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2 공학석사학위논문 A method of engagement simulation of engineering level considering the detection and maneuvering performance 탐지및기동성능을고려한함정의 공학급교전시뮬레이션방법연구 017 년 월 서울대학교대학원 조선해양공학과 정동훈

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4 Abstract A method of engagement simulation of engineering level considering the detection and maneuvering performance Many different engagement situations require naval ships to achieve some level of effectiveness. And, the performance of the naval ships is very important for such effectiveness. There have been many studies about analyzing the effectiveness and the performance. The former is largely related to the engagement level models and simulations and the latter is largely related to the engineering level models and simulations. However, there have been few studies to consider both the engagement level and the engineering level. This study proposes a simulation core applying the engineering level models to the engagement simulations, which makes it possible to consider both the engagement level and the engineering level. This simulation core considers the maneuvering and detection performance of naval ships through the Engineering model of the simulation core. The Engineering model applies maneuvering equations, the control of hydroplanes, a passive sonar equation, and beam patterns. Also, the simulation core considers engagement scenarios, and the flexibility and the reusability of naval ship models through the DEVS & DTSS model of the simulation core. The DEVS & DTSS model applies Discrete EVent system Specification (DEVS) and Discrete Time System Specification (DTSS). To verify the applicability of the simulation core, this simulation core was applied to detection performance simulations, maneuvering performance simulations, and engagement i

5 simulations. The results of these simulations ensures that the simulation core of this study considers both the engagement level and the engineering level, and features the flexibility and reusability of models. Keywords: Naval ships; Engagement level; Engineering level; Modeling and simulation; Engineering model; DEVS & DTSS model Student number: ii

6 Contents Abstract... i Introduction Modeling and simulation in naval applications Engagement simulation of engineering level Flexibility and reusability of models Related works Summary of this study... 9 Simulation core for the engagement simulation of engineering level Discrete event system specification and discrete time system specification Discrete event system specification Dicrete time system spcification Combined discrete event and discrete time system specification Example of discrete event system specification and discrete time system specification...19 Modeling of the maneuvering performance of naval ships with engineering level Maneuvering equations...9 i

7 Maneuvering equations Verification of the implementation of manevuering equations Control of hydroplanes...36 Modeling of the detection performance of naval ships with engineering level Passive sonar equation Beam pattern Beam pattern Verification of the implementation of beam patterns Comparison with the engagement simulation of no engineering level Modeling of the maneuvering performance and the detection performance with no engineering level Comparison between the engagement simulation of engineering level and the engagement simulation of no engineering level...53 Applications Detection performance simulation Variations of the specification for the passive sonars of a submarine Case study Maneuvering performance simulation Variations of the specification for the hydroplanes of a submarine Case study Engagement simulation Variations of the engagement situations Case study... 8 Conclusions... 9 ii

8 References APPENDICES A. Standard sets of manevering euqations A.1. Definitions of symbols...97 A.. Standard sets of maneuvering equations...99 B. Values of hydrodynamic coefficients 국문초록 iii

9 Figures Figure 1-1 Modeling and simulation in naval applications... 1 Figure 1- Hierarchy of modeling and simulation in naval applications... Figure 1-3 Engagement level and engineering level... 3 Figure 1-4 Engagement simulation of engineering level... 4 Figure 1-5 Flexibility and reusability of models... 5 Figure -1 Configuration of the simulation core and GUI Figure - Simulation GUI... 1 Figure 3-1 Configuration of discrete event system specification Figure 3- Configuration of discrete time system specification Figure 3-3 Configuration of combined DEVS and DTSS Figure 3-4 Configuration of the command system model and the maneuver system model Figure 3-5 Progress of the simulation [1]... 0 Figure 3-6 Progress of the simulation []... 1 Figure 3-7 Progress of the simulation [3]... Figure 3-8 Progress of the simulation [4]... 3 Figure 3-9 Progress of the simulation [5]... 4 Figure 3-10 Progress of the simulation [6]... 5 Figure 3-11 Progress of the simulation [7]... 6 Figure 3-1 Progress of the simulation [8]... 7 Figure 3-13 Progress of the simulation [9]... 8 Figure 4-1 Motion of submarines and surface ships... 9 Figure 4- Change from inertial frame to body-fixed frame Figure 4-3 Depth change simulation (target depth: m, forward speed: 4.63 m/s) Figure 4-4 Depth change simulation (target depth: m, forward speed: 9.17 m/s) Figure 4-5 Control of hydroplanes Figure 5-1 Overview from noise radiation to the detection of radiated noise Figure 5- Differences in the phases of the noise at each hydrophone iv

10 Figure 5-3 Intentional differences in the phases of the noise at each hydrophone Figure 5-4 Beam pattern of a linear hydrophone array (look angle: 0 ) Figure 5-5 Beam pattern of a linear hydrophone array (look angle: 30 ) Figure 5-6 Beam pattern of a linear hydrophone array (look angle: 60 ) Figure 5-7 Beam pattern of a linear hydrophone array (look angle: 90 ) Figure 5-8 Beam pattern of a linear hydrophone array Figure 5-9 Beam pattern of a circular hydrophone array Figure 6-1 Maneuvering performance of no engineering level Figure 6- Detection performance of no engineering level... 5 Figure 6-3 Scenario for the comparison with the engagement simulation of no engineering level Figure 7-1 Specifications of the passive sonars of a submarine Figure 7- Beam pattern of a circular array sonar (diameter: 3 m) Figure 7-3 Beam pattern of a circular array sonar (diameter: 4 m) Figure 7-4 Beam pattern of a circular array sonar (diameter: 5 m) Figure 7-5 Beam pattern of a linear array sonar (length: 5 m) Figure 7-6 Beam pattern of a linear array sonar (length: 30 m) Figure 7-7 Beam pattern of a linear array sonar (length: 35 m) Figure 7-8 First scenario for the detection performance simulation Figure 7-9 Array gain of the circular array sonar (diameter: 3 m) Figure 7-10 Array gain of the circular array sonar (diameter: 4 m) Figure 7-11 Array gain of the circular array sonar (diameter: 5 m)... 6 Figure 7-1 Array gain of the linear array sonar (length: 5 m)... 6 Figure 7-13 Array gain of the linear array sonar (length: 30 m) Figure 7-14 Array gain of the linear array sonar (length: 35 m) Figure 7-15 Second scenario for the detection performance simulation Figure 7-16 Beam width of the circular array sonar (diameter: 3 m) Figure 7-17 Beam width of the circular array sonar (diameter: 4 m) Figure 7-18 Beam width of the circular array sonar (diameter: 5 m) Figure 7-19 Beam width of the linear array sonar (length: 5 m) Figure 7-0 Beam width of the linear array sonar (length: 30 m) v

11 Figure 7-1 Beam width of the linear array sonar (length: 35 m) Figure 7- Specifications of the hydroplanes of a submarine Figure 7-3 Specifications of the bow plane Figure 7-4 Specifications of the stern plane Figure 7-5 Specification of the upper rudder Figure 7-6 Specification of the lower rudder Figure 7-7 First scenario for the maneuvering performance simulation... 7 Figure 7-8 Depth variations in the Case C1 and the Case C Figure 7-9 Pitch angle variations in the Case C1 and the Case C Figure 7-30 Deflection of the bow plane in the Case C1 and the Case C Figure 7-31 Deflection of the stern plane in the Case C1 and the Case C Figure 7-3 Depth variations in the Case C8 and the Case C Figure 7-33 Second scenario for the maneuvering performance simulation Figure 7-34 Trajectories in the Case D and the Case D Figure 7-35 Yaw angle variations in the Case D and the Case D Figure 7-36 Deflection of the upper rudder and the lower rudder in the Case D and the Case D Figure 7-37 Variations of the engagement situations Figure 7-38 Progress of the Case E1 simulation [1] Figure 7-39 Progress of the Case E1 simulation (the map view of the simulation GUI) [1] Figure 7-40 Progress of the Case E1 simulation (and the map view of the simulation GUI) [] Figure 7-41 Progress of the Case E1 simulation (and the map view of the simulation GUI) [3] Figure 7-4 Progress of the Case E and the Case E3 simulation (and the map view of the simulation GUI) Figure 7-43 Progress of the Case E simulation (and the map view of the simulation GUI) Figure 7-44 Progress of the Case E3 simulation (and the map view of the simulation GUI) Figure 7-45 Progress of the Case E4 and the Case E5 simulation [1] Figure 7-46 Progress of the Case E4 and the Case E5 simulation (the map view of the vi

12 simulation GUI) [1] Figure 7-47 Progress of the Case E4 and the Case E5 simulation (and the map view of the simulation GUI) [] Figure 7-48 Progress of the Case E4 and the Case E5 simulation (and the map view of the simulation GUI) [3] Figure 7-49 Progress of the Case E4 simulation (and the map view of the simulation GUI) Figure 7-50 Progress of the Case E5 simulation (and the map view of the simulation GUI) vii

