Underwater acoustic signal recognition and fusion method

Abstract

The present invention discloses an underwater acoustic signal recognition and fusion method, which belongs to the technical field of underwater acoustic signal recognition and is used for underwater acoustic signal recognition, including node weight setting based on Euclidean distance and zero-sum game strategy and recognition fusion based on dynamic Bayes and Chair-Varshney criterion; node weight setting based on Euclidean distance and zero-sum game strategy is to use the Euclidean distance between different nodes and targets for weight calculation, construct a zero-sum game matrix based on node distance weight, and optimize using genetic algorithm GA based on the zero-sum game model; use weighted moving average method to dynamically adjust prior probability, and use Kalman filtering to smooth recognition fusion fluctuations. Compared with the prior art, the present invention overcomes the sparsity of deployed nodes and the weak connectivity of underwater acoustic communication, enhances stability, improves reliability, and the final fusion result is more stable and smooth, and is not affected by the interference of complex underwater multi-node environment.

Description

Technical Field

[0001] The invention discloses an underwater acoustic signal recognition and fusion method, and belongs to the technical field of underwater acoustic signal recognition. Background Art

[0002] In the field of marine development, accurate detection and identification of underwater targets is crucial. For example, in marine resource exploration, it is necessary to identify targets such as mineral deposit structures and shipwrecks on the seabed. Traditional two-dimensional sonar systems can provide target location and shape information to a certain extent, but with the increasing complexity of the underwater environment and the continuous improvement of target recognition accuracy requirements, their limitations are gradually emerging. The underwater environment is complex and changeable, and there are various interference factors. Such factors as biological noise in the ocean, water flow noise, and seabed terrain reflections can affect the quality of the sonar signal, causing the target echo signal to be submerged or distorted. It is difficult for two-dimensional sonar to fully characterize the complete characteristics of these complex targets and cannot meet the needs of high-precision recognition.

[0003] The effectiveness of Byzantine theory in recognition fusion is undeniable. However, in the application of underwater acoustic signal recognition and fusion, due to the sparsity of the deployed nodes and the weak connectivity of underwater acoustic communication, after a large number of preliminary experimental verifications, it was found that the fusion effect after direct Byzantine isolation of underwater nodes is not ideal. Therefore, the present invention adopts a Byzantine node isolation scheme based on Euclidean distance and zero-sum game strategy, and then adopts a multi-step optimization algorithm based on genetic algorithm, Bayesian theory and Kalman filtering to perform corresponding fusion on the recognition results of different nodes. Summary of the invention

[0004] The purpose of the present invention is to provide a method for identifying and fusing underwater acoustic signals to solve the problem in the prior art that it is difficult to identify underwater acoustic signals through sonar fusion.

[0005] Underwater acoustic signal recognition and fusion methods, including node weight setting based on Euclidean distance and zero-sum game strategy and recognition fusion based on dynamic Bayesian and Chair-Varshney criteria;

[0006] The node weight setting based on Euclidean distance and zero-sum game strategy includes using the Euclidean distance between different nodes and the target for weight calculation, constructing a zero-sum game matrix based on node distance weight, and using genetic algorithm GA for optimization based on the zero-sum game model;

[0007] Recognition fusion based on dynamic Bayesian and Chair-Varshney criteria includes using weighted moving average method to dynamically adjust prior probability and using Kalman filtering to smooth recognition fusion fluctuations.

[0008] In the three-dimensional spatial distribution of nodes, two nodes and The Euclidean distance between for:

[0009] ;

[0010] In the sonar fusion system, the Euclidean distance between different nodes and the target is used to calculate the weight. The closer the node is to the target, the higher the weight, and the farther the node is from the target, the lower the weight. Byzantine isolation is implemented, so that the node data close to the target accounts for a large proportion in the fusion process.

