Musical-Noise-Free Blind Speech Extraction Using ICA-Based Noise Estimation with Channel Selection

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(1)International Workshop on Acoustic Signal Enhancement 2012， 4 -6 September 2012， Aachen. MUSICAL-NOISE-FREE BLIND SPEECH EXTRACTION USING ICA-BASED NOISE ESTIMATION WITH CHANNEL SELECTION ↑Ryoichi Miyazaki，↑Hiroshi Saruwatari，↑Kiyohiro Shikano， +Kazunobu Kondo ↑Nara Institute of Science and Technology， Nara， 630-0192 Japan +Yamaha Corporate Research & Development Center， Shizuoka， 438・0192 Japan. ABSTRACT. In this paper， we propose a modified musical-noise-free blind spatial subtraction array (BSSA) based on JCA-based iterative nois巴 estima tion with channel selection. Jn our previous study， w巴 have proposed a modified BSSA consisting of dynarnic noise estimation by JCA組d musical-noise-fr巴e iterative sp巴ctral subtraction (SS)， where multiple iterative SS are applied to each of chann巴ls. This method achieves less musical noise property， but instead always suff<巴rs from large speech distortion because of no justification of applying lCA to such signals nonIinearly distorted by ss. ln this paper， first， we出巴orelI cally clarify that the degradation in JCA obeys an amplitude variation in room transfer functions between th巴 target user and microphones. Next， we introduce a channel sel巴ction strategy into ICA， where w巴 automatically choos巴 less varied inputs to maintain high accuracy of noise estimation. From objective and subjectiv巴巴vah胤聞lS， we re veal that the proposed method outperforms the conventional method lndex TermsーBlind speech extraction， musical-noise-free， higher-order statistics， channel selection 1. INTRODUCTION. To achieve high-quality speech 巴nhancem巴nt， n01ωreduction using a microphone array has been widely studied [1]. ln recent y回rs， we previously proposed a blind spatial subtraction array (BSSA) [2] that consists of accurate noise estimation by ind巴pendent compo nent analysis (ICA) [3] and the following speech 巴xtractlOn proω dure based on nonlinear noise r巴duction such as spectral subtraction (SS) [4]. Ho岬ever， BSSA always suffers from artificial distortion， so-called musical noise， owing to nonlinear signal processing. To solve this probl巴m， we have proposed iterative BSSA [5] consisting of dynamic noise estimation by JCA and musical-noise free iterative SS [6]， where multiple iterative SS ar官appliedωeach of channels. This method can generate almost no musical nois巴 even with increasing noise reduclion， but inSlead always su仔ers from l紅ge speech distortion because of no justification of applying lCA to such signals nonlinearly distorted by SS Therefo叩， in this paper， first， we出回retica11y clarify出直t白e d巴gradation in lCA ob巴ys an amplitude variation in room transfer functions between the target user and microphones. Next， to re duce speech distortion， we introduce a channel selection s汀ategy mto ICA， where we automatically choo唱巴 less varied inputs to maintain high a心curacy of noise estimation. From the evaluation experiments， it was shown that iterative BSSA with channel selection outperforms the conventional iterative BSSA in terms of speech distortion， but， there is a 汀ade-o仔 between the amount of musical nois巴E巴neraUo日 This work was supported by the MIC SCOPE， and JST Core Research of Evolution Science and Technology (CREST)， Japan.. and speech distortion at the conventional BSSA and iterative BSSA with channel selection. In the pr巴ference test， iterative BSSA with channel selection indicated a higher preferenc巴 score than the con ventional BSSA. Thus， iterative BSSA has an advantage in terrns of total sound quality over the conventional BSSA 2. RELATED WORKS 2.1. Conventional non-iterative SS [4]. w巴 apply short-time Fourier analysis to th巴 observed signal， which is a mixture of target speech and noise， to obtain the time-fr巴quency signal. We formulate conventional non-iterative SS [4] in the time frequ巴ncy domain as follows:. y(f， T). =<. { ゾIx(f， T)12ーβE[INI2] exp(jarg(x(f， T))) (if Ix(f， TW > ßE[INI2])， l ηx(f，T) (otherwise)，. (1). where y(f， T) is the enhanced target speech signal， x(f， T) is the observ巴d signal， f d巴notes th巴 frequency subband， T is the frame index， ß is the oversubtraction parameter， and ηis the flooring pa rameter. Here， E[ INI2] is the expectation of the random variable INI2 co汀巴sponding to the noise power spectra. 