13 Tables Table 1-1 Hierarchy of modeling and simulation in naval applications... Table 1- Summary of the studies and this study... 8 Table 3-1 Fundamental elements of discrete event system specification Table 3- Fundamental elements of discrete time system specification Table 3-3 Fundamental elements of combined DEVS and DTSS Table 6-1 Results of comparison with the engagement simulation of no engineering level Table 7-1 Results of the first scenario simulations Table 7- Results of the second scenario simulations Table 7-3 Hydrodynamic coefficients according to the area of the hydroplanes... 7 Table 7-4 Results of the first scenario simulations Table 7-5 Results of the second scenario simulations Table 7-6 Variations of the engagement situations... 8 Table 7-7 Properties of torpedoes... 8 viii

14 Introduction 1.1. Modeling and simulation in naval applications Broadly defined, modeling is a method for organizing knowledge accumulated through observation or deduced from underlying principles, while simulation refers to a method for implementing a model over time (Etter, 013). In naval applications, such Modeling and Simulation (M & S) is used effectively for analyzing and developing the strategies and tactics of naval ships, and the performance of naval ships as shown in Figure 1-1. Figure 1-1 Modeling and simulation in naval applications The M & S in naval applications could be categorized according the fidelity of it. The greater fidelity, the more detailed the items you are attempting to simulate. For example, a low fidelity model of a rocket system might represent the rocket as a solid object whereas 1

15 a higher fidelity model might include fins, fuel system, guidance system, and load capacity of the rocket (Parnell, 008). There are four general classifications: theater, mission, engagement, and engineering as presented in Figure 1- and Table 1-1. The theater level models and simulations are generally applied to evaluate force structures or strategies. Next, the mission level models and simulations are normally applied to evaluate force employment concepts. Third, the engagement level models and simulations are mostly applied to evaluate system alternatives or tactics. Lastly, the engineering level models and simulations are mainly applied to design and evaluate systems or support system testing. Figure 1- Hierarchy of modeling and simulation in naval applications Table 1-1 Hierarchy of modeling and simulation in naval applications Level Output General applications Theater Force dynamics Evaluate force structures Evaluate strategies Mission Mission effectiveness Evaluate force employment concepts Evaluate system alternatives Engagement System effectiveness Train system operators Evaluate tactics Engineering System performance Design and evaluate (sub)systems Support system testing

16 1.. Engagement simulation of engineering level As present in Section 1.1, there are four general classifications in naval applications: theater, mission, engagement, and engineering. Especially this study focuses on the engagement level and the engineering level. Figure 1-3 Engagement level and engineering level As shown in Figure 1-3, the engagement level models and simulations are used for evaluating the effectiveness of an individual system against another system in one-on-one, few-on-few, and many-on-many scenarios. And, the engineering level models and simulations provide measures of performance, concerning such issues as design, cost, manufacturing, and supportability. They can include physics-based models of components, 3

17 subsystems, and systems (Johnson, 1998). In other words, the engagement level models and simulations are for analyzing and developing the tactics of naval ships in engagement scenarios, and the engineering level models and simulations are for analyzing and developing the performance of naval ships. This study proposes the simulation core for the engagement simulation of engineering level, applying the engineering level models to the engagement level simulations. This simulation core could make it possible that the tactics of naval ships in engagement scenarios could be evaluated, considering the performance of the naval ships as shown in Figure 1-4. Figure 1-4 Engagement simulation of engineering level 4

18 1.3. Flexibility and reusability of models Naval ships are assigned to various engagement situations and include many types of surface ships and submarines. The surface ships and submarines also have various specifications. This make sure that if the structure of models is not well defined, it is very confusing and ineffective to simulate the various engagement situations and the various naval ships. To improve the confusion and the ineffectiveness, the structure of models should be well defined considering the flexibility and reusability of models. Figure 1-5 Flexibility and reusability of models As shown in Figure 1-5, the simulation core proposed in this study considers the flexibility and reusability of models. The flexibility and reusability of models make it possible to carry out various engagement simulations with various naval ship models. 5

19 1.4. Related works Engagement level models and simulations are for analyzing and developing the tactics of naval ships in engagement scenarios, and engineering level models and simulations are for analyzing and developing the performance of naval ships. And, many studies have been carried out about these two levels in naval applications. However, there are few studies that take into account of both two levels. Also, there are few studies considering the flexibility and reusability of models. The examples of studies about such Modeling and Simulation (M & S) of the engagement level and the engineering level are as follows. Lind (014) focused on the maneuvering performance of submarines. The engineering level models and simulations for the maneuvering performance were considered, applying maneuvering equations and the control of hydroplanes. However, the detection performance of submarines were not considered; nor were engagement scenarios. Khaledi et al. (014) analyzed the detection performance of Unmanned Underwater Vehicles (UUVs). The engineering level models and simulations for the detection performance were considered by applying an active sonar equation. However, the maneuvering performance of the UUVs were not considered; nor were engagement scenarios. Kaymal (013) analyzed which ship design factors were key drivers in the effectiveness of surface ships in Anti-SUrface Warfare (ASUW), based on realistic engagement scenarios. Although the key factors were compared for various ASUW scenarios, the engineering level models and simulations were not considered. Hwang et al. (011) focused on the maneuvering and detection performance of UUVs 6

20 in engagement scenarios. The engineering level models and simulations for the maneuvering performance were considered by applying maneuvering equations, and the control of hydroplanes. However, in the case of the detection performance, it is hard to say that the engineering level models and simulations for the detection performance were considered. The detection performance was just considered by the default values of detection probability. Cho and Kim (01) analyzed the detection performance of Unmanned Underwater Vehicles (UUVs). The engineering level models and simulations for the detection performance were considered by applying a passive sonar equation and beam patterns. However, the engineering level models and simulations for the maneuvering performance of naval ships were not considered. The path of naval ships with constant speed was just considered. Son (01) focused on the maneuvering performance of submarines. The engineering level models and simulations for the maneuvering performance were considered, applying maneuvering equations. Also, Discrete EVent System specification (DEVS) and Discrete Time System Specification (DTSS) were applied for the flexibility and reusability of models. However, the engineering level models and simulations for the detection performance of the submarines were not considered. These studies show that there are few studies which take into account of both the engineering level and the engagement level, and that there are few studies considering the flexibility and reusability of models. This study takes into account of both two levels, and the flexibility and reusability of models as shown in Table 1-. In this study, a simulation core is proposed. And, this simulation core can consider the maneuvering and detection performance with high fidelity, applying maneuvering equations, the control of 7

21 hydroplanes, a passive sonar equation, and beam patterns. Also, DEVS and DTSS are applied, which making the structure of simulation models flexible and reusable. In addition, these specifications enable simulations to progress over discrete events and discrete times following engagement scenarios. Table 1- Summary of the studies and this study Studies Maneuvering performance Detection performance Engagement scenarios Flexibility and reusability of models Lind O X X X Khaledi et al. X O X X Kaymal X X O X Hwang et al. Cho and Kim. Son et al. This study O X O X X O O X O X O O O O O O 8

22 1.5. Summary of this study Many different engagement situations require naval ships to achieve some level of effectiveness. And, the performance of the naval ships is very important for such effectiveness. There have been many studies about analyzing the effectiveness and the performance. The former is largely related to the engagement level models and simulations and the latter is largely related to the engineering level models and simulations. However, there have been few studies to consider both the engagement level and the engineering level. This study proposes a simulation core applying the engineering level models to the engagement simulations. This simulation core make it possible to consider the engagement level and the engineering level together. In addition, the simulation core features the flexibility and reusability of models so that it is easier to simulate various engagement situations with various naval ships. The simulation core has the naval ship models which consist of command system models, maneuver system models, detection system models, and weapon system models. Especially, the maneuver system models represent the maneuvering performance considering maneuvering equations and the control of hydroplanes. And, the detection system models represent the detection performance considering a passive sonar equation and beam patterns. Also, all these models follow Discrete EVent System specification (DEVS), Discrete Time System Specification (DTSS), and combined DEVS and DTSS. This makes the models be flexible and reusable, and the simulation progress over discrete events and discrete times. To verify the applicability of the simulation core, this simulation core was applied to detection performance simulations, maneuvering performance simulations, and 9

23 engagement simulations. The detection performance simulations were carried out by changing the specifications of the passive sonars of a submarine in different scenarios. The maneuvering performance simulations were carried out by changing the specification of the hydroplanes of a submarine in different scenarios. And, the engagement simulations were carried out by changing the engagement situations such as the number of naval ships engaged, the tactics of the naval ships, and the weapons of the naval ships in different scenarios. The results of these simulations ensures that the simulation core of this study considers both the engagement level and the engineering level, and features the flexibility and reusability of models. 10

