extracting bladeÂŒvortex interactions using continuous ... · nasa, bell helicopter, and the u.s....

JOURNAL OF THE AMERICAN HELICOPTER SOCIETY 62 022001 (2017)

Extracting BladendashVortex Interactions Using ContinuousWavelet Transforms

James H Stephenson Charles E TinneyUS Army Aviation Development Directorate Applied Research Laboratories

Aviation amp Missile Research Development amp Engineering Center The University of Texas at AustinHampton VA Austin TX

A framework for using continuous wavelet transforms to isolate and extract bladendashvortex interaction noise from helicopteracoustic signals is described The extraction method allows for the investigation of bladendashvortex interactions independentof other sound sources Experimentally acquired acoustic data from full-scale helicopter flyover tests are first transformedinto time-frequency space through the wavelet transformation with bladendashvortex interactions identified and filtered bytheir high-amplitude high-frequency impulsive content The filtered wavelet coefficients are then used to create a pressuresignal solely related to bladendashvortex interactions Analysis of a synthetic data set is conducted and shows that bladendashvortexinteractions can be accurately extracted so long as the bladendashvortex interaction wavelet energy is comparable to the waveletenergy in the main rotor harmonic

Motivation

Of continuing importance to the rotorcraft community is the predic-tion understanding and mitigation of bladendashvortex interactions (BVI)BVI typically occurs in descending flight when a blade passes in closeproximity to the tip vortex generated by a preceding blade The topichas been the subject of interest for several decades now with reviewsbeing provided by Schmitz and Yu (Refs 1 2) Aside from the unde-sirable vibratory loads that are caused by BVI a strong noise signalis produced with sound waves propagating predominantly forward andbelow the vehicle This results in high community annoyance levelsin and around civilian heliports which poses limitations on the flightenvelope

To better understand the mechanisms affecting BVI noise as well asto develop methods of mitigation it is preferred that one isolate its signalfrom other sources of noise produced by the rotorcraft This is especiallydifficult where full-scale flyover studies are concerned as one is requiredto contend with engine and tail rotor noise noise scattering from thefuselage as well as atmospheric effects Only a few methods have beendeveloped to isolate BVI noise from the total acoustic signal producedby the rotorcraft and its environment Davis et al (Ref 3) employed adiscrete wavelet transform to identify the frequency subband in whichBVI noise occurs The BVI subband was then recreated by filtering outall other subbands before returning the signal to the time domain Theprocess is straightforward and has been shown to work remarkably well

Manuscript received March 2015 accepted November 2016

provided there is little to no energy related to other acoustic phenomenain the subband of interest Sickenberger et al (Ref 4) on the other handperformed the extraction method in the time domain whereby the BVInoise was first identified by its impulsive content before being croppedfrom the original data However they do not provide sufficient informa-tion to recreate their extraction technique Instead Sickenberger et alfocus on the postprocessing description whereby the ldquoholerdquo that resultedfrom the cropping process was filled using a discrete Fourier transformmethod

In the work presented here continuous wavelet transforms are usedto quantify the various acoustic phenomena recorded by a stationary ob-server during several flyovers of a full-scale Bell 430 helicopter Theseacoustic signals were acquired during a test campaign conducted byNASA Bell Helicopter and the US Army This collaborative effortinvestigated both steady and transient flight maneuvers which encom-passed a total of 410 data points A detailed description of this testcampaign can be found in Ref 5 with preliminary findings showingthat large increases in helicopter noise correlates well with cyclic inputsalone In the present study we seek to expand the work of Stephensonand Tinney (Refs 6 7) by developing a framework for identifying andextracting acoustic signals related to BVI noise that occur during vari-ous flight maneuvers of a full-scale helicopter User-defined thresholdsguided by features related to the operating environment of the rotor-craft are inserted to improve the robustness of the BVI sound extractionprocess The technique is first described using a sample set of full-scaledata It is then exercised using synthetic data to gauge its robustness priorto being applied to several microphones throughout a fast advancing sideroll maneuver of a Bell 430 rotorcraft In doing so one can isolate theeffects that transient maneuvers have on the impulsive BVI noise

DOI 104050JAHS62022001 Ccopy 2017 AHS International022001-1

J H STEPHENSON JOURNAL OF THE AMERICAN HELICOPTER SOCIETY

Wavelet Transforms

A methodology capable of handling transient phenomenon is re-quired if one is interested in characterizing the spectral properties ofa BVI signal as standard statistical methods are no longer applicableThe approach employed here is a continuation of the work in Ref 8whereby continuous wavelet transforms are utilized to investigate thespectral characteristics of several different full-scale acoustic measure-ments as a function of time Wavelet transforms are only one of manytechniques that reside under the timescale analysis category the in-terested reader is referred to Refs 9ndash12 for an in-depth discussionon these techniques As a matter of completeness a short review onwavelet analysis is provided before discussing the extraction method forBVI noise

Wavelet transforms temporally convolve an a priori known function(the ldquomotherrdquo wavelet (ψw)) with a signal to reveal its time varying spec-tral content In doing so the spectral characteristics associated with lo-calized bursts are preserved The convolution comprises various scales(l) that decompose the signal into timescale space as follows

p(l t) = 1radicl

int infin

minusinfinp(t prime) ψlowast

w

(t prime minus t

l

)dt (1)

where p(l t) are the wavelet coefficients In general small and largewavelet scales represent high and low frequencies respectively Albeitwavelets do not require a one-to-one correspondence between scale and(Fourier) frequency as discussed in Ref 10

Like the Fourier transform wavelet analysis comprises a transformpair with the inverse wavelet transform being defined as

p(t) = 1

Cψ

int infin

minusinfin

intl

1radiclprime

p(lprime t) ψw

(t prime minus t

lprime

)dlprime dt

lprime2(2)

where Cψ is the admissibility criterion (Ref 12) Equation (2) allows oneto reconstruct the original signal or any portion thereof should a timedomain representation of discrete spectral bands be of interest (Ref 12)Therefore perfect reconstruction of the original signal is possible whenthe scale space integral is performed across all decomposed scales Thescale-normalized energy density E(l t) is then given as

E(l t) = 1

Cψ

|p(l t)|2l2

(3)

and is known as the wavelet power spectrum (WPS) The WPS in scalespace is directly analogous to the power spectral density in frequencyspace obtained through the Fourier transform For the current investi-gation only wavelets that have a simple transformation from scale tofrequency space (E(lj ti) rarr E(fj ti)) will be used Thus calculationof sound pressure levels (SPL) can be determined in a fully equivalentmanner as

SPL(t) = 10 log10

(intf

E(f t)df

p2ref

)(4)

with pref being a reference pressure valued at 20 μParadic

HzGiven the plethora of wavelet shapes that are available to choose

from it is necessary to determine which wavelet shape best fits the sig-nal being processed One such metric for quantifying this is the Shannonentropy cost function described in Ref 13 For steady-level flight andadvancing side roll maneuvers Ref 8 used this cost function to showthat the Morlet wavelet red with a nondimensional frequency (ωψ ) of6 is the ldquobestrdquo wavelet in evaluating helicopter acoustic signals Theldquobestrdquo wavelet in this sense was determined to be the wavelet that ad-equately characterizes the signal in the fewest number of scales at the

fewest points in time Hence the Morlet wavelet with ωψ = 6 will beused in the current study