2.2. Iterative SS [7]. To achieve high-quality noise reduction with low musical noise， an improved method based on iterative SS was proposed in previous studies [7]. This method is perforrned through signal proc巴ssmg， m which the following weak SS processes are recursively appli巴d to th巴 noise signal. (1) Th巴 average power sp巴ctrum of th巴 input noise is estimated. (11) The estimated nois巴 prototyp巴 is then subtracted from 出e input with the par釘neters specifica11y set for weak subtraction， e.g.， a large flooring parameterηand a small subtraction parameter β. (III) W，巴then retum to st巴p (1) and substitute the r巴sultant output (partially noise reduced signal) for the input signal. 2.3. Mathematical metric of musical noise generation via higher order statistics for non-iterative SS [6]. In this study， we apply the kurtosis ratio to a noise-only rime frequency period of th巴 subject signal for th巴 ass巴ssment of musical. noise [6]. This meas町e is defined as kurtosis ratio. = kurtproc/kurtorg，. (2). wher巴kurtproc is the kurtosis of th巴 processed signal and kurtorg is the kurtosis of the observed signal. Kurtosis is defined as. kurt=μ4/μ1. (3).

(2) Jooo. Aσ ，，，，， z. p x e α -. α 一α Z一町. 一一. z p. 。一 →. xmP(x )dx， whereμm is themth引der moment given byμm = and P(x) is the proba幼bilitザy d巴nsi幻ity flωu山I削 doma創1汀lß】 s剖ignal x. A kurtosis ratio of unity corresponds to no musical noise. This m巴asure increases as th巴 amount of generat巴d musical nOlse Ißcreases. In this paper， we assume that the input signal x in the power sp巴ctral domain is mod巴l巴d using the gamma distribution as. = Jooo. (4). wh巴re，αis the shape paramet巴にo is the scale parameter， and r(α) t'Jt-l exp ( - )d . IS批伊una function， defined as r(α) Using (4)， the mth-order moment after SS，μm， is given by [6]. t t. μm=O;;'M(αn，ß，η，m)，. (5). where On andαn ar巴 the scale and the shape parameter for noise， and. M(αn，ß，η，m). =). ι t r(m+ l )r(αn+m-l，βαn) :( 一βαn) 一一ハー一'. 2 + η mγ(αn+m，βαn)/r(αn).. 一一tの). (6). r(b，α) and γ(b，α)訂巴 the upp巴r and lower incomplet巴 gamma functions d必E負fìn巴ed aおs r(伊b，α吋) = and γ(作b，α吋) = 1 叫( dtム， respe氏倒削ct叩tive均 From (2勾)， (σ3)， (5幻)， and (6め)， t山h巴. J:taα. Jboo ta-→le目xp(←一tの)d必t. kurtosis ratio aft巴r SS can be expr巴ss巴d as kurtosisratio =. 2 (αn，ß，η，2) ん1(αn，β，η，4)/ん1 ，-��--'&Jr;..I :1 ��'I.. ��--U l ':.';:I�:. M(αn，0，0，4)/M2(αn，0，0，2). (7). Fig. 1. Block diagram of iterativeBSSA.. 3. THEORETICAL ANALYSIS OF DEGRADATION II唱ICA AND ITS IMPROVEMENT 3.1. Accuracy of wavefront estimated by ICA after SS. In this subsection， we discuss the accuracy of the estimated noise sig nal in each iteration of iterativeBSSA to clarify why i印刷iveBSSA distorts the speech component. In actual environments， not only point-source noise but also non-point-source ( e.g.， diffuse) noise of ten exists. It is known白紙ICA is proficient in noise estirnation rather than speech estimation under such a noise condition [2]. This is b巴cause the target speech can be regard巴d as a point-source sig nal (thus， th巴 wavefront is static in 巴ach subband) and ICA acts as an effective blocking fiIter of the speech wavefront even in a time Ißvanant mann巴r， resulting in good noise estimation. However， in iterative BSSA， we should address the inherent question of whether the distorted speech wavefront after nonlinear noise reduction such as SS can be blocked by ICA or not; thus， the speech component after channel-wis巴 SS can become a point sourc巴 agalß or not. Hereaft巴r， we quantify the degree of point-source-liken巴ss for SS叩pli巴d spe四h signals. For convenience of discussion， a simple two-channel array model is assumed. First， we defin巴血e speech component in each channel after channel-wise SS as. =. 