#### Abstract

Reservoir dams are mostly built in alpine valley areas. The water surface of the river valley is narrow and the geometric features of hydraulic structures are complex, which result in different absorption, reflection, and diffraction effects on sound waves for various propagation media. Further, for relatively narrow underwater water space where the underwater detection equipment is located, there is significant interference to the underwater acoustic communication signal. This is a major challenge to underwater positioning technology. Therefore, in this study, the scattering effect of different markers placed on a dam face on the sound waves emitted by sonar carried by a remote control unmanned submersible in a reservoir environment was investigated. The singular boundary method was used to develop a simulation model of the scattering effect on the sound waves of three different markers (i.e., cross boards, spherical bodies, and square plates) placed on a dam face in the deepwater environment of a reservoir. The scattering effect of typical geometrical markers was also investigated with respect to the sound waves of different frequencies and different incident angles. The sound pressure level (SPL) was used as an indicator for determining the scattering effect, so that the geometry of the marker with well scattering effect could be determined. In this study, the Guanyinyan hydropower dam was considered as the research area. The results show that the scattering SPL of the cross board is higher than those of the spherical body and the square plate, i.e., using the cross board as a marker produces the most accurate positioning of the underwater detection remote control unmanned submersible of a dam project in the deepwater environment of a reservoir.

#### 1. Introduction

Reservoir dam is not only an important structure for regulating the spatial and temporal distributions of water resources, but also for optimizing the allocation of water resources. It is also an important component of a flood control system in rivers. According to the 2016 Statistic Bulletin on China Water Activities [1], 98,460 reservoir dams of various types were built in China, with a total storage capacity of 896.7 billion m^{3}. As an important infrastructure for the national economy and the people’s livelihood, the safety risks of the reservoir dam cannot be ignored during both the construction stage and the operational stage [2]. Further, although China’s high dam construction started only in the recent past, it has developed rapidly. The world’s most comprehensive water conservancy and hydropower project, the Three Gorges Project (TGP), and a number of 300 m high dams, such as Jinping-I, Xiaowan, Nuozhadu, and Xiluodu hydropower stations, have been built. Moreover, a number of new 300 m high dams, such as Baihetan, Wudongde, Lianghekou, and Shuangjiangkou, are still under construction. China is the country with the largest number of high dams above 200 m. In future, with the aging of these dams, they may face various hidden dangers. For serious situations, reinforcements to the dams are required to be carried out. During the reinforcement process of a reservoir dam, it is generally not possible to completely empty the reservoir. Nonetheless, for some reservoir dams, the reservoirs should be emptied in order to carry out reinforcements to the dams. However, due to the effects on the environment or economic cost, it is not practical to empty these reservoirs, which is otherwise actually required so that the reinforcement work can be carried out under dry condition. Therefore, without emptying the reservoirs, the detection of faults and maintenance and reinforcement works on the dams have to be carried out under water. This presents major technical difficulties in carrying out the work. Thus, the dam engineering industry encounters these challenges and look for appropriate solutions [3].

