Order tracking signal processing for open rotor acoustics

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Journal of Sound and Vibration

Journal of Sound and Vibration ] (]]]]) ]]]–]]]

http://d0022-46

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journal homepage: www.elsevier.com/locate/jsvi

Order tracking signal processing for open rotor acoustics

David B. Stephens a,n, Håvard Vold b

a NASA Glenn Research Center, Cleveland, OH 44135, United Statesb ATA Engineering, Inc., San Diego, CA 92103, United States

a r t i c l e i n f o

Article history:Received 12 June 2013Received in revised form13 March 2014Accepted 1 April 2014
Handling Editor: K. Shin
each rotor, even as the rotation rate of the two rotors varies. This is a major improvement

x.doi.org/10.1016/j.jsv.2014.04.0050X/Published by Elsevier Ltd.

esponding author.ail addresses: [email protected] (D.B.

e cite this article as: D.B. Stephens,d and Vibration (2014), http://dx.doi.o

a b s t r a c t

Counter-rotating open rotor acoustic measurements were processed using a two-shaftVold–Kalman order tracking filter, providing new insight into the complicated noisegeneration mechanisms of this type of system. The multi-shaft formulation of the Vold–Kalman filter can determine a time-accurate output of shaft order tones associated with

over the usual short time Fourier transform method for many applications. It was foundthat the contribution from each rotor to the individual tones varies strongly as a functionof shaft order and operating condition. The order tracking filter is also demonstrated as arobust tool for separating the tonal and broadband components of a signal for which theusual shaft phase averaging methods fail.

Published by Elsevier Ltd.

1. Introduction

Noise from aircraft engines is often described as containing both tonal and broadband components. Early jet engines forcommercial aircraft primarily relied on the jet exhaust for thrust, but concerns about fuel efficiency and noise bothmotivated the modern design of a relatively smaller gas generator core driving a large fan. This has led to a situation wheretonal and broadband noise can be present at nearly equal power levels in an aircraft noise signature, or in model scaletesting. Wright [1] indicates that the relative importance and causes of discrete and broadband noise from rotors have beena point of discussion since the days of biplanes. He created an aggregate spectrum that incorporated many sound generatingmechanisms found in typical rotors. He described the dominant feature of such sound spectra as a continuous spectrum,roughly parabolic in decibels plotted against the logarithm of frequency. Saule [2] discusses the identification of a broadbandbaseline that is generally continuous and touches most of the minima of the spectra, except underneath discrete tones.This definition may have some uncertainty if the tones are broad or have skirts. A recent publication by Parry et al. [3]considered the relative contribution of tones and broadband on a third octave basis to the total sound signature of a modelopen rotor rig, and found that broadband noise is important even to systems with a profusion of strong tones.

Separating broadband and tonal signals is useful for comparing experimental measurements with theoretical predictions.These predictions often rely on significant simplifications and may be limited to describing either tonal or broadband sound.Even in engine component testing, such as a single stage fan, many sound source mechanisms may contribute to the totalradiated sound field. For example, a single stage fan may have turbulence interaction noise, loading noise, rotor–stator

Stephens), [email protected] (H. Vold).

& H. Vold, Order tracking signal processing for open rotor acoustics, Journal ofrg/10.1016/j.jsv.2014.04.005i

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http://dx.doi.org/10.1016/j.jsv.2014.04.005



mailto:[email protected]

mailto:[email protected]





D.B. Stephens, H. Vold / Journal of Sound and Vibration ] (]]]]) ]]]–]]]2

interaction noise, trailing edge noise and other mechanisms. These are often estimated separately and combined to give aprediction for the total sound field of the system. Isolating the individual sources from the measured sound as much aspossible is useful for validating each portion of the prediction. Additionally, experiments feature additional complicationsthat often do not exist in analytical theories or simulations. Barry and Moore [4] discuss some causes of amplitude andfrequency modulation in fan noise experiments, including vibration, atmospheric scattering and engine speed fluctuations.The present report will show the limits of the usual tone and broadband separation methods when applied to open rotorsand offer a new method.

The report on propeller noise by Magliozzi et al. [5] presents a three-component definition of aeroacoustic sound fromturbomachinery:

harmonic noise is periodic in rotor rotation and has a discrete spectrum,broadband noise is random with a continuous spectrum, andnarrow-band random noise is almost periodic but does not repeat exactly with rotor rotation.For a single rotor system, the sound radiated to the acoustic far field is a combination of harmonic and broadband noise.

