# Experimental Study on Echo Characteristics of Multistatic Large-Scale Underwater Complex Target

Authors: Zhu Ling-Guo; Zhao An-Bang; Liu Wen-zhang; Han Jing; Wang Shu-tao; Ma Zhong-cheng
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

Target acoustic scattering is the primary characteristic of target echo stealth performance, and it is an important sign of the viability of large-scale complex targets underwater. In a test band, owing to the superposition of scattered waves and the elastic echo produced by shells, liquid tanks, partition plates, ribs, etc., a target exhibits an extremely complex echo phenomenon. Accurate measurement and evaluation of the acoustic scattering characteristics of underwater complex targets can be achieved via experimental research on the echo characteristics of large-scale scaled models. In this study, the contribution and regularity of the strong reflection source of underwater complex targets in various azimuths, structures, and locations were analyzed quantitatively as a basis for in-depth research and understanding of the echo characteristics of underwater complex targets.


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## Body

## 1. Introduction

The study of the complex echo characteristics of underwater targets is primarily based on the theory of elastic spherical shell [1, 2], infinite cylindrical shell [3–5], and finite cylindrical shell [6–8] acoustic scattering. In recent years, significant progress has been made in studies on sound scattering of finite cylindrical shells [9–11] with ring ribs and ring-ribbed plates. However, for large-scale underwater complex targets such as submarines, it is difficult to perform accurate theoretical calculation and numerical simulation because of their complex shape and structure.Experimental research has been performed on pool and lake echo characteristics [12, 13] using models of different scales to verify theoretical research results, which has promoted the development of theoretical prediction and practice. However, because of model size limitations, it is difficult to study ribbed plates, ribs, and other small parts. The more similar the size and material of the model to the actual target are, the closer the echo characteristic to the actual target is, and a large-scale scaled model is an effective method of studying the acoustic reflection characteristics of a target object. Moreover, such a model can achieve strong controllability and provides accurate measurement of target characteristics. This is the primary direction of practice research.In this study, a high-performance test facility was used to test large-scale underwater complex targets under single base and bistatic conditions. The azimuth and echo intensity of a strong target echo source were predicted using the planar element method. The characteristics of the target echo were studied under the bistatic condition, and the fine feature of target echo energy distribution was studied under the single base condition.


## 2. Theoretical Analysis and Simulation Analysis

In studies of the large-scale model transmission mechanism of the outer shell and ribbed plate of an actual target, they are approximately regarded as flat plates on two sides of water. Thus, the transmission coefficients of flat plates with different thicknesses are calculated and analyzed. Because a nonpressure shell is thin, energy is transmitted throughout a test band. Thus, the objective strength of the nonpressure shell is extremely low and can be neglected in simulations. When the incident angle is 90°, ribbed plate backreflection is extremely weak, and a pressure shell plays a major role in echo.As shown in Figure1, the time factor exp⁡-iωt is omitted, and the incident wave potential function φi is set.(1)φi=Ar1exp⁡ikr1Figure 1
Schematic of sound ray.A sound wave is incident from pointM1 to surface S, and the scattered sound field at point M2 is calculated. The Helmholtz integral equation of the scattering problem is applied as follows:(2)∅sr2→=-14π∫S∅s∂∂neikr2r2-∂∅s∂neikr2r2dSwhere n→ is the outer normal of the surface. The Kirchhoff approximation is derived under the condition that the far-field condition is not satisfied, and the scattered sound field is obtained under the bistatic base condition.(3)∅sr2→=-A4π∫S0eikk1+k2r1r2ir2-1r2cos⁡α1+ir1-1r1cos⁡α2dSAccording to the definition, the backscatter area is(4)σ=limr0→∞⁡4πr02φsφi2=k2πI2Therefore(5)TS=10log⁡σ4π=10log⁡1λ2I2For the single base condition,(6)∅s=-A2π∫S0eikrr2ikr-1rcos⁡αdSAccording to the definition, the backscatter area is(7)σr-1,r-2=limr2→∞⁡4πr22φsr-2φir-12=k2πI2Therefore(8)TSr-1,r-2=10log⁡σr-1,r-24π=10log⁡1λ2I2It is difficult to directly apply the rigorous theory to solve the scattering sound field and the analysis of the echo characteristic of the complex target. In the application of the planar element method [14], it is assumed that the target surface is divided into an N × M grid. The segmented step length is 1/6 wavelengths, and I is obtained by the sum of plate element integrals. Using (5) and (8), the bistatic and single base target strength of the entire target is calculated.


