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Proceedings of the XIV International Symposium on Dynamic Problems of Mechanics (DINAME 2011),
Fleury, A. T., Kurka, P. R. G. (Editors), ABCM, São Sebastião, SP , Brazil, March 13th - March 18th, 2011
Multi-Harmonic Adaptive Control for Roughness
J.A. Mosquera Sánchez1, K. Janssens2, H. Van der Auweraer2, L.P.R. de Oliveira1
1 Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo.
Av. Trabalhador Sancarlense, 400. CEP: 13566–590, São Carlos – SP, Brazil.
2 LMS International, Interleuvenlaan 68, B 3001, Leuven - Belgium
Abstract: Roughness, as well as Loudness, Sharpness, and Fluctuation Strength are psychoacoustic metrics that allow
correlating acoustic stimuli, e.g. of an engine, with the subjectiveness of human auditory sensation. As far as vehicle
sound quality is concerned, the analysis of roughness leads to the understanding of certain types of noise inside the
cabin and allows the engineer to design features that will impact heavily on the sound quality of the car and influence
the global qualitative assessment a particular vehicles. This paper presents a novel approach to the control of
roughness, specifically designed to tackle combustion engine noise inside vehicles, including adaptive algorithms with
confirmed effectiveness, such as the NEX-LMS, and efficient procedures for calculating the aforementioned
psychoacoustic metric, which are directly related to the engine orders, emphasizing the study of the multi-harmonic
characteristic of the disturbance. However, for such a controller to be effective, it is necessary to understand the
phenomena bearing Roughness generation and transmission, as well as the issues during control design, such as the
proper choice and placement of sensors and actuators, control strategy, the natures of both transient and stationary
noise sources and the various routines to be used in data processing, which, among others, might affect the system
performance. As a result, engine sound quality improvement is achieved by means of an adaptive control scheme that
enables the equalization of multiple harmonics.
Keywords: Active Roughness Control, Adaptive Algorithms, Multi-Harmonic Engine Disturbance, Sound Quality
NOMENCLATURE
AC = AC envelope value, Hz
a = half-order amplitude, dB SPL
DC = DC envelope value, Hz
d = input signal, dB SPL
e = error signal, dB SPL
f = frequency, hertz
g = frequency correction,
dimensionless
k = cross-correlation, dimensionless
m = modulation index, dimensionless
N = scheduled gain, dimensionless
R = roughness, asper
r = partial roughness, asper
S = secondary path, dimensionless
Ŝ = secondary path estimate,
dimensionless
w = adaptive coefficients,
dimensionless
x = reference signal, dB SPL
y = adaptive out, dimensionless
z = critical band, bark
Greek Symbols
ΔL = temporal masking depth, dB/Bark
β = gain factor, dimensionless
φ
= half-order phase, dimensionless
µ = adaptive step size, dimensionless
Subscripts
i = relative to critical band number
j = relative to half-order number
k = relative to channel number in the
ANC system
mod = relative to frequency
modulation
1 = relative to the first responsible
half-order for roughness
2 = relative to the second responsible
half-order for roughness
3 = relative to the third responsible
half-order for roughness
INTRODUCTION
The majority of problems in vehicle acoustics are concerned with acoustic comfort, rather than hearing damage
(Wang et al., 2007). The passenger of a vehicle has to be seen as part of a vibro-acoustic system and, consequently, the
subjective judgment of pleasantness or sound comfort is influenced by both sound and vibration (Genuit, 2004). To
improve the aforementioned acoustic comfort in vehicle design, researchers should first understand how to evaluate a
noise sample (Wang et al., 2007) and, from this perspective, some of the many sound sources that contribute to the
interior sound of a vehicle may be tuned to enhance the vehicle sound appreciation invoking desired emotional
responses, while others should be suppressed to reduce annoyance. Active noise control systems tend to be designed
with a target on sound pressure level reduction; however, the perceived control efficiency for the occupants can be more
accurately assessed if psychoacoustic metrics are taken into account (de Oliveira, 2010). Hence, to go from acoustic
design to sound quality design, the actual temporal and spectral signal structures from the controlled sound need to be
optimized to meet sound quality targets (Van der Auweraer et al., 2007).