[0011] The inverse of the distance is used as the basis of the weight, and the distances between multiple nodes and the target are converted into weights for the fusion algorithm:

[0012] ;

[0013] In the formula, For nodes and targets The Euclidean distance between For the goal The weight of

[0014] The weights are normalized so that the sum of the weights of all nodes is 1, expressed as:

[0015] ;

[0016] In the formula, For the goal The average weight of is the total number of targets.

[0017] The data fusion process between nodes is regarded as a competitive relationship. Different nodes compete for the influence on the final decision through weight competition. A zero-sum game matrix based on node distance weight is constructed. nodes, the matrix elements are:

[0018] ;

[0019] In the formula, For the The node is relative to The competitive advantage of nodes, For the goal The average weight of

[0020] if , indicating the nodes have an advantage in weight distribution; if , indicating the The nodes have an advantage in weight distribution; the diagonal elements of the matrix are zero, indicating that there is no competition between the node and its own weight;

[0021] Construct a game matrix to quantify the competitive relationship between nodes, identify the optimal weight distribution scheme by analyzing the game matrix, find the optimal pure strategy or mixed strategy, and determine the final weight of each node.

[0022] Check whether there is a saddle point in the matrix. The existence of a saddle point indicates that there is a stable optimal pure strategy in the game, indicating that the weight of a certain node is optimal, and the strategy of a certain node will not change when the weights of other nodes are adjusted;

[0023] If there is a saddle point, it means that the strategy corresponding to the saddle point is the optimal strategy, and the node corresponding to the saddle point is selected as the main weight distribution object; if there is no saddle point, the optimal weight distribution needs to be found by solving the mixed strategy.

[0024] The solution of the hybrid strategy is implemented by linear programming method, which maximizes the minimum benefit of distributed nodes to obtain a balanced weight distribution scheme;

[0025] By calculating the minimum value of each row and the maximum value of each column in the matrix, we can determine whether a saddle point exists:

[0026] ;

[0027] If the above equation holds, it indicates that there is a saddle point;

[0028] In the formula, Represents the game matrix The maximum value of each column, Represents the game matrix The minimum value for each row.

[0029] Determine the node's hybrid strategy by solving a linear programming problem:

[0030] ;

[0031] In the formula, To minimize the linear function, , is the parameter vector, for The transpose of is a variable vector, is the objective function, Subject to the following conditions, is the matrix in the equality constraint, is the vector in the equality constraint, and For variables The upper and lower bounds of .

[0032] GA is a global optimization algorithm based on biological evolution theory, including selection, crossover and mutation. The process is initial population generation, fitness evaluation, selection, crossover, mutation, and iterative evolution.

[0033] The weight constraints obtained from the zero-sum game in GA are set as:

[0034] ;

[0035] 100 individuals were selected as the population size to ensure diversity and optimization accuracy; the maximum number of iterations was set to 100 to balance the calculation time and optimization effect; the crossover rate and mutation rate were set to 0.8 and 0.01 respectively to maintain the diversity of the population and accelerate convergence;

[0036] After the GA algorithm is used to globally optimize the weight function, two local optimization algorithms, simulated annealing and gradient descent, are used to perform fine-tuning based on the global optimization of the GA algorithm.

[0037] The Bayesian formula describes the rule for updating the hypothesis probability given the observed data:

[0038] ;

[0039] In the formula, is the posterior probability, is the likelihood probability, is the prior probability of the hypothesis, is the marginal probability that the hypothesis holds true under the observed data;

[0040] The Bayesian formula combines the prior probability with the observed data to achieve dynamic updating of the hypothesis probability. In a dynamic environment, an adaptive dynamic prior probability is introduced to dynamically adjust the prior probability used in the sensor recognition process to adapt to different environmental changes. The calculation of the dynamic prior probability is based on the historical performance of the sensor and changes in the current environment.

