Integrated Detection Method of Underwater Acoustic Fuze Based on IEMD, VIFD and ED

Transcription

1 Advaces i Applied Acoustics Vol. Iss., November Itegrated Detectio Method of Uderwater Acoustic Fuze Based o IEMD, VIFD ad ED Qiao Hu Sciece ad Techology o Uderwater Iformatio ad Cotrol Laboratory, Xi a, 775, Chia The 75 Research Istitute, Chia Shipbuildig Idustry Corporatio, Xi a 775, Chia hqxjtu@hotmail.com Abstract I this paper, i order to solve the problem of accurately detectig the uderwater acoustic fuze i the complicated atural iterfereces, with the differet macrostructure ad microstructure betwee the target echo sigals ad the iterfereces such as reverberatio, a ovel itegrated detectio method of uderwater acoustic fuze is proposed, where firstly these differet itrisic mode fuctios (IMFs) are decomposed via the improved empirical mode decompositio (IEMD) from origial sigals received by the fuze system, to separate the target echo sigal from the reverberatio, ad secodly the statistics of variace-ofistataeous-frequecy detectio (VIFD) ad eergy detectio (ED) are obtaied from IMFs ad combied as a itegrated detector to detect the uderwater acoustic fuze excelletly. Through lake tests, this method is applied to the uderwater acoustic fuze detectio, ad these testig results show that the proposed method has better detectio performace tha the traditioal detectio method, such as eergy detectio ad variace-of-istataeous-frequecy detectio. Keywords Uderwater Acoustic Fuze; Itegrated Detectio; Improved Empirical Mode Decompositio ; Variace of Istataeous Frequecy Itroductio The backgroud iterferece of uderwater active acoustic fuze system (UAAFS) icludes the atural iterferece, such as the atural oise i marie eviromet, the radiated oise of uderwater vehicles ad warships, the ocea reverberatio ad the wake scatterig iterferece, i additio to the artificial iterferece, such as a sigle or series of explosios iterferece ad coutermeasure equipmet iterferece. The atural ad artificial iterferece usually be cosidered i UAAFS []. Especially i shallow water ad short-rage, the reverberatio iterferig with the target echo sigal is a major iterferece factor i the echo aalysis ad processig, where the amplitude of valid target sigal may be submerged, so that the target characteristics ca t be discrimiated from the amplitude of fuze sigal []. Therefore, it is very importat that the target echo features are extracted from the uderwater acoustic reverberatio, ad it is a prerequisite for the subsequet processig of the target echo. Empirical Mode Decompositio (EMD) ca adaptively decompose the complicated multi-compoet sigal ito a umber of sigle compoet sigals accordig to the local characteristic time scales of the sigal, where the target sigal ad the iterferece sigal is broke dow ito these differet itrisic mode fuctios (IMF) [3-4]. With the differet modal characteristics betwee the target sigal ad the iterferece sigal, the local features of the weak target sigal ca be ehaced. I fact, the modulatio characteristic of the trasmitted sigal is ot the same through the uderwater target ad the surface or seabed, so that for the target sigal ad the iterferece sigal, there are the essetial differeces amog Doppler frequecy, eergy ad delay [5]. Therefore, i this paper, a improved EMD (IEMD) algorithm based o widowed ad adjacet additio IMF is proposed to separate the target echo sigal from the reverberatio. Some traditioal detectio methods, such as match filter detectio, correlatio detectio ad eergy detectio, are usually applied to uderwater target echo detectio [6-7]. The matched filter detector ad the correlatio detector are optimal to detect the determiate sigal from the white oise backgroud i the ideal chael. Due to the complexity of the uderwater acoustic chael ad multi-path effects,

