A New Method for Active Cancellation of Engine Order Noise in a Passenger Car

applied sciences

Article A New Method for Active Cancellation of Engine Order Noise in a Passenger Car

Sang-Kwon Lee * ID , Seungmin Lee, Jiseon Back and Taejin Shin Acoustics and Vibration Signal Processing Lab., Department of Mechanical Engineering, Inha University, Incheon 22201, Korea; [email protected] (S.L.); [email protected] (J.B.); [email protected] (T.S.) * Correspondence: [email protected]; Tel.: +82-032-860-7305

Received: 8 June 2018; Accepted: 14 August 2018; Published: 17 August 2018

Featured Application: The proposed framework is highly suitable for audio applications for active sound noise cancellation and active sound design in a vehicle.

Abstract: This paper presents a novel active noise cancellation (ANC) method to reduce the engine noise inside the cabin of a car. During the last three decades, many methods have been developed for the active control of a quasi-stationary narrowband sinusoidal signal. However, since the interior noise signal is non-stationary with a fast frequency variation when the car accelerates rapidly, these methods cannot stably reduce the interior noise. The proposed method can reduce the interior noise stably even if the speed of the car is changed quickly. The method uses an adaptive ﬁlter with an optimal weight vector for the active control of such an engine noise. The method of determining the optimal weight vector of an adaptive ﬁlter is demonstrated. In order to validate the advantages of the proposed method, a conventional method and the proposed method are simulated with three synthesized signals. Finally, the proposed method is applied to the cancellation of booming noise in a sport utility vehicle. We demonstrate that the performance of the ANC system with the proposed algorithm is excellent for the attenuation of engine noise inside the cabin of a car.

Keywords: adaptive ﬁlter; optimized ﬁlter; active noise cancellation; active sound design; sound quality; vehicle

1. Introduction While driving a passenger car, a driver can hear many types of sounds inside the car [1]. Among them, the engine is one of the dominant noise sources and influences the sound quality of the interior environment [2]. The frequency components of engine noise are correlated to the rotating speed of the crankshaft (i.e., rpm) of an engine and its harmonics [3]. These harmonic components are called ‘orders’. This correlation relationship between the engine noise and the rotating speed enables the control of the engine sound by using active control systems. Active noise control (ANC) has received considerable attention in recent decades, owing to its superior advantages in cancelling low frequency noise as compared to passive methods [4,5]. Adaptive feedforward control systems are very popular in active control systems (such as ANC) for the reduction of engine noise inside a car cabin [4–7]. This system uses an order signal as a reference. Order signals are sinusoidal signals within a narrow band, and can be synthesized by using the controller area network (CAN) bus (or a tachometer) in a car. The frequency of the order signal is changed in the run-up condition of the engine speed, and is a non-stationary signal. Many adaptive filters can be used in ANC systems [8]. In previous studies, the filtered x-LMS algorithm (FxLMS) based on the adaptive notch filter (ANF) has been widely used for the ANC of engine noise [7]. The filter length of the adaptive filter and the step-size should be carefully selected to ensure that the least mean squares (LMS) algorithm converges

Appl. Sci. 2018, 8, 1394; doi:10.3390/app8081394 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 1394 2 of 22 rapidly and is stable. Haykin [9] discussed the method to select the appropriate filter length and step size parameter. Although there are some implementations of variable length LMS adaptive filters, their performance is not steady [10]. Bilcu et al. introduced a variable LMS adaptive filter [11]. They suggested an implementation of multiple adaptive filters with variable lengths. Nascimento [12] proposed a method to speed up this convergence rate by varying the length of the adaptive filter, utilizing the larger step sizes allowed for short filters. These studies show the possibility of acquiring a rapid convergence when the optimal length of an adaptive filter is applied to the control of engine noise inside the cabin of a car. An adaptive notch filter used for the ANC of engine noise removes the primary spectral components within a narrowband centered at the frequency of reference. The filter length of the adaptive notch filter used in this study is short and two weights have been used. The other inherent feature of the LMS algorithm is the step size, and it requires careful adjustment. A small step size, required for small excess mean square error, results in slow convergence. A large step size, required for fast adaptation, may result in the loss of stability. Therefore, many modifications of the LMS algorithm, where the step size changes during the adaptation process depending on particular characteristics, have been developed [9,13]. The performance of the adaptive notch filter depends heavily on the accuracy of the frequency of the reference signal because the bandwidth of the adaptive notch filter is proportional to the convergence step size [14,15]. The frequency change of the reference signal deteriorates the performance of an ANC system [16]. Therefore, in order to improve the convergence rate, the optimization of the step size in the adaptive notch filter is required for the ANC of engine noise [6]. Bismor [17] reviewed seventeen of the best-known variable step size LMS (VS-LMS) algorithms to the degree of detail that allows implementing them. The performance of the algorithms is compared in typical applications. According to the conclusion of this review, no VS-LMS algorithm appears to be as versatile, easy to use, and well-suited for real-time applications as the normalized least mean squares filter (NLMS). Recently, an NEX_LMS algorithm that uses the normalized signal as a reference has been proposed to improve the convergence rate for active sound quality control [18]. It improved the convergence rate of an ANC system using the Filtered-X LMS (FxLMS) algorithm, and achieved a large order-level reduction of the stationary disturbance of engine noise. An adaptive recursive algorithm has been proposed for the fast convergence of a controller in the ANC system of a short duct [19] for a non-stationary signal. In the present study, the optimized weights-FxLMS (OW-FxLMS) algorithm is proposed. Our goal is to control amplitude- and frequency-modulated noise, such as the order components of engine noise inside a car, with fast convergence. The performance of the algorithm is investigated with computer simulations and an experimental application in a car. The application purpose of this algorithm is to control the envelope of amplitude modulation signal and to generate the target sound with good sound quality inside of a car. The target sound is designed by the combination of the engine orders sound [20]. The sound quality of the target sound is determined by the sound quality index based on booming sound and modulation sound [21]. The booming sound and modulation sound were determined by the sound pressure level of the engine order sounds. Therefore, in order to design the amplitude of the target, the amplitude of the engine order sound should be controlled. The proposed optimized weights-FxLMS (OW-FxLMS) algorithm is suitable for this application. In Section2, the novel OW-FxLMS algorithm is proposed. The utility of the proposed algorithm is validated in Section3. The adaption for the proposed algorithm is explained in Section4. The application of the algorithm to control of the interior noise is presented in Section5. Finally, the conclusion is presented in Section6.

2. Development of Novel Algorithm for Control of Amplitude of Order Sound

2.1. Conventional Method for ANC of Engine Noise The FxLMS-algorithm-based adaptive notch ﬁlter has been used for the active noise cancellation of engine noise [4,5,22]. It is called the “conventional method” in the paper. The scheme of this Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 22

2. Development of Novel Algorithm for Control of Amplitude of Order Sound

2.1. Conventional Method for ANC of Engine Noise The FxLMS-algorithm-based adaptive notch filter has been used for the active noise Appl.cancellation Sci. 2018, 8, 1394 of engine noise [4,5,22]. It is called the “conventional method” in the paper. The 3scheme of 22 of this ANC system is shown in Figure 1. This system uses two single sinusoidal reference signals, x0 and x1, and two single weights, w0 and w1, to control the engine noise. S(z) is the secondary path of ANC system is shown in Figure1. This system uses two single sinusoidal reference signals, x and x , the transfer function, and Szˆ() is the estimation of the secondary path. A suitable reference0 signal1 and two single weights, w0 and w1, to control the engine noise. S(z) is the secondary path of the transfer can be generated synthetically by measuring the current rotation speed fki of the engine and utilizing function, and Sˆ(z) is the estimation of the secondary path. A suitable reference signal can be generated a discrete-time oscillator [23]. The primary disturbancei d(n) comprises a multi-sinusoidal signal, synthetically by measuring the current rotation speed fk of the engine and utilizing a discrete-time which is the engine noise inside the cabin of a car. The multi-sinusoidal signal is correlated to the oscillator [23]. The primary disturbance d(n) comprises a multi-sinusoidal signal, which is the engine reference signals. In order to control the multi-sinusoidal signal, this scheme could be expanded to a noise inside the cabin of a car. The multi-sinusoidal signal is correlated to the reference signals. In order multi-input/multi-output FxLMS control algorithm [6,7]. In the simplified single-frequency ANC to control the multi-sinusoidal signal, this scheme could be expanded to a multi-input/multi-output system as shown in Figure 1, yk(n) is given by FxLMS control algorithm [6,7]. In the simplified single-frequency ANC system as shown in Figure1, yk(n) is given by yn()=+ w () nxn () w () nxn () (1) k kkkkk0, 0, 1, 1, y (n) = w0,k(n)x0,k(n) + w1,k(n)x1,k(n) (1) The two weights w(n) of the adaptive filter are updated as The two weights w(n) of the adaptive filter are updated as += +μ ' wn0,kkkk(1)() wn 0, enxn ()() 0, w (n + ) = w (n) + e (n)x0 (n) (2) 0,k 1 +=0,k +µ μk 0,k' wn1,kkkk(1)() wn 1, enxn ()()0 1, (2) w1,k(n + 1) = w1,k(n) + µek(n)x1,k(n) ' wherewhereµ isμ theis the step step size size controlling controlling the the stable stable convergence convergence of of the the controller controller and andx 0xn(n)()is the is the filtered filtered versionversion of xof(n x)( andn) and is givenis given by by

M M 0 xn' ()=−= sxnmˆ ( ), i 0, 1 xi,k(nik),, = ∑sˆmx mi,k ik(n − m), i = 0, 1 (3)(3) m=1m=1 where sˆ is an Mth-order estimate of the secondary path impulse response. where sˆm ism an Mth-order estimate of the secondary path impulse response.

