An underwater vehicle optimal cooperative detection array position method

Abstract

This invention provides a method for optimizing cooperative detection array positions for underwater vehicles (AUVs). It constructs a target optimization function for AUV cooperative detection array positions by coupling AUV detection errors with their own positional errors, aiming to minimize the global average detection error. This ensures that passively detected AUVs construct array positions with maximum cooperative detection accuracy. An improved HS-DPSO fusion algorithm iteratively optimizes the target optimization function. During local optimization, a dynamic inertial weight adjustment strategy combining normal distribution randomness and an adaptive expectation mechanism is employed. This allows the inertial weights to fluctuate dynamically and regularly in each iteration, enhancing the algorithm's ability to escape local optima. Furthermore, the adaptive random weight expectation value is dynamically adjusted using random numbers, avoiding the limitations of manually pre-setting fixed random weight expectation values ​​and improving the algorithm's adaptability to different detection scenarios. This method enables each passively detected AUV to quickly obtain its optimal cooperative detection position, improving the efficiency and accuracy of AUV formation cooperative detection.

Description

Technical Field

[0001] This invention belongs to the field of underwater target detection technology, specifically relating to an optimized cooperative detection array method for underwater vehicles. Background Technology

[0002] The ocean, covering 71% of the Earth's surface, is a vital support system for life on Earth and contains abundant biological, mineral, and renewable resources, serving as a strategic space for the sustainable development of human society. With the increasing demands for marine resource development and environmental protection, autonomous underwater vehicles (AUVs), with their autonomy, flexibility, and efficiency, have become core equipment for marine environmental detection, resource exploration, and scientific research. Among these, multi-AUV collaborative detection technology, through a distributed operation mode, can significantly expand the detection range, reduce operating costs, and improve data acquisition efficiency, thus becoming a research hotspot in the field of marine exploration.

[0003] Currently, multi-AUV cooperative detection arrays are mainly based on fixed geometric arrays (such as triangular, linear, and circular arrays). While their control logic is simple, they lack mission adaptability, failing to consider the heterogeneity of different mission payloads and the random distribution characteristics of the measured targets within the sea area. This leads to a severe mismatch between array configurations and actual detection mission scenarios, directly restricting detection accuracy and operational efficiency. Furthermore, in terms of cooperative detection accuracy modeling, existing research generally treats AUV detection errors and their own positioning errors as independent variables, completely ignoring the statistical correlation between them. Moreover, no explicit error propagation mathematical model has been established, causing deviations between cooperative detection accuracy assessment results and actual operating conditions, failing to provide effective theoretical guidance for multi-AUV cooperative detection mode shape optimization. At the array position optimization algorithm level, traditional intelligent optimization methods (such as particle swarm optimization, ant colony optimization, and traditional harmony search algorithms) are widely used in multi-AUV cooperative site calculations due to their global search capabilities, but their inherent limitations restrict the implementation effectiveness of large-scale cooperative detection. Taking the traditional Discrete Particle Swarm Optimization (DPSO) algorithm as an example, its iterative mechanism, which relies on group experience and individual historical optimal solutions, faces the problem of solution space dimension explosion when the number of AUVs increases: the solution space dimension increases exponentially with the number of AUVs, the efficiency of information interaction between individuals decreases sharply, the algorithm is prone to getting trapped in local optima, and the convergence speed decreases significantly, which may lead to distortion of the multi-AUV cooperative detection array, the appearance of detection blind zones, or even detection mission failure. On the other hand, the traditional Harmony Search algorithm (HS) has the problems of weak global search capability and insufficient local optimization accuracy, and it is difficult to meet the requirements of high-precision array position optimization when used alone. The existing HS-DPSO fusion algorithm is just a simple combination of the two algorithms, without targeted improvements to the core iterative mechanism, and cannot solve the above-mentioned problems of dimension explosion and local optima. As a result, the existing method is difficult to meet the requirements of high real-time performance, high robustness, and high precision of multi-AUV cooperative detection in complex marine environments.

[0004] In summary, existing multi-AUV cooperative array optimization techniques suffer from three major technical bottlenecks: First, the contradiction between fixed array design and the dynamic mission requirements of randomly distributed targets leads to insufficient adaptability to detection scenarios; second, the decoupling modeling of detection errors and self-positioning errors results in distorted accuracy assessments and the lack of an effective error propagation model to support optimization; third, the curse of dimensionality and convergence defects of traditional optimization algorithms and simple fusion algorithms restrict the engineering feasibility of large-scale cooperative detection. Therefore, it is urgent to develop novel multi-AUV cooperative detection array optimization techniques that combine dynamic adaptability to mission scenarios, error correlation modeling capabilities, and efficient convergence characteristics to fully unleash the technical potential of multi-AUV cooperative detection in complex marine scenarios. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing multi-AUV cooperative array optimization methods in terms of array dynamic adaptability, error modeling correlation, and algorithm convergence performance, and to provide a method for optimizing cooperative underwater vehicle detection array positions. This invention establishes a precise error propagation model by coupling AUV detection errors with their own position errors, designs a target optimization function adapted to global detection, and proposes an improved HS-DPSO fusion algorithm to achieve efficient optimization solutions. Ultimately, it achieves the dynamic optimal configuration of multi-AUV cooperative detection array positions, significantly improving detection accuracy and operational efficiency.

[0006] To achieve the above objectives, the technical solution provided by this invention is:

[0007] A method for optimizing cooperative detection array positions for underwater vehicles includes the following steps:

[0008] Step 1, Construct a joint active and passive AUV detection model:

[0009] A right-handed Cartesian coordinate system is established with the center of the detection area as the origin. The x-axis and y-axis are located on the horizontal plane of the detection area, and the z-axis is perpendicular to the horizontal plane of the detection area and pointing upwards. A joint detection model of active and passive AUVs is constructed, which includes one active detection AUV, the target being detected, and multiple passive detection AUVs. The active detection AUV and the passive detection AUV constitute an active and passive detection system. The target being detected is detected using a joint active and passive detection strategy. The target being detected is within the effective detection range of all AUVs, and all AUVs are located at the same depth in the detection area.

[0010] Step 2: Establish the target position error equation and the target positioning error covariance estimation equation:

[0011] Define basic parameters, including: the position coordinates of the actively detected AUV. , No. Position coordinates of the passive detection AUV The position coordinates of the target being measured The distance from the target to the active-detection AUV and the actual distance from each passive-detection AUV to the target; where the position coordinates of the active-detection AUV are included. It remains unchanged throughout the entire iterative optimization process;

[0012] Based on the defined basic parameters and the active / passive AUV joint detection model constructed in step 1, the target position equation is established. After Taylor expansion, the target position error equation is obtained. Then, construct the detection error covariance matrix and the self-position error covariance matrix for all passively detected AUVs respectively, and obtain the target positioning error covariance estimation equation by solving the target position error equation using the pseudo-inverse method:

[0013]

[0014] in, These are the active and passive detection system array positions, representing the combination of positions for all passively detected AUVs. ; This indicates the position coordinates of the first passive detection AUV. This indicates the position coordinates of the second passive detection AUV. Indicates the first The location coordinates of the passive detection AUV; This represents the positioning error matrix of the active and passive detection systems for the target being measured. This represents the self-position error matrix of all passively detected AUVs; It is the detection error matrix for all passively detected AUVs; It is a spatial correlation coefficient matrix; It is the covariance matrix of the positioning error of the measured target; The mathematical symbol represents covariance;

[0015] Step 3: Calculate the target positioning error covariance matrix based on the target positioning error covariance estimation equation. Combined with the covariance matrix of the positioning error of the measured target To meet the quantitative requirements of three-dimensional spatial detection accuracy, an objective optimization function for the AUV cooperative detection array position is constructed with the goal of minimizing the global average detection error. :

[0016]

[0017] In the formula, This indicates the total number of rows in the grid cells of the detected sea area; This indicates the total number of columns in the grid cells of the detected sea area; It is the area of ​​a single grid cell; It is the total area of ​​the sea area being surveyed; Indicates the position of the active and passive detection system array At that time, the first Line 1 At the geometric center of the column grid cell value;

[0018] Step 4: The improved HS-DPSO fusion algorithm is used to optimize the objective function of the established AUV cooperative detection array positions, obtaining the optimal cooperative detection positions for all passively detected AUVs.

