浅海环境中水下物体声目标强度物理意义的讨论及模式滤波测量法.pdf

Discussion on the Physical Significance of the Acoustic Target Strength of an Underwater Object in Shallow Water and Modal-Filtering Measurement ZHANG Bo 1, 2, 3, ZHANG Xue-gang1, MA Zhong-cheng1 (1. Science and Technology on Underwater Test and Control Laboratory, Dalian 116013, China; 2. University of Chinese Academy of Science, Beijing 100190, China; 3. State Key Laboratory of Acoustics; Institute of Acoustics; Chinese Academy of Sciences, Beijing 100190, China) Abstract: The acoustic target strength (TS) of an underwater platform is usually tested in shallow water. Utilizing normal mode theory, the analytical formula of the TS of an underwater object in shal鄄 low water is derived, based on the average-measurement method, and its physical significance is an鄄 alyzed deeply. Analysis shows that, as for as a certain azimuth, TS is dependent on the target scat鄄 tering function values at a few vertical incident angles, 兹m, and scattering angles, 兹n. 兹mand 兹nare discrete, their values depending on normal-mode order, m, n. Furthermore, TS is concerned with both the marine environment and the testing range, and it is approximately equal to the free-field target strength, TSfree, when the testing range is large enough. A new TS measurement method put forward, namely Modal-Filtering Measurement (MFM), based on a vertical source array and a verti鄄 cal hydrophone array. According to theoretical analysis, MFM method performs well in both interface reverberation resistance and testing efficiency, compared with the average-measurement method and the classical vertical array method, its result is closer to TSfree. Key words: shallow water; average-measurement method; acoustic target strength; modal-filtering; single mode CLC number: O427Document code: Adoi: 10.3969/j.issn.1007-7294.2015.03.010 0 Introduction At the present stage, the acoustic target strength (TS) of an underwater platform is usual鄄 ly tested in shallow water (SW). Direct method of measurement requires precise information of transmission losses, which is not practical in SW environment. Urick et al1put forward an in鄄 direct method of measurement-the transponder method, which does not requires knowledge of transmission losses. However, transmission losses can not beremovedcompletely even if the transponder method is adopted, because of the unusually acoustic complexity of SW envi鄄 ronment, which leads to high uncertainty of measurement. Received date：2014-07-09 Foundation item: Supported by the Advance Research Project (51303030408) Biography：ZHANG Bo(1982-), male, engineer, E-mail: popo6189; ZHANG Xue-gang(1980-), male, senior engineer. Article ID：1007-7294（2015）03-0322-15 第19卷第3期船舶力学Vol.19 No.3 2015年3月Journal of Ship MechanicsMar. 2015 In order to measure the TS of an underwater platform accurately, measures must be taken to eliminate the influence of sound-field spatial fluctuations on the testing results. Based on the transponder method, testing techniques which can be utilized are as follows: (1) Measures repeatedly in different distances, and then take the average values. That is the Horizontal-Average Measurement (HAM). (2) Measures repeatedly at different depths, and then take the average values. That is the Vertical-Average Measurement (VAM). (3) Utilize a source/receiver array with directivity in the vertical plane to decrease inter鄄 face interference and to reduce sound-field spatial fluctuations. In this paper, that is referred to as Classical Vertical Array Measurement (CVAM). HAM is usually used because