Submarine concealment optimization method based on game theory and linear programming in complex terrain

Abstract

The invention discloses a submarine concealment optimization method based on a game theory and linear programming in a complex terrain, which considers the influence of the complex terrain on submarine concealment in a researched sea area. The method comprises the following steps: performing sound field calculation in an activity depth range of sonar carried by a submarine and a water surface vessel, obtaining a detection probability matrix based on a sonar equation, and determining an income matrix of the submarine on the basis of a game theory; and further solving a revenue matrix through a linear programming method, and quantitatively optimizing a submarine depth strategy. Compared with a traditional method, the submarine concealment optimization method has remarkable advantages in the aspects of concealment optimization, calculation efficiency and adaptability, is suitable for a complex submarine environment, and provides a reliable, simple, convenient and efficient solution for submarine concealment optimization.

Description

Technical Field

[0001] The present invention belongs to the technical field of submarines, and particularly relates to a method for optimizing the stealth of a submarine based on game theory and linear programming under complex terrain. Background Art

[0002] In modern naval warfare, the stealth of a submarine is directly related to the success or failure of its mission. With the rapid development of sonar detection technology, the resolution and detection ability of sonar have been significantly improved, and the survival ability of submarines in complex terrain and dynamic marine environments has been severely challenged. Therefore, how to formulate an efficient and quantitative stealth optimization strategy to avoid sonar detection has become a key issue in current research.

[0003] The existing technologies mainly adopt strategy optimization methods such as empirical rule methods and numerical simulation methods. However, these methods have certain limitations when dealing with complex terrain and multi-variable confrontation environments, and the specific analysis is as follows:

[0004] (1) Stealth optimization based on empirical rules. Traditional methods are mostly based on empirical rules, and the stealth of a submarine is optimized through qualitative analysis of sonar detection probability. Although basic avoidance strategies are achieved, the multi-path effect of sound wave propagation, terrain shielding effect, and influence of environmental noise cannot be fully considered under complex terrain, resulting in large deviations in stealth evaluation and optimization results.

[0005] (2) Numerical simulation methods. Numerical simulation methods have high requirements for computing resources, and the computing efficiency is low when facing complex environments. Moreover, they mainly focus on sound field analysis and lack the ability to quantitatively evaluate stealth. Therefore, simply relying on numerical simulation methods may not be sufficient to comprehensively evaluate the stealth of a submarine.

[0006] In summary, there are many deficiencies in the existing technologies for optimizing the stealth of submarines under complex terrain conditions, including low computing efficiency, only qualitative analysis of stealth, and insufficient reliability of optimization results. Therefore, there is an urgent need for a method based on game theory to construct an adversarial model between a submarine and sonar, and use linear programming technology to solve the optimization strategy of submarine stealth, providing an efficient and accurate technical means for submarine stealth optimization under complex terrain, thereby making up for the deficiencies of the existing technologies. Summary of the Invention

[0007] To overcome the deficiencies of the prior art, the present invention provides an optimization method for submarine stealth based on game theory and linear programming in complex terrains, taking into account the influence of complex terrains on submarine stealth in the studied sea area. Within the active depth range of sonars carried by submarines and surface ships, acoustic field calculations are performed, and a detection probability matrix is obtained based on the sonar equation. Under the basis of game theory, the profit matrix of the submarine is determined. Further, the profit matrix is solved by linear programming methods, and the submarine depth strategy is quantitatively optimized. Compared with traditional methods, the present invention has significant advantages in terms of stealth optimization, calculation efficiency, and adaptability, is applicable to complex seabed environments, and provides a reliable, simple, and efficient solution for submarine stealth optimization.

[0008] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0009] Step 1: Detection probability modeling;

[0010] Determine the depth range in which the submarine and sonar operate, then create the complex terrain required for the ray model, perform acoustic field calculations, and obtain the propagation loss values at different sound source depths and receiving depths; establish a model based on the sonar equation, and the narrowband passive sonar equation under coherent processing and narrowband passive detection:

[0011] SE = SL - TL - NL + (AG - BW) - DT (1)

[0012] Where, SE is the signal margin received by the passive sonar; SL is the narrowband sound source level of the submarine's radiated noise; TL is the acoustic propagation loss value from the position of the submarine to the sonar position; NL is the ocean background noise related to the sea state; AG is the array gain; BW is the analysis bandwidth; DT is the detection threshold of the passive sonar detection system;

[0013] According to formula (1), the specific formula for the detection probability matrix is as shown in formula (2):

[0014]

[0015] Step 2: Game equilibrium model;

[0016] Apply matrix game to the submarine, and define a measurement criterion for the submarine called profit; the profit is the negative value of the expectation of the passive detection probability of the sonar within a certain radius; in a two-dimensional scenario, the profit is represented by U:

