Active Control of Vehicle Powertrain and Road Noise
A dissertation submitted to the
Graduate School of the University of Cincinnati
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
in the School of Dynamic Systems, Mechanical Engineering
of the College of Engineering and Applied Science
June 2011
By
Jie Duan
B.S., Electronic Science and Engineering, Nanjing University, P.R. China, 2006
M.S., Mechanical Engineering, University of Cincinnati, USA, 2009
Committee chair: Dr. Teik C. Lim
Members: Dr. Ronald L. Huston
Dr. Jay H. Kim
Dr. Manish Kumar
Dr. David F. Thompson
ABSTRACT
Noise, vibration, and harshness (NVH) has been an important factor in the development of modern motor vehicles since the 1980s. One of the challenges is the control of low-frequency powertrain and road noise inside passenger cabin. Traditional passive control approach uses heavier and/or thicker materials for low-frequency noise reduction, which worsens the fuel efficiency of the vehicle due to the added weight. To satisfy the increasing demand for both fuel efficiency and better NVH performance, active noise control (ANC) that works better at low- frequency noise attenuation with slight increase in weight, can be a promising solution. The most common ANC system uses feedforward control approach formulated with filtered-x least mean square (FXLMS) algorithm. However, the conventional method experiences some difficulties when applying to vehicle low-frequency acoustic noise control. The focus of this dissertation is to develop a feasible ANC system with advanced control algorithms for use inside the passenger compartment of motor vehicles.
Powertrain noise that is dominated by a large number of harmonics is most perceivable when vehicle is at idle or changing speed conditions. Because of the tonal nature, it can negatively impact sound quality inside the passenger cabin. The slow convergence behavior of the conventional FXLMS algorithm is one of the factors that degrade the overall performance of powertrain noise control. In this dissertation, virtual secondary path algorithm is proposed to improve the convergence of the adaptive algorithm. Another challenge is to control multiple orders of powertrain response simultaneously. When the conventional FXLMS algorithm is applied, harmonic interference may occur that often results in overshoot at some adjacent orders.
Twin-FXLMS algorithm is proposed to address this problem, by splitting the adaptive filter into two sets, such that the adjacent sinusoids are spaced out farther apart. In addition, traditional
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ANC system is aimed to reduce the sound pressure level as much as possible. However, powertrain response carries some useful information about the engine speed and power. To achieve a better vehicle interior sound quality, active powertrain response tuning system is presented to either enhance or attenuate the powertrain order selectively.
Road noise is the dominant source when the vehicle is driving at middle or high speed. In contrast to powertrain noise, road noise is more fatiguing and irritating than having benefit. Thus, road noise must be well treated. In practice, it is difficult to obtain reference signals that are well correlated with the targeted noise in a broad frequency range. A combined feedforward-feedback control approach is proposed to solve this problem, which is uniquely formulated with subband
FXLMS algorithm. In addition, the computational complexity is another important consideration of the control algorithm. However, the conventional FXLMS algorithm can requite huge computational burden, especially for the multi-reference multi-channel control system. Here, time-frequency-domain FXLMS algorithm is utilized to significantly reduce the computational complexity. Furthermore, a novel channel equalization concept is proposed to overcome the channel dependent convergence behavior of the multichannel FXLMS algorithm.
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ACKNOWLEDGMENTS
I would like to thank my research advisor, Dr. Teik C. Lim, for giving me the opportunity to be introduced to the field of active control. I thank him for his helpful guidance, support, advice, encouragement, and patience during my doctoral studies. Also, my gratitude is expressed to Dr. Jay H. Kim, Dr. David F. Thompson, Dr. Manish Kumar, and Dr. Ronald L. Houston for serving as my doctoral supervisory committee members.
Among the many colleagues in the Vibro-Acoustics and Sound Quality Research
Laboratory here at University of Cincinnati, I would like to express my appreciation to Dr.
Mingfeng Li for helping me with the fundamental knowledge on active noise control, and reading and revising this dissertation. Working with him has been a truly exciting experience. I also wish to thank Dr. Pravin Sondkar, Dr. Brent Budd, Dr. Tao Peng, Mr. Junyi Yang, Mr.
Guohua Sun and many others for their help in this research and most important their friendship.
This research has been partially supported by Ford Motor Company. I wish to thank Dr.