On the other hand, the counter-rotating open rotor system discussed in this report is dominated by narrow-band randomnoise with a smaller broadband component. This will be illustrated in Section 2.2. The present paper discusses the use of theVold–Kalman filter [6–8] to quantify the narrow-band random noise component that is indeed a superposition of twoharmonic tones, each one coherent with its own rotor shaft. Section 2 describes the open rotor experiment and discusses theshortcomings of using conventional phase averaging for identifying tones. Section 3 discusses spectral methods for tone andbroadband separation. The theory behind the Vold–Kalman filter is presented in Section 4, some limited results from theapplication of the filter to open rotor acoustic data is presented in Section 5 and conclusions are provided in Section 6.

2. Open rotor experiment

Recent renewed interest in counter-rotating open rotor propulsion systems has been the impetus behind several modelscale wind tunnel tests. The NASA Open Rotor Propulsion Rig (ORPR) was used as the drive system for one such test done incollaboration with GE Aviation. This drive rig was built and operated in the late 1980s, and underwent a substantialrestoration program during 2009 in order to correct any detrimental effects of long-term storage. The restoration activityconsisted of a general inspection and rebuild of the mechanical components, construction of a new swept rig support strut,refurbishment of the forward and aft rotating force balances and installation of a telemetry system. This rig was operated ina low-speed test campaign from late 2009 to late 2010 in the 9�15 Low Speed Wind Tunnel at NASA Glenn Research Center.The refurbished ORPR installed in the 9�15 wind tunnel is shown in Fig. 1. The traversing microphone system is shown inthe foreground.

The ORPR drive system consists of two counter rotating spools with a non-rotating center shaft. Each of the two counterrotating spools is attached to a two-stage air turbine on the aft end that can produce up to 560 kW (750 HP). The two airturbines are supplied by 2 MPa (300 psi) air heated to 90 1C (200 1F), and can be controlled using a feedback system to drivethe rotor speeds to more than 8000 RPM with an accuracy of 715 RPM. The air turbines in the ORPR are individuallycontrolled and not mechanically coupled. Since the supply air arrives at the facility at 450 psi, a supply-side valve was used

Fig. 1. Open Rotor Propulsion Rig in 9�15 Wind Tunnel at NASA Glenn Research Center. NASA Image C-2010-3454.

Please cite this article as: D.B. Stephens, & H. Vold, Order tracking signal processing for open rotor acoustics, Journal ofSound and Vibration (2014), http://dx.doi.org/10.1016/j.jsv.2014.04.005i




Aft Rotor Turbine Supply Valve

Wind Tunnel Floor

Laboratory Air System Supply

Front Rotor Turbine Supply Valve

Shared Regulator Valve

Front RotorAft RotorAft Rotor Drive Turbine

Front Rotor Drive Turbine

Fig. 2. Open Rotor Propulsion Rig in 9�15 Wind Tunnel at NASA Glenn Research Center. Sketch not to scale.

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D.B. Stephens, H. Vold / Journal of Sound and Vibration ] (]]]]) ]]]–]]] 3

as a regulator to attempt to maintain a 300 psi charge to the two valves controlling the air turbines. A schematic showingmany of these features is given in Fig. 2.

Due to the use of independent air turbines, the rotation rate of the two rotors varies slightly and the phase is not lockedbetween the rotors. A chart showing the rotation speed of the two rotors during a typical 15 s measurement is shown inFig. 3.

2.1. Acoustic instrumentation

Acoustic instrumentation was a single Brüel and Kjær 4939 6.35 mm (1/4 in.) microphone with the standard UA-0385nose cone for making in-flow microphone measurements. This microphone was mounted on a linear traverse offset on a1.52 m (5 ft) sideline from the centerline of the model. The sideline measurement covers the observation angles between17.61 and 1401 from the upstream axis of the fan, at 18 locations. An R.C. Electronics Inc. DataMAX II data recorder was usedto record 15-s samples at 200 kHz, along with the once-per-revolution signals from the front and aft rotors. It is useful todefine the dimensionless frequency shaft order as SO¼ f =Ω, where f is the frequency and Ω is the shaft rate. The presentopen rotor system featured blade counts of 12 on the forward rotor and 10 on the aft rotor, so strong blade rate tones aregenerated at SO¼10 and SO¼12. The blade count mismatch results in a large number of interaction tones which occur atshaft orders of

SOðm;nÞ ¼ 12mþ10n; (1)

as long as the shaft rates are nearly equal, where m and n are integers denoting the front and rear blade passing tone order.For all of the data presented in this paper, the two rotors were feedback-controlled to the same average rotation speed.Some results from the acoustic data acquired during this test have been summarized in Elliot [12] and Stephens and Envia[13] and Berton [14].