[0017]

[0018] Where, R represents the left and right calculation radius centered on the submarine in the two-dimensional scenario; P is the detection probability of the sonar for the submarine, that is, the probability of the submarine being detected; d represents the depth of the sonar, z represents the depth of the submarine, and r represents the distance between the submarine and the sonar;

[0019] Step 3: Solve the payoff matrix by linear programming;

[0020] Minimizing the maximum loss of the submarine is specified as follows:

[0021]

[0022] where V is the maximum loss of the submarine, U(z i , d j ) is the payoff matrix, Z i represents the probability that the submarine selects depth z i , m represents the number of different depths z i that the submarine can select, and j represents the number of different depths d j that the sonar can select;

[0023] Maximizing the minimum payoff of the variable sonar carried by the surface ship is specified as follows:

[0024]

[0025] where W is the minimum payoff of the sonar, D i represents the probability that the sonar selects depth z i , n represents the number of different depths z i that the sonar can select, and j represents the number of different depths d j that the submarine can select;

[0026] The optimized depth of the submarine is obtained by solving the payoff matrix U(i, j) through linear programming. Based on this depth, the stealth analysis of the submarine is carried out.

[0027] Preferably, the ray model is the Bellhop model.

[0028] A computer program that causes a computer to execute the above submarine stealth optimization method.

[0029] An electronic device, comprising: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory so that the electronic device executes the above submarine stealth optimization method.

[0030] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the above submarine stealth optimization method is implemented.

[0031] A chip, comprising: a processor, which is used to call and run a computer program from a memory, so that a device installed with the chip executes the above submarine stealth optimization method.

[0032] A computer program product, the computer program product includes a computer storage medium, the computer storage medium stores a computer program, the computer program includes instructions that can be executed by at least one processor, and when the instructions are executed by the at least one processor, the above-mentioned submarine stealth optimization method is implemented.

[0033] The beneficial effects of the present invention are as follows:

[0034] (1) The present invention uses a matrix game model to model the interaction relationship between submarines and sonars, comprehensively considering the mutual influence of the strategies of both sides. Through the zero-sum game theory of game theory, the optimal submarine strategy is found to avoid being detected by the enemy sonar. This method has stronger adaptability compared with conventional static strategies.

[0035] (2) The present invention uses linear programming to solve the optimal strategies of submarines and sonars, can handle various constraint conditions, and perform real-time optimization in complex environments. Compared with traditional non-linear optimization methods, linear programming has higher computational efficiency and accuracy, and can quickly find the optimal solution in a large-scale parameter space.

[0036] (3) The present invention uses the Bellhop model to calculate the sound field, considering the changes in seabed topography and sound propagation loss, and accurately simulates the interaction between submarines and sonars. Conventional methods often ignore the influence of complex topography on sonar detection performance, which may lead to inaccurate estimation of submarine stealth. By considering complex topography such as seamounts in the present invention, the stealth of submarines can be calculated more accurately, providing a more reliable stealth optimization scheme. Brief Description of the Drawings

[0037] Figure 1 For the modeling results of the passive sonar detection probability at different source depths based on the munk sound speed curve and seamount topography, (a) the source depth is 300m, the modeling results of the passive detection probability, (b) the source depth is 1000m, the modeling results of the passive detection probability;

[0038] Figure 2 It is the flow chart of the method framework of the present invention;

[0039] Figure 3 For the propagation loss results obtained based on the sound speed profile and topography, (a) the sound speed profile used in the simulation, (b) the seamount topography and propagation loss map;

[0040] Figure 4Optimal depth strategy probability distribution for different horizontal distances of the submarine from the center of the seamount. (a) Payoff matrix when the submarine is at a horizontal distance of 0 km from the seamount, (b) Payoff matrix when the submarine is at a horizontal distance of 5 km from the seamount, (c) Payoff matrix when the submarine is at a horizontal distance of 10 km from the seamount, (d) Payoff matrix when the submarine is at a horizontal distance of 15 km from the seamount;

[0041] Figure 5 Optimal depth strategy probability distribution for different horizontal distances of the submarine from the center of the seamount. Detailed implementation manner

[0042] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0043] The present invention proposes a method for optimizing the concealment strategy based on game theory. By constructing a game equilibrium model and using linear programming techniques to solve the optimal mixed strategy, the concealment strategy of the submarine in complex terrain is optimized, providing theoretical support and technical guidance for the quantitative research on the concealment of the submarine.

[0044] In the sea area studied by the present invention, the influence of complex terrain on the concealment of the submarine is considered. Within the active depth range of the sonar carried by the submarine and the surface ship, the acoustic field is calculated, and the detection probability matrix is obtained based on the sonar equation. Under the basis of game theory, the payoff matrix of the submarine is determined. Further, the payoff matrix is solved by linear programming method, and the depth strategy of the submarine is quantitatively optimized. The process is divided into the following three steps:

[0045] Step 1: Detection probability modeling.

