A multi-node water surface platform search formation parameter multi-objective optimization method

Abstract

The application provides a multi-node water surface platform search array parameter multi-objective optimization method, on the basis of defining a region dynamic coverage evaluation index and search array parameterization characterization, using a multi-objective particle swarm optimization algorithm to solve a multi-dimensional decision vector, multi-objective optimization problem of multi-node water surface platform array parameter optimization, improving the effective coverage rate while improving the coverage speed. The application introduces a target existence probability, realizes the performance evaluation of the coverage effect, uses the parameterized characterization array and platform spacing to reduce the difficulty of obtaining the optimal search path, and uses the multi-objective particle swarm optimization algorithm to solve the array parameters, thereby improving the optimization efficiency of the parameter optimization method.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-node water surface platform search path, and mainly relates to a multi-node water surface platform search formation parameter multi-objective optimization method. BACKGROUND

[0002] Most of the conventional multi-node water surface platform search path optimization methods for regional coverage establish optimization models for a single optimization target, and face the challenge of model mismatch in a complex dynamic environment. In addition, since the multi-node water surface platform search often uses a fixed formation to cover the search area when performing a search task, frequent changes in speed and direction can seriously affect the performance of sonar equipment detection. Therefore, a reasonable search formation is an effective means to improve the search efficiency of the multi-node water surface platform.

[0003] The closest prior art: In the prior art, domestic and foreign scholars mainly design the optimization of multi-node water surface platform formation according to the combat scenario. Han Qing introduces in detail the common formation types such as single column, single row, echelon, azimuth team and chevron team and their uses. Li Hao establishes a comprehensive evaluation index system for the typical formation search formation and applies the triangular fuzzy comprehensive evaluation method to optimize the formation search formation. In addition, Guo Chuanfu discusses the towed array sonar model and determines the platform configuration when the formation uses the towed array sonar to search, which has a certain reference value for the optimization of search formation.

[0004] 1. The existing technology for optimizing the search path of the multi-node water surface platform mainly focuses on a single optimization target and ignores the optimization of the search path in a complex dynamic environment, which cannot optimize multiple indicators at the same time.

[0005] 2. The consideration of the search efficiency of the multi-node water surface platform in a dynamic environment is lacking, which cannot fully exert the performance of the sonar detection of the multi-node water surface platform search. SUMMARY

[0006] The present application aims to overcome the deficiencies in the prior art and provide a multi-node water surface platform search formation parameter multi-objective optimization method.

[0007] The purpose of the present application is achieved by the following technical scheme. A multi-node water surface platform search formation parameter multi-objective optimization method includes the following steps:

[0008] Step 1: Characterize various formations involved in search task planning in a parameterized form, and apply the multi-objective particle swarm optimization algorithm based on the hierarchical sequence method to the optimization of formation parameters. In the optimization process, multiple targets are optimized in turn according to the importance ranking, and the efficient optimization of multi-objective search efficiency is realized.

[0009] Step 2: Introduce the probability of target existence to construct a search performance evaluation index, which reflects the coverage rate and speed of the dynamic environment during the search process.

[0010] In step 1, a set of array parameters is treated as a particle, and the particle swarm optimization algorithm is used to adjust the parameters of each particle to obtain the optimal multi-objective solution. A multi-objective optimization problem with n-dimensional decision variables and m-dimensional objective variables is expressed as:

[0011]

[0012] The decision vector is X = (x1, x2, ..., x...). n ), and the space it resides in is Ω, Ω={X∈R n The target space is the space containing the m-dimensional vector F(X); the m targets are sorted according to their importance, assuming the sorting result is f1(X)>f2(X)>,...,>f m (X), of which f1(X) is the most important, f m (X) is the least important; during the optimization process, multiple objectives are optimized sequentially according to their importance; the optimization process is as follows: first, solve the optimization problem min f1(X), where X∈Ω, to obtain the optimal solution X. (1) and the optimal value f1 * Then solve the optimization problem min f2(X), where X∈Ω1=Ω∩{Xf1(X)≤f1} *}, thus obtaining the optimal solution X (2) and optimal value Repeat the above process to solve the optimization problem with m objectives, and obtain an optimal decision vector X. opt .

[0013] In step 2, the probability of target existence is introduced to construct a multi-node surface platform coverage performance evaluation function;

[0014] Step 2.1: Single-objective evaluation indicator: Regional coverage rate

[0015] For the entire search region, in order to construct the optimization objective function, the region coverage Q(k) is defined as the average probability of the target existing within the region, i.e.