2 Advaces i Applied Acoustics Vol. Iss., November the detectio performace of the theoretical detector ofte has a serious declie i practical applicatios [8]. With the differece of power level (or amplitude) betwee the target echo sigal plus oise ad the oise, eergy detector is oly utilized to detect the chage of the iput oise amplitude mea which stads for the target sigal or the oise, ad do t cosider the details of echo sigal ad iterferece [9]. As a ew target detectio method with the costat false alarm rate, the variace-of-istataeous-frequecy detectio (VIFD) uses the details of the istataeous frequecy ad these statistical characteristics of the echo sigal ad the iterferece to detect the target from the reverberatio, which is idepedet of the variety of the backgroud iterferece without the target echo sigal []. I egieerig applicatios, the sigle VIFD method eeds to be combied with other detectio methods to improve the detectio ad atijammig capability. O the basis of the above discussio, a ovel itegrated detectio method of uderwater acoustic fuze based o the IEMD, the eergy detector ad the VIFD method is proposed, where the validity is verified with the egieerig applicatio. Improved Emd Blackma widowed EMD (WEMD) EMD has bee pioeered by N.E. Huag et al. for adaptively represetig o-statioary sigals as sums of differet simple itrisic modes of oscillatios [3]. With the EMD method, a sigal could be decomposed ito a umber of Itrisic Mode Fuctios (IMFs), each of which must satisfy the two defiitio: () I the whole data set, the umber of extrema ad the umber of zero-crossigs must either equal or differ at most by oe. () At ay poit, the mea value of the evelope defied by local maxima ad the evelope defied by the local miima is zero. With a series of siftig, ay sigal x ( ca be decomposed with EMD as follows = fi + r Thus, oe ca achieve a decompositio of the sigal ito -IMFs ad a residue. The IMFs f i ( ad residue r ( iclude differet frequecy bads ragig from high to low. The EMD techiques provide a multiscale aalysis of the sigal as a sum of orthogoal () sigals correspodig to differet time scales. I order to reduce or elimiate edpoit effects i applicatio of EMD method, a ew boudary processig method based o Blackma widow is preseted []. With this method, the aalyzed sigal x ( is preprocessed by multiplyig with the defied widow fuctio w (, so that the amplitudes of the sigal remai i middle ad reduce i both eds. The, EMD is used to aalyze the preprocessed sigal x = w(. Accordig to Eq. (), x ( ca be defied as = fi + r So we ca obtai the recostruct fuctio of the Blackma widowed EMD method as fi r = + w( w( Also take the lake-test echo sigal as a example i Fig., ad the decomposed results with the proposed method are show i Fig.. With the statistical aalysis, the ratios of the sum of the first four IMFs eergy to origial sigal s eergy are more tha 99%. So we oly cosider the first four IMFs f ~ f 4 i Fig., where it is obvious that the proposed boudary processig method sacrifices a few ed poits but protects the most middle poits of the sigal from beig polluted () (3) FIG. THE ACTUAL UNDERWATER ECHO SIGNAL.5 f f -.5. f f FIG. THE IMFS WITH WINDOWED EMD 3

3 Advaces i Applied Acoustics Vol. Iss., November The joit processig method with widowed ad adjacet additio EMD I Fig., the experimetal studies verified that the widowed EMD method ca eormously decrease the boudary distortio. However, our research shows that sometimes oise will icrease the EMD error so greatly that the IMFs are distorted seriously ad fail to illustrate the actual modes ivolved i the sigal. I order to solve the problem that the characteristic iformatio of a itrisic oscillatio mode is split ito two or more itrisic mode fuctios, the joit processig method with widowed ad adjacet additio EMD is proposed to icrease the precisio of EMD. The proposed joit processig method is based o the followig three steps: ) Compute the istataeous frequecy (IF) ω ( of every IMF via the widowed EMD. For oe IMF f i ( i Eq. (3), we ca always have its Hilbert trasform as fi t H fi t P dτ π ( ) [ ( )] = (4) t τ where P meas the Cauchy pricipal compoet. The we ca have a aalytic sigal as jθi A[ fi ] = fi + jh[ fi ] = ai e (5) H[ f ( )] with ai = fi + H [ fi( ], i t θ i = arcta[ ]. So the IF fi( ω i ( ca be expressed as dθi ω i = (6) d( ) Cosider the adjacet IMFs usig a rectagular slidig time widow. If their IFs chage suddely durig the same period, the adjacet IMFs should be added to form the ew IMFs ( Cf k. 3) Together make up the real IMFs with the ew Cf k ( ad the residual f i (. I order to verify the effectiveess of the joit processig method with widowed ad adjacet additio EMD, the lake-test echo sigal i Fig. is aalyzed, ad the four IFs ω ~ ω 4 i Fig. 3 are obtaied with Eq. (6), correspodig to the four IMFs f ~ f4 i Fig.. Compared Fig. with Fig. 3, it ca be see that the relative IF ω chages smoothly ad its value is maximum amog these IFs ω ~ ω. The value of 4 ω is cosistet