2.2. Phase averaged acoustics

For a single shaft system like a conventional fan, the harmonic sound is well defined. Measurements of the radiatedsound measured by any single microphone can be either synchronously acquired [15] or acquired at arbitrary time andphase averaged by an encoder indicating the shaft position to give the periodic portion of the pressure signal. To express thisin an equation

pðθÞ ¼ pðtÞθ ; (2)

where p is the unsteady pressure, t is the measurement time, θ is the phase of the rotor with the overbar indicating averageover θ. The periodic portion of the signal can be subtracted from the total signal to give the broadband component of theradiated sound. This method works well for single shaft systems, even if the fan speed is not perfectly steady. A typical resultfrom applying this technique to fan data is shown in Fig. 4. This figure shows that the tonal content of the fan noise iscaptured in the phase averaging, showing one peak for each fan blade. Phase averaging for quantifying tone and broadbandacoustic levels works for a single shaft system.

For a two-shaft system, a different phase averaged signal results depending on which the shaft is considered. Both phaseaveraged signals were calculated for a typical open rotor sound spectrum and are shown in Fig. 5. It is immediately apparentthat only a portion of the tone energy is captured in the resulting phase average signals. Specifically, the blade passing tonesare captured (SO¼10 for the aft rotor, SO¼12 for the forward rotor) but most other tones are not. Phase averaging does notaccurately quantify all the tone levels for a two shaft system. This can be explained because the relative phase of the

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Fig. 4. Total ( ) and phase averaged ( ) sound from a single shaft fan is shown in the (a) time domain and (b) frequency domain.

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uncoupled shafts changes arbitrarily each rotation, which makes conventional phase averaging essentially impossible. Evenconsidering individual rotations that by chance have the same number of samples, the relative phase angle of the two rotorsmay be different. Phase averaging isolates only the individual rotor contributions and leaves interaction tones in thebroadband spectrum. Other signal processing methods were explored.

3. Frequency-domain processing

All of the pressure spectral density plots shown in this report were calculated using an 8192 point fast Fourier transformalgorithm resulting in a 12.2 Hz bin width frommeasurements at 100 kHz. This is more than enough frequency resolution toseparately identify shaft order tones, which were typically around 110 Hz apart. The tone and broadband components of asignal may be estimated from a frequency spectrum using a post-processing algorithm, although the authors are not awareof a generally accepted process for doing this. Stephens and Envia [13] used a peak finding algorithm to identify peaks of acertain size and remove them from a given spectrum. The gaps were filled by interpolation, resulting in a broadbandspectrum. Parry et al. [3] used a moving median filter as a tone deletion method. One advantage to this method is that itrequires only one parameter: the filter width. A small modification to the moving median filter was found to be useful. Theoutput from the filter was compared with the input spectra and the minimum value at each frequency was chosen. Thiseliminates the possibility that the broadband curve can be higher than the input spectra at some frequencies. This situationis a problem if the difference between the total and broadband spectra is to be used as the tone spectrum. The filter widthparameter should be chosen such that it is larger than the number of frequency bins in each tone, but small enough so that itdoes not touch two tones at once. For the open rotor data presented here, any number between 76 and 712 points fromthe center point returned largely the same spectra.

Open rotor data is shown in Fig. 6(a) along with broadband spectra determined by both a moving median filter and thepeak-finding algorithm. Fig. 6(b) shows the difference between the moving median and the proposed “modified” movingmedian filter, with the axes zoomed in to illustrate the differences. The moving median is seen to be a satisfactory methodfor filling a broadband spectrum underneath tones.

4. Vold–Kalman processing

4.1. Mathematical background

The Vold–Kalman filter [6–11] is a time domain tracking filter that extracts time histories of harmonics relative to one ormore independently running shafts. The filter acts as a concurrent set of narrow bandpass filters, where the instantaneouscenter frequency of each band is controlled by the rotational speed of the shaft which generates the correspondingharmonic. The Vold–Kalman filter provides for narrow band tracking, and hence, the shaft speed and position informationmust be precise lest the filter extract unintended frequency bands.

4.1.1. The anatomy of responses from rotating and reciprocating machineryThe time histories of mechanical response from machinery will contain components of different nature, from

various sources, such as periodic loads, shock-like transients, longer term transients and flow noise, such as from vortexshedding and turbulence. The Vold–Kalman filter is designed to extract subsets of the periodic components, and in order to

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Fig. 6. Examples of frequency-domain signal processing are given. In (a), the total spectra ( ), moving median results ( ) and peak finding minimumresults ( ) are shown in wide view. Part (b) shows the total spectra ( ), moving median results ( ) and modified moving median results ( ) areshown in a narrow view.






understand the environment in which it operates, we appeal to a general finding from the statistical theory of locallystationary processes, named the Wold decomposition [16].