[0041] The weighted moving average dynamically adjusts the prior probability:

[0042] ;

[0043] In the formula, For time The dynamic prior probability of is the smoothing factor, which controls the sensitivity of the prior probability to the current data and historical data. For time The posterior probability calculated based on the new observation data;

[0044] Will and The Chair-Varshney criterion is improved, and the final fusion confidence is determined by calculating the joint probability of the recognition results of each node:

[0045] ;

[0046] In the formula, It is the recognition fusion result obtained by dynamic Bayes and Chair-Varshney. For the goal The posterior probability of .

[0047] Kalman filtering is used to smooth the recognition fusion results obtained by dynamic Bayes and Chair-Varshney, including:

[0048] Initialize state estimate and covariance :

[0049] ;

[0050] ;

[0051] In the formula, is the set value;

[0052] According to the Kalman filter algorithm, the state update and covariance update are performed, and the Kalman gain for:

[0053] ;

[0054] In the formula, is the updated covariance, is the measurement noise covariance;

[0055] Update status estimated to be:

[0056] ;

[0057] In the formula, is the updated state estimate, is the predicted state;

[0058] The updated covariance is:

[0059] ;

[0060] In the formula, is the prediction covariance.

[0061] Compared with the prior art, the present invention has the following beneficial effects: the fusion scheme of the present invention can overcome the sparsity of the deployed nodes and the weak connectivity of underwater acoustic communication, and combines the multi-step optimization algorithm to perform corresponding fusion of the recognition results of different nodes, thereby enhancing the stability of the algorithm, and improving the reliability of the fusion algorithm, so that the sensor data closer to the target occupies a larger proportion in the fusion process, and the weight distribution is close to the global optimum in a wider search space. The final fusion result is more stable and smooth, and is not affected by the interference of the complex environment of multiple nodes underwater. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is the first fusion result of the present invention;

[0063] Figure 2 This is the second fusion result of the present invention;

[0064] Figure 3 This is the third fusion result of the present invention. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] Underwater acoustic signal recognition and fusion methods, including node weight setting based on Euclidean distance and zero-sum game strategy and recognition fusion based on dynamic Bayesian and Chair-Varshney criteria;

[0067] The node weight setting based on Euclidean distance and zero-sum game strategy includes using the Euclidean distance between different nodes and the target for weight calculation, constructing a zero-sum game matrix based on node distance weight, and using genetic algorithm GA for optimization based on the zero-sum game model;

[0068] Recognition fusion based on dynamic Bayesian and Chair-Varshney criteria includes using weighted moving average method to dynamically adjust prior probability and using Kalman filtering to smooth recognition fusion fluctuations.

[0069] In the three-dimensional spatial distribution of nodes, two nodes and The Euclidean distance between for:

[0070] ;

[0071] In the sonar fusion system, the Euclidean distance between different nodes and the target is used to calculate the weight. The closer the node is to the target, the higher the weight, and the farther the node is from the target, the lower the weight. Byzantine isolation is implemented, so that the node data close to the target accounts for a large proportion in the fusion process.

[0072] The inverse of the distance is used as the basis of the weight, and the distances between multiple nodes and the target are converted into weights for the fusion algorithm:

[0073] ;

[0074] In the formula, For nodes and targets The Euclidean distance between For the goal The weight of

[0075] The weights are normalized so that the sum of the weights of all nodes is 1, expressed as:

[0076] ;

[0077] In the formula, For the goal The average weight of is the total number of targets.

[0078] The data fusion process between nodes is regarded as a competitive relationship. Different nodes compete for the influence on the final decision through weight competition. A zero-sum game matrix based on node distance weight is constructed. nodes, the matrix elements are:

[0079] ;

[0080] In the formula, For the The node is relative to The competitive advantage of nodes, For the goal The average weight of

[0081] if , indicating the nodes have an advantage in weight distribution; if , indicating the The nodes have an advantage in weight distribution; the diagonal elements of the matrix are zero, indicating that there is no competition between the node and its own weight;

[0082] Construct a game matrix to quantify the competitive relationship between nodes, identify the optimal weight distribution scheme by analyzing the game matrix, find the optimal pure strategy or mixed strategy, and determine the final weight of each node.