When dealing with sound quality (SQ) issues in a vehicle interior, it is often possible to identify four types of
problems: (i) pure level harmonic problems: when only noise level is tackled and broadband noise reduction is needed,
e.g., booming; (ii) tonal problems: similar to the aforementioned pure level problems, but strictly related to a single
harmonic, i.e., with a specific sensation of frequency which may be annoying; typically related to sensations like pitch
Multi-Harmonic Adaptive Control for Roughness
or tonality as appearing in gear whines, exhausts, etc; (iii) continuity problems: another type of harmonic level problem,
continuity problems are often related to low order levels at certain RPMs, which can affect the perception of power and
sportiveness. In opposition to booming, that could be seen as a discontinuity towards higher levels, the focus here is to
get the order levels to evolve as smooth as possible with respect to RPM, and (iv) multiple-harmonic problems: when
amplitude and phase relation of multiple orders are responsible for the wanted (or unwanted) sound characteristics, such
as in roughness, muddiness, rumble, etc. (de Oliveira, 2010)
As far as the active control of noise is concerned, the problems in category (i) can be dealt with linear, time-
invariant broadband controllers. The same controllers can be used in (ii), although adaptive schemes could be a better
alternative, as the disturbance is rather periodic and a coherent reference signal would be readily available. Problems of
continuity (iii) require the controller not only to track the order, but also to drive the error to a desired level (rather than
zero); which means that the controller has to be capable of matching a desired order profile either by reducing or
amplifying the order level at different RPMs. Problems in category (iv) require, in addition to (iii), that the controller
tracks amplitude and/or phase relation of multiple orders (de Oliveira, 2010).
The aim of this research is to address the problems in category (iv), changing the sound perception of an engine in a
passenger vehicle from a psychoacoustic perspective by affecting Roughness. In order to do so, a variation of the NEX-
LMS scheme in a multi-order implementation is used. The NEX-LMS was recently proposed by (de Oliveira, 2010), as
a fast-converging order level equalization controller that has the advantage of acting on a narrowband, allowing the
present multi-order implementation. The results presented here are obtained with a cabin model excited with
synthesized engine sound at different RPMs. The orders responsible for the Roughness are then targeted such that the
desired levels are achieved after convergence. The sound, measured at the driver´s head position, is used as an error
signal in the adaptive control scheme, which works with structural actuators on the main transfer path, in this case, the
firewall.
ROUGHNESS OF ENGINE NOISE
Sound quality can be defined as the degree to which the totality of the individual requirements made on an auditory
event is met (Genuit, 2004). In the automotive sector, the sound quality of both the exterior and interior of the vehicle
has been converted into a marketing tool to attract more consumers (Redel-Macías, Berckmans and Cubero-Atienza,
2010), due to that the acoustic characteristics of a vehicle today mean an integral part of product identity, significantly
influencing customer’s decision (Genuit, 2004). Thereby, the reduction of sound pressure level often does not lead to
subjectively perceived improvements. Sometimes, they are even contrary to essential characteristics of a product, i.e., if
significantly low levels do not represent the power of a sporty car. In consequence, sound quality is an essential part of
vehicle quality (Genuit, 2004).
In sound-quality engineering, basic psychoacoustic quantities like loudness, sharpness, roughness and fluctuation
strength play an important role. Roughness is used in sound-quality engineering, e.g., to stress the feature of sportiness
in a car-engine sound (Fastl, 2005). As far as combustion engines are concerned, Roughness can be understood as a
result of two or more neighboring orders interacting with each other and producing modulation at a certain frequency
range. It is known, from psychoacoustic literature, that the amplitude modulations related to adjacent integer and half-
integer engine orders contribute to the Roughness of an engine sound (Janssens et al., 2007).
(a)
(b)
Figure 1: Waterfall and spectrogram analyses of evaluated engine noise.
Auditory Roughness is a term that was introduced by von Helmholtz in 1877 to describe the perception experienced
when two sounds with proximal frequency components are heard simultaneously (Pressnitzer and McAdams, 1999).
Roughness or “sensory dissonance” is also related to the perception of amplitude fluctuations and characterizes the
texture of a sound in terms of impure or unpleasant qualities (de Baene et al., 2004). Roughness of signals with strong
temporal structure is caused by amplitude and frequency modulations, i.e., quick changes in level and frequency and
J. A. Mosquera Sánchez, K. Janssens, H. Van der Auweraer, L. P. R. de Oliveira
due to the filtering properties of the outer ear, each change in frequency results at the same time in a more or less strong
change in amplitude (Genuit, 2004). To define the Roughness of 1asper (In Latin, the word asper characterizes rough),
it has chosen the 60dB, 1KHz tone that is 100% modulated in amplitude at a modulation frequency of 70Hz. The
Roughness R of any sound can be calculated using the equation (Zwicker and Fastl, 1999):
𝑅=0.3(𝑓
!"#)∆𝐿!𝑧𝑑𝑧
!"!"#$
!!!!![𝑎𝑠𝑝𝑒𝑟], (1)
where fmod is the modulation frequency in kHz and ∆𝐿! is the temporal masking depth, in dB/Bark (critical bands)
(Zwicker and Fastl, 1999). Using a 100% amplitude-modulated 1KHz tone and increasing the modulation frequency
from low to high values, three different areas of sensation are traversed. At very low modulation frequencies the
loudness changes slowly up and down. At about 15Hz, another type of sensation, Roughness, starts to increase. It
reaches its maximum near modulation frequencies of 70Hz and decreases at higher modulation frequencies. As
roughness decreases, the sensation of hearing three separately audible tones increases. This sensation is small for
modulation frequencies near 150Hz; it increases strongly, however, for larger modulation frequencies. This behavior
indicates that Roughness is created by the relatively quick changes produced by modulation frequencies in the region
between about 15Hz to 300Hz. There is no need for exact periodical modulation, but the spectrum of the modulating
function has to be between 15Hz and 300Hz in order to produce roughness. For this reason, most narrow-band noises
sound rough even though there is no periodical change in envelope or frequency (Zwicker and Fastl, 1999).
