Quadratic-Nonlinearity Index Based on Bicoherence and its Application in Condition Monitoring of Drive-Train Components (original) (raw)
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2012 IEEE International Instrumentation and Measurement Technology Conference Proceedings, 2012
This paper introduces a quadratic-nonlinearity powers-index spectrum (QN LP I(f)) measure that describes quantitatively how much of the mean square power at certain frequency f is generated by nonlinear quadratic interaction between different frequencies inside signal spectrum. The proposed index QN LP I(f) is based on the bicoherence spectrum, and the index can be simply seen as summary of the information contained in the bicoherence spectrum in two dimensional graph which makes it easier to interpret. The proposed index is studied first using computer generated data and then applied to real-world vibration data from a helicopter drive train to characterize different mechanical faults. This work advances the development of health indicators based on higher order statistics to assess fault conditions in mechanical systems.
IFAC Proceedings Volumes, 2008
Bicoherence or Bispectrum analysis is emerging as a new powerful technique in signal processing, especially in areas where traditional linear spectral analysis provides insufficient information. It is most effective in analyzing systems with non-linear coupling between frequencies. Faults in rotating machineries leave their signature on the vibration signal sensors and generally manifest themselves as a non-linear transformation in the vibration signal. Bicoherence analysis detects and quantifies the presence of non-linearity in the signal and thus indicates the severity of the fault in the machine. This paper demonstrates the use of bicoherence analysis on both simulated and rig-generated vibration data from a rub-effected rotor-stator system, and shows the application of bicoherence analysis on industrial data from final tailing pumps to detect impeller wear in an oil-sands plant.
IEEE Transactions on Aerospace and Electronic Systems, 2014
Based on cross-bispectrum, quadratic-nonlinearity coupling between two vibration signals is proposed and used to assess health conditions of rotating shafts in an AH-64D helicopter tail rotor drive train. Vibration data are gathered from two bearings supporting the shaft in an experimental helicopter drive train simulating different shaft conditions, namely, baseline, misalignment, imbalance, and combination of misalignment and imbalance. The proposed metric shows better capabilities in distinguishing different shaft settings than the conventional linear coupling based on cross-power spectrum.
Fault detection of rotating machinery from Bicoherence analysis of vibration data
6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, 2006, 2006
The vibration signal carries the signature of the fault in most rotating equipments, and early fault detection of a fault is possible by analyzing the signal using different signal processing techniques. In this paper we consider gearboxes as a typical representation of a rotating or cyclo-stationary process. Faults in gearboxes leave their signature on the vibration signal with an increased presence of non-linearity. Bicoherence analysis detects and quantifies the non-linearity present in the signal and thus indicates the severity of the fault present in the gearbox. Time synchronous averaging is used to find the proper representation of one period of the cyclo-stationary vibration signal. A pilot plant case study is presented to demonstrate the practicality and utility of the proposed technique.
2012 IEEE Aerospace Conference, 2012
For efficient maintenance of a diverse fleet of aging air-and rotorcraft, effective condition based maintenance (CBM) must be established based on rotating components monitored vibration signals. Traditional linear spectral analysis techniques of the vibration signals, based on auto-power spectrum, are used as common tools of rotating components diagnoses. Unfortunately, linear spectral analysis techniques are of limited value when various spectral components interact with one another due to nonlinear or parametric process. In such a case, higher order spectral (HOS) techniques are recommended to accurately and completely characterize the vibration signals. Since the nonlinearities result in new spectral components being formed with coherency in phase, the detection of such phase coherence may be carried out with the aid of higher order spectra. In this paper, we use the bispectrum as a higher order spectral analysis tool to investigate nonlinear wave-wave interaction in vibration signals. Accelerometer data has been collected from baseline tests of accelerated conditioning in tail rotor drive-train components of an AH-64 helicopter drive-train research test bed simulating drive-train conditions. Through bispectrum analysis, we compare the harmonics interaction patterns contained in vibration signals from different physical setting of helicopter drive train and compare that with classical power spectral density plots. The analysis advances the development of higher order statistics and two dimensional frequency health indicators in order to qualify health conditions in mechanical systems.