[0083] Check whether there is a saddle point in the matrix. The existence of a saddle point indicates that there is a stable optimal pure strategy in the game, indicating that the weight of a certain node is optimal, and the strategy of a certain node will not change when the weights of other nodes are adjusted;

[0084] If there is a saddle point, it means that the strategy corresponding to the saddle point is the optimal strategy, and the node corresponding to the saddle point is selected as the main weight distribution object; if there is no saddle point, the optimal weight distribution needs to be found by solving the mixed strategy.

[0085] The solution of the hybrid strategy is implemented by linear programming method, which maximizes the minimum benefit of distributed nodes to obtain a balanced weight distribution scheme;

[0086] By calculating the minimum value of each row and the maximum value of each column in the matrix, we can determine whether a saddle point exists:

[0087] ;

[0088] If the above equation holds, it indicates that there is a saddle point;

[0089] In the formula, Represents the game matrix The maximum value of each column, Represents the game matrix The minimum value for each row.

[0090] Determine the node's hybrid strategy by solving a linear programming problem:

[0091] ;

[0092] In the formula, To minimize the linear function, , is the parameter vector, for The transpose of is a variable vector, is the objective function, Subject to the following conditions, is the matrix in the equality constraint, is the vector in the equality constraint, and For variables The upper and lower bounds of .

[0093] GA is a global optimization algorithm based on biological evolution theory, including selection, crossover and mutation. The process is initial population generation, fitness evaluation, selection, crossover, mutation, and iterative evolution.

[0094] The weight constraints obtained from the zero-sum game in GA are set as:

[0095] ;

[0096] 100 individuals were selected as the population size to ensure diversity and optimization accuracy; the maximum number of iterations was set to 100 to balance the calculation time and optimization effect; the crossover rate and mutation rate were set to 0.8 and 0.01 respectively to maintain the diversity of the population and accelerate convergence;

[0097] After the GA algorithm is used to globally optimize the weight function, two local optimization algorithms, simulated annealing and gradient descent, are used to perform fine-tuning based on the global optimization of the GA algorithm.

[0098] The Bayesian formula describes the rule for updating the hypothesis probability given the observed data:

[0099] ;

[0100] In the formula, is the posterior probability, is the likelihood probability, is the prior probability of the hypothesis, is the marginal probability that the hypothesis holds true under the observed data;

[0101] The Bayesian formula combines the prior probability with the observed data to achieve dynamic updating of the hypothesis probability. In a dynamic environment, an adaptive dynamic prior probability is introduced to dynamically adjust the prior probability used in the sensor recognition process to adapt to different environmental changes. The calculation of the dynamic prior probability is based on the historical performance of the sensor and changes in the current environment.

[0102] The weighted moving average dynamically adjusts the prior probability:

[0103] ;

[0104] In the formula, For time The dynamic prior probability of is the smoothing factor, which controls the sensitivity of the prior probability to the current data and historical data. For time The posterior probability calculated based on the new observation data;

[0105] Will and The Chair-Varshney criterion is improved, and the final fusion confidence is determined by calculating the joint probability of the recognition results of each node:

[0106] ;

[0107] In the formula, It is the recognition fusion result obtained by dynamic Bayes and Chair-Varshney. For the goal The posterior probability of .

[0108] Kalman filtering is used to smooth the recognition fusion results obtained by dynamic Bayes and Chair-Varshney, including:

[0109] Initialize state estimate and covariance :

[0110] ;

[0111] ;

[0112] In the formula, is the set value;

[0113] According to the Kalman filter algorithm, the state update and covariance update are performed, and the Kalman gain for:

[0114] ;

[0115] In the formula, is the updated covariance, is the measurement noise covariance;

[0116] Update status estimated to be:

[0117] ;

[0118] In the formula, is the updated state estimate, is the predicted state;

[0119] The updated covariance is:

[0120] ;

[0121] In the formula, is the prediction covariance.