At present, in addition to diving operations, the underwater unmanned detection technology is mostly used for observation and operation in the underwater environment, e.g., the unmanned detection method in which detection at a specified underwater position is carried out, and the detection equipment is carried using a remote operated vehicle (ROV). This method can perform the task without manpower (i.e., diver). It is suitable for tasks that are difficult to accomplish manually in a complex and dangerous environment or in a deepwater environment. There are many advantages, including deep operational depth, long operational period, high degree of safety, strong economy, and powerful function. Moreover, it can also perform underwater video detection and observation in real time, which has been widely used in China and other countries in the deepwater environment, such as the ocean environment, and high dam and large reservoir. In the process of underwater target detection, ROV needs to solve its own positioning issues. At present, satellite technology (e.g., GPS, Galileo system, and BeiDou system) is usually used as the main technical means for the positioning of water targets, supplemented by inertia and other positioning technologies. When the target is under water, the application of satellite positioning is restricted due to the strong absorption effects of water medium on the radio waves. Therefore, the underwater acoustic positioning technology with the sound wave as the information carrier is mainly used. It is not only used for the positioning and navigation of the target, but also serves as an effective auxiliary calibration method for the inertial positioning and navigation technology [4]. The underwater acoustic positioning technology was first applied in the military, due to the demand for marine development, exploration, and resource exploitation. This technology was then applied to various commercial and civil engineering projects, providing important positioning, navigation, and communication support for the seafloor prospecting equipment, such as ROV [5]. By installing and deploying acoustic positioning equipment on the ships which are on the water surface, underwater mobile platforms, and operational sea areas, the real-time monitoring of underwater target positions from the water surface and the information interaction between water surface and underwater platforms can be realized. This is essential for marine scientific investigation, marine resource exploration, marine resource development, deep-sea space station construction, and other projects [6]. Owing to the open space above and below the water surface and less signal interference, the underwater positioning of operating ROV under the marine environment is mainly based on the hydroacoustic positioning method of geometric principles, i.e., the underwater positioning is realized through acoustic response by combining satellite positioning technology and underwater acoustic active positioning technology [7–9]. The corresponding acoustic measurement technology is mainly divided into the following three technologies: ultrashort baseline, short baseline, and long baseline. The distance from the detected object to ROV is calculated by measuring the time and velocity of sound wave transmission in water, and then the azimuth of underwater communication unit to the target object is calculated by measuring the phase change. Moreover, the position of working ROV can be accurately obtained by calculating trigonometric functions [10]. Among them, the ultrashort baseline positioning system is an essential high-precision underwater acoustic positioning equipment for modern deep-sea workboat, providing high-precision underwater positioning for various underwater targets equipped with underwater acoustic transponders, such as various types of submersibles, underwater weapons, and seafloor fixed facilities [11]. To overcome the influence of complex marine environment and operating platform and obtain stable and reliable positioning data under deep sea is an internationally recognized important problem that needs to be solved using high-precision positioning technology.

The water area of a reservoir is much smaller than that of the marine environment and the depth of water is also less. Different from the open water area of the marine environment, the width of the water area of the plain-type reservoir is usually hundreds of meters, while the width of water area of a canyon reservoir is only tens of meters. Furthermore, hydraulic structures of the reservoir environment have complicated geometrical characteristics and a variety of propagation media, e.g., the media composition below the water surface of reservoir area is complex, probably made up of fresh efflorescence, bare rocks, gravels, pebbles, sand, silt, and even plants or garbage submerged at the bottom of the reservoir. The abovementioned different media have different reflection characteristics on sound waves, making the sound wave emitted by an underwater acoustic positioning system to form multipath reflection on both sides of the mountain and at the bottom of the reservoir. Further, the hydraulic structures with different geometric shapes for water drainage and delivery also form various absorption, reflection, and diffraction effects on the sound waves. Therefore, it is difficult to detect and construct the underwater structures of high dams and large reservoirs. Among them, the positioning of underwater equipment is the difficulty and hotspot of underwater engineering detection and construction. Therefore, the markers with different geometric shapes were selected and placed on the upstream face of a dam in this study. The acoustic scattering effects of different markers were compared by investigating the sound waves emitted by a sonar that was carried by a ROV in the deepwater environment of a reservoir. This is to enable the selection of a suitable geometry with better scattering effect as a marker for accurate positioning of underwater detection ROV in a deepwater environment of a reservoir.