The shape of the Morlet wavelet is shown in Fig 1 and is one ofthe more commonly used wavelets today due to the simplicity of its im-plementation The Morlet wavelet is constructed by modulating a com-plex sinusoidal wave by way of a Gaussian function and offers goodfrequency and temporal resolution when compared to other wavelets(Ref 12) The frequency domain representation of the Morlet waveletis shown in Fig 1 (right) and is defined analytically by Torrence andCompo (Ref 14) as

ψM (l ω ωψ ) =radic

2πlfs

Nπminus14 H (ω) eminus(lωminusωψ )22 (5)

Here N is the number of samples in the discretized signal with a sam-pling rate of fs and H (ω) is the Heaviside function This frequencydomain representation of the Morlet wavelet allows for the waveletconvolution to be performed as a single multiplication in frequencyspace thereby reducing processing time significantly Applications ofthe Morlet wavelet to transient signals range from atmospheric model-ing (Ref 14) to shock-wave boundary layer interactions (Ref 15) andunderwater acoustic sensing (Ref 16)

Technical Overview

Measurements of a full-scale Bell 430 helicopter undergoing variousflight maneuvers were conducted at Eglin Air Force Base during thesummer of 2011 A full description of this test campaign is provided inRef 5 with relevant details being described herein

The main rotor on the Bell model 430 has four blades that are splitinto two tip-path planes so that one pair of opposing blades tracks ata slightly higher elevation than the other pair Specifications concern-ing both the main and tail rotors are provided in Table 1 Acousticdata were acquired using up to 30 ground-based microphones that were

tl lω (2π)

ψM

(tl

6)

ψM

(lω6

)

04

08

00

0

0

1

minus1minus4 minus2minus2 22

Fig 1 Time domain (left) and frequency domain (right) representa-tions of the Morlet wavelet (ψM (t l ωψ ) isin C)

Table 1 Bell 430 rotor specifications

Main RotorNumber of blades 4Radius (R) 64 mChord (c) 034 mRotation rate () 3486 RPMBlade pass frequency (f MR) 232 Hz

Tail Rotor

Number of blades 2Radius 1 mRotation rate 18807 RPMBlade pass frequency (f TR) 627 Hz

022001-2

EXTRACTING BLADEndashVORTEX INTERACTIONS USING CONTINUOUS WAVELET TRANSFORMS 2017

operated wirelessly from the control center Microphones comprised12 inch BampK type 4189 free-field capsules with diaphragms inverted635 mm above a 381-mm diameter round ground board These micro-phones have a frequency range from 20 Hz to 20 kHz with a dynamicrange from 165 up to 134 dB Each microphone system was surveyedwith a differential global positioning system receiver for accurate posi-tioning relative to the vehicle All microphone channels were sampled at(fs) 25 kHz with 16 bit resolution

Acoustic pressure time series were first transformed from time of ob-servation to time of emission using a time domain de-Dopplerizationalgorithm described by Greenwood and Schmitz (Ref 17) The de-Dopplerization algorithm employs a linear interpolation scheme to ad-just the pressure at time of reception to time of emission by account-ing for the distance between the vehicle and microphone as well as thespeed of sound The wavelet transform can be applied to either time ofemission or time of reception signals time of emission is used here toaccurately relate measured acoustics with the vehicle state conditionsthroughout a transient maneuver Pressure amplitudes are also scaled toadjust for spherical spreading losses so that the microphone pressuresignals are scaled uniformly to 100 m from the vehicle No other post-processing of the pressure signals is performed

Data from a transient fast advancing side-roll maneuver are investi-gated here Figure 2 provides the ground track of the vehicle maneuverwith respect to each of the microphones The transient maneuver wasinitiated at approximately 1 s into the 10-s path of interest Each markon the ground track in Fig 2 corresponds to a 1-s interval Averaged rel-evant flight parameters include a ground speed of 415 m sminus1 a medianheight of 415 m and a gross weight of 387 kN Vehicle parameters forroll attitude (φ) and rate of change (φ) during the flight path are shown inFig 3 The attitude and rate of change for roll confirm that the maneuverinitiated approximately 1 s into the 10-s path of interest Each dynamicmaneuver in the full experiment was designed to focus on a single pilotinput and so the advancing side-roll maneuver has negligible pitch at-titude or pitch rates of change (Ref 6) The peak roll rate achieved for

X (m)

Y(m

)

StartSecondEndMicrophone

f-ARFlight path

minus100

minus100

100

100

minus200

minus200 200

0

0

Fig 2 Vehicle ground track of the fast advancing side roll maneuver(f-AR) of the Bell 430 helicopter across the microphone array

Time (s)

40

20

2 4 6 8 10

0

0

φ ()φ (s)

Fig 3 Vehicle roll attitude (φ) and roll rate (φ) throughout the fastadvancing side roll maneuver

this maneuver never exceeds 18 deg sminus1 and the transient portion takesa duration of approximately 3 s

BladendashVortex Interaction Extraction Method

BVI noise is the predominant source of increased SPL during tran-sient maneuvers as described in Refs 18ndash20 Albeit methods to extractthe noise signal related to the transient BVI phenomenon have provendifficult to develop Challenges stem from the broad range of aerody-namic conditions that the helicopter experiences as it proceeds throughits flight path Thus any changes to the local aerodynamics say fromwind gusts or a transient maneuver will affect the signal associated withBVI That is changes in advance ratio inflow ratio coefficient of thrustand trace Mach number are known to noticeably influence the radiatednoise pattern as discussed in Refs 21ndash23 Therefore it is advantageousto have a BVI noise extraction technique that can adapt to changes in theamplitude and frequency of the radiated noise since these are affected bythe aerodynamic conditions just described Subsequently a high-pass orband-pass filter alone is not advisable as it would not adapt to changesin frequency Furthermore a high-pass frequency filter would also ex-tract higher frequency information not necessarily associated with BVIThe basis for the extraction technique described here is the continuouswavelet transform and is a natural extension to the method described byRef 3 The strength of this approach is in its ability to neglect higherharmonic information unrelated to BVI

We begin by providing a sample time-frequency representation(shown in Fig 4 as wavelet power spectra) of an acoustic signal duringtransient maneuvering of a helicopter Three columns have been addedto the left side of this WPS to identify (from left to right) the main rotorharmonics (fMR) tail rotor harmonics (fTR) and summed combinationsof the two (αfMR + βfTR) These columns identify harmonics in fre-quency space and not signal amplitude Below the wavelet power spectrais the corresponding pressure signal in the time domain Multiple mainrotor tail rotor and combinations thereof have been further defined bydashed horizontal lines in the WPS itself Several unique spectral fea-tures that are of interest to this study have also been identified in Fig 4These include a full blade passage tail rotor noise signal and BVI noisesignal The tail rotor noise signal is primarily identified in the midrangefrequency whereas the BVI noise signals are identified by their higherharmonics (Refs 3 6 23 24)

It can be seen in Fig 4 that when BVI occurs the wavelet transformrepresents it as similar peak strength when compared with the main rotorharmonic This was shown previously in Ref 6 during an investigationof multiple flight conditions Therefore a filtering method can be devel-oped given the simultaneous occurrence of higher harmonic content thatexceeds some amplitude threshold relative to the strength of the mainrotor harmonic

Filter description

The method for filtering BVI signals is first described and imple-mented on a sample WPS It is then exercised on a synthetic set of datato determine whether or not the method can accurately recreate BVI sig-nals from only the high-amplitude and high-frequency components ofthe signal