[0122] The nodes in the present invention are specifically sensors in the embodiment, and the normalization process ensures that the contribution of each node is relative rather than absolute during the fusion process, thereby enhancing the stability of the algorithm. However, the weight allocation method based solely on distance has certain limitations when facing the complexity of multi-node systems. Since there may be mutual interference between nodes, a single distance weight cannot accurately reflect these complex interaction effects. Therefore, relevant theories of game theory are introduced to more comprehensively consider the relationship between nodes and optimize the weights.

[0123] The sensor mixing strategy is determined by solving the following linear programming problem:

[0124] ;

[0125] in, The definition of depends on the game matrix The structure of The mixed strategy obtained by solving the linear programming represents the optimal weight distribution of the sensors. Although the zero-sum game model can reflect the competitive relationship between sensors to a certain extent and obtain a balanced weight distribution scheme through saddle points and mixed strategies, the model still has some limitations: ① Limitation of model assumptions: The zero-sum game assumes that the relationship between all nodes is completely competitive (that is, the gain of one node is equal to the loss of another node). However, in practical applications, the relationship between nodes may not always be zero-sum. For example, some sensors may work collaboratively instead of competing with each other. The zero-sum game model cannot fully capture this cooperative relationship; ② Non-convexity and local optimal solution: The mixed strategy solution in the zero-sum game relies on linear programming, and the solution obtained by linear programming is usually the global optimal solution. However, in some complex distributed sonar configurations, the actual weight distribution may not be a convex set that can be described by linear programming. Therefore, the result of directly using linear programming may fall into the local optimal solution and cannot fully utilize the information of all nodes; ③ Dynamic and non-deterministic environment: The zero-sum game method is usually based on the static environment assumption, assuming that the state and external conditions of all nodes remain unchanged during the game. However, in actual application scenarios, nodes may be affected by environmental changes, signal interference or other random factors, causing their performance to change dynamically. The zero-sum game approach is difficult to cope with such uncertainty and dynamism.

[0126] Further optimization using genetic algorithm (GA) based on the zero-sum game model can make full use of the advantages of both: ① Combining preliminary optimization with global exploration: The zero-sum game model provides a preliminary weight selection scheme based on theoretical analysis, which can be used as the initial population of the genetic algorithm. GA is used to further optimize this initialization so that the weight distribution is close to the global optimum in a wider search space; ② Dynamic adjustment strategy: Based on the initial weight distribution determined by the zero-sum game, GA can dynamically adjust the weight when the node environment and performance change to ensure that the system is in the best state; ③ Better solution for complex environment: GA's global search and evolution mechanism can overcome the limitations of the zero-sum game model, especially when the underwater distributed sonar network environment is complex and nonlinear relationships are prominent, GA can better find the optimal solution for weight distribution.

[0127] GA is a global optimization algorithm based on biological evolution theory, including three main steps: selection, crossover and mutation. The process of genetic algorithm is as follows: initial population generation includes generating an initial population containing different weight distribution schemes (individuals); fitness evaluation includes defining fitness function and evaluating the quality of each individual; selection operation includes selecting individuals according to fitness value, and the survival of the fittest; crossover operation includes simulating gene recombination, crossover between selected individuals, and generating new individuals; mutation operation includes introducing random changes in the generated new individuals to increase the diversity of the population; iterative evolution includes repeating selection, crossover and mutation operations until the preset number of iterations is reached or the termination condition is met.

[0128] Based on the above theory, the target recognition types and results for a given 10 nodes are shown in Table 1.

[0129] Table 1. Basic probability assignment of 10-node target recognition

[0130] ;

[0131] In the table, , , Represent three different underwater targets respectively. The final fusion result is as follows Figure 1 As shown in the table, although nodes 3, 5, and 7 have flipped recognition probabilities, the Byzantine node isolation theory can effectively integrate the recognition confidence detected by each node, and the result after recognition is still the existence of the target, that is, the recognition result is correct. After 10 nodes are integrated, the recognition target confidence can reach 0.9927, which is 0.1927 higher than the highest recognition accuracy of a single node, effectively proving the effectiveness and reliability of the algorithm.