[0046] First, it is necessary to determine the depth range in which the submarine and the sonar are active. Then, create the complex terrain required for the ray model (Bellhop model), calculate the acoustic field, and obtain the propagation loss values at different source depths and receiving depths. Based on the sonar equation, a model is established. The narrowband passive sonar equation under coherent processing and narrowband passive detection:

[0047] SE = SL - TL - NL + (AG - BW) - DT (1)

[0048] Among them, SE is the signal margin received by the passive sonar; SL is the narrowband source level of the submarine's radiated noise; TL is the acoustic propagation loss value from the position of the submarine to the position of the sonar; NL is the ocean background noise related to the sea state; AG is the array gain; BW is the analysis bandwidth; DT is the detection threshold of the passive sonar detection system.

[0049] According to the above formula, the specific formula of the specific detection probability matrix can be obtained, and the detection probability P d Is closely related to the signal margin SE. The larger the signal margin, the greater the detection probability.

[0050]

[0051] Step 2: Game equilibrium model.

[0052] Secondly, apply matrix game to our submarine and define a measure of success for the submarine called payoff. Since the submarine has to avoid passive detection by anti-submarine ships, its payoff is the negative of the expected value of the probability of passive detection by sonar within a certain radius. In a two-dimensional scenario, the payoff is represented by U:

[0053]

[0054] R represents the left and right calculation radius centered on the submarine in a two-dimensional scenario; P is the detection probability of the sonar for the submarine, that is, the probability of the submarine being detected. Therefore, for the discrete distribution of d and z values U(z i , d j ), the payoff matrix U ij . can be generated. Setting the payoff of the sonar to -U(z i , d j ) will turn the situation into a two-person zero-sum game. This ensures that neither party can change their strategy in a way that is beneficial to both, leaving no room for cooperation.

[0055] Step 3: Solve the payoff matrix by linear programming.

[0056] Finally, after obtaining the above payoff matrix, solve for the optimal depth of the submarine through linear programming. The specific operations are as follows:

[0057] Minimize the maximum loss of the submarine as follows:

[0058]

[0059] where V is the maximum loss of the submarine, U(z i , d j ) is the payoff matrix, Z i represents the probability that the submarine selects depth z i , m represents the number of different depths z i that the submarine can select, and j represents the number of different depths d j that the sonar can select;

[0060] Since the surface ship carries a variable sonar, maximize the minimum payoff of the variable sonar as follows:

[0061]

[0062] where W is the minimum payoff of the sonar, D i represents the sonar selecting depth z iThe probability; n represents the number of different depths z that the sonar can select, and j represents the number of different depths d that the submarine can select; i ; j of;

[0063] The optimal depth of the submarine can be obtained by solving the payoff matrix through linear programming. Based on this depth, the stealth analysis of the submarine can be carried out.

[0064] Through the model of the passive sonar equation, the present invention calculates the signal excess SE of the submarine at different depths and sonar depths, and further derives the detection probability matrix. This detection probability matrix is used to describe the probability that the submarine is detected by the sonar. The greater the signal excess, the higher the detection probability. In this way, a mathematical basis for the detection probability can be provided for subsequent game analysis.

[0065] The method of the present invention defines the payoff of the submarine (i.e., the negative value of the expected probability of avoiding being detected by the sonar) in a two-dimensional scenario, and applies it to the game between the submarine and the sonar through the construction of the payoff matrix. By setting the payoff of the sonar to be the opposite of that of the submarine, this game is transformed into a zero-sum game, ensuring that the strategy optimization between the submarine and the sonar can reach the optimal equilibrium.

[0066] The method of the present invention solves the optimal strategy of the submarine through linear programming, aiming to minimize the maximum loss of the submarine and maximize the minimum payoff of the sonar. After obtaining the optimized depth strategy, a quantitative analysis of the submarine's stealth is carried out to evaluate the detection probability of the submarine at this depth, thereby further improving the survival ability and stealth of the submarine.

[0067] Embodiment:

[0068] Figure 1 In it, the results of the passive sonar detection probability modeling at different sound source depths based on the Munk sound speed curve and seamount terrain are given respectively. Among them, Figure (a) shows the results of passive detection under the condition of a sound source depth of 300 m, and Figure (b) gives the results under the condition of a sound source depth of 1000 m. The modeling of the passive sonar detection probability can further provide theoretical support for the optimal depth of the submarine under complex conditions.