### 2.1. Ribbed Plate and Inner Shell Simulation under Bistatic Base Condition

It is known from Figure2 that theoretical simulations show that except for a maximum value of θ = 90°−β/2 = 55° (θ is the incident angle, and β is the split angle) there is a high peak close to an incident angle of 145°. Moreover, when the incident angle is 145°, the ribbed plates are perpendicular to the middle line of the incident sound ray and reflected sound ray. This peak is caused by reflection from the ribbed plates.Figure 2
Simulation results when the split angle is 70°.


### 2.2. Ribbed Plate and Inner Shell Simulation under Single Base Condition

At the experimental distance, the target can be decomposed into three parts: similar cone structure of the bow, similar cone structure of the stern, and main cylindrical structure. Their target strength and azimuth characteristics are shown in Figures3 and 4.Figure 3
Target strength and azimuth characteristics of each part.Figure 4
Target strength and azimuth characteristics.In the test range, the simulation results show that the maximum echo of the similar cone structure of the bow, the similar cone structure of the stern, and the main cylindrical structure appears at 82.3°, 99.8°, and 90°, respectively.


## 2.1. Ribbed Plate and Inner Shell Simulation under Bistatic Base Condition

It is known from Figure2 that theoretical simulations show that except for a maximum value of θ = 90°−β/2 = 55° (θ is the incident angle, and β is the split angle) there is a high peak close to an incident angle of 145°. Moreover, when the incident angle is 145°, the ribbed plates are perpendicular to the middle line of the incident sound ray and reflected sound ray. This peak is caused by reflection from the ribbed plates.Figure 2
Simulation results when the split angle is 70°.


## 2.2. Ribbed Plate and Inner Shell Simulation under Single Base Condition

At the experimental distance, the target can be decomposed into three parts: similar cone structure of the bow, similar cone structure of the stern, and main cylindrical structure. Their target strength and azimuth characteristics are shown in Figures3 and 4.Figure 3
Target strength and azimuth characteristics of each part.Figure 4
Target strength and azimuth characteristics.In the test range, the simulation results show that the maximum echo of the similar cone structure of the bow, the similar cone structure of the stern, and the main cylindrical structure appears at 82.3°, 99.8°, and 90°, respectively.


## 3. Experimental Verification

The Dalian Scientific Test and Control Technology Institute conducted an experimental study in the southern Dalian sea at a low frequency to study the broadband and multistation echo characteristics of a large-scale underwater complex target scaled model.


### 3.1. Experimental Implementation under Bistatic Base Condition

As shown in Figures5 and 6, an emission array is mounted at the stern of a measuring ship, and the model is mounted on the first hanger rod of the ship’s water well. The model enters the water at 10 m, comprising a 5 m hanger rod and a 5 m soft connection portion. The auxiliary ship is outfitted with a separate receiving system. The split angle (β) is fixed, and the submarine model rotates to obtain omnidirectional echo data of the model.Figure 5
Experimental implementation plan.Figure 6
Auxiliary ship maneuver mode.


### 3.2. Experimental Implementation Process under Single Base Condition

As shown in Figures5 and 6, a transmitting and receiving transducer array is fixed on the same hanger rod, and the depth of the sound center is consistent with the depth of the submarine model waterline. A continuously rotating submarine model is considered, in which the rotation angle ranges within 0–180°, and the broadband echo of the submarine model is tested.


## 3.1. Experimental Implementation under Bistatic Base Condition

As shown in Figures5 and 6, an emission array is mounted at the stern of a measuring ship, and the model is mounted on the first hanger rod of the ship’s water well. The model enters the water at 10 m, comprising a 5 m hanger rod and a 5 m soft connection portion. The auxiliary ship is outfitted with a separate receiving system. The split angle (β) is fixed, and the submarine model rotates to obtain omnidirectional echo data of the model.Figure 5
Experimental implementation plan.Figure 6
Auxiliary ship maneuver mode.