24 Simulation core for the engagement simulation of engineering level This study proposes a simulation core and Graphic User Interface (GUI) for the engagement simulation of engineering level, and Figure -1 presents their configuration. The first layer, named Simulation GUI, corresponds to the simulation GUI, and the second layer, named Simulation core, corresponds to the simulation core. Figure -1 Configuration of the simulation core and GUI. Figure -1(1) and Figure -1() show that the Simulation GUI plays supportive roles in simulations. Figure - shows that the ribbon menu, model view, map view, and property view provide users with interfaces to manage and visualize simulations. The ribbon menu is for generating models, starting or stopping simulations, and so on. The model view shows 11

25 the list of generated models. The map view shows the progress of simulations. Lastly, the property view presents the data of generated models, and reports the result of simulations. Figure - Simulation GUI The Simulation core includes the DEVS & DTSS model, Engineering model, Surface ship model, and Submarine model. The DEVS & DTSS model (Figure -1 (3)) represents the state changes of naval ships over discrete events and discrete times, following Discrete EVent System specification (DEVS) and Discrete Time System Specification (DTSS). The Engineering model (Figure -1 (4)) represents the performance of naval ships and the environment which could affect the performance of the naval ships. First, the Motion model represents the maneuvering performance of the naval ships by applying maneuvering equations and the control of hydroplanes. And, the Noise model represents the noise level of the naval ships. Then, the Sonar model represents the detection performance of the naval ships by applying a passive sonar equation and beam patterns. Lastly, the Space model represents the environment 1

26 which could affect the performance of the naval ships. For example, the Space model calculates the distance and time for the radiated noise from the naval ships to propagate to the other naval ships. Based on such DEVS & DTSS model and Engineering model, surface ships and submarines can be represented by the naval ship models: Surface ship model and Submarine model (Figure -1 (5) and (6)). The naval ship models correspond to the Coupled model in DEVS & DTSS model, and are composed of the Command system model, Maneuver system model, Detection system model, and Weapon system model. The Command system model, Maneuver system model, Detection system model, Weapon system model correspond to the Atomic model in DEVS & DTSS model. And, the Command system model represents commanders and issues orders following defined scenarios. Each order works as a discrete event to the Maneuver system model and Detection system model. Then, the Maneuver system model and Detection system model operate at the word of the orders, calculating maneuvering equations, the control of hydroplanes, a passive sonar equation, and beam patterns every discrete times through the Motion model and Sonar model, respectively. And, the Weapon system model represents the decoys and torpedoes of naval ships. The decoys are devices intended to deceive enemy forces into attacking them, and so protect real naval ships. The torpedoes are self-propelled weapons with explosive warheads. In this way, once simulation operators organize scenarios and input data through Simulation GUI, (Figure -1(7)) Simulation core carries out the engagement simulations of engineering level according to discrete events and discrete times. (Figure -1(8)) And, the progress and results of the simulations could be checked through Simulation GUI. (Figure -1(9)) 13

27 Discrete event system specification and discrete time system specification Modeling and Simulation (M & S) is not done by writing out the systems themselves, but indirectly by using system specifications. System specifications are shorthand means of specifying systems. And, there are various types of system specifications according to the purpose, time advancing method, execution method, and execution environment of the M & S. Among them, Discrete EVent System specification (DEVS), Discrete Time System Specification (DTSS), and combined DEVS and DTSS are applied in this study. These are widely used in the M & S. The first two system specifications are proposed by Zeigler et al. (000). The DEVS makes it possible to carry out the M & S over discrete events and the DTSS makes it possible to carry out the M & S over discrete times. Praehofer (1991) proposed the combined DEVS and DTSS which makes it possible to carry out the M & S over discrete events and discrete times. Meanwhile, these three system specifications include atomic models and coupled models. The atomic models are the smallest constituent units of simulations and composed of the fundamental elements of the three system specifications. The coupled models provide the method of the assembly of several atomic and/or coupled models to build complex systems. Such atomic models and coupled models make the three system specifications feature the flexibility and reusability. In this study, the DEVS, the DTSS, and the combined DEVS and DTSS are applied to model and simulate the state changes of naval ships according to some events and time advance. The following would explain these system specifications. 14

28 3.1. Discrete event system specification Discrete EVent System specification (DEVS) is a system specification that advances the time of simulations by changing the states of models according to defined events. The DEVS processes the events which would affect the states of models in order of the time of the events. That is, when the events are processed, the states of the models would change and the time of the simulations would advance. The configurations and the fundamental elements of the DEVS are presented in Figure 3-1 and Table 3-1. Figure 3-1 Configuration of discrete event system specification Table 3-1 Fundamental elements of discrete event system specification Elements State variable Input & Output External transition function Time advance function Output function Internal transition function Functions State variable represents the states of models. Models exchange data among them through Input & Output. External transition function changes the states of models when external events generate. Time advance function defines the next event time according to the durations for the states of models. Output function outputs data when internal events generate. Internal transition function changes the states of models when internal events generate. 15

29 3.. Dicrete time system spcification Discrete Time System Specification (DTSS) is a system specification that calculates and updates the states of models at every time step. This system specification is largely used for analyzing mechanical systems which would change at every time step. However, in the case of systems featuring that there would be no change over and over the time step, this system specification might be not effective. If the value of the time step is adjusted to be large for improving the effectiveness, some changes in the large time step could be ignored. The configurations and the fundamental elements of the DTSS are presented in Figure 3-1 and Table 3-1. Figure 3- Configuration of discrete time system specification Table 3- Fundamental elements of discrete time system specification Elements State variable Input & Output State transition function Output function Functions State variable represents the states of models. Models exchange data among them through Input & Output. State transition function updates the states of models at every time step. Output function outputs data at every time step. 16

30 3.3. Combined discrete event and discrete time system specification Combined DEVS and DTSS is a system specification that is the combination of Discrete EVent System specification (DEVS) and Discrete Time System Specification (DTSS). This combined DEVS and DTSS progresses simulations according to defined events and, in the case of the specific state of models, progresses simulations with the states of models being updated at every time step. That is, the combined DEVS and DTSS could progress simulations over discrete events and discrete times. The configuration and the fundamental elements of the combined DEVS and DTSS are presented in Figure 3-3 and Table 3-3. Figure 3-3 Configuration of combined DEVS and DTSS 17

31 Table 3-3 Fundamental elements of combined DEVS and DTSS Elements Functions State variable DEVS State variable DEVS represents the states of models in DEVS part. State variable DTSS State variable DTSS represents the states of models in DTSS part. Input & Output Models exchange data among them through Input & Output in DEVS part. External transition function External transition function changes the states of models when external events generate in DEVS part. Time advance function defines the next event time Time advance function according to the durations for the states of models in DEVS part. Output function Output function outputs data when internal events generate in DEVS part. Internal transition function Internal transition function changes the states of models when internal events generate in DEVS part. Integration function Integration function updates the states of models at every time step in DTSS part. State event function State event function generates internal events when the defined criteria is satisfied 18

32 3.4. Example of discrete event system specification and discrete time system specification This section shows an example of Discrete EVent System specification (DEVS) and Discrete Time System Specification (DTSS). This example consists of the command system model and the maneuver system model of a submarine. The scenario of this example is organized as follows: - The command system model issues orders to the maneuver system model. The orders are about target locations to move to. - The maneuver system model moves to the target locations and reports to the command system model upon arrival to the target locations. Figure 3-4 Configuration of the command system model and the maneuver system model 19

33 As shown in Figure 3-4, under the above scenario, the DEVS should be applied to the command system model so that this model could process such events as issuing orders and being reported. And, the state variable of this model is assumed to have Ordering and Reported. Meanwhile, the combined DEVS and DTSS should be applied to the maneuver system model so that the maneuver system model could process such events as being ordered and reporting, and update the location of the submarine at every time step. And, the state variable of this model is assumed to have Ordered and Reporting. The following would explain how the command system model and the maneuver system model progress the simulation according to discrete events and discrete times. Figure 3-5 Progress of the simulation [1] [1] The initial state of the command system model is Ordering and that of the maneuver system model is Reporting. (Figure 3-5(1)) Time advance function defines the next event time according to the duration for the state of each model. (Figure 3-5()) Since the 0

34 duration for Ordering is assumed to be 1 s, the next event time of the command system model is 1 s and the event of the command system model is added to the event list (1 C means that the event of the command system model would generate when the current time is 1 s). (Figure 3-5(3)) In the case of the maneuver system model, the duration for Reporting means that there is no event to add. Figure 3-6 Progress of the simulation [] [] Since there is no event of which time is same with the current time, the current time is changed to 1 s which is the next event time of the first event in the event list. (Figure 3-6(1)) 1

35 Figure 3-7 Progress of the simulation [3] [3] The event of which time is same with the current time generates and Output function outputs data. (Figure 3-7(1) and ()) In this simulation, the event is an internal event of the command system model to issue an order to the maneuver system model. And, the data is the order about the first target location.