[0019] Using the detection area as the solution space of the algorithm, the core parameters of the improved HS algorithm and the improved DPSO algorithm are initialized, and a harmony memory is constructed and dynamically updated with harmony vectors and the harmony memory. Then, the harmony vectors are treated as particles, and the particle velocity, position, dynamic inertial weight, and adaptive random weight expectation value are updated by the improved DPSO algorithm. At the same time, the individual historical optimal solution and the global optimal solution are iteratively updated. A fusion iterative strategy of one global search of the improved HS algorithm and multiple local optimizations of the improved DPSO algorithm is adopted. After iterating to the maximum number of iterations of the improved HS algorithm, the final global optimal solution is output, which is the optimal cooperative detection position of all passive detection AUVs.

[0020] The formula for updating the dynamic inertia weight is as follows:

[0021]

[0022] The formula for updating the expected value of adaptive random weights is:

[0023]

[0024] In the formula, It is the first Dynamic inertia weights during the next iteration; It is the first Expected value of adaptive random weights in the next iteration; It is the standard deviation of the inertial weight perturbation, which is a preset fixed parameter set according to the algorithm's convergence requirements; It is a random number that follows a standard normal distribution, i.e. ; and These are the lower and upper bounds of the expected value of the adaptive random weights, respectively. exist Internal adaptive adjustment avoids the limitations of manually preset fixed values; It is a random number that is uniformly distributed within the interval [0,1].

[0025] Furthermore, in step 2, when constructing the detection error covariance matrix for all passively detected AUVs, it is assumed that the detection errors of passively detected AUVs follow a normal distribution with a standard deviation of 1, and the covariance of the detection errors of any two passively detected AUVs is expressed as:

[0026]

[0027] in, For the first Passive detection AUV and the first The correlation coefficient of detection errors between passively detected AUVs, when hour The value is 1, when hour The value is 0.5; and The first The standard deviation of the detection error of a passive detection AUV and the first The standard deviation of the detection error of a passive detection AUV and All are 1; For the first The detection error of a passively detected AUV. For the first The detection error of a passively detected AUV.

[0028] Furthermore, in step 2, when constructing the covariance matrix of the self-position error of all passively detected AUVs, it is assumed that the self-position errors of all passively detected AUVs are independently distributed on the x, y, and z axes, and the distribution function is... The covariance of the self-position error of any two passively detected AUVs is expressed as:

[0029]

[0030] In the formula, This indicates that the mean is 0 and the standard deviation is 0. The normal distribution; and They represent the first The self-position error matrix of the passive detection AUV and the first The self-position error matrix of a passive detection AUV; This indicates the positional error of the AUV being actively detected. and They represent the first The self-position error of a passive detection AUV and the first The positional error of a passively detected AUV; The mathematical symbol represents covariance; This is a mathematical symbol representing a weighted average.

[0031] Furthermore, in step 4, the core parameters for improving the HS algorithm include the maximum number of iterations. Harmony memory bank value probability Perturbation probability value Fine-tuning the width Harmony memory size ;

[0032] The core parameters for improving the DPSO algorithm include the maximum number of iterations. First learning factor Second learning factor Upper limit of the expected value of adaptive random weights and lower limit .

[0033] Furthermore, the specific steps for dynamically updating the acoustic vector in step 4 are as follows:

[0034] Step a1: Generate uniformly distributed random numbers , If random numbers Less than the probability of taking a value from the harmony memory bank Then from the harmony memory bank A harmonic vector is randomly selected as the new harmonic vector. Otherwise, a new harmony vector is randomly generated within the probed sea area. ;

[0035] Step a2, if the new harmony vector Taken from the harmony memory bank Then, uniformly distributed random numbers are generated. and The new harmony vector is then finely perturbed according to the following formula:

[0036]

[0037] In the formula, This represents the probability value of the disturbance. To fine-tune the width, the value range is [0.01, 0.1], and the unit is km; and for A random number that is uniformly distributed within an interval;

[0038] Step a3: Real-time determination of the new harmonic vector after perturbation fine-tuning Is it within the detection area? If so, retain the new harmony vector after perturbation fine-tuning. If the detection area is exceeded, return to readjust the fine-tuning width. And regenerate random numbers and Perform perturbation fine-tuning until a new harmonic vector is achieved. Within the scope of the exploration area.

[0039] Furthermore, in step a1, for a single passive detection AUV, a new harmony vector is randomly generated within the detection area. At that time, the new harmony vector is randomly generated according to the following formula. x-axis and y-axis coordinate components:

[0040] Formula for generating x-axis coordinate components:

[0041] Formula for generating y-axis coordinate components:

[0042] in, and These are the x-axis and y-axis coordinate components of the new harmony vector, respectively. and These represent the lower and upper boundaries of the probed sea area along the x-axis, respectively. and These represent the lower and upper boundaries of the probed sea area along the y-axis, respectively. and All Uniformly distributed random numbers within an interval, and mutually independent, used for independent sampling in each axis direction.

[0043] Furthermore, the method for updating the harmony memory bank in step 4 is as follows:

[0044] Calculate the new harmony vector fitness value Find the harmony memory bank The harmony vector with the smallest fitness value As the worst harmonic vector, the harmonic memory is updated according to the principle of selective retention. To ensure harmony memory The system always stores high-quality candidate solutions within the solution space:

[0045] If the fitness value of the new harmony vector Larger than the harmonic memory bank The fitness value corresponding to the worst sum of sound vectors Then use the new harmony vector and its fitness value Replace the harmony memory bank The worst harmony vector and its fitness value are used to iteratively update the harmony memory; if the fitness value of the new harmony vector is... Less than or equal to the harmony memory bank The fitness value corresponding to the worst sum of sound vectors Then maintain the harmony memory bank constant.

[0046] Furthermore, in step 4, the improved DPSO algorithm updates the particle velocity and position using the following formula:

[0047] Particle velocity update formula:

[0048]

[0049] In the formula, It is the particle number, corresponding to the [number]. One harmonic vector; Indicates the first iteration Indicates the first The next iteration; and They are the first The particle in the first Velocity and position at the next iteration; It is the first The particle reached the [number]th [number]. The individual historical optimal solution in the next iteration; The algorithm is up to the 1st The global optimal solution for the next iteration; It is the first The particle in the first Speed ​​during the next iteration; and These are the first learning factor and the second learning factor, respectively. and A random number uniformly distributed within the interval [0,1]. It is the first Dynamic inertia weights during the next iteration;

[0050] Particle position update formula:

[0051]

[0052] In the formula, It is the first The particle in the first The position at the next iteration; It is the first The particle in the first The position at the next iteration; The position update coefficient is dimensionless and its value range is: This is used to control the proportion of velocity contribution to position update in each iteration, preventing position jumps from exceeding the solution space range.