#### 2. Research Method and Technical Route

Among various forms of energy radiation in water, sound wave has the best propagation performance. When a sound wave propagates in a medium and encounters obstacle, sound scattering is generated. The obstacles that cause sound scattering can be a single object or multiple objects. A reasonable arrangement of markers in the sound field can distinguish the effect of sound scattering on the sound wave propagation, which can be used as a basis for accurate positioning of underwater detection in a reservoir. Therefore, a study of sound wave propagation in the reservoir environment has important scientific significance and application value. At present, there are three main methods for solving sound radiation problems according to different analyses of the sound frequencies, namely, finite element method (FEM) [12, 13], boundary element method (BEM), and statistical energy analysis (SEA) method [14–18]. When the FEM is utilized to solve the sound field, the time (transient problem) and space need to be discrete. In order to ensure the calculation accuracy, for a linear element, the element length should be 1/6–1/10 of the analyzed wavelength. For an isoparametric element, the element length should be 1/3–1/4 of the analyzed wavelength. Therefore, as the calculation frequency increases, the element density increases significantly, and the number of calculations also increases significantly. Moreover, the FEM is not suitable for solving an unbounded sound field because it needs to divide the space for calculations into elements. As the distribution of the sound field in the high-frequency section follows the statistical law, the statistical energy analysis method solves the sound field from the statistical perspective, which is applicable to the high-frequency sound with dense modes. By using the FEM to solve the medium-frequency section of a sound field, the number of calculations becomes too cumbersome, the frequency is not high enough to satisfy the characteristics of statistical acoustics, and the error from the statistical energy analysis method is also too large. Therefore, to find a solution for the medium-frequency sound radiation has always been a difficult problem in acoustics. Thus, utilization of the BEM to solve the medium-frequency section of a sound field is a possibility; however, there are still the nonuniqueness problems of singular frequency, singular integral, and hypersingular integral, and the potential problems of high-order matrix inversion [12] associated with it.

In order to overcome the shortcomings encountered in the abovementioned numerical methods, a type of semianalytical strong format numerical method—singular boundary method developed by Chen and his coworkers [19]—has been used. With respect to the dependence on the numerical methods based on a grid and the solution methods of common sound radiation problem based on statistical characteristics, the singular boundary method is a type of radial basis function method with a boundary matching point. By introducing the concept of source point intensity factor to replace the singular item of basic solution at the source point, the method has the characteristics of no grids, no integrals, simple programming, and easy to use. Many scholars have carried out a lot of research studies on the determination of the source intensity factor to improve the numerical accuracy and stability of the singular boundary method [20, 21]. Generally, there are five different schemes, such as the inverse interpolation technique [22], the boundary inverse interpolation technique [23, 24], the integral mean value technique [25], the explicit empirical formula method [26, 27], and the rigid body displacement method [28].

Specifically in the field of acoustics, comparing with the finite element method, the singular boundary method only requires boundary matching points, which can reduce the computational dimensions by one. Further, the basic solution has been used as the interpolation basis function, which can automatically satisfy the radiation condition at infinite distance, thereby avoiding the difficulty of artificial interception of the computational domain in the finite element method [29]. Comparing with the boundary element method, the singular boundary method produces the resultant matrix with the similar or smaller conditioning number, while it does not need to divide the grid and avoids the complicated singular integral calculations, so that the numerical solution with higher accuracy and more stability can be obtained at a lower computational cost.

In this study, the singular boundary method is used to investigate the sound wave scattering effects of markers placed on dam face in the deepwater reservoir. The sound wave emitted from a sonar carried by a ROV has been taken as the research object. A simulation model of acoustic scattering by the markers with different geometric shapes has been used to investigate the scattering effects of different shapes of markers in a reservoir on the sound wave with sonars. By comparing the scattering effects of different shapes of markers with those of the typical geometrical shapes on sound waves of different frequencies and different incident angles, the shape with a scattering effect as a marker which can position the underwater detection ROV in a reservoir more accurately has been selected.

