AUV-UFastSLAM algorithm based on whale optimization algorithm optimization

Abstract

This invention discloses an AUV-UFastSLAM algorithm optimized based on the whale algorithm, comprising a series of processes including initialization, prediction, sampling, map updating, and resampling. This method optimizes the particle sampling process using the whale algorithm, enabling the particle swarm to move towards a high-likelihood region, making the AUV pose estimation closer to the true value. An inertia weight factor is introduced to improve the whale algorithm's position update formula, increasing the population convergence speed and accuracy. Simultaneously, Cauchy mutation is used to randomly perturb the optimal neighborhood to increase population diversity and improve the algorithm's global search capability. An improved resampling method is used for particle filtering to ensure particle diversity. Through these adjustments, the accuracy of AUV simultaneous localization and map creation is improved.

Description

Technical Field

[0001] This invention relates to the field of simultaneous localization and mapping (SLAM) for autonomous underwater vehicles (AUVs), specifically to an AUV-UFastSLAM algorithm optimized based on the whale algorithm, belonging to the field of robot navigation technology. Background Technology

[0002] The method of a mobile robot creating a map of an unknown environment using its own sensors and using the created map for localization when its own position and orientation are uncertain is called the simultaneous localization and mapping (SLAM) problem.

[0003] Research on autonomous navigation for autonomous underwater vehicles (AUVs) is of great significance to the development of AUVs. Most current autonomous navigation methods can ensure that mobile robots can move and perform tasks in known environments. However, in real-world environments, especially underwater environments, map information is rarely available. Therefore, to achieve fully autonomous navigation, robots must have the ability to simultaneously locate and create maps.

[0004] Since Smith et al. proposed the simultaneous localization and mapping (SLAM) algorithm based on the Extended Kalman Filter (EKF), the EKF has become a major method for studying robot SLAM problems. However, with in-depth research, it has been found that the EKF method has two obvious drawbacks in practical applications: first, the computational complexity is proportional to the square of the number of detected landmarks in the environment, making it difficult to meet the requirements of large-scale map creation and real-time performance; second, the EKF algorithm is insufficient in handling data association problems.

[0005] To address the problems of the Extended Kalman Filter (EKF), Montemelo et al. proposed the FastSLAM algorithm. This algorithm divides the SLAM problem into two processes: robot pose estimation and landmark position estimation based on pose estimation. A particle filter is used for robot pose estimation, and an EKF is used for landmark position estimation. In pose estimation, each particle represents a possible trajectory for the robot, and the weight of each particle represents the quality of its corresponding possible trajectory. The EKF performs landmark position estimation for each particle, so the landmark position estimates for each particle are independent. Therefore, in the FastSLAM algorithm, the data association between each particle is also independent. When some particles have problems, they will decay during the resampling stage, thus not affecting the overall estimation of the robot SLAM algorithm, solving the two major shortcomings of the EKF in SLAM algorithms.

[0006] However, FastSLAM itself still has its drawbacks: in a standard FastSLAM process, the particle resampling process will cause particles with large weights to be selected multiple times, resulting in a decrease in sample diversity and a particle poverty problem. This may eventually lead to a decrease in particle filtering accuracy, which in turn will reduce the accuracy of robot pose estimation, or even cause map loss. Summary of the Invention

[0007] The purpose of this invention is to provide an AUV-UFastSLAM algorithm based on the whale algorithm optimization. The sampling process in the UFastSLAM algorithm for AUVs is improved by using the whale algorithm. By improving the position update formula and search strategy in the iteration process of the whale algorithm, the search range is expanded while ensuring the local optimization capability of the algorithm. Furthermore, the resampling method in particle filtering is improved. These improvements address the shortcomings of particle degradation and loss of diversity in the UFastSLAM algorithm, thereby improving the accuracy of AUV autonomous navigation.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] An AUV-UFastSLAM algorithm optimized based on the whale algorithm, comprising the following steps:

[0010] (1) Initialization: Obtain the initial pose information of the AUV;

[0011] (2) Prediction: Based on the motion prediction equation and sensor observation equation of the AUV, the state value x of the particle at time t is calculated. t and observed value z t Unscented particle filtering is used to predict the pose and landmarks of the AUV;

[0012] (3) Sampling: The proposal distribution function is generated by the unscented Kalman filter algorithm, and N particles are sampled from the proposal distribution function. The weight of each particle is calculated. The sampling process is optimized by the improved whale algorithm for the generated N particles. During the algorithm iteration process, the particles are guided to continuously approach the posterior probability distribution of the real system state, so that the particle distribution is closer to the posterior probability distribution of the actual AUV pose. After the iteration is completed, the weights of the N particles are updated and normalized.