## 3.2. Experimental Implementation Process under Single Base Condition

As shown in Figures5 and 6, a transmitting and receiving transducer array is fixed on the same hanger rod, and the depth of the sound center is consistent with the depth of the submarine model waterline. A continuously rotating submarine model is considered, in which the rotation angle ranges within 0–180°, and the broadband echo of the submarine model is tested.


## 4. Data Analysis

### 4.1. Echo Intensity Azimuth Characteristics under Bistatic Base Condition

As shown in Figures7 and 8, the target echo intensity is at the maximum when the incident angle is 56.2°. At this time, the midline direction of the transmitted and received “split angle” is the vertical target axis direction. Therefore, the echo intensity is the highest; its value is close to the maximum target strength value of 90° under the single base condition. In addition to the maximum at the incident angle of 56.2°, there is a peak at an incident angle of 146.5°, and the echo intensity is approximately 10 dB lower than the echo intensity at 56.2°.Figure 7
Echo intensity 2D azimuth characteristics.Figure 8
Echo intensity 3D azimuth characteristics.


### 4.2. Strong Reflection Source Analysis under Bistatic Base Condition

When the split angle is 68°, the azimuth of the incident angle of 56.2° is the abeam azimuth. Figure9 and Table 1 show the distribution of the abeam azimuth strong reflection source.Table 1
Distribution values of the abeam azimuth strong reflection source.
60° strong reflection source Abeam outer shell Inner shell Fairwater 1 Fairwater 2 Flexural wave 1 Flexural wave 2 Flexural wave 3 Total Energy ratio 3.4 56.5 14.0 9.2 10.9 1.9 0.7 97.6Figure 9
Energy distribution in abeam azimuth.When the incident angle is in the abeam direction under the bistatic base condition, the energy of the echo primarily results from the reflection of the outer shell, inner shell, fairwater, and flexural wave. The total energy of the inner shell in the strong reflection azimuth is more than 55% of the total energy of the echo. As shown in Figures8 and 9, the reflection of the inner shell plays a major role at approximately 15° from the abeam azimuth.Close to an incident angle of 56°, there are three echo pulses after the hull reflection wave. The pulse time intervals are 1.665 ms, 1.619 ms, and 1.665 ms according to the target, the transmitting and receiving array, and seabed and surface geometry, respectively. The minimum sea surface multipath echo is 2.17 ms, and the minimum seabed multipath echo is 16.68 ms. It can be concluded that the three echo pulses are not multipath echoes but elastic echoes.At this time, the target can be approximated as a finite cylindrical shell, with Ka = 35, where K is the wave number and a is the thickness of the cylindrical shell. Because of the larger Ka, the target can be approximated using flat plate results. The coincidence frequencies of the steel plate and target are fh = 0.2 MHz·mm and fh = 0.15 MHz·mm, respectively. Coincidence resonance occurs as these frequencies are similar. According to the cylindrical shell theory [14] by Marston et al., the frequency of the flexural wave does not reach the coincidence frequency and the flexural wave is subsonic. The sound velocity of the flexural wave is 1132 m/s, and the primary part of the flexural wave is a subsonic A0 wave [14]. The total energy of the flexural wave is 13.5% of the total energy of the echo.As shown in Figure10 and Table 2, the incident angle is 146.5°, the axis of the target is parallel to the midline direction of transmitting and receiving sound ray, and the energy of the echo is primarily from the ribbed plate. The total energy of the ribbed plate is approximately 80% of the total energy of the echo.Table 2
Ribbed plates and their energy ratios.
Ribbed plate 1 2 3 4 5 6 7 8 Total Energy ratio Energy ratio 1.5 1.8 0.9 3.2 3.7 5.9 3.8 6.4  Ribbed plate 9 10 11 12 13 14 15 16  Energy ratio 2.8 3.0 1.8 4.2 3.0 1.7 3.0 1.2  Ribbed plate 17 18 19 20 21 22 23 24  Energy ratio 8.1 1.0 3.3 1.7 2.8 8.0 7.0 1.9 81.9Figure 10
Energy distribution at submaximum point of echo intensity.