[0016]

[0017] In the formula, P T (i,j,k) represents the probability that the target exists at grid position (i,j) at time k; n x and n y n represents the number of grid cells along the X and Y axes of the region, respectively. x n y Let P be the total number of grid cells in the region, and let P be the initial probability of the target's existence.T (i,j,1) = 0.5, where i < n x , j < n y ; the smaller the coverage Q(k) value is, the better the area coverage performance at k moment is;

[0018] Step 2.2: Multi-objective evaluation index: area coverage rate, coverage speed

[0019] According to the actual operational requirements in the search path planning, the area coverage rate and the coverage speed are taken as two optimization objectives of the multi-objective particle swarm algorithm, and are defined as follows:

[0020]

[0021] In the formula, k represents the detection moment, K represents the total length of the search task; when the optimization objective is f1, the area coverage rate at the end of the optimization search task is optimized; when the optimization objective is f2, the proportion of the time length used when the average existence probability of the target is 0.2 in the search process to the total length of the task is optimized, and the smaller the value is, the faster the coverage speed is.

[0022] The present application has the beneficial effects that the present application is mainly applied to the field of search path planning of multi-node water surface platforms, and proposes to adopt the particle swarm algorithm based on the hierarchical sequence method to simultaneously optimize two key indexes in the search process of the multi-node water surface platforms: the area coverage rate and the coverage speed, so as to solve the optimal search array parameters, and to plan the search array of the multi-node water surface platforms in the dynamic environment which can better meet the coverage performance. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained according to these drawings without any creative labor for those skilled in the art.

[0024] Figure 1 It is a schematic diagram of the area coverage rate changing with the search time, which represents the curve of the area coverage rate changing with the search time in the search process of the multi-node water surface platforms and the value of the two optimization objectives.

[0025] Figure 2 It is a schematic diagram of the Z-shaped back-and-forth transformation process, which represents the schematic diagram of the array transformation process with the array parameters, and the search array is characterized by the parameters.

[0026] Figure 3 It is a comparison curve of the optimization objective 1: the area coverage rate changing with the iteration number in the optimization iteration process of the conventional particle swarm algorithm and the multi-objective particle swarm algorithm.

[0027] Figure 4Comparison curves of the changes in coverage speed with the number of iterations during the optimization iteration process of conventional particle swarm optimization algorithm and multi-objective particle swarm optimization algorithm. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0029] This invention relates to a multi-objective optimization method for the search array parameters of a multi-node surface platform. The core steps of this method include:

[0030] Step 1: Hierarchical Sequencing Method

[0031] Traditional particle swarm optimization (PSO) algorithms typically optimize only a single objective function. However, in actual optimization processes, it is often necessary to optimize multiple metrics simultaneously. To meet this need, this invention proposes a multi-objective PSO algorithm that employs a hierarchical sequence method to simultaneously optimize multiple objectives.

[0032] Hierarchical sequence optimization is a commonly used method for multi-objective optimization. It sorts multiple objective functions according to priority and optimizes them layer by layer. By employing hierarchical sequence optimization, multiple objectives can be optimized simultaneously within the particle swarm optimization algorithm. Specifically, a set of array parameters can be regarded as a particle, and the search mechanism of the particle swarm optimization algorithm can be used to adjust the parameters of each particle to obtain the optimal multi-objective solution. A multi-objective optimization problem with n-dimensional decision variables and m-dimensional objective variables can be represented as:

[0033]

[0034] The decision vector is X = (x1, x2, ..., x...). n ), and the space it resides in is Ω, Ω={X∈R n The target space is the space containing the m-dimensional vector F(X). Following the hierarchical sequence method, the m targets are sorted according to their importance, assuming the sorting result is f1(X)>f2(X)>,...,>f m (X), of which f1(X) is the most important, f m (X) is the least important. During the optimization process, multiple objectives are optimized sequentially according to their importance. The optimization process is as follows: First, solve the optimization problem min f1(X), where X∈Ω, to obtain the optimal solution X. (1) and the optimal value f1 *; then solve the optimization problem min f2(X), where X e Q1 = Q n {X f1(X) < f1 *}, get the optimal solution X (2) and the optimal value Repeat the above process to complete the solution of m target optimization problem, obtained a optimal decision vector X opt .