[0053] Furthermore, the method for iteratively updating the individual historical optimal solution and the global optimal solution in step 4 is as follows:

[0054] Update the individual's historical best solution: Calculate the fitness value of each updated particle. and its individual historical best fitness value If a comparison is made, Then replace the position of the current particle with the position of the first particle. Individual historical optimal solution of each harmony vector and use the current number Fitness value of each particle Update the corresponding number The individual historical best fitness value of each harmony vector Otherwise, keep the first The individual historical optimal solution and the corresponding individual historical optimal fitness value of each harmony vector remain unchanged;

[0055] Update the global optimum: Iterate through the historical best fitness values ​​of all updated particles. and compared with the current global optimal fitness value If a comparison is made, Then the current global optimal solution is replaced with the updated individual historical optimal solution of the particle. And use the updated individual historical best fitness value of the particle. Replace the current global best fitness value Otherwise, keep the current global optimal solution and its corresponding global optimal fitness value unchanged.

[0056] Each updated particle corresponds to a harmony memory. The harmonic vectors in.

[0057] Further, step 3 constructs the objective optimization function for the AUV cooperative detection array, including the following sub-steps:

[0058] Step 3.1, assuming that the standard deviation of the self-position error components of each AUV is the same on each coordinate axis of the coordinate system, based on the covariance matrix of the positioning error of the measured target. Furthermore, using the geometrical attenuation factor (GDOP) as a quantitative indicator of the detection accuracy of multi-AUV collaborative detection, a collaborative detection accuracy equation for the active-passive detection system is established as follows: ;

[0059] in, These are the active and passive detection system array positions, representing the combination of positions for all passively detected AUVs. , This indicates the position coordinates of the first passive detection AUV. This indicates the position coordinates of the second passive detection AUV. Indicates the first The location coordinates of the passive detection AUV; Indicates the position of the active and passive detection system array The geometrical attenuation factor at time is used to represent the quantized value of the detection accuracy and is dimensionless. The x-axis component represents the covariance of the positioning error of the measured target. The component of the covariance of the positioning error of the measured target on the y-axis; This represents the component of the covariance of the positioning error of the measured target on the z-axis, with a value of 0. , and The covariance matrix of the positioning error of the measured target The solution is obtained;

[0060] Step 3.2: Discretize the sea area to be detected into grid cells of equal area. Combining the cooperative detection accuracy equation of the active and passive detection systems established in Step 3.1, construct an objective optimization function for the AUV cooperative detection array position with the goal of minimizing the average detection error across the entire area. .

[0061] The advantages of this invention are:

[0062] 1. This invention proposes an optimized cooperative detection array method for underwater vehicles (AUVs). It couples and models the AUV detection error with the AUV's own position error. By constructing the target's position error equation, the detection error covariance matrix of all passively detected AUVs, and the AUV's own position error covariance matrix, and using a pseudo-inverse method to solve the target's position error equation, it obtains the target's positioning error covariance estimation equation. This fundamentally solves the accuracy assessment distortion problem caused by error decoupling in existing technologies. Based on the target's positioning error covariance estimation equation, it constructs a target optimization function for the AUV cooperative detection array, with the goal of minimizing the global average detection error. This allows each passively detected AUV to construct a dynamic array position according to the maximum cooperative detection accuracy, abandoning the traditional fixed geometric array design approach and achieving precise matching between the detection array and dynamic mission requirements. Simultaneously, it employs an improved HS-DPSO fusion algorithm (Harmony Search-DPSO (HS-DPSO, representing a deep fusion of improved harmony search and improved particle swarm optimization) optimizes the objective function, enabling each passive detection AUV in an AUV formation to quickly obtain its optimal cooperative detection position. This improves the efficiency and accuracy of AUV formation cooperative detection, solving the problems of long calculation time, low accuracy, and difficulty in implementation of traditional cooperative detection array position calculation methods. In this embodiment, the detection error of the active and passive detection system is as low as 0.0253 km, and its detection performance is significantly better than traditional algorithms.

[0063] 2. In the local optimization stage of the improved HS-DPSO fusion algorithm of this invention, a dynamic inertial weight adjustment strategy is designed by combining normal distribution randomness and adaptive expectation mechanism. This allows the inertial weight to fluctuate dynamically and regularly in each iteration, effectively enhancing the algorithm's ability to escape local optima and solving the defect of traditional DPSO algorithms being prone to getting trapped in local optima. At the same time, by dynamically and adaptively adjusting the expected value of random weights within a set interval using random numbers, the limitations of manually pre-setting fixed expected values ​​of random weights are avoided, improving the algorithm's adaptability and robustness to different ocean exploration scenarios and different AUV numbers. In addition, this invention adopts a fusion iteration strategy of one improved HS algorithm global search combined with multiple improved DPSO algorithm local optimizations, effectively solving the problem of solution space dimension explosion in multi-AUV collaborative detection, and significantly improving the algorithm's convergence speed. In the embodiment of this invention, the detection performance score reaches above 9.5 at the 110th iteration, which is much faster than the 200-300 iterations of traditional algorithms, meeting the high real-time requirements in complex ocean environments.

[0064] 3. The method of this invention has accurate modeling, simple algorithm implementation, and strong engineering operability. It does not require modification of AUV hardware. The optimal configuration of AUV cooperative detection array positions can be achieved only through software algorithm optimization, which reduces the cost of engineering application. It can also flexibly adapt to different numbers of active and passive AUV formations, providing effective theoretical support and feasible technical solutions for the engineering implementation of large-scale multi-AUV cooperative detection. Attached Figure Description

[0065] Figure 1 This is a flowchart of the underwater vehicle optimized cooperative detection array method of the present invention;

[0066] Figure 2 This is a schematic diagram of the AUV formation active and passive joint detection layout mode in an embodiment of the present invention;

[0067] Figure 3 This is a schematic diagram of the initial positions of each AUV in the AUV formation in an embodiment of the present invention; the gray circles in the diagram represent active detection AUVs, and the three black circles represent three passive detection AUVs respectively;

[0068] Figure 4 This is a convergence curve of the detection performance score for AUV formation detection array planning using the improved HS-DPSO fusion algorithm of this invention.

[0069] Figure 5 The diagram shows the optimized AUV formation positions obtained using the improved HS-DPSO fusion algorithm of this invention; the gray circles in the diagram represent active detection AUVs, and the three black circles represent three passive detection AUVs respectively.

[0070] Figure 6This is a convergence curve of the detection performance score for AUV formation detection array planning using the traditional DPSO algorithm. Figure 6 (a) and the optimized formation position results of AUVs (in the figure) Figure 6 (b) in the middle); where Figure 6 In (b), the gray circle represents an active detection AUV, and the three black circles represent three passive detection AUVs.