[0132] For a given 10-node target, the target recognition types and results are shown in Table 2.

[0133] Table 2. Basic probability assignment of 10-node target recognition

[0134] ;

[0135] In the table, , They represent two different states of the same underwater target. The final fusion result is as follows: Figure 2As shown in the table, although the probability of flipping recognition occurs in nodes 1, 5, 6, and 9, the Byzantine node isolation theory can effectively integrate the recognition confidence detected by each node, and the result after recognition is still the existence of the target, that is, the recognition result is correct. After 10 nodes are integrated, the recognition target confidence can reach 0.8998, which is 0.2166 higher than the highest recognition accuracy of a single node. This result further verifies that the proposed method can still reliably integrate information and draw correct conclusions when facing multiple node misidentifications, demonstrating the excellent performance of the algorithm in complex underwater environments, that is, it has good fault tolerance for node recognition errors.

[0136] For a given 10-node target, the target recognition types and results are shown in Table 3.

[0137] Table 3. Basic probability assignment of 10-node target recognition

[0138] ;

[0139] The final fusion result is as follows Figure 3 As shown in the table, it can be seen that the recognition probabilities of nodes 3, 4, 7, 8, and 10 are significantly lower than those of other nodes. However, it can be seen from the fusion results in Figure 3 that the fusion method of the present invention successfully integrates the information of each node, and the recognition result correctly indicates the existence of the target. The confidence of the identified target after fusion is 0.6070, which verifies the ability of this method to reliably integrate information and accurately judge the target in the multi-node misidentification scenario, reflecting the adaptability and stability of the algorithm in complex underwater environments.

[0140] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features may be replaced by equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying and fusing underwater acoustic signals, characterized in that: Including node weight setting based on Euclidean distance and zero-sum game strategy and recognition fusion based on dynamic Bayesian and Chair-Varshney criteria; The node weight setting based on Euclidean distance and zero-sum game strategy includes using the Euclidean distance between different nodes and the target for weight calculation, constructing a zero-sum game matrix based on node distance weight, and using genetic algorithm GA for optimization based on the zero-sum game model; The recognition fusion based on dynamic Bayes and Chair-Varshney criteria includes using weighted moving average method to dynamically adjust the prior probability and using Kalman filter to smooth the recognition fusion fluctuations; In the three-dimensional spatial distribution of nodes, two nodes and The Euclidean distance between for: ； In the sonar fusion system, the Euclidean distance between different nodes and the target is used to calculate the weight. The closer the node is to the target, the higher the weight, and the farther the node is from the target, the lower the weight. Byzantine isolation is implemented, so that the node data close to the target accounts for a large proportion in the fusion process. The inverse of the distance is used as the basis of the weight, and the distances between multiple nodes and the target are converted into weights for the fusion algorithm: ； In the formula, For nodes and targets The Euclidean distance between For the goal The weight of The weights are normalized so that the sum of the weights of all nodes is 1, expressed as: ； In the formula, For the goal The average weight of is the total number of targets; The data fusion process between nodes is regarded as a competitive relationship. Different nodes compete for the influence on the final decision through weight competition. A zero-sum game matrix based on node distance weight is constructed. nodes, the matrix elements are: ； In the formula, For the The node is relative to The competitive advantage of nodes, For the goal The average weight of if , indicating the nodes have an advantage in weight distribution; if , indicating the The nodes have an advantage in weight distribution; the diagonal elements of the matrix are zero, indicating that there is no competition between the node and its own weight; Construct a game matrix to quantify the competitive relationship between nodes, identify the optimal weight distribution scheme by analyzing the game matrix, find the optimal pure strategy or mixed strategy, and determine the final weight of each node.