4.1.2. The Wold decomposition of a stochastic processIn the late 1930s, Herman Wold, a Norwegian–Swedish mathematician, formulated the first versions of what would

become known as the Wold decomposition of any stationary stochastic process into the uncorrelated sum of a deterministicprocess and a purely indeterministic process. The deterministic process could be regarded as a sum of sine waves withvarious phases and amplitudes, and the purely indeterministic component could be represented as a white noise processfiltered by an (infinite) moving average filter.

The sine waves would have point spectra with finite spectral mass at discrete frequencies, while the purely indeterministiccomponent would have an absolutely continuous spectral density, corresponding to a broadband noise process.

4.1.3. The structure of orders, tones and harmonicsIn rotating and reciprocating machinery there exist one or more rotating shafts which may be coupled mechanically

through gears, belt and chains, or, electronically through feedback control systems. The rotations of these shafts will causeperiodic vibrations, modulated by gears meshing, belts driving pulleys, cams operating valve trains and axial and thrustbearings supporting shafts, pulleys and gears. The periods of these vibrations will be purely kinematic functions of themechanical layout of the machinery. The combustion or pressure cycles of such machines will also produce periodicexcitation.

Let us denote the instantaneous speed of a shaft in revolutions per second as ωðtÞ. The instantaneous rotationaldisplacement is the time integral of the speed, and we define the complex phasor pk(t) belonging to the order k as

pkðtÞ ¼ exp 2πikZ t

0ωðuÞ du

� �: (3)

The order k does not have to be an integer; toothed gears give rise to rational orders, and rolling element bearings andpulleys most often produce irrational orders.

We can now define a complex order time history xk(t) as

xkðtÞ ¼ AkðtÞpkðtÞ ¼ AkðtÞ exp 2πikZ t

0ωðuÞ du

� �; (4)

where Ak(t) is a slowly varying complex envelope.This allows us to express the general case of a vibration or acoustic time history resulting from the periodic components

of a rotating or reciprocating machine as

xðtÞ ¼ ∑sAS

∑kAKs

AskðtÞpskðtÞ ¼ ∑sAS

∑kAKs

AskðtÞ exp 2πikZ t

0ωsðuÞ du

� �; (5)

where S is the set of all independently moving shafts and Ks is the discrete set of relevant orders, negative as well aspositive, generated by shaft s.

Since Eq. (5) is a sum of sine waves, this time history is a completely deterministic process in the language of the Wolddecomposition [16]. Because of this property, each order, when observed synchronously with multiple sensors, is fullyself-coherent, which makes feasible to construct spatial mappings of each order as a function of time, RPM or frequency,see, e.g., [17].

In the real world, whenwe measure the structural and acoustic responses from rotating and reciprocating machinery, wewill, in addition to the sum of periodic signals x(t) from Eq. (5), also record the effects of flow noise, turbulence and transientevents, such that the total measured signal y(t) will be of the form

yðtÞ ¼ xðtÞþνðtÞ; (6)

where νðtÞ is causal, is uncorrelated with x(t), and has an absolutely continuous spectrum without point masses. Thebroadband signal νðtÞ is thereby the purely indeterministic component of the Wold decomposition.

4.1.4. The formulation of the Vold–Kalman filterWe shall now assume that we have digitized a finite alias free response time history yðnÞ;nA ½0;1;…;N�, where the

sampling rate has been set to 1 sample per second without any loss of generality. We also assume that we have obtained theshaft speeds ωsðnÞ for the shafts sAS by observing encoders or tachometers.

Order tracking is now the art and science of estimating the complex envelopes Ask(n) from the recorded response andshaft speeds for the orders kAKs, restricted to the orders being lower in frequency than the Nyquist frequency of 0.5 Hz.

The Vold–Kalman filter is related to the classical Kalman filter [18] by compromising between structural equations anddata equations, although in the Vold–Kalman filter one only uses the ratio between the two sets of equations.

The structural equation specifies that the envelope functions should be smooth, slowly varying functions. One way ofspecifying this for the envelope Ask(n) is to demand that a repeated difference should be small, e.g., satisfy an equation such





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as one of the following:

∇AskðnÞ ¼ Askðnþ1Þ�AskðnÞ ¼ ϵðnÞ; (7)

∇2AskðnÞ ¼ Askðnþ2Þ�2Askðnþ1ÞþAskðnÞ ¼ ϵðnÞ; (8)

∇3AskðnÞ ¼ Askðnþ3Þ�3Askðnþ2Þþ3Askðnþ1Þ�AskðnÞ ¼ ϵðnÞ; (9)

where the sequence ϵðnÞ is small in some sense. The exponent q in the difference operator ∇q is customarily named the polecount of the Vold–Kalman filter. The coefficients of the expanded iterated differences are seen to build the famous Pascaltriangle.