36 Figure 3-8 Progress of the simulation [4] [4] The order from the command system model is considered as an external event to the maneuver system model. (Figure 3-8(1)) Since the external event generates, External transition function changes the state of the maneuver system model to Ordered. (Figure 3-8()) The state being changed, Time advance function defines the next event time according to the duration for the state. But, in this simulation, there is no event to add because the duration for Ordered is. (Figure 3-8(3)) Meanwhile, when the state of the maneuver system model is Ordered, Integration function and State event function are activated to update the location of the submarine at every time step. (Figure 3-8(4)) 3

37 Figure 3-9 Progress of the simulation [5] [5] In the case of the command system model, after Output function, Internal transition function changes the state of this model to Reported. (Figure 3-9(1)) The state being changed, Time advance function defines the next event time according to the duration for the state. (Figure 3-9()) But, in this simulation, there is no event to add because the duration for Reported is. 4

38 Figure 3-10 Progress of the simulation [6] [6] At this moment, there is no event in the event list. (Figure 3-10(1)) However, since Integration function and State event function are activated, the simulation could keep going. Integration function calculates the location of the submarine of the next time step. (Figure 3-10()) Then, State event function checks whether or not the submarine arrives to the first target location. (Figure 3-10(3)) Since the submarine of the next time step does not arrive to the first target location, there is no event to add and only the current time is changed by the time step (0.5 s). (Figure 3-10(4)) 5

39 Figure 3-11 Progress of the simulation [7] [7] Integration function calculates the location of the submarine of the next time step once again. (Figure 3-11 (1)) Then, State event function also checks whether or not the submarine arrives to the first target location once again. (Figure 3-11 ()) In this case, since the submarine of the next time step arrives to the first target location, the next event time is defined according to the time step and the event of the maneuver system model is added to the event list ( M means that the event of the maneuver system model would generate when the current time is s). (Figure 3-11 (3)) And, the current time is changed to s which is the next event time of the first event in the event list. (Figure 3-11 (4)) 6

40 Figure 3-1 Progress of the simulation [8] [8] The event of which time is same with the current time generates and Output function outputs data. (Figure 3-1 (1) and ()) In this simulation, the event is an internal event of the maneuver system model to report to the command system model. And, the data is a report about the arrival to the first target location. After Output function, Internal transition function changes the state of this model to Reporting. (Figure 3-9(3)) 7

41 Figure 3-13 Progress of the simulation [9] [9] The report from the maneuver system model is considered as an external event to the command system model. (Figure 3-13 (1)) Since the external event generates, External transition function changes the state of the command system model to Ordering. (Figure 3-13 ()) And, to move to the second target location, the command system model and the maneuver system model follow the same procedure. This example shows that the command system model issues orders and the maneuver system model moves to the target locations according to discrete events and discrete times. And it could be said that applying the DEVS and DTSS makes such simulation possible. 8

42 Modeling of the maneuvering performance of naval ships with engineering level In this study, maneuvering equations and the control of hydroplanes are applied for modeling the maneuvering performance of naval ships with engineering level. The maneuvering equations represent the motion of the naval ships and the control of hydroplanes represents how the naval ships control the hydroplanes of the naval ships. The following would explain what the maneuvering equations is and how the control of hydroplanes is Maneuvering equations Maneuvering equations Figure 4-1 Motion of submarines and surface ships In general, as shown in Figure 4-1, submarines are assumed to have 6 Degrees-Of- Freedom (DOF) motion of surge, sway, heave, roll, pitch, and yaw. Surface ships are assumed to have 3 DOF motion of surge, sway, and yaw. Such motion of the naval ships (submarines and surface ships) depends on various external forces and moments exerted 9

43 on the naval ships. The relationship between the external forces (and moments) and the motion of naval ships could be defined by maneuvering equations as presented in Eqs. (4-1)-(4-6) (Gertler, 1967). And, these maneuvering equations from Gertler (1967) have been known as the standard sets of maneuvering equations. Each equation represents the motion of surge, sway, heave, roll, pitch, and yaw, respectively. m[ u vr + wq x q + r + y pq r + z pr + q = X G( ) G( ) G( )] m[ v wp + ur y r + p + z qr p + x qp + r = Y G( ) G( ) G( )] m[ w uq + vp z p + q + x rp q + y rq + p = Z G( ) G( ) G( )] I p + ( I I ) qr x z y ( r pq) I xz ( r q ) I yz ( pr q) I xy + m[ y ( w uq + vp) z ( v wp + ur)] = K G I q + ( I I ) rp y x z ( p qr) I xy ( p r ) I zx ( qp r) I yz + m[ z ( u vr + wq) x ( w uq + vp)] = M G I r + ( I I ) pq z y x ( q rp) I yz ( q p ) I xy ( rq p) I zx + m[ x ( v wp + ur) y ( u vr + wq)] = N G G G G (4-1) (4-) (4-3) (4-4) (4-5) (4-6) where, m is the mass, (I x, I y, I z, I xy, I yz, I zx) is the mass moment of inertia, and (x G, y G, z G) is the center of gravity. (u, v, w) is the body-fixed linear velocity and (p, q, r) is the bodyfixed angular velocity. (X, Y, Z) is the external force and (K, M, N) is the external moment. These maneuvering equations could be obtained by changing the Newton-Euler equation 30

44 from inertial frame to body-fixed frame as shown in Figure 4-. Figure 4- Change from inertial frame to body-fixed frame Several earlier studies about the maneuvering equations have been carried out and, among them, the linearized maneuvering equations from Babaoglu (1998) are applied in this study. Babaoglu (1998) proposed the linearized maneuvering equations, linearizing the standard sets of maneuvering equations from Gertler (1967) with some assumptions. Also, Babaoglu (1998) proved that the linearized maneuvering equations are much simpler than the standard sets of maneuvering equations, and the linearized maneuvering equations works in almost the same way the standard sets of maneuvering equations does. The standard sets of maneuvering equations are given on Appendix A and the assumptions are listed as follow: (1) Forward speed can be taken as constant. () Roll angle is assumed to be small. (3) Cross-products of inertia can be neglected. (4) All terms including W i can be discarded. Since it is assumed that the submarine is in trim, weight of water blown from a particular ballast tank, W i must equal zero. (5) All terms involving nonlinearity are neglected. (6) Vertical motion is decoupled from horizontal motion. 31

45 Defining the above six assumptions, Babaoglu (1988) derived the linearized maneuvering equations given by Eqs. (4-7)-(4-1). Each equation represents the motion of surge, sway, heave, roll, pitch, and yaw, respectively. u = U ( const.) (4-7) ρ ( ) ρ 3 + l ( Yv v + Yrur + Ypup) ρ + l ( Yvuv + u Yδ rδ r) 4 mv mur = l Yr r + Yp p ρ ρ 3 + l ( Zw w + Zquq) ρ + l ( Zwuw + u ( Zδsδs + Zδbδb)) 4 mw umq = l Zq q (4-8) (4-9) ρ 5 Ixp = l( Kp p + Kr r ) ρ 4 + l ( K pup + Krur + Kv v) ρ 3 + l ( Kvuv + u Kδ rδ r) + Bz φ B ρ 5 Iq y = lmq q ρ 4 + l ( M quq + M w w) ρ 3 + l ( M wuw + u ( Mδsδs + Mδbδb)) + Bz θ B (4-10) (4-11) 3

46 ρ 5 Ir z = l( Nr r + Np p ) ρ 4 + l ( Nrur + N pup + Nv v ) ρ 3 + l ( Nvuv + u Nδ rδ r) (4-1) where, ρ is the mass density of sea water. l is the overall length of a naval ship. δr is the deflection of a rudder, and δb and δs are the deflection of a bow plane and stern plane, respectively. B is the buoyancy force and z B is the z coordinate of the center of buoyancy. Φ and θ are the roll angle and the pitch angle, respectively. (Y subscript, Z subscript) and (K subscript, M subscript, N subscript) are the hydrodynamic coefficients used in representing (Y, Z) and (K, M, N) as a function of the subscripts, respectively. The values of these hydrodynamic coefficients are given on Appendix B. In the case of the submarines, since the submarines are assumed to have 6 DOF motion, the motion of the submarines could be represented by Eqs. (4-7)-(4-1). On the other hand, in the case of the surface ships, since the surface ships are assumed to have 3 DOF motion, the motion of the surface ships could be represented by Eqs. (4-13)-(4-15). u = U ( const.) (4-13) ρ 4 ρ 3 mv mur = l Yr r + l ( Yv v + Yrur) ρ + l ( Yvuv + u Yδ rδ r) (4-14) 33