Quite simply the filtering method acts as a boxcar function in thetime-frequency domain and is described as follows

p(fj ti) =

⎧⎪⎨⎪⎩

p(fj ti) if fj gt fcut and

E(fj ti) gt E(fMR ti) + Acut

0 otherwise

(6)

022001-3


1 fMR

2 fMR

3 fMR

4 fMR

5 fMR

10 fMR

20 fMR

30 fMR

1 fTR

2 fTR

10 fTR

fMR

+ fTR

2fMR

+ fTR

BVI

Tail Rotor

Blade passage

65

70

75

80

85

90

95

101

102

103

Fre

quen

cy (

Hz)

Mai

n ro

tor

Tai

l rot

orC

ombi

nati

ons

1075 1100 1125 1150 1175 1200 1225minus10

0

10

Time (s)

Pre

ssur

e (P

a)

Fig 4 Sample wavelet power spectrogram identifying key fea-tures associated with full-scale helicopter acoustic signals Verticalcolumns on the left ordinate identify main rotor harmonics ( fMR)tail rotor harmonics ( fTR) and summed combinations of the two(α fMR + β fTR)

where p(fj ti) are wavelet coefficients defined by Eq (1) that corre-spond to wavelet scales (lj ) The wavelet coefficients are only extractedat each instance in time if they simultaneously exceed a user-definedfrequency (fcut) and amplitude (Acut) threshold The frequency thresh-old is based on harmonics of the main rotor frequency whereas the am-plitude threshold is relative to the energy in the main rotor harmonic(E(fMR ti)) Thus a positive value of Acut represents BVI pulses that arestronger than the main rotor harmonic whereas a negative value of Acut

allows for the extraction of BVI signals that are weaker than the mainrotor harmonic This filtering method can easily be tailored to removeany transient signal that is consistently identifiable in the time-frequencyspace and so this technique is not restricted to problems concerned withBVI noise alone

The tuning parameters used here for the removal of BVI noise emit-ted from the Bell 430 were determined to be fcut = 7fMR (1642 Hz)and Acut = minus6 dB using 21 microphones for three different helicoptermaneuvers The selection of tuning parameters is discussed in Section53 of Ref 25 but are fairly insensitive to selection in fcut and AcutThis is true so long as the user stays within reasonable bounds such asfcut of 5ndash9 fMR and Acut of minus4 to minus9 dB for conventional helicopters Aschematic describing this BVI extraction technique is provided in Fig 5

minus10minus10

1010

00

65

65

65

75

75

75

85

85

85

95

95

95

105

105

105

101

101

101

102

102

102

103

103

103

30

30

30304

304

304

304304

304308

308

308

308308

308312

312

312

312312

312316

316

316

316316

316

Wavelet transform Eq (1)

Inverse wavelet

Transform Eq (2)

Blade-vortex interactionfilter Eq (6)

Blade-vortex interaction signal Residual signal

minus10

10

0

Fig 5 Schematic diagram of the full BVI extraction process fromoriginal pressure signal through to the final extracted signals

complete from transforming the original pressure signal through the useof the wavelet transform filtering the transformed data via Eq (6) andthen inverse transforming the filtered data to construct the associatedpressure signals

A sample test of the filtering method just described is now performedusing a pressure signal extracted during the fast advancing side roll ma-neuver shown in Fig 2 The original WPS is illustrated in Fig 6(a)where the spectrogram is shown to be similar in structure and patternas the transformed signal displayed in Fig 4 This sample signal spansjust over one complete rotor revolution as is evidenced by the four BVIpulses as well as several negative pressure spikes associated with thetail rotor thickness noise The WPS shows a strong (85 dB) main rotorharmonic with defined higher frequency energy spikes associated witheach BVI signal

The filtering method is applied to the raw signal in Fig 6(a) withthe BVI-extracted signal shown in Fig 6(b) followed by the signalrsquosremaining residual in Fig 6(c) Five distinct events are manifest in theextracted BVI pressure signal Differences between each of the events

022001-4


t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(a)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(b)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(c)

Fig 6 BVI extraction technique applied to a sample WPS extractedduring a transient fast advancing side roll maneuver of a Bell 430helicopter (a) Original (b) BVI extracted and (c) residual signalsIn each subfigure the spectrogram is shown immediately above itscorresponding pressure time history

relate to the split tip-path plane of the Bell 430 helicopter as well asleakage of the tail rotor signal which shifts in time Because the tail rotoralso produces energy in the high-frequency bands a small portion of thetail rotor signal is removed during the filtering process For example thetail rotor signal is noticeable at the end of the first BVI pulse interactionnear 301 s and is seen to extend the BVI extracted spectra into lowerfrequencies around 200 Hz This tail rotor signal further expresses itselfas a slight negative pressure peak in the reconstructed pressure signal atthe end of the first BVI pulse Frequency components associated with

the tail rotor can also be seen in the second BVI pulse (just after 304 s)but do not appear in the final two complete pulses (at 309 and 313 s)

In comparing the residual signal (without BVI) in Fig 6(c) to theoriginal signal in Fig 6(a) the overall shape of the pressure signal ispreserved with only the BVI signal removed A small pressure riseis seen at each blade passage which is slightly larger in magnitudethan what one might have anticipated This pressure rise is particularlyevident in the first and third BVI events and suggests that the full BVIsignal is not represented entirely by its higher harmonic componentsbut also exists in some limited lower frequency content as well This isanticipated since BVI can occur at every blade passage some energyassociated with these interactions must be in the main blade pass fre-quency as suggested by Martin and Hardin (Ref 24) Closer inspectionof the main rotor harmonic signal in either Fig 6(a) or 6(c) reveals howthe energy for f 100 Hz does not change during BVI events Thisprevents the lower harmonics from being removed from the WPS by anywavelet-based filtering technique as the energy in the lower harmonicsattributed to BVI is indistinguishable from the rest of the signal

Synthetic signal analysis

Now that the general technique has been described we investigatesome sample signals to further understand its sensitivity to changes inthe user-defined frequency and amplitude thresholds Determining howthe energy of BVI is distributed in spectral space is a nontrivial taskReference 4 performed a Fourier transform on a cropped BVI event asample of which is provided in Fig 7 Sickenbergerrsquos Fourier transformshown in Fig 7(b) shows that the energy of a BVI event is distributedsomewhat uniformly across all but the midrange frequencies This iscontrary to what is seen in the WPS of Fig 6(a) where the energy isfocused primarily in the higher frequencies The distribution of energyfound by Sickenberger et al is most likely influenced by the size of theinterrogation window and therefore large frequency bin size necessaryto investigate a BVI pulse in isolation (Refs 6 25)

To determine a more realistic energy distribution a ldquotypicalrdquo BVInoise signal must be constructed Since the noise signal of a BVI event

Fig 7 (a) Extracted BVI pressure signal and (b) associated Fouriertransform produced in Sickenberger et al (Ref 4)

022001-5


is highly dependent on the aerodynamics surrounding each BVI a ldquotyp-icalrdquo signal is difficult to define Here we will attempt to synthesize datafrom a microphone signal located at (X Y ) = (10 20) m in Fig 2 Theresultant WPS for this signal is shown in Fig 8 and corresponds to onecomplete rotor revolution during a fast advancing side-roll maneuver ofthe Bell 430 helicopter To create a ldquolsquotypicalrdquo BVI pulse the four BVIpulses shown in Fig 8 are extracted their negative pressure peaks arealigned in time and then the resulting signal is averaged This creates asingle BVI event that is the average shape of the four constituent eventsand maintains the strength of the negative pressure peak that dominatesthe BVI signal To ensure zero acoustic pressure at the beginning andending of the signal the averaged pressure signal is passed through aGaussian window the result of which is shown in Fig 9 and will becalled the ldquotypicalrdquo or synthesized BVI pulse