FigureFigure 1. Narrowband1. Narrowband FxLMS FxLMS algorithm algorithm based based adaptive adaptive notch notch ﬁlter. filter.

The adaptive notch filter removes the primary spectral components within a narrow band The adaptive notch filter removes the primary spectral components within a narrow band centered centered at the frequency fki (t) of the reference signal. The performance of the adaptive notch filter to at the frequency f i (t) of the reference signal. The performance of the adaptive notch filter to cancel a cancel a sinusoidalk signal depends heavily on the accuracy of the frequency of the reference signal sinusoidal signal depends heavily on the accuracy of the frequency of the reference signal [16] since [16] since the center frequency of the notch filter depends on the sinusoidal reference signal, whose the center frequency of the notch filter depends on the sinusoidal reference signal, whose frequency is frequency is equal to the frequency of the sinusoidal noise to be cancelled. The increment of step size equal to the frequency of the sinusoidal noise to be cancelled. The increment of step size µ results in μ results in a stability problem because, in an adaptive notch filter, the convergence step size is a stability problem because, in an adaptive notch filter, the convergence step size is proportional to proportional to the bandwidth of the filter [9,15] and the higher the step size, the higher the the bandwidth of the filter [9,15] and the higher the step size, the higher the bandwidth. Considering bandwidth. Considering stability, the optimal step size is proposed [7] as follows: stability, the optimal step size is proposed [7] as follows: 4 0 <<μ 4 2 (4) 0 < µ < LA (4) LA2 where L is filter length of adaptive filter and A is the amplitude of the sinusoidal reference. The 3 dB bandwidth B of the notch filter can be estimated as

µLA2 B ≈ (5) 4π∆ Appl. Sci. 2018, 8, 1394 4 of 22 where ∆ is sampling time. From Equation (8), when the instantaneous frequency of the sinusoidal reference varies rapidly, the bandwidth B adaptive ﬁlter should be very narrow in order to track the time varying frequency and thus, the step size µ decreases. The small step size µ yields a slow convergence. The slow convergence cannot track the subsequent rapid varying frequency of the sinusoidal reference. Therefore, except for a quasi-stationary sweep of the instantaneous frequency of the sinusoidal reference, this system is not appropriate for controlling a frequency-modulated signal with a quickly variable bandwidth. Moreover, the performance of this ANC system is reduced when the run-up speed of the engine is changed rapidly [10,12]. Through further improvements, a new LMS algorithm based on the variable step size is proposed. Several variable step size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance of the algorithm, but a major drawback is the complexity in the theoretical analysis of the resultant algorithms [16]. According to conclusion of this review, most of the VS-LMS algorithms suggest a general modiﬁcation that can simplify the choice of the upper bound for the step size. For the variable step size, the NLMS algorithm is employed and uses the following equation:

µ µ < < = < < 0 µ 2 , 0 µ 2 (6) kx(n)k LPˆx(n) where µ a scalar that allows for a change of adaptive speed and is an estimate of the power of x(n) at time n. In order to further stabilize the digital implementation of the LMS algorithm, a technique known as leakage is used. In the leaky NLMS algorithm [9,14] the weight vector is updated by the following equation: 0 w0,k(n + 1) = γw0,k(n) + µek(n)x0,k(n) 0 (7) w1,k(n + 1) = γw1,k(n) + µek(n)x1,k(n) where γ is the leakage factor and satisﬁes the following condition for the leaky NLMS algorithm [24].

γ − 1 ≤ µ < µ + 1 (8)

2.2. Novel Optimized Weights-LMS Algorithm: OW-FxLMS We propose a new algorithm to improve the performance of the FxLMS algorithm to control an amplitude- and frequency-modulated signal such as an engine harmonic order signal. The main objective the proposal algorithm is to control the amplitude of time varying engine order sounds with fast frequency change. In order to achieve this purpose, the design principles of the new ANC algorithm are that the frequency bandwidth of the adaptive filter should be wide and include the frequency of the engine order sound signal to be controlled by the adaptive filter. However, the limitation of this adaptive filter cannot control each order sound separately if frequencies of order sounds are too close, because the frequency bandwidth is wide. This is the limitation of the proposed algorithm. In order to overcome this limitation, the weighting of the adaptive filter should optimized. Therefore, in this section, the OW-FxLMS is proposed. In order to trace a fast frequency change of the order sound signal, the optimized sufficient frequency bandwidth is required. The frequency bandwidth of an adaptive filter for tracking the frequency modulated signal is determined by the length of the weight vector [8,9,14]. The proposed algorithm is an FxLMS-algorithm-based adaptive filter with an optimal length of the weight vector wk (n). We determined the optimal length of the weight vector in order to trace a frequency-modulated signal such as an engine order signal. The frequency bandwidth between orders for rotating machinery is given by RPM × ∆k f (RPM, k) = (9) OB 60 where ∆k is the difference between the orders to be controlled. According to the theory of adaptive signal processing [9], the frequency bandwidth of an adaptive filter is given by fWB = 2 fs/L where Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 22

frequency-modulated signal such as an engine order signal. The frequency bandwidth between orders for rotating machinery is given by ×Δ = RPM k fRPMkOB(,) (9) 60 where ∆k is the difference between the orders to be controlled. According to the theory of adaptive

= s Appl.signal Sci. 2018processing, 8, 1394 [9], the frequency bandwidth of an adaptive filter is given by ffLWB2/ s where5 of 22 f is the sampling frequency. The optimal frequency bandwidth fWB of an adaptive filter to be used by a

controller should be less than the frequency bandwidth fRPMkOB (,) between the orders to be fs is the sampling frequency. The optimal frequency bandwidth f WB of an adaptive filter to be used controlled by a controller. The adaptive filter is a moving bandpass filter with different center by a controller should be less than the frequency bandwidth fOB(RPM, k) between the orders to befrequencies. controlled The by a frequency controller. bandwidth The adaptive of the filter frequency-modulated is a moving bandpass signal filter to be with cancelled different should center be frequencies.less than the The bandwidth frequency of bandwidth the adaptive of thefilter frequency-modulated in the proposed OW-FxLMS signal to algorithm. be cancelled Therefore, should be in lessthe than ANC the system bandwidth shown of in the Figure adaptive 2, yk filter(n) is ingiven the proposedby OW-FxLMS algorithm. Therefore, in the L −1 ANC system shown in Figure2, yk (n) is given by o ==T − y()nnnwnxnlwx ()() l ()( ) (10) l=0 Lo−1 y(n) = wT(n)x(n) = w (n)x(n − l) (10) And the proposed OW-FxLMS algorithm is given∑ byl l=0 wwLLoo(1)()nnenn+= +μ ()() x ' (11) And the proposed OW-FxLMS algorithmkkkk is given by

where the length of weight vectorLo is the optimalLo length L0. It is 0given by wk (n + 1) = wk (n) + µek(n)xk(n) (11) 2 × f 260××fs LL==s , or (12) where the length of weight vector is theoo optimalf length L0RPM. It is×Δ given k by OB 2 × fs 2 × 60 × fs The step size parameter μL oshould= be , orcarefullyLo = selected to ensure that the LMS algorithm(12) converges rapidly and is stable. Haykin f(9)OB proposed theRPM condition× ∆k to select the appropriate step size parameterThe step as size follows: parameter µ should be carefully selected to ensure that the LMS algorithm converges rapidly and is stable. Haykin (9) proposed the condition2 to select the appropriate step size parameter 0 <<μ (13) as follows: LP 2o x 0 < µ < (13) where Px denotes the power of x(n). From EquationsLo P(12)x and (13), when the power of the reference wheresignalP changes,x denotes if the Lo is power changed, of x (then). Fromstep size Equations μ should (12) also and be (13),changed when according the power to ofthe the convergence reference signaltheory changes, of the LMS if Lo algorithm.is changed, In the practice step size [7],µ theshould relationship also be changed between according step size toand the filter convergence length for theoryconvergence of the LMS is as algorithm.follows: In practice [7], the relationship between step size and ﬁlter length for convergence is as follows: 0.01 0.1 0.01 <<μ 0.1 (14) LP< µ < LP (14) LoPxooxxLoPx

FigureFigure 2. 2.OW-FxLMS OW-FxLMS control control algorithm algorithm based based adaptive adaptive ﬁlter filter with with optimized optimized weights weights (OW). (OW).