47 ρ 5 Ir z = lnr r ρ 4 + l ( Nrur + Nv v ) ρ 3 + l ( Nvuv + u Nδ rδ r) (4-15) Verification of the implementation of manevuering equations As presented in sub-section 4.1.1, the linearized maneuvering equations from Babaoglu (1998) are applied in this study. The verification of the linearized maneuvering equations was carried out and presented in Babaoglu (1998). Under the verification of the linearized maneuvering equations by Babaoglu (1998), the verification of the implementation of the linearized maneuvering equations was carried out in this study. The depth change simulation under the same conditions with that of the depth change simulation by Babaoglu (1998) was carried out and the results of this study were compared to that of Babaoglu (1998) as shown in Figure 4-3 and Figure 4-4. Figure 4-3 shows the results of the depth change simulation when the target depth is m (100 ft) and the forward speed is 4.63 m/s (9 knots). Figure 4-4 shows the results of the depth change simulation when the target depth is m (100 ft) and the forward speed is 9.17 m/s (1 knots). Considering the restriction that the results of Babaoglu (1998) are displayed by taking the points on the graph in Babaoglu (1998), the results of this study could be thought to be consistent with that of Babaoglu (1998) well. It could be said that there is no problem in implementing the linearized maneuvering equations. 34

48 Figure 4-3 Depth change simulation (target depth: m, forward speed: 4.63 m/s) Figure 4-4 Depth change simulation (target depth: m, forward speed: 9.17 m/s) 35

49 4.. Control of hydroplanes The naval ships would control their hydroplanes to change their direction of heading. As shown in Figure 4-5, surface ships and submarines could change their direction of heading in the yaw motion by controlling their rudders (vertical hydroplanes) and submarines could change their direction of heading in the pitch motion by controlling their bow planes and stern planes (horizontal hydroplanes). That is, naval ships change the deflection of their hydroplanes so that the forces and moments exerted on the hydroplanes would make the naval ships change their direction of heading. In this study, this relationship is considered through the terms including the deflections of the hydroplanes of naval ships in the linearized maneuvering equations as shown in sub-section And, how far the deflection of the hydroplanes would be changed is important and this is determined by how much the force and moment are required to change the direction of heading. Then, such required force and moment should be determined by considering the differences between the direction of heading and the desired direction to target positions. In this study, this is carried out by applying Proportional-Integral-Derivative (PID) controller. Figure 4-5 Control of hydroplanes The PID controller is a widely used type of feedback controller, which consists of 36

50 proportional, integral, and derivative parts as presented in Eq. (4-16) (Karl and Tore, 1995). The first term refers to the proportional part, the second term refers to the integral part, and the last term refers to the derivative part. t 1 d (4-16) ut () = K et () + e( τ) dτ Td et () T + i dt 0 where, K, T i, and T d are the gain parameters for the proportional, integral, and derivative parts, respectively. t is the time. e(t) is the error and u(t) is the output of the PID controller. In this study, the error corresponds to the differences between the direction of heading and the desired direction to the target positions. And the output corresponds to the required force and moment to change the direction of heading. 37

51 Modeling of the detection performance of naval ships with engineering level In this study, a passive sonar equation and beam patterns are applied for modeling the detection performance of naval ships with engineering level. The passive sonar equation represents the possibility of the detection of radiated noise from targets by the passive sonars of the naval ships. And, the beam patterns represent the spatial filtering of the passive sonars of the naval ships. The following would explain what the passive sonar equation and the beam patterns are Passive sonar equation The passive sonars of naval ships detect the noise which is radiated from targets and propagates in the form of acoustic wave. Figure 5-1 shows an overview from noise radiation to the detection of the radiated noise by the passive sonars. Figure 5-1(1) shows that first, the targets radiate noise. And, the radiated noise would propagate in all directions and far away, undergoing the loss of acoustic wave energy and the addition to background noise (Figure 5-1()). The background noise is any noise other than the radiated noise from the targets. Once the total noise, the radiated noise added to the background noise, propagates to the passive sonars, the passive sonars analyze the total noise (Figure 5-1(3)). Finally, sonar operators would determine whether or not the radiated noise is detected (Figure 5-1(4)). 38

52 Figure 5-1 Overview from noise radiation to the detection of radiated noise Such detection of radiated noise can be expressed as a passive sonar equation (Michael, 010): SE = SL PL NL BW + AG DT (5-1) The first term, the Source Level (SL), is the magnitude of the radiated noise, whose major sources are the engines and the propellers of the targets. The characteristics of the radiated noise vary, depending on the type and operational conditions of the targets, which would become some clues for the classification of the targets. In this study, the sources and the characteristics of the radiated noise are not considered and the data in Urick (1983) is 39

53 used for the values of the SL. The second term, Propagation Loss (PL), refers to the loss of acoustic wave energy that the radiated noise undergoes when propagating. This loss of acoustic wave energy results mainly from the spreading and the attenuation of acoustic wave. In this study, Eq. (5-) (Michael, 010) is used to determine the values of the PL. This equation considers the spreading and the attenuation of acoustic wave, and the reflection of acoustic wave from the sea surface. PL = kz z r 4 αr s t 10log10 e sin ( ) r (5-) where, r is the horizontal separation between the passive sonars and the targets, and this refers to the effect of the spreading of acoustic wave. α is the attenuation factor and this refers to the effect of the attenuation of acoustic wave. In this study, the data in Michael (010) is used for the values of the attenuation factor. k is the wave number. z s and z t are the depth of the passive sonars and the targets, respectively. The third term, Noise Level (NL), is the magnitude of the background noise. In this study, the data in Urick (1983) is used for the values of the NL. The fourth and fifth terms, BandWidth (BW) and Array Gain (AG), are related to signal processing. The passive sonars analyze the total noise, the radiated noise added to the background noise, by signal processing. The results of the signal processing are the magnitudes of the total noise according to the bearings and the frequencies. And, some loss and gain of acoustic wave energy would generate from the signal processing. The loss of acoustic wave energy generates because the signal processing is carried out in the defined range of frequencies called as processing bandwidth. Such loss of acoustic wave energy is 40

54 expressed as BW and the values of BW is determined by Eq. (5-3) (Michael, 010). (5-3) BW = 10 log 10 δ f where, δf is the processing bandwidth. Meanwhile, the gain of acoustic wave energy generates because of spatial filtering. The spatial filtering involves sampling acoustic wave in space to remove any noise of undesired directions, which would make the noise of desired directions more clear. The spatial filtering is largely determined by the beam patterns of hydrophone arrays. (The beam patterns would be explained in detail in sub-section 5..1.) Such gain of acoustic wave energy is expressed as AG and the value of AG could be determined by Eq. (5-4) (Michael, 010). AG = 10 log 10 Q N N Q B( Ω) dω Ω (5-4) where, Q N is the mean square pressure of the background noise within the processing bandwidth. The mean square pressure of noise corresponds to the magnitude of the noise. Ω is the solid angle. Q N Ω is the mean square pressure of the background noise per unit solid angle. B(Ω) is the beam pattern according to the solid angles. In this study, it is assumed that the background noise is isotropic and only horizontal directions are considered and then, Eq. (5-4) could be changed as presented in Eq. (5-5). 41

55 AG = 10log 10 Q N N Q B( Ω) dω Ω N Q 1 = 10log10 = 10log N 10 Q B( θ) dθ B( θ) dθ π π π = 10log10 B( θ) dθ (5-5) where, θ is the angle. B(θ) is the beam pattern according to the angles. The sixth term, Detection Threshold (DT) is the criteria for determining whether or not the radiated noise is detected. The values of DT could be determined by Eq. (5-6) (Michael, 010). DT = log 1 p fa (5-6) where, p fa is the false alarm probability. Finally, Signal Excess (SE) expresses the amount of excess of DT. The sonar operators would check the values of SE and decide whether or not the radiated noise is detected. Consequently, the sonar operators could know there are targets in the directions of the radiated noise. Since there is no real sonar operator in this study, whether or not the radiated noise is detected would be determined by the probability of detection which is assumed to be given by following log-normal distribution over SE (Ferla, 1991): 4

56 x σ 1 SE Pd ( SE) = e dx πσ (5-7) where, P d is the probability of detection. σ is the standard deviation. 43

57 5.. Beam pattern Beam pattern The passive sonars of naval ships carry out spatial filtering which involves sampling noise in space to remove any noise of undesired direction. In other words, the spatial filtering makes the noise of desired directions more clear. This spatial filtering helps sonar operators not only to detect the radiated noise from targets but also to know the directions of the radiated noise. Such spatial filtering is largely determined by the beam patterns of the hydrophone arrays at the passive sonars. A hydrophone is a device designed to be used for receiving underwater noise. The hydrophone arrays are the collections of the hydrophones and there are various types of the hydrophone arrays according to the configuration of the hydrophone arrays. And, the beam patterns of the hydrophone arrays represent how the measured magnitude of noise varies depending on the direction of the noise. The noise would propagate to the hydrophone arrays in the form of acoustic wave and then the differences in the phases of acoustic wave at each hydrophone would occur. These differences result in the beam patterns. Figure 5- shows how the differences in the phases of acoustic wave at each hydrophone occur in a linear hydrophone array. If acoustic wave comes perpendicularly to the linear hydrophone array, the phases of acoustic wave at each hydrophone are same. Meanwhile, if acoustic wave comes obliquely to the linear hydrophone array, the phases of the acoustic wave at each hydrophone are different, and then the acoustic wave energy would be lost. In other words, the measured magnitude of the noise coming obliquely is smaller than that of the noise coming perpendicularly. In contrast, it is able to lose the energy of acoustic wave coming perpendicularly, the 44