As can be seen in Fig 9 the synthesized BVI pressure signal is com-posed of one primary pair of negativendashpositive pulses and occurs overa time span of less than 10 ms The synthesized BVI signal is then re-produced at the main rotor blade passage frequency to generate a pres-sure signal comprising only ldquotypicalrdquo BVI pulses A wavelet transformis then performed on a string of such interactions with the WPS beingshown in Fig 10

The findings demonstrate that the majority of the wavelet trans-formed energy contained within a BVI event is indeed confined to thehigher harmonics As a comparison a Fourier transform of the samesynthesized data corresponding to a full 1-s of BVI pulses is provided inFig 11 The spectral peaks occur at each main rotor harmonic with theenergy content also residing in the high-frequency bands The full signalis used in the Fourier transform to ensure that both the window size andfrequency resolution provide adequate estimates of the signalrsquos spectralcontent Again the energy is focused predominantly in the higher fre-

t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

10

minus100

101

102

103

Fig 8 Wavelet power spectra and associated pressure signal ex-tracted from microphone located at (X = 10 m Y = minus20 m)

t (ms)

p(P

a)

25 50 75

10

minus10

0

0

Fig 9 ldquoTypicalrdquo BVI pressure signal extracted and averaged fromthe data provided in Fig 8

t (s)

f(H

z)

p(P

a)

300 305 310 315 320

45

55

65

75

85

95

105

1010

minus100

102

103

Fig 10 Wavelet power spectra of the ldquotypicalrdquo BVI pressure signalNote that the contour levels have changed so that the lower har-monic energy of the BVI can be seen

f (Hz)

p(d

B)

20

30

40

50

60

70

80

90

101 102 103

Fig 11 Fourier transform of the full ldquotypicalrdquo BVI pressure signal

quencies in contrast to the findings of Sickenberger et al (Ref 4) butin agreement with Hardin and Lamkin (Ref 22)

Synthetic signal wavelet transform Using wavelet transforms the sig-nal related to the main rotor harmonic can also be extracted at discreteinstances in time Extracting the main rotor harmonic by itself allows theenergy in the harmonic to be scaled independently of the strength of theBVI events Figure 12 shows a scaled main rotor harmonic signal super-imposed with the ldquotypicalrdquo BVI signal shown in Fig 10 In Fig 12 themain rotor energy (MRE) is scaled to be 3 dB greater than the peak BVIenergy ( MRE = 3 dB)

Recall from before that the filtering method given in Eq (6) requiredthe simultaneous occurrence of energy above a certain frequency anda given amplitude that was measured in relation to the main rotor har-monic energy level Thus varying the energy level of the main rotor har-monic allows one to investigate how the main rotor harmonic strengthaffects the resulting extracted BVI signal Signals representing variousmain rotor harmonic strengths are shown in Fig 13 In each successivefigure the main rotor harmonic has been uniformly scaled to a higherenergy value denoted by MRE

The BVI extraction technique with cutoffs of (fcut = 7fMR Acut =minus6 dB) is then applied to this set of artificial data The resulting ex-tracted pressure signals are shown in Fig 14 where labels are consistentwith Fig 13 It can be seen that as the energy in the main rotor harmonicincreases relative to the strength of the BVI signal then less and less ofthe BVI signal is extracted Finally when the energy in the main rotor

022001-6


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

100

1010

minus100

103

Fig 12 Extracted wavelet power spectra of the ldquotypicalrdquo BVI pres-sure signal superimposed on a scaled main rotor harmonic signal

t (s)

f(H

z)p

(Pa)

310 312

101

102

103

100

minus10

(a)t (s)

310 312

(b)t (s)

310 312

(c)t (s)

310 312

(d)t (s)

310 312

65

75

85

95

105

(e)

Fig 13 ldquoTypicalrdquo BVI superimposed onto a main rotor signal ofvarying strengths Main rotor peak energy strengths relative to thepeak BVI signal ( MRE) are (a) minus13 (b) 0 (c) 3 (d) 5 and(e) 7 dB

harmonic is 5 dB or more than the peak BVI energy little to no signalis extracted This is expected as the amplitude cutoff for extracting BVIsignals was set at 6 dB below the main rotor harmonic energy level

Synthetic signal Fourier transform A similar extraction technique canbe performed on the signals shown in Fig 13 using the Fourier trans-form The signals shown in Fig 13 can be high-pass filtered by applyinga Fourier transform to the signals and then setting energy in frequenciesbelow 7 fMR to zero Since BVI signals are predominantly located inthe higher frequency range this technique should remove the acousticsignal unrelated to BVI A sample of this filtering technique is shown inFig 15

The main rotor harmonic is the strongest frequency in the signalshown in Fig 15 peaking at close to 100 dB However the main ro-tor harmonic has affected the energy in the higher frequencies as wellIf this figure is compared to the original ldquotypicalrdquo BVI spectra seen inFig 11 it is seen that the higher frequency components have been af-fected by the main rotor harmonic energy Increased energy in the mainrotor harmonic has increased the broadband energy of the higher fre-quency components and a subsequent decrease in peak energy is alsoseen for the high-frequency tonal components This is in contrast to whatwas previously viewed in the wavelet power spectra of Fig 13(e) where

t (s)

p(P

a)

310310310 311311311

(a)ΔMRE= minus13 (b) Δ MRE = 0

(c) Δ MRE = 3 (d) Δ MRE = 5 (e) Δ MRE = 7

Original

10

10

minus10

minus10

0

0

5

5

minus5

minus5

Fig 14 BVI signal extracted from Fig 13 Original superimposedBVI signal is also provided MRE provided in units of decibels

f (Hz)p

(dB

)20

30

40

50

60

70

80

90

100

101 102 103

FTFilt

fcut

Fig 15 Fourier transform (FT) and filtered spectra (Filt) of the BVIsignal with scaled MRE MRE = 7 dB for the case shown

energy content in the higher frequencies was unaffected by amplitudemodifications in the lower frequencies

The filtered Fourier spectra for each signal shown in Fig 13 are theninverse transformed with the resulting pressure signals shown in Fig 16Here the lower harmonic energy is still present in the filtered signalsThis was expected as it was noted that the energy from the main rotorharmonic was distributed into the higher frequencies as well Since thismethod is a relatively simple high-pass filter the extraction techniqueremoves a portion of the signal at all instances in time regardless of en-ergy fluctuations in the main rotor harmonic A comparison of the over-all effectiveness at isolating BVI signals is now conducted between thehigh-pass Fourier transform filter and the wavelet-based BVI extractiontechnique

Synthetic signal wavelet and Fourier transform comparison Analyzingthe SPL of the resulting extracted pressure signals from both the wavelettransform and Fourier transform techniques provides a means for quan-tifying the effect that the MRE level has on the extracted signal TheSPL relative to the original ldquotypicalrdquo BVI signal can be calculated asfollows

SPL = 20 log10

PiRMS

PoRMS

(7)

In Eq (7) RMS stands for the root mean square of the signal P i repre-sents the ith energy level of the main rotor harmonic and o is the valuefor the original ldquotypicalrdquo BVI pressure signal Thus when SPL = 0the extracted signal contains the same energy as the original ldquotypicalrdquo