When the input signal has varying frequency, the NLMS algorithm with variable step size should be used for further improvements. Therefore, the estimated power Pˆx(n) of x(n) at time n should be computed dynamically and thus, the variable step size is changed corresponding to Equation (6) because the optimal ﬁlter length Lo is constant. Finally, the pseudo code for the proposed OW-FxLMS algorithm is presented in Table1. Appl. Sci. 2018, 8, 1394 6 of 22

Table 1. Pseudo code of the OW-FxLMS algorithm.

Parameters: Lo = Number of Taps 0 < µ < 2 Initial condition: w (0) = 0 Use Equation (16) Data x0(n) = x (n) ⊗ sˆ(n), x0(n); L -by-1 tap input vector n o x (n): Normalized sinusoidal signal (a) Given: n sˆ(n): Measured impulse response of the 2nd d(n): desired response at time n path of the system includes electric part. Note: ⊗ means convolution (b) To be computed: w(n + 1) = estimate of tap-weight vector at time n + 1 Computation: n = 0, 1, 2, . . . e(n) = d(n) − wT(n)x0(n) x0 (n) Lo( + ) = Lo( ) + k ( ) wk n 1 wk n 0 2 µek n kxk (n)k

3. Simulation and Validation of the Proposed Algorithm

3.1. Synthesizing the Engine Noise Signal Inside a Car Cabin Engine noise is a periodic signal. From the theory of Fourier series expansion, a periodic signal (such as engine noise) can be decomposed into a sum of sinusoidal signals with the fundamental frequency and its harmonic frequencies [25]. These harmonic sinusoidal signals are called order signals. The frequency of the ﬁrst-order signal matches the rotating speed of the crankshaft [3]. The frequency of a one-half order signal matches the fundamental frequency because the engine ﬁres once whenever the crankshaft rotates 720◦. Therefore, the frequency components of engine noise are comprised of the rotating speed of the crankshaft and its harmonic. The engine noise is transferred to the inside the cabin of a car through an airborne path and a structure-borne path [2,5,26]. Therefore, the amplitude of each order signal is modulated according to the resonance of the structure and the cavity. When the speed of the engine changes, the rotating frequency of the crankshaft also changes. Therefore, the engine noise inside the cabin of a car is comprised of the sum of amplitude and frequency modulated order signals. This is mathematically expressed as follows:

K x(t) = ∑ xk(n) = Ak(t) exp(jθk(t)), k = 0.5, 1, 1.5, 2 . . . , K (15) k=0.5 where xk(t) is the kth order signal, Ak is its amplitude, and θk is its phase (which includes the information of the instantaneous frequency fi). The instantaneous frequency of the kth order signal is given by [27] 1 dθ (t) f i(t) = k (16) k 2π dt For the order signal, this instantaneous frequency can be expressed in terms of the engine speed and is given by RPM f i(t) = × k (17) k 60 If the engine speed is accelerated linearly, the instantaneous frequency is a linear equation and i is given by fk(t) = at + b, where a is the sweep rate of the rotational speed and b is the initial instantaneous frequency at the starting rotational speed. If the engine speed is accelerated nonlinearly, the instantaneous frequency becomes a nonlinear equation. In this section, three signals are synthesized for the simulation. The sampling frequency used to synthesize the signals is 3000 Hz. Signal 1 is a second-order signal with a linear instantaneous frequency, and its initial frequency i f2(t) is 20 Hz, which corresponds to 600 rpm. The ﬁnal run-up frequency is 200 Hz, which corresponds to 6000 rpm. The run-up time from 600 rpm to 6000 rpm is 5 s. This run-up time corresponds to a short Appl. Sci. 2018, 8, 1394 7 of 22 duration and the instantaneous frequency is changed quickly during this run-up time. The amplitude of the signal is unity. It is given mathematically by

rpm(t) S (t) = sin(2π f i(t)t), f i (t) = × k + f , f = 20 Hz (18) 1 k k=2 60 0 0 Signal 2 is comprised of the sum of the second-order, fourth-order, and sixth-order signals. The initial frequencies of each order are 20, 40, and 60 Hz, respectively, which correspond to 600 rpm. The ﬁnal frequencies are 200, 400, and 600 Hz, respectively, which correspond to 6000 rpm. A run-up time of 5 s was used.

3.2. Validation of the Proposed Algorithm When the speed of the engine changes, the engine noise inside the cabin of a car is comprised of the sum of amplitude- and frequency-modulated order signals. Section 3.1 presents the details for when two synthesized signals were simulated. In this section, details for when the synthesized signals were used for the validation of the control performance of the OW-FxLMS algorithm are presented. These results were compared with the conventional method, which is the LMS-algorithm-based adaptive notch filter. The conventional method cannot control the amplitude of the time-varying engine order sound because the frequency of the engine order sound is changed quickly when the rotating speed of the crankshaft increases or decreases. The secondary path was not used in this validation in order to exclude its influence. Signal 1. Frequency-modulated signal (single order signal) A frequency-modulated signal with a single order is applied to the ANC system with different algorithms. Figure3 illustrates the time history of error signals controlled by the NLMS algorithm-based adaptive notch filter with two weights (L = 2). Different step sizes are used to observe the resulting effect of convergence. In Figure3, the letter “u” denotes step size. Figure3a–c illustrate the time history of errors controlled by the NLMS-algorithm-based adaptive notch filter with different step sizes of µ = 0.5, µ = 2, and µ = 3, respectively, but the leakage factor is 0.5. Figure3d shows the comparison of power spectrum density (PSD). From these results, it can be observed that the convergence of the error signal is fast initially as the step size increases, but that the amplitude of the error signal diverges eventually. The adaptive notch filter cannot trace and control the time-varying signal with fast frequency change. Because the frequency bandwidth of the notch filter is very narrow it is not suitable when the frequency of the signal to be controlled is changed. Therefore, it is finally diverged. Subsequently, in order to observe the effect of leakage, different leakage factors are applied to the leaky NLMS algorithm in Equation (11) with the same step size (µ = 2). Appl. Sci. 2018, 8, 1394 8 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 22

(a) (b)

Figure 3. Time history and PSD of signal 1 controlled by the normalized least mean squares filter Figure 3. Time history and PSD of signal 1 controlled by the normalized least mean squares ﬁlter (NLMS) algorithm-based adaptive notch filter with two weights (L = 2) and leakage factor (γ = 0.5). (NLMS) algorithm-based adaptive notch ﬁlter with two weights (L = 2) and leakage factor (γ = 0.5). (a) Time history ( μ = 0.5); (b) Time history ( μ = 2); and (c) Time history ( μ = 3); and (d) PSD. (a) Time history (µ = 0.5); (b) Time history (µ = 2); and (c) Time history (µ = 3); and (d) PSD.