with the Dopler frequecy of uderwater target, so the IMF f stads for the target echo sigal (correspodig to i Fig. 4). Relative IF / Hz FIG. 3 THE INSTANTANEOUS FREQUENCIES WITH WINDOWED EMD Due to the iterferece effects of itermittece ad reverberatio, the echo sigal of the iterface reverberatio is broke dow ito f ~ f3, ad the decompositio process is distorted. Accordig to the above three steps of the proposed joit processig approach, the IFs ω ad ω 3 are processed to judge whether these IFs chage suddely via the rectagular widow slidig alog the time axis with a legth of 5 data poits ( see the two dotted lies i Fig. 3). It ca be see that ω ad ω 3 chage suddely i the widow betwee 3-poit ad 58-poit. So the adjacet IMF f ad f 3 should be added to form the ew IMF, Cf = f + f3 (correspodig to Cf i Fig. 4). The last IF ω 4 shows that f 4 is a slowly varyig echo evelope compoet, ad the evelope legth aroud 55-poit coicides with the pulse width of the target echo, which idicates that f 4 is the target echo evelope compoet (correspodig to i Fig. 4). Therefore, with widowed ad adjacet additio EMD method, these IMFs ~ Cf3 are show i Fig. 4, which stad for the target echo, the reverberatio ad the target echo evelope compoet, respectively Cf FIG. 4 THE IMFS WITH WINDOWED AND ADJACENT ADDITION EMD I fact, the modulatio characteristic of the trasmitted sigal is ot the same through the 4

4 Advaces i Applied Acoustics Vol. Iss., November uderwater target ad the surface or seabed, so that for the target sigal ad the iterferece sigal, there are the essetial differeces amog Doppler frequecy, eergy ad delay. I theory, due to the differet mode characteristics betwee the echo of the uderwater target acoustic fuze ad the reverberatio, ad the differet modulatio characteristic of the trasmitted sigal betwee the uderwater target ad the surface, there are essetial differeces betwee the uderwater target echo ad the reverberatio received by UAAFS i the Doppler frequecy, eergy, delay, etc. So the IMFs of the uderwater target acoustic fuze sigal ca be extracted from the reverberatio via the proposed joit processig method. Covetioal Detectio Methods for Uderwater Acoustic Fuze Eergy detector The eergy detector ca be expressed as the followig biary detectio [6] : H : x[ = [ H : x[ = s[ + [ i =,,, N i =,,, N where H deotes that the receivig uderwater acoustic sigal is oly the reverberatio iterferece, ad H deotes that the receivig uderwater acoustic sigal cotais the uderwater target echo ad the reverberatio, with x [ for the receivig uderwater acoustic sigal, s [ ad [ for the target sigal ad the iterferece, respectively. Accordig to the Neyma-Pearso detectio criteria, the eergy detectio statistic (EDS) E (x) ca be expressed as follows N (7) H N E( x) = x ( i) / σ > r' (8) H where x ( i) is the eergy ad σ is the variace of the uderwater acoustic sigal x [. Comparig E (x) with detectio threshold r ' ad takig the result as the basis of judgmet, we have the ituitive coclusio that E (x) will icrease whe x [ cotais the fuze target echo. Correspodig to these ew IMFs ~ i Fig. 4, these ormalized test statistics of eergy detectio i Fig. 5 are calculated accordig to the slidig time widow with the same legth to the trasmittig pulse width. For, the maximum EDS (75-poi is.5db higher tha the secod-largest EDS (58-poi, ad for, the maximum EDS (75-poi is 4.8dB higher tha the secod-largest EDS (75-poi, which shows that the uderwater target ca be detected with the target echo sigal or the target echo evelope compoet FIG. 5 THE NORMALIZED TEST STATISTICS OF ENERGY DETECTION Variace-of-istataeous-frequecy detectio The mea of the istataeous frequecy of the siglefrequecy sigal plus iterferece oise (SFSPIN) is the carrier frequecy, ad its istataeous frequecy variace ca be expressed as [] : q W f ( f f) + ( q + ) ( q + ) σ (9) where q is the sigal to oise ratio, f is ceter frequecy, f ad W stad for the ceter frequecy ad badwidth of SFSPIN. It ca be see that σ f is a mootoically decreasig fuctio with q, so we ca take the real-time / σ f as the VIFD statistics (VIFDS), ad compare / σ f with the detectio threshold r '' via biary detectio. The target echo sigal will appear whe σ f > r' ', ad the reverberatio or the oise iterferece oise iterferece σ ''. f r Though fidig the startig poit of this istataeous frequecy variace sequece whe σ f > r' ', we ca extract the target echo from the various oise iterferece, ad thus costruct the detector IF (x) of VIFD. These ormalized test statistics of VIFD i Fig. 6 are calculated accordig to the slidig time widow with the same legth to the trasmittig pulse width, correspodig to ~ i Fig. 4. I Fig. 6, the test results of VIFD are similar to EDS i Fig. 5. For, the maximum VIFDS is.db higher tha the secod-largest VIFDS, ad for, the Cf 5