[0035] Step 2: multi-node water surface platform coverage performance evaluation function

[0036] Step 2.1: single target evaluation index: area coverage rate

[0037] For the entire search area, in order to construct the optimization objective function, the area coverage rate Q(k) is defined as the average probability value of the target existing in the region, that is

[0038]

[0039] In the formula, P T (i,j,k) represents the probability of target existing at grid position (i,j) at time k; n x And n y Respectively represent the number of grid along the X axis and Y axis of the region, n x n y The total number of grids in the region, the initial probability of target existing P T (i,j,1) = 0.5, where i < n x ,j < n y . The smaller the value of coverage rate Q(k) represents the better the performance of the region at time k.

[0040] Step 2.2: multi-objective evaluation index: area coverage rate, coverage speed

[0041] According to the actual operational requirements in the search path planning, the area coverage rate and the coverage speed are taken as two optimization objectives of the multi-objective particle swarm algorithm, which are defined as follows:

[0042]

[0043] In the formula, k represents the detection time, and K represents the total duration of the search task. When the optimization objective is f1, the area coverage rate at the end of the search task is optimized; when the optimization objective is f2, the proportion of the time used when the average probability of the target existing in the search process is 0.2 to the total duration of the task is optimized, and the smaller the value represents the faster the coverage speed. The area coverage rate curve changing with search time in the search process of multi-node water surface platform and the value of two optimization objectives are shown in Figure 1 .

[0044] Step 3: algorithm application and pseudo code

[0045] Compared with the conventional particle swarm algorithm, the improved multi-objective particle swarm algorithm can select optimization focus according to operational requirements, adjust the optimization order of the objective function, give the optimal combination of the array pattern and the distance parameter in accordance with the actual search process of the sonar, and fully exert the operational capability of the sonar equipment. The pseudo code of the algorithm is as follows:

[0046] Table 1 Pseudo code of multi-objective particle swarm algorithm

[0047]

[0048]

[0049] Embodiment: The typical specific implementation steps of the method are as follows:

[0050] Step 1: Modeling of search task;

[0051] Step 1.1: Regularization of search area;

[0052] The irregular search area is simplified into a rectangular, trapezoidal or sector area. The search area simplification process is not involved in the present application.

[0053] Step 1.2: Analysis of sound propagation;

[0054] The sound propagation law of the sonar operating frequency is analyzed in view of the historical or on-site measured environmental hydrological data. The sound propagation analysis process is not involved in the present application.

[0055] Step 1.3: Analysis of sonar detection performance in search area;

[0056] The regional sonar detection performance in the complex marine environment is analyzed in view of the multi-node water surface platform search task area. The performance analysis process is not involved in the present application.

[0057] Step 1.4: Sonar operating parameter setting;

[0058] The appropriate sonar operating parameters and sonar detection intervals are set in view of the sound propagation law. The sonar operating parameter setting process is not involved in the present application.

[0059] Step 2: Parameterization of array pattern;

[0060] Various array patterns involved in the search task planning are characterized in a parameterized form, mainly including straight-line back-and-forth, rectangular encircling, Z-shaped back-and-forth and the like, and the corresponding template parameters include direction, speed, barrier distance and the like. The array pattern parameterization process is not involved in the present application, and only the parameter type of particle swarm optimization is described by taking the Z-shaped back-and-forth array pattern parameterization as an example.

[0061] When a multi-node surface platform performs a search mission, the node formation and the spacing between each node need to be considered. This invention uses a Z-shaped reciprocating motion as an example to parameterize the node formation and spacing involved in the search mission. The spacing between nodes in the formation is determined by various parameters. The Z-shaped reciprocating search formation establishes a Cartesian coordinate system with the major axis parallel to the search area as the horizontal axis, the minor axis parallel to the search area as the vertical axis, and the lower left corner of the search area as the origin.

[0062] The original Z-shaped round-trip formation consists of a path for each node composed of edges AB, BC, and CD of length *a*, parallel to the Y-axis. The interval between each node's path is *b*, and the departure interval is *d*, generally d ≤ *a*. There are I such paths. First, the angle ∠BCD between edges BC and CD in the original formation is set to 2α degrees. Then, the entire formation is rotated clockwise by β degrees around the region center to obtain the Z-shaped round-trip formation. The transformation process is as follows: Figure 2 As shown. After the transformation, each node's route resembles the letter "Z". Each node searches back and forth along the route, hence the name "Z-shaped back and forth". When the search formation is Z-shaped back and forth, the tactical template parameters include length a, route spacing b, route angle α, rotation angle β, and node departure distance d, where (x0, y0) is the center position of the search area.