[0071] Figure 7 This is a convergence curve of the detection performance score for AUV formation detection array planning using the traditional HS algorithm. Figure 7 (a) and the optimized formation position results of AUVs (in the figure) Figure 7 (b) in the middle); where Figure 7 In (b), the gray circles represent active detection AUVs, and the black circles represent three passive detection AUVs. Detailed Implementation

[0072] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0073] Reference Figure 1 and Figure 2 This embodiment provides a preferred embodiment of an AUV formation including one active detection AUV and three passive detection AUVs, and specifically describes the process of the AUV optimized cooperative detection array method of the present invention. In this embodiment, the target to be measured is set to be within the effective detection range of all AUVs, and all AUVs are located at the same depth in the detection area. The calculation of the multi-AUV cooperative detection array position is simplified to a position optimization problem in two-dimensional planar motion with global detection accuracy as the optimization index, specifically including the following steps:

[0074] Step 1: Construct a joint active and passive AUV detection model.

[0075] Assuming the size of the sea area to be explored is With the center of the sea area being explored as the origin of the coordinate system, a right-handed Cartesian coordinate system is established: the x-axis and y-axis lie on the plane of the sea area being explored, and the z-axis is perpendicular to the plane of the sea area being explored and pointing upwards.

[0076] A joint detection model of active and passive AUVs was constructed, comprising one active detection AUV, the target being detected, and three passive detection AUVs. The active detection AUV and the three passive detection AUVs constitute an active-passive detection system. A joint active-passive detection strategy is adopted, with the active detection AUV achieving coarse target localization and the multiple distributed passive detection AUVs achieving precise target localization, fully leveraging the synergistic optimization of active and passive detection.

[0077] Step 2, establish the target position error equation and the target positioning error covariance estimation equation, which specifically includes the following sub-steps:

[0078] Step 2.1: Establish the position equation of the target being measured.

[0079] Define basic parameters: The position coordinates of the actively detected AUV are... The position coordinates of the three passive detection AUVs are as follows: , , The position coordinates of the target being measured are The distance from the target to the active detection AUV The actual distances from each passive detection AUV to the target are as follows: , , Among them, the location coordinates of the actively detected AUV. It remains unchanged throughout the subsequent iterative optimization process.

[0080] Based on the fundamental parameters defined above and the active / passive AUV joint detection model constructed in step 1, the position equation of the target under test is established as follows:

[0081] (1)

[0082] In the formula, , and These are the distances between the first, second, and third passive detection AUVs and the targets they were detected by; It is the distance from the target being measured to the active-detection AUV; , and These are the actual distances from the first, second, and third passive detection AUVs to the targets being measured.

[0083] Step 2.2: Establish the position error equation of the target under test.

[0084] The target position equation established in step 2.1 is subjected to Taylor expansion to obtain the target position error equation, which reflects the coupling relationship between the detection error of the passive detection AUV, its own position error and the target positioning error.

[0085] The equation for the position error of the measured target is:

[0086] (2)

[0087] in, This is the detection error matrix for all passively detected AUVs, and its specific expression is:

[0088] (3)

[0089] (4)

[0090] This is the spatial correlation coefficient matrix, used to reflect the spatial geometric relationship between the measured target's location and the AUV's location; its specific expression is:

[0091] (5)

[0092] This represents the positioning error matrix of the active and passive detection systems for the target being measured. .

[0093] This represents the self-position error matrix of all passively detected AUVs. .

[0094] In the formula:

[0095] (6)

[0096] (7)

[0097] In the above formula, , and These are the detection errors of the first, second, and third passive detection AUVs, respectively. To actively detect the AUV's own position error; , and These are the positional errors of the first, second, and third passive detection AUVs, respectively. , and These are the actual distances from the first, second, and third passive detection AUVs to the target being measured; The distance from the target to the actively detected AUV; The mathematical symbol represents covariance; This is a mathematical symbol representing a weighted average.

[0098] Step 2.3: Construct the detection error covariance matrix for all passively detected AUVs.

[0099] Assume that the detection error of a passively detected AUV follows a normal distribution with a standard deviation of 1, and express the covariance of the detection errors of any two passively detected AUVs as:

[0100] (8)

[0101] In the formula, For the first Passive detection AUV and the first The correlation coefficient of detection errors between passively detected AUVs, when hour The value is 1, when hour The value is 0.5; and The first The standard deviation of the detection error of a passive detection AUV and the first The standard deviation of the detection error of a passive detection AUV and All are 1; For the first The detection error of a passively detected AUV. For the first The detection error of a passively detected AUV; in this embodiment .

[0102] Based on formula (8), the detection error covariance matrix of all passively detected AUVs in this embodiment is constructed as follows:

[0103] (9)

[0104] Step 2.4: Construct the self-position error covariance matrix for all passive detection AUVs.

[0105] Assume that the position errors of all passively detected AUVs are independently distributed along the x, y, and z axes, and that the distribution function is... The covariance of the self-position error of any two passively detected AUVs is expressed as:

[0106] (10)

[0107] In the formula, This indicates that the mean is 0 and the standard deviation is 0. The normal distribution; and They represent the first The self-position error matrix of the passive detection AUV and the first The self-position error matrix of a passive detection AUV; This indicates the positional error of the AUV being actively detected. and They represent the first The self-position error of a passive detection AUV and the first The positional error of the passively detected AUV; in this embodiment .

[0108] Based on formula (10), the self-position error covariance matrix of all passively detected AUVs in this embodiment is constructed as follows:

[0109] (11)

[0110] Step 2.5: Establish the covariance estimation equation for the positioning error of the target under test.

[0111] By combining the detection error covariance matrices of all passively detected AUVs and the self-position error covariance matrices of all passively detected AUVs, the position error equation of the measured target is solved by the pseudo-inverse method, and the positioning error covariance estimation equation of the measured target is obtained, thus realizing the coupled quantification of the detection error and self-position error of the passively detected AUV.

[0112] The equation for estimating the covariance of the target positioning error is:

[0113] (12)

[0114] In this embodiment:

[0115] (13)

[0116] In the formula, This represents the positioning error matrix of the active and passive detection systems for the target being measured. This represents the self-position error matrix of all passively detected AUVs; It is the detection error matrix for all passively detected AUVs; This is the spatial correlation coefficient matrix; Let be the covariance matrix of the positioning error of the target being measured.

[0117] Step 3: With minimizing the global average detection error as the optimization objective, construct the objective optimization function for the AUV cooperative detection array. .

[0118] This step uses the Geometric Dilution of Precision (GDOP) as a quantitative indicator of detection accuracy, and constructs an objective optimization function for the AUV collaborative detection array by combining the discretization of the entire sea area grid. Specifically, it includes the following sub-steps:

[0119] Step 3.1: Establish the collaborative detection accuracy equation for the active and passive detection systems.

[0120] Assuming that the standard deviations of the self-positioning error components of each AUV on the x, y, and z axes of the coordinate system are the same, based on the covariance matrix of the positioning error of the measured target... Furthermore, in conjunction with the quantitative requirements for three-dimensional spatial detection accuracy, a collaborative detection accuracy equation for active and passive detection systems is established to quantify the detection accuracy at different array positions.