The sound wave formed by three continuous half-order components of the engine revolution is related to the
rumbling sound quality. In general, the degree of the rumbling sound quality is related to the magnitude of the envelope,
the modulation frequency and the carrier frequency of the sound wave. When the revolution of the engine changes, the
sound wave formed by three continuous half-order components is not only amplitude-modulated signal any more. In
this case, the time history of this sound wave becomes the amplitude-phase-modulated signal. Mathematically, this
signal can be expressed by the sum of three analytic signals, as follows (Lee, 2008):
𝑥𝑡=𝑎!𝑡𝑒!!!!+!𝑎!𝑡𝑒!!!!+!𝑎!𝑡𝑒!!!!, (2)
where 𝑎!𝑡, 𝑎!𝑡 and 𝑎!𝑡!are the functions associated with amplitude modulation and 𝜙!𝑡, 𝜙!𝑡 and 𝜙!𝑡 are
the functions associated with frequency modulation (Lee, 2008). It has been observed in numerous tests, concentrating
on powertrain related vehicle interior roughness, which perceived roughness could be assessed by available methods
only in the case of loudness differences. It seems that loudness correlates quite well with calculated roughness, which is
a well-known fact from psychoacoustical literature. For noises with equal loudness however, the correlation between
perceived and calculated roughness vanishes (Hoeldrich and Pflueger, 1999).
(a)
(b)
Figure 2: Roughness calculation methods: (a) Time-Domain; (b) Order-based (Janssens et al., 2007)
The roughness calculation is based on a decomposition of the sound in different critical bands. After filtering, the
modulation depth is calculated per critical band and then transformed into a partial roughness by applying
psychoacoustic weighting functions. The total roughness is finally obtained from the summation of weighted partial
roughness values across critical bands (Hoeldrich and Pflueger, 1999) (Janssens et al., 2007). The drawbacks of this
classical roughness approach are two-fold: The first one is related to the calculation speed of the algorithm. The critical
band filtering, the many FFT and inverse FFT operations and the Hilbert Transform to calculate the sound envelope for
each critical band are time-demanding operations which make the algorithm slow and not applicable in real-time
operation. The second disadvantage is related to the unclear relationship between the roughness and the order signature
of the engine sound. For example, when the algorithm identifies a roughness problem at a certain engine RPM, it
remains unclear which orders need to be modified and in which way: level decrease or increase? Phase change?
(Janssens et al., 2007).
Multi-Harmonic Adaptive Control for Roughness
Thus, since Roughness is produced by amplitude and phase variations of certain relationships between half engine
orders, it is necessary to know which orders are responsible for the Roughness. The methodology used in this research
to find the orders responsible for the production of roughness perceived in the cabin of a car is based entirely on the
'order-based' algorithm summarized in Fig. 2b, which allows a direct relationship with the psychoacoustic phenomenon
and the half-order amplitudes/phases that cause it. Therefore, the aforementioned methodology is summarized in the
following stages:
1. Using the order-level vs. RPM profile obtained during engine run-up, shown in Fig. 1; calculate the engine
Roughness signature by means of 20 interacting half-orders. The results are presented in Fig. 3a.
2. Find the critical RPMs with the highest Roughness values (red markers in Fig. 3a). The order-based Loudness
calculation is presented to show that an auditory event described as rough may not necessarily be qualified as
loud, as displayed in Fig. 3b.
3. Recalculate R by means of each 3-adjacent-half-orders (Janssens et al., 2007) (Lee, 2008) (de Oliveira, 2010) to
obtain the orders responsible for the modulation.
4. From psychoacoustic literature it is known that Roughness is caused by amplitude and/or phase interactions of
the modulating signals. Hence, in this work we have initially investigated the amplitude interactions; the next
step is the construction of the ‘feasible amplitude roughness-space’ that can be generated by dealings with
different amplitude levels of these orders. The construction of the amplitude R-space can display the range of
possibilities that the sound quality engineer may have when designing the sound profile for that engine. The R-
space also indicates the feasible space for the design of the ANC system presented here.
(a)
(b)
Figure 3: Order-based engine sound calculations: (a) Roughness; (b) Loudness.
MULTI-HARMONIC ADAPTIVE CONTROL FOR ROUGHNESS
Most noise sources can be classified as broadband or narrowband. Narrowband noise concentrates most of its energy
at specific frequencies, and this noise is related to rotating or repetitive machines, so it is periodic or nearly periodic.