2. The underwater acoustic signal recognition and fusion method according to claim 1 is characterized in that: Check whether there is a saddle point in the matrix. The existence of a saddle point indicates that there is a stable optimal pure strategy in the game, indicating that the weight of a certain node is optimal, and the strategy of a certain node will not change when the weights of other nodes are adjusted; If there is a saddle point, it means that the strategy corresponding to the saddle point is the optimal strategy, and the node corresponding to the saddle point is selected as the main weight distribution object; if there is no saddle point, the optimal weight distribution needs to be found by solving the mixed strategy.

3. The underwater acoustic signal recognition and fusion method according to claim 2 is characterized in that: The solution of the hybrid strategy is implemented by linear programming method, which maximizes the minimum benefit of distributed nodes to obtain a balanced weight distribution scheme; By calculating the minimum value of each row and the maximum value of each column in the matrix, we can determine whether a saddle point exists: ； If the above equation holds, it indicates that there is a saddle point; In the formula, Represents the game matrix The maximum value of each column, Represents the game matrix The minimum value for each row.

4. The underwater acoustic signal recognition and fusion method according to claim 3 is characterized in that: Determine the node's hybrid strategy by solving a linear programming problem: ； In the formula, To minimize the linear function, , is the parameter vector, for The transpose of is a variable vector, is the objective function, Subject to the following conditions, is the matrix in the equality constraint, is the vector in the equality constraint, and For variables The upper and lower bounds of .

5. The underwater acoustic signal recognition and fusion method according to claim 4 is characterized in that: GA is a global optimization algorithm based on biological evolution theory, including selection, crossover and mutation. The process is initial population generation, fitness evaluation, selection, crossover, mutation, and iterative evolution. The weight constraints obtained from the zero-sum game in GA are set as: ； 100 individuals were selected as the population size to ensure diversity and optimization accuracy; the maximum number of iterations was set to 100 to balance the calculation time and optimization effect; the crossover rate and mutation rate were set to 0.8 and 0.01 respectively to maintain the diversity of the population and accelerate convergence; After the GA algorithm is used to globally optimize the weight function, two local optimization algorithms, simulated annealing and gradient descent, are used to perform fine-tuning based on the global optimization of the GA algorithm.

6. The underwater acoustic signal recognition and fusion method according to claim 5 is characterized in that: The Bayesian formula describes the rule for updating the hypothesis probability given the observed data: ； In the formula, is the posterior probability, is the likelihood probability, is the prior probability of the hypothesis, is the marginal probability that the hypothesis holds true under the observed data; The Bayesian formula combines the prior probability with the observed data to achieve dynamic updating of the hypothesis probability. In a dynamic environment, an adaptive dynamic prior probability is introduced to dynamically adjust the prior probability used in the sensor recognition process to adapt to different environmental changes. The calculation of the dynamic prior probability is based on the historical performance of the sensor and changes in the current environment.

7. The underwater acoustic signal recognition and fusion method according to claim 6 is characterized in that: The weighted moving average dynamically adjusts the prior probability: ； In the formula, For time The dynamic prior probability of is the smoothing factor, which controls the sensitivity of the prior probability to the current data and historical data. For time The posterior probability calculated based on the new observation data; Will and The Chair-Varshney criterion is improved, and the final fusion confidence is determined by calculating the joint probability of the recognition results of each node: ； In the formula, It is the recognition fusion result obtained by dynamic Bayes and Chair-Varshney. For the goal The posterior probability of .

8. The underwater acoustic signal recognition and fusion method according to claim 7 is characterized in that: Kalman filtering is used to smooth the recognition fusion results obtained by dynamic Bayes and Chair-Varshney, including: Initialize state estimate and covariance : ； ； In the formula, is the set value; According to the Kalman filter algorithm, the state update and covariance update are performed, and the Kalman gain for: ； In the formula, is the updated covariance, is the measurement noise covariance; Update status estimated to be: ； In the formula, is the updated state estimate, is the predicted state; The updated covariance is: ； In the formula, is the prediction covariance.

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