[0121] The cooperative detection accuracy equation of active and passive detection systems:

[0122] (14)

[0123] in, These are the active and passive detection system array positions, representing the combination of positions for all passively detected AUVs. , This indicates the position coordinates of the first passive detection AUV. This indicates the position coordinates of the second passive detection AUV. Indicates the first The location coordinates of the passive detection AUV; Indicates the position of the active and passive detection system array The geometrical attenuation factor at time is used to represent the quantized value of the detection accuracy and is dimensionless. The x-axis component represents the covariance of the positioning error of the measured target. The component of the covariance of the positioning error of the measured target on the y-axis; This represents the component of the covariance of the positioning error of the measured target on the z-axis, with a value of 0. , and The covariance matrix of the positioning error of the measured target The solution is obtained.

[0124] Step 3.2: Construct the objective optimization function for the AUV cooperative detection array.

[0125] In this embodiment, for The sea area to be explored is discretized into equal-area grids, dividing the sea area into... Each grid cell represents a potential location where the target may be detected, achieving coverage of all potential targets within the detection area with no blind spots.

[0126] Define the mesh parameters as follows:

[0127] This represents the total number of rows in the grid cells of the detected sea area, in this embodiment. It is 200; This represents the total number of columns in the grid cells of the detected sea area, as shown in this embodiment. The value is 200; the area of ​​a single grid cell in this embodiment is... ; This represents the total area of ​​the sea area being surveyed, in this embodiment... ; and These represent the lower and upper boundaries of the probed sea area along the x-axis, respectively. In this embodiment... , ; and These represent the lower and upper boundaries of the probed sea area along the y-axis, respectively. In this embodiment... , .

[0128] Based on the above grid parameters and the cooperative detection accuracy equation of the active and passive detection systems shown in formula (14), a target optimization function for the AUV cooperative detection array position is constructed with the goal of minimizing the global average detection error. for:

[0129] (15)

[0130] In the formula, This indicates the total number of rows in the grid cells of the detected sea area; This indicates the total number of columns in the grid cells of the detected sea area; It is the area of ​​a single grid cell; It is the total area of ​​the sea area being surveyed; Indicates the position of the active and passive detection system array At that time, the first Line 1 At the geometric center of the column grid cell The goal is to minimize this objective function to achieve the optimal average detection accuracy for all potential targets within the detection area. The optimal locations for all passively detected AUVs are strictly limited to the detection area to ensure the feasibility of the project.

[0131] Step 4: The target optimization function of the established AUV cooperative detection array is optimized using the improved HS-DPSO fusion algorithm to obtain the optimal cooperative detection position of all passive detection AUVs.

[0132] An improved HS-DPSO fusion algorithm is used to optimize the target function of the AUV cooperative detection array established in step 3. The optimization solution is achieved by deeply integrating the improved HS algorithm for global search and the improved DPSO algorithm for local optimization, which solves the problems of dimensional explosion, local optima, and slow convergence of traditional algorithms, and obtains the optimal cooperative detection position for each passive detection AUV.

[0133] The solution space of the algorithm of this invention is the range of the sea area to be detected, that is... , The locations of all passively detected AUVs are confined within the solution space, ensuring practical feasibility of the project. Step 4 specifically includes the following steps:

[0134] Step 4.1, algorithm parameter initialization.

[0135] The core parameters of the improved HS algorithm (i.e., the improved harmony search algorithm) and the improved DPSO algorithm (i.e., the improved particle swarm optimization algorithm) are initialized respectively. The parameter values ​​are combined with the underwater detection scenario and engineering practice to ensure the convergence and robustness of the algorithm.

[0136] (1) Improved core parameters of the HS algorithm (only for improving the global search of the HS algorithm)

[0137] To improve the maximum number of iterations of the HS algorithm, this embodiment... ; Let be the probability of values ​​taken from the harmony memory, and represent the probability of selecting a solution from the memory. In this embodiment ; The perturbation probability value represents the probability of perturbing the selected solution. In this embodiment ; The fine-tuning width represents the amplitude of the disturbance, measured in kilometers. In this embodiment ; The size of the harmony memory represents the number of candidate solutions stored in the harmony memory. In this embodiment... .

[0138] (2) Improved core parameters of the DPSO algorithm (only for improving local optimization of the DPSO algorithm)

[0139] To improve the maximum number of iterations of the DPSO algorithm, this embodiment... ; To improve the first learning factor of the DPSO algorithm, which represents the historically optimal learning weight of an individual, this embodiment... ; To improve the second learning factor of the DPSO algorithm, which represents the globally optimal learning weight, this embodiment... ; This is the upper limit of the expected value of the adaptive random weights. As a lower bound of the expected value of adaptive random weights, in this embodiment and The values ​​are 0.8 and 0.1 respectively.

[0140] Step 4.2, initialize the harmony memory.

[0141] Using the area of ​​the sea to be explored as the solution space of the algorithm, random generation is performed within the solution space. The _n_ harmonic vectors, as candidate solutions for the improved HS algorithm, are denoted as _n_. ,in ; Single harmonic vector and active / passive detection system array position One-to-one correspondence, that is ,in , and They represent the first The position coordinates of the first, second, and third passive detection AUVs in the harmonic vector.

[0142] Calculate each harmony vector fitness value This is used to represent the quality of the algorithm solution, and is expressed as the objective optimization function of the AUV cooperative detection array position. The derivative of is used as the fitness value, i.e. The higher the fitness value, the better the detection performance of the active and passive detection system array.

[0143] Constructing a harmony memory: Store harmony vectors and their corresponding fitness values, as well as individual historical best solutions and their corresponding individual historical best fitness values, into the harmony memory. In Chinese, the harmonic memory bank The expression form is:

[0144] (16)

[0145] in, Indicates the first The individual historical optimal solution of each harmonic vector, initially... ; For the first The individual historical best fitness value of each harmony vector, initially... .

[0146] Simultaneously define the global optimal solution This is used to represent the optimal harmony vector among all harmony vectors, initially taken from the harmony memory library. The harmony vector with the highest fitness value, i.e. ,in This only indicates that the global optimal solution is selected from all harmony vectors; the global optimal fitness value is defined. , used to represent the fitness value of the global optimal solution, initially .

[0147] Step 4.3: Dynamically update the harmony vector.

[0148] In this embodiment, dynamic updates of the harmony vectors are achieved through random selection and perturbation fine-tuning, ensuring the breadth of the solution space search, avoiding the algorithm from getting trapped in local optima, and generating new harmony vectors. Specifically, it includes the following sub-steps:

[0149] Step 4.3.1: Generate uniformly distributed random numbers. , If random numbers Less than the probability of taking a value from the harmony memory bank Then from the harmony memory bank A harmonic vector is randomly selected as the new harmonic vector. Otherwise, a new harmony vector is randomly generated within the probed sea area. Taking a single passive detection AUV as an example, the formula for randomly generating the x-axis and y-axis coordinate components of the new harmony vector is:

[0150] Formula for generating x-axis coordinate components: (17)

[0151] Formula for generating y-axis coordinate components: (18)

[0152] in, and These are the x-axis and y-axis coordinate components of the new harmony vector, respectively. and These represent the lower and upper boundaries of the probed sea area along the x-axis, respectively. and These represent the lower and upper boundaries of the probed sea area along the y-axis, respectively. and All Uniformly distributed random numbers within an interval, and mutually independent, used for independent sampling in each axis direction.

[0153] The generated x-axis and y-axis coordinate components are combined to form a two-dimensional coordinate point, which naturally satisfies... , To ensure that the randomly generated new harmony vectors It remains within the detection area at all times.