For periodic noise caused by rotating machinery, narrowband techniques have been developed that are very effective in
reducing repetitive noise. Since all the repetitive noise is at harmonics of the machine’s basic rotational rate, the control
system will cancel these known frequencies (Kuo and Morgan, 1996).
ANC is based on either feedforward control, where a coherent reference noise input is sensed before it propagates
past the secondary source, or feedback control, where the active noise controller attempts to cancel the noise without the
benefit of an “upstream” reference input. Feedforward ANC is generally more robust than feedback ANC, particularly
when the feedforward system has a reference input isolated from the secondary anti-noise source. This technique has
the following advantages: (i) undesired acoustic feedback from the cancelling loudspeaker back to the reference
microphone is avoided; therefore, FIR filters can be used instead of IIR filters, thereby enabling guaranteed stability, (ii)
nonlinearities and aging problems associated with the reference microphone are avoided, (iii) the periodicity of the
noise removes the causality constraint, thereby allowing more flexible positioning of the secondary loudspeaker and
longer controller delays, (iv) the use of an internally generated reference signal results in selectivity, specifically the
ability to control each harmonic independently, and (v) it is only necessary to model the acoustic plant transfer function
over frequencies in the vicinity of the harmonic tones (Kuo and Morgan, 1996).
Extending (iv), a sinusoidal signal can be used as a reference signal to cancel exact components of narrowband noise.
This technique takes advantage of the correlation between the noise that contaminates the desired signal and a reference
signal generated in the control (Kuo and Morgan, 1996). Thus, it is necessary to know beforehand the spectral
components that request to control, in which case the roughness control implies knowledge of the responsible orders of
the phenomenon.
The first active controllers aimed at SQ improvement appeared in the early 1990´s by Kuo, Ji and Jiang (1993) and
Eatwell (1995) and is called Active Noise Equalizer (ANE) as shown in Fig. 4(a). Designed to equalize, rather than
J. A. Mosquera Sánchez, K. Janssens, H. Van der Auweraer, L. P. R. de Oliveira
reduce noise levels, the ANE as first introduced by Kuo, Ji and Jiang (1993), is capable of tuning the amplitude of a
sinusoidal disturbance. It works on the principle of an adaptive notch-filter, as the reference fed to the LMS algorithm is
a sine wave, allowing the controller to observe and control only at that specific frequency. However, if the objective is
to independently tune multiple orders, the narrowband action of the ANE is desired, as a finite number of ANEs can be
cascaded, each with reference signals according to the disturbance component, without interfering with each other.
(a)
(b)
Figure 4: Single-Frequency ANEs (SFANE): (a) (Kuo, Ji and Jiang, 1993); (b) (de Oliveira, 2010)
The first implementation of such a scheme is reported in Sommerfeldt and Samuels (2001) where ANEs are
cascaded to cover 8 harmonic components of the periodic disturbance signal. A similar multi-harmonic version of the
ANE scheme was proposed for reshaping multi-tonal stationary noise by de Diego et al. (2000) in a setup similar to the
one by Gonzalez et al. (2003), i.e. with microphones as sensors and speakers as secondary actuators in a room treated
with absorbing material (passive control). In this case, the authors proposed a multi-channel implementation of the ANE
and found out that the effect of such controllers was present on an area around the error sensors which were large
enough to cover the listener’s head motion. The movement of the head, assessed with an instrumented human torso, did
not affect the controller efficiency, nor its stability, which is a rather important conclusion as far as automotive
application is concerned.
The aim of the implemented NEX-LMS control scheme is to achieve a desired sound quality target in an authentic
ASQC manner (de Oliveira, 2010), by means of harmonic control of Roughness. In this control scheme, the
minimization of the mean square error – the most common used performance criteria for digital filter adaptation – is
achieved by means of steepest-decent methods, which results in the least mean square (LMS) algorithm. In real-life
applications, the output of the filter W (see Fig. 4 and Fig. 5) is fed to the secondary actuator, therefore it is influenced
by the secondary path dynamics S(z) before it becomes the physical quantity y(n) that superposes with the primary
disturbance (de Oliveira, 2010). There are a number of possible schemes that can be used to compensate for the effect
of S(z). The first solution is to place an inverse filter (1/S(z)), in series with S(z) to remove its effect. The second solution
is to place an identical filter in the reference signal path to the weight update of the LMS algorithm, which realizes the
filtered-X LMS (FxLMS) algorithm. Since an inverse does not necessarily exist for S(z), the FxLMS algorithm is
generally the most effective approach (Kuo and Morgan, 1996). An expression for the FxLMS is given by:
𝑤𝑛+1=𝑤𝑛+𝜇𝑠𝑛∗𝑥𝑛𝑒𝑛 (3)
Where µ is the convergence coefficient, e(n) the instantaneous error, i. e., the difference between the disturbance
signal d(n) and the controller output signal y(n), x(n) the reference signal, Ŝ(z) the secondary path coefficients and ∗
denotes linear convolution (Kuo and Morgan, 1996). The NEX-LMS adaptive scheme features a normalization filter in
the form of the scheduled gain N, as displayed in Fig. 4b, which compensates for S(z) such that the filtered signal
𝑠𝑛∗𝑥𝑛 has the same power throughout the frequency band of interest; it means that the performance is
optimized for a fixed µ. For practical applications, N is kept within a safety margin (de Oliveira, 2010):
!.!"