Figure 4a–c illustrates the time history of the error signal controlled by the Figure4a–c illustrates the time history of the error signal controlled by the NLMS-algorithm-based NLMS-algorithm-based adaptive notch filter with different leakage factors of γ = 0.5, γ = 0.7, and γ = adaptive notch filter with different leakage factors of γ = 0.5, γ = 0.7, and γ = 1.0, respectively, 1.0, respectively, and the step size is 0.5. In Figure 4, the letter “g” denotes leakage factor. According and the step size is 0.5. In Figure4, the letter “g” denotes leakage factor. According to these results, to these results, the amplitude of the error signal diverges eventually. Even with the selection of any the amplitude of the error signal diverges eventually. Even with the selection of any leakage factor, leakage factor, the controller cannot work stably. Subsequently, in order to observe the effect of the controller cannot work stably. Subsequently, in order to observe the effect of frequency variation, frequency variation, reference signals with five different sweep rates are used. reference signals with five different sweep rates are used. Figure 5 shows the variation of instantaneous frequency (fi = rpm/60) of the five references. The Figure5 shows the variation of instantaneous frequency ( fi = rpm/60) of the five references. sweep time is 5 s for all the references. The selected sweep rates, which are calculated using ∆fi/∆time, The sweep time is 5 s for all the references. The selected sweep rates, which are calculated using are 4, 6, 8, 16, and 36 s. ∆f /∆time, are 4, 6, 8, 16, and 36 s. i Figure 6 illustrates the time history and PSDs of the error signals controlled by the leaky NLMS Figure6 illustrates the time history and PSDs of the error signals controlled by the leaky NLMS algorithm-based adaptive notch filter with two weights (L = 2), leakage factor (γ = 1), and step size algorithm-based adaptive notch filter with two weights (L = 2), leakage factor (γ = 1), and step size μ = 2. These results demonstrate that the error signals do not converge and are not stable for all the µ = 2. These results demonstrate that the error signals do not converge and are not stable for all the cases with different sweep rates. Finally, we attempted to determine the optimal step size and cases with different sweep rates. Finally, we attempted to determine the optimal step size and leakageμ leakagefactor for factor signal for 1. signal Using 1. theUsing previous the previous simulation simulation results, results, we first we used first used the step the sizestep ofsizeµ of= 2 and = 2leakage and leakage factor factor of γ = of 1 inγ = this 1 in simulation. this simulation. Appl. Sci. 2018, 8, 1394 9 of 22 Appl.Appl. Sci. Sci. 2018 2018, 8, ,x 8 FOR, x FOR PEER PEER REVIEW REVIEW 9 of9 22of 22

(a) (a) (b) (b)

FigureFigure 4. Time4. Time history history and and PSD PSD of ofsignal signal 1 controlled 1 controlled by bythe the NLMS NLMS algorithm-based algorithm-based adaptive adaptive notch notch Figure 4. Time history and PSD of signal 1 controlled by the NLMS algorithm-based adaptive notch filterfilter with with two two weights weights (L =(L 2) = and2) and leakage leakage factor factor (γ (=γ 0.5). = 0.5). (a) ( Timea) Time history history (γ (=γ 0.5); = 0.5); (b )( bTime) Time history history ﬁlter with two weights (L = 2) and leakage factor (γ = 0.5). (a) Time history (γ = 0.5); (b) Time history (γ (=γ 0.7); = 0.7); and and (c) (Timec) Time history history (γ (=γ 1); = 1);and and (d )( dPSD.) PSD. (γ = 0.7); and (c) Time history (γ = 1); and (d) PSD.

60006000 sr sr= 36 = 36 sr = 16 5000 sr = 16 5000 sr sr= 8 = 8 sr sr= 6 = 6 40004000 sr sr= 4 = 4

30003000

20002000

10001000

0 0 012345012345 TimeTime(s)(s)

FigureFigure 5. Variation5. Variation of instantaneousof instantaneous frequency frequency (fi =(f irpm/60) = rpm/60) of fiveof five references. references. Figure 5. Variation of instantaneous frequency (fi = rpm/60) of ﬁve references. Appl. Sci. 2018, 8, 1394 10 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 22 Sound Press (pa)

Sound Press (pa)

Figure 6. Cont. Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 22 Appl. Sci. 2018, 8, 1394 11 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 20 11 of 22 2 No-ANC SR=36 No 0 ANF-LMS 1.5 ANC 20 2 -20 No-ANC 1 SR=36 No 0 ANF-LMS 1.5 ANC -40 0.5 -20 1 -60 0 -40 0.5 -80 -0.5 -60 0

Sound Press (pa) -100 -1 -80 -0.5 -120

Sound Press (pa) -1.5 -100 -1 -140 -2 -120 0 50 100 150 200 250 300 -1.5 012345 Frequency (Hz) -140 0 50 100 150 200 250 300 Figure-2 6. Time history and PSD of the signal 1 with different sweep rate controlled by the Leaky 012345 Frequency (Hz) NLMS algorithm-based adaptive notch filter with two weights (L = 2), leakage factor (γ = 1), and step FigureFigure 6. Time historyhistoryand and PSD PSD of of the the signal signal 1 with 1 with different different sweep sweep rate controlledrate controlled by the by Leaky the Leaky NLMS size μ = 2. NLMSalgorithm-based algorithm-based adaptive adaptive notch notch ﬁlter withfilter twowith weights two weights (L = 2), (L leakage= 2), leakage factor factor (γ = ( 1),γ = and 1), and step step size sizeµ = 2.μ = 2. The time history of the error signal is shown in Figure 7a. The error signal still diverges. In order to converge the error signal, we decreased the step size from μ = 2 to μ = 1.75 and the TheThe time historyhistory ofof the the error error signal signal is shownis shown in Figure in Figure7a. The 7a. error The signalerror stillsignal diverges. still diverges. In order In to leakage factor from γ = 1 to γ = 0.75 corresponding to the rule of leaky LMS algorithm. The error orderconverge to converge the error signal,the error we signal, decreased we thedecreased step size the from stepµ = size 2 to fromµ = 1.75 μ and= 2 theto leakageμ = 1.75 factor and from the signal converges initially as shown in Figure 7b but eventually it diverges. For faster convergence at leakageγ = 1 to factorγ = 0.75 from corresponding γ = 1 to γ = to 0.75 the rulecorresponding of leaky LMS to algorithm.the rule of The leaky error LMS signal algorithm. converges The initially error the start, we increased the step size from μ = 2 to μ = 2.75. In this case, a jump in the error signal signalas shown converges in Figure initially7b but as eventually shown in Figure it diverges. 7b but For eventually faster convergence it diverges. atFor the faster start, convergence we increased at appears initially as shown in Figure 7c and eventually the error diverges. In any of the cases, the PSD thethe start, step sizewe increased from µ = 2the to stepµ = 2.75.size from In this μ case, = 2 ato jump μ =in 2.75. the errorIn this signal case, appearsa jump in initially the error as shownsignal of the error signal is not attenuated as shown in Figure 7d. It can be concluded that the leaky appearsin Figure initially7c and as eventually shown in the Figure error 7c diverges. and eventual In anyly the of the error cases, diverges. the PSD In any of the of errorthe cases, signal the is PSD not NLMS-algorithm-based adaptive notch filter is not suitable for active cancellation of the rapid ofattenuated the error as signal shown is in not Figure attenuated7d. It can as be shown concluded in Figure that the 7d. leaky It can NLMS-algorithm-based be concluded that the adaptive leaky frequency varying disturbances. NLMS-algorithm-basednotch ﬁlter is not suitable adaptive for active notch cancellation filter is of not the suitable rapid frequency for active varying cancellation disturbances. of the rapid frequency varying disturbances.

(a) (b)

(a) (b) PSD PSD

FigureFigure 7. 7.Time Time history history and (andc) PSD PSD of of signal signal 1 1 controlled controlled by by the the NLMS NLMS algorithm-based algorithm-based(d) adaptive adaptive notch notch ﬁlterfilter with with two two weights weights (L (=L 2)= 2) (a )(a Time) Time history history (µ =( μ 2, γ == 2, 1); γ (=b )1); Time (b) historyTime history (µ = 1.75, ( μγ== 1.75, 0.75); γ and= 0.75); (c) Figure 7. Time history and PSD of signal 1 controlled by the NLMS algorithm-based adaptive notch Timeand ( historyc) Time ( µhistory= 2.75, ( γμ== 0.75)2.75, andγ = 0.75) (d) PSD. and (d) PSD. filter with two weights (L = 2) (a) Time history ( μ = 2, γ = 1); (b) Time history ( μ = 1.75, γ = 0.75); and (c) Time history ( μ = 2.75, γ = 0.75) and (d) PSD. Appl.Appl. Sci. Sci.2018 2018, ,8 8,, 1394 x FOR PEER REVIEW 1212 of of22 22