[0154] Step 4.3.2, if the new harmony vector Taken from the harmony memory bank First, generate uniformly distributed random numbers. and Then, the new harmony vector is perturbed and fine-tuned according to the following formula to increase the diversity of solutions and expand the search range:

[0155] (19)

[0156] In the formula, the perturbation probability value in this embodiment ; To fine-tune the width, the value range is [0.01, 0.1], and the unit is km. In this embodiment... The value is 0.05; and for A random number that is uniformly distributed within an interval.

[0157] Step 4.3.3: After perturbation fine-tuning, determine the new harmony vector after perturbation fine-tuning in real time. Is it within the detection area? If so, retain the new harmony vector after perturbation fine-tuning. If the probe goes beyond the detection area, it will be necessary to return and readjust the fine-tuning width. And regenerate random numbers and Perform perturbation fine-tuning until a new harmonic vector is achieved. Within the scope of the exploration area, ensure the effectiveness of the project implementation.

[0158] Step 4.4, update the harmony memory bank.

[0159] Calculate the new harmony vector obtained in step 4.3 fitness value Find the harmony memory bank The harmonic vector with the smallest fitness value is selected as the worst harmonic vector. Update the harmony memory bank according to the principle of selective retention. To ensure the memory bank The system always stores high-quality candidate solutions within the solution space:

[0160] If the fitness value of the new harmony vector Larger than the harmonic memory bank The fitness value corresponding to the worst sum of sound vectors Then use the new harmony vector and its fitness value Replace the harmony memory bank The worst harmonic vectors and their fitness values ​​are used to implement a harmonic memory library. Iterative updates; if the fitness value of the new harmony vector... Less than or equal to the harmony memory bank The fitness value corresponding to the worst sum of sound vectors Then maintain the harmony memory bank constant.

[0161] Step 4.5: Local optimization of acoustic vectors using the improved DPSO algorithm.

[0162] Updated harmony memory bank Each harmony vector in the algorithm is considered a particle, representing an optimized individual in the improved DPSO algorithm; the position of each particle corresponds one-to-one with a harmony vector, and the particle velocity is denoted as . , used to represent the magnitude of particle position adjustment. An improved DPSO algorithm is used to locally optimize the velocity and position of each particle. Through an improved strategy of dynamic inertial weights and adaptive random weight expectation values, the local optimum problem of the traditional DPSO algorithm is solved. The optimization rule is:

[0163] Particle velocity update formula:

[0164] (20)

[0165] In the formula, It is the particle number, corresponding to the [number]. One harmonic vector; Indicates the first iteration Indicates the first The next iteration; and They are the first The particle in the first Velocity and position at the next iteration; It is the first The particle reached the [number]th [number]. The individual historical optimal solution in the next iteration; The algorithm is up to the 1st The global optimal solution for the next iteration; It is the first The particle in the first Speed ​​during the next iteration; and These are the first learning factor and the second learning factor, respectively. In this embodiment, we take... ; and It is a random number uniformly distributed within the interval [0,1]. It is the first Dynamic inertia weights in the next iteration.

[0166] The particle position update formula is:

[0167] (twenty one)

[0168] In the formula, It is the first The particle in the first The position at the next iteration; It is the first The particle in the first The position at the next iteration; It is the position update coefficient, dimensionless, and its value range is: This is used to control the proportion of velocity contribution to position update in each iteration, preventing position jumps from exceeding the solution space range.

[0169] The formula for updating dynamic inertia weights is:

[0170] (twenty two)

[0171] In the formula, It is the first Dynamic inertia weights during the next iteration; It is the first Expected value of adaptive random weights in the next iteration; This is the standard deviation of the inertia weight perturbation, a preset fixed parameter that can be set according to the algorithm's convergence requirements. In this embodiment, it is set to... ; It is a random number that follows a standard normal distribution, i.e. .

[0172] The formula for updating the expected value of adaptive random weights is:

[0173] (twenty three)

[0174] In the formula, It is the first Expected value of adaptive random weights in the next iteration; and These are the lower and upper bounds of the expected value of the adaptive random weights, respectively. exist Internal adaptive adjustment avoids the limitations of manually preset fixed values. In this embodiment, , ; It is a random number uniformly distributed in the interval [0,1].

[0175] This invention combines a dynamic inertia weight adjustment strategy designed with normal distribution randomness and an adaptive expectation mechanism, which enables the inertia weight to fluctuate regularly and dynamically in each iteration, effectively enhancing the algorithm's ability to escape local optima. At the same time, by dynamically adjusting the adaptive random weight expectation value using random numbers, it avoids the limitations of manually pre-setting a fixed random weight expectation value and improves the algorithm's adaptability to different detection scenarios.

[0176] Step 4.6: Iteratively update the individual historical optimal solution and the global optimal solution.

[0177] After improving the local optimization of the DPSO algorithm, the individual historical optimal solution of the particle and the global optimal solution of the algorithm are iteratively updated to ensure that the algorithm always converges towards the optimal solution. The specific update method is as follows:

[0178] Update the individual historical optimal solution: for each particle (corresponding to the harmony memory bank) (using the harmony vector in the equation), calculate the updated particle fitness value. and its individual historical best fitness value If a comparison is made, Then replace the position of the current particle with the position of the first particle. Individual historical optimal solution of each harmony vector and use the current number Fitness value of each particle Update the corresponding number The individual historical best fitness value of each harmony vector Otherwise, keep the first The individual historical optimal solution and the corresponding individual historical optimal fitness value of each harmony vector remain unchanged.

[0179] Update the global optimal solution: Traverse all updated particles (corresponding to the harmony memory). The individual's historical best fitness value (in harmony vectors). and compared with the current global optimal fitness value If a comparison is made, Then the current global optimal solution is replaced with the updated individual historical optimal solution of the particle. And use the updated individual historical best fitness value of the particle. Replace the current global best fitness value Otherwise, keep the current global optimal solution and its corresponding global optimal fitness value unchanged.

[0180] Step 4.7: Iterative optimization and output of the optimal result.

[0181] An iterative strategy combining a single improved HS algorithm for global search and multiple improved DPSO algorithm for local optimization is adopted to achieve a deep fusion of global search and local optimization, fully exploring high-quality solutions within the solution space. The specific iterative rules are as follows:

[0182] After each improved HS algorithm global search in steps 4.3-4 is completed, steps 4.5-4.6 are executed. The improved DPSO algorithm features local optimization to fully explore the optimal space of high-quality candidate solutions.

[0183] After each improvement to the DPSO algorithm with local optimization, the harmony memory is updated synchronously. Each harmonic vector, fitness value, and individual historical best solution and global best solution.

[0184] Repeat the iterative fusion operation of the improved HS algorithm global search and the improved DPSO algorithm local optimization until the maximum number of iterations of the improved HS algorithm is reached. This concludes the entire iterative optimization process.

[0185] After the iterative optimization process is completed, the final global optimal solution is output. The final globally optimal solution represents the optimal combination of position coordinates for all passively detected AUVs to cooperate in detection. In this embodiment, the initial positions of each AUV in the AUV formation before optimization are as follows: Figure 3 As shown, Figure 4 The convergence process of the detection performance score for AUV formation detection position planning using the improved HS-DPSO fusion algorithm of this invention is shown. Figure 5 The optimal detection positions of each AUV in the AUV formation obtained using the improved HS-DPSO fusion algorithm of this invention are shown. The optimal position coordinates of the three passive detection AUVs obtained after optimization are as follows: , and The average detection error of the active and passive detection systems is as low as 0.0253 km, achieving high-precision collaborative detection. Since the location of the active detection AUV was initially designated at the origin, and all passive detection AUVs were set to be on the same plane, the z-coordinate of the three passive detection AUVs in this embodiment is 0.