[0063] Figure 2 Assume the system consists of I nodes, with node i initially positioned at position X. i (0)=(x i (0),y i (0)), i = 1, 2, ..., I. The coordinates of the four points A, B, C, and D in the Z-shaped round trip track of the i-th node are (x, y, y) and (x, y, y) respectively. Ai ,y Ai ), (x Bi ,y Bi ), (x Ci ,y Ci ), (x Di ,y Di Its expression is:

[0064]

[0065] Formula (4) provides the mathematical representation of the search path parameterization for multi-node surface platforms;

[0066] When performing a search mission, each node travels along the sides of the formation to complete the search mission.

[0067] Step 3: Optimization method for search formation parameters based on multi-objective particle swarm optimization algorithm

[0068] Step 3.1: Particle Swarm Optimization Algorithm

[0069] The particle swarm algorithm is used for optimizing the parameters of the Z-shaped shuttle formation, and the principle of the particle swarm algorithm is not involved in the application, but only the principle is described.

[0070] The particle swarm optimization algorithm is a population-based optimization algorithm, and the population is called a particle swarm, and the individual in the particle swarm is called a particle. i (t), (i=1, 2,..., N), wherein the i-th particle is represented as an m-dimensional vector x i (i=1, 2,..., I), which represents the particle position; the “flying” speed of the i-th particle is also an m-dimensional vector, denoted as v i . Let f be the optimization objective function to be maximized, then the particle swarm optimization algorithm updates the position and speed of the particle individual according to formula (5).

[0071]

[0072] In formula (5), w is an inertia factor; and are called particle acceleration coefficients; r1 and r2 are random numbers between 0 and 1; p

[0073]

[0074] p g (t) is the optimal position searched by the entire particle swarm so far (the global optimal value of the population), that is:

[0075] p g (t)∈{p1(t),p2(t),...,p N (t)f(p g (t)=max{f(p1(t)),f(p2(t)),...,f(p N (t))})} (10)

[0076] Each particle in the particle swarm algorithm searches for an optimal solution in the search space individually, and records it as the current individual extreme value; the individual extreme value is shared with other particles in the entire particle swarm, and the optimal individual extreme value is used as the current global optimal solution p g of the entire particle swarm. All particles in the particle swarm adjust their speed and position according to their current individual extreme value p i and the global optimal solution p g shared by the entire particle swarm at present.

[0077] Implementation details of particle swarm optimization algorithm: Table 1 pseudo code and formula (5), (6), (7) provide the implementation details of the multi-objective particle swarm optimization algorithm in the present application, including parameter setting, iteration process, multi-objective fitness value optimization process, etc.

[0078] Step 3.2: array parameter optimization

[0079] According to the Z-shaped round-trip array parameters corresponding to each particle in the particle swarm optimization algorithm, the multi-node water surface platform route is calculated, the sonar detection efficiency is analyzed according to the sonar working mode, the fitness value corresponding to each particle parameter is calculated by formula (2) and formula (3), and the particle best position and best fitness value are updated through the pseudo code steps shown in Table 1.

[0080] Step 3.3: optimization result analysis

[0081] In order to verify the effectiveness of the method, the simulation test is carried out by taking the maximum coverage range at the end of the search task as an example. The change of the area coverage rate and the coverage speed with the search time in the optimization iteration process of the conventional particle swarm algorithm and the multi-objective particle swarm algorithm optimization array parameter is analyzed and compared, and the change process with the iteration number is shown in Figure 3 and Figure 4

[0082] In Figure 3 , it can be seen that the two curves show similar trends, which shows that in the optimization process, the effective area coverage rate of the two algorithms gradually decreases with the increase of the iteration number. Under the same iteration number, the final coverage effect of the multi-objective particle swarm algorithm is better than that of the conventional particle swarm algorithm.

[0083] In Figure 4 , it can be seen that the change trend of the two curves is different. The conventional particle swarm algorithm does not optimize the area coverage speed in the optimization process, so the area coverage speed naturally changes with the increase of the effective area coverage rate, and the coverage speed of the next iteration may be slower than that of the previous iteration. The multi-objective particle swarm algorithm optimizes the area coverage rate and the area coverage speed at the same time in the optimization process, so it will not appear in the conventional particle swarm algorithm. The final coverage speed is also faster than that of the conventional particle swarm algorithm.