2.4. Musical-noise-free speech enhancement. れ(1，r) =ん(!)s(f，r) +ムsl (1，r )，. (8). In [6]， we have proposed musical-noise-free noise r巴duction， wher巴 no musical noise is generated even for a high SNR in iterative SS. The authors have deriv巴d the optimal parameters satisfying the musical-noise-台ee condition by finding a fixed-point status in由E kurtosis ratio [6]. Given the noise shape paramet巴r αn， we can choose combinations of the oversubtraction parameterβand the flooring p紅arneterηthat simultaneously sati均the musicaトnoise free cond】tlOn.. ゐ(1，r). (9). 2.5. Conventional BSSA and iterative BSSA. In the previous musical-nois巴・free noise r巴duction， we assum巴d that th巴 input noise signal is stationary， m巴aning that we can estimate the expectation of a noise signal from a time-frequency period of a signal that contains only nois巴， i.e.， speech absence. However， in actual environments， e.g.， a nonstationary noise field， it is necess紅y to dynarnically estimate the nois巴 power spectral d巴nSlty. To solve this problem， we previously proposedBSSA [2]， which involves a∞urate noise estimalion by ICA followed by a speech 巴x traction procedure bas巴d on SS. BSSA improves the nois巴 r巴duc tion performance， particularly in the pres巴nce of both of diffuse and nonstationary noises. However，BSSA always suffers from musical noise owing to SS. To achieve low musical noise g巴n巴ration， we have r巴cently pro posed iterative BSSA [5] (see Fig. 1). This method consists of iter ative blind dynamic noise estimation by ICA and musical-noise-fr巴E spe巴ch extraction by modified iterativ巴 SS， where multiple iterative SS is applied to each channel while m 創ntaining the multトchannel property reused for ICA. The main drawback of this method is a generation of large speech distortion， instead of less musical noise.. h2(1)s(f，r) + ßS2(1，r)，. where 5k(l，r) is the speech component after channel-wise SS， hk(1) is the transfer function from th巴 target signal position to each. microphone at the kth channel， and ムsk(!，r) is the speech com ponent d凶tort巴d by channel-wise SS. AIso， we assume that s(f， r ) ，ムsl(1，r)， and ßS2(1，r) are uncorrelated with each other. Obvト ously， 51(1，r) and 52(1，r) can be regard巴d as being gen巴削ed by a point source if ßSl(1， r) and ßS2(1， r ) are zero， i.巴， a valid static blocking filter can be obtained by ICA. However，江ムsl(1，r) and ßS 2(1， r ) become nonzero as a result of SS， ICA does not have a va1id speech blocking filter with a static (time-invariant) form Second， the cosine distance between spe巴ch power spectra 2 151(1，r)1 and 152(1，rW is introduc巴d in each frequency subband to indicate the degree of point-source-likeness， as. Z.，. 15 1 ( J，r W I 52( J，r W. COS(f) = Iー. ム 'ー. 、. 、. 宇 'ー. 、. ・. (10). From (10) ， th巴 cosine distance reaches its maximum valu巴 of unity if and only ifムsl(1，r) =ムS2(1，r) = 0， regardless of the val U巴s of hl(1) and h2(1)， meaning that the SS-applied speech signals 51(1， r) and 52(1，r) can be assum巴d to be produced by the point source. The value of COS(I) decreases with increasing magnitudes ofムSI (1，r) andムS2(1，r) as well as th巴 di仔erence b巴tween hj (1) and h2(1); this indicates the non-po川-source state. Third， we evaluate th巴 degre巴 of point-source-likeness in each iteration of iterative BSSA by using COS(I). We statistically estト mate the distort巴d speech component of the enhanced signal in each iteration. Her巴， we assume that the original speech power spectrum.