of its lower technical difficulty. VAM, by contrast, has high鄄 er technical difficulty, but it has higher testing efficiency and effectiveness. Both of them, with similar physical significance, are referred to asAverage Methodsin this paper. CVAM is a complementary method, which is often applied together with HAM. More detailed characteris鄄 tics about Average Methods can be found in Ref.2. Employing these techniques,the equal transmission losses conditionwill be satisfied. Consequently, transmission losses will beremovedalmost completely, and the testing accu鄄 racy is improved. However, what is the physical significance of the TS measured utilizing these techniques? And is it the same with the TS measured in free space? We have no answers to these questions yet. The principle of the transponder method is briefly reviewed in Sec.1, followed by a nor鄄 mal-mode expression of TS in SW environment, based on Ingenitos single-scattering-object- model3-4and VAM. Section 3 presents an analysis of the physical significance of the TS of an underwater platform in SW environment, which is measured utilizing Average Methods, and the differences between TS and TSfreeare analyzed. It indicates clearly that TS is approximately e鄄 qual to TSfree, when the testing range is so large that only the first normal mode plays a leading role. However, the lager the testing range, the lower the signal-to-noise ratio (SNR). On this view, in Sec 4, a new measurement method is introduced, namely Modal-Filtering Measure鄄 ment (MFM), which is based on a vertical transmitting array and a vertical receiving array, ac鄄 cording to single-mode excitation theory5-8and modal-filtering theory9-10. In Sec 5, MFM and the other methods are analyzed comparatively. Finally, we provide our concluding remarks in the last section. 1 Acoustic target strength and transponder method Consider a plane wave incident on the target. TS is a measure of how much of the incident sound is scattered back in the direction of the sonar. TS is given by TS=10lg Ir /I i r=1m (1) 第3期ZHANG Bo et al: Discussion on the Physical Significance323 where Iiis the incident intensity, and Irthe scattered. Ir r=1m is the scattered intensity 1 m away from the effective acoustic center of the target, which is usually measured in far field and then converted into the value 1 m away from the effective acoustic center. According to the active sonar equation, TS can be written as TS=EL- SL-TL1-TL2! (2) where EL is echo level, SL is source level, TL1is transmission loss from source to target, and TL2is transmission loss from target to source. Eq.(2) is the expression of TS measured by the direct method of measurement. Direct method of mea鄄 surement requires precise informa鄄 tion of transmission losses, which is not practical in SW environment. For that reason, Urick et al1put forward an indirect method of measurement- the transponder method, which does not require knowledge of transmis鄄 sion losses. Fig.1 is a sketch map of the transponder method. TS measured by the transponder method is written as TS=A+K(3) where A=ELT-ELK. ELTis echo level of the target, ELKis pulse level of the transponder at re鄄 ceiver No.1, and K is the difference between pulse level of the transponder and incident sound level at receiver No.2. The precondition of Eq.(3), namelythe equal transmission losses condition, is that the transmission losses from the source to each point in the volume occupied by the target are e鄄 qual. In fact, however, this precondition can not be met perfectly in SW environment. So trans鄄 mission losses can not beremovedcompletely even if the transponder method is adopted. 