[0084] ​On the basis of defining the regional dynamic coverage evaluation index and the parameterized representation of search formation, the application uses the multi-objective particle swarm optimization algorithm to solve the multi-dimensional decision vector and multi-objective optimization problem of multi-node water surface platform formation parameter optimization, improve the effective coverage rate while improving the coverage speed. The application introduces the target existence probability to realize the performance evaluation of the coverage effect; the parameterized representation formation and platform spacing are used to reduce the difficulty of obtaining the optimal search path; the multi-objective particle swarm optimization algorithm is used to solve the formation parameters, and the optimization efficiency of the parameter optimization method is improved. The simulation results show that the search formation given by the formation parameter optimization method can meet the regional coverage demand in a complex dynamic environment, can ensure that there is extra time to search the searched area again, reduces the target loss problem caused by target motion, and improves the target discovery probability.

[0085] Noun explanation of related technical terms

[0086] 1. Target existence probability: the probability of target existing in a specific position, used for evaluating search performance;

[0087] 2. Parameterized representation: the characteristics of a complex system or model are represented by a set of parameters to facilitate mathematical modeling and optimization;

[0088] 3. Particle swarm optimization algorithm: an optimization algorithm based on swarm intelligence, which simulates the social behavior of bird or fish groups to seek optimal solution.

[0089] The above is only a specific embodiment of the application, but the protection scope of the application is not limited to this, any person skilled in the art can easily think of changes or replacements within the scope disclosed by the application, which should be covered in the protection scope of the application. Therefore, the protection scope of the application should be subject to the protection scope of the claims.

Claims

1. A multi-node water surface platform search formation parameter multi-objective optimization method, characterized in that: The steps include the following: Step 1: Characterize various array patterns participating in search task planning in a parameterized form, and apply a multi-objective particle swarm optimization algorithm based on a hierarchical sequence method to array parameter optimization. In the optimization process, multiple objectives are optimized in turn according to importance ranking, and efficient optimization of multi-objective search effectiveness is realized. Step 2: Introduce target existence probability to construct search effectiveness evaluation indexes, reflecting the coverage rate and coverage speed of the dynamic environment in the search process. In step 1, a group of array parameters is regarded as a particle, and the search mechanism of the particle swarm algorithm is used to adjust the parameters of each particle to obtain the optimal multi-objective solution. A multi-objective optimization problem with n-dimensional decision variables and m-dimensional objective variables is represented as: The decision vector is X = (x1, x2, ..., x...). n ), and the space it resides in is Ω, Ω={X∈R n The target space is the space containing the m-dimensional vector F(X); the m targets are sorted according to their importance, assuming the sorting result is f1(X)>f2(X)>,...,>f m (X), of which f1(X) is the most important, f m (X) is the least important; during the optimization process, multiple objectives are optimized sequentially according to their importance; the optimization process is as follows: first, solve the optimization problem min f1(X), where X∈Ω, to obtain the optimal solution X. (1) and the optimal value f1 * Then solve the optimization problem min f2(X), where X∈Ω1=Ω∩{X|f1(X)≤f1} * }, thus obtaining the optimal solution X (2) and optimal value Repeat the above process to solve the optimization problem with m objectives, and obtain an optimal decision vector X. opt ; In step 2, the target existence probability is introduced to construct the multi-node water surface platform coverage performance evaluation function. Step 2.1: Single-objective evaluation index: regional coverage rate For the entire search area, in order to construct the optimization objective function, the regional coverage rate Q(k) is defined as the average target existence probability value in the region, that is In the formula, P T (i,j,k) represents the target existence probability at the grid position (i,j) at the k moment; n x and n y respectively represent the grid separation numbers along the X and Y axes of the region, n x n y is the total number of grids in the region, and the target initial existence probability P T (i,j,1) = 0.5, wherein i < n x and j < n y ; the smaller the coverage Q(k) value is, the better the region coverage performance at the k moment is. Step 2.2: Multi-objective evaluation index: regional coverage rate, coverage speed According to the actual operational requirements in search path planning, the regional coverage rate and coverage speed are taken as two optimization objectives of the multi-objective particle swarm algorithm, and are defined as follows: In the formula, k represents the detection time, and K represents the total search task duration. When the optimization objective is f1, the regional coverage rate at the end of the search task is optimized. When the optimization objective is f2, the proportion of the time length used when the average target existence probability in the search process is 0.2 to the total task duration is optimized. The smaller this value is, the faster the coverage speed is.

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