!(!)<𝑁(𝜔)<!.!
!(!) (4)
The NEX-LMS scheme uses the gain β in a way similar to the one proposed by Kuo, Ji and Jiang (1993), exposed in
Fig. 4a. The difference in NEX-LMS is that, thanks to the use of the estimated primary disturbance d’(n), the
equalization needs to be applied only once, after the filter W (see Fig. 4b). Due to the equalization, the resulting error
after convergence tends to d(n), is given by (de Oliveira, 2010):
𝑒𝑛=𝑑𝑛−𝛽𝑦 𝑛≈1−𝛽𝑑𝑛 (5)
Multi-Harmonic Adaptive Control for Roughness
In this way, the residual error amplitude can be controlled by adjusting β. Therefore, the NEX-LMS exhibits four
operating modes: β = 1 (maximum achievable reduction); 0 < β < 1 (linear disturb reduction); β = 0 (neutral mode) and
β < 0 (amplification mode) (de Oliveira, 2010).
(a)
(b)
Figure 5: (a) Multi-harmonic adaptive control scheme; (b) details of the kth channel
The NEX-LMS scheme, given its characteristics and its optimized form, is suitable for harmonic-type disturbance
controlling, such as those described and cataloged in the introduction as iv-type problems of SQ in vehicles. Its
capability dealing with harmonic problems not only as a notch system but also as an equalizer system is very desirable
in this problem, since an overall reduction of half-orders responsible by Roughness can lead to continuity – iii-type –
problems, or even i-type sound quality engine problems.
As seen in Fig. 3, the problem of Roughness cannot be treated simply under the classical philosophy of ANC overall
reduction, but it must be found a balance between the components that produce the sensation in order to obtain SQ of
engines. However, as has been shown by various authors (Fastl, 2005) (Filippou et al., 2003) (Kuwano et al., 1997),
which for a given listener may be SQ in the sense described in this document (Genuit, 2004) for another listener may
not be that. Thus, the goal of proposed control system is to be able to reach any desired point of SQ, and not to raise the
‘minimum roughness’ as if it were the only goal that should get the control system, and therefore, knowledge of the
roughness-space can help a sound engineer to make decisions with respect to the auditory sensation for transmitting in
some listeners and the control system must be able to reach any desired roughness condition.
ROUGHNESS CALCULATIONS AND CONTROLLER SIMULATION
This section presents Roughness calculations for two stationary engine speeds, whose selection is based on the
highest Roughness values obtained for the engine run-up presented in Fig. 3a. As the target of this research is to show
the performance of the adopted control scheme for harmonic Roughness control, results found by computational
simulation of the engine orders are presented.
(a)
(b)
Figure 6: Order Amplitudes and Phases: (a) 5750rpm; (b) 3200rpm
Figure 6 shows the order levels and phase relations for 5750rpm and 3200rpm. Notice that, Roughness was not
produced by the most powerful orders, but certain relations of amplitudes and/or phases are the cause of that auditory
sensation. In this study, the target is the amplitude relations of the orders responsible for most of the modulation,
leaving for future work the analyses of phase relation and its control, which as is well known from psychoacoustic
literature, shows a stronger relationship with the origin of Roughness (Pressnitzer and McAdams, 1999) (Zwicker and
Fastl, 1999) (Hoeldrich and Pflueger, 1999).
J. A. Mosquera Sánchez, K. Janssens, H. Van der Auweraer, L. P. R. de Oliveira
Order-based Roughness Calculation Results
After finding stationary engine speeds that exhibit the highest values of Roughness, we proceed to find the half-
orders that cause it. The procedure adopted in this paper is to calculate the Roughness produced by interaction of 3-half-
adjacent orders, once the auditory sensation produced by the interaction of distant signals in frequency does not cause
the acoustic phenomenon. Taking the two stationary engine speeds with the largest Roughness values, it can be seen
that the modulating orders are not necessarily those which exhibit the highest amplitude values. It must be remembered
that the interactions of vibrations phase are closely related to the sensation.