2 TS in SW environment 2.1 Target scattering sound field The geometry of target scattering in SW waveg鄄 uide is shown in Fig.2. In this section, it is assumed that the ocean waveguide is range independent, i.e., the sound speed varies only with depth. Assuming az鄄 imuthal symmetry and using cylindrical coordinates, the horizontal distance from the origin to some point in the channel is r, with the pressure release surface at z=0 and the bottom interface at z=H. A water layer Fig.1 Sketch map of the transponder method Fig.2 Sketch map of target scattering in SW waveguide 324船舶力学第19卷第3期 of constant thickness H, with density 1and sound-speed dependence c1(z), overlies a fluid ho鄄 mogeneous halfspace bottom of density 2and sound-speed c2. The source at (0, 0, zs) emits har鄄 monic waves with time dependence e -it , where is angular frequency. In Fig.2, r 軆 t and r 軆 r denote range vectors, from the source to the target and from the target to the receiver respectively. With the lateral wave and multiple scattering between the target and the boundaries ne鄄 glected, the acoustic field scattered by the target can be expressed in terms of normal modes and plane-wave scattering functions: pTzs; rt, zt, rr, zr 軆軆= i 2k m 移 n 移追m zs移 移追nzr移 移e iknrr+kmrr 移移 kmrtknrr 姨 NmNn e i酌mztei酌nztG mn +-ei酌mzte-i酌nztG mn +-e-i酌mztei酌nztG mn -+e-i酌mzte-i酌nztG mn - 移移 where 追m移移z =Nm e i酌mz -e -i酌mz 移移(5) Gmn + =G 兹 m, 准s; 兹n, 准r 移移,Gmn +- =G 兹 m, 准s; 仔-兹n, 准r 移移 Gmn -+=G 仔-兹 m, 准s; 兹n, 准r 移移,Gmn -=G 仔-兹 m, 准s; 仔-兹n, 准r 移移 where 追m移移z , kmand 酌mdenote the eigenfunction, horizontal and vertical wavenumber of the mth mode respectively, 兹m=cos -1 酌m/移移 k , N m is the normalization constant, and G is the free- field scattering function of the target, ps移移r = e ikr kr G 兹 i, 准i; 兹s, 准s 移移(7) where 兹i兹s 移 移is vertical incident (scattering) angle, and 准i准s移 移incident (scattering) azimuth angle. In a monostatic context, considering Eq.(5) and its derivative, Eq.(4) will be simplified to pTzs; r, zt 移移=i m 移 n 移追m zs移 移追mzt移移Hmn追nzs移 移追nzt移移e i k n+km 移移 r rkmkn 姨 (8) where Hmn= 1 4k Gmn +G mn +-+G mn -+G mn - 移移+ B A Gmn +G mn +-G mn -+-G mn - 移移 姨 + C A Gmn +-G mn +-+G mn -+-G mn - 移移+ D A -Gmn +G mn +-+G mn -+-G mn - 移移姨 A=追mzt 軆移追nzt軆移B=追m z t 軆移追nzt軆移/i酌m C=追mzt 軆移追n z t 軆移/i酌n D=追m z t 軆移追n z t 軆移/酌m酌n By Eq.(8), the scattering acoustic field of the target is expressed as the product of incident and scattering normal modes. H represents a mode-to-mode coupling matrix between the normal modes emitted by the source, 追m軆移z , and the normal modes, 追n軆移z , received by the receiver. 2.2 Acoustic target strength According to Eq.(3), TS can be expressed as (4) (6) (9) (10) 第3期ZHANG Bo et al: Discussion on the Physical Significance325 TS=10log10pTpT * /pKpK * ?+K(11) From Eq.(8), we can obtain pTpT * =专inc+专coh(12) where 专incis the incoherent component, and 专cohcoherent. 专inc= m 移 n 移追m zs? ? 2 追mzt? 2 Hmn 2 追nzs? ? 2 追nzt? 2/k mknr 2 专coh= m 移 mm 移 n 移 nn 移追m zs? ?追m * zs? ?追mzt?追m * zt?HmnHmn * 追nzs ? ?追n * zs? ?追nzt?追n * zt?e ikn-kn+km-km ? r /kmkmknkn 姨 r 2 When an average method, e.g. VAM, is applied, the coherent component,专coh, becomes null. Then we obtain pTpT * = m 移 n 移Amn追m zt? 2 Hmn 2 追nzt ? 2/k mknr 2 (13) where Amn=追mzs ? ? 2 追nzs ? ? 2. The meaning of is f?z= 1 H H z=0 乙f? z dz (14) Similarly, for theechoof the transponder pKpK * =Q 2 m 移 n 移Amn追m zk? ? 2 Smn 2 追nzk ? ? 