### 4.3. Echo Intensity Azimuth Characteristics under Single Base Condition

As shown in Figures11 and 12, the echo maximum of similar cone structure of the bow, similar cone structure of the stern, and the main cylindrical structure appears at 81.6°, 100.3 °, and 90°, respectively. The comparison between theoretical simulation and experimental results is shown in Table 3.Table 3
Comparison of theoretical and experimental results.
Result Similar cone of the bow (°) Main cylindrical structure (°) Similar cone of the stern (°) Remarks Test result 81.6 90.6 100.3 Test distance  Theoretical research 81.9 90 99.5 Test distance and target size  Simulation study 82.3 90 99. 8 Test distance and target size  Theoretical research 85 90 96.4 Far field and target size  Simulation study 85 90 96 Far field and target sizeFigure 11
Echo intensity 2D azimuth characteristics.Figure 12
Echo intensity 3D azimuth characteristics.


### 4.4. Strong Reflection Source Analysis under Single Base Condition

As shown in Figures13 and 14 and Table 4, sound waves are incident from the model header, and echo energy primarily results from the ribbed plate and fairwater. The total energy of the ribbed plate is approximately 60% of the total energy of the echo, and the total energy of the fairwater is approximately 15% of the total energy of the echo. Because of the ribbed plate block, rib echo is not clear and elastic echo is not evident.Table 4
Ribbed plate energy ratio of the bow.
Ribbed plate 1 2 3 4 5 6 7 8 9 Total Energy ratio Energy ratio 1.9 3.3 5.1 1.4 1.9 2.9 1.6 4.3 1.6  Ribbed plate 10 11 12 13 14 15 16 17 18  Energy ratio 3.2 2.0 1.5 2.9 3.0 2.7 6.4 7.0 1.7  Ribbed plate 19 20 21 22 23 24 25 26  Energy ratio 1.6 3.3 1.1 2.43 1.7 1.7 0.6 0.5  74.5Figure 13
Echo intensity 2D azimuth characteristics of the bow.Figure 14
Echo intensity 3D azimuth characteristics of the bow.As shown in Figures15, 16, and 17 and Table 5, in the abeam azimuth (±15°), the energy of the echo primarily results from the reflection of the outer shell, inner shell, and fairwater. In the strong reflection azimuth, the reflection energy of the inner shell exceeds 60% of the total energy of the echo, and the total energy of the strong echo source exceeds 90% of the total energy of the echo. In the nonstrong reflecting azimuth, the reflection energy of the inner shell accounts for approximately 10%–20% of the total energy of the echo, and it is equivalent to several other strong reflection sources. The total energy of the strong echo source is more than 85% of the total energy of the echo.Table 5
Energy ratio of strong reflection source.
100.3° strong reflection source Abeam shell Inner shell similar cone of the stern Fairwater 1 Fairwater 2 Stern outer shell Bow outer shell Flexural wave Total Energy ratio 7.0 72.9 7.1 5.3 0.6 2.4 0.4 95.6  90.6° strong reflection source Abeam shell Inner shell main cylindrical structure Fairwater 1 Fairwater 2 Bow outer shell Stern outer shell Flexural wave Total  Energy ratio 6.8 68.5 10.3 11.0 0.2 0.5 1.0 98.3  81.6° strong reflection source Abeam shell Inner shell similar cone of the bow Bow outer shell Fairwater 1 Fairwater 2 Stern outer shell Flexural wave Total  Energy ratio 4.6 66.8 4.8 7.7 1.7 8.4 2.9 96.8  92° strong reflection source Abeam shell Moving bright spot of inner shell Fairwater 1 Fairwater 2 Stern outer shell Bow outer shell Flexural wave Total  Energy ratio 8.6 60.2 8.2 10.0 1.3 1.5 7.6 97.4  84° strong reflection source Abeam shell Moving bright spot of inner shell Bow outer shell Fairwater 1 Fairwater 2 Stern outer shell Flexural wave Total  Energy ratio 21.4 9.5 11.3 18.2 10.4 7.8 7.0 85.7  97° strong reflection source Abeam shell Moving bright spot of inner shell Fairwater 1 Fairwater 2 Stern outer shell Bow outer shell Flexural wave Total  Energy ratio 11.4 21.0 20.9 15.2 7.1 15. 0 0.7 91.2Figure 15
Echo intensity 3D azimuth characteristics in abeam azimuth.Figure 16
Echo intensity 2D azimuth characteristics in abeam azimuth.Figure 17
Typical azimuth echo intensity 2D energy ratio.
(a)
Incident angle is 81.6° (b)
Incident angle is 90° (c)
Incident angle is 92° (d)
Incident angle is 100.3° (e)
Incident angle is 84° (f)
Incident angle is 97°There is a clear flexural wave after the hull reflection wave, and the sound velocity is 1109 m/s, which is the subsonic A0 wave. The maximum energy of the flexural wave is 7.6% of the echo energy, and the maximum angle is 88°.When the acoustic wave is obliquely incident (15°–75°, 105°–165°), the primary reflected energy of the outer shell, inner shell, and fairwater cannot be returned to the direction of incidence. The geometrical scattering of the ribbed plate, outer rib, and fairwater plays a major role, accounting for approximately 70% of the total energy of echo. The geometric reflection of the outer shell and inner shell is not strong, and the elastic echo is not evident.As shown in Figures18 and 19 and Tables 6 and 7, sound waves are incident from the tail of the model and echo energy primarily results from the ribbed plate. The total echo energy of the ribbed plate is approximately 75% of the total echo energy. The echoes of the inner and outer ribs are clear. The echo energies of each outer rib and each inner rib are approximately 0.5% and 0.1% of the total echo energy, respectively. The inner rib echo is elastic waves caused by discontinuities in the welded joint, and the elastic echo of other parts is not evident.Table 6
Ribbed plate energy ratio at 180°.
Ribbed plate 1 2 3 4 5 6 7 8 9 Total energy ratio Energy ratio 5.9 3.6 6.2 7.4 12.5 14.4 6.1 1.1 2.0  ribbed plate 10 11 12 13 14 15 16 17 18  Energy ratio 1.1 2.0 3.6 1.4 0.7 1.1 0.9 2.7 1.5 74.5Table 7
Outer rib energy ratio at 180°.
Outer rib 1 2 3 5 6 7 8 9 10 Average energy ratio Energy ratio 1.02 0.72 0.52 0.30 0.54 0.49 0.50 0.44 0.50 0.54Figure 18
Echo intensity 2D azimuth characteristics of the stern.Figure 19
Echo intensity 3D azimuth characteristics of the stern.