In addition to the smoothness condition of the structural equation, the estimated complex envelope function mustsomehow be related to the measured data, and this is achieved by the data equation

∑sAS

∑kAKs

AskðnÞpskðnÞ ¼ yðnÞ�νðnÞ; (10)

which is seen to be a reordered discrete version of Eqs. (5) and (6).We see that the unknown complex envelope functions Ask(n) occur in linear expressions with measured coefficients on

the left hand side of the structural and data equations, so we can construct a weighted linear least squares problem bychoosing a weighting function rðnÞ;nA ½0;1;…;N�, and discarding the unmeasured functions ϵðnÞ and νðnÞ as nuisanceparameters to obtain the linear, overdetermined set of equations

rðnÞ∇qAskðnÞ � 0 (11)

∑sAS

∑kAKs

AskðnÞpskðnÞ � yðnÞ; (12)

where a large value of r(n) enforces smoothness around the time point n, while a small value permits the observed data todominate the estimation at this time point. The choice of the weighting function r(n) determines the bandwidth and theresolution of the results [19]. The attainable filter shapes are shown in Fig. 7, where the frequency axis is normalized to 1 Hzsampling rate. In practice, because of numerical dynamic range issues, one normally uses between one and three poles.

The fundamental equations (11) and (12) are normally solved as a linear least squares problem, but because of numericalissues when narrow bandwidths are specified, we have applied an orthogonal decomposition method called the QRdecomposition [20] which permits narrower bandwidths than the published solutions. We have also applied an improvedequation sequencing which allows for direct high speed banded solution schemes for the dual rotor case.

4.1.5. Comparison with the Hilbert–Huang transformThe reader may be interested to know how the Vold–Kalman filter relates to the Hilbert–Huang transform, which is the

combined use of the Hilbert transform and empirical mode decomposition.The Hilbert transform ~xðtÞ of a signal x(t) can be used to define an analytic signal, zðtÞ ¼ xðtÞþ i ~xðtÞ, where the envelope

signal of x(t) is defined as jzðtÞj and the instantaneous phase signal of x(t) is defined as argðzðtÞÞ [21]. This is somewhat similarto the description of the signal xk(t) used in Eq. (4) although for the Vold–Kalman filter the phase is computed from the





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Fig. 8. Comparison of single versus multi-shaft Vold–Kalman filter processing. Total signal ( ), signal remaining after two single Vold–Kalman filteringoperations ( ), signal remaining after multi-shaft Vold–Kalman filter ( ).


tachometer signal rather than generated from the signal itself. Likewise, the envelope Ak(t) used in the Vold–Kalman filter isgenerated using the structural equation described in Section 4.1.4 while the Hilbert transform produces an envelope fromthe signal itself.

Empirical mode decomposition is a data-driven algorithm for finding so-called intrinsic mode functions, a small numberof intrinsic mode functions which usually suffice to describe even a complicated signal [22]. Empirical mode decompositionacts essentially as a dyadic filter bank [23], meaning frequencies must be a factor of two apart in order to be adequatelyseparated. The small number of intrinsic mode functions means that each will include many tones when the method isapplied to the present data set, since consecutive tones are much less than an order of two apart in frequency.

Since we have accurate estimates of the instantaneous angular displacements from the tachometer measurements, thecomplex phasor is already known, such that the Vold–Kalman filter needs only to perform the linear estimation of thecomplex envelopes. The Hilbert–Huang transform is a technique for the more general situations where the frequencyproperties also must be estimated in parallel with the complex envelope. The dual open rotor system has two rotorsmounted on counter-rotating shafts whose speeds are weakly coupled through a control system. Each shaft is furnishedwith a tachometer which gives one pulse per revolution. Since the inertias in the shafts act as mechanical low-pass filters,we can construct exceedingly accurate time histories of angular displacement and velocity. The Vold–Kalman filter is a purelinear and time domain procedure, where the unknown parameters, the complex envelopes, are estimated from an implicitsimultaneous equation set and the result is a very precise extraction of the shaft order coherent tones. In an experimentwhere we have speed signals for the rotors, the empirical mode decomposition and Hilbert transform procedure will bestatistically inferior to the Vold–Kalman filter. As a note, Wang and Heyns [24] have investigated the combined use ofempirical mode decomposition and the Vold–Kalman filter.

4.2. Explanation and illustration of capabilities

A first attempt at implementing Vold–Kalman filtering was made using two single-shaft filters in succession. Thisresulted in filtering that was effective for blade rate tones and higher multiples, but only marginally successful at filteringinteraction tone orders, that is m and na0 as given in Eq. (1). As shown in Fig. 8, the repeated single shaft processing doesnot effectively extract the interaction tones. The multi-shaft filter is far more effective at filtering the interaction tones.

