Fine Time-frequency Resolution Research Articles

Time-frequency space vector modulus analysis of motor current for planetary gearbox fault diagnosis under variable speed conditions

Abstract Motor current signature analysis is a promising technique for electromechanical system fault detection, and has been studied under steady states. In this paper, a planetary gearbox fault diagnosis method under variable speed conditions using stator current signal is proposed. In order to thoroughly understand the frequency characteristics of current signals, an analytical amplitude modulation and phase modulation (AM-PM) current model considering gear fault modulation effects is presented. Two more aspects of endeavor are made to highlight gear fault signatures in stator current signals in context of inconspicuousness and time variability. Firstly, to address the sideband complexity and power supply dominance issues inherent with stator current signals, squared space vector modulus (SVM) together with its time-varying spectral characteristics in planetary gearbox fault cases under variable speed conditions are mathematically derived. Secondly, to reveal time-varying fault features in details, polynomial chirplet transform (PCT) is improved by iterative algorithm, and merits of fine time-frequency resolution and cross term free nature are achieved. The effectiveness of the proposed method is illustrated by numerical simulation, and is further validated by lab experiments on a real world 4 kW induction motor driven planetary gearbox test rig.

Adaptive iterative generalized demodulation for nonstationary complex signal analysis: Principle and application in rotating machinery fault diagnosis

Abstract Effective identification of signal frequency contents and their time variability is a key to success in rotating machinery fault diagnosis under nonstationary conditions. Fine time-frequency resolution and free from both inner and outer interferences are necessary to achieve this purpose. Iterative generalized demodulation (IGD) can separate a nonstationary multi-component signal into constituent mono-components, and derive quality time-frequency representation based on Hilbert spectrum of each mono-component, thus offering an effective approach to nonstationary complex signal analysis. Nevertheless, it requires prior expertise knowledge about signal structure to ascertain true constituent components and construct proper demodulation phase functions. This leads to a major difficulty in real signal analysis tasks, where expertise knowledge is usually unavailable and signal time-frequency structure identification via visual observation is susceptible to noise interferences. To address this issue, the capability of surrogate test technique in recognizing true signal components is exploited, and thereby an adaptive iterative generalized demodulation (AIGD) is proposed. Proper demodulation phase functions corresponding to constituent components are derived accordingly, and Hilbert spectra of all constituent mono-components are superposed to generate time-frequency representation (TFR). This method features good merits, such as fine time-frequency resolution and free of both inner and outer interferences. Additionally, it neither relies on prior expertise knowledge about signals, nor needs to construct any basis function. It is highly adaptive to reveal the frequency contents and track their time variability of a signal, and provides an effective approach to nonstationary complex multi-component signal analysis. It is illustrated and validated via numerical simulations, lab experiments of a planetary gearbox and rolling bearings, and on-site tests of a hydraulic turbine in a hydraulic power plant.

Iterative generalized time–frequency reassignment for planetary gearbox fault diagnosis under nonstationary conditions

Planetary gearboxes are widely used in many sorts of machinery, for its large transmission ratio and high load bearing capacity in a compact structure. Their fault diagnosis relies on effective identification of fault characteristic frequencies. However, in addition to the vibration complexity caused by intricate mechanical kinematics, volatile external conditions result in time-varying running speed and/or load, and therefore nonstationary vibration signals. This usually leads to time-varying complex fault characteristics, and adds difficulty to planetary gearbox fault diagnosis. Time–frequency analysis is an effective approach to extracting the frequency components and their time variation of nonstationary signals. Nevertheless, the commonly used time–frequency analysis methods suffer from poor time–frequency resolution as well as outer and inner interferences, which hinder accurate identification of time-varying fault characteristic frequencies. Although time–frequency reassignment improves the time–frequency readability, it is essentially subject to the constraints of mono-component and symmetric time–frequency distribution about true instantaneous frequency. Hence, it is still susceptible to erroneous energy reallocation or even generates pseudo interferences, particularly for multi-component signals of highly nonlinear instantaneous frequency. In this paper, to overcome the limitations of time–frequency reassignment, we propose an improvement with fine time–frequency resolution and free from interferences for highly nonstationary multi-component signals, by exploiting the merits of iterative generalized demodulation. The signal is firstly decomposed into mono-components of constant frequency by iterative generalized demodulation. Time–frequency reassignment is then applied to each generalized demodulated mono-component, obtaining a fine time–frequency distribution. Finally, the time–frequency distribution of each signal component is restored and superposed to get the time–frequency distribution of original signal. The proposed method is validated using both numerical simulated and lab experimental planetary gearbox vibration signals. The time-varying gear fault symptoms are successfully extracted, showing effectiveness of the proposed iterative generalized time–frequency reassignment method in planetary gearbox fault diagnosis under nonstationary conditions.