58 hydrophones making differences in the phases of acoustic wave at each hydrophone intentionally as shown in Figure 5-3. In this case, the measured magnitude of the noise coming obliquely is bigger than that of the noise coming perpendicularly. In this way, the measured magnitude of the noise could vary depending on the direction of the noise, and this is represented by the beam patterns. Figure 5- Differences in the phases of the noise at each hydrophone Figure 5-3 Intentional differences in the phases of the noise at each hydrophone 45

59 In this study, the beam patterns of linear hydrophone arrays and circular hydrophone arrays are applied and could be expressed as Eq. (5-8) (Michael, 010) and Eq. (5-9) (Li, 011), respectively. bu u u k θ φ L ( ) = sinc, = (sin sin ) (5-8) bu u u 4πr θ φ ( ) = [J 0( )], = sin λ (5-9) where, b(u) is the beam pattern. sinc is the sinc function and J 0 is the zero order Bessel function. k is the wave number and λ is the wave length. L is the length of linear hydrophone arrays and r is the radius of circular hydrophone arrays. θ is the bearing angle which corresponds to the direction of noise. ϕ is the look angle which corresponds to the desired direction of detection. The figures (Figure 5-4-Figure 5-7) show the beam patterns of a linear hydrophone array according to the change of the look angle when the wave number is 4.0 and the length of the linear hydrophone array is 30 m. For example, as shown in Figure 5-4, if the noise comes from the direction of 0, the measured magnitude of the noise is reduced by 0 db. And, if the noise comes from the direction of 60, the measured magnitude of the noise is reduced by 35 db. 46

60 Figure 5-4 Beam pattern of a linear hydrophone array (look angle: 0 ) Figure 5-5 Beam pattern of a linear hydrophone array (look angle: 30 ) 47

61 Figure 5-6 Beam pattern of a linear hydrophone array (look angle: 60 ) Figure 5-7 Beam pattern of a linear hydrophone array (look angle: 90 ) 5... Verification of the implementation of beam patterns As presented in sub-section 5..1, the beam patterns of linear hydrophone arrays and circular hydrophone arrays are applied in this study. The derivation and verification of the equations for the beam patterns of linear hydrophone arrays and circular hydrophone arrays (Eq. (5-8), Ep. (5-9)) were carried out and presented in Michael (010) and Li (011), 48

62 respectively. Under the verification of the equations for the beam patterns by Michael (010) and Li (011), the verification of the implementation of the equations for the beam patterns was carried out in this study. Figure 5-8 shows the beam patterns of a linear hydrophone array when the length of the linear hydrophone array is five times the wave length and the look angle is 0. Figure 5-9 shows the beam patterns of a circular hydrophone array when the diameter of the circular hydrophone array is five times the wave length and the look angle is 60. Considering the restriction that the results of Michael (010) and Li (011) are displayed by taking the points on the graph in Michael (010) and Li (011), the beam patterns of this study could be thought to be consistent with that of Michael (010) and Li (011) well. It could be said that there is no problem in implementing the equations for the beam patterns. Figure 5-8 Beam pattern of a linear hydrophone array 49

63 Figure 5-9 Beam pattern of a circular hydrophone array 50

64 Comparison with the engagement simulation of no engineering level The simulation core proposed by this study considers maneuvering equations, the control of hydroplanes, a passive sonar equation, and beam patterns. These considerations make it possible to carry out the engagement simulations of engineering level. The engagement simulations of engineering level could be closer to reality than the engagement simulations of no engineering level. This chapter shows the differences between the engagement simulation of engineering level and that of no engineering level Modeling of the maneuvering performance and the detection performance with no engineering level For the comparison with the engagement simulation of no engineering level, the maneuvering performance and the detection performance with no engineering level were modelled additionally as follows. Figure 6-1 Maneuvering performance of no engineering level First, the maneuvering performance with no engineering level was modelled by 51

65 considering the direction to the next target position and the speed as shown in Figure 6-1. This makes naval ships move to target positions along a straight path between target positions with the speed. However, in reality, naval ships could not move to target positions along the straight path. This is because the duration for the naval ships to change the direction of heading to the next target position makes the naval ships be off the straight path. Figure 6- Detection performance of no engineering level Next, the detection performance with no engineering level was modelled by considering the fixed detection range and the fixed probability of detection as shown in Figure 6-. That it, if a target is within the fixed detection range, the detection of the target would be determined by the fixed probability of detection. This does not consider that the probability of detection increases as targets get closer. 5

66 6.. Comparison between the engagement simulation of engineering level and the engagement simulation of no engineering level Figure 6-3 Scenario for the comparison with the engagement simulation of no engineering level As shown in Figure 6-3, the scenario for the comparison with the engagement simulation of no engineering level was that our forces consisted of one submarine which patrolled along the defined rectangular path at speed 10 knots and detected enemy forces. The enemy forces consisted of four surface ships which did not move and of which noise level was 00 db. The specifications for the submarine referred to the 14-class submarine. And, the specifications for the surface ships referred to the gearing-class destroyer. Carrying out the simulation, the patrol time and the detection count were checked as shown in Table 6-1. The patrol time represents the time which it would take for the submarine to patrol along the defined path. The detection count represents how many times the submarine detected the surface ships during the patrol. 53

67 Table 6-1 Results of comparison with the engagement simulation of no engineering level Engineering level No engineering level Patrol time [s] 7,797 7,675 Detection count [times] Enemy 1 7,144 3,685 Enemy 7,180 3,687 Enemy 3 7,180 3,681 Enemy 4 7,38 3,683 In the case of the patrol time, the value from the simulation of engineering level is bigger. This is because the simulation of no engineering level did not consider the duration for the naval ships to change the direction of heading to the next target position. And, in the case of the detection count, the values from the simulation with engineering level are bigger. This is because the simulation of no engineering level did not consider that the probability of detection increases as targets get closer. Above simple example shows that the engagement simulation of no engineering level could not consider some facts which should be considered to carry out simulations closer to reality. This is why the engagement simulation of engineering level is important. 54

68 Applications To verify the applicability of the simulation core, this simulation core was applied to detection performance simulations, maneuvering performance simulations, and engagement simulations. The results of these simulations ensures that the simulation core of this study considers both the engagement level and the engineering level, and features the flexibility and reusability of models. The following would show these simulations Detection performance simulation The detection performance simulations were carried out by changing the specifications of the passive sonars of a submarine in different scenarios Variations of the specification for the passive sonars of a submarine Figure 7-1 Specifications of the passive sonars of a submarine 55

69 As shown in Figure 7-1, this study referred to the 14-class submarine, and the diameter of Cylindrical Array Sonar (CAS) and the length of Flank Array Sonar (FAS) were estimated to be 4 m and 30 m, respectively. In the detection performance simulations, the CAS and the FAS were assumed to be a circular array sonar and a linear array sonar. Then, the diameter of the circular array sonar was changed from 3 m to 5 m. The length of the linear array sonar was changed from 5 m to 35 m. The figures (Figure 7--Figure 7-7) show the beam patterns of the circular array sonar and the linear array sonar according to the diameter and the length. As shown in these figures, the longer the diameter and the length, the wider the beam width. The width in which the maximum value decreases to the 3 db is called as the beam width. The beam width corresponds to the resolution which is the ability to resolve adjacent targets. And, the narrower the beam width, the better the resolution. Figure 7- Beam pattern of a circular array sonar (diameter: 3 m) 56

70 Figure 7-3 Beam pattern of a circular array sonar (diameter: 4 m) Figure 7-4 Beam pattern of a circular array sonar (diameter: 5 m) 57

71 Figure 7-5 Beam pattern of a linear array sonar (length: 5 m) Figure 7-6 Beam pattern of a linear array sonar (length: 30 m) 58

72 Figure 7-7 Beam pattern of a linear array sonar (length: 35 m) Case study The detection performance simulations were carried out by changing the diameter and the length of the circular array sonar and the linear array sonar in the two different scenarios. Figure 7-8 First scenario for the detection performance simulation As shown in Figure 7-8, the first scenario was that our forces consisted of one submarine 59

