Extracting and Characterizing Blade-Vortex Interaction Noise with Wavelets Wyah Davis Charles Pezeshki M. .m.mne . Mosher GradtcafeAssisfartf Associafr Pmfessor Research Scietlrirr Deparmrent of Mechanical and Materials Engineering, NASA Ames Research Cetzfeq Washington Sfate Universify, Moffetf Field. CA Pullman. WA Applications of a discrete implementation of the wavelet transform (WT) to the analysis of blade-vortex interaction (BVI) noise are presented. The method decompe5 a signal into a seriesof orthogonal subhand9 logarithmically spaced in frequency while simultanwusly p-wing temporal information. A BVI detection algorithm was developed which takes advantage of the prominence of BVI noise in certain subbands. A method for extracting BVI noise fmm other noise sources is described. Three metrics are tested for suilahility as BVI estimators. One of these, a motmean-square (RMS) metric, characterizes BVI noise severity, but q u i r e s the added computational effort of inverting the transform. The other two metrirs are computed using the information available from the WT. The first of t h w , computed fmm the amplitudes of BVI event. in a single suhband, cor- relates with peak-to-peak pressure and is relatively insensitive to noise. The second of these, based on the exponential behav- iorof peak amplitudes across subhands, is apparently unable to characterize BVI noiseseverity and is highly sensitive to noise. Introduction Rackground Considerable attention has been devoted in rccent years toward devel- The Wavelet Transform oping a bctter understanding of blade-vortex interaction (BVI) noise. When BVI noise occurs, it tends to dominate other noise sources and con- Classical methods of signal analysis typically eramine a signal in ei- tains most of its energy in the frequency range important to human sensi- ther the time-domain or the frequency-domain via Fourier trmsfoms. One tivity (Refs. 1.2). Consequently, the rotorcraft industry has been motivated method of describing non-stationary signal events is through the use ofthe to improve noise reduction technology. short-time Fourier transform (STFC). The STFl is calculaled hy sliding a Cooperative research between NASA and the major helicopter prw window along the signal and taking the discrete Fourier transform of thc ducers (Boeing, Sikorsky, McDonnell Douglas, and Bell) has produced portion of the signal seen by the window. significant progress toward BVI noise abatement. Recently, investigations While the S T F l can Sully describe the time-frequency rclationships in into various control schemes to reduce rotor impulsive noise have pro a signal, it is not a panicularly efficient operator. Impulsive signal events duced encouraging resulls. One successful method is Higher Harmonic are very locali/zd in the time domain and vely non-localized in frequency. Control (HHC), the superposing of periodic pitch control inpuls on the col- Fourier waveforms, on the other hand, are localized in frequency and non- lective and cyclic flight control inputs. HHC has yielded noise reductions localized in time. In order to fully describe an impulsive event, the STFT of 5-7 dB in open-loop schemes (Refs. 3,4), and reductions of about 5 dB must be performed with a variety of window sizes, which complicalcs the in closed-loop schemes (Ref. 5). More recently, Individual Blade Control inversion process and adds to the overall computational cost. The wavelet I (IBC) has reduced BV1 noise by up to 7 dB (Ref. 6). transform (WT), however, can achieve good temporal localization while I The size of the matrices necessary to implement closed-loop HHC and maintaining a resolution in frequency that is suflicicnt Cor hursty or im- IBC controls may present a computational challenge. Fourier modes of pulsive signal events. This property makes it an eflicient tool for the analy- HHCWC inputs and the measured BVI noise outputs are uscd to calcu- sis of helicopter BV1 noise. late the uansfer mauix. There are usually only a few harmonic inputs, so The WT has been used in a wide range of applicdtio~is, such as pitch the characterization of BVL noise by Fourier coeficients is the dominant detection in speech signals (Ref. 7). the detection and identification of o h contributor to the size of the Lransfer matrix. A more compact represents- jecls submerged underwater (Ref. 8). and the analysis of turhulcnt flow 1 tion of BVI noise is desirable to reduce computation time. The wavelet data (Refs. 9, 10). In addition, Mallat has shown that the wavelct rcpre- transform (WT) may provide a path to such a representation. sentation can be used to compute a metric, known as the Lipschic< cxpm nent, which measures the regularity of sharp signal variations (Refs. I I, 12, 13). The Lipschit7,exponent of a singularity or sharp variation in a sig- Presemtedatthe American~cacoptersoci~ty 51st~~n~al~~~~~,~~n~~~~,~x, nal can k computed directly Cram the maxima of the WT (RCSS. 12, 13). M~~ 9-11, 1995. copyright 0 1995 by the ~ ~ ~ , i ~ ~ ~ ~ ~ b ~ ~ ~ t ~ ~ sociery, I~C. ,411 This property has heen used to chardctcriu: the sevcrity of signal singu- rights resewed. Manuscript rcccived May 1995; accepted Fch. 1997. larities in turbulent data (Ref. 10). and for edge detection and image dc- 264