A velocity synchrosqueezing transform for fault diagnosis of planetary gearboxes under nonstationary conditions

Time–frequency analysis is widely used in the field of machinery condition monitoring and fault diagnosis under nonstationary conditions. Among the time–frequency methods synchrosqueezing transform outperforms others in providing fine-resolution time–frequency representation. However, it suffers from time–frequency smear when analysing nonstationary signals. To address this issue, this paper proposes a new synchrosqueezing-transform-based method which works by (1) mapping the raw nonstationary vibration signal into a corresponding stationary angle domain signal to meet the stationarity requirement of the synchrosqueezing transform, (2) performing the synchrosqueezing transform of the corresponding signal and (3) restoring the time–frequency representation of the raw signal from the synchrosqueezing transform result of the corresponding signal. As the synchrosqueezing transform is applied to the stationary corresponding signal, the time–frequency smear is eliminated in the synchrosqueezing transform result of the corresponding signal and the final signal time–frequency representation. As such the proposed method can generate a smear-free time–frequency representation with fine time–frequency resolution and thus provide more reliable diagnosis decisions. A fast implementation algorithm is also developed to simplify the implementation of the proposed method. The effectiveness of the proposed method is validated using both simulated and experimental vibration signals of planetary gearboxes.

Application of Reassigned Wavelet Scalogram in Wind Turbine Planetary Gearbox Fault Diagnosis under Nonstationary Conditions

Wind turbine planetary gearboxes often run under nonstationary conditions due to volatile wind conditions, thus resulting in nonstationary vibration signals. Time-frequency analysis gives insight into the structure of an arbitrary nonstationary signal in joint time-frequency domain, but conventional time-frequency representations suffer from either time-frequency smearing or cross-term interferences. Reassigned wavelet scalogram has merits of fine time-frequency resolution and cross-term free nature but has very limited applications in machinery fault diagnosis. In this paper, we use reassigned wavelet scalogram to extract fault feature from wind turbine planetary gearbox vibration signals. Both experimental and in situ vibration signals are used to evaluate the effectiveness of reassigned wavelet scalogram in fault diagnosis of wind turbine planetary gearbox. For experimental evaluation, the gear characteristic instantaneous frequency curves on time-frequency plane are clearly pinpointed in both local and distributed sun gear fault cases. For in situ evaluation, the periodical impulses due to planet gear fault are also clearly identified. The results verify the feasibility and effectiveness of reassigned wavelet scalogram in planetary gearbox fault diagnosis under nonstationary conditions.

Fault diagnosis of wind turbine planetary gearbox under nonstationary conditions via adaptive optimal kernel time–frequency analysis

Planetary gearboxes play an important role in wind turbine (WT) drivetrains. WTs usually work under time-varying running conditions due to the volatile wind conditions. The planetary gearbox vibration signals in such an environment are hence highly nonstationary. Conventional spectral analysis and demodulation analysis methods are unable to identify the characteristic frequency of gear fault from such nonstationary signals. As such, this paper presents a time–frequency analysis methods to reveal the constituent frequency components of nonstationary signals and their time-varying features for WT planetary gearbox monitoring. More specifically, we exploit the adaptive optimal kernel (AOK) method for this challenging application because of its fine time–frequency resolution and cross-term free nature, as demonstrated by our simulation analysis. In this study, the AOK method has been applied to identify the time-varying characteristic frequencies of gear fault or to extract different levels of impulses induced by gear faults from lab WT experimental signals and in-situ WT signals under time-varying running conditions. We have demonstrated that the AOK is effective diagnosis of: (a) both the local damage (a single chipped tooth) and distributed faults (wear of all teeth), (b) both sun gear and planet gear faults, and (c) faults with very weak signature (e.g., the sun gear fault at the low speed stage of a WT planetary gearbox).

Assessment of the dynamic interactions between heart rate and arterial pressure by the cross time–frequency analysis

In this study, a framework for the characterization of the dynamic interactions between RR variability (RRV) and systolic arterial pressure variability (SAPV) is proposed. The methodology accounts for the intrinsic non-stationarity of the cardiovascular system and includes the assessment of both the strength and the prevalent direction of local coupling. The smoothed pseudo-Wigner–Ville distribution (SPWVD) is used to estimate the time–frequency (TF) power, coherence, and phase-difference spectra with fine TF resolution. The interactions between the signals are quantified by time-varying indices, including the local coupling, phase differences, time delay, and baroreflex sensitivity (BRS). Every index is extracted from a specific TF region, localized by combining information from the different spectra. In 14 healthy subjects, a head-up tilt provoked an abrupt decrease in the cardiovascular coupling; a rapid change in the phase difference (from 0.37 ± 0.23 to −0.27 ± 0.22 rad) and time delay (from 0.26 ± 0.14 to −0.16 ± 0.16 s) in the high-frequency band; and a decrease in the BRS (from 23.72 ± 7.66 to 6.92 ± 2.51 ms mmHg−1). In the low-frequency range, during a head-up tilt, restoration of the baseline level of cardiovascular coupling took about 2 min and SAPV preceded RRV by about 0.85 s during the whole test. The analysis of the Eurobavar data set, which includes subjects with intact as well as impaired baroreflex, showed that the presented methodology represents an improved TF generalization of traditional time-invariant methodologies and can reveal dysfunctions in subjects with baroreflex impairment. Additionally, the results also suggest the use of non-stationary signal-processing techniques to analyze signals recorded under conditions that are usually supposed to be stationary.