Figure 8a shows a comparison between the time history of error signals controlled by the Figure8a shows a comparison between the time history of error signals controlled by the LMS-algorithm-based adaptive notch filter and the OW-LMS algorithm. The error signal controlled LMS-algorithm-based adaptive notch filter and the OW-LMS algorithm. The error signal controlled by by the adaptive notch filter shows incomplete convergence as the frequency increases according to the adaptive notch filter shows incomplete convergence as the frequency increases according to the the time increment. However, the OW-LMS algorithm with a short length (L = 30) of weight vectors timeis sufficient increment. to However,attenuate thethis OW-LMS frequency algorithm modulated with signal. a short The length results (L = show 30) of fast weight and vectors stable is sufficientconvergence. to attenuate The PSD this function frequency of the modulated error signals signal. is compared, The results and show the results fast and are stableplotted convergence. as shown Thein PSDFigure function 8c. According of the error to signalsthese isresults, compared, the OW-LMS and the results algorithm are plotted exhibits as shownsuperior in Figurecontrol8 c. Accordingperformance to these compared results, to thethe OW-LMS conventional algorithm method exhibits for the superior frequency-modulated control performance signal. compared Figure 8e to theshows conventional an image methodmap of the for power the frequency-modulated spectrum of the weight signal. vector Figure of the8e showsadaptive an filter image used map in of the the powerOW-LMS spectrum algorithm. of the This weight map vector shows of the the adaptive adaptive performance filter used inof thethe OW-LMSfilter. Since algorithm. the length This of the map showsweight the vector adaptive is 30, performancethe frequency of bandwidth the filter. Sinceof the the filter length is 200 of Hz the as weight shown vector in Figure is 30, 8g. the In frequencythe case bandwidthof signal 1, of according the filter to is 200Equation Hz as (15), shown the inoptimal Figure 8lengthg. In the(L) caseof the of weight signal 1,vector according is changed to Equation from (15),300 the(at 600 optimal rpm) lengthto 60 (at (L 6000) of therpm) weight because vector ∆k is is 1 changed(single frequency) from 300 and (at 600 fs is rpm) 3000 toHz. 60 If (at we 6000 use the rpm) becauseadaptive∆ kfilteris 1 with (single the frequency)largest optimal and fslength is 3000 (L = Hz. 300) If of we weight use the vector, adaptive the convergence filter with the is faster largest optimaland more length stable (L as= compared 300) of weight to other vector, algorithms the convergence as shown in isFigure faster 8b. and The more attenuation stable aslevel compared of the toerror other signal algorithms is the largest as shown in Figure in Figure 8d. The8b. Thefreque attenuationncy bandwidth level of the adaptive error signal filter is is the narrow largest as in Figureshown8d. in TheFigure frequency 8f,h. bandwidth of the adaptive filter is narrow as shown in Figure8f,h.

2 off L=300 1

Sound Press (pa) -1

-2 012345 Time(s) (a) (b)

(e) (f)

Figure 8. Cont. Appl. Sci. 2018, 8, 1394 13 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 22

0 rpm = 4199.64 -20

-40

-60

-80

-100 0 500 1000 1500 Frequency (Hz) (g) (h)

FigureFigure 8. 8.Time Time history history andand PSDPSD ofof signalsignal 11 controlledcontrolled by the leaky LMS-algorithm-based adaptive adaptive notchnotch ﬁlter filter ((µμ= 0.5,= 0.5,γ =γ= 0.5) 0.5) andand thethe OW-LMS algorithm algorithm ( (μµ = =1). 1). (a) Comparison between between the the time time historyhistory of of the the conventional conventional method method and and OW-LMS OW-LMS ( L(L= = 30); 30); ( b(b)) Comparison Comparison between between the the time time history history of non-controlof non-control and and OW-LMS OW-LMS (L (=L 300);= 300); (c ()c Comparison) Comparison between between thethe PSDPSD of conventional conventional method method and and OW-LMSOW-LMS ( L(L= = 30); 30);( d(d)) ComparisonComparison betweenbetween the PSD of of non-control non-control and and OW-LMS OW-LMS (L (L == 300); 300); (e ()e Image) Image plotplot of of spectrum spectrum of of weight weight vectorvector associatedassociated with rpm ( L = 30); 30); ( (ff)) Image Image plot plot of of spectrum spectrum of of weight weight vectorvector associated associated with with rpm rpm (L(L= = 300);300); ((ff)) SpectrumSpectrum of weight vector vector ( (LL == 30) 30) at at 4200 4200 rpm rpm (h (h) Spectrum) Spectrum ofof weight weight vector vector ( L(L= = 300)300) atat 42004200 rpm.rpm.

InIn conclusion, conclusion, inin thethe casecase ofof aa sinusoidalsinusoidal signalsignal with single frequency frequency modulation modulation (i.e., (i.e., single single orderorder signal),signal), thethe OW-LMS algorithm algorithm with with the the opti optimalmal length length of weight of weight vector vector can be can used be usedfor forsufficient sufficient control control of ofthe the error error signal. signal. Its Itsconver convergencegence performance performance is isbetter better than than that that of ofthe the conventionalconventional algorithm. algorithm. SignalSignal 2 .2. Frequency-modulated Frequency-modulated signalsignal (multi-order(multi-order signal) A frequency-modulated signal with three orders is applied to the two ANC systems again. A frequency-modulated signal with three orders is applied to the two ANC systems again. Figure 9a illustrates the time history of signal 2 controlled by the conventional method. The Figure9a illustrates the time history of signal 2 controlled by the conventional method. The controller controller cannot sufficiently reduce the order signals without divergence. Figure 9b illustrates the cannot sufficiently reduce the order signals without divergence. Figure9b illustrates the time history time history of signal 2 controlled by the OW-LMS algorithm. Two weight vectors were used in the of signal 2 controlled by the OW-LMS algorithm. Two weight vectors were used in the controller. controller. The controller with a long weight vector (L = 300) converged after 1 s, whereas the The controller with a long weight vector (L = 300) converged after 1 s, whereas the controller with controller with a short weight vector (L = 30) converged after 2 s. From Equation (15), the optimal a short weight vector (L = 30) converged after 2 s. From Equation (15), the optimal filter length is filter length is 18,000/RPM since ∆k is 2 and the sampling frequency is 3000 Hz. Therefore, the length 18,000/RPM since ∆k is 2 and the sampling frequency is 3000 Hz. Therefore, the length of the weight of the weight vector should be 300 since the minimum rotational speed is 600 rpm (10 Hz) for this vectorsignal. should As the be rotational 300 since speed the minimum increases, rotational the length speed of weight is 600 vector rpm (10 can Hz) be fordecreased this signal. for stable As the rotationalcontrol. In speed this increases,simulation, the the length controller of weight with a vector long weight can be decreasedvector (L = for 300) stable converged control. at In low this simulation,rotational speed, the controller but the with controlle a longr with weight a short vector weight (L = 300) vector converged (L = 30) atconverged low rotational at high speed, rotational but the controllerspeed. Figure with a9c,d short show weight the vectorshort-time (L = 30)Fourier converged transform at high (STFT) rotational for the speed. signals Figure controlled9c,d show by the the short-timeOW-LMS Fourieralgorithm. transform Expectedly, (STFT) at a for low the rotational signals controlled speed of less by thethan OW-LMS 1 s, the controller algorithm. with Expectedly, a short atweight a low rotationalvector still speedconverges of less as shown than 1 in s, theFigure controller 9c, whereas with the a short controller weight with vector a long still weight converges vector as shownhas converged, in Figure 9asc, shown whereas in theFigure controller 9d. Figure with 9e ashows long weightthe STFT vector for the has error converged, signal controlled as shown by in Figurethe conventional9d. Figure9 ealgorithm. shows the The STFT order for error the errorsignal signal was not controlled completely by theattenuated conventional by the algorithm.controller Thewith order the errorconventional signal was algorithm. not completely Figure attenuated9f shows a by comparison the controller of PSD with functions the conventional of error algorithm. signals Figureobtained9f shows by the a three comparison controllers. of PSDFrom functions these result ofs, error we determined signals obtained that the by OW-LMS the three algorithm controllers. is Fromsuperior these for results, the active we determined control of thata frequency the OW-LMS modulated algorithm signal is superior compared for theto the active conventional control of a frequencymethod. modulated signal compared to the conventional method. Appl. Sci. 2018, 8, 1394 14 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 22

5 5 off No-ANC L=30 on L=300

0 0 Sound Press (pa) Sound Press

-5 -5 012345 012345 Time(s) Time(s) (a) (b)

-60

-80

-100

-120

-140 No-ANC ANF-LMS -160 OW-LMS L=30 OW-LMS L=300 -180 0 200 400 600 800 1000 Frequency (Hz)

(e) (f)

Figure 9. Simulation for signal 2 controlled by the LMS-algorithm-based adaptive notch filter and the Figure 9. Simulation for signal 2 controlled by the LMS-algorithm-based adaptive notch filter and OW-LMS algorithm. (a) Time history controlled by LMS-algorithm-based adaptive notch filter; (b) the OW-LMS algorithm. (a) Time history controlled by LMS-algorithm-based adaptive notch filter; Time history controlled by OW-LMS algorithm; (c) Short-time Fourier transform (STFT) of signal 2 (b) Time history controlled by OW-LMS algorithm; (c) Short-time Fourier transform (STFT) of signal controlled by OW-LMS (L = 30); (d) STFT of signal 2 controlled by OW-LMS (L = 300); (e) STFT of 2 controlled by OW-LMS (L = 30); (d) STFT of signal 2 controlled by OW-LMS (L = 300); (e) STFT of signal 2 controlled by LMS algorithm-based adaptive notch filter; (f) Comparison of PSD of signal 2 signal 2 controlled by LMS algorithm-based adaptive notch filter; (f) Comparison of PSD of signal 2 controlledcontrolled by each algorithm.