### 4.5. Frequency Domain Characteristics

The frequency domain analysis of the target echo shows that the energy of the echo signal varies with time. Thus, the energy distribution characteristic of the wideband echo in each frequency band is obtained, which reflects the target reflection and scattering ability.As shown in Figures12 and 21(b), eight large bright lines appear between 0–75° and 115–180°, and the number of interference fringes increases linearly with frequency. This is Bragg scattering by periodic ring ribs and nonperiodic rib generation. The flexural wave caused by the ribs and the elastic echo caused by the resonance of the ribs are not evident.Comparing Figures20 and 21(a), the spectrum of a single bright spot is smooth, and the spectrum of the synthesized highlights shows eight distinct small lines, indicating that interference exists between the strong reflection sources at 75–115°.Figure 20
Frequency domain energy distribution of strong reflection source in abeam azimuth.
(a)
Frequency domain energy distribution of outer shell echo (b)
Frequency domain energy distribution of inner shell echo (c)
Frequency domain energy distribution of fairwater 1 echo (d)
Frequency domain energy distribution of fairwater 2 echoFigure 21
Frequency domain energy distribution under single base condition.
(a)
75–115° frequency domain energy distribution (b)
0–90° frequency domain energy distribution


## 4.1. Echo Intensity Azimuth Characteristics under Bistatic Base Condition

As shown in Figures7 and 8, the target echo intensity is at the maximum when the incident angle is 56.2°. At this time, the midline direction of the transmitted and received “split angle” is the vertical target axis direction. Therefore, the echo intensity is the highest; its value is close to the maximum target strength value of 90° under the single base condition. In addition to the maximum at the incident angle of 56.2°, there is a peak at an incident angle of 146.5°, and the echo intensity is approximately 10 dB lower than the echo intensity at 56.2°.Figure 7
Echo intensity 2D azimuth characteristics.Figure 8
Echo intensity 3D azimuth characteristics.