022001-7


t (s)

p(P

a)

310310310 311311311

(a)ΔMRE= minus13 (b)Δ MRE = 0

(c) Δ MRE = 3 (d)Δ MRE = 5 (e) Δ MRE = 7

Original10

10

minus10

minus10

0

0

5

5

minus5

minus5

Fig 16 BVI signal filtered through Fourier transform from Fig 13Original superimposed BVI signal is also provided MRE pro-vided in units of decibels

BVI signal Otherwise the metric indicates whether the extracted signalhas more ( SPL gt 0) or less ( SPL lt 0) energy than the originalldquotypicalrdquo BVI signal

The main rotor scaling process was performed for relative mainrotor energies ranging from 35 dB below the peak BVI signal( MRE = minus35) to 7 dB above Each extraction technique was ap-plied to every MRE value and the extracted signals are analyzed usingthe metric given in Eq (7) It can be seen in Fig 17 that the Fouriertransform extraction method requires the main rotor harmonic energy tobe significantly below the peak BVI level ( MRE 0) in order forproper reconstruction of the BVI event When the main rotor harmonicenergy is half the strength of the peak BVI energy ( MRE = minus3 dB)then the reconstructed signal is accurate within 2 dB However the em-ployed metric only investigates the fluctuating component of the signaland does not properly take into account the slow main rotor harmonicfluctuations that are still visible in the extracted signal

Furthermore the accuracy of this technique is true only for the signalinvestigated which was steady with identical BVIs occurring at a fixedtime interval In a transient signal like those exhibited by a maneuveringhelicopter the Fourier transform extraction method is expected to per-form quite poorly in capturing and filtering individual BVI events Thisis due to the very small time windows over which BVIs occur It wasshown previously in Ref 6 that the Fourier transform does not provideconsistent spectra at such small window sizes and so the filtering andreconstruction process will be severely affected by the necessary win-dow size Furthermore due to the way the Fourier transform distributesenergy it is highly unlikely that the main rotor harmonic energy levelwill be less than the peak energy levels related to BVI signals and thusthis technique is insufficient for analysis purposes

The wavelet transform extraction technique however shows thatwhen BVIs are as strong as (or more energetic than) the main ro-tor harmonic ( MRE le 0) the extracted signal is correct within1 dB When the main rotor harmonic energy is more energetic than theenergy in the BVI signals especially 2 dB above the peak value( MRE = 2) then the resulting wavelet transform extracted signal isno longer indicative of the original BVI signal (| SPL| ge 3) Further-more the extracted signal does not show any presence of the main rotorharmonic energy as was seen in the Fourier transform case Preliminaryresults from Ref 6 and Fig 4 shows that when BVI events occur theirpeak energies are in general more energetic (using Wavelet transforms)than the main rotor harmonic energy ( MRE lt 0) Thus unless other-wise noted it will be assumed with some confidence that BVIs identifiedand extracted through this method represent the ldquotruerdquo (within plusmn1 dB)BVI signal

0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT

Fig 17 SPL comparison of extracted ldquotypicalrdquo BVI for varyingmain rotor harmonic energies Comparisons for both wavelet trans-form (WT) and Fourier transform (FT) are provided Extractionof half the BVI energy is identified by dashed lines for the wavelettransform case

Results

The BVI extraction method is applied to all microphones throughoutthe fast advancing side roll maneuver Some samples of the results areprovided here to show the strengths and weaknesses of the techniquewhereas a full analysis of the maneuver can be found in Ref 25

Figure 18 shows the original extracted BVI signal and residual pres-sure signal extracted from two different microphones 05 s into the ma-neuver Figure 18(a) shows a signal extracted from an azimuthal angle(ψ) of 173 and an elevation (θ ) relative to the tip-path plane of the ve-hicle of minus28 This signal contains the peak measured BVI energy atthe 05-s mark and the extraction method has adequately identified andremoved the BVI signal Only the BVI signal has been removed as evi-denced by the zero acoustic pressure level between each blade passage

Figure 18(b) however is extracted from the plane of the rotor(134 minus3) at the same time as Fig 18(a) This figure clearly doesnot contain any BVI noise but does show a strong thickness noise sig-nal produced by the main rotor The extracted BVI signal for this mi-crophone is shown in the center of Fig 18(b) and it is seen that the

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)

Fig 18 Pressure signals extracted from 05 s into the fast advancingside roll maneuver Signals extracted from (a) peak BVI microphonelocated at (ψ = 173 θ = minus28) and (b) an in-plane microphonelocated at (134minus3)

022001-8


extraction method has neither identified nor removed a pressure signalThis is exactly what was desired as no BVI signal is seen in the originalpressure signal It is clear that the residual signal is identical to the origi-nal signal showing that wavelet transforms are capable of perfect signalreconstruction

There are two instances when the extraction method is known to per-form suboptimally (Ref 25) The first instance of suboptimal perfor-mance occurs when there is a strong energy signal unrelated to BVIevents that occurs in the same frequency range of interest Figure 19(a)shows one such case of this occurring Here the tail rotor signal pos-sesses a substantial amount of energy in the its higher harmonic com-ponents This can happen due to changes in loading on the tail rotoror even mainndashtail rotor interactions However when this does occur theBVI noise signal is typically much stronger than the extracted tail ro-tor signal and so the relevant increase in SPL for this scenario is small(Ref 25)

The primary instance of suboptimal extraction performance occurswhen the main rotor harmonic signal is weak A weak main rotor har-monic signal leads to a low overall amplitude cutoff which can allowfor the extraction of higher frequency content unrelated to BVI noiseFigure 19(b) provides an example where there is no strong presence ofthe main rotor harmonic and so the energy cutoff is quite low This hasallowed for the extraction of seemingly random noise

The latter deficiency in the extraction technique can be mitigated eas-ily in two different ways First since the failure occurs due to a low mainrotor harmonic energy level a third cutoff can be defined such that theenergy in the main rotor harmonic must exceed some nominal value be-fore the extraction technique is employed This is not ideal as the lowerenergy value will be arbitrary and need to be determined for every situ-ation The second way to mitigate the effects of the erroneous results isto use engineering judgment When BVI noise occurs the BVI SPL isgenerally within a few decibels of the overall SPL at that instant in timeand direction However the SPL calculated when only random noise isextracted is significantly lower (9+ dB) than that of typical BVI soundlevels (Ref 25) Thus when small BVI SPLs are detected it is mostlikely the result of the extraction technique removing only unrelatedhigher frequency noise from the signal

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)

Fig 19 Pressure signals extracted from (a) 15 and (b) 25 s intothe fast advancing side roll maneuver Microphone (a) is extractedfrom the peak BVI microphone located at (ψ = 179 θ = minus17)whereas microphone (b) is located at an elevation of minus80 below therotor and now slightly left of center at ψ = 218

Conclusions

An experimental investigation of the acoustic signal emitted duringa fast advancing side transient roll maneuver of a Bell model 430 heli-copter was conducted A method for the identification and extraction ofBVI noise was developed to assist in determining the relevant physicsthat affects BVI during transient flight

The BVI extraction method that was developed identifies and iso-lates high-frequency high-amplitude pressure signals based on physi-cally relevant tuning parameters The filtering method was based on pre-vious analytical research that showed BVI noise exists predominantly inthe higher frequency range of a signal (Refs 23 24) This was furtherconfirmed in previous research where it was shown that BVI noise isquite energetic relative to the overall pressure signal when such noise ispresent (Ref 6)