Vold–Kalman filtering can be used to accurately isolate each tone in the time domain while preserving accurate phaseinformation, as shown in Fig. 9(a). This figure was created by filtering the total signal through the multi-shaft Vold–Kalmanfilter repeatedly, once for each shaft order from 10 to 100. Only integer shaft orders were expected because the systemcontains no gears or belts, although the processing method could handle these as discussed in Section 4.1.3. The sum of theshaft order signals is the tonal content while the remaining signal is broadband. Shaft orders below 10 were filtered out forplotting Fig. 9(a) using a digital high-pass Butterworth filter. The energy in each tone can be calculated from the standarddeviation of the Vold–Kalman filter output since the filter tracks shaft orders, however the spectral density of the filteroutput is shown in Fig. 9(b) for comparison with Fig. 5(b). Fig. 9(a) can be compared with Fig. 5(a) to illustrate the differencein the time domain between phase averaging and Vold–Kalman filtering. For the processing shown here, the data wasdownsampled by a factor of two (from 200 kHz sample rate to 100 kHz sample rate) to decrease computation time. A twopole Vold–Kalman filter was used for all the data processing shown in this report.

The calculated spectral density of the signal after filtering is shown in Fig. 9(b). The broadband spectrum is generatedfrom the signal that remains after all shaft order tones from 10 to 100 have been filtered out. Attempting to use the order





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Fig. 9. An example is given showing Vold–Kalman filter working in (a) the time domain and (b) the frequency domain. Total signal ( ), tones extracted byVold–Kalman filter ( ), signal remaining after multi-shaft Vold–Kalman filter ( ).

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tracking filter for frequencies below SO¼10 sometimes resulted in attempting to invert a singular matrix as the two shaftphasors become close to coherent at low orders. These frequencies were thus excluded from the calculations. Thecorrelation coefficient between the two shaft rates was found to give an indication of when this might be a problem, withvalues above roughly 0.9 being necessary but not sufficient for creating a singular matrix. Shaft orders higher than 100 weredisregarded as being of relatively small amplitude and with frequencies higher than those of interest. It can be qualitativelyobserved that the broadband spectrum is similar to that resulting from the spectral methods shown in Fig. 6(a), althoughthere is slightly more energy removed at each shaft order than with spectral methods. This can be affected by changing thebandwidth of the Vold–Kalman filter. Fig. 9 was created by finding an optimum filter bandwidth for each shaft order.The Matlab function fminbnd was used to minimize the resulting ‘divots’ in the spectrum. The bandwidth was allowed tovary between 1 and 7 Hz, with 1 Hz being the minimum stable bandwidth. A larger bandwidth results in a more aggressivefilter. The optimized bandwidth for each shaft order is shown in Fig. 10. It can be seen that a wider bandwidth is not neededfor SO¼22, which is the first interaction tone, but is needed for SO¼32, 34, 42, 44, 46, which are the next 5 interactiontones. SO¼22 is never a major tone for this system.

4.3. Additional information gained by Vold–Kalman filtering

The Vold–Kalman filter results in phase-accurate time histories of pressures tracked for each shaft order. Using the multi-shaft Vold–Kalman filter, the contribution that is coherent with each shaft order can be found. For an example operatingcondition, the envelope of these two time signals is shown in Fig. 11 for SO¼32 and SO¼34. These two shaft orders werechosen because they are the two strongest tones. The variation in the signal level is related to the variation in the rotor





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Time, s

Fig. 12. Tone level fluctuations are given for the four highest amplitude shaft orders during a typical 15 second recording, separated into contributions from(a) the front rotor and (b) the aft rotor. SO¼32 ( ), SO¼34 ( ), SO¼10 ( ), and SO¼42 ( ).


rotation speeds, and data for this same measurement is shown in Fig. 3. Readily apparent in Fig. 3 are the two peaks in thefront rotor shaft rate at about 2 and 3 s, with one peak found in the aft rotor shaft rate at 2 s. As shown in Fig. 11(b), thiscauses two peaks in the SO¼34 noise caused by the front rotor. Fig. 11(a) shows two peaks in the noise from both rotors,although for SO¼32 the aft rotor is the dominant noise source. These fluctuations seem to be closely related to the shaft ratevariation given in Fig. 3.