[0013] (4) Map update: Based on the environmental observation information associated with the particle state output after sampling optimization, the location of the landmark is estimated by using unscented Kalman filtering, and the map information at the current time is updated;

[0014] (5) Resampling: Calculate the effective number of particles in the particle set. When the effective number of particles is less than the set threshold, the particle set is resampled using an improved resampling method.

[0015] (6) Iterate through the above steps to perform simultaneous AUV localization and map building.

[0016] Furthermore, the objective of this invention can also be achieved through the following technical measures:

[0017] The aforementioned AUV-UFastSLAM algorithm based on the whale algorithm optimization includes the initialization process in step (1) as follows: obtaining the initial position information of the AUV through either the Global Positioning System (GPS) or the Ultra-Short Baseline Transmission (USBL). The GPS obtains the longitude and latitude information of the AUV, while the USBL obtains the position of the AUV relative to the USBL transmitter station. One method can be used alone, or the two methods can be combined to improve the accuracy of the initial position estimation of the AUV. Initial velocity and attitude information are obtained through the Doppler log (DVL) and gyroscope. The Doppler log (DVL) collects one or more of the three-axis velocity information of the AUV. The gyroscope collects one or more of the yaw angle, roll angle, and pitch angle information of the AUV.

[0018] The aforementioned AUV-UFastSLAM algorithm optimized based on the whale algorithm, in step (2), calculates the particle state value x at time t based on the motion prediction equation and sensor observation equation of the AUV. t and observed value z t Unscented particle filtering is used to predict the pose and landmarks of the AUV. The AUV motion prediction equation and the sensor observation equation are as follows:

[0019] x t =f(x) t-1 ,u t ,ω t (1)

[0020] z t =h(x t ,v t (2)

[0021] In the formula, x t z t Let x be the state vector and observation vector of the system at time t, respectively. t-1 Let u be the state vector of the system at time t-1. t For motion control at time t, f(·) and h(·) are nonlinear functions of the state and observation, respectively, and w t To satisfy the condition that the mean is zero, the covariance is Q. t Process noise, v t To satisfy the condition that the mean is zero, the covariance is R. t Observation noise.

[0022] The aforementioned AUV-UFastSLAM algorithm optimized based on the whale algorithm, specifically includes step (3):

[0023] Step (3.1): Generate the proposal distribution function using the unscented Kalman filter algorithm, sample N particles from the proposal distribution function, calculate the weight of each particle, and take the particle with the largest weight at the current time as the global optimum X. * (t);

[0024] Step (3.2): During the iteration process of the whale algorithm, the current optimal value is only updated when there is a whale individual that is better than the current optimal value. This reduces the number of updates to the optimal value, thus affecting the search efficiency of the algorithm. Cauchy mutation is introduced to improve the search strategy of the whale algorithm, thereby increasing population diversity and improving the algorithm's global search capability. The standard Cauchy distribution function formula is shown in equation (3):

[0025]

[0026] After obtaining the optimal solution, the formula for the optimal neighborhood random perturbation is shown in equation (4):

[0027]

[0028] Where r is a random number between [0,1], For the newly generated neighborhood position, when r < 0.5, use formula (4) for X. * (t) Neighborhood random perturbation; when r≥0.5, the newly generated neighborhood position is still the optimal whale position, and the fitness of the newly generated neighborhood position is... Fitness w(X) higher than the original optimum * When (t)), then for X * (t) is updated. The update process is shown in equation (5):

[0029]

[0030] Step (3.3): To address the weakness of the optimal whale position in the early stages of the whale algorithm having a weak impact on other individuals and being prone to getting trapped in local optima in the later stages of iteration, an inertial weight factor wt is introduced during the whale position update process to improve the position update formula and adjust the algorithm's global search and local optimization capabilities. The adaptive weight formula is shown in Equation (6), and the improved position update formula is shown in Equation (7):

[0031]

[0032]

[0033] Where wt is the inertia weight factor, t is the current iteration number, and Tmax Let w1 be the initial weight, w2 be the final weight, and w1 > w2; X * (t) represents the optimal position of the whale at time t, and X(t+1) represents the updated position of the other whales at time t+1. Combining the monotonically decreasing law of the negative power of e on (-∞,+∞) in equation (6), wt will have a large value in the early stage of the algorithm, which will enable the algorithm to reach the vicinity of the optimal value at a faster speed and improve the global search capability of the whale algorithm in the early stage. As the number of iterations increases, the value of wt gradually decreases, which strengthens the local optimization capability of the algorithm in the later stage, making the algorithm get closer and closer to the optimal value in the iteration, thereby improving the population convergence speed and accuracy.