73 which moved along the straight path at speed 10 knots and detected enemy forces. The enemy forces consisted of ten surface ships which were located in the specified area randomly and did not move, and of which noise level was 15 db. The specifications for the submarine referred to the 14-class submarine. And, the specifications for the surface ships referred to the gearing-class destroyer. The criteria for the detection performance was assumed that the submarine should detect the five surface ships out of ten surface ships at least. Table 7-1 Results of the first scenario simulations Case Array diameter / length [m] The number of Circular Linear detected enemy forces A A A A A A The first scenario simulations were carried out, using the one of the circular array sonar and the linear array sonar, and changing the diameter and the length as shown in Table 7-1. The number of detected targets in Table 7-1 is the mean value of ten times simulations of each case. This is because the location of the surface ships were randomized at every simulation. In this scenario, it is said that the linear array sonar is more suitable than the circular array sonar. And, the longer the length of the linear array sonar, the more suitable the detection performance. These results correspond to the Array Gain (AG) at around 0 as shown in the figures. (Figure 7-9-Figure 7-14, The AG at around 0 is marked with a bluedashed rectangular.) In a passive sonar equation (Section 5.1), the probability of detection 60

74 becomes higher as the value of the AG becomes larger. The values of AG at around 0 of the linear array sonar are larger than that of the circular array sonar. And, the longer the length of the linear array sonar, the larger the values of AG at around 0. Meanwhile, the values of the AG of the circular array sonar are same regardless of the bearing angles because the array configuration of the circular array sonar is the circle. Figure 7-9 Array gain of the circular array sonar (diameter: 3 m) Figure 7-10 Array gain of the circular array sonar (diameter: 4 m) 61

75 Figure 7-11 Array gain of the circular array sonar (diameter: 5 m) Figure 7-1 Array gain of the linear array sonar (length: 5 m) 6

76 Figure 7-13 Array gain of the linear array sonar (length: 30 m) Figure 7-14 Array gain of the linear array sonar (length: 35 m) Among these six cases, Case A5 and Case A6 satisfy the criteria for the detection performance. And, considering that the length of the FAS of the 14-class submarine is 30 m, it is said that Case A5 is the most suitable case. 63

77 Figure 7-15 Second scenario for the detection performance simulation Then, as shown in Figure 7-15, the second scenario was that our forces consisted of one submarine which moved along the straight path at speed 10 knots and detected enemy forces. The enemy forces consisted of two submarines which moved along the straight path adjacently at speed 10 knots and of which noise level was 15 db. The specifications for the submarines referred to the 14-class submarine. The criteria for the detection performance was assumed that the submarine should detect the two adjacent surface ships. Table 7- Results of the second scenario simulations Case Array diameter / length [m] The number of Circular Linear detected enemy forces B1 3-1 B 4 - B3 5 - B4-5 1 B B6-35 The second scenario simulations were carried out, using the one of the circular array sonar and the linear array sonar, and changing the diameter and the length as shown in Table

78 In this scenario, it is said that the circular array sonar is more suitable than the linear array sonar. And, the longer the diameter of the circular array sonar, the more suitable the detection performance. These results correspond to the beam width at around 90 as shown in the figures. (Figure 7-16-Figure 7-1, The beam width at around 90 is marked with a blue-dashed rectangular.) The resolution which is the ability to resolve adjacent targets becomes better as the value of the beam width becomes smaller. The values of the beam width at around 90 of the circular array sonar are smaller than that of the linear array sonar. And, the longer the diameter of the circular array sonar, the smaller the values of beam width at around 90. Meanwhile, the values of the beam width of the circular array sonar are same regardless of the bearing angles because the array configuration of the circular array sonar is the circle. Figure 7-16 Beam width of the circular array sonar (diameter: 3 m) 65

79 Figure 7-17 Beam width of the circular array sonar (diameter: 4 m) Figure 7-18 Beam width of the circular array sonar (diameter: 5 m) 66

80 Figure 7-19 Beam width of the linear array sonar (length: 5 m) Figure 7-0 Beam width of the linear array sonar (length: 30 m) 67

81 Figure 7-1 Beam width of the linear array sonar (length: 35 m) Among these six cases, Case B, Case B3 and Case B6 satisfy the criteria for the detection performance. And, considering that the diameter and length of the CAS and the FAS of the 14-class submarine are 4 m and 30 m, respectively it is said that Case B is the most suitable. 68

82 7.. Maneuvering performance simulation The maneuvering performance simulations were carried out by changing the specifications of the hydroplanes of a submarine in different scenarios Variations of the specification for the hydroplanes of a submarine Figure 7- Specifications of the hydroplanes of a submarine As shown in Figure 7-, this study referred to the 14-class submarine. And, the specifications of the hydroplanes of the 14-class submarine were estimated as shown in the figures. (Figure 7-3-Figure 7-6) Figure 7-3 Specifications of the bow plane 69

83 Figure 7-4 Specifications of the stern plane Figure 7-5 Specification of the upper rudder Figure 7-6 Specification of the lower rudder Under these specifications, the hydrodynamic coefficients could be determined by Eqs. (7-1)-(7-4). (Bohlmann, 003) 70

84 S Zδ = a k L M ( P) ( P) ( P) ( P) x = Z L δ( P) δ( P) ( P) S Yδ = a k L N ( R) ( R) ( R) ( R) x = Y L δ( R) δ( R) ( R) (7-1) (7-) (7-3) (7-4) where, (P) is a bow or stern plane, and (R) is an upper or lower rudder. Z δ(p), M δ(p), Y δ(r), and N δ(r) are hydrodynamic coefficients representing normal force, pitching moment, lateral force, and yawing moment as a function of hydroplanes, respectively. δ(p) is the deflection of a bow or stern plane, and δ(r) is the deflection of an upper or lower rudder. L is the length of a submarine. S (P) is the area of a bow or stern plane, and S (R) is the area of an upper or lower rudder. x (P) is the lever arm from the center of gravity to a bow or stern plane, and x (R) is the lever arm from the center of gravity to an upper or lower rudder. a (P) is the lift slope of a bow or stern plane, and a (R) is the lift slope of an upper or lower rudder. In the maneuvering performance simulations, the areas of the above estimated hydroplanes were changed to be half times, and one and half times. As given by Eqs. (7-1)- (7-4), such area changes of the hydroplanes caused the values of the hydrodynamic coefficients to be changed. The values of the hydrodynamic coefficients are as presented in Table 7-3. And, it was assumed that the values of the other hydrodynamic coefficients would not be changed. The values of the other hydrodynamic coefficients are given on Appendix B. 71

85 Table 7-3 Hydrodynamic coefficients according to the area of the hydroplanes Area of hydroplanes 0.5 times 1 times 1.5 times Z δb Z δs M δb M δs Y δr= Y Upper δr+ Y Lower δr Y Upper δr Y Lower δr N δr= N Upper δr+ N Lower δr N Upper δr N Lower δr Case study The maneuvering performance simulations were carried out by changing the areas of the hydroplanes in the two different scenarios. Figure 7-7 First scenario for the maneuvering performance simulation As shown in Figure 7-7, the first scenario was that a submarine dived as changing the pitch angle of the submarine by controlling the deflection of the bow plane and the stern plane. The forward speed of the submarine was 10 knots. The specifications for the 7

86 submarine referred to the 14-class submarine. The maximum deflection of the bow plane and the stern plane were assumed to be 5 and 10, respectively. And, the limit of the pitch angle was assumed to be 30. The criteria for the maneuvering performance was assumed that the submarine should dive to the target depth 300 m within 155 s. The tolerance of the target depth was assumed to be 1 m. The areas of the bow plane and the stern plane of the 14-class submarine were estimated to be 4.16 m and 7.95 m, respectively. These two values were estimated according to the specifications shown in Figure 7-3 and Figure 7-4. The first scenario simulations were carried out, changing the areas of the bow plane and the stern plane to be half times, and one and half times as shown in Table 7-4. The arrival time in Table 7-4 is the time for the submarine to dive to the target depth 300 m. Table 7-4 Results of the first scenario simulations Case Area of the hydroplanes [m ] Bow plane Stern plane The arrival time [s] C C C C C C C C C In this scenario, it is said that the wider the areas of the bow plane and the stern plane, the shorter the arrival time. The following would explain about this tendency through the Case C1 and the Case C8. The arrival time of the Case C1, 53.8 s, is the longest and that of the Case C8, 15.9 s, is the shortest. And, the areas of the bow plane and the stern plane of the Case C8 are wider than those of the Case C1. Figure 7-8 shows the depth variations 73

87 of the submarine in the Case C1 and the Case C8. Figure 7-8 Depth variations in the Case C1 and the Case C8 And, Figure 7-9 shows the pitch angle variations in the Case C1 and the Case C8. As shown in Figure 7-9, the pitch angle in the Case C1 was changed more slowly than in the Case C8. Figure 7-9 Pitch angle variations in the Case C1 and the Case C8 Then, Figure 7-30 and Figure 7-31 show the deflection of the bow plane and the stern plane 74

88 in the Case C1 and the Case C8. As shown in these two figures, the time during which the deflection was the maximum value or the minimum value was longer in the Case C1 than in the Case C8. Figure 7-30 Deflection of the bow plane in the Case C1 and the Case C8 Figure 7-31 Deflection of the stern plane in the Case C1 and the Case C8 Overall, the smaller the areas of the bow plane and the stern plane, the longer the time for the bow plane and the stern plane to be hold at the maximum or minimum deflection. Then, 75