2/k mknr 2 (15) where Q is the amplification factor of the transponder, K=20log10Q. If the transponder is om鄄 nidirectional, Smn=1, Eq.(15) becomes pKpK * =Q 2 m 移 n 移Amn追m zk? ? 2 追nzk ? ? 2/k mknr 2 (16) Inserting Eq.(13) and Eq.(16) into Eq.(11), we get TS=10log10 m 移 n 移Amn追m zt? 2 Hmn 2 追nzt ? 2/k mkn m 移 n 移Amn追m zk? ? 2 追nzk ? ? 2/k mkn (17) In the preceding derivation, the eigen-attenuation 茁mof normal modes is neglected. If it is taken into account, TS becomes TS=10log10 m 移 n 移Amn追m zt? 2 Hmn 2 追nzt ? 2e-2茁m+茁n? r /kmkn m 移 n 移Amn追m zk? ? 2 追nzk ? ? 2e-2茁m+茁n? r /kmkn (18) So far, we obtain the analytical expression of the acoustic target strength of an object in SW environment with VAM applied. According to the normal mode orthonormality condition, 326船舶力学第19卷第3期 Eq.(18) can be simplified as TS10log10 m 移 n 移Amn e -2 茁 m+茁n 移移 r kmkn Gmn +G mn +-+G mn -+G mn - 2 16k 2 / m 移 n 移Amn e -2 茁 m+茁n 移移 r kmkn 移 移 移 移 移 移 移 移 (19) 3 Physical significance of the acoustic TS in SW environment According to Eq.(8), TSfreein a monostatic context is TSfree=10log10 G 兹, 准; 仔-兹, 移移准 2/k2 移移(20) where, the expression of TSfreeis given beforehand in order to be analyzed comparatively with TS in SW environment. 3.1 Physical significance According to Eq.(18), TS in SW environment is concerned with both the free-field scat鄄 tering function G 兹i, 准; 兹s,移移准 and external factors such as marine environment and testing range. The situation that we considered is monostatic, so the horizontal incident and scatter鄄 ing azimuth angles are equal. So TS measured by the Average Methods in SW environment is remarkably different from TSfreeexpressed by Eq.(20), which is only related to the free-field scattering function of the target. For a constant azimuth angle, 准, G 兹i, 准; 兹s,移移准 is a function of 兹iand 兹s. The geometry of 兹iand 兹sis illustrated in Fig.3. Considering a coordinate system in Fig.4, with horizontal axis 兹s, TSfreeis dependent on nothing but the values of G associated with the points on the line 兹i +兹s=仔. For instance, when 兹i=仔/2, TSfreeis dependent only on the point P0仔/2, 仔/ 移移 2, as shown in Fig.4(a). However, by contrast, we can see from Eq.(6), (9) and (18) that TS in SW environment is concerned with the MM points, Pmn兹m, 兹n 移移, distributed around P0on the 兹i兹s plane, as shown in Fig.4(b), where M is the number of propagating modes. Fig.3 The geometry of incidentFig.4 Relationship between TS and incident and and scattering anglescattering angles According to Eq.(19), the value of TS in SW environment depends on the lower order modes more than on the higher order ones, because the lower order ones have smaller eigen- attenuation 茁m. In addition, we know that 兹=cos -1 酌m/移移kand the vertical wave number 酌mis 第3期ZHANG Bo et al: Discussion on the Physical Significance327 in direct proportion to the mode order, so it is clear that the higher the mode order, m or n, grows, the bigger the distance between Pmnand P0becomes. In consideration of the above two points, we draw a circular area on the 兹i兹splane in Fig.4(b), with deeper color in the center and lighter color all around. The color changing deeper means that the mode order becomes lower and the related values of G have greater influence on TS in SW environment. Furthermore, the larg鄄 er the range r becomes, the lighter the color all around changes. That is to say, the larger the range becomes, the less influence the higher order modes have on TS in SW environment. A simulated relationship between the relative eigen-transmission-loss TL茁of normal modes and grazing angle 琢mis illustrated in Fig.5, with a frequency 1 kHz