Graphical methods of finding the vibrations responsible for Roughness are shown in Fig. 7a and Fig. 7c for 5750rpm
and Fig. 8a and Fig. 8c in the 3200rpm situation. As explained in the section dedicated to the description of Roughness,
this method involves finding the responsible half-orders by means of successive calculations of roughness for three-
adjacent-half-orders whose separation in frequency does not exceed 250Hz, entirely based on the Janssens et al. (2007)
algorithm. Thereby, varying the amplitudes of the involved 3-half-orders, and recalculating the roughness taking all the
orders in a stationary engine speed, a SQ-space can be built, as shown in Fig. 7b and Fig. 7d for 5750rpm, and Fig. 8b
and Fig. 8d for 3200rpm, in which there is a set of possible order amplitudes that can be achieved by the proposed
active control scheme.
(a)
(b)
(c)
(d)
Figure 7: Roughness calculations for 5750rpm: (a) 3-D Roughness searching; (b) 3-D Roughness-space; (c)
Roughness searching XZ-plane; (d) Roughness-space XZ-plane
According to psychoacoustic literature, widely in-frequency separated signals each other often do not generate any
Roughness, which can be seen in Fig. 7a, Fig. 7c, Fig. 8a and Fig.8c. Figure 7a and Fig. 7c for 5750rpm case show that
the lower engine orders contribute significantly to the Roughness perception of the phenomenon: 1, 2 and 3 engine
orders. The SQ-space generated by the variation of amplitudes of the above orders shows that there is a small area of
maximum Roughness (red area in Fig. 7b and Fig. 7d) and a larger area which exhibits approximately constant
Roughness (green area). This SQ-space shows that the total amplitude reduction of the responsible orders for
Roughness does not necessarily imply the total Roughness reduction, because once made such a reduction, the
perceived roughness will be produced by the other half-orders. Therefore, the philosophy of minimizing the amplitudes
of the engine orders could expose other problems.
In that sense, the result for 3200rpm is revealing in terms of SQ-space. The responsible orders are higher (5.5, 6 and
6.5), as shown in Fig. 8a and Fig. 8c. The fact of raising the order amplitudes lies in an overall reduction in perceived
Roughness (blue area in Fig. 8a and Fig. 8c), and to reduce the order amplitudes will produce higher Roughness (red
area). As in the 5750rpm situation, reduction of the responsible order amplitudes will cause Roughness by other engine
Multi-Harmonic Adaptive Control for Roughness
orders, and this case clearly shows that reducing amplitudes of orders whose frequencies are above 250Hz (5.5, 6 and
6.5 half-orders) the Roughness caused by orders below the mentioned frequency limit becomes important, as predicted
by the psychoacoustic literature.
(a)
(b)
(c)
(d)
Figure 8: Roughness calculations for 3200rpm: (a) 3-D Roughness searching; (b) 3-D Roughness-space; (c)
Roughness searching XZ-plane; (d) Roughness-space XZ-plane
A further analysis was done; it consists of seeking for the maximum reachable amplitude by the responsible half-
orders that cause roughness during engine run-up and of calculating the roughness which could be generated if those
half-orders would reach those highs. In Fig. 7b and Fig. 7d, it can be observed that, although the original Roughness
situation is high (red-diamond markers), this event can be even worse if during the engine acceleration any responsible
half-order would reach the aforementioned maximum amplitude. Even under these unexpected conditions, the control
system scheme implemented is efficient, as shown in Table 2 and Table 3. It is worth noticing that the minimum and
maximum Roughness points are listed in the charts as simple reference values, since the decision on the amount of
desired roughness for the sound design of a particular engine should be made by the SQ engineer. Moreover, the target
SQ does not always mean minimizing psychoacoustic metrics, as an engine that should sound sporty would be a perfect
counterexample to that philosophy.
Characteristics of Controller Design and Simulation
Roughness control was explored by simulating the two selected stationary inputs to the system: 5750rpm and
3200rpm. Once we know the half-orders responsible for the problem, the reference of the system will be sinusoidal
signals whose frequencies are equal to those of the half-orders, for each tested engine speed, with constant unit
amplitude and zero phase, as the present analysis focuses on amplitude interactions. Thus, the selected control scheme,
with single-input-single-output (SISO system) and with a known harmonic disturbance is implemented, gathering in
parallel three adaptive control channels based on the NEX-LMS algorithm for each of the harmonics to be controlled, as
exposed in Fig. 5a and Fig. 5b.
As seen in equation (3), a set of control parameters should be selected such that a rapid and accurate assessment of
pseudo-error is achieved without causing instability. A fixed parameter for all channels is the size of the filter W(z)
which, as seen in the details of the kth channel in Fig. 5b, has two 101-order weights. From the ANC literature, it is
known that a good estimate of the secondary path contributes to the successful operation of the system (Kuo and
Morgan, 1996); hence, a secondary path copy of 1001 elements was realized. Finally, the success of NEX-LMS scheme
lies in the neutralization of undesired effects of the paths’ dynamics, which is the role of the scheduled gain as described
J. A. Mosquera Sánchez, K. Janssens, H. Van der Auweraer, L. P. R. de Oliveira
in Eq. 4. The system is simulated in MATLAB/Simulink under a sampling rate of 2KHz. In Table 1 a summary of the
selected parameters and overall reductions achieved in responsible engine orders by means of percentages are shown for
the multi-harmonic control scheme.