[0034] Step (3.4): Determine whether the maximum number of iterations T has been reached. max If not achieved, proceed to step (3.2);

[0035] Step (3.5): Update and normalize the particle weights, and output the particle states.

[0036] The aforementioned AUV-UFastSLAM algorithm optimized based on the whale algorithm, specifically includes step (5):

[0037] Step (5.1): Perform resampling determination and set the effective particle number threshold N. th When the effective number of particles N eff Less than the effective particle number threshold N th If resampling is performed, it is performed; otherwise, it is not performed. The effective particle number is calculated as shown in equation (8):

[0038]

[0039] in, The weight of the i-th particle after normalization;

[0040] Step (5.2): When performing resampling, first set two threshold values ​​w based on the effective particle number. l and w h As a screening threshold for particles, w l and w h The value of w is between 0 and 1. l <w h The N particles at that moment are divided into three intervals according to their weights, where the weights satisfy... The particles are those with appropriate weights, and no resampling is performed; only for... and Resampling of particles;

[0041] Step (5.3): Calculate the mean of N particles using formula (9), and select L weights that satisfy the following conditions. Show The number of particles is set to a threshold value N. p When L≥N p When L < N, it indicates that there are too many particles with excessively large or small weights, requiring multiple replications of a few high-weight particles. p When the particle weight distribution is relatively uniform, there are fewer particles with excessively large or small weights. In this case, it is necessary to replicate as many large-weight particles as possible. The specific replication formula is shown in equation (10):

[0042]

[0043]

[0044] Among them, M c w represents the number of particle replications. means为 The average weight of N particles, To Round the result up. To The result is rounded down, and the copying process only applies to... and The particles are copied in descending order of particle weight. The process stops when the number of copied particles reaches L. The newly copied L particles are then combined with the NL particles that were not resampled to form a new particle set, increasing particle diversity. If the number of copied particles is less than L after the copying process ends, then... Randomly replicate particles to bring the total number of particles to L;

[0045] Step (5.4): Reset the weights of the newly generated N particles to...

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] 1. The Unscented FastSLAM algorithm used in this invention has better robustness and accuracy for AUV autonomous navigation compared to other SLAM algorithms;

[0048] 2. This invention uses an improved whale algorithm to optimize the sampling process of UFastSLAM. Through the improved search strategy, the population diversity is increased and the global search capability of the algorithm is improved. Through the improved position update formula, a balance between global search capability and local optimization capability is achieved. Through the above adjustments, the particle set is concentrated in the high likelihood region, solving the problems of particle degradation and loss of particle diversity, and improving the autonomous navigation accuracy of AUV.

[0049] 3. The present invention adopts an improved resampling method, which reduces the resampling time and increases the diversity of particles. Attached Figure Description

[0050] Figure 1 This is a flowchart of the whale-optimized AUV-UFastSLAM algorithm of the present invention;

[0051] Figure 2 This is a flowchart of the improved whale algorithm of the present invention;

[0052] Figure 3 This is a flowchart of the improved resampling process of the present invention. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0054] like Figure 1 The diagram shows the flowchart of the Unscented FastSLAM algorithm applied to AUVs, optimized based on the improved whale algorithm, illustrating the processing procedure of the improved AUV-UFastSLAM. The specific steps are as follows:

[0055] Step 1: The AUV obtains initial position information through the Global Positioning System (GPS) or Ultra-Short Baseline (USBL); and obtains initial attitude information through the Doppler log (DVL) and gyroscope.

[0056] Step 2: Calculate the particle state value x at time t based on the AUV's motion prediction equation and sensor observation equation. t and observed value z t The pose and landmarks of the AUV are predicted using an unscented particle filter (UPF). The AUV motion prediction equation and the sensor observation equation are as follows:

[0057] x t =f(x) t-1 u t ω t (1)

[0058] z t =h(x t v t (2)

[0059] In the formula, x t z t Let x be the state vector and observation vector of the system at time t, respectively. t-1 Let u be the state vector of the system at time t-1. t For motion control at time t, f(·) and h(·) are nonlinear functions of the state and observation, respectively, and w t To satisfy the condition that the mean is zero, the covariance is Q. t Process noise, v t To satisfy the condition that the mean is zero, the covariance is R.t Observation noise.