and different ranges. TL茁denotes the relative value of transmission loss caused by normal mode eigen-attenuation, TL茁m, ? r =-20log10 e -茁m-茁1 ? r ?. The simulation parameters are as follows: Ex1 A point source emits harmonic acoustic waves with time dependence e -i棕t . H=100 m, c1=1 500 m/s, 籽1 =1 g/cm 3, c 2=1 600 m/s, 籽2=1.8 g/cm 3, 琢=0.3f 1.8 dB/m (f in units of kHz). All of the symbols mean the same as in Sec 2.1. Considering the threshold value of TL茁as 3 dB, the first 46, 35, 23 and 15 normal modes will play the dominate role on TS at a horizontal distance of 0.7, 2, 4 and 8 km, with a corresponding maximum grazing angle 20, 15, 10 and 7 degrees respectively. As for the target, the range of the corresponding vertical incident angle 兹i(scatter鄄 ing angle 兹s) is70, 110 ? ,75, 105 ? ,80, 100 ? and83, 97 ? respectively. For the sake of being more intuitive, we usedegreeinstead ofradianin units. In a word, the far鄄 ther the distance, the smaller the number of the normal modes playing the dominate role. If the range becomes so large that only the first normal mode plays a leading role, Eq.(18) is simplified to TS=10log10 追1zt ? 4 H11 2 追1zk ? ? 4 (21) In the vertical plane, put the target and the transponder nearly at the wave loop of the first normal mode, then we have 追1zt ?追1zk? ?. So we obtain TS20log10H11(22) As for the first normal mode, it is clear that k1k and 兹1仔/2. According to Eq.(6), we have Gmn +G mn +-G mn -+G mn -G 仔/2, 准; 仔/2, ? 准(23) Then Eq.(9) can be rewritten as Fig.5 Simulated relationship between TL茁 and 琢mat 1 kHz. TL茁is relative ei- gen-transmission-loss of normal m- odes, 琢mis grazing angle. 328船舶力学第19卷第3期 Hmn= 1 4k Gmn +G mn +-+G mn -+G mn - ? 1 k G 仔/2, 准; 仔/2,? ?准(24) Inserted into Eq.(22), it is obtained that TS20log10G 仔/2, 准; 仔/2,?准/?k(25) Eq.(25) indicates clearly that TS in SW environment is approximately equal to TSfree 仔/2, 仔/ ?2 , when the range becomes so large that only the first normal mode plays a leading role. Note that it is impractical to try to acquire a TS approaching TSfree仔/2, 仔/?2by means of increasing the testing distance continually, because SNR of echo decreases with the testing distance. For that reason, we will introduce a testing method only utilizing the first normal mode, namely Modal-Filtering Measurement (MFM), in Sec 4. 3.2 Simulation analysis of TS in SW environment In the context of Ex1, we analyze the difference between TS in SW environment and TSfree 仔/2, 仔/ ? 2 , with frequency 100 Hz-5 kHz and distance 700 m-100 km. In order to compare the influence of different scattering functions G on TS, we consider three different targets: a 10 m-radius rigid sphere, Target No.1 and Target No.2, with scattering functions Gsphere, G1and G2respectively. The expression of Gsphereis3 Gsphere=i m=0 移- ? 1 m 2m+ ? 1 j / m k ? ? a hm ? ? 1 k ? ? a Pm cos 兹 s+兹i ?移移(26) where i is the imaginary unit, and jm?x , hm ? ? 1 ? xand Pm?xis spherical Bessel function, spheri鄄 cal Hankel function of the first kind and Legendre function of the mth order respectively. According to Lambert scattering model, we define G1and G2as: G1= 25 sin兹isin兹s? 2 1+5 sin兹i-sin兹s 3k (27) G2= 25 sin兹isin兹s? 2 1+5 sin兹i-sin兹s k(28) In the coordinate system of Fig.4, Gsphere, G1and G2are symmetrical about the line 兹i=兹s and the line 兹i+兹s=仔. The associated values of TSfreeare shown in Fig.6. 啄TS is the difference of TS and TSfree, defined as 啄TS=TS-TSfree仔/2, 仔/ ? 2(29) Fig.6 The values of TSfreeof the rigid sphere, Target No.1 and Target No.2 第3期ZHANG Bo et al: Discussion on the Phys