Mohammed A. Hassan

Quadratic-Nonlinearity Index Based on Bicoherence and its Application in Condition Monitoring of Drive-Train Components

A new concept of the quadratic-nonlinearity power-index spectrum, QNLPI(f), that can be used in signal detection and classification, is proposed based on the bicoherence spectrum. The proposed QNLPI(f) is derived as a projection of the 3-D bicoherence spectrum into 2-D spectrum that quantitatively describes how much of the mean square power at a certain frequency f is generated by nonlinear quadratic interaction between different frequencies. The proposed index, QNLPI(f), can be used to simplify the study of bispectrum and bicoherence signal spectra. It also inherits useful characteristics from the bicoherence such as high immunity to additive gaussian noise, high capability of nonlinear-system identifications, and amplification invariance. Concept of the proposed index and its computational considerations are discussed first using computer-generated data and then applied to real-world vibration data from a helicopter drive train to assess health conditions of different mechanical faults as a part of condition-based maintenance.

Analysis of nonlinear vibration-interaction using higher order spectra to diagnose aerospace system faults

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.

Design of advanced time-frequency mutual information measures for aerospace diagnostics and prognostics

Accelerometer data has been gathered from accelerated conditioning in grease lubricated and lubrication deprived gear meshes in AH-64 helicopter intermediate and tail rotor gearbox, which are commonly problematic components of the Apache helicopter platform. These tests were performed in a controlled drive-train research test bed, simulating drive-train conditions to improve diagnostic and prognostic capabilities of Condition Based Maintenance (CBM) practices in Integrated Vehicle Health Monitoring System - Health Usage Monitoring System (IVHMS-HUMS) and other comparable CBM packages, as monitored by a standardized Digital Source Collector (DSC) system. Time-frequency representations of vibration measurement collected from two spaced sensors are used to provide signature analysis of transient system harmonics. Furthermore, the time-frequency mutual information advanced signal processing technique is then proposed and validated using vibration data. The measure advances the development of mutual information health indicators to quantify degradation of the helicopter power train. The AH-64 test systems perform under stress in realistic loading conditions and lifetime accelerated aircraft aging is monitored using the proposed advanced signal processing techniques for baseline tests for comparison with faulted conditions.1 2

Condition monitoring of helicopter drive shafts using quadratic-nonlinearity metric based on cross-bispectrum

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.

Quadratic-nonlinearity power-index spectrum and its application in condition based maintenance (CBM) of helicopter drive trains

This paper introduces a quadratic-nonlinearity powers-index spectrum (QNLPI(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 QNLPI(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.

A wavelet–based index for fault detection and its application in condition monitoring of helicopter drive–train components

This paper presents a new condition indicator using wavelet analysis for the purpose of fault detection in an AH–64 gearbox. Historically, vibration–based condition indicators from employed component monitoring equipment are derived from both temporal and spectral domain analysis. However, these indicators failed to accurately capture high order correlations for the gearbox study addressed in this paper. An improved approach is necessary to overcome limitations of traditional vibrational monitoring techniques. The proposed condition indicator is derived from the Morlet continuous wavelet .transform The power spectra obtained from the wavelet transform coefficients at a certain scale or frequency are added together and then are normalised to one composite signal, denoted by a numeric index. Concepts of the wavelet index are discussed. This index is applied using real–world vibration data from a tail rotor gearbox with an output seal leak as part of condition–based maintenance practices. Results demonstrate potential of the proposed wavelet index to more effectively capture the fault when compared to gearbox condition indicators. [Received 24 January 2014; Revised 28 August 2014; Accepted 3 October 2014]

Mechanical fault detection and classification using pattern recognition based on bispectrum algorithm

Higher order spectral analysis of vibration signals is an efficient tool in condition monitoring and fault detection and diagnosis of rotating machinery. In this paper, features extracted from vibration bispectrum are used in fault classification of critical rotating components in the AH-64D helicopter tail rotor drive train system. Different classifiers are used to compare the performance of the proposed algorithm based on bispectrum to the traditional algorithms based on linear auto- and cross-power spectral analysis techniques. Principal component analysis (PCA) is used to reduce the size of features extracted from vibration bispectrum and linear spectral analysis, then the reduced set is used to train different classifiers. Using different criteria such as accuracy, precision, sensitivity, F score, true alarm, and error classification accuracy (ECA), the performance of the proposed algorithm is evaluated and compared against similar classification algorithms. The proposed method is verified using real-world data collected from a dedicated AH-64D helicopter drive-train research test bed at the CPM center, University of South Carolina. The proposed algorithm increases the accuracy of fault detection to 96.88%, precession to 95.83%, sensitivity to 95.83%.

Cross-bispectral analysis for detection and diagnosis of helicopter trail-rotor drive-shaft problems

Based on cross-bispectrum, Cross-Quadratic-Coupling spectrum, CQC(f), is developed and used to assess different health conditions of an AH-64D (Apache) helicopter tail-rotor drive-shafts. CQC(f) is derived as a projection of the three-dimensional cross-bispectrum into two-dimensional spectrum that quantitatively describes quadratic coupling power at certain frequency in single-frequency space. Hence, the proposed CQC(f) simplifies the study of cross-bispectrum and inherits its useful characteristics such as high immunity to additive Gaussian noise and high capability of nonlinear-systems identification. Real-world vibration data are collected from a dedicated research test bed emulating full-scale AH-64D helicopter drive-train. Using the proposed index, different quadratic-nonlinear harmonic frequency patterns are detected and used to uniquely identify different cases of drive-shafts mechanical faults, such as angular misalignment and imbalance, compared to baseline case, which helps in gaining more diagnostic/prognostic capabilities. Magnitude response of the proposed CQC(f) is compared to the magnitude response of the conventional cross-power spectrum in terms of immunity to white Gaussian noise, and both analytical and experimental results shows superior performance of the proposed coupling spectrum.