The main characteristics/features outlining this study are as follows: (1) 1090EP/1090EP-1 programmable sonar transmitter was used as the transmitting source of underwater sonar carried by ROV operating in the deepwater environment of the reservoir, and the frequency range of the emitted sound wave was 7–14 kHz. The transmitting source was about 100 m away from the upstream surface of the dam. (2) Three types of typical marker shapes placed on the upstream face of the dam are as follows: ①cross board (side length = 0.5 m and thickness = 0.02 m); ②sphere (diameter = 0.2656 m); and ③square plate (length = width = 0.5 m and thickness = 0.02 m). The marker placed on the face of the dam was 100 m away from the sonar. The dam face is much larger than the size of the marker; therefore, sound waves can be regarded as plane wave propagation, and the velocity of sound waves in water is 1,480 ms^{−1} (Figure 1). Moreover, the scattering effects of three different types of markers placed on the dam face were calculated and analyzed for sound waves with different incident angles. According to the working form of the ROV for underwater detection in a reservoir, the main calculation was conducted by approximating the sound wave emitted from the underwater sonar carried by the ROV and the marker on the face of the dam as a plane. Therefore, the calculations were carried out under the following two conditions: ①the sonar and marker in Figure 1 are in the same horizontal plane, i.e., the angle with *XZ* plane is 0°; and ②the angle between the sonar and the marker is 15°, i.e., the angle with *XZ* plane is 15°.

#### 3. Simulation Modeling of Sound Scattering by Marker

First, the basic assumptions in the simulation model are as follows:(1)It is assumed that the underwater medium behind the reservoir dam is ideal fluid, and thus, the viscosity of the acoustic medium is ignored(2)The medium is assumed to be uniform and static, i.e., the medium displacement is zero when there is no sound wave, and physical quantities such as static pressure and density do not change with time and position(3)It is assumed that the propagation process of sound wave is adiabatic, i.e., the compression and expansion of sound wave can cause the variation in medium temperature, and the temperature of different particles is different(4)The amplitude of the sound wave is assumed to be very small. Specifically, the sound pressure is much smaller than the static pressure of the medium, the medium displacement is much smaller than the wavelength, its velocity is much smaller than the sound velocity, and the variation in density is much smaller than the density itself

Based on the abovementioned assumptions, considering the absence of external force and injected medium, the linear transient sound wave equation [30] is represented as follows:where *p* is the sound pressure and *C* is the velocity of the sound wave propagation in the medium. Considering the incidence of simple harmonic sound field, i.e., , and introducing the method of separation of variable [26], equation (1) can be simplified as the steady-state sound wave Helmholtz equation.

By incorporating the above-stated assumptions, the Helmholtz equation for an infinite domain can be simplified, i.e., the partial differential equation is as follows:where is the wave number and is the angular frequency; is the infinite computational domain; is the absolute hard boundary, i.e., Neumann boundary; is the unit normal vector; and is the vibration velocity distribution of particles on the boundary. For physical mechanical problems in an infinite domain, a certain limiting condition should be imposed at infinity with the consideration of physics, i.e., the so-called boundary condition at infinity. For the Helmholtz equation, the boundary condition at infinity is as follows [31]:

This is the Sommerfeld radiation condition, where dim is the dimension of the problem, *k* is the wave number, and .

The SBM selects the basic solution that automatically satisfies the boundary conditions at infinity as the interpolation basis function; therefore, there is no need to consider the boundary conditions at infinity in the numerical calculations, and it is particularly suitable for solving infinite domain problems [15, 16]. For the three-dimensional (3D) infinite domain Helmholtz equation, the numerical solution can be expressed as a linear combination of a set of basic equations [32] as follows:where *N* is the number of source points , is the undetermined unknown coefficient, the basic solution of the Helmholtz equation in a 3D infinite domain is , and is the Euclidean distance between the matching point and the source point . If the boundary matching point overlaps with the source point , i.e., , the source point singularity appears in the basic solution function. To overcome this difficulty, the basic solution method arranges the source point on a false boundary outside the physical region so that cannot overlap with . However, the SBM still arranges and on the boundary of a computational domain, and the concept of source point intensity factor is introduced to replace the singular item in equation (5) when and overlap. Therefore, the interpolation equation of the SBM can be expressed as follows:where is the undetermined coefficient and [24] and are the source point intensity factors corresponding to the basic solution and the normal derivative of the basic solution, respectively. In fact, these factors correspond to the diagonal elements of the interpolation matrix of the basic solution and the normal derivative of the basic solution, respectively.