[0069] Figure 2 In it, a framework flowchart of the submarine stealth optimization method based on game theory and linear programming under complex terrain is given. The implementation process is divided into three processes: (1) Calculate the propagation loss value by inputting the depth range, sound speed profile, and terrain of the submarine and the surface ship sonar into Bellhop. (2) Combine the calculated propagation loss, sonar equation, and detection probability function to obtain the payoff matrix. (3) Solve the payoff matrix through linear programming to obtain the optimal strategy of the submarine.

[0070] Figure 3The propagation loss results obtained based on the given sound speed profile and terrain are presented.

[0071] Figure 4 The payoff matrix under different positions of the submarine relative to the seamount is presented. It can be seen from the figure that the optimal depth of the submarine varies with its distance from the seamount. When the distance from the seamount is 0 km, as shown in Fig. (a), the optimal depth of the submarine is 140 - 160 m with the maximum payoff. When the distance from the seamount is 15 km, as shown in Fig. (d), the optimal depths of the submarine are 30 m and 400 m with the maximum payoff.

[0072] Figure 5 The probability distribution of the optimal depth strategy for different horizontal distances of the submarine from the center of the seamount is presented. It can be seen from the figure that in the area far from the seamount, the probability distribution is concentrated. When approaching the center of the seamount, the concealment of the submarine changes significantly. In the 0 - 1 km area, the depth of the submarine is concentrated at 100 - 160 m; in the 2 - 3 km area, the depth is concentrated at 350 - 400 m to utilize the seamount for shielding detection. In the area 4 km and beyond, the shielding effect weakens, and the submarine depth strategy tends to be shallower (30 - 50 m) and deeper water layers (350 - 400 m), with a lower probability for the middle water layer strategy.

[0073] The present invention has achieved obvious implementation effects under seamount terrain conditions and can effectively improve the concealment of submarines in complex environments. By modeling the game relationship between the submarine and sonar and combining with the complex ocean terrain, the optimal optimization of the submarine strategy is realized. Compared with traditional methods, the present invention has significant advantages in terms of concealment optimization, computational efficiency, and adaptability, is applicable to complex seabed environments, and provides a reliable, simple, and efficient solution for submarine concealment optimization.

Claims

1. A method for optimizing submarine stealth under complex terrain based on game theory and linear programming, characterized in that: The steps include: Step 1: Detection probability modeling; Determine the depth range of submarine and sonar activities, then create the complex terrain required by the ray model, perform sound field calculations, and obtain the propagation loss values ​​at different sound source depths and receiving depths; establish a model based on the sonar equation, the narrowband passive sonar equation under coherent processing and narrowband passive detection: SE=SL-TL-NL+(AG-BW)-DT (1) Among them, SE is the signal margin received by the passive sonar; SL is the narrowband sound source level of the submarine radiation noise; TL is the sound propagation loss value from the submarine's position to the sonar position; NL is the ocean background noise related to the sea conditions; AG is the array gain; BW is the analysis bandwidth; DT is the detection threshold of the passive sonar detection system; According to formula (1), the specific detection probability matrix is ​​obtained as formula (2): Step 2: Game equilibrium model; Applying matrix game to submarines, a metric is defined for submarines called payoff; the payoff is the expected negative value of the probability of passive sonar detection within a certain radius; in a two-dimensional scenario, payoff is represented by U: Among them, R represents the left and right calculation radius centered on the submarine in a two-dimensional scene; P is the detection probability of the submarine by the sonar, that is, the probability of the submarine being detected; d represents the depth of the sonar, z represents the depth of the submarine, and r represents the distance between the submarine and the sonar; Step 3: Solve the profit matrix by linear programming; The maximum loss minimization for submarines is stipulated as follows: Among them, V is the maximum loss of the submarine, U(z i ,d j ) is the payoff matrix, Z i Indicates the submarine's selected depth z i The probability of m represents the different depths z that the submarine can choose i The number of j represents the different depths d that the sonar can choose j the number of Since the surface ship carries variable sonar, the minimum benefit maximization of variable sonar is stipulated as follows: Where W is the minimum benefit of sonar, D i Indicates the sonar selected depth z i The probability of n representing the different depths z that the sonar can choose i The number of j represents the different depths d that the submarine can choose j the number of The optimal depth of the submarine is obtained by solving the profit matrix U(i,j) through linear programming. Based on this depth, the stealth analysis of the submarine is carried out.

2. According to claim 1, a method for optimizing submarine concealment based on game theory and linear programming in complex terrain is characterized in that: The ray model is a Bellhop model.

3. A computer program, characterized in that The computer program enables a computer to execute the method according to any one of claims 1 to 2.

4. An electronic device, characterized in that: include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the method as claimed in any one of claims 1 to 2.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 2 is implemented.

6. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes a method as claimed in any one of claims 1 to 2.

7. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 2 is implemented.

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