Table 1: Controller Simulation Summary: Characteristics and Results
Engine Speed
5750[rpm]
3200[rpm]
Responsible Orders
1
2
3
5.5
6
6.5
µANC
5x10-12
5x10-12
5x10-12
5x10-13
1x10-11
1x10-9
Order-level Reduction
99.24%
87.35%
93.59%
80.35%
94.13%
37.13%
Controller Results
The results for the control of engine orders 1, 2 and 3 responsible for the roughness at 5750rpm is shown in Figure
9Fig. 9a, b, which shows the effectiveness of the designed system, achieving significant reductions either starting from
the hypothetical situation of a roughness value even higher than the obtained during analyzed engine acceleration. A
reduction of 99.24% was obtained for the half-order 1 (100 Hz) but not for the other 2 orders, although a great deal of
reduction was obtained as well. Comparing these graphs with Fig. 7b and Fig. 7d, it can be noticed that it is not
necessary that the controller reaches those endpoints of reduction, since as for reductions below 70dB to the 1st half-
order, no better results in the roughness reduction can be obtained; Table 2 and Table 3 support this reasoning.
(a)
(b)
Figure 9: Controller Simulation Results for RPM = 5750: (a) 3-D waterfall; (b) Magnitude vs. βi-order
Concerning the control system implemented at 3200rpm, it can be seen in Fig. 8b and Fig. 8d that, although the
controller is not capable of reaching 100% reduction, the Roughness area (SQ-space) can be explored largely by
manipulating the equalizing gain β for each channel of the proposed controller, as seen in Fig. 10a, Fig. 10b; and Fig. 9a
and Fig. 9b in the 5750rpm case. It is worth noticing that the orders involved in the generation of roughness at this
engine speed are closer together than in the first case, but the controller also showed effectiveness and complete
independence in controlling only the three responsible half-orders without affecting the others.
Table 2: Harmonic Control Results for RPM = 5750
Engine
Order
Passive (β = 0)
β = 0.25
β = 0.5
β = 0.75
β = 1
aj[dB]
R[asper]
aj[dB]
R[asper]
aj[dB]
R[asper]
aj[dB]
R[asper]
aj[dB]
R[asper]
1
100.45
2.4728
66.31
1.3729
41.93
1.3545
22.88
1.3531
0.757
1.3530
2
99.2
71.65
48.85
28.70
12.54
3
91.90
67.63
45.3
24.48
5.89
The high rates of convergence exhibited by the system allows real-time processing, which enables sound engineers
to play different conditions in what-if scenarios (Janssens et al., 2007) and to design accurately the engine SQ.
Table 3: Harmonic Control Results for RPM = 3200
Engine
Order
Passive (β = 0)
β = 0.25
β = 0.5
β = 0.75
β = 1
aj[dB]
R[asper]
aj[dB]
R[asper]
aj[dB]
R[asper]
aj[dB]
R[asper]
aj[dB]
R[asper]
5.5
85.92
66.78
46.56
27.35
16.88
6
90.68
2.2290
69.56
1.4551
48.22
1.2821
26.77
1.3043
5.32
1.3013
6.5
88.73
77.29
67.42
59.93
55.78
Multi-Harmonic Adaptive Control for Roughness
(a)
(b)
Figure 10: Controller Simulation Results for RPM = 3200: (a) 3-D waterfall; (b) Magnitude vs. βi-order
CONCLUSIONS
This paper demonstrates the effectiveness of the NEX-LMS control scheme for the treatment of multi-harmonic
disturbances. The metric known as psychoacoustics Roughness can be treated adequately by the implemented control
scheme, since it can explore various amplitude conditions generated by the interaction of the half-orders responsible for
Roughness, thus achieving the desired engine SQ attributes. The advantages of the NEX-LMS control scheme for multi-
harmonic problems are demonstrated in this paper. Features such as the order-level reduction, independent tuning of
distinct orders and the control performance are addressed, realizing what was predicted at the control concept design.
The approach based on the identification of the half-orders responsible for Roughness is suitable for the selection of the
control reference signal. As demonstrated in this paper, it is possible to significantly affect the overall roughness of a
multi-harmonic noise by manipulation of the amplitude of its harmonic components. It is also successfully
demonstrated that a multi-channel implementation of the NEX-LMS algorithm can perform such manipulation.
The control of non-stationary disturbance and the influence of the phase relations are currently under investigation.
The next step in this research lies with the phase control of the engine orders that cause the problem.