## 4.2. Strong Reflection Source Analysis under Bistatic Base Condition

When the split angle is 68°, the azimuth of the incident angle of 56.2° is the abeam azimuth. Figure9 and Table 1 show the distribution of the abeam azimuth strong reflection source.Table 1
Distribution values of the abeam azimuth strong reflection source.
60° strong reflection source Abeam outer shell Inner shell Fairwater 1 Fairwater 2 Flexural wave 1 Flexural wave 2 Flexural wave 3 Total Energy ratio 3.4 56.5 14.0 9.2 10.9 1.9 0.7 97.6Figure 9
Energy distribution in abeam azimuth.When the incident angle is in the abeam direction under the bistatic base condition, the energy of the echo primarily results from the reflection of the outer shell, inner shell, fairwater, and flexural wave. The total energy of the inner shell in the strong reflection azimuth is more than 55% of the total energy of the echo. As shown in Figures8 and 9, the reflection of the inner shell plays a major role at approximately 15° from the abeam azimuth.Close to an incident angle of 56°, there are three echo pulses after the hull reflection wave. The pulse time intervals are 1.665 ms, 1.619 ms, and 1.665 ms according to the target, the transmitting and receiving array, and seabed and surface geometry, respectively. The minimum sea surface multipath echo is 2.17 ms, and the minimum seabed multipath echo is 16.68 ms. It can be concluded that the three echo pulses are not multipath echoes but elastic echoes.At this time, the target can be approximated as a finite cylindrical shell, with Ka = 35, where K is the wave number and a is the thickness of the cylindrical shell. Because of the larger Ka, the target can be approximated using flat plate results. The coincidence frequencies of the steel plate and target are fh = 0.2 MHz·mm and fh = 0.15 MHz·mm, respectively. Coincidence resonance occurs as these frequencies are similar. According to the cylindrical shell theory [14] by Marston et al., the frequency of the flexural wave does not reach the coincidence frequency and the flexural wave is subsonic. The sound velocity of the flexural wave is 1132 m/s, and the primary part of the flexural wave is a subsonic A0 wave [14]. The total energy of the flexural wave is 13.5% of the total energy of the echo.As shown in Figure10 and Table 2, the incident angle is 146.5°, the axis of the target is parallel to the midline direction of transmitting and receiving sound ray, and the energy of the echo is primarily from the ribbed plate. The total energy of the ribbed plate is approximately 80% of the total energy of the echo.Table 2
Ribbed plates and their energy ratios.
Ribbed plate 1 2 3 4 5 6 7 8 Total Energy ratio Energy ratio 1.5 1.8 0.9 3.2 3.7 5.9 3.8 6.4  Ribbed plate 9 10 11 12 13 14 15 16  Energy ratio 2.8 3.0 1.8 4.2 3.0 1.7 3.0 1.2  Ribbed plate 17 18 19 20 21 22 23 24  Energy ratio 8.1 1.0 3.3 1.7 2.8 8.0 7.0 1.9 81.9Figure 10
Energy distribution at submaximum point of echo intensity.


## 4.3. Echo Intensity Azimuth Characteristics under Single Base Condition

As shown in Figures11 and 12, the echo maximum of similar cone structure of the bow, similar cone structure of the stern, and the main cylindrical structure appears at 81.6°, 100.3 °, and 90°, respectively. The comparison between theoretical simulation and experimental results is shown in Table 3.Table 3
Comparison of theoretical and experimental results.
Result Similar cone of the bow (°) Main cylindrical structure (°) Similar cone of the stern (°) Remarks Test result 81.6 90.6 100.3 Test distance  Theoretical research 81.9 90 99.5 Test distance and target size  Simulation study 82.3 90 99. 8 Test distance and target size  Theoretical research 85 90 96.4 Far field and target size  Simulation study 85 90 96 Far field and target sizeFigure 11
Echo intensity 2D azimuth characteristics.Figure 12
Echo intensity 3D azimuth characteristics.