[0060] Step 3: As Figure 2 As shown, an unscented Kalman filter is used to generate a proposal distribution function, and N particles are sampled from the proposal distribution function. Weights are calculated for each particle, and an improved whale algorithm is used to optimize the sampling process for the generated N particles. During the algorithm iteration, the particles are guided to continuously approach the posterior probability distribution of the real system state, making the particle distribution closer to the posterior probability distribution of the actual AUV pose. After the iteration, the weights of the N particles are updated and normalized, specifically including the following steps:

[0061] Step (3.1): Generate the proposal distribution function using the unscented Kalman filter algorithm, sample N particles from the proposal distribution function, calculate the weight of each particle, and take the particle with the largest weight at the current time as the global optimum X. * (t);

[0062] Step (3.2): During the iteration process of the whale algorithm, the current optimal value is only updated when there is a whale individual that is better than the current optimal value. This reduces the number of updates to the optimal value, thus affecting the search efficiency of the algorithm. Cauchy mutation is introduced to improve the search strategy of the whale algorithm, thereby increasing population diversity and improving the algorithm's global search capability. The standard Cauchy distribution function formula is shown in equation (3):

[0063]

[0064] After obtaining the optimal solution, the formula for the optimal neighborhood random perturbation is shown in equation (4):

[0065]

[0066] Where r is a random number between [0, 1], For the newly generated neighborhood position, when r < 0.5, use formula (4) for X. * (t) Neighborhood random perturbation; when r≥0.5, the newly generated neighborhood position is still the optimal whale position, and the fitness of the newly generated neighborhood position is... Fitness w(X) higher than the original optimum * When (t)), then for X * (t) is updated. The update process is shown in equation (5):

[0067]

[0068] Step (3.3): To address the weakness of the optimal whale position in the early stages of the whale algorithm having a weak impact on other individuals and being prone to getting trapped in local optima in the later stages of iteration, an inertial weight factor wt is introduced during the whale position update process to improve the position update formula and adjust the algorithm's global search and local optimization capabilities. The adaptive weight formula is shown in Equation (6), and the improved position update formula is shown in Equation (7):

[0069]

[0070]

[0071] Where wt is the inertia weight factor, t is the current iteration number, and T max Let w1 be the maximum number of iterations, w2 be the initial weight, and w1 > w2; X * (t) represents the optimal position of the whale at time t, and X(t+1) represents the updated position of the other whales at time t+1. Combining the monotonically decreasing law of the negative power of e on (-∞, +∞) in equation (6), wt will have a large value in the early stage of the algorithm, which will enable the algorithm to reach the vicinity of the optimal value at a faster speed and improve the global search capability of the whale algorithm in the early stage. As the number of iterations increases, the value of wt gradually decreases, which strengthens the local optimization capability of the algorithm in the later stage, making the algorithm get closer and closer to the optimal value in the iteration, thereby improving the population convergence speed and accuracy.

[0072] Step (3.4): Determine whether the maximum number of iterations T has been reached. max If not achieved, proceed to step (3.2);

[0073] Step (3.5): Update and normalize the particle weights, and output the particle states.

[0074] Step 4: Based on the environmental observation information associated with each particle, use unscented Kalman filtering to estimate the landmark position and update the map information at the current time.

[0075] Step 5: As Figure 3 As shown, the effective number of particles in the particle set is calculated. When the effective number of particles is less than a set threshold, an improved resampling method is used to resample the particle set. The improved resampling method includes the following steps:

[0076] Step (5.1): Perform resampling determination and set the effective particle number threshold N. th When the effective number of particles N eff Less than the effective particle number threshold N th If resampling is performed, it is performed; otherwise, it is not performed. The effective particle number is calculated as shown in equation (8):

[0077]

[0078] in, The weight of the i-th particle after normalization;

[0079] Step (5.2): When performing resampling, first set two threshold values ​​w based on the effective particle number. l and w h As a screening threshold for particles, w l and w h The value of w is between 0 and 1. l <w h The N particles at that moment are divided into three intervals according to their weights, where the weights satisfy... The particles are those with appropriate weights, and no resampling is performed; only for... and Resampling of particles;