5 Advaces i Applied Acoustics Vol. Iss., November maximum VIFDS is.9db higher tha the secodlargest VIFDS. From the Fig. 5 ad Fig. 6, it ca be see that the uderwater target ca be detected with the target echo sigal usig EDS or VIFDS. However for, the testig performace of EDS is iferior to the VIFDS, because the frequecy is lower ad the waveform chages slowly, where the detailed varieties of VIFDS are ot so obvious FIG. 6 THE NORMALIZED STATISTICS OF VIFD Itegrated Detectio Method for Uderwater Acoutic Fuze O the basis of discussio above, eergy detector is suitable to detectig the chage of the eergy mea of the target sigal or the oise, ad do t cosider their details. O the cotrary, VIFD is applied o detailed observatios of IF of the echo sigal ad the iterferece to detect the target from the reverberatio. So this paper presets a ovel itegrated detectio method, where eergy detector ad VIFD are combied to improve the detectio performace of a sigle detector with the macro ad micro iformatio. The structure of itegrated detectio (ID) method is as show i Fig.7, where these ew adjacet additio IMFs are decomposed from the received acoustic fuze data via the joit processig method with widowed ad adjacet additio EMD, ad VIFDS IF i ad EDS Ei are obtaied from these above IMFs. Thus the test statistics of the ID method ca be show as Ei i = IFi λ () Assumig the probability of false alarm ad the detectio threshold r, we have the detectio results via biary detectio: H comes ito existece ad the target will appear whe λ i > r ; ad H exists ad there is o a target r whe λ i r. So the ID system for uderwater acoustic fuze ca be built to detect the uderwater target optimally. With the ID method, these ormalized test statistics λ i are show i Fig. 8, correspodig to ~ i Fig. 4, where for, the maximum test statistic is 7.dB Cf higher tha the secod-largest, ad for, the maximum is.6db higher tha the secod-largest. Comparig Fig. 8 with Fig. 5 ad Fig. 6, it ca be see that for, the detectio gai of the ID method is about 5dB higher tha the sigle method s, ad for, the detectio gai is 7~dB higher tha the sigle method s, which idicates that the ID method combies these advatages of ED ad VIFD, ad has a better detectio performace. Uderwater target echo, reverberatio iterferece, etc. Received fuze data Widowed EMD f f f i f IMFs ω ω ωi ω IF ω Rectagular slidig time widow Cf k Adjacet additio IMFs Slidig time widow with the same legth to the trasmittig pulse width VIFDS IF i Test statistics of ID λ i Η : λi > r Η: λi r Test results = EDS E i Ei IFi FIG. 7 THE FLOW CHART OF ID FOR UNDERWATER ACOUSTIC FUZE FIG. 8 THE NORMALIZED STATISTICS OF ID Egieerig Applicaitos I order to verify the detectio ability ad validity, we take the lake-test fuze echo sigal of uderwater acoustic target for example, ad compare the performace of the itegrated detectio method with ED ad VIFD. The received lake-test fuze echo sigal i a received cycle is show i Fig x 4 FIG. 9 THE ACTUAL UNDERWATER ECHO SIGNAL WITHIN ACOUSTIC PERIOD Cf 6

6 Advaces i Applied Acoustics Vol. Iss., November The adjacet additio IMF is obtaied from the echo sigal i Fig. 9 via the joit processig method with widowed ad adjacet additio EMD, ad the ormalized test statistics (the maximum test statistics are db) are calculated ad show as i Fig. through ED, VIFD ad ID. Ad for the three types of detectio method, the mea ad the secod-largest statistics have bee listed i Table ED VIFD ID x 4 FIG. THE NORMALIZED STATISTICS OF THREE DETECTION METHODS TABLE THE PERFORMANCE COMPARISON OF THREE ACOUSTIC FUZE DETECTION METHODS Type of detectio method The test statistics (db) Mea Secod-largest ED VIFD ID It ca be see from Fig. ad Table that for ID method, the test statistic whe the target appears is about.5db higher tha the average of reverberatio s, ad the detectio gai icrease to 6.7 db ad.6 db respectively, compared with ED ad VIFD. It idicates that the detectio performace of ID is greatly improved, ad its ihibitory effect