Grosveld et al. [25] considered the temporal character of aircraft noise and used a Short Time Fourier Transform toquantify fluctuations in individual rotor tones as a way to improve time-independent noise predictions. Their method used atime overlap of 92 percent to achieve a balance between a frequency resolution and sample time to quantify tone levelvariations. The Vold–Kalman filter can provide this result without the need for a Fourier transform or time averaging thatwould smear out the tone levels. For the same operating condition as Fig. 11, Fig. 12 shows the four loudest tone levels as afunction of measurement time calculated from the envelope of the Vold–Kalman filtered shaft order signal. The most stableof these four tones is the SO¼10 tone from the aft rotor, which is generated by steady loading. The levels of the interactiontones on the other hand are much more sensitive to small changes in rotor speed or tunnel unsteadiness. The aft rotor isprimarily responsible for tone contributions of SO¼32 and 42 while SO¼34 emanates primarily from the front rotor.

4.4. Processing time using Vold–Kalman filtering

The processing reported in this document was conducted using Matlab on an Intel i7-2760QM. Filtering the entire 15 srecord sampled at 100 kHz took approximately 12 s for one shaft order. This is fast enough for real time processing of oneshaft order, although that was not the aim of the present project. The filter converges extremely quickly even with very






narrow filter width, so if the rotor system was more steady a much shorter record than 15 s could be used. Quantitativerecommendations regarding using the Vold–Kalman filter to reduce test time are beyond the scope of the present report.The spectral processing methods presented in Section 3 are extremely quick, taking only around 0.1 s to process a 8192 pointspectrum.

5. Processing results for various operating conditions

The open rotor was run at a variety of configurations. The blade pitch angles were set to either approach or take-offconditions while rotor speed was varied. Tunnel speed was Mach 0.20 for all the data shown in this report. The Vold–Kalman filter was used to separate the contribution to each shaft order tone from each rotor. In Figs. 13–16(a), spectra areshown with a black line indicating the broadband result from the Vold–Kalman filter, and a forward and aft rotorcontribution for each shaft order tone up to orders m¼5 and n¼5. In Figs. 13–16(b), the expected blade rate and interactiontones are shown in a grid with boxes colored to indicate whether the tone is forward (blue) or aft (red) dominated,determined by a difference in level of more than 3 dB. If the difference between the rotor contributions is 3 dB or less, the

0 20 40 60 80 10050

60

70

80

90

100

110

Shaft Order

Pres

sure

Spe

ctra

l Den

sity

, dB

0 1 2 3 4 5

0

1

2

3

4

5

0,5SO=50

1,5SO=62

2,5SO=74

3,5SO=86

4,5SO=98

0,4SO=40

1,4SO=52

2,4SO=64

3,4SO=76

4,4SO=88

5,4 SO=100

0,3SO=30

1,3SO=42

2,3SO=54

3,3SO=66

4,3SO=78

5,3SO=90

n

0,2SO=20

1,2SO=32

2,2SO=44

3,2SO=56

4,2SO=68

5,2SO=80

0,1SO=10

1,1SO=22

2,1SO=34

3,1SO=46

4,1SO=58

5,1SO=70

1,0SO=12

2,0SO=24

3,0SO=36

4,0SO=48

5,0SO=60

m

Fig. 13. Open rotor tone levels at approach pitch angles and low shaft power condition are given in chart (a) as spectra showing total signal ( ), forwardrotor tones ( ), aft rotor tones ( ) and broadband ( ). A grid showing which rotor is predominately responsible for each tone is given as chart (b)(forward, aft, both, no tone). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

0 20 40 60 80 10050

60

70

80

90

100

110

Shaft Order

Pres

sure

Spe

ctra

l Den

sity

, dB

0 1 2 3 4 5

0

1

2

3

4

5

0,5SO=50

1,5SO=62

2,5SO=74

3,5SO=86

4,5SO=98

0,4SO=40

1,4SO=52

2,4SO=64

3,4SO=76

4,4SO=88

5,4 SO=100

0,3SO=30

1,3SO=42

2,3SO=54

3,3SO=66

4,3SO=78

5,3SO=90

n

0,2SO=20

1,2SO=32

2,2SO=44

3,2SO=56

4,2SO=68

5,2SO=80

0,1SO=10

1,1SO=22

2,1SO=34

3,1SO=46

4,1SO=58

5,1SO=70

1,0SO=12

2,0SO=24

3,0SO=36

4,0SO=48

5,0SO=60

m

Fig. 14. Open rotor tone levels at approach pitch angles and high shaft power condition are given in chart (a) as spectra showing total signal ( ), forwardrotor tones ( ), aft rotor tones ( ) and broadband ( ). A grid showing which rotor is predominately responsible for each tone is given as chart (b)(forward, aft, both, no tone). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)