[0080] Step (5.3): Calculate the mean of N particles using formula (9), and select L weights that satisfy the following conditions. and The number of particles is set to a threshold value N. p When L≥N p When L < N, it indicates that there are too many particles with excessively large or small weights, requiring multiple replications of a few high-weight particles. p When the particle weight distribution is relatively uniform, there are fewer particles with excessively large or small weights. In this case, it is necessary to replicate as many large-weight particles as possible. The specific replication formula is shown in equation (10):

[0081]

[0082]

[0083] Among them, M c w represents the number of particle replications. means Let be the average weight of N particles. To Round the result up. To The result is rounded down, and the copying process only applies to... and The particles are copied in descending order of particle weight. The process stops when the number of copied particles reaches L. The newly copied L particles are then combined with the NL particles that were not resampled to form a new particle set, increasing particle diversity. If the number of copied particles is less than L after the copying process ends, then... Randomly replicate particles to bring the total number of particles to L;

[0084] Step (5.4): Reset the weights of the newly generated N particles to...

[0085] Step 6: Iterate through the above steps to perform simultaneous AUV localization and map building.

[0086] This invention improves the Unscented FastSLAM algorithm applied to AUVs by proposing an AUV-UFastSLAM algorithm optimized based on the whale algorithm. This algorithm moves the particle swarm towards a high-likelihood region, making the AUV pose estimation closer to the true value and solving the particle degradation problem. An inertia weighting factor is used to improve the position update formula of the whale algorithm, increasing the population convergence speed and accuracy. Simultaneously, Cauchy mutation is used to randomly perturb the optimal neighborhood to increase population diversity and improve the algorithm's global search capability. An improved resampling method is used for particle filtering to ensure particle diversity. Through these adjustments, the accuracy of AUV simultaneous localization and map creation is improved.

[0087] In addition to the above embodiments, the present invention may have other implementation methods. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. An AUV-UFastSLAM method optimized based on the whale algorithm, characterized in that, The method includes the following steps: (1) Initialization: Obtain the initial pose information of the AUV; (2) Prediction: Based on the motion prediction equation of the AUV and the sensor observation equation, the state value of the particle at time t is calculated. and observed values Unscented particle filtering is used to predict the pose and landmarks of the AUV; (3) Sampling: The proposal distribution function is generated by the unscented Kalman filter algorithm, and N particles are sampled from the proposal distribution function. The weight of each particle is calculated. The sampling process is optimized by the improved whale algorithm for the generated N particles. During the algorithm iteration process, the particles are guided to continuously approach the posterior probability distribution of the real system state, so that the particle distribution is closer to the posterior probability distribution of the actual AUV pose. After the iteration is completed, the weights of the N particles are updated and normalized. (4) Map update: Based on the environmental observation information associated with the particle state output after sampling optimization, the location of the landmark is estimated by using unscented Kalman filtering, and the map information at the current time is updated; (5) Resampling: Calculate the effective number of particles in the particle set. When the effective number of particles is less than a set threshold, resample the particle set using an improved resampling method, including the following steps: Step (5.1): Perform resampling determination and set the effective particle number threshold. When the number of effective particles Less than the effective particle number threshold If resampling is performed, it is performed; otherwise, it is not performed. The effective particle number is calculated as shown in equation (8): in, The weight of the i-th particle after normalization; Step (5.2): When performing resampling, first set two threshold values ​​based on the effective particle number. and As a screening threshold for particles, and The value of is between 0 and 1 and The N particles at that moment are divided into three intervals according to their weights, where the weights satisfy... The particles are those with appropriate weights, and no resampling is performed; only for... and Resampling of particles; Step (5.3): Calculate the mean of N particles using formula (9), and select L weights that satisfy the following conditions. and The number of particles is set to a threshold. ,when This indicates that there are too many particles with excessively large or small weights, requiring multiple replications of a few high-weight particles. When the particle weight distribution is relatively uniform, there are fewer particles with excessively large or small weights. In this case, it is necessary to replicate as many large-weight particles as possible. The specific replication formula is shown in equation (10): in, For the number of particle replications, Let be the average weight of N particles. To Round the result up. To The result is rounded down, and the copying process only applies to... and The particles are copied in descending order of particle weight. The process stops when L particles have been copied. The newly copied L particles are then combined with the NL particles that were not resampled to form a new particle set, increasing particle diversity. If the number of copied particles is less than L after the copying process, then... Randomly replicate particles to bring the total number of particles to L; Step (5.4): Reset the weights of the newly generated N particles to... ; (6) Iterate through the above steps to perform simultaneous AUV localization and map building.

2. The AUV-UFastSLAM method based on the whale algorithm optimization as described in claim 1, characterized in that, The initialization process in step (1) obtains the initial position information of the AUV through either the Global Positioning System (GPS) or the Ultra-Short Baseline Transmitter (USBL). The GPS obtains the longitude and latitude information of the AUV, while the USBL obtains the position of the AUV relative to the USBL transmitter station. One method can be used alone, or the two methods can be combined to improve the accuracy of the initial position estimation of the AUV. Initial velocity and attitude information are obtained through the Doppler log (DVL) and gyroscope. The Doppler log (DVL) collects one or more of the three-axis velocity information of the AUV. The gyroscope collects one or more of the yaw angle, roll angle, and pitch angle information of the AUV.

3. The AUV-UFastSLAM method based on the whale algorithm optimization as described in claim 1, characterized in that, Step (2) calculates the particle state value at time t based on the motion prediction equation and sensor observation equation of the AUV. and observed values Unscented particle filtering is used to predict the pose and landmarks of the AUV. The AUV motion prediction equation and the sensor observation equation are as follows: In the formula, , These are the system's state vector and observation vector at time t, respectively. Let be the state vector of the system at time t-1. For motion control at time t, , These are nonlinear functions representing the state and the observation, respectively. To satisfy the condition that the mean is zero, the covariance is Process noise, To satisfy the condition that the mean is zero, the covariance is Observation noise.

4. The AUV-UFastSLAM method based on the whale algorithm optimization as described in claim 1, characterized in that, Step (3) uses the unscented Kalman filter algorithm to generate a proposal distribution function, samples N particles from the proposal distribution function, calculates the weight of each particle, and optimizes the sampling process for the generated N particles using the improved whale algorithm, including the following steps: Step (3.1): Generate the proposal distribution function using the unscented Kalman filter algorithm, sample N particles from the proposal distribution function, calculate the weight of each particle, and take the particle with the largest weight at the current time as the global optimum. ; Step (3.2): During the iteration process of the whale algorithm, the current optimal value will only be updated when there is a whale individual that is better than the current optimal value. This will reduce the number of updates to the optimal value, thus affecting the search efficiency of the algorithm. Cauchy mutation is introduced to improve the search strategy of the whale algorithm, so as to increase the population diversity and improve the global search capability of the algorithm. The standard Cauchy distribution function formula is shown in equation (3): After obtaining the optimal solution, the formula for the optimal neighborhood random perturbation is shown in equation (4): Where r is a random number between [0,1] For the newly generated neighborhood location, when r < 0.5, use formula (4) to... Neighborhood random perturbation; when r≥0.5, the newly generated neighborhood position is still the optimal whale position, and the fitness of the newly generated neighborhood position... Fitness higher than the original optimum At that time, then for The update process is shown in equation (5): Step (3.3): To address the weakness of the optimal whale position in the early stages of the whale algorithm having a weak impact on other individuals and being prone to getting trapped in local optima in the later stages of iteration, an inertia weight factor is introduced during the whale position update process. The position update formula is improved to adjust the global search and local optimization capabilities of the algorithm. The adaptive weight formula is shown in equation (6), and the improved position update formula is shown in equation (7). in, Here, T is the inertia weighting factor, t is the current iteration number, and T is the current iteration number. max The maximum number of iterations, As the initial weight, For the final weight, and ; The optimal position of the whale at time t is given. This represents the updated positions of the remaining whales at time t+1; combined with the negative power of e in equation (6) The algorithm exhibits a monotonically decreasing trend in the early stages. A larger value will allow the algorithm to reach the vicinity of the optimum more quickly, improving the global search capability of the whale algorithm in the early stages; as the number of iterations increases, The value of gradually decreases, which strengthens the local optimization ability of the algorithm in the later stage, making the algorithm get closer and closer to the optimal value in the iteration, thereby improving the population convergence speed and accuracy. Step (3.4): Determine if the maximum number of iterations T has been reached. max If not achieved, proceed to step (3.2); Step (3.5): Update and normalize the particle weights, and output the particle states.

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