack, AiCIM is only relevant to the phase of the vibration signal, i.e. amplitude independent. As a result, AiCIM successfully eliminates the dependence on the signal amplitude and is more sensitive to the weak crack. Both the numerical and experimental results demonstrate that AiCIM behaves best to extract the fast-oscillated feature of the fast time-varying vibration induced by the shaft crack in comparison with other time–frequency analysis methods, and AiCIM effectively suppress the effect of noises on the instantaneous frequency estimation because of its amplitude-independent property. Influences of the crack parameters on the nonlinear instantaneous frequency are finally discussed with AiCIM. This study provides a potential way to the online crack identification.

scholarly journals Estimating the Instantaneous Frequency of Linear and Nonlinear Frequency Modulated Radar Signals—A Comparative Study

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2840
Author(s):  
Hubert Milczarek ◽  
Czesław Leśnik ◽  
Igor Djurović ◽  
Adam Kawalec
Keyword(s):  
Instantaneous Frequency ◽  
Early Warning Systems ◽  
Vital Role ◽  
Estimation Methods ◽  
Radar Signal ◽  
Nonlinear Frequency ◽  
Modulation Recognition ◽  
Electronic Warfare ◽  
Time Frequency ◽  
Radar Signals

Automatic modulation recognition plays a vital role in electronic warfare. Modern electronic intelligence and electronic support measures systems are able to automatically distinguish the modulation type of an intercepted radar signal by means of real-time intra-pulse analysis. This extra information can facilitate deinterleaving process as well as be utilized in early warning systems or give better insight into the performance of hostile radars. Existing modulation recognition algorithms usually extract signal features from one of the rudimentary waveform characteristics, namely instantaneous frequency (IF). Currently, there are a small number of studies concerning IF estimation methods, specifically for radar signals, whereas estimator accuracy may adversely affect the performance of the whole classification process. In this paper, five popular methods of evaluating the IF–law of frequency modulated radar signals are compared. The considered algorithms incorporate the two most prevalent estimation techniques, i.e., phase finite differences and time-frequency representations. The novel approach based on the generalized quasi-maximum likelihood (QML) method is also proposed. The results of simulation experiments show that the proposed QML estimator is significantly more accurate than the other considered techniques. Furthermore, for the first time in the publicly available literature, multipath influence on IF estimates has been investigated.

scholarly journals RANSAC algorithm for instantaneous frequency estimation and reconstruction of frequency-modulated undersampled signals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Igor Djurović
Keyword(s):  
Instantaneous Frequency ◽  
Matching Pursuit ◽  
Frequency Estimation ◽  
Consensus Algorithm ◽  
Multidimensional Space ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Polynomial Phase ◽  
Fm Signals ◽  
Fifth Order

AbstractFrequency modulated (FM) signals sampled below the Nyquist rate or with missing samples (nowadays part of wider compressive sensing (CS) framework) are considered. Recently proposed matching pursuit and greedy techniques are inefficient for signals with several phase parameters since they require a search over multidimensional space. An alternative is proposed here based on the random samples consensus algorithm (RANSAC) applied to the instantaneous frequency (IF) estimates obtained from the time-frequency (TF) representation of recordings (undersampled or signal with missing samples). The O’Shea refinement strategy is employed to refine results. The proposed technique is tested against third- and fifth-order polynomial phase signals (PPS) and also for signals corrupted by noise.

Kalman filter identification method for micro-vibration transfer paths of satellites

2021 ◽  
pp. 095441002110533
Author(s):  
Yan Shen ◽  
Yang Xu ◽  
Xiaowei Sheng ◽  
Xianbo Yin
Keyword(s):  
Kalman Filter ◽  
Correlation Coefficients ◽  
Vibration Signal ◽  
Satellite System ◽  
Solar Array ◽  
Target Point ◽  
Mechanical Equipment ◽  
Displacement Response ◽  
Transfer Path ◽  
Identification Method

Micro-vibrations on-board a satellite have degrading effects on the performance of certain payloads like observation cameras. The major sources of vibrations include momentum wheels, solar array drives, other rotary mechanical equipment, etc. These vibrations result in loss of the pointing precision and image quality of the payload through intricate transfer paths. To improve the accuracy of a satellite system with many vibration sources and complex transfer paths, it is necessary to determine the main transfer path of vibration. In this study, a path identification method is proposed and applied to the transfer system from the momentum wheel to the camera mount. First, the observer/Kalman filter identification (OKID) algorithm is used to acquire the state-space equation of each path subsystem. Then, the subsystem order is obtained based on the slope of the singular entropy increment. In the next phase, combined with the measured disturbance force of the momentum wheel, the displacement response of the target point is predicted. Finally, the dominant transfer path of vibration is achieved by calculating the vibration contribution of each path to the response point. The results indicate that the dominant transfer path is the axial path of the horizontal momentum wheel, which contributes to the vibration of the camera mount at most. Effective vibration reduction measures should be taken to this path to suppress the vibration signal. In comparing the identified displacement response with the finite element response of the camera mount under different noise conditions, the correlation coefficients are >0.85, which proves the accuracy and anti-noise capability of the identification method.

scholarly journals Source reconstruction for bioluminescence tomography via L1∕2 regularization

2018 ◽  
Vol 11 (02) ◽  
pp. 1750014 ◽  
Author(s):  
Jingjing Yu ◽  
Qiyue Li ◽  
Haiyu Wang
Keyword(s):  
Image Quality ◽  
Matching Pursuit ◽  
Imaging Modality ◽  
Reconstruction Algorithm ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Preclinical Research ◽  
Bioluminescence Tomography ◽  
Comparison Results ◽  
Stable Reconstruction

Bioluminescence tomography (BLT) is an important noninvasive optical molecular imaging modality in preclinical research. To improve the image quality, reconstruction algorithms have to deal with the inherent ill-posedness of BLT inverse problem. The sparse characteristic of bioluminescent sources in spatial distribution has been widely explored in BLT and many L1-regularized methods have been investigated due to the sparsity-inducing properties of L1 norm. In this paper, we present a reconstruction method based on L[Formula: see text] regularization to enhance sparsity of BLT solution and solve the nonconvex L[Formula: see text] norm problem by converting it to a series of weighted L1 homotopy minimization problems with iteratively updated weights. To assess the performance of the proposed reconstruction algorithm, simulations on a heterogeneous mouse model are designed to compare it with three representative sparse reconstruction algorithms, including the weighted interior-point, L1 homotopy, and the Stagewise Orthogonal Matching Pursuit algorithm. Simulation results show that the proposed method yield stable reconstruction results under different noise levels. Quantitative comparison results demonstrate that the proposed algorithm outperforms the competitor algorithms in location accuracy, multiple-source resolving and image quality.

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