for the iterferece oise (the secod-largest test statistic) is better tha ED ad VIFD. I additio, the umber of data poit is labeled as P whe the value of test statistic is equal to, which idicates that the target appears. Ad the time delay from the target to the received platform ca be show as τ = P / fs, where f s is the samplig frequecy. So the distace R betwee the target ad the acoustic fuze received platform ca be show as c R τ = () Through lots of experimets, the calculatio results show that the estimated distaces R agreed with the practical coditios. Moreover, we took a large umber of uderwater acoustic echo sigals as testig samples to detect the uderwater target, ad foud that the ID method has more macro ad micro iformatio tha ED ad VIFD, with combiig the advatages of ED ad VIFD. All these idicate that the ID method has more capacity of reliability ad robustess, ad holds sigificat promise i the acoustic fuze detectio for the uderwater movig target. Coclusios I this paper, a ovel itegrated detectio (ID) method of uderwater acoustic fuze based o IEMD, viz., the joit processig method with widowed ad adjacet additio EMD, eergy detectio (ED) ad variace-ofistataeous-frequecy detectio (VIFD) is proposed. The proposed method is applied to the uderwater acoustic fuze detectio, ad these testig results are show as followig: ) The improved EMD method based o the widowed EMD ad the adjacet additio EMD ca eormously decrease the boudary distortio ad over-decompositio pheomea effectively, ad has a better decompositio ability, compared with the covetioal EMD method. Ad the IEMD ca decompose the target echo sigal from the reverberatio iterferece, due to the differet mode characteristics betwee the target echo ad the reverberatio, ad the differet modulatio characteristic of the trasmitted sigal betwee the uderwater target ad the surface. ) The ID method has more capacity of atiiterferece, reliability ad robustess tha the sigle ED or VIFD method, ad holds sigificat promise i the acoustic fuze detectio for the uderwater movig target. ACKNOWLEDGMENT This work was fiacially supported by the Shaaxi Sc iece ad Techology Research ad Developmet Pro gram (NO.KJXX-9). REFERENCES [] X.Che, T. Jiag,X. F. Li, Implemetatio of O-lad Simulatio of Torpedo Active Ultrasoic Fuze. Torpedo Techology, 6(5):34-37(8). [] S. G. Chamberlai, J. C. Galli, A Model for Numerical Simulatio of Nostatioary Soar Reverberatio usig Liear Spectral Predictio. IEEE Joural of Oceaic Egieerig, 8():-36(983). 7

7 Advaces i Applied Acoustics Vol. Iss., November [3] N. E. Huag, Z. She, S. R. Log, a New View of Noliear Water Waves: the Hilbert Spectrum. Aual Reviews of Fluid Mechaics, 3:47-457(999). [4] Q. Hu, B. A. Hao, L. X. Lv, et al, Hybrid Itelliget Detectio for Uderwater Acoustic Target Usig EMD, Feature Distace Evaluatio Techique ad FSVDD, Iteratioal Cogress o Image ad Sigal Processig ( 8), IEEE,5(4): 548. [5] V. Carmillet, P. O. Amblard, G. Jourdai, Detectio of Phase- or Frequecy- Modulated Sigals i Reverberatio Noise. Joural of the Acoustical Society of America, 5(6): (999). [6] M. K. Steve, Fudametals of Statistical Sigal Processig, Volume II: Detectio Theory, Pearso Educatio Publishers, Pretice Hall PTR (998). [7] H. C. Sog, W. S. Hodgkiss, W. A. Kuperma, Experimetal Demostratio of Adaptive Reverberatio Nullig usig Time Reversal. Joural of the Acoustical Society of America, 8(3):38-387(5). [8] D. H. Chambers, J. V. Cady, S. K. Lehma, Time Reversal ad the Spatial-temporal Matched Filter. Jouralof the Acoustical Society of America, 6(3):348-35(4). [9] V. I. Kostylev, Eergy Detectio of A Sigal with Radom Amplitude. IEEE Iteratioal Coferece o Commuicatio (), Russia:Voroezh,, 3():66-6. [] G. L. Liag, Study o Trasiet Parameter Sequece of Echoed Sigal ad its Applicatio. Harbi Egieerig Uiversity doctoral dissertatio (997). [] Q. Hu, B. A. Hao, L. X. Lv, et al, Feature Extractio Model for Uderwater Target Radiated Noise. Torpedo Techology, 6(6):38-43(8). Dr. Qiao Hu received the Bachelor of Sciece degree i ad the Ph.D. degree i 6 i Mechaical Egieerig from Xi a Jiaotog Uiversity, P. R. Chia, ad worked as a postdoctoral fellow ad is curretly a seior egieer both i the 75 research istitute, chia shipbuildig Idustry Corporatio. His research iterests iclude uderwater acoustic sigal processig techiques ad hybrid itelliget target detectio based o patter recogitio techiques. 8