Nonlinearity detection using new signal analysis methods for global health monitoring
Scientia Iranica
Statistical pattern recognition has emerged as a promising and practical technique for data-based health monitoring of civil structures. This paper is intended to detect nonlinearity changes resulting from damage by some simple but effective signal analysis methods. The primary idea behind these methods is to use measured time-domain vibration signals based on exploratory data analysis without applying any feature extraction. Firstly, statistical moments and central tendency measurements on the basis of the theory of exploratory data analysis are considered as damage indicators to monitor their changes and detect any substantial variations in measured vibration signals. Subsequently, cross correlation and convolution methods are proposed to measure the similarity and overlap between the measured signals of the undamaged and damaged conditions. The main innovation of this study is the capability of the proposed signal analysis methods for implementing nonlinear damage detection without any feature extraction. Numerical and experimental models of civil structures are employed to demonstrate the effectiveness and performance of the proposed methods. Results show that nonlinearity changes caused by damage lead to reductions in the values of cross correlation and convolution methods. Moreover, some statistical criteria are applicable tools for the global structural health monitoring.
Bicoherence analysis of nonstationary and nonlinear processes
Cornell University - arXiv, 2018
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic bicoherence, unfortunately, tends to give false positives-high bicoherence values without actual nonlinear coupling of different frequency components-for signals exhibiting rapidly changing amplitudes and limited length. The effect of false positive values can lead to misinterpretation of results, therefore a more prudent analysis is necessary in such cases. This paper analyses the properties of bispectrum and bicoherence in detail, generalizing these quantities to nonstationary processes. A step-by-step method is proposed to filter out false positives at a given confidence level for the case of nonstationary signals. We present a number of test cases, where the method is demonstrated on simple physics-based numerical systems. The approach and methodology introduced in the paper can be generalized to lower and higher order coherence calculations.
Looking for a vibrational measure of vehicle powertrain damage using multifractal analysis
2014
The paper proposes the Detrended Fluctuation Analysis (DFA) of the vibration signal for diagnosing of mechanical defects of the vehicle powertrain. The DFA allows investigations of the observed signals with regard to their multifractality. The results of vibration signal analysis of the engine with the damaged exhaust valve and with the unsuitable exhaust valve clearance are presented. During road test the acceleration vibration signal was recorded with additional signals for synchronization and engine timing. The vibration data are analysed by DFA and the resultant scaling-law curve with crossover points are obtained. The estimated Hurst exponents are used in the selection procedure of diagnostic features.
Comparison of statistical indices using third order statistics for nonlinearity detection
Signal Processing, 2004
In this paper we discuss the e ciency of nonlinearity indices based on higher order statistics in order to detect nonlinearities in an observed signal, the signal being the output of a transmission channel (possibly nonlinear) the input of which is not accessible. Nonlinearity detection is the ÿrst step of nonlinearity analysis, this step being followed by nonlinearity location of the nonlinear components (in the Fourier domain) and quantiÿcation of these components. The main results reported in this paper are, ÿrst, a systematic survey of the robustness of hypothesis testing for each index and, second, the derivation of indices which neither involve the ratio of estimated quantities (such as bicoherence) nor phase unwrapping (such as the bicepstrum). The robustness of hypothesis testing is veriÿed by calculating type II error probability (i.e. the error of declaring that the time series has been produced by a linear system while produced by a nonlinear one). To calculate this error, the observed time series is assumed to be the output of a second-order Volterra model driven by a Gaussian distributed noise. Obviously, the assumption of such a model might seem restrictive, but the results obtained allow us to draw some deÿnitive conclusions about the robustness of the indices presented. The calculation is performed ÿrst from a theoretical spectrum and bispectrum and, second, from estimated indices. These indices are estimated from linear and nonlinear time series having the same spectrum. The estimation of the type II error probability on estimated indices allows the veriÿcation of the assumptions used to derive the theoretical index probability density function. ?
This paper considers the properties of a bispectrum estimate when applied to a system with quadratic nonlinearity excited by the superposition of harmonics in the presence of additive Gaussian noise. This is compared using signal-to-noise ratios, to the power spectrum. Numerical examples were included to verify the results. In addition, an application of the use of the bispectrum to detect rotor faults in rotating machinery through detection of quadratic phase coupling is presented. The paper aims to clarify the use of the bispectrum to detect non-linearity in time series and presents the background theory on the bis-pectrum and in its application. Further, we show how patterns in the bispectrum are useful for identifying the frequency (or bifrequency) components involved in the non-linear interaction. The properties of interest are insensitivity to Gaussian noise and it's ability to detect quadratic phase coupling. The study aims to expand the domain of induction machines faults diagnosis. To verify the theoretical development, stator currents which were collected from a test bed based on a 18.5 kW three-phase squirrel cage induction machine have been used in a steady-state condition.