(3) 0. Value 01 TFR(I) 2 (Ih1(1)/h2(1)1 ). 0.9. 一0-ー1.0. 20 8 '". 一仁〉ー0.9. � 0.7. ーゼ:;-0.8. c 帥. 80.6 0.5 ト 3. I=1 1 4. 5. 4 2 15 5 4. で5 i=6 i=7. 争、_:. 6. 7. 8. ー〈トー0.7. -・←-0.6. -・1-0.5. 9 10 11 12 13 14 15. 。o. 一合「ー0.4. Noise reduction rate [dB]. Fig.2. Relation between number of iterations of iterative BSSA and cosine distance. Input SNR is 0 dB.. Is(f，r)12 obりs a gamma distribution with a shape pararr削er ofO.1. (this is a typical value for speech). Also， the amount of residual noise after the ith iteration is given. ， . μtiJ = 9nMi(αn， ß，η1)α�-i. ( 1 1). Next， we assum巴 that speech and noise are disjoint， i.e.， th巴r巴 are no overlaps in the time-frequency domain， and that speech distortion is caused by subtracting the average noise from the pure speech com. ponent. Thus， the sp悶h component Ist+1J(f，rW at the kth chan n巴1 aft巴r the ith iteration is repres巴nt巴d by subtracting the amount of residual nois巴 (1 1) as. 1 Ist+ J(f，r)12 =. ， ( IsrJ(f，r)12 - ß9nMi(αll， ß，η1)αl-t (ifjstJ(frW ， >β9nM'(αu， ß，η1)α�--i) ，， (otherwise) ， l '1)2lstJ(frW. �. (12). Here， we define the input SNR as the average of both channel SNRs，. の1&ーフフ ISNR(f) = 一一ょ(lh1(fW + Ih (f)I< ). 2 2αn9n If we normalize the sp巴巴ch scale parameter the noise scale parameter 9n is giv巴n by. 9s to unity， from. 。n = 0.1(lh1(f)12 + Ih (f)12)/(2αnISNR(f)). 2. (13) (13)，. (14). Furthermore， we de血児白E住ansfer function ratio (TFR) as. TFR(f) = Ih1(f)/ h (f)12， 2. (15). and if we normalize Ih1 (f)12 to unity in 巴ach台叫uency subband， Ih1(fW + Ih (fW b巴comes1 +1/TFR(f). Finally， we express 2 (12) in lerms of ISNR(J) and TFR(f) as. (. l st+勺，r)12 =. ldl…O.l(関川βη1)αJ (if IstJ(f，rW > ßQ勺2415(mM'(αn， ß，η1 ， )αご)， rwise ) '1)2IstJ(f，rW (othe. (16). As can be seen， the speech component is subjected to greater sub traction and d凶tortion as ISNR(f) and/or TFR(f) d巴crease. Figure 2 shows the relation between the TFR and the corre sponding value of COS(f) caJcuJat巴d by (10) and (16)目In Fig. 2， we plot th巴 av巴rage of COS(f) over the whole frequency subbands.. 1000 2000 3000 4000 5000 6000 7000 8000 Frequency [Hz). Fig. 3. Typical 巴xampl巴s of TFR(f) (lh1 (f)/九 (fW ) in each fre 2 quency subband， where solid and broken Iines are different combi nations of microphones. The nois巴 shape parameterαn is set to 0.2 with the assumption of super-Gaussian noise， the input SNR is set to 0 dB， and th巴TFR is set from 0.4 to 1.0 (1ん(f)1 is fixed to 1.0). Note that the宵R is highly correlated to the room reverberation and the intereJ巴ment spacing of th巴 microphone array; we d巴termined the range of th巴 TFR by simulating a typical moderately reverberant room and the ar ray with 2.15 cm interelement spacing us巴d in S巴ct. 4. From Fig. 2， when the TFR is dropped to 0.4 and i is mor巴 than 3， th巴 d巴gre巴 of pomt-sourc巴-Iikeness is lower than 0.6. Thus， more than 40% of the speech components cannot be regarded as a point source， and this leads to poor noise estimation. 