Ming-Ran Lee, Dr. Ming-Te Cheng, Dr. Takeshi Abe, and Mr. Wayne Vanhaaften for their insightful suggestions and help in various experiments. I would also like to acknowledge that financial support was provided by the School of Dynamic Systems at University of Cincinnati and Ford Motor Company.
Finally, I would like to thank my parents for their love and encouragement.
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TABLE OF CONTENTS
ABSTRACT ...... iii
ACKNOWLEDGMENTS ...... vi
TABLE OF CONTENTS ...... vii
LIST OF FIGURES ...... x
LIST OF SYMBOLS ...... xvii
Chapter 1. Introduction ...... 1
1.1 Background ...... 1
1.2 Active Noise Control ...... 3
1.3 Organization of the Dissertation ...... 5
Chapter 2. Literature Review...... 9
2.1 Journal and Conference Papers Review ...... 10
2.2 Patents Review ...... 19
2.3 Summary ...... 29
Chapter 3. Virtual Secondary Path Algorithm for Multichannel Active Control of Powertrain
Noise ...... 31
3.1 Introduction ...... 31
3.2 Convergence Analysis of MIMO FXLMS Algorithm ...... 34
3.3 Channel Equalization Algorithm for Powertrain Noise ...... 41
3.4 Numerical Simulation ...... 49
3.5 Conclusions ...... 54
Chapter 4. Twin-FXLMS Algorithm for Active Control of Transient Powertrain Noise ...... 55
4.1 Introduction ...... 55
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4.2 Basic Configuration of Twin-FXLMS Algorithm ...... 57
4.3 Nonlinearity of FXLMS Algorithm ...... 60
4.4 Numerical Simulation ...... 61
4.5 Conclusions ...... 74
Chapter 5. An Active Sound Tuning System using Computational-Efficient Algorithm for
Powertrain Response ...... 75
5.1 Introduction ...... 75
5.2 Time-Frequency-Domain Active Sound Tuning System Applied to Powertrain Response77
5.2.1 Window-Function Implementation ...... 80
5.2.2 Overlap-Save Implementation ...... 83
5.3 Computational Complexity Analysis ...... 84
5.4 Numerical Simulation ...... 87
5.5 Conclusions ...... 95
Chapter 6. A Combined Feedforward-Feedback Active Control of Road Noise ...... 97
6.1 Introduction ...... 97
6.2 Selection of Reference Accelerometers ...... 99
6.3 Control System Design ...... 104
6.3.1 Combined Feedforward-Feedback Controller ...... 104
6.3.2 Feedforward Control Algorithm ...... 107
6.3.3 Feedback Control Algorithm ...... 112
6.4 Numerical Simulation ...... 113
6.5 Conclusions ...... 120
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Chapter 7. A Computational-Efficient Algorithm for Multichannel Active Control of Road
Noise ...... 122
7.1 Introduction ...... 123
7.2 Multi-Reference Multi-Channel ANC System by using FXLMS Algorithm ...... 124
7.3 Multi-Reference Multi-Channel ANC System by using TF-FXLMS Algorithm ...... 128
7.4 Computational Complexity Analysis ...... 131
7.5 Numerical Simulation ...... 137
7.6 Conclusions ...... 146
Chapter 8. Channel Equalization Algorithm for Multichannel Active Control of Road Noise
...... 147
8.1 Introduction ...... 147
8.2 Multichannel ANC System for Road Noise...... 149
8.3 Channel Equalization Algorithm for Road Noise ...... 153
8.4 Numerical Simulation ...... 161
8.5 Conclusions ...... 168
Chapter 9. Conclusions and Recommendations ...... 169
9.1 Conclusions ...... 169
9.2 Recommendations for Future Studies ...... 175
BIBLIOGRAPHY ...... 177
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LIST OF FIGURES
Figure 1-1. Active noise control based on the principle of superposition. The left column plots
the primary and secondary wave, and the right column plots the resultant sound by
adding the two waves: (a) ap=1, a p =∆= 1,φ 0 ; (b) ap=1, a p =∆= 1,φ 0.5 π ; (c)
ap=1, a p =∆= 1,φ 0.9 π ; (d) ap=1, a p = 0.8, ∆=φ π ; (e) ap=1, a p =∆= 1, φ π . (Keys:
solid red line , resultant wave; dashed black line , primary wave; and
dotted blue line , secondary wave)...... 4
Figure 3-1. Basic configuration of the proposed MIMO ANC systems with virtual secondary path
algorithm for treating vehicle interi or powertrain noise...... 34
Figure 3-2. Magnitude and phase responses of estimated and EE virtual secondary path: (a)
Magnitude response ; (b) Phase response. (Keys: solid black line , estimated
secondary path; and dotted blue line , EE virtual secondary path)...... 41
Figure 3-3. Proposed 2I2O ANC system...... 46 ) Figure 3-4. Magnitude responses of four estimated secondary path transfer functions: (a) S11 and
) ) ) S21 ; (b) S12 and S22 ...... 47
Figure 3-5. Magnitude responses of four EE -CE virtual secondary path transfer functions: (a)
e e e e S11 and S21 ; (b) S21 and S22 ...... 49
Figure 3-6 Comparison of active noise control results between EE virtual secondary path
algorithm and the EE-CE virtual secondary path algorithm: (a) Error 1; (b) Error 2.