## 4.4. Strong Reflection Source Analysis under Single Base Condition

As shown in Figures13 and 14 and Table 4, sound waves are incident from the model header, and echo energy primarily results from the ribbed plate and fairwater. The total energy of the ribbed plate is approximately 60% of the total energy of the echo, and the total energy of the fairwater is approximately 15% of the total energy of the echo. Because of the ribbed plate block, rib echo is not clear and elastic echo is not evident.Table 4
Ribbed plate energy ratio of the bow.
Ribbed plate 1 2 3 4 5 6 7 8 9 Total Energy ratio Energy ratio 1.9 3.3 5.1 1.4 1.9 2.9 1.6 4.3 1.6  Ribbed plate 10 11 12 13 14 15 16 17 18  Energy ratio 3.2 2.0 1.5 2.9 3.0 2.7 6.4 7.0 1.7  Ribbed plate 19 20 21 22 23 24 25 26  Energy ratio 1.6 3.3 1.1 2.43 1.7 1.7 0.6 0.5  74.5Figure 13
Echo intensity 2D azimuth characteristics of the bow.Figure 14
Echo intensity 3D azimuth characteristics of the bow.As shown in Figures15, 16, and 17 and Table 5, in the abeam azimuth (±15°), the energy of the echo primarily results from the reflection of the outer shell, inner shell, and fairwater. In the strong reflection azimuth, the reflection energy of the inner shell exceeds 60% of the total energy of the echo, and the total energy of the strong echo source exceeds 90% of the total energy of the echo. In the nonstrong reflecting azimuth, the reflection energy of the inner shell accounts for approximately 10%–20% of the total energy of the echo, and it is equivalent to several other strong reflection sources. The total energy of the strong echo source is more than 85% of the total energy of the echo.Table 5
Energy ratio of strong reflection source.
100.3° strong reflection source Abeam shell Inner shell similar cone of the stern Fairwater 1 Fairwater 2 Stern outer shell Bow outer shell Flexural wave Total Energy ratio 7.0 72.9 7.1 5.3 0.6 2.4 0.4 95.6  90.6° strong reflection source Abeam shell Inner shell main cylindrical structure Fairwater 1 Fairwater 2 Bow outer shell Stern outer shell Flexural wave Total  Energy ratio 6.8 68.5 10.3 11.0 0.2 0.5 1.0 98.3  81.6° strong reflection source Abeam shell Inner shell similar cone of the bow Bow outer shell Fairwater 1 Fairwater 2 Stern outer shell Flexural wave Total  Energy ratio 4.6 66.8 4.8 7.7 1.7 8.4 2.9 96.8  92° strong reflection source Abeam shell Moving bright spot of inner shell Fairwater 1 Fairwater 2 Stern outer shell Bow outer shell Flexural wave Total  Energy ratio 8.6 60.2 8.2 10.0 1.3 1.5 7.6 97.4  84° strong reflection source Abeam shell Moving bright spot of inner shell Bow outer shell Fairwater 1 Fairwater 2 Stern outer shell Flexural wave Total  Energy ratio 21.4 9.5 11.3 18.2 10.4 7.8 7.0 85.7  97° strong reflection source Abeam shell Moving bright spot of inner shell Fairwater 1 Fairwater 2 Stern outer shell Bow outer shell Flexural wave Total  Energy ratio 11.4 21.0 20.9 15.2 7.1 15. 0 0.7 91.2Figure 15
Echo intensity 3D azimuth characteristics in abeam azimuth.Figure 16
Echo intensity 2D azimuth characteristics in abeam azimuth.Figure 17
Typical azimuth echo intensity 2D energy ratio.
(a)
Incident angle is 81.6° (b)
Incident angle is 90° (c)
Incident angle is 92° (d)
Incident angle is 100.3° (e)
Incident angle is 84° (f)
Incident angle is 97°There is a clear flexural wave after the hull reflection wave, and the sound velocity is 1109 m/s, which is the subsonic A0 wave. The maximum energy of the flexural wave is 7.6% of the echo energy, and the maximum angle is 88°.When the acoustic wave is obliquely incident (15°–75°, 105°–165°), the primary reflected energy of the outer shell, inner shell, and fairwater cannot be returned to the direction of incidence. The geometrical scattering of the ribbed plate, outer rib, and fairwater plays a major role, accounting for approximately 70% of the total energy of echo. The geometric reflection of the outer shell and inner shell is not strong, and the elastic echo is not evident.As shown in Figures18 and 19 and Tables 6 and 7, sound waves are incident from the tail of the model and echo energy primarily results from the ribbed plate. The total echo energy of the ribbed plate is approximately 75% of the total echo energy. The echoes of the inner and outer ribs are clear. The echo energies of each outer rib and each inner rib are approximately 0.5% and 0.1% of the total echo energy, respectively. The inner rib echo is elastic waves caused by discontinuities in the welded joint, and the elastic echo of other parts is not evident.Table 6
Ribbed plate energy ratio at 180°.
Ribbed plate 1 2 3 4 5 6 7 8 9 Total energy ratio Energy ratio 5.9 3.6 6.2 7.4 12.5 14.4 6.1 1.1 2.0  ribbed plate 10 11 12 13 14 15 16 17 18  Energy ratio 1.1 2.0 3.6 1.4 0.7 1.1 0.9 2.7 1.5 74.5Table 7
Outer rib energy ratio at 180°.
Outer rib 1 2 3 5 6 7 8 9 10 Average energy ratio Energy ratio 1.02 0.72 0.52 0.30 0.54 0.49 0.50 0.44 0.50 0.54Figure 18
Echo intensity 2D azimuth characteristics of the stern.Figure 19
Echo intensity 3D azimuth characteristics of the stern.