The BVI extraction method was first implemented on a syntheticpressure signal comprised solely of ldquotypicalrdquo BVI events It was shownthat the extraction method could adequately recreate the pressure signalof a BVI event from only its high-frequency high-amplitude wavelet co-efficients Furthermore this method was compared to a high-frequencyfiltering of the data using the Fourier transform It was shown that theFourier transform was inadequate for extracting the BVI data as the mainrotor harmonic was still present in the extracted pressure signals

Most importantly however the BVI extraction method was shownto work well on several sample microphone signals The method is ableto capture pulse-to-pulse variability in the BVI signal is easily imple-mentable and has only two physically relevant tuning parameters Therewas one primary limitation to successful interpretation of the extractionresults However with judicious use of engineering judgment this lim-itation can easily be mitigated by rejecting extracted signals when theirSPL is significantly below (9+ dB) that of the overall SPL at that point

Acknowledgments

The flight test data were acquired during a joint test program betweenNASA Langley Research Center Bell Helicopter Textron and the USArmy Aeroflightdynamics Directorate Special thanks to Dr Eric Green-wood Dr Ben Sim and Michael E Watts for their invaluable assistancethroughout this project

References

1Schmitz F H and Yu Y H ldquoHelicopter Impulsive Noise The-oretical and Experimental Statusrdquo Technical Memorandum 84390NASA Ames Research Center Moffett Field CA November 1983

2Schmitz F H and Yu Y H ldquoHelicopter Impulsive Noise The-oretical and Experimental Statusrdquo Journal of Sound and VibrationVol 109 (3) 1986 pp 361ndash422

3Davis W Pezeshki C and Mosher M ldquoExtracting and Charac-terizing BladendashVortex Interaction Noise with Waveletsrdquo Journal of theAmerican Helicopter Society Vol 42 (3) 1997 pp 264ndash271

4Sickenberger R Gopalan G and Schmitz F H ldquoHelicopterNear-Horizon Harmonic Noise Radiation due to Cyclic Pitch TransientControlrdquo American Helicopter Society 67 Proceedings Virginia BeachVA May 3ndash5 2011

5Watts M E Greenwood E Smith C D Snider R andConner D A ldquoManeuver Acoustic Flight Test of the Bell 430 Heli-copter Data Reportrdquo Technical Memorandum NASATM-2014-218266NASA Langley Research Center Hampton VA May 2014

6Stephenson J H and Tinney C E ldquoTime Frequency Analysis ofSound from a Manuevering Rotorcraftrdquo American Helicopter Society69th Annual Forum Proceedings Phoenix AZ May 21ndash23 2013

022001-9


7Stephenson J H and Tinney C E ldquoTime Frequency Analysis ofSound from a Manuevering Rotorcraftrdquo American Helicopter Society70th Annual Forum Proceedings Montreal Quebec Canada May 20ndash22 2014

8Stephenson J H Tinney C E Greenwood E and WattsM E ldquoExtracting BladendashVortex Interactions Using Continuous WaveletTransformsrdquo Journal of Sound and Vibration Vol 333 (21) 2014pp 5324ndash5339

9Cohen L ldquoTimendashFrequency DistributionsmdashA Reviewrdquo Proceed-ings of the IEEE Vol 77 (7) 1989 pp 941ndash981

10Farge M ldquoWavelet Transforms and Their Applications to Turbu-lencerdquo Annual Review of Fluid Mechanics Vol 24 1998 pp 395ndash457

11Lewalle J Delville J and Bonnet J ldquoDecomposition of Mix-ing Layer Turbulence into Coherent Structures and Background Fluctu-ationsrdquo Flow Turbulence and Combustion Vol 64 2000 pp 301ndash328

12Addison P S The Illustrated Wavelet Transform Handbook Tayloramp Francis Group New York NY 2002 pp 1ndash64

13Coifman R and Wickerhauser M ldquoEntropy-Based Algorithmsfor Best Basis Selectionrdquo IEEE Transactions on Information TheoryVol 38 (2) March 1992 pp 713ndash718

14Torrence C and Compo G P ldquoA Practical Guide to WaveletAnalysisrdquo Bulletin of the American Meteorological Society Vol 79 (1)1998 pp 61ndash78

15Baars W J and Tinney C E ldquoTransient Wall Pressure in anOverexpanded and Large Area Ratio Nozzlerdquo Experiments in FluidsVol 54 (2) 2013 pp 1ndash17

16Dolder C N Haberman M R and Tinney C E ldquoA LaboratoryScale Piezoelectric Array for Underwater Measurements of the Fluctu-ating Wall Pressure beneath Turbulent Boundary Layersrdquo MeasurementScience Technology Vol 23 (4) 2012 pp 1ndash11

17Greenwood E and Schmitz F H ldquoSeparation of Main and TailRotor Noise from Ground-Based Acoustic Measurementsrdquo Journal ofAircraft Vol 51 (2) March 2014 pp 464ndash472

18Bres G A Brentner K S Perez G and Jones H E ldquoManeu-vering Rotorcraft Noise Predictionrdquo Journal of Sound and VibrationVol 275 2004 pp 719ndash738

19Perez G Brentner K S Bres G A and Jones H E ldquoA FirstStep toward Prediction of Rotorcraft Maneuver Noiserdquo Journal of theAmerican Helicopter Society Vol 50 (3) 2005 pp 230ndash237

20Chen H Brentner K S Ananthan S and Leishman J G ldquoAComputational Study of Helicopter Rotor Wakes and Noise Generatedduring Transient Maneuversrdquo Journal of the American Helicopter Soci-ety Vol 53 (1) 2008 pp 37ndash55

21Splettstoesser W R Schultz K J Boxwell D A and SchmitzF H ldquoHelicopter Model Rotor-Blade Vortex Interaction ImpulsiveNoise Scalability and Parametric Variationsrdquo Technical Memorandum86007 NASA Ames Research Center Moffett Field CA December1984

22Hardin J C and Lamkin S L ldquoConcepts for Reduction ofBladeVortex Interaction Noiserdquo Journal of Aircraft Vol 24 (2) 1986pp 120ndash125

23Widnall S ldquoHelicopter Noise Due to Blade-Vortex InteractionrdquoJournal of the Acoustical Society of America Vol 50 (1) 1971 pp 354ndash365

24Martin R M and Hardin J C ldquoSpectral Characteristics of RotorBladeVortex Interaction Noiserdquo Journal of Aircraft Vol 25 (1) 1988pp 62ndash68

25Stephenson J H ldquoExtraction of Blade Vortex Interactions fromHelicopter Transient Maneuvering Noiserdquo PhD Thesis University ofTexas at Austin Austin TX 2014

022001-10


Wavelet Transforms

A methodology capable of handling transient phenomenon is re-quired if one is interested in characterizing the spectral properties ofa BVI signal as standard statistical methods are no longer applicableThe approach employed here is a continuation of the work in Ref 8whereby continuous wavelet transforms are utilized to investigate thespectral characteristics of several different full-scale acoustic measure-ments as a function of time Wavelet transforms are only one of manytechniques that reside under the timescale analysis category the in-terested reader is referred to Refs 9ndash12 for an in-depth discussionon these techniques As a matter of completeness a short review onwavelet analysis is provided before discussing the extraction method forBVI noise