(Keys: solid black line , baseline noise response; dashed blue line , EE
virtual secondary path algorithm; and dotted red line , EE-CE virtual secondary
path)...... 52
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Figure 3-7. Comparison of active noise control results between the EE -CE virtual secondary
path algorithm with a nd without turning point: (a) Error 1; (b) Error 2. (Keys: solid
black line , baseline noise response; dashed blue line , without turning
point; and dotted red line , with turning point)...... 54
Figure 4-1. Basic configuration of the proposed active noise control system based on the twin -
FXLMS algorithm...... 57
Figure 4-2. Estimated engine speed from tachometer signal for the ramp -up engine speed case.
...... 62
Figure 4-3. Frequency response function of the secondary path dynamics...... 63
Figure 4-4. Comparison of control results between conventional FXLMS and twin -FXLMS
algorithms: (a) 1.5 th order; (b) 2 nd order; (c) 2.5 th order; (d) 3 rd order; (e) 3.5 th order.
(Keys: solid black line , baseline nois e response; dashed blue line ,
conventional FXLMS algorithm; and dotted red line , proposed twin -FXLMS
algorithm)...... 67
Figure 4-5. Effects of adaptive filter length on nonlinearity phenomenon by using the
conventional FXLMS algorithm: (a) 1.5 th order; (b) 2 nd order; (c) 2.5 th order; (d) 3 rd
order; (e) 3.5 th order. (Keys: solid black line , baseline noise response; dashed
blue line , L=128; and dotted red line , L=256)...... 70
Figure 4-6. Effects of adaptive filter length on nonlinearity phenomenon by using the twin -
FXLMS algorithm: (a) 1.5 th order; (b) 2 nd order; (c) 2.5 th order; (d) 3 rd order; (e) 3.5 th
order. (Keys: solid black line , baseline noi se response; dashed blue line ,
L=64; and dotted red line , L=128)...... 74
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Figure 5-1. Block diagram of the proposed AST system for vehicle powertrain response with
window-function implementation of TF -FXLMS algorithm...... 78
Figure 5-2. Block diagram of the proposed AST system for vehicle powertrain response with
overlap-save implementation of TF -FXLMS algorithm...... 79
Figure 5-3. Normalized computa tional complexity based on the number of computations, I=256.
(Keys: up-triangle marker , real multiplications; circle marker , real
additions; dashed blue line , window-function implementation; and solid black line
, overlap-save implementation)...... 86
Figure 5-4. Magnitude and phase responses of the estimated secondary path transfer function. 88
Figure 5-5. Active sound tuning simulation results for a constant engine speed of 3500 rpm case.
(Keys: solid black line , baseline noise response; dashed blue line ,
window-function implementation of TF -FXLMS; dotted red line , overlap-save
implementation of TF-FXLMS; and asterisk *, desired value)...... 89
Figure 5-6. Active sound tuning simulation results for an engine speed ramp -up case: (a) 3 rd
order response reduction. (b) 4 th order response enhancement. (Keys: solid black line
, baseline noise response; dashed blue line , window -function
implementation of TF -FXLMS algorithm; dotted red line , overlap-save
implementation of TF-FXLMS algorithm; and asterisk *, desired value)...... 92
Figure 5-7. Comparison of the performance of TF -FXLMS algorithms with or without gradient
estimate adjust factor: (a) 3 rd order response reduction; (b) 4 th order response
enhancement. (Keys: solid black line , baseline noise re sponse; dotted red line
, without gradient estimate adjust factor ; dashed-dotted green line , with
gradient estimate adjust factor; and a sterisk *, desired value)...... 95
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Figure 6-1. Principle component analysis of twenty -one accelerometer signals...... 102
Figure 6-2. Multiple coherence function and potential maximum noise reduction in decibels of
best set of six accelerometers, along with sound pressure level of typical road noise.