4. OW-FxLMS Algorithm for ANC of Engine Noise 4. OW-FxLMS Algorithm for ANC of Engine Noise The active noise canceller of the OW-FxLMS algorithm can be used to eliminate intense The active noise canceller of the OW-FxLMS algorithm can be used to eliminate intense sinusoidal sinusoidal sounds with frequency modulation. This method is applied to engine noise cancellation sounds with frequency modulation. This method is applied to engine noise cancellation inside a vehicle inside a vehicle because the engine noise is dominant. The engine noise is comprised of multiple because the engine noise is dominant. The engine noise is comprised of multiple intense sinusoidal intense sinusoidal signals. This signal is synchronized with the rotating speed of the engine and is a signals. This signal is synchronized with the rotating speed of the engine and is a frequency-modulated frequency-modulated signal. Other noise sources such as wind noise, tire noise, and high noise signal. Other noise sources such as wind noise, tire noise, and high noise environments interfere with environments interfere with the engine noise [1]. the engine noise [1]. Figure 10 illustrates an active noise canceller for the engine noise of a vehicle. The canceller Figure 10 illustrates an active noise canceller for the engine noise of a vehicle. The canceller employs controller area network (CAN) bus data or a directional sensor to measure the employs controller area network (CAN) bus data or a directional sensor to measure the instantaneous instantaneous frequency fi corresponding to the rotating frequency of the engine, and four microphones to measure the interior noise containing engine noise and other noise. The measured instantaneous frequency is used for the generation of the reference signal. A recursive discrete-time Appl. Sci. 2018, 8, 1394 15 of 22 frequency f corresponding to the rotating frequency of the engine, and four microphones to measure Appl. Sci. 2018,i 8, x FOR PEER REVIEW 15 of 22 Appl.the interiorSci. 2018, noise8, x FOR containing PEER REVIEW engine noise and other noise. The measured instantaneous frequency15 of 22 is oscillatorused for the is generationused to generate of the referencethe reference signal. signal A recursive [23]. The discrete-time reference oscillatorsignal is isprocessed used to generate by the oscillator is used to generate the reference signal [23]. The reference signal is processed by the adaptivethe reference filter signalto equalize [23]. Theit with reference the engine signal no isise processed component by of the the adaptive primary ﬁlter noise to contaminated equalize it with by adaptive filter to equalize it with the engine noise component of the primary noise contaminated by thethe other engine noise noise signals. component It is subsequently of the primary subtract noiseed to contaminated cancel out the by engine the other noise noise component signals. in Itthe is the other noise signals. It is subsequently subtracted to cancel out the engine noise component in the primarysubsequently noise. subtracted to cancel out the engine noise component in the primary noise. primary noise.

Figure 10. Block diagram of active control of interior noise in a test vehicle based on the OW-FxLMS FigureFigure 10. 10. BlockBlock diagram diagram of active of active control control of interior ofinterior noise in noisea test vehicle in a test based vehicle on the based OW-FxLMS on the algorithm. algorithm.OW-FxLMS algorithm.

Figure 11 shows the block diagram of the FxLMS-algorithm-based adaptive notch filter and the FigureFigure 1111 showsshows the the block block diagram diagram of of the the FxLMS-algorithm-based FxLMS-algorithm-based adaptive adaptive notch notch filter filter and and the the OW- FxLMS algorithm for the application of ANC to engine noise inside a vehicle. In the FxLMS OW-OW- FxLMS FxLMS algorithm algorithm for for the the application application of of ANC ANC to engine noise inside a vehicle. In In the the FxLMS FxLMS -algorithm-based adaptive notch filter, two adaptive weights, wi1 (n) and wi2 (n), were used for each -algorithm-based adaptive adaptive notch notch filter, filter, two adaptiveadaptive weights,weights, wii1 ((nn)) and and wii22 ((nn),), were were used used for for each each order. In the OW- FxLMS algorithm, the adaptive weight vector w(n) with different filter lengths order.order. In the OW-OW- FxLMSFxLMS algorithm, algorithm, the the adaptive adaptive weight weight vector vectorw( nw)( withn) with different different filter filter lengths lengths was was used for each order. The length of each weight vector was related to the total delay of the ANC wasused used for each for each order. order. The lengthThe length of each of weighteach weight vector vector was related was related to the totalto the delay total ofdelay the ANCof the system. ANC system. The secondary path was considered for the application of ANC to engine noise. system.The secondary The secondary path was path considered was considered for the application for the application of ANC of to ANC engine to noise. engine noise.

(a) (b) (a) (b) Figure 11. Active noise cancelling system for attenuation of engine noise associated with multiple Figure 11. Active noise cancelling system for attenuation of engine noise associated with multiple harmonicFigure 11. orderActive components noise cancelling of the system engine for rotation attenuation frequency of engine using noise (a) associatedFxLMS-algorithm-based with multiple harmonic order components of the engine rotation frequency using (a) FxLMS-algorithm-based adaptiveharmonic notch order filter, components and (b) the of OW- the engineFxLMS rotationalgorithm. frequency using (a) FxLMS-algorithm-based adaptive notch filter, and (b) the OW- FxLMS algorithm. adaptive notch ﬁlter, and (b) the OW- FxLMS algorithm. Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 22

A sport utility vehicle was used for the application of ANC to interior noise. The test car is SNATAFE made by Hyundai motor company as shown in Figure 12. A 2.2 L diesel engine was used in the powertrain of this vehicle. The instruments used for the ANC were loaded inside the vehicle. The equipment used in the ANC system is shown in Figure 13.

Appl. Sci. 2018, 8, 1394 16 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 22

5. Application of the OW-Fxlms Algorithm to ANC of Interior Noise

5.1. Experimental Setup (a) and Procedure (b) (c)

FigurA sporte 12 utility. Test car vehicle for the was active used control for thethe of interior applicationapplication noise ( ofa) ANCerrorANC microphone toto interiorinterior; noise.noise.(b) the The secondary test car is SNATAFEspeaker mademade and controller byby HyundaiHyundai (c) controller motormotor companycomp monitor.any asas shownshown in FigureFigure 1212.. A 2.2 L diesel engine was used in the powertrain of this vehicle. The The instruments instruments used used for for the the ANC ANC were were loaded loaded inside inside the the vehicle. vehicle. The equipmentFour microphones used in thewere ANC used systemsy forstem the isis shownshownmeasurement inin FigureFigure of 1313.error. signals, and were attached to the roof of the vehicle. Five speakers were used as the secondary sound sources required to cancel the primary noise sources inside the vehicle [26]. The error signals were transferred to the input channels of a DSP control board (Ds 1104, dSPACE, Paderborn, Germany) via a signal conditioner (441-A42, PCB Company, Depew, NY, USA). The software used to implement the adaptive algorithm is MATLAB (Simulink, MathWorks, Natick, MA, USA). The pulse signal, including the speed data of the engine, was detected by a camshaft position sensor and transferred to the input channels of the dSPACE control board. Both input data streams were transferred to the control computer via an analog-to-digital (A/D) converter in the dSPACE control board. The pulse signal was used for the calculation(a) of the instantaneous(b) frequency and reference signal.(c) The reference signalFigure was convolved12. Test car byfor the the estimatedactive control impulse of interior response noise of(a )the error secondar microphone;y path. (b )The the signalsecondary was the Figure 12. Test car for the active control of interior noise (a) error microphone; (b) the secondary input x’(n) of the LMS algorithm. The adaptive filter w(n) was updated by using error data e(n) and speaker and controller (c)) controllercontroller monitor.monitor. input data x ‘(n). Four microphones were used for the measurement of error signals, and were attached to the roof of the vehicle. Five speakers were used as the secondary sound sources required to cancel the primary noise sources inside the vehicle [26]. The error signals were transferred to the input channels of a DSP control board (Ds 1104, dSPACE, Paderborn, Germany) via a signal conditioner (441-A42, PCB Company, Depew, NY, USA). The software used to implement the adaptive algorithm is MATLAB (Simulink, MathWorks, Natick, MA, USA). The pulse signal, including the speed data of the engine, was detected by a camshaft position sensor and transferred to the input channels of the dSPACE control board. Both input data streams were transferred to the control computer via an analog-to-digital (A/D) converter in the dSPACE control board. The pulse signal was used for the calculation of the instantaneous frequency and reference signal. The reference signal was convolved by the estimated impulse response of the secondary path. The signal was the input x’(n) of the LMS algorithm. The adaptive filter w(n) was updated by using error data e(n) and input data x’(n).