3.2. Channel selection in ICA. In this subsection， we propose a channel s巴lection strategy in ICA for achieving high accuracy of noise estimation. As mentioned prevト ously， speech distortion is su句ect吋to ISNR(f) and TFR(f)， and the accuracy of noise estimation is degrad巴d along with its sp巴巴ch distortion. Figure 3 shows a typical 巴xample of the TFR. From Fig. 3， we can confirrn that the TFRs in different combinations of microphon巴s are nol the same in 巴ach frequency subband; in a spe cific fr巴quency， one microphone pair has higher TFR(f) than an other pair， and vice versa in another fr巴quency. Thus， we are abl巴 to seJect the appropriat巴 combination of the microphones to obtain higherTFR. Therefore， we introduce the channel s巴lection method into ICA in each frequency subband， where we automatically choose less var ied inputs to maintain high accuracy of noise estimation. Hereafter， we d巴scribe the detail of the chanr】巴1 selection method. First， we cal culate the average power of th巴 observed signaJ Xk(f，r) at the kth chann巴1 as. ，. Er [IXk(f， r ) 12] =Er[IS(f，r)12]lhk(f)12 + Er[lnk(f， r)12].. (17). Her巴 Er[ls(f，rW ] is a constant， and iげfw巴 as“m則s乱su叩H川r町町I 白eld， E rベ[1同ηkバ(fr吋)川|門2可 ] i凶s als加sωoa c∞o叩nsta伽n川t. Thus， we can estimate the ， relative order of Ihk(f)ドby comparing (17) for every k. Next， we sort Er[lXk(f， r ) 12] in descending order and select the channels k corresponding to high amplitude of Ihk(f)ド satisfying the following condition. mFL[|ZK(fr)|21・5三Er[lxk(f，rW]，. (18). where ç( <1) is th巴 threshold for the selectiol】. Finally， we perform noise estimation bas巴d on ICA using the select巴d channels in each frequency subband， and we apply the pro jection back operation to remove the ambiguity of the amplitude and cons廿uct the estimated noise signal.

(4) 一o-川= 一 -K一-. S二計 e二一川二. A'' vト ' 一T il l-. 一. ea -一一IhH M 一一 -F. 』 wk d V4副畑町M 一R S M. n 日 a副 uh. E c l. 凶. ・ n o ・ 1. c. FL W 叶 ea. E. ' ' 凶. m. 創. d. d. 14s. ・』-u 05. a. u ・. i M. 窃。00 盟百官』モO一】 - 由主 co. 5 I s O. r. 一w二一A一一一S一一. A= 一I. 一一一 “日一e. 一町一戸. 一・一. uuuuu u e. u. k. Since we found the above-mentioned 汀ade-o仔， w巴 next conducted a subjective evaluation for settling the performance competition. In this evaluation，we presented a pair of signals process巴d by the con v巴ntional BSSA and new iterative BSSA in random order to eight examinees， who selected which signal they pref，巴町巴d. The result of the experim巴nt is shown in Fig. 6. It is found that new iterative. -----EC H -n a a d 1 1 1 1 1 3 4 1 ー1 1 111 -u h. 4.3. Subjective evaluation. f O U. First， Fig. 4 shows the typical example of the number of s巴lect巴d chanr】巴Is in each fr巴quency subband based on the propos巴d channel sel巴ctlOn m巴thod for museum noise，and th巴 threshold ç】s set to 0.5. As shown Fig. 4， we use di仔'erent number of microphones in ICA in each frequency subband. This indicates that th巴 channel selection method automatically removes the undesirable channel(s) that has a risk of decreasing the degree of point-sourc巴ーlikeness. Next， Fig. 5 shows a exampl巴 of behaviors for the proposed iterative BSSA under each of noise conditions. ln these 白gures， we depict血e values of the kurtosis ratio defin巴d by (2) and cep合 stral distortion at each iteration; these scor巴s indicat巴 the創nount of musical noise generat巴d and spe巴ch distortion， respectively. The kurtosis ratio for iterative BSSA with/without channel selection in Fig. 5 (a ) is close to 1.0， meanir】g that musical-noise-fr.