(Keys: solid blue line , sound pressure level of typical road noise, labeled as the
left y-axis; dashed green line , multiple reference function, labeled as the right y -
axis; dotted red line , potential maximum noise reduction; and shadow area
, frequency range that has high SPL of road noise but low multiple coherence
value)...... 103
Figure 6-3. Block diagram of the proposed combined feedforward -feedback active road noise
control system...... 105
Figure 6-4. Feedforward control part of the proposed active road noise control system based on
subband FXLMS algorithm...... 108
Figure 6-5. Feedback control part of the proposed active road noise control system based on
IMC architecture with FXLMS algorithm...... 112
Figure 6-6. IRF and FRF of the measured secondary path: (a) IRF; (b) FRF...... 115
Figure 6-7. Comparison of feedforward active noise control results between the subband FXLMS
algorithm and the conventional time -domain FXLMS algorithm. (Keys: solid black line
, baseline road noise response; dashe d blue line , subband FXLMS
algorithm; and dotted red line , conventional time-domain FXLMS algorithm). 117
Figure 6-8. Comparison between feedforward road noise control result by using subband
FXLMS algorithm and potential maximum noise reduction. (Keys: solid black line ,
baseline road noise response; dashed blue line , subband FXLMS algorithm; and
solid gray line , po tential maximum noise reduction)...... 118
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Figure 6-9. Feedback active noise control result based on IMC architecture with FXLMS
algorithm. (Keys: solid black line , baseline road noise response; and dotted red
line , feedback-only control based on IMC architecture with FXLMS algorithm).
...... 119
Figure 6-10. Comparison of active noise control results between the proposed combined
feedforward-feedback control system and the feedforward only control system with
subband FXLMS algorithm. (Keys: solid black line , baseline road noise response;
dashed blue line , combined feedforward -feedback control system; and dotted red
line , feedforward -only control system with subband FXLMS algorithm)...... 120
Figure 7-1. Block diagram of the multi -reference multi-channel active road noise control system
with conventional FXLMS algorithm...... 126
Figure 7-2. Block diagram of the proposed multi -reference multi-channel active road noise
control system with TF-FXLMS algorithm...... 129
Figure 7-3. Normalized computational complexities with M= [1:8], K=[1:8], J=6, L=256, I=256:
(a) Real multiplications; (b) Real additions...... 135
Figure 7-4. Normalized computational complexities with M=2 , K=2, J=[1:10], L=256, I=256 .
(Keys: solid line with up -triangle marker , real multiplications; and solid line with
circle marker , real additions)...... 136
Figure 7-5. Normalized computational complexitie s with M=2 , K=2, J=6, L=[32, 64, 128, 256,
512, 1024, 2048], I=256 . (Keys: solid line with up-triangle marker , real
multiplications; and solid line with circle marker , real additions)...... 136
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Figure 7-6. Normalized computational complexities with M=2 , K=2, J=6, L=256 , I=[32, 64, 128,
256, 512, 1024, 2048] . (Keys: solid line with up-triangle marker , real
multiplications; and solid line with circle marker , real additions)...... 137 ) Figure 7-7. Magnitude and phase responses of the sec ondary path transfer functions: (a) S11
) ) ) ( ) and S21 ( ); (b) S22 ( ) and S12 ( )...... 139
Figure 7-8. Multiple coherence function between a set of reference signals and targeted road
noise: (a) Error 1; (b) Error 2...... 143
Figure 7-9. Comparison of active noise control results between using conventional FXLMS
algorithm and proposed TF -FXLMS algorithm with six reference acceleromet ers: (a)
Error 1; (b) Error 2. (Keys: solid black line , baseline road noise response;
dashed blue line , conventional FXLMS algorithm; and dotted red line ,
proposed TF-FXLMS algorithm)...... 144
Figure 7-10. Comparison of active control results between the conventional FXLMS algorithm
with two reference accelerometers and the TF -FXLMS algorithm with six reference
accelerometers: (a) Error 1. (b) Error (2). (Keys: solid black line , baseline road
noise response; dashed blue line , conventional FXLMS algorithm; and dotted red
line , proposed TF -FXLMS algorithm)...... 146
Figure 8-1. Block diagram of the multichannel ANC system using conventional FXLMS
algorithm for treating road noise...... 150