Figure 13. Equipment in the ANC system for active control of interior noise in a test vehicle. Figure 13. Equipment in the ANC system for active control of interior noise in a test vehicle. 5.2. Measurement of the Impulse Response of the Secondary Path Four microphones were used for the measurement of error signals, and were attached to the roofThe of the impulse vehicle. response Five speakers of the secondary were used path as the was secondary estimated sound by using sources the LMS required algorithm. to cancel A blockthe primary diagram noise for the sources estimation inside of the the vehicle impulse [26 response]. The error in the signals secondary were transferredpath is given to in the [26]. input A randomchannels white of a DSP signal control was used board as (Ds the 1104, input dSPACE, data because Paderborn, we assume Germany) that the via asecondary signal conditioner path is a linear(441-A42, system. PCB The Company, impulse Depew, response NY, of USA). the secondary The software path usedwas obtained to implement after thesufficient adaptive convergence. algorithm Theis MATLAB transfer function (Simulink, S(z MathWorks,) of the secondary Natick, path MA, was USA). obtained The pulseby performing signal, including the z-transform the speed for data the impulseof the engine, response. was The detected results by are a camshaftplotted inposition Figure 14 sensor. and transferred to the input channels of the dSPACE control board. Both input data streams were transferred to the control computer via an analog-to-digital (A/D) converter in the dSPACE control board. The pulse signal was used for the calculation of the instantaneous frequency and reference signal. The reference signal was convolved by the estimated impulse response of the secondary path. The signal was the input x’(n) of the LMS Figure 13. Equipment in the ANC system for active control of interior noise in a test vehicle. algorithm. The adaptive ﬁlter w(n) was updated by using error data e(n) and input data x’(n). 5.2. Measurement of the Impulse Response of the Secondary Path The impulse response of the secondary path was estimated by using the LMS algorithm. A block diagram for the estimation of the impulse response in the secondary path is given in [26]. A random white signal was used as the input data because we assume that the secondary path is a Appl. Sci. 2018, 8, 1394 17 of 22

5.2. Measurement of the Impulse Response of the Secondary Path The impulse response of the secondary path was estimated by using the LMS algorithm. A block diagramAppl. Sci. 2018 for the, 8, x estimationFOR PEER REVIEW of the impulse response in the secondary path is given in [26]. A random17 of 22 white signal was used as the input data because we assume that the secondary path is a linear system. Thelinear impulse system. response The ofimpulse the secondary response path of was the obtained secondary after path sufﬁcient was convergence.obtained after The sufficient transfer functionconvergence.S(z) of The the transfer secondary function path was S(z) obtained of the secondary by performing path was the z-transformobtained by for performing the impulse the response.z-transform The for results the impuls are plottede response. in Figure The 14 results. are plotted in Figure 14.

(a) (b)

Figure 14. Transfer function S(z) of the secondary path and impulse response s(n) of the secondary Figure 14. Transfer function S(z) of the secondary path and impulse response s(n) of the secondary path.path. (a ()a Transfer) Transfer function; function; (b ()b Impulse) Impulse response. response.

5.3. Application of Adaptive Algorithms to ANC for Interior Noise 5.3. Application of Adaptive Algorithms to ANC for Interior Noise In order to drive the vehicle with the ANC system on the road, five speakers, a control In order to drive the vehicle with the ANC system on the road, five speakers, a control computer, computer, monitor, and the dSPACE control board were placed in the test vehicle, and the monitor, and the dSPACE control board were placed in the test vehicle, and the microphones microphones were attached to the roof of the test vehicle. In this case, a multichannel ANC system were attached to the roof of the test vehicle. In this case, a multichannel ANC system was used. was used. The algorithm is the expansion of a channel ANC. The Simulink based block diagram The algorithm is the expansion of a channel ANC. The Simulink based block diagram used for this used for this test is plotted as shown in Figure 15. There are 5 subsystems which include adaptive test is plotted as shown in Figure 15. There are 5 subsystems which include adaptive order filter order filter and OW-FXLMS algorithm to control the interior noise measured by 4 microphone and 5 and OW-FXLMS algorithm to control the interior noise measured by 4 microphone and 5 secondary secondary speakers. S1, S2, S3, S4 and S5 means the secondary speaker and M1, M2, M3 and M4 speakers. S1, S2, S3, S4 and S5 means the secondary speaker and M1, M2, M3 and M4 means the means the microphone attached in the car. The primary source which was recorded inside of test car microphone attached in the car. The primary source which was recorded inside of test car and supplied and supplied to the multi-channel ANC system. In each subsystem, the OW-FXLMS algorithms to the multi-channel ANC system. In each subsystem, the OW-FXLMS algorithms update the adaptive update the adaptive filter using the error signals (E1, E2, E3, E4) measured from 4 microphones and filter using the error signals (E1, E2, E3, E4) measured from 4 microphones and primary source signal. primary source signal. For example, the output of subsystem 1 is the sound signal for speaker S1 For example, the output of subsystem 1 is the sound signal for speaker S1 sound and error signals (e1j) sound and error signals (e1j) which is related to each j-th reference order signal. The sum of error which is related to each j-th reference order signal. The sum of error signals (e1j) is the error signal of signals (e1j) is the error signal of M1. In the real time process, primary source is not necessary and M1. In the real time process, primary source is not necessary and the signals from error microphones the signals from error microphones become noise source signal. become noise source signal. Appl. Sci. 2018, 8, 1394 18 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 18 of 22

Figure 15. Multichannel ANC algorithm with 5 subsystems used for this test based on Simulink. Figure 15. Multichannel ANC algorithm with 5 subsystems used for this test based on Simulink. When the engine speed increased under a no-load condition, the ANC system was operated and theWhen sound the pressureengine speed of the increased interior noise under was a measuredno-load condition, by error microphones.the ANC system The was engine operated speed wasand increasedthe sound frompressure 1000 of rpm the to interior 4500 rpm. noise The was engine measured was underby error the microphones. no-load condition The engine for this speed test, andwas theincreased engine from speed 1000 was rpm increased to 4500 rapidly rpm. The from engine 800 rpmwas atunder idle the to 4500 no-load rpm condition during the for course this test, of 2and s. Figurethe engine 16a speed illustrates was increased a comparison rapidly of thefrom time 800 history rpm at ofidle the to interior4500 rpm noise during at the the drivercourse seat, of 2 whichs. Figure was 16a controlled illustrates by a comparison two active control of the time systems. history Figure of the 16 interiorb illustrates noise the at the spectrum driver seat, analysis which of thewas interior controlled noise by signal. two active The PSDcontrol of thesystems. interior Figure noise 16b signal illustrates was reduced the spectrum to 30 dB analysis above 80of Hz.the Figureinterior 16 noisec,d illustrate signal. The the resultsPSD of of the order interior analysis nois ofe signal the interior was reduced noise. At to 1200 30 dB rpm, above there 80 is Hz. a booming Figure noise,16c,d andillustrate the other the results wide booming of order noise analysis occurred of the from interior 3000 tonoise. 4500 At rpm. 1200 These rpm, booming there is noisesa booming were attenuatednoise, and bythe the other controllers. wide booming The controller noise occurred with the OW-from FxLMS3000 to algorithm 4500 rpm. with These a short booming filter lengthnoises (wereL = 30) attenuated demonstrated by the the controllers. best performance The controller among with the threethe OW- algorithms. FxLMS algorithm Since the optimalwith a short length filter of weightlength vector(L = 30) is demonstrated 18,000/RPM, a the short best filter performance length (L = among 30) is sufficient the three for algorithms. the control Since of these the booming optimal noises.length of This weight algorithm vector achieved is 18,000/RPM, a significant a short reduction filter length in the (Linterior = 30) is noisesufficient around for the 4500 control rpm, which of these is thebooming second-order noises. boomThis algorithm noise as shown achieved in Figure a significant 16c,d. The reduction sound pressurein the interior level (SPL) noise of around the interior 4500 noiserpm, which was reduced is the second-order to 25 dB. boom noise as shown in Figure 16c,d. The sound pressure level (SPL) of theThis interior booming noise noisewas reduced corresponds to 25 todB. the resonance of the second path, as shown in Figure 14. The OW-FxLMSThis booming algorithm noise corresponds with a long lengthto the resonance (L = 300) and of the the second FxLMS-algorithm-based path, as shown inadaptive Figure 14. notch The filterOW-FxLMS reduced algorithm the booming with noise, a long but length not sufficiently, (L = 300) and since the the FxLMS-algorithm-based frequency bandwidth ofadaptive the adaptive notch filtersfilter reduced used for the these booming algorithms noise, is but too not narrow sufficient to reducely, since wideband the frequency noise, ba andndwidth the speed of the is changedadaptive filters used for these algorithms is too narrow to reduce wideband noise, and the speed is changed too quickly (within 2 s). The disadvantage of the OW- FxLMS algorithm with a long length (L = 30) is too quickly (within 2 s). The disadvantage of the OW- FxLMS algorithm with a long length (L = 30) is the generation of a beating sound at idle speed owing to its wide bandwidth. However, the sound the generation of a beating sound at idle speed owing to its wide bandwidth. However, the sound pressure of the beat noise was too low to be heard. pressure of the beat noise was too low to be heard. Appl. Sci. 2018, 8, 1394 19 of 22 Appl. Sci. 2018, 8, x FOR PEER REVIEW 19 of 22