## 4.5. Frequency Domain Characteristics

The frequency domain analysis of the target echo shows that the energy of the echo signal varies with time. Thus, the energy distribution characteristic of the wideband echo in each frequency band is obtained, which reflects the target reflection and scattering ability.As shown in Figures12 and 21(b), eight large bright lines appear between 0–75° and 115–180°, and the number of interference fringes increases linearly with frequency. This is Bragg scattering by periodic ring ribs and nonperiodic rib generation. The flexural wave caused by the ribs and the elastic echo caused by the resonance of the ribs are not evident.Comparing Figures20 and 21(a), the spectrum of a single bright spot is smooth, and the spectrum of the synthesized highlights shows eight distinct small lines, indicating that interference exists between the strong reflection sources at 75–115°.Figure 20
Frequency domain energy distribution of strong reflection source in abeam azimuth.
(a)
Frequency domain energy distribution of outer shell echo (b)
Frequency domain energy distribution of inner shell echo (c)
Frequency domain energy distribution of fairwater 1 echo (d)
Frequency domain energy distribution of fairwater 2 echoFigure 21
Frequency domain energy distribution under single base condition.
(a)
75–115° frequency domain energy distribution (b)
0–90° frequency domain energy distribution


## 5. Conclusions

(1) For the corresponding entity object, in the 2–4 kHz band, clear flexural waves are observed in the abeam azimuth. There are three echo pulses under the bistatic base condition. The sound velocity of the flexural wave is 1132 m/s, and the total energy of the flexural wave is 13.5% of the total energy of the echo; the maximum angle is 56.2°. There is a clear flexural wave under the single base condition, and the sound velocity is 1109 m/s. The maximum energy of the flexural wave is 7.6% of the echo energy, and the maximum angle is 88°.(2) Under the bistatic base condition, except for a maximum value ofθ = 90°−β/2 = 55°, there is a high peak close to an incident angle of 145°, and the echo intensity is approximately 10 dB lower than the echo intensity at 56.2°. When the incident angle is 145°, this peak is caused by reflection from the vertical ribbed plates at the middle line of the incident sound ray and reflected sound ray. The echo energy of the ribbed plate is approximately 80% of the total echo energy.(3) Under the single base condition, the energy of the echo primarily results from the reflection of the outer shell, inner shell, and fairwater in the abeam azimuth. In the strong reflection azimuth, the reflection energy of the inner shell exceeds 60% of the total energy of the echo, and the total energy of the strong echo source exceeds 90% of the total energy of the echo. In the nonstrong reflecting azimuth, the reflection energy of the inner shell accounts for ~10–20% of the total energy of the echo, and it is equivalent to several other strong reflection sources. The total energy of the strong echo source is more than 85% of the total energy of the echo. When sound waves are incident from the head and tail of the model, the scattering of the ribbed plate and fairwater plays a major role, accounting for approximately 75% of the total energy of echo.(4) Eight large bright lines appear between 0–75° and 115–180°, and the number of interference fringes increases linearly with frequency, which are characteristic of Bragg scattering by periodic ring ribs and nonperiodic rib generation. The flexural wave caused by ribs and the elastic echo caused by the resonance of ribs are not evident. The spectrum of a single bright spot is smooth, and the spectrum of the synthesized highlights shows eight distinct small bright lines, indicating that interference exists between the strong reflection sources at 75–115°.



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*Source: 7852795-2018-06-12.xml*