In order to use the interpolation expression (equations (5) and (6)) to solve the propagation problem of sound waves, the core of the SBM is to determine the source point intensity factor related to the problem. The source point intensity factors and are obtained from the following empirical equations:where is the influence range of the source point , is the surface area, is the characteristic radius, and is the curvature radius of the source point .

After determining the source point intensity factor by using equations (7) and (8), the interpolation equations (5) and (6) of the SBM can be used to solve the infinite domain Helmholtz problem and determine the unknown coefficient . Then, the interpolation expression of the SBM is used to obtain the solutions and of any point in the computational domain.

#### 4. Analysis of Numerical Simulation Results

In this study, the Guanyinyan hydropower station project was used as the research site. The project is located in the middle reaches of Jinsha River at the junction of Huaping County of Lijiang City in Yunnan Province and Panzhihua City in Sichuan Province, China. It is the last of the eight cascade power stations planned for the middle reaches of Jinsha River. The hub consists of a dam, flood discharge, and sand flushing buildings, water diversion and electric power generation system, and other buildings. The hub layout is shown in Figure 2. The dam is a mixed dam consisting of a roller-compacted concrete (RCC) gravity dam on the left bank and in the middle of the river and a clay core-wall rockfill dam on the right bank. The maximum height of the RCC gravity dam is 159 m, and the maximum height of the core-wall rockfill dam is 71 m. The normal water storage level is 1134.00 m, corresponding reservoir storage capacity is 2.072 billion m^{3}, and the regulating storage capacity is 555 million m^{3}. The installed hydropower capacity is 3,000 MW. The markers with different geometric shapes were placed on the upstream face of the dam.

To simulate the scattering effects of the markers with different geometric shapes on the sound waves emitted from the ROV, three typical markers were placed on the dam face (Figure 3). Their shapes are as follows: ①cross board (side length = 0.5 m and thickness = 0.02 m); ②sphere (diameter = 0.2656 m); and ③square plate (length = width = 0.5 m and thickness = 0.02 m). There are 6,722 discrete points on the surface of the cross board, 6316 discrete points on the surface of the sphere, and 6000 discrete points on the surface of the square plate. The distributions of the discrete points of the three markers on the dam face are shown in Figure 4.

**(a)**

**(b)**

**(c)**

The scattering effects of the three markers on the sound waves of different frequencies and different incident angles were compared. The frequencies of the sound waves are 7, 10, and 14 kHz, respectively. The incident angles, i.e., the included angles with *XZ* plane, are 0° and 15°, as shown in Figure 1. In order to quantify the numerical simulation results, the sound pressure level (SPL) was used as the indicator to determine the scattering effect. The equation for SPL is as follows [33]:where is the sound pressure and is the reference sound pressure in water ().

##### 4.1. Sonar and Marker Are in the Same Plane

The sonar and marker being in the same plane, the scattering effects of the three typical markers on the sound waves of 7, 10, and 14 kHz were simulated by the SBM. Figure 5 shows the calculated SPL of the three markers subjected to the sound waves of 7, 10, and 14 kHz.

**(a)**

**(b)**

**(c)**

Figures 5(a) and 5(b) demonstrate that for the markers subjected to the sound waves of 7 and 10 kHz, the scattering SPLs of the cross board and the sphere are about the same, and their scattering effects are higher than that of the square plate. Further, the scattering directivity of the cross board is clearer than that of the sphere, i.e., the scattering SPL of the cross board is higher in the wave propagation direction than that of the sphere. Figure 5(c) exhibits that for the markers subjected to the sound wave of 14 kHz, the scattering SPLs of the sphere and the square plate are about the same, and their scattering effects are worse than that of the cross board. Further, the scattering directivity of the sphere is clearer than that of the square plate, i.e., the scattering SPL of the sphere in the wave propagation direction is higher than that of the square plate.

