Analysis of Nonlinear Vibration-Interaction Using Higher Order Spectra to Diagnose Aerospace System Faults Mohammed A. Hassan, David Coats, Kareem Gouda*, Yong-June Shin, and Abdel Bayoumi* Department of Electrical Engineering/ Department of Mechanical Engineering* University of South Carolina 301 Main Street Columbia, SC 803-454-9461 shinjune@cec.sc.edu, bayoumi@cec.sc.edu Abstract— For efficient maintenance of a diverse fleet of ag- ing air- and rotorcraft, effective condition based maintenance (CBM) must be established based on rotating components mon- itored vibration signals. Traditional linear spectral analysis techniques of the vibration signals, based on auto-power spec- trum, are used as common tools of rotating components diag- noses. 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 co- herence 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. TABLE OF CONTENTS 1 I NTRODUCTION .................................. 1 2 STATISTICAL RELATIONSHIPS BETWEEN VI - BRATION SIGNALS ............................... 2 3 EXPERIMENT SETUP AND DATA DESCRIPTION .. 3 4 APPLICATION OF BISPECTRUM TO ANALYZE VIBRATION INTERACTIONS ...................... 4 5 NUMBER OF NONLINEAR HARMONIC I NTER- ACTION AS A CI ................................. 6 6 CONCLUSION .................................... 7 ACKNOWLEDGMENTS ........................... 7 REFERENCES .................................... 7 BIOGRAPHY ..................................... 8 1. I NTRODUCTION Condition Based Maintenance (CBM) is a practice that rec- ommends maintenance actions for machines, or systems, based on the continuous condition-monitoring of their com- 978-1-4577-0557-1/12/$26.00 c ⃝2012 IEEE. 1 IEEEAC Paper #1345, Version 4, 04/01/2012. ponents [1], [2]. In contrast, traditional time-based mainte- nance (TBM) involves replacing existing parts after a certain time period or a certain number of operational hours. Im- plementation of the CBM helps to avoid failures in critical parts due to unexpected wear which may cause operational downtime and/or potential safety hazards [3], [4], [5]. We have sought to improve the accuracy of condition indicators (CIs) used in the Vibration Management Enhancement Pro- gram. VMEP implementation resulted in on-board Modern Signal Processing Unit (a vibration data acquisition and signal-processing equipment for the health monitoring of critical mechanical components) for AH-64 (Apache), UH- 60 (Blackhawk) and CH-47 (Chinook) fleets [6] and aims to provide rotorcraft maintainers with a collection of diagnos- tic and progressively prognostic vibration-based indicators summarized by CIs or Health Indicators (HIs), which collect several CI metrics. Pre-established and baseline measure- ments of these typically one-dimensional CI and HI values from existing historical data and testbed verifications under extreme conditions provide rankings for the status of individ- ual aerospace and rotorcraft components with ratings such as “Good,” “Caution,” and “Exceeded,” which in turn provide maintainers of these fleets proactive time-independent condi- tion based maintenance decision making [7]. Our aim is to improve the effectiveness of the MSPU by de- veloping new general methods for fault analysis that could be used in existing or new CIs. Unfortunately, some of the exist- ing CIs based on conventional time or spectral analysis have limited diagnostic capabilities and are used to detect more than one fault associated with the same rotating component. For example, SP2 (Spectral Peak 2) is currently employed in the MSPU to detect unbalanced and/or misaligned shafts in a tail rotor drive-train of a rotorcraft [8]. However, this CI does not specify whether the fault is unbalance, misalignment or a combination of those faults. The maintainers are told to check for more than one source that might cause that CI to exceed its limit. We use the concept of higher order spectra in vibration analysis toward the development of more robust diagnostic CI metrics, as well as the furthered understanding of underlying physical and electromechanical interactions. In order to obtain better understanding of the fault sources, statistical relationship (or, dependence) between vibration signals can be investigated using various orders of the corre- lation function. The Fourier transform of the auto-correlation is the classical auto-power spectrum which is one of the most commonly used tools in spectrum analysis [9], [10]. Simi- larly, higher-order correlations, and their Fourier transforms describe higher order statistical relationships. Higher order spectral densities (HOS), such as bispectrum and trispectrum, 1