Figure 8-2. Block diagram of the proposed multichannel ANC system with channel equalization
algorithm for treating road noise...... 155
Figure 8-3. Magnitude spectrums of original and equalized reference signals: (a) Original
reference signals; (b) Equalized reference signals...... 160
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) Figure 8-4. Magnitude responses of four estimated secondary path transfer functions: (a) S11
) ) ) ( ) and S21 ( ); (b) S22 ( ) and S12 ( )...... 161
Figure 8-5. Magnitude responses of virtual secondary path transfer functions by using channel
) ) equalization algorithm. (Keys: S ( ) and S ( ))...... 161 22 12
Figure 8-6. Multiple coherence functions between a set of reference signals and targeted road
noises. (Keys: solid black line , error 1; and dotted blue line , error 2). . 163
Figure 8-7. Comparison of active noise control results between using conventional FXLMS
algorithm and proposed channel equalization algorithm: (a) Error 1; (b) Error 2. (Keys:
solid black line , baseline road noise response; dashed blue line ,
conventional FXLMS algorithm; and dotted red line , proposed channel
equalization algorithm)...... 165
Figure 8-8. Magnitude spectrums of assumed reference signals...... 166
Figure 8-9. Comparison of active noise control results between using conventional FXLMS
algorithm and proposed channel equalization algorithm by using assumed reference
signals: (a) Error 1; (b) Error 2. (Keys: solid black line , baseline road noise
response; dashe d blue line , conventional FXLMS algorithm; and dotted red line
, proposed channel equalization algorithm)...... 168
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LIST OF SYMBOLS
frequency-domain pseudo-error signal vector at index frequency-domain the k-th error signal vector at index frequency-domain power estimate vector of the jkm -th filtered reference signal index power spectrum matrix of filtered reference signal frequency response of secondary path matrix frequency response of estimated secondary path matrix virtual secondary path matrix feedforward control filter frequency-domain reference signal matrix frequency-domain filtered reference signal matrix frequency-domain reference signal vector at index frequency-domain the j-th filtered reference signal vector at index frequency-domain the jkm -th filtered reference signal vector at index gradient estimate matrix derivative operation with respect to the adaptive filter gradient estimate of TF-FXLMS algorithm at index gradient estimate of the adaptive filter of TF-FXLMS algorithm at index signal vector of the estimated primary disturbance error signal picked by error microphones
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gain vector for adjusting reference signals primary powertrain noise at error microphones impulse response of secondary path matrix impulse response of estimated secondary path matrix. a small amount of white noise for MIMO system identification coefficient vector of the first adaptive filter of the twin-FXLMS algorithm
coefficient vector of the second adaptive filter of the twin-FXLMS algorithm
coefficient vector/matrix of adaptive filter reference signal equalized reference signal the first reference signal vector of the twin-FXLMS algorithm the second reference signal vector of the twin-FXLMS algorithm filtered reference signal the first filtered reference signal vector of the twin-FXLMS algorithm the first filtered reference signal vector of the twin-FXLMS algorithm the km -th filtered reference signal vector filtered by the km -th estimated secondary path for single reference control system ̂ the jkm -th filtered reference signal vector that is obtained by filtering by the estimated secondary path for multiple references ̂ control system
adjust factor of gradient estimate xviii
adjust factor of gradient estimate for adaptive filter at index decimation factor Z-transform of the error signal statistical expectation operator ∙ spectrum density of the output signal cross spectrum density of input signal and output signal cross spectrum density function of input signals and extraneous noise output spectrum predicted linear output spectrum frequency response function of the transfer path from the input signal to the output signal m-th filter bank order of estimated secondary path filter number of reference sensors number of error microphones number of secondary speakers number of subband of SFXLMS algorithm block size maximum potential noise reduction of sound pressure level at frequency