##### 4.2. The Angle between Sonar and Horizontal Planes where Markers Are Located Is 15°

When the angle between the sonar and the horizontal plane where the markers are located is 15°, the scattering effects of the three typical markers on the sound waves of 7, 10, and 14 kHz were simulated by the SBM. Figure 6 shows the calculated SPL of the three markers subjected to the sound waves of 7, 10, and 14 kHz, respectively.

**(a)**

**(b)**

**(c)**

Figures 6(a) and 6(b) show that for the markers subjected to the sound waves of 7 and 10 kHz, the scattering SPLs of the cross board and the square plate are about the same, and their scattering scopes are bigger than that of the sphere. Figure 6(c) demonstrates that for the markers subjected to the sound wave of 14 kHz, the scattering SPL of the cross board is higher than that of the square plate, and the scattering SPL of the square plate is higher than that of the sphere. The cross board has the biggest scattering scope.

In conclusion, the scattering effects of the three markers (i.e., cross board, sphere, and square plate) placed on the dam face on the sound waves of 7, 10, and 14 kHz and at the incident angles of 0° and 15° (i.e., the included angles with the *XZ* plane) were investigated, and the SPL was used as the indicator of the scattering effects. The results show that the scattering sound pressure level of the cross board is higher than those of the sphere and the square plate, i.e., the scattering effect of the cross board is optimum. Thus, the cross board can be used as the marker placed on the upstream face of the dam under the reservoir environment and as the main reference for ROV underwater detection and positioning.

#### 5. Conclusion

By analyzing the difference between the reservoir deepwater environment and the marine environment, this study clarified the main factors that cause the difficulty in accurate positioning of a ROV in a reservoir. Reservoir dams are mostly built in alpine valley areas. The water surface of the river valley is narrow, and the geometric features of hydraulic structures are complex, resulting in different absorption, reflection, and diffraction effects on sound waves for various propagation media. Further, for relatively narrow underwater water space where the underwater detection equipment is located, there is significant interference to the underwater acoustic communication signal. This is a major challenge to underwater positioning technology. Therefore, in this study, a semianalytical strong format singular boundary method was used. With the sound waves emitted from a sonar carried by a ROV as the research object, the simulation model of sound wave scattering by markers of three geometric shapes was developed. The Guanyinyan hydropower station dam was used as the research site to investigate the scattering effects of the three markers of different geometrical shapes placed in reservoir deepwater environment on sound waves emitted from the sonar that is carried by ROV. The results show that when the sonar and the marker are in the same plane, the cross board shows the best scattering effect followed by the sphere, and the square plate has the worst scattering effect. Moreover, the scattering directivity of the cross board is clearer than those of the sphere and the square plate, i.e., the scattering sound pressure level of the cross board is higher in the wave propagation direction than those of the sphere and the square plate.

When the angle between the sonar and the horizontal plane where the markers are located is 15°, the scattering sound pressure levels of the cross board and the square plate subjected to the sound wave of 7 and 10 kHz are about the same, and their scattering effects are better than that of the sphere. For the markers subjected to the sound wave of 14 kHz, the scattering effect of the cross board is better than those of the square plate and the sphere. Therefore, by comparing the scattering effects of the three markers (i.e., cross board, sphere, and square plate) placed on the dam face on the sound waves of 7, 10, and 14 kHz and at the incident angles of 0° and 15°, the results show that the scattering sound pressure level of the cross board is the highest, and its scattering effect is the best. Thus, the cross board can be used as the marker placed on the upstream face of the dam under the reservoir environment and as the main reference for ROV underwater detection and positioning. Based on the abovementioned research, it is conducive to the accurate positioning of the underwater safety hazard of the reservoir dam. In future, high-precision instruments and high-dimensional algorithms can be further studied for underwater intelligent detection, providing technical support for reservoir dam safety.

#### Data Availability

The data used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

The authors greatly acknowledge the support from the National Key Research and Development Program of China (Grant nos. 2016YFC0401603 and 2016YFC0401605), the Natural Science Foundation of China (Grant nos. 51679151 and 41671504), and the Fund of Nanjing Hydraulic Research Institute (Grant no. Y717012).