0 20 40 60 80 10050

60

70

80

90

100

110

Shaft Order

Pres

sure

Spe

ctra

l Den

sity

, dB

0 1 2 3 4 5

0

1

2

3

4

5

0,5SO=50

1,5SO=62

2,5SO=74

3,5SO=86

4,5SO=98

0,4SO=40

1,4SO=52

2,4SO=64

3,4SO=76

4,4SO=88

5,4 SO=100

0,3SO=30

1,3SO=42

2,3SO=54

3,3SO=66

4,3SO=78

5,3SO=90

n

0,2SO=20

1,2SO=32

2,2SO=44

3,2SO=56

4,2SO=68

5,2SO=80

0,1SO=10

1,1SO=22

2,1SO=34

3,1SO=46

4,1SO=58

5,1SO=70

1,0SO=12

2,0SO=24

3,0SO=36

4,0SO=48

5,0SO=60

m

Fig. 15. Open rotor tone levels at nominal take off pitch angles and low shaft power condition are given in chart (a) as spectra showing total signal ( ),forward rotor tones ( ), aft rotor tones ( ) and broadband ( ). A grid showing which rotor is predominately responsible for each tone is given aschart (b) (forward, aft, both, no tone). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of thispaper.)

0 20 40 60 80 10050

60

70

80

90

100

110

Shaft Order

Pres

sure

Spe

ctra

l Den

sity

, dB

0 1 2 3 4 5

0

1

2

3

4

5

0,5SO=50

1,5SO=62

2,5SO=74

3,5SO=86

4,5SO=98

0,4SO=40

1,4SO=52

2,4SO=64

3,4SO=76

4,4SO=88

5,4 SO=100

0,3SO=30

1,3SO=42

2,3SO=54

3,3SO=66

4,3SO=78

5,3SO=90

n

0,2SO=20

1,2SO=32

2,2SO=44

3,2SO=56

4,2SO=68

5,2SO=80

0,1SO=10

1,1SO=22

2,1SO=34

3,1SO=46

4,1SO=58

5,1SO=70

1,0SO=12

2,0SO=24

3,0SO=36

4,0SO=48

5,0SO=60

m

Fig. 16. Open rotor tone levels at nominal take off pitch angles and high shaft power condition are given in chart (a) as spectra showing total signal ( ),forward rotor tones ( ), aft rotor tones ( ) and broadband ( ). A grid showing which rotor is predominately responsible for each tone is given aschart (b) (forward, aft, both, no tone). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of thispaper.)


box is colored green. If the total tone level is less than 3 dB above the broadband, the box is left white. These contributionscould also be identified using a phased array of microphones to localize the sound sources.

Figs. 13 and 14 correspond to the open rotor with approach pitch angle settings, at low and high power respectively.At low power, the loudest tones are seen to be around 20 dB above the broadband while some of the expected tones arenon-contributors. At this low power point (800 N [180 lbs] thrust), loading noise is a smaller contribution. At high power(2380 N [535 lbs] thrust) the largest tones are well over 30 dB above the broadband and all expected tones are contributors.The contributions per rotor are generally split into whichever (m,n) tone order is larger. The broadband spectrum at highpower has broad haystacks around SO¼22, 32 and 42.

Figs. 15 and 16 show analogous results for the open rotor at take-off pitch angle settings. For these cases the broadbandspectra show few spectral features although the levels increase from around 55 dB at low power (800 N [180 lbs] thrust) to70 dB at high power (2590 N [582 lbs] thrust). There are considerably more evenly split tones, indicated by green boxes.At low power the front rotor dominates more tones while the aft rotor dominates more tones at high power. This is probablydue to the increase in unsteady loading of the aft rotor due to the front rotor wake as thrust levels are increased.






6. Conclusions

The utility of an order tracking Vold–Kalman filter for processing aeroacoustic measurements has been demonstrated.The filter provides a time-domain method for isolating shaft order tones despite variations in rotor speeds. Additionally, themulti-shaft Vold–Kalman filter can isolate the time-domain contribution of each rotor to the total shaft order energy bytracking each rotor tachometer, as long as the shaft rates are slightly different. The output from the filter is a much higherresolution tone level indicator than the short time Fourier transform. The forward and aft tone contributions provide insightinto difference between the noise generated at approach versus nominal take-off pitch angles for the open rotor systembeing tested. After filtering the tones, the residual time-histories are unbiased representations of the broadband noisecomponents.

Acknowledgments

This paper was funded by the NASA Fixed Wing project with Dr. Ruben Del Rosario as the project manager. The authorswould also like to thank ATA Engineering, Inc., for their support and usage of proprietary software. The work was performedunder the Space Act Agreement: SAA3-1239, ATA Engineering, Inc., “Joint Publication On Order Tracking Methods ForQuantifying Noise From Open Rotors.” The open rotor wind tunnel test was performed as a collaboration between the NASAEnvironmentally Responsible Aviation project and GE Aviation.

References

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Order tracking signal processing for open rotor acoustics

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