Wavelet transforms temporally convolve an a priori known function(the ldquomotherrdquo wavelet (ψw)) with a signal to reveal its time varying spec-tral content In doing so the spectral characteristics associated with lo-calized bursts are preserved The convolution comprises various scales(l) that decompose the signal into timescale space as follows

p(l t) = 1radicl

int infin

minusinfinp(t prime) ψlowast

w

(t prime minus t

l

)dt (1)

where p(l t) are the wavelet coefficients In general small and largewavelet scales represent high and low frequencies respectively Albeitwavelets do not require a one-to-one correspondence between scale and(Fourier) frequency as discussed in Ref 10

Like the Fourier transform wavelet analysis comprises a transformpair with the inverse wavelet transform being defined as

p(t) = 1

Cψ

int infin

minusinfin

intl

1radiclprime

p(lprime t) ψw

(t prime minus t

lprime

)dlprime dt

lprime2(2)

where Cψ is the admissibility criterion (Ref 12) Equation (2) allows oneto reconstruct the original signal or any portion thereof should a timedomain representation of discrete spectral bands be of interest (Ref 12)Therefore perfect reconstruction of the original signal is possible whenthe scale space integral is performed across all decomposed scales Thescale-normalized energy density E(l t) is then given as

E(l t) = 1

Cψ

|p(l t)|2l2

(3)

and is known as the wavelet power spectrum (WPS) The WPS in scalespace is directly analogous to the power spectral density in frequencyspace obtained through the Fourier transform For the current investi-gation only wavelets that have a simple transformation from scale tofrequency space (E(lj ti) rarr E(fj ti)) will be used Thus calculationof sound pressure levels (SPL) can be determined in a fully equivalentmanner as

SPL(t) = 10 log10

(intf

E(f t)df

p2ref

)(4)

with pref being a reference pressure valued at 20 μParadic

HzGiven the plethora of wavelet shapes that are available to choose

from it is necessary to determine which wavelet shape best fits the sig-nal being processed One such metric for quantifying this is the Shannonentropy cost function described in Ref 13 For steady-level flight andadvancing side roll maneuvers Ref 8 used this cost function to showthat the Morlet wavelet red with a nondimensional frequency (ωψ ) of6 is the ldquobestrdquo wavelet in evaluating helicopter acoustic signals Theldquobestrdquo wavelet in this sense was determined to be the wavelet that ad-equately characterizes the signal in the fewest number of scales at the

fewest points in time Hence the Morlet wavelet with ωψ = 6 will beused in the current study

The shape of the Morlet wavelet is shown in Fig 1 and is one ofthe more commonly used wavelets today due to the simplicity of its im-plementation The Morlet wavelet is constructed by modulating a com-plex sinusoidal wave by way of a Gaussian function and offers goodfrequency and temporal resolution when compared to other wavelets(Ref 12) The frequency domain representation of the Morlet waveletis shown in Fig 1 (right) and is defined analytically by Torrence andCompo (Ref 14) as

ψM (l ω ωψ ) =radic

2πlfs

Nπminus14 H (ω) eminus(lωminusωψ )22 (5)

Here N is the number of samples in the discretized signal with a sam-pling rate of fs and H (ω) is the Heaviside function This frequencydomain representation of the Morlet wavelet allows for the waveletconvolution to be performed as a single multiplication in frequencyspace thereby reducing processing time significantly Applications ofthe Morlet wavelet to transient signals range from atmospheric model-ing (Ref 14) to shock-wave boundary layer interactions (Ref 15) andunderwater acoustic sensing (Ref 16)

Technical Overview

Measurements of a full-scale Bell 430 helicopter undergoing variousflight maneuvers were conducted at Eglin Air Force Base during thesummer of 2011 A full description of this test campaign is provided inRef 5 with relevant details being described herein

The main rotor on the Bell model 430 has four blades that are splitinto two tip-path planes so that one pair of opposing blades tracks ata slightly higher elevation than the other pair Specifications concern-ing both the main and tail rotors are provided in Table 1 Acousticdata were acquired using up to 30 ground-based microphones that were

tl lω (2π)

ψM

(tl

6)

ψM

(lω6

)

04

08

00

0

0

1

minus1minus4 minus2minus2 22

Fig 1 Time domain (left) and frequency domain (right) representa-tions of the Morlet wavelet (ψM (t l ωψ ) isin C)

Table 1 Bell 430 rotor specifications

Main RotorNumber of blades 4Radius (R) 64 mChord (c) 034 mRotation rate () 3486 RPMBlade pass frequency (f MR) 232 Hz

Tail Rotor

Number of blades 2Radius 1 mRotation rate 18807 RPMBlade pass frequency (f TR) 627 Hz

022001-2





X (m)

Y(m

)


f-ARFlight path

minus100

minus100

100

100

minus200

minus200 200

0

0


Time (s)

40

20

2 4 6 8 10

0

0

φ ()φ (s)







Filter description



p(fj ti) =

⎧⎪⎨⎪⎩



0 otherwise

(6)

022001-3


1 fMR

2 fMR

3 fMR

4 fMR

5 fMR

10 fMR

20 fMR

30 fMR

1 fTR

2 fTR

10 fTR

fMR

+ fTR

2fMR

+ fTR

BVI

Tail Rotor

Blade passage

65

70

75

80

85

90

95

101

102

103

Fre

quen

cy (

Hz)

Mai

n ro

tor

Tai

l rot

orC

ombi

nati

ons

1075 1100 1125 1150 1175 1200 1225minus10

0

10

Time (s)

Pre

ssur

e (P

a)





minus10minus10

1010

00

65

65

65

75

75

75

85

85

85

95

95

95

105

105

105

101

101

101

102

102

102

103

103

103

30

30

30304

304

304

304304

304308

308

308

308308

308312

312

312

312312

312316

316

316

316316

316


Inverse wavelet

Transform Eq (2)



minus10

10

0





022001-4


t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(a)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(b)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(c)









022001-5





t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

10

minus100

101

102

103


t (ms)

p(P

a)

25 50 75

10

minus10

0

0


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

45

55

65

75

85

95

105

1010

minus100

102

103


f (Hz)

p(d

B)

20

30

40

50

60

70

80

90

101 102 103






022001-6


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

100

1010

minus100

103


t (s)

f(H

z)p

(Pa)

310 312

101

102

103

100

minus10

(a)t (s)

310 312

(b)t (s)

310 312

(c)t (s)

310 312

(d)t (s)

310 312

65

75

85

95

105

(e)





t (s)

p(P

a)

310310310 311311311



Original

10

10

minus10

minus10

0

0

5

5

minus5

minus5


f (Hz)p

(dB

)20

30

40

50

60

70

80

90

100

101 102 103

FTFilt

fcut





SPL = 20 log10

PiRMS

PoRMS

(7)


022001-7


t (s)

p(P

a)

310310310 311311311



Original10

10

minus10

minus10

0

0

5

5

minus5

minus5






0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT


Results




Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)


022001-8






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10





X (m)

Y(m

)


f-ARFlight path

minus100

minus100

100

100

minus200

minus200 200

0

0


Time (s)

40

20

2 4 6 8 10

0

0

φ ()φ (s)







Filter description



p(fj ti) =

⎧⎪⎨⎪⎩



0 otherwise

(6)

022001-3


1 fMR

2 fMR

3 fMR

4 fMR

5 fMR

10 fMR

20 fMR

30 fMR

1 fTR

2 fTR

10 fTR

fMR

+ fTR

2fMR

+ fTR

BVI

Tail Rotor

Blade passage

65

70

75

80

85

90

95

101

102

103

Fre

quen

cy (

Hz)