[0186] To verify the superiority of the improved HS-DPSO fusion algorithm of this invention, this embodiment uses the traditional DPSO algorithm, the traditional HS algorithm, and the improved HS-DPSO fusion algorithm of this invention to optimize the array positions of the same AUV formation. The iterative optimization capability of the objective optimization function is converted into a detection performance score to quantify the algorithm optimization effect. The score range is 0-10 points, with higher scores indicating better detection performance. The core parameters of the three algorithms are shown in Tables 1-3, and the optimization results and detection performance scores are shown in Table 4.

[0187] Table 1. Relevant core parameters of the traditional DPSO algorithm

[0188]

[0189] In Table 1, The maximum velocity of the particle. and These are the maximum and minimum values ​​of the inertia weight, respectively; these three parameters are only used in the traditional DPSO algorithm, while the meanings of the other parameters are consistent with the improved DPSO algorithm in this invention.

[0190] Table 2. Relevant core parameters of the traditional HS algorithm

[0191]

[0192] In Table 2, nNew is the number of new harmonics generated in each iteration. This parameter is only used in the traditional HS algorithm, and the meanings of the other parameters are the same as those in the HS algorithm of this invention.

[0193] Table 3. Relevant core parameters of the improved HS-DPSO fusion algorithm of this invention.

[0194]

[0195] Table 4. Position coordinates and detection performance scores of passively detected AUVs obtained by the three algorithms.

[0196]

[0197] Combined with Table 4 and Figures 4-7 As can be seen from the convergence curve of the detection performance score and the optimization results of the AUV formation, the improved HS-DPSO fusion algorithm of this invention has the following significant advantages compared with the traditional DPSO algorithm and the traditional HS algorithm:

[0198] (1) Faster convergence speed: The improved HS-DPSO fusion algorithm of this invention achieves a detection performance score of over 9.5 in the 110th iteration, which is much faster than the convergence effect of the traditional algorithm which requires 200-300 iterations, and meets the high real-time requirements in complex marine environments.

[0199] (2) Superior detection performance: The detection performance score of the improved HS-DPSO fusion algorithm of this invention is 9.7168, which is significantly higher than the traditional DPSO algorithm's 9.6764 and the traditional HS algorithm's 9.4356. The average detection error across the entire domain is as low as 0.0253km, and the detection accuracy is greatly improved.

[0200] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing cooperative detection array positions for underwater vehicles, characterized in that, Includes the following steps: Step 1, Construct a joint active and passive AUV detection model: A right-handed Cartesian coordinate system is established with the center of the detection area as the origin. The x-axis and y-axis are located on the horizontal plane of the detection area, and the z-axis is perpendicular to the horizontal plane of the detection area and pointing upwards. A joint detection model of active and passive AUVs is constructed, which includes one active detection AUV, the target being detected, and multiple passive detection AUVs. The active detection AUV and the passive detection AUV constitute an active and passive detection system, and the target being detected is detected by a joint active and passive detection strategy. The target being measured is within the effective detection range of all AUVs, and all AUVs are located at the same depth in the detection area; Step 2: Establish the target position error equation and the target positioning error covariance estimation equation: Define basic parameters, including: the position coordinates of the actively detected AUV. , No. Position coordinates of the passive detection AUV The position coordinates of the target being measured The distance from the target to the active-detection AUV and the actual distance from each passive-detection AUV to the target; where the position coordinates of the active-detection AUV are included. It remains unchanged throughout the entire iterative optimization process; Based on the defined basic parameters and the active / passive AUV joint detection model constructed in step 1, the target position equation is established. After Taylor expansion, the target position error equation is obtained. Then, the detection error covariance matrix and the self-position error covariance matrix of all passively detected AUVs are constructed respectively, and the position error equation of the measured target is solved by the pseudo-inverse method to obtain the estimation equation of the positioning error covariance of the measured target: in, This refers to the active and passive detection system array positions, representing the combined positions of all AUVs. ; This indicates the position coordinates of the first passive detection AUV. This indicates the position coordinates of the second passive detection AUV. Indicates the first The location coordinates of the passive detection AUV; This represents the positioning error matrix of the active and passive detection systems for the target being measured. This represents the self-position error matrix of all passively detected AUVs; It is the detection error matrix for all passively detected AUVs; It is a spatial correlation coefficient matrix; It is the covariance matrix of the positioning error of the measured target; The mathematical symbol represents covariance; Step 3: Calculate the target positioning error covariance matrix based on the target positioning error covariance estimation equation. Combined with the covariance matrix of the measured target positioning error To meet the quantitative requirements of three-dimensional spatial detection accuracy, an objective optimization function for the AUV cooperative detection array position is constructed with the goal of minimizing the global average detection error. : In the formula, This indicates the total number of rows in the grid cells of the detected sea area; This indicates the total number of columns in the grid cells of the detected sea area; It is the area of ​​a single grid cell; It is the total area of ​​the sea area being surveyed; Indicates the position of the active and passive detection system array At that time, the first Line 1 At the geometric center of the column grid cell value; Step 4: The improved HS-DPSO fusion algorithm is used to optimize the objective function of the established AUV cooperative detection array positions, obtaining the optimal cooperative detection positions for all passively detected AUVs. Using the detection area as the solution space of the algorithm, the core parameters of the improved HS algorithm and the improved DPSO algorithm are initialized, and a harmony memory is constructed and dynamically updated with harmony vectors and the harmony memory. Then, the harmony vectors are treated as particles, and the particle velocity, position, dynamic inertial weight, and adaptive random weight expectation value are updated by the improved DPSO algorithm. At the same time, the individual historical optimal solution and the global optimal solution are iteratively updated. A fusion iterative strategy of one global search of the improved HS algorithm and multiple local optimizations of the improved DPSO algorithm is adopted. After iterating to the maximum number of iterations of the improved HS algorithm, the final global optimal solution is output, which is the optimal cooperative detection position of all passive detection AUVs. The formula for updating the dynamic inertia weight is as follows: The formula for updating the expected value of adaptive random weights is: In the formula, It is the first Dynamic inertia weights during the next iteration; It is the first Expected value of adaptive random weights in the next iteration; It is the standard deviation of the inertial weight perturbation, which is a preset fixed parameter set according to the algorithm's convergence requirements; It is a random number that follows a standard normal distribution, i.e. ; and These are the lower and upper bounds of the expected value of the adaptive random weights, respectively. exist Internal adaptive adjustment avoids the limitations of manually preset fixed values; It is a random number that is uniformly distributed within the interval [0,1].

2. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 1, characterized in that, In step 2, when constructing the detection error covariance matrix for all passively detected AUVs, it is assumed that the detection errors of passively detected AUVs follow a normal distribution with a standard deviation of 1, and the covariance of the detection errors of any two passively detected AUVs is expressed as: in, For the first Passive detection AUV and the first The correlation coefficient of detection errors between passively detected AUVs, when hour The value is 1, when hour The value is 0.5; and The first The standard deviation of the detection error of a passive detection AUV and the first The standard deviation of the detection error of a passive detection AUV and All are 1; For the first The detection error of a passively detected AUV. For the first The detection error of a passively detected AUV.

3. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 2, characterized in that, In step 2, when constructing the covariance matrix of the self-position error of all passively detected AUVs, it is assumed that the self-position errors of all passively detected AUVs are independently distributed on the x, y, and z axes, and the distribution function is... The covariance of the self-position error of any two passively detected AUVs is expressed as: In the formula, This indicates that the mean is 0 and the standard deviation is 0. The normal distribution; and They represent the first The self-position error matrix of the passive detection AUV and the first The self-position error matrix of a passive detection AUV; This indicates the positional error of the AUV being actively detected. and They represent the first The self-position error of a passive detection AUV and the first The positional error of a passively detected AUV; The mathematical symbol represents covariance; This is a mathematical symbol representing a weighted average.

4. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 1, characterized in that, In step 4, the core parameters of the improved HS algorithm include the maximum number of iterations. Harmony memory bank value probability Perturbation probability value Fine-tuning the width Harmony memory size ; The core parameters of the improved DPSO algorithm include the maximum number of iterations. First learning factor Second learning factor Upper limit of the expected value of adaptive random weights and lower limit .

5. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 1, characterized in that, The specific steps for dynamically updating the acoustic vectors in step 4 are as follows: Step a1: Generate uniformly distributed random numbers , ; If random number Less than the probability of taking a value from the harmony memory bank Then from the harmony memory bank A harmonic vector is randomly selected as the new harmonic vector. ; Otherwise, a new harmony vector is randomly generated within the probed sea area. ; Step a2, if the new harmony vector Taken from the harmony memory bank Then, uniformly distributed random numbers are generated. and The new harmony vector is then finely perturbed according to the following formula: In the formula, This represents the probability value of the disturbance. To fine-tune the width, the value range is [0.01, 0.1], and the unit is km; and for A random number that is uniformly distributed within an interval; Step a3: Real-time determination of the new harmonic vector after perturbation fine-tuning Is it within the detection area? If so, retain the new harmony vector after perturbation fine-tuning. ; If the detection area is exceeded, return to readjust the fine-tuning width. And regenerate random numbers and Perform perturbation fine-tuning until a new harmonic vector is achieved. Within the scope of the exploration area.

6. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 5, characterized in that, In step a1, for a single passive detection AUV, a new harmony vector is randomly generated within the detection area. At that time, the new harmony vector is randomly generated according to the following formula. x-axis and y-axis coordinate components: Formula for generating x-axis coordinate components: Formula for generating y-axis coordinate components: in, and These are the x-axis and y-axis coordinate components of the new harmony vector, respectively. and These represent the lower and upper boundaries of the probed sea area along the x-axis, respectively. and These represent the lower and upper boundaries of the probed sea area along the y-axis, respectively. and All Uniformly distributed random numbers within an interval, and mutually independent, used for independent sampling in each axis direction.

7. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 6, characterized in that, The method for updating the harmony memory bank in step 4 is as follows: Calculate the new harmony vector fitness value Find the harmony memory bank The harmony vector with the smallest fitness value As the worst harmonic vector, the harmonic memory is updated according to the principle of selective retention. To ensure harmony memory The system always stores high-quality candidate solutions within the solution space: If the fitness value of the new harmony vector Larger than the harmonic memory bank The fitness value corresponding to the worst sum of sound vectors Then use the new harmony vector and its fitness value Replace the harmony memory bank The worst harmonic vectors and their fitness values ​​are used to implement a harmonic memory library. Iterative updates; if the fitness value of the new harmony vector... Less than or equal to the harmony memory bank The fitness value corresponding to the worst sum of sound vectors Then maintain the harmony memory bank constant.

8. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 7, characterized in that, In step 4, the improved DPSO algorithm updates the particle velocity and position using the following formula: Particle velocity update formula: In the formula, It is the particle number, corresponding to the [number]. One harmonic vector; Indicates the first iteration Indicates the first The next iteration; and They are the first The particle in the first Velocity and position at the next iteration; It is the first The particle reached the [number]th [number]. The individual historical optimal solution in the next iteration; The algorithm is up to the 1st The global optimal solution for the next iteration; It is the first The particle in the first Speed ​​during the next iteration; and These are the first learning factor and the second learning factor, respectively. and A random number uniformly distributed within the interval [0,1]. It is the first Dynamic inertia weights during the next iteration; Particle position update formula: In the formula, It is the first The particle in the first The position at the next iteration; It is the first The particle in the first The position at the next iteration; The position update coefficient is dimensionless and its value range is: This is used to control the proportion of velocity contribution to position update in each iteration, preventing position jumps from exceeding the solution space range.

9. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 1, characterized in that, The method for iteratively updating the individual historical optimal solution and the global optimal solution in step 4 is as follows: Update the individual's historical best solution: Calculate the fitness value of each updated particle. and its individual historical best fitness value If a comparison is made, Then replace the position of the current particle with the position of the first particle. Individual historical optimal solution of each harmony vector and use the current number Fitness value of each particle Update the corresponding number The individual historical best fitness value of each harmony vector Otherwise, keep the first The individual historical optimal solution and the corresponding individual historical optimal fitness value of each harmony vector remain unchanged; Update the global optimum: Iterate through the historical best fitness values ​​of all updated particles. and compared with the current global optimal fitness value If a comparison is made, Then the current global optimal solution is replaced with the updated individual historical optimal solution of the particle. And use the updated individual historical best fitness value of the particle. Replace the current global best fitness value Otherwise, keep the current global optimal solution and its corresponding global optimal fitness value unchanged. Each updated particle corresponds to a harmony memory. The harmonic vectors in.

10. The method for optimizing cooperative detection array positions for underwater vehicles according to claim 1, characterized in that, Step 3 constructs the objective optimization function for the AUV cooperative detection array, including the following sub-steps: Step 3.1, assuming that the standard deviation of the self-position error components of each AUV is the same on each coordinate axis of the coordinate system, based on the covariance matrix of the positioning error of the measured target. Furthermore, using the geometrical attenuation factor (GDOP) as a quantitative indicator of the detection accuracy of multi-AUV collaborative detection, a collaborative detection accuracy equation for the active-passive detection system is established as follows: ; in, These are the active and passive detection system array positions, representing the combination of positions for all passively detected AUVs. , This indicates the position coordinates of the first passive detection AUV. This indicates the position coordinates of the second passive detection AUV. Indicates the first The location coordinates of the passive detection AUV; Indicates the position of the active and passive detection system array The geometrical attenuation factor at time is used to represent the quantized value of the detection accuracy and is dimensionless. The x-axis component represents the covariance of the positioning error of the measured target. The component of the covariance of the positioning error of the measured target on the y-axis; This represents the component of the covariance of the positioning error of the measured target on the z-axis, with a value of 0. , and The covariance matrix of the positioning error of the measured target The solution is obtained; Step 3.2: Discretize the sea area to be detected into grid cells of equal area. Combining the cooperative detection accuracy equation of the active and passive detection systems established in Step 3.1, construct an objective optimization function for the AUV cooperative detection array position with the goal of minimizing the average detection error across the entire area. .

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