2 5000 OFF ANF 4500 1.5 L300 L30 RPM 4000 1

3500 0.5 3000 0 2500 Rpm -0.5

Sound Press (pa) 2000

-1 1500

-1.5 1000

-2 500 012345678910 Time (s) (a) (b)

Figure 16. Comparison of sound pressure level (SPL) controlled actively by the Figure 16. Comparison of sound pressure level (SPL) controlled actively by the FxLMS-algorithm-based FxLMS-algorithm-based adaptive notch filter and the OW-FxLMS algorithm at the driver seat. The adaptive notch ﬁlter and the OW-FxLMS algorithm at the driver seat. The driving conditions are a driving conditions are a no-load condition and fast run-up. (a) Time history; (b) PSD; (c) Overall level no-load condition and fast run-up. (a) Time history; (b) PSD; (c) Overall level of SPL; (d) SPL of the secondof SPL; order.(d) SPL of the second order.

5.4. Performance of the ANC System with OW-FxLMS 5.4. Performance of the ANC System with OW-FxLMS Figure 17 shows the sound pressure of the interior noise in the test vehicle while driving on the Figure 17 shows the sound pressure of the interior noise in the test vehicle while driving on the road. The upper solid line is the SPL of the interior noise, and the lower dotted line is the actively road. The upper solid line is the SPL of the interior noise, and the lower dotted line is the actively controlled SPL. Figure 17a shows the overall sound pressure, and Figure 17b shows the sound controlled SPL. Figure 17a shows the overall sound pressure, and Figure 17b shows the sound pressure pressure of the second-order component of the engine rotating frequency. The second order is of the second-order component of the engine rotating frequency. The second order is generally related generally related to the booming noise. The engine was under full load for this test while driving the to the booming noise. The engine was under full load for this test while driving the car on the road car on the road and the engine speed increased rapidly from 1000 to 4500 rpm during the course of and the engine speed increased rapidly from 1000 to 4500 rpm during the course of 10 s. In this case, 10 s. In this case, the higher orders were not controlled because the calculation speed of the ANC the higher orders were not controlled because the calculation speed of the ANC system was beyond the system was beyond the capacity of dSPACE, and the noise of the second order was dominant. From capacity of dSPACE, and the noise of the second order was dominant. From these results, we suggest these results, we suggest that the new ANC system using the OW-FxLMS algorithm performed well that the new ANC system using the OW-FxLMS algorithm performed well in reducing the sound in reducing the sound pressure of the interior noise related to the harmonic components of engine pressure of the interior noise related to the harmonic components of engine rotating speed. Figure 18 rotating speed. Figure 18 shows the performance of the ANC system with the new algorithm for full shows the performance of the ANC system with the new algorithm for full load condition of the engine. load condition of the engine. Figure 18a,b the results of active noise cancellation at left seat (driver Figure 18a,b the results of active noise cancellation at left seat (driver seat) and at right seat (passenger seat) and at right seat (passenger seat) respectively. seat) respectively. Appl.Appl. Sci. 2018,, 88,, 1394x FOR PEER REVIEW 2020 ofof 2222 Appl. Sci. 2018, 8, x FOR PEER REVIEW 20 of 22

(a) (b) (a) (b) Figure 17. Performance of the ANC system with the new algorithm. (a) Overall level; (b) Second Figure 17.17. PerformancePerformanceof of the the ANC ANC system system with with the the new new algorithm. algorithm. (a)Overall (a) Overall level; level; (b) Second (b) Second order. order. The driving condition is the road condition. (Solid line: ANC off. Dotted line: ANC on.). Theorder. driving The driving condition condition is the road is the condition. road conditio (Solidn. line:(Solid ANC line: off. ANC Dotted off. Dotted line: ANC line: on.).ANC on.).

(a) (a)

(b) (b) Figure 18. Performance of the ANC system with the new algorithm for full load condition of the Figure 18. Performance of the ANC system with the new algorithm for full load condition of the Figureengine. 18. (a)Performance Left seat (driver of the seat) ANC and system (b) right with seat the new(passenger algorithm seat) for (S fullolid load line: condition ANC off. of Dotted the engine. line: engine. (a) Left seat (driver seat) and (b) right seat (passenger seat) (Solid line: ANC off. Dotted line: (ANCa) Left on.). seat (driver seat) and (b) right seat (passenger seat) (Solid line: ANC off. Dotted line: ANC on.). ANC on.).

6. Conclusions 6. Conclusions We presentpresent aa newnew algorithmalgorithm toto controlcontrol thethe engineengine noisenoise inin thethe cabincabin ofof aa car.car. TheThe proposedproposed We present a new algorithm to control the engine noise in the cabin of a car. The proposed algorithm is called the OW-FxLMSOW-FxLMS algorithm,algorithm, which uses an adaptive filterfilter with an optimaloptimal filterfilter algorithm is called the OW-FxLMS algorithm, which uses an adaptive filter with an optimal filter length. The optimal filter length is determined to have a frequency bandwidth less than the length. The optimal filter length is determined to have a frequency bandwidth less than the Appl. Sci. 2018, 8, 1394 21 of 22 length. The optimal filter length is determined to have a frequency bandwidth less than the frequency bandwidth between the orders to be controlled by the controller. This algorithm is suitable for the reduction of engine noise associated with the rotating frequency of the engine. In the last thirty years, many algorithms have been developed for the control of engine noise. In this study, as a representation of the conventional methods, the performance of the FxLMS-algorithm-based adaptive notch filter was tested for comparison with the performance of the new algorithm. Three signals were synthesized for the simulation. According to our simulation results, both algorithms are suitable for the control of a sinusoidal signal with constant frequency. However, the OW-FxLMS algorithm is superior to the conventional algorithm for the control of amplitude- and frequency-modulated sinusoidal signals, such as the engine noise with fast frequency change when the car is accelerated for a short time. The algorithm was applied to the control of booming noise in a sport utility car to test the practical implementation of the proposed algorithm. The SPL of the interior noise of this test car was actively controlled by this algorithm, and was attenuated to 25 dB under a no-load condition, whereas the reduction of the sound pressure was attenuated to 2–3 dB by the conventional algorithm. Finally, the ANC system with the proposed algorithm was used to control the interior noise while driving on the road. Under full engine load, the SPL of the interior noise in the test vehicle was significantly reduced. The performance of the new ANC system is therefore, excellent for the attenuation of engine noise in the cabin of a car.

Author Contributions: S.-K.L. contributed to simulation and algorithm development and writing the paper. S.L. contributed to Simulink programming. T.S. contribution to the vehicle experimental test. Funding: This work was supported by Mid-career Researcher Program through NRF of Korea grant funded by the MEST (No. 2016R1A2B2006669). Acknowledgments: This work was supported by Inha University. Conﬂicts of Interest: This work was supported by Inha University.

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