ACKNOWLEDGMENTS
This research is supported by the São Paulo State Research Agency – FAPESP – grant # 2010/02198-4. The
research of J.A. Mosquera Sánchez is supported by FAPESP - grant # 2010/03556-1.
REFERENCES
de Baene, W., Vandierendonck, A., Leman, M., Widmann, A. and Tervaniemi, M. (2004) 'Roughness perception in
sounds: behavioral and ERP evidence', Biological Psychology, no. 67, pp. 319-330.
de Diego, M., Gonzalez, A., Garcia, C. and Ferrer, M. (2000) 'Some practical insights in multichannel active noise
control equalization', Proceedings of the 2000 IEEE International Conference on Acoustics, Speech and Signal
Processing - ICASSP, 837-840.
de Oliveira, L.P.R. (2010) 'NEX-LMS: A novel adaptive control scheme for harmonic sound quality control',
Mechanical Systems and Signal Processing, vol. doi: 10.1016/j.ymssp.2008.05.005.
de Oliveira, L.P.R. (2010) 'Review and future perspectives on active sound quality control', Proceedings of the
International Conference on Noise and Vibration Engineering, Leuven.
Eatwell, G.P. (1995) 'Active control of sound quality', Proceedings of the 1995 International Congress on Noise Control
Engineering - INTERNOISE'95, Newport-Beach, 521-524.
Fastl, H. (2005) 'Psychoacoustics and Sound Quality', in Blauert, J. Communication Acoustics, 1st edition, Springer.
Filippou, T.G., Fastl, H., Kuwano, S., Namba, S., Nakamura, S. and Uchida, H. (2003) 'Door sound and image of cars',
DAGA'03, Oldemburg.
Genuit, K. (2004) 'The sound quality of vehicle interior noise: a challenge for the NVH-engineers', Int. J. Vehicle Noise
and Vibration, vol. 1, no. 1/2, pp. 158 - 168.
Gonzalez, A., Ferrer, M., de Diego, M., Pinero, G. and Garcia-Bonito, J.J. (2003) 'Sound quality of low-frequency and
car engine noises after noise control', Journal of Sound and Vibration, no. 265, pp. 663-679.
J. A. Mosquera Sánchez, K. Janssens, H. Van der Auweraer, L. P. R. de Oliveira
Hoeldrich, R. and Pflueger, M. (1999) 'A parameterized model of psychoacoustical roughness for objective vehicle
noise quality evaluation', Proc. 137th meeting of the Acoustical Society of America, Berlin.
Janssens, K., Ahrens, S., Bertrand, A., Lanslots, J., Van der Ponseele, P., Vecchio, A. and Van der Auweraer, H. (2007)
'An on-line, order-based roughness algorithm', SAE International.
Kuo, S.M., Ji, M.J. and Jiang, X.H. (1993) 'Development and experiment of narrowband active noise equalizer', Noise
Control Engineering Journal, no. 3, pp. 281-288.
Kuo, S.M. and Morgan, D.R. (1996) Active Noise Control Systems: Algorithms and DSP Implementations, New York:
John Wiley & Sons.
Kuwano, S., Namba, S., Fastl, H. and Schick, A. (1997) 'Evaluation of the impression of danger signals - comparison
between Japanese and German subjects', in Schick, A. and Klatte, M. Contributions to Psychological Acoustics,
Oldemburg: BIS.
Lee, S.-K. (2008) 'Objective evaluation of interior sound quality in passengers cars during acceleration', Journal of
Sound and Vibration, no. 310, pp. 149 - 168.
Pressnitzer, D. and McAdams, S. (1999) 'Two phase effects in roughness perception', J. Acoust. Soc. Am., vol. 105, no.
5, May, pp. 2773 - 2782.
Redel-Macías, M.D., Berckmans, D. and Cubero-Atienza, A.J. (2010) 'Modelo de identificación de fuentes sonoras:
Aplicación al ruido de motor de un automóvil', Revista Iberoamericana de Automática e Informática Industrial, vol.
7, no. 3, pp. 34 - 41, Available: 1697-7912.
Sommerfeldt, S.D. and Samuels, T.O. (2001) 'Incorporation of loudness measures in active noise control', J. Acoust. Soc.
Am., no. 2, pp. 591-599.
Van der Auweraer, H., Janssens, K., de Oliveira, L.P.R., da Silva, M. and Desmet, W. (2007) 'Virtual prototyping for
sound quality design of automobiles', Sound and Vibration, April, pp. 26 - 30.
Wang, Y.S., Lee, C.M., Kim, D.G. and Xu, Y. (2007) 'Sound-quality prediction for nonstationary vehicle interior noise
based on wavelet pre-processing neural network model', Journal of Sound and Vibration, no. 299, pp. 933-947.
Zwicker, E. and Fastl, H. (1999) Psychoacoustics: Facts and Models, 2nd edition, Berlin: Springer.
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