Mai

n ro

tor

Tai

l rot

orC

ombi

nati

ons

1075 1100 1125 1150 1175 1200 1225minus10

0

10

Time (s)

Pre

ssur

e (P

a)





minus10minus10

1010

00

65

65

65

75

75

75

85

85

85

95

95

95

105

105

105

101

101

101

102

102

102

103

103

103

30

30

30304

304

304

304304

304308

308

308

308308

308312

312

312

312312

312316

316

316

316316

316


Inverse wavelet

Transform Eq (2)



minus10

10

0





022001-4


t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(a)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(b)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(c)









022001-5





t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

10

minus100

101

102

103


t (ms)

p(P

a)

25 50 75

10

minus10

0

0


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

45

55

65

75

85

95

105

1010

minus100

102

103


f (Hz)

p(d

B)

20

30

40

50

60

70

80

90

101 102 103






022001-6


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

100

1010

minus100

103


t (s)

f(H

z)p

(Pa)

310 312

101

102

103

100

minus10

(a)t (s)

310 312

(b)t (s)

310 312

(c)t (s)

310 312

(d)t (s)

310 312

65

75

85

95

105

(e)





t (s)

p(P

a)

310310310 311311311



Original

10

10

minus10

minus10

0

0

5

5

minus5

minus5


f (Hz)p

(dB

)20

30

40

50

60

70

80

90

100

101 102 103

FTFilt

fcut





SPL = 20 log10

PiRMS

PoRMS

(7)


022001-7


t (s)

p(P

a)

310310310 311311311



Original10

10

minus10

minus10

0

0

5

5

minus5

minus5






0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT


Results




Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)


022001-8






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10


1 fMR

2 fMR

3 fMR

4 fMR

5 fMR

10 fMR

20 fMR

30 fMR

1 fTR

2 fTR

10 fTR

fMR

+ fTR

2fMR

+ fTR

BVI

Tail Rotor

Blade passage

65

70

75

80

85

90

95

101

102

103

Fre

quen

cy (

Hz)

Mai

n ro

tor

Tai

l rot

orC

ombi

nati

ons

1075 1100 1125 1150 1175 1200 1225minus10

0

10

Time (s)

Pre

ssur

e (P

a)





minus10minus10

1010

00

65

65

65

75

75

75

85

85

85

95

95

95

105

105

105

101

101

101

102

102

102

103

103

103

30

30

30304

304

304

304304

304308

308

308

308308

308312

312

312

312312

312316

316

316

316316

316


Inverse wavelet

Transform Eq (2)



minus10

10

0





022001-4


t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(a)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(b)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(c)









022001-5





t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

10

minus100

101

102

103


t (ms)

p(P

a)

25 50 75

10

minus10

0

0


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

45

55

65

75

85

95

105

1010

minus100

102

103


f (Hz)

p(d

B)

20

30

40

50

60

70

80

90

101 102 103






022001-6


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

100

1010

minus100

103


t (s)

f(H

z)p

(Pa)

310 312

101

102

103

100

minus10

(a)t (s)

310 312

(b)t (s)

310 312

(c)t (s)

310 312

(d)t (s)

310 312

65

75

85

95

105

(e)





t (s)

p(P

a)

310310310 311311311



Original

10

10

minus10

minus10

0

0

5

5

minus5

minus5


f (Hz)p

(dB

)20

30

40

50

60

70

80

90

100

101 102 103

FTFilt

fcut





SPL = 20 log10

PiRMS

PoRMS

(7)


022001-7


t (s)

p(P

a)

310310310 311311311



Original10

10

minus10

minus10

0

0

5

5

minus5

minus5






0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT


Results




Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)


022001-8






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10


t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(a)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(b)

t (s)

f(H

z)

p(P

a)

300 304 312 316

65

75

85

95

105

10

minus100

101

102

103

(c)









022001-5





t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

10

minus100

101

102

103


t (ms)

p(P

a)

25 50 75

10

minus10

0

0


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

45

55

65

75

85

95

105

1010

minus100

102

103


f (Hz)

p(d

B)

20

30

40

50

60

70

80

90

101 102 103






022001-6


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

100

1010

minus100

103


t (s)

f(H

z)p

(Pa)

310 312

101

102

103

100

minus10

(a)t (s)

310 312

(b)t (s)

310 312

(c)t (s)

310 312

(d)t (s)

310 312

65

75

85

95

105

(e)





t (s)

p(P

a)

310310310 311311311



Original

10

10

minus10

minus10

0

0

5

5

minus5

minus5


f (Hz)p

(dB

)20

30

40

50

60

70

80

90

100

101 102 103

FTFilt

fcut





SPL = 20 log10

PiRMS

PoRMS

(7)


022001-7


t (s)

p(P

a)

310310310 311311311



Original10

10

minus10

minus10

0

0

5

5

minus5

minus5






0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT


Results




Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)


022001-8






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10





t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

10

minus100

101

102

103


t (ms)

p(P

a)

25 50 75

10

minus10

0

0


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

45

55

65

75

85

95

105

1010

minus100

102

103


f (Hz)

p(d

B)

20

30

40

50

60

70

80

90

101 102 103






022001-6


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

100

1010

minus100

103


t (s)

f(H

z)p

(Pa)

310 312

101

102

103

100

minus10

(a)t (s)

310 312

(b)t (s)

310 312

(c)t (s)

310 312

(d)t (s)

310 312

65

75

85

95

105

(e)





t (s)

p(P

a)

310310310 311311311



Original

10

10

minus10

minus10

0

0

5

5

minus5

minus5


f (Hz)p

(dB

)20

30

40

50

60

70

80

90

100

101 102 103

FTFilt

fcut





SPL = 20 log10

PiRMS

PoRMS

(7)


022001-7


t (s)

p(P

a)

310310310 311311311



Original10

10

minus10

minus10

0

0

5

5

minus5

minus5






0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT


Results




Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)


022001-8






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10


t (s)

f(H

z)

p(P

a)

300 305 310 315 320

65

75

85

95

105

70

80

90

100

100

1010

minus100

103


t (s)

f(H

z)p

(Pa)

310 312

101

102

103

100

minus10

(a)t (s)

310 312

(b)t (s)

310 312

(c)t (s)

310 312

(d)t (s)

310 312

65

75

85

95

105

(e)





t (s)

p(P

a)

310310310 311311311



Original

10

10

minus10

minus10

0

0

5

5

minus5

minus5


f (Hz)p

(dB

)20

30

40

50

60

70

80

90

100

101 102 103

FTFilt

fcut





SPL = 20 log10

PiRMS

PoRMS

(7)


022001-7


t (s)

p(P

a)

310310310 311311311



Original10

10

minus10

minus10

0

0

5

5

minus5

minus5






0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT


Results




Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)


022001-8






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10


t (s)

p(P

a)

310310310 311311311



Original10

10

minus10

minus10

0

0

5

5

minus5

minus5






0

0

3

3

minus3

minus3 6minus6

minus6minus9minus12

ΔSP

L

Δ MRE

WTFT


Results




Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

0375 0465 0555

(b)


022001-8






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10






Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

1375 1465 1555

(a)

Original

BVI

Residual15

15

15

10

10

10

5

5

5

0

0

0

minus5

minus5

minus5

2375 2465 2555

(b)


Conclusions





Acknowledgments


References







022001-9





















022001-10





















022001-10

extracting bladeÂŒvortex interactions using continuous ... · nasa, bell helicopter, and the u.s....

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