巴巴 nOlse re duction is achieved. AIso， Fig. 5 (b) shows that speech distortion of the propos巴d iterative BSSA with channel selection is lower than that of the original iterativ巴 BSSA. However，as shown in Fig. 5 (b)， a trade-o仔 exists between the amount of musical noise generation and speech distortion in the conventional BSSA and the proposed iterative BSSA except for the entrance hall noise cas巴.. c. 4ふObjective evaluation. l. We conduct巴d objectiv巴 and su同巴ctive evaluation experiments to confirm出e validity of the proposed method. We used an eight element microphon巴 array with an interelement spacing of 2.15 cm， and the direction of the target speech was set to be normal to th巴 ar ray. The size of the experimental room was 4.2 x 3.5 x 3.0 m3 and the r巴verberation time was approximately 200 ms. AlI the signals used in this experiment were sampled at 16 k Hz with 16-bit accu racy. The observed signal consisted of the target signal of six speak ers (three males and thr巴e females) and four types of reaトrecorded diffuse noise (museum noise，railway station noise，回血c noise，加d entrance hall noise) 巴mltt巴d from eight suπounding loudspeakers. Th巴 input SNR was 0 dB. The FFT size was 1024，and th巴 frame shift length was 256. We compare the proposed method with the conventional BSSA and iterative BSSA under the same noise reduc tion rate (NRR) [2] condition， wh巴re the NRR is set to 10 dB.. E. 4.1. Experimental conditions. ・. 4. EVALUATION EXPERIMENTS AND RESULTS. m E. 5 E 4 L 劃・. F 比M nu. Fig. 4. Typical example of number of sel巴cted channels.. 4 Ill111. 8000. 一一 A一「l l 一一、加 5 VA-九日一-日二. 7000. E仇一一一. 6000. ・・・・・・』附 -創 /一ソ T. 5000. 1 1 』刷 M Ja h Rs L 圃m a u -au. 4000. Frequency [Hz]. e h二二一 m F」二. 氏二一 ] 二 -n二一町二 ) -川一-a 一- ，。、 -r-. 3000. : E. 回一川コ nu 《U n ltH 一 @ 一一一一一 : 一一 -川匂置二凶 = 一回 E -H こ ;1 、J 斗内O ' ' 必 B内4 UH E U i I | hH ] l l 一二時割二 E i - I r i 二 -泊 E w n 川 i j i 」t 副一・ ; i 時時・」二。，』 ‘， O Z 伺』 ω a o t コ￥. 一一m一「 qd 一円u 口一一. nu aU 7' au 民d AU寸qu n4 4，同一也 c c g 七万曲目U 由一由的』O 』由 a E コ Z. 1000 2000. (b). 口Conventional BSSA ト斗95% confidential interval 図Iterative BSSA with channel se. ぶぶミミぶぶぶぶぷぶぶぶ際社→ Preference 5∞re [%] 日g. 6. Su対ective evaluation result.. BSSA gains a higher preference score than the conv巴ntional BSSA， indicating the higher sound quality of the proposed method in terms of human perception. 5. CONCLUSION. In出is paper， we propose a modified musical-noise-free BSSA based on ICA-based iterative noise estimation with channel selec tion. From 0句巴ctive and Sl判巴ctive evaluation 巴xperiments，it巴rative BSSA with the channel sele氾tion is advantageous to th巴 conven tional BSSA and the conventional iterative BSSA in terms of sound quality. 6. REFERENCES. [1] J. Benesty， S. Makino， J. Chen， Springer- Ver1ag，2005.. Speech Enhancement，. [2] Y. Takahashi， T. Takatani， K. 0叫(0， H. Saruwatari， K. Shikano， “Blind spatial subtraction array for speech en hancement in noisy environment，" IEEE Trans. Audio， Speech， and Lang. Process.， vo1.17，no.4， pp.650-664，2009.. [3] P. Comon，“Ind巴pend巴nt component analysis，a new concept?，" Signal Processing， vo1.36，pp.287-314， 1994.. [4] S. F. Boll， “Suppression of acoustic noise in sp巴ech using spec. tral subtraction， " IEEE Trans. Acoustics， Speech， and Signal Process.， vo1.27， no.2， pp.113-120， 1979.. [5] R. Miyazaki， H. Saruwatari， K. Shikano，K. Kondo， “Musical noise-fr巴e blind sp巴巴ch extraction using ICA-based noise 巴stl mation and it巴rativ巴 sp巴ctral subtraction，" Proc. ISSPA20J2 (in printing) [6] R. Miyaz心ci，H. Saruwatari，K. Shikano，K. Kondo， “Musical noise-free sp巴巴ch enhancement: theory and evaluation，" Proc. ICASSP20J2， pp.4565-4568，2012.. [7] S. Li，J.-Q. Wang，M. Niu， X.-J. Jing，T. Liu， “Iterative sp削ral subtraction method for millimeter-wave conducted speech en hancement， " Joumal of 8iomedical Science and Engineering， vo1.20 10， no.3， pp.187-192，2010.

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