89 the pitch angle would be changed slowly, and the depth would be changed slowly. In the result, the smaller the areas of the upper rudder and the lower rudder, the longer for the submarine to dive to the target depth. However, this tendency does not hold at Case C6 and Case C9. This is because there was no overshot in the Case C6 and the Case C9. As shown in Figure 7-3, the depth variation of the submarine in the Case C9 had no overshot compared to that of the submarine in the Case C8. Figure 7-3 Depth variations in the Case C8 and the Case C9 Among these nine cases, Case C5 and C8 satisfy the criteria for the maneuvering performance. And, considering that the areas of the bow plane and the stern plane of the 14-class submarine are 4.16 m and 7.95 m, respectively, it is said that Case C5 is the most suitable case. 76

90 Figure 7-33 Second scenario for the maneuvering performance simulation Then, as shown in Figure 7-33, the second scenario was that a submarine patrolled along the ten positions as changing the yaw angle of the submarine by controlling the deflection of the upper rudder and the lower rudder. The forward speed of the submarine was 10 knots. The specifications for the submarine referred to the 14-class submarine. It was assumed that the deflection of the upper rudder and the lower rudder would be changed equally. The maximum deflections of the upper rudder and the lower rudder were assumed to be 40. The criteria for the maneuvering performance was assumed that the submarine should patrol along the ten positions within,10 s. The areas of the upper rudder and the lower rudder of the 14-class submarine were estimated to be 11.3 m and 1.94 m, respectively. These two values were estimated according to the specifications shown in Figure 7-5 and Figure 7-6. The second scenario simulations were carried out, changing the areas of the upper rudder and the lower rudder to be half times, and one and half times as shown in Table 7-5. The arrival time in Table 7-5 is the time for the submarine to patrol along the ten positions. The hyphen, -, in Table 7-5 means that the submarine failed to patrol along the ten positions in the Case D1. 77

91 Table 7-5 Results of the second scenario simulations Case Area of the rudders [m ] Upper rudder Lower rudder The arrival time [s] D D ,89. D ,10.0 D4 6.47,85.0 D ,09.0 D ,176.8 D7 6.47,08.4 D ,176.4 D ,156.5 In this scenario, it is said that the wider the areas of the upper rudder and the lower udder, the shorter the arrival time. The following would explain about this tendency through the Case D and the Case D9. The arrival time of the Case D,,89. s, is the longest and that of the Case D9,,156.5 s, is the shortest. And, the areas of the upper rudder and the lower rudder of the Case D9 are wider than those of the Case D. Figure 7-34 shows the trajectories of the submarines in the Case D and the Case D9. As shown in Figure 7-34, the submarine got more far away from the position in the Case D than in the Case D9. Figure 7-34 Trajectories in the Case D and the Case D9 78

92 And, Figure 7-35 shows the yaw angle variations in the Case D and the Case D9. As shown in Figure 7-35, the yaw angle in the Case D was changed more slowly than in the Case D9. Figure 7-35 Yaw angle variations in the Case D and the Case D9 79

93 Then, Figure 7-36 shows the deflection of the upper rudder and lower rudder in the Case D and the Case D9. As shown in Figure 7-36, the time during while the deflection was the maximum value or the minimum value was longer in the Case D than in the Case D9. Figure 7-36 Deflection of the upper rudder and the lower rudder in the Case D and the Case D9 Overall, the smaller the areas of the upper rudder and the lower rudder, the longer the time for the upper rudder and the lower rudder to be hold at the maximum or minimum deflection. Then, the yaw angle would be changed slowly, and the submarine would get far away from the patrol position more. In the result, the smaller the areas of the upper udder and the lower rudder, the longer for the submarine to patrol along the ten positions. 80

94 7.3. Engagement simulation The engagement simulations were carried out by changing the engagement situations in different scenarios Variations of the engagement situations Figure 7-37 Variations of the engagement situations The simulation core of this study features the flexibility and reusability of models so that it is easier to simulate various engagement situations with various naval ship models which consists of different command systems, weapon systems, detection systems, and maneuver systems as shown in Figure Applying such simulation core, the engagement simulations were carried out by changing the engagement situations such as the number of naval ships engaged, the tactics of the naval ships, and the weapons of the naval ships. 81

95 7.3.. Case study The engagement simulations were carried out for the five cases as presented in Table 7-6, checking whether or not the our forces would succeed to attack the enemy forces. And, Table 7-7 presents the properties of torpedoes. In these cases, the specifications for the maneuvering and detection performance of the submarines and the surface ships referred to the 14-class submarine and the gearing-class surface ship, respectively. The following would explain these cases. Table 7-6 Variations of the engagement situations Number Tactics Weapon Case Our Enemy Our Enemy Our Enemy Success forces forces forces forces forces forces E1 Patrol - O Torpedo1 E 1 1 X E3 Attack Torpedo O Evade Decoy E4 Torpedo1 Torpedo1 Torpedo1 X 3 E5 Torpedo1 Torpedo3 Torpedo1 O Table 7-7 Properties of torpedoes Torpedo Speed [knots] Lifespan [min] Torpedo1 0 0 Torpedo 0 30 Torpedo [Case E1] The scenario of the Case E1 was that our forces consisted of one submarine which would attack the enemy forces, and enemy forces consisted of one surface ship which would patrol along the defined path. First, as shown in Figure 7-38 and Figure 7-39, the submarine and the surface ships moved along the defined path. 8

96 Figure 7-38 Progress of the Case E1 simulation [1] Figure 7-39 Progress of the Case E1 simulation (the map view of the simulation GUI) [1] Next, as shown in Figure 7-40, the submarine detected and tracked the surface ships. 83

97 Figure 7-40 Progress of the Case E1 simulation (and the map view of the simulation GUI) [] Then, as shown in Figure 7-41, the submarine launched a torpedo and succeeded to attack the surface ships. Figure 7-41 Progress of the Case E1 simulation (and the map view of the simulation GUI) [3] 84

98 [Case E & Case E3] The scenario of the Case E and the Case E3 was that our forces consisted of one submarine which would attack the enemy forces, and enemy forces consisted of one surface ship which would evade after detecting the our forces. The progress of the Case E and the Case E3 was identical with that of the Case E1 until the surface ships launched the decoys as shown in Figure 7-4. Figure 7-4 Progress of the Case E and the Case E3 simulation (and the map view of the simulation GUI) Next, in the Case E, the submarine failed to attack the surface ship because the decoys succeeded to interrupt the torpedo as shown in Figure On the other hand, in the Case E3, the submarines succeeded to attack the surface ship because the decoys failed to interrupt the torpedo as shown in Figure The lifespan of the torpedo in the Case E3 was longer than that of the torpedo in the Case E, which was the reason why the submarine in the Case E3 succeeded to attack the surface ships. 85

99 Figure 7-43 Progress of the Case E simulation (and the map view of the simulation GUI) Figure 7-44 Progress of the Case E3 simulation (and the map view of the simulation GUI) 86

100 [Case E4 & Case E5] The scenario of the Case E4 and the Case E5 was that our forces consisted of three submarines which would attack the enemy forces, and enemy forces consisted of two surface ships which would evade after detecting the our forces. For convenience to indicate the submarines and the surface ships, the submarines are indicated as OurForce1, OurForce, and OurForce3, and the surface ships are indicated as EnemyForce1 and EnemyFormce. First, as shown in Figure 7-45 and Figure 7-46, the submarines and the surface ships moved along the defined path. Figure 7-45 Progress of the Case E4 and the Case E5 simulation [1] 87

101 Figure 7-46 Progress of the Case E4 and the Case E5 simulation (the map view of the simulation GUI) [1] Next, as shown in Figure 7-47, OurForce1 failed to attack EnemyForce. Figure 7-47 Progress of the Case E4 and the Case E5 simulation (and the map view of the simulation GUI) [] 88

102 Then, as shown in Figure 7-48, OurForce3 succeeded to attack EnemyForce and EnemyForce1 launched the decoys after detecting the torpedo launched by OurFroce. Until this situation, the progress of the Case E4 and the Case E5 are identical each other. Figure 7-48 Progress of the Case E4 and the Case E5 simulation (and the map view of the simulation GUI) [3] In the Case E4, OurForce failed to attack EnemyForce1 because the decoys succeeded to interrupt the torpedo as shown in Figure On the other hand, in the Case E5, OurForce succeeded to attack EnemyForce1 because the decoys failed to interrupt the torpedo as shown in Figure The lifespan of the torpedo of OurForce in the Case E5 was longer than that of OurForce in the Case E4, and the speed of the torpedo of OurForce in the Case E5 was faster than that of OurForce in the Case E4, which was the reason why the our forces in the Case E5 succeeded to attack all the enemy forces. 89

103 Figure 7-49 Progress of the Case E4 simulation (and the map view of the simulation GUI) Figure 7-50 Progress of the Case E5 simulation (and the map view of the simulation GUI) 90