Dynamic weighting ship thrust distribution method based on parallel saltcat sea gull optimization algorithm

Abstract

The invention discloses a dynamic weighted ship thrust distribution method based on a parallel saltcat sea gull optimization algorithm, and the method comprises the steps: obtaining a global optimal individual solution XSCO of a thrust distribution mathematic model through employing the saltcat optimization algorithm, obtaining a local optimal individual solution XSOA of the thrust distribution mathematic model through employing the sea gull optimization algorithm, and achieving the dynamic weighted ship thrust distribution. And obtaining a mixed optimal solution of the thrust distribution mathematical model on the basis of the dynamically adjusted weight of the solution of the saltcat optimization algorithm and the weight of the solution of the sea gull optimization algorithm, so as to realize the distribution of the ship thrust. According to the ship thrust distribution method, the saloon optimization algorithm and the seagull optimization algorithm are combined, the problem of falling into local optimum can be effectively avoided, accurate and efficient thrust distribution is achieved, and the positioning accuracy and energy efficiency of the ship are improved. Based on the weight of the solution of the Karat optimization algorithm and the weight of the solution of the sea gull optimization algorithm which are dynamically adjusted, the rapid self-adaptive adjustment capability can be achieved under the complex sea condition, and the stability and economical efficiency of the ship are guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of ship power system optimization, and in particular to a dynamic weighted ship thrust distribution method based on a parallel Sand Cat Seagull optimization algorithm. Background Art

[0002] The optimization and intelligent control of ship power systems is one of the important technologies for achieving efficient marine development. In particular, in the fields of high-end marine engineering equipment such as marine oil and gas exploration, deep-sea scientific research, offshore wind power installation, maritime rescue, and polar scientific research, the dynamic positioning (DP) technology of intelligent ships has become the core support.

[0003] Dynamic positioning technology refers to the use of computer-controlled propulsion systems to enable ships to maintain stability at a specified location or move precisely along a planned trajectory without relying on anchoring or mooring equipment. DP systems mainly rely on omnidirectional thrusters (such as tunnel thrusters, pod thrusters, and pump-jet thrusters) to provide thrust. Through thrust distribution optimization algorithms, multiple thrusters work together to resist environmental interference such as wind, waves, and currents, achieving high-precision ship maneuvering control. The optimization goals of thrust distribution include: (1) accurately meeting the ship's attitude control requirements and reducing positioning errors; (2) minimizing fuel consumption and improving energy utilization; (3) balancing thruster loads, reducing wear, and extending equipment life; and (4) meeting the physical constraints of the thrusters to avoid damage to the equipment due to excessive torque.

[0004] At present, the thrust distribution problem of DP ships still faces many challenges: (1) High-dimensional nonlinear optimization problem: DP ships are usually equipped with 6-8 thrusters, and the thrust size and direction constitute a high-dimensional nonlinear optimization problem, which is difficult to solve; (2) High computational complexity and high real-time requirements: Traditional analytical methods (such as quadratic programming QP) are difficult to meet the real-time optimization requirements, and the optimization algorithm needs to take into account both accuracy and computational efficiency; (3) Local optimality problem: Heuristic optimization algorithms (such as genetic algorithm GA, particle swarm optimization PSO) are prone to fall into local optimality, resulting in the thrust distribution scheme being unable to achieve global optimality; (4) Insufficient dynamic adaptability: Under complex sea conditions, the wind, wave and current environment is highly disturbed, and the thrust distribution strategy needs to have the ability to quickly adapt to ensure the stability and economy of the ship. In summary, the existing thrust distribution optimization methods still have limitations in terms of computational efficiency, global optimization capability, and adaptability, and are difficult to meet the real-time optimization requirements of DP ships under complex working conditions. Summary of the Invention

[0005] The present invention discloses a dynamic weighted ship thrust distribution method based on a parallel Sand Cat-Seagull optimization algorithm to overcome the above technical problems.

[0006] In order to achieve the above object, the technical solution of the present invention is:

[0007] A dynamic weighted ship thrust distribution method based on a parallel Sand Cat Seagull optimization algorithm comprises the following steps:

[0008] Step 1: Obtain the current position and target position of the ship to obtain the longitudinal force, lateral force and turning moment required for the ship's motion;

[0009] Step 2: Establish a thrust distribution mathematical model based on the longitudinal force, lateral force and rotational torque required for the ship's motion;

[0010] Step 3: Use the Sandcat optimization algorithm to obtain the global optimal individual solution X of the thrust distribution mathematical model SCO , using the Seagull optimization algorithm to obtain the local optimal individual solution of the thrust distribution mathematical model SOA ;

[0011] Step 4: Initialize the weights of the solutions of the Sand Cat optimization algorithm and the Seagull optimization algorithm, and according to the global optimal individual solution and the local optimal individual solution, and based on the dynamically adjusted weights of the solutions of the Sand Cat optimization algorithm and the Seagull optimization algorithm, obtain the hybrid optimal solution of the thrust distribution mathematical model to achieve the distribution of ship thrust.

[0012] Furthermore, the thrust distribution mathematical model is established as follows:

[0013]

[0014]

[0015] in,

[0016]

[0017] s=τ-B(α)T

[0018]

[0019] Where: MinJ(α,T) represents the ship thrust target allocation function; α represents the thruster direction angle; T represents the thrust of the thruster; (·)′ represents the transposition; W is the weight coefficient; P total represents the total power consumption of all thrusters; s represents the slack variable; Q and Ω are both positive definite diagonal matrices; α0 represents the azimuth angle of each thruster in the previous cycle; Indicates the actual rate of change of thruster power; is the expected propeller power change rate; K represents the weight coefficient matrix; δ is the adjustment coefficient; ε represents a constant used to ensure that the denominator is not zero, where ε>0; det(·) represents the determinant calculation; i represents the index number of the propeller; I represents the total number of propellers; P iP represents the power consumption of the i-th propeller; τ represents the theoretical control force of the three degrees of freedom of the ship; B(α) represents the propeller configuration matrix; P 0i P represents the power consumption of the i-th propeller in the previous distribution period; (α-α0) represents the difference between the azimuth angle of the i-th propeller in the current distribution period and the azimuth angle of the i-th propeller in the previous distribution period; P represents the power consumption of the i-th propeller in the previous distribution period; (α-α0) represents the difference between the azimuth angle of the i-th propeller in the current distribution period and the azimuth angle of the i-th propeller in the previous distribution period; i C represents the correction coefficient; T i T represents the thrust of the i-th propeller; T 0i T represents the thrust of the i-th propeller in the previous distribution period; G represents the weight coefficient of the propeller load balancing term; T represents the average value of the thrust of all propellers.

[0020] Further, the formulae for obtaining the longitudinal force, lateral force and turning moment required for the ship motion are as follows:

[0021]

[0022] X V , Y V , N V represent the longitudinal force, lateral force and turning moment required for the ship motion, respectively; Θ PID represents the PID controller; D represents the environmental feedforward compensation; D V represents the dynamic damping;

[0023] wherein,

[0024]

[0025] e = η d - η

[0026] K p , K d , K i represent the proportional coefficient, derivative coefficient and integral coefficient in the PID controller, respectively; e represents the ship attitude error; represents the first-order derivative of e; k represents time; η d represents the target position and heading in the North-East coordinate system; η represents the current position and heading of the ship in the North-East coordinate system.

[0027] Further, the method for obtaining the local optimal individual solution X SOA of the thrust distribution mathematical model is as follows:

[0028] S321: Initialize the gull population using Latin hypercube distribution;

[0029] S322: generating a random number p for the seagull individual in the seagull population; and obtaining an updated position of the seagull individual;

[0030] wherein, when the seagull behavior random number p > p H , the formula used to obtain the updated position of the seagull individual is as follows:

[0031] D x (t H ) = |C x (t H ) + M x (t H )|

[0032] C x (t H ) = A x p x (t H )

[0033] A = 2 - (t H x (2 / T Hmax ))

[0034] M x (t H ) = B x (p bs (t H ) - p x (t H ))

[0035] B = 2 x A 2 x r d

[0036] In the formula, D x (t H ) is the distance between the seagull individual and the best seagull individual; M x (t H ) is the convergence direction of the best seagull individual, i.e., the direction of the optimal seagull; C x (t H ) is the new position that can be moved without conflict; |·| is the absolute value; T Hmax is the maximum number of iterations of the seagull optimization algorithm; p x (t H ) is the updated position of the seagull individual; p bs (t H ) is the position of the best seagull individual in the population; A is the migration behavior control factor of the seagull; r d is a uniformly distributed random number; B is a search balance factor used to balance the seagull algorithm; p H represents the seagull behavior judgment index; t H represents the iteration number of the seagull optimization algorithm;

[0037] When the seagull behavior is random number p≤ρ H The formula for obtaining the updated position of the seagull individual is as follows:

[0038] x=r×cos(θ H )

[0039] y=r×sin(θ H )

[0040] z=r×θ H

[0041]

[0042] p x (t H )=p bs (t H )+D x (t H )×x×y×z

[0043] wherein r is the flight radius; x, y, and z are the coordinate values of the seagull individual in the geographic coordinate system; θ H is a random number between [0, 2]; u and v are constants for defining the spiral shape; p x (t H ) is the updated position of the seagull individual;

[0044] S323: Based on the thrust allocation mathematical model, the fitness of the updated position of the seagull individual is obtained to obtain the local optimal individual solution X SOA of the thrust allocation mathematical model.

[0045] Further, the formula for obtaining the hybrid optimal solution of the thrust allocation mathematical model is as follows:

[0046] X=W1·X SCO +W2·X SOA

[0047] W1+W2=1

[0048] wherein X represents the hybrid optimal solution; W1 represents the weight of the solution of the sand cat optimization algorithm; W2 represents the weight of the solution of the seagull optimization algorithm; X SCO represents the global optimal individual solution of the thrust allocation mathematical model; X SOA represents the local optimal individual solution of the thrust allocation mathematical model.

[0049] Further, the method for dynamically adjusting the weight of the solution of the sand cat optimization algorithm and the weight of the solution of the seagull optimization algorithm is as follows:

[0050] S41: Obtain the evaluation function value of the weight:

[0051] E = W1 x Δf + W2 x Var norm norm

[0052] where e represents the evaluation function value of the weight; Δf norm represents the normalized fitness variation value; Var norm represents the normalized search variable variance;

[0053] where,

[0054] Δf = |f best -f best-prev |

[0055]

[0056] where Δf represents the fitness variation value; f best is the fitness value of the optimal solution in the current iteration, f best-prev is the fitness value of the optimal solution in the last iteration; Var X is the search variable variance; U represents the number of search solutions; u represents the index number of the search solution; ub represents the maximum upper bound of the global search space; lb represents the minimum lower bound of the global search space; x u is the value of the u-th search solution, μ X is the mean value of the search solution, and ε is a constant for avoiding zero denominator.

[0057] S42: Obtain the fitness threshold of the hybrid solution:

[0058] tol(t) = tol min +(tol max -tol min )·e (-λt)

[0059] where tol(t) represents the fitness threshold at the current iteration step; tol min , tol max are the set minimum fitness threshold and maximum fitness threshold, respectively; t represents the iteration step index; and λ is the decay rate.

[0060] S43: When E < tol(t), reduce the weight W1 of the solution of the sand cat optimization algorithm and increase the weight W2 of the solution of the seagull optimization algorithm.

[0061] When E > tol(t), increase the weight W1 of the solution of the sand cat optimization algorithm and reduce the weight W2 of the solution of the seagull optimization algorithm.

[0062] ​When E = tol(t), the weight W1 of the solution of the sand cat optimization algorithm and the weight W2 of the solution of the albatross optimization algorithm are both unchanged.

[0063] Beneficial effects: the dynamic weighted ship thrust distribution method based on the parallel sand cat-albatross optimization algorithm of the application establishes a thrust distribution mathematical model according to the longitudinal force, lateral force and turning moment required by ship movement; the sand cat optimization algorithm is adopted to obtain the globally optimal individual solution X SCO of the thrust distribution mathematical model, the albatross optimization algorithm is adopted to obtain the locally optimal individual solution X SOA of the thrust distribution mathematical model, and the mixed optimal solution of the thrust distribution mathematical model is obtained based on the dynamically adjusted weight of the solution of the sand cat optimization algorithm and the weight of the solution of the albatross optimization algorithm, so as to realize the distribution of the ship thrust. The application does not need to perform high-dimensional nonlinear optimization, has low calculation complexity, can effectively avoid the problem of falling into local optimization by combining the sand cat optimization algorithm and the albatross optimization algorithm, realizes accurate and efficient thrust distribution, and improves the positioning accuracy and energy efficiency of the ship. Based on the dynamically adjusted weight of the solution of the sand cat optimization algorithm and the weight of the solution of the albatross optimization algorithm, the ship can also have the ability of rapid self-adaptive adjustment in complex sea conditions, and the stability and economy of the ship are ensured. The application has strong global search capability, efficient calculation and strong environmental adaptability, greatly improves the intelligent level of DP ship thrust distribution, and promotes the ocean equipment technology in China to a higher level. BRIEF DESCRIPTION OF DRAWINGS

[0064] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced below. Obviously, the drawings in the following description are some embodiments of the application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0065] Figure 1 The dynamic weighted ship thrust distribution method flow chart of the application;

[0066] Figure 2 The ship thrust distribution system structure flow chart in the embodiment of the application;

[0067] Figure 3 The energy consumption comparison chart of the dynamic weighted ship thrust distribution method in the embodiment of the application and the distribution result of the existing method;

[0068] Figure 4 The total thrust comparison chart of the dynamic weighted ship thrust distribution method in the embodiment of the application and the distribution result of the existing method. DETAILED DESCRIPTION

[0069] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0070] The embodiment introduces a dynamic weighted ship thrust distribution method based on a parallel sand cat-seagull optimization algorithm, including the following steps, as shown in Figure 1

[0071] Step 1: Obtain the current position and target position of the ship to obtain the longitudinal force, lateral force and turning moment required for the ship movement;

[0072] Specifically, the control system of the dynamic positioning system (DPS) calculates the control instructions of the three degrees of freedom (longitudinal force, lateral force and turning moment) required for the ship movement, i.e. the longitudinal force, lateral force and turning moment required for the ship movement, according to the deviation of the current position and target position of the ship, using a PID controller; wherein the deviation of the current position and target position of the ship is obtained by measuring the current position of the ship by the position reference system and comparing with the target position set by the control system, and the PID controller calculates the control instructions according to the deviation to realize dynamic positioning control;

[0073] Preferably, the formula used to obtain the longitudinal force, lateral force and turning moment required for the ship movement is as follows:

[0074]

[0075] In the formula, X V ,Y V ,N V respectively represent the longitudinal force, lateral force and turning moment required for the ship movement; Θ PID represents the PID controller; represents the environmental feedforward compensation; D V represents the dynamic damping;

[0076] wherein,

[0077]

[0078] e = η d - η (3)

[0079] In the formula, K p ,K d ,K i respectively represent the proportional coefficient, the differential coefficient and the integral coefficient in the PID controller; e represents the ship attitude error;​ denotes the first derivative of e; k denotes time; η d denotes the target position and heading in the North-East coordinate system; η denotes the current position and heading of the vessel in the North-East coordinate system.

[0080] Specifically, in a dynamic positioning system (DPS), a control system acquires the current position and heading of the vessel through sensors (such as GPS, compass, inertial navigation system) carried by the vessel in real time, compares them with the target position, and obtains three degrees of freedom errors: longitudinal error, lateral error, and plane rotation error. Then, a PID controller outputs the required control instructions, including longitudinal force, lateral force, and rotation torque, according to these errors, to counteract external disturbances (such as wind, wave, and current) and maintain the stable position and attitude of the vessel. These control instructions will eventually be passed to the thrust allocation module to be converted into thrust and direction instructions for each propeller, achieving dynamic precise positioning.

[0081] Step 2: Establish a thrust allocation mathematical model;

[0082] Specifically, the control instructions are converted into the thrust and azimuth angle of each propeller through the thrust allocation mathematical model. The thrust allocation mathematical model generally considers the physical limitations of the propeller, such as maximum thrust, forbidden angle, and speed limit of the propeller, etc. Thrust allocation is often considered as an optimization problem, aiming to minimize energy consumption, thrust error, and propeller wear, while also considering the stability of the power system and the non-singular structure of the vessel propeller.

[0083] The thrust allocation mathematical model adds two new items: the stability of the power system and the non-singular structure of the vessel propeller, compared with the traditional model.

[0084] Preferably, the thrust allocation mathematical model is established as follows:

[0085]

[0086] wherein,

[0087]

[0088]

[0089] In the formula: MinJ(α, T) represents the vessel thrust target allocation function; α represents the propeller direction angle; T represents the thrust of the propeller; (·)′ represents transposition; W is the weight coefficient; P total represents the total power consumption of all propellers; s represents the slack variable; Q and Ω are both positive definite diagonal matrices, representing the weight of the corresponding items; α0 represents the azimuth angle of each propeller in the previous period; represents the actual propeller power change rate; desired propeller power variation rate; K represents a weight coefficient matrix, representing the proportion of the item in the entire objective function, the greater the value, the more gentle the power variation, which should be adjusted according to actual needs; δ is an adjustment coefficient, wherein δ > 0; ε represents a constant for ensuring that the denominator is not zero, wherein ε > 0; det(·) represents the determinant calculation; i represents the index number of the propeller; I represents the total number of propellers; P i represents the power consumption of the i th propeller; τ is the theoretical control force of the three degrees of freedom of the ship; B(α) represents the propeller configuration matrix; P 0i represents the power consumption of the i th propeller in the last distribution period; (α-α0) represents the difference between the azimuth of each propeller in the current distribution period and the azimuth of each propeller in the last period; is the power variation rate of other electrical equipment on the ship, since the present embodiment does not consider other electrical loads, therefore can be regarded as 0; C i represents a correction coefficient; T i represents the thrust of the i th propeller; T 0i represents the thrust of the i th propeller in the last distribution period; G represents the weight coefficient of the propeller load balancing term; represents the average value of the thrust of all propellers.

[0090] In the thrust distribution mathematical model of the present embodiment, since the weight coefficient of the propeller load balancing term and the average value of the thrust are introduced, the thrust of each propeller can be close to the overall average, avoiding overloading or idling of individual propellers, which is beneficial to balancing power consumption, prolonging the service life of the propeller, and reducing local mechanical or thermal damage.

[0091] Specifically, in order to simplify the calculation of the model, the power consumption of the propeller in the present embodiment is approximately equal to the output power of the propeller under the condition of ignoring transmission and motor efficiency loss, and the method for obtaining the power consumption is as follows:

[0092] Obtain the propeller thrust and torque:

[0093]

[0094] In the formula: D p represents the diameter of the propeller; ρ represents the density of seawater; K T represents the thrust coefficient; K Q represents the torque coefficient; H represents the propeller torque, which is generally affected by multiple factors, including the diameter D p of the propeller, the fixed parameter θ p and the time-varying parameter x p , n represents the propeller speed; θ p represents the fixed parameter; x p represents the time-varying parameter;

[0095] The propeller power consumption is represented as follows:

[0096]

[0097] According to formula (5) and formula (6), the relationship between the propeller power consumption and the propeller thrust is represented as follows:

[0098]

[0099] Wherein, P represents the propeller power; p represents the seawater density; K T represents the thrust coefficient; K Q represents the torque coefficient; D p represents the propeller diameter; and T is the propeller thrust.

[0100] Step 3: obtaining the global optimal individual solution X SCO of the thrust distribution mathematical model by using the sand cat optimization algorithm, and obtaining the local optimal individual solution X SOA of the thrust distribution mathematical model by using the seagull optimization algorithm.

[0101] Specifically, according to the thrust distribution mathematical model, the sand cat optimization algorithm and the seagull optimization algorithm are used to solve the thrust distribution problem by using the dynamic weight optimization method, and the optimization performance is enhanced.

[0102] Preferably, the method for obtaining the global optimal individual solution X SCO of the thrust distribution mathematical model is as follows:

[0103] Specifically, in the sand cat optimization algorithm and the seagull optimization algorithm, the Latin hypercube distribution method is used for population initialization, the sand cat optimization algorithm and the seagull optimization algorithm are used for searching at the same time, the sand cat optimization algorithm focuses on global search, the seagull optimization algorithm focuses on local development, the optimization results of the two are dynamically weighted, and a preliminary solution that minimizes the value of the thrust distribution mathematical model is obtained, that is, the relatively optimal propeller thrust and direction angle.

[0104] Specifically, the method for obtaining the global optimal individual solution X SCO of the thrust distribution mathematical model is as follows:

[0105] S311: initializing the population in the sand cat optimization algorithm;

[0106] Specifically, in the search space of the propeller parameters, the sand cat population is initialized by using the Latin hypercube distribution, each sand cat individual represents the azimuth angle and the thrust of the propeller, a plurality of initial sand cats are formed, and each individual in each sand cat group represents a set of solutions of the ship thrust target distribution function with respect to the thrust of the propeller and the azimuth angle of the propeller.

[0107] Initialize parameters of the sand cat optimization algorithm, wherein the initialized parameters include a number N of sand cat individuals CAT , a maximum number T of iterations of the sand cat optimization algorithm CATmax , a step factor S max , a jump probability P j , a convergence threshold ∈, and a migration probability P m ;

[0108] S312: According to the current state of each sand cat, the fitness function value of the sand cat individual is calculated based on the thrust allocation mathematical model (in this embodiment, the thrust allocation mathematical model is taken as the fitness function of the sand cat optimization algorithm), and the sand cat position corresponding to the maximum fitness value is taken as the optimal sand cat position, and the global optimal position information is updated;

[0109] S313: The roulette wheel selection method is used to calculate and assign a new jump direction angle value a CAT of the sand cat individual in the next step, so as to adjust the search direction and improve the convergence of the algorithm, and the value affects the search direction of the sand cat;

[0110] S314: A conversion coefficient R is calculated to update the position of the sand cat population; wherein the conversion coefficient is used to determine whether the sand cat individual should currently perform global search or local optimization, if R>1, the sand cat individual enters the "search prey" mode, explores new possible solutions in a larger range, and enhances the diversity of the population; if R≤1, the sand cat individual enters the "attack prey" mode, and uses a local search strategy to find better solutions around the existing solutions, so as to accelerate convergence;

[0111] Specifically, the conversion coefficient R is used to distinguish different search strategies in the sand cat optimization algorithm, so that the individual switches between different search modes, so as to balance between global exploration and local development. The conversion coefficient R mainly affects the behavior mode of the sand cat, and determines whether it is searching for prey or attacking prey. The calculation method is specifically as follows:

[0112] R = 2r G ·rand(0,1)-r G (8)

[0113] In the formula, R represents the conversion coefficient; r G is the sensitivity coefficient of the sand cat group; rand(0,1) represents a function of generating a random number between (0,1);

[0114] Wherein,

[0115]

[0116] In the formula, S MThe hearing coefficient of the cat colony is simulated as the hearing characteristics of the cat. Since the cat is very sensitive to low-frequency sound of 2 kHz, the S M is 2, and can be set to other values according to the solution of the actual problem; t CAT and T CATmax are respectively the current iteration number of the cat optimization algorithm and the maximum iteration number of the cat optimization algorithm;

[0117] Specifically, the method for updating the position of the cat colony is as follows:

[0118] When the conversion coefficient R>1, the cat colony enters the search stage, and the Zth cat in the cat colony updates the position according to the following formula:

[0119] X Z (t CAT +1)=r Z [X best (t CAT )-rand(0,1)·X Z (t CAT )] (10)

[0120] In the formula, X Z (t CAT +1) represents the position of the Zth cat at the t CAT +1th iteration; r Z is the sensitivity coefficient of the Zth cat; X Z (t CAT ) represents the position of the Zth cat at the t CAT th iteration; X best (t CAT ) is the position of the optimal cat in the cat colony at the t CAT th iteration,

[0121] wherein,

[0122] r Z =r G ·rand(0,1) (11)

[0123] In the formula, r G is the sensitivity coefficient of the cat colony;

[0124] When the conversion coefficient R≤1, the cat colony enters the development stage, and the Zth cat in the cat colony updates the position according to the following formula:

[0125] X Z (t CAT +1)=X best (t CAT )-r Z ·X rand (tCAT )·cos(α CAT ) (12)

[0126] Where: X rand (t CAT ) represents a random position; α CAT is the angle value of the next jump direction of the sand cat individual, which is a random angle in the range of 0-360°, simulating the sand cat's search behavior with the current position as the center;

[0127] in,

[0128] X rand (t CAT )=rand(0,1)·X best (t CAT )-X Z (t CAT ) (13)

[0129] Where: X best (t CAT ) is the tth CAT The position of the best sand cat in the sand cat group at the iteration;

[0130] Specifically, this embodiment achieves an effective balance between the two stages through adaptive conversion between the exploration stage and the development stage, ensuring the global and local optimization capabilities of the algorithm until the predetermined convergence condition is met, that is, the objective function converges to a certain threshold or reaches the maximum number of iterations, and the global optimal individual solution X is output. SCO .

[0131] S315: Determine whether the preset termination condition is met and decide whether the optimization process is terminated. The termination condition includes but is not limited to reaching the maximum number of iterations T of the Sand Cat optimization algorithm. CATmax Or the objective function converges to the set convergence threshold ∈; when the termination condition is reached, the current relatively optimal solution X is output best (t CAT ).

[0132] S316: The current relatively optimal solution obtained by each sand cat population is X best (t CAT ) to obtain a relatively optimal parameter solution domain and output the global optimal individual solution X based on the thrust distribution mathematical model. SCO .

[0133] Preferably, the local optimal individual solution X of the thrust distribution mathematical model is obtained SOA The method is as follows:

[0134] S321: initializing the gull population with Latin hypercube distribution, each gull individual representing the azimuth angle and thrust of the propeller, thereby forming a number of initial gulls, and each gull individual in the gull population representing a set of solutions of the ship thrust target allocation function with respect to the thrust of the propeller and the azimuth angle of the propeller.

[0135] S322: generating a gull individual behavior random number p for the gull individual in the gull population; obtaining the position of the updated gull individual;

[0136] Specifically, after initialization, the gull optimization algorithm updates and optimizes the population through two strategies (migration stage and hunting stage), and uses a random number to determine the migration behavior or hunting behavior. In each iteration, we select the migration behavior or hunting behavior through a random number. For each gull individual, a gull behavior random number p ~ U(0, 1) is generated, and when p ≤ p H , the hunting behavior is selected, and when p > p H , the migration behavior is selected. Wherein, U(0, 1) represents a uniform distribution from 0 to 1;

[0137] When the gull behavior random number p > p H , the migration behavior is selected:

[0138] D x (t H ) = |C x (t H ) + M x (t H )| (14)

[0139] C x (t H ) = A x p x (t H ) (15)

[0140] A = 2 - (t H x (2 / T Hmax )) (16)

[0141] M x (t H ) = B x (p bs (t H ) - p x (t H )) (17)

[0142] B = 2 x A 2 x r d (18)

[0143] In the formula: D x (t H ) is the distance between the gull individual and the best gull individual; Mx (t H ) is the convergence direction of the best seagull individual, that is, the direction of the optimal seagull; C x (t H ) is the new position that can be moved without conflict; |·| is the absolute value; T Hmax The maximum number of iterations for the Seagull optimization algorithm; p x (t H ) is the updated position of the individual seagull; p bs (t H ) is the position of the best seagull individual in the population; A is the control factor of seagull migration behavior; r d is a uniformly distributed random number; B is the search balance factor, which is used to weigh the Seagull algorithm; ρ H represents the seagull behavior judgment index; t H Indicates the iteration number of the Seagull optimization algorithm;

[0144] When the seagull behavior random number p≤ρ H , select the predation behavior:

[0145] x=r×cos(θ H ) (19)

[0146] y=r×sin(θ H ) (20)

[0147] z=r×θ H (twenty one)

[0148]

[0149] p x (t H )=p bs (t H )+D x (t H )×x×y×z (23)

[0150] Where r is the flight radius; x, y, z are the coordinates of the seagull in the geographic coordinate system; θ H is a random number between [0,2], representing the attack angle of the seagull; u and v are constants used to define the spiral shape; p x (t H ) is the updated position of the individual seagull;

[0151] S323: Based on the thrust distribution mathematical model, obtain the fitness of the updated seagull individual position to obtain the local optimal individual solution X of the thrust distribution mathematical model. SOA .

[0152] Specifically, in each iteration, the fitness of each seagull individual is calculated (in this embodiment, the thrust allocation mathematical model is taken as the fitness function of the seagull optimization algorithm) to evaluate the energy consumption of the seagull individual. The smaller the value of the fitness function, the better the solution of the seagull individual. Then, the seagull individuals are selected according to the calculated fitness values, and the seagull individuals with lower fitness (i.e., the seagull individuals with the smallest energy consumption) are preferentially selected as new candidate solutions, and the current optimal solution is retained. In this way, the population is updated, and the individuals with poor fitness are gradually eliminated to ensure the stability of the optimal solution, while maintaining the diversity of the population and improving the search efficiency. Until the predetermined convergence condition is met, i.e., the objective function converges to a certain threshold or the maximum number of iterations is reached, the local optimal individual solution X SOA .

[0153] Step 4: Initialize the weight of the solution of the sand cat optimization algorithm and the weight of the solution of the seagull optimization algorithm, obtain the hybrid optimal solution of the thrust allocation mathematical model according to the global optimal individual solution and the local optimal individual solution, and based on the dynamically adjusted weight of the solution of the sand cat optimization algorithm and the weight of the solution of the seagull optimization algorithm, realize the distribution of the ship thrust.

[0154] Specifically, according to the optimization result, the control system transmits the thrust allocation scheme to the propeller controllers on the ship. These controllers convert the received thrust and azimuth angle information into specific actions to adjust the thrust size and direction of the propeller.

[0155] Preferably, the formula used to obtain the hybrid optimal solution of the thrust allocation mathematical model is:

[0156] X = W1 · X SCO + W2 · X SOA (24)

[0157] W1 + W2 = 1 (25) In the formula, X represents the hybrid optimal solution; W1 represents the weight of the solution of the sand cat optimization algorithm; W2 represents the weight of the solution of the seagull optimization algorithm; X SCO represents the global optimal individual solution of the thrust allocation mathematical model; X SOA represents the local optimal individual solution of the thrust allocation mathematical model;

[0158] Preferably, the method for dynamically adjusting the weight of the solution of the sand cat optimization algorithm and the weight of the solution of the seagull optimization algorithm is as follows:

[0159] S41: Obtain the evaluation function value of the weight:

[0160] E = W1 x Af norm + W2 x Var norm (26)

[0161] In the formula, E represents the evaluation function value of the weight; Afnorm represents the normalized fitness variation value; Var norm represents the normalized variance of search variables;

[0162] wherein,

[0163] Δf = |f best -f best-prev | (27)

[0164]

[0165]

[0166] wherein: Δf represents the fitness variation value; f best is the fitness value of the optimal solution in the current iteration, f best-prev is the fitness value of the optimal solution in the last iteration; Var X is the variance of search variables; U represents the number of search solutions; u represents the index number of search solutions; ub represents the maximum upper bound of the global search space; lb represents the minimum lower bound of the global search space; x u is the value of the u-th search solution, μ X is the mean value of search solutions, and ε is a constant for avoiding zero denominator.

[0167] S42: Obtain the fitness threshold of the hybrid solution:

[0168] tol(t) = tol min +(tol max -tol min )·e (-λt) (16)

[0169] wherein: tol(t) represents the fitness threshold at the current iteration step; tol min , tol max are the set minimum fitness threshold and maximum fitness threshold, respectively; t represents the iteration step index; λ is the decay rate for controlling the speed of tol(t) change, which is a positive constant, usually small.

[0170] S43: When E < tol(t), reduce the weight W1 of the solution of the sand cat optimization algorithm and increase the weight W2 of the solution of the seagull optimization algorithm.

[0171] When E > tol(t), increase the weight W1 of the solution of the sand cat optimization algorithm and reduce the weight W2 of the solution of the seagull optimization algorithm; in the embodiment, the weight of the solution of the sand cat optimization algorithm and the weight of the solution of the seagull optimization algorithm are adjusted according to the set adjustment step.

[0172] When E=tol(t), the weight W1 of the solution of the Sand Cat optimization algorithm and the weight W2 of the solution of the Seagull optimization algorithm remain unchanged.

[0173] In this embodiment, the weights W1=0.7 and W2=0.3 are initialized to ensure that the optimization starts with focusing on the global exploration of the Sand Cat optimization algorithm. As the number of iterations changes, W1 and W2 are dynamically adjusted, and the later stage focuses on the local development of the Seagull optimization algorithm.

[0174] Specifically, the weights W1 and W2 are dynamically adjusted to optimize the ratio of global search and local search through the weight evaluation function value E and the fitness threshold tol(t) at the current iteration step. <tol(t)时,表示优化过程较为稳定,适应度变化较小,或者解的多样性较小,这通常是搜索已经进入局部最优,或者需要更多局部优化的迹象。在这种情况下,应该减小全局搜索的权重W1,并增加局部搜索的权重W2。同样的若关系对调,则表示优化过程仍在进行中,适应度变化较大,或者搜索空间的解还在变化,说明全局搜索还在进行,需要继续进行广泛的探索。在这种情况下,应该增大全局搜索的权重W1,并减小局部搜索的权重W2。

[0175] Specifically, based on the optimization results, the control system transmits the thrust distribution plan to the ship's thruster controllers. These controllers convert the received thrust and azimuth information into specific actions, thereby adjusting the thrust magnitude and direction of the thrusters, thus forming a closed-loop control. This method combines the advantages of the SCO and SOA algorithms, running the two optimization algorithms in parallel and adjusting their contribution ratios through a dynamic weighting method to achieve precise optimization of the ship's thrust distribution. This method fully utilizes the complementary advantages of the two algorithms to achieve a ship thrust distribution method.

[0176] like Figure 3 and Figure 4 The comparison diagrams of the ship thrust distribution results obtained by the dynamic weighting method in this embodiment and the traditional calculation method are respectively shown. Figure 3 As can be seen in the figure, the ship thrust distribution results obtained using the dynamic weighting method of this embodiment maintain relatively stable power consumption and total thrust throughout the entire process, demonstrating that the method of this embodiment can effectively constrain power changes. Furthermore, the total energy consumption and total thrust shown by the distribution results of this embodiment are generally lower than those obtained by existing methods. This embodiment has a significant advantage in reducing energy loss and is of great significance in terms of energy conservation.

[0177] The application is based on a dynamic weighted ship thrust distribution method combining parallel sand cat optimization algorithm and seagull optimization algorithm, global exploration and local development optimization strategy, global search and fine adjustment of ship thrust distribution problem, and can realize better thrust distribution scheme in complex sea conditions. The embodiment not only improves the ship dynamic positioning accuracy, but also optimizes the propeller load distribution, reduces the energy consumption, prolongs the service life of the propeller, and has high engineering application value.

[0178] Finally, it should be pointed out that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A dynamic weighted ship thrust distribution method based on the parallel Sand Cat Seagull optimization algorithm, characterized in that: It includes the following steps: Step 1: Obtain the current position and target position of the ship to obtain the longitudinal force, lateral force, and turning moment required for the ship's movement; Step 2: Establish a thrust allocation mathematical model according to the longitudinal force, lateral force, and turning moment required for the ship's movement; Step 3: Use the Sandcat optimization algorithm to obtain the global optimal individual solution X of the thrust distribution mathematical model SCO , using the Seagull optimization algorithm to obtain the local optimal individual solution of the thrust distribution mathematical model SOA ; Step 4: Initialize the weights of the solutions of the sand cat optimization algorithm and the weights of the solutions of the seagull optimization algorithm. According to the global optimal individual solution and the local optimal individual solution, and based on the dynamically adjusted weights of the solutions of the sand cat optimization algorithm and the weights of the solutions of the seagull optimization algorithm, obtain the hybrid optimal solution of the thrust allocation mathematical model to achieve the allocation of the ship's thrust.

2. The method for dynamically weighted ship thrust distribution based on the parallel Sand Cat Seagull optimization algorithm according to claim 1 is characterized in that: The thrust allocation mathematical model is established as follows: Where, s = τ - B(α)T Where: MinJ(α,T) represents the ship thrust target allocation function; α represents the thruster direction angle; T represents the thrust of the thruster; (·)′ represents the transposition; W is the weight coefficient; P total represents the total power consumption of all thrusters; s represents the slack variable; Q and Ω are both positive definite diagonal matrices; α0 represents the azimuth angle of each thruster in the previous cycle; Indicates the actual rate of change of thruster power; is the expected propeller power change rate; K represents the weight coefficient matrix; δ is the adjustment coefficient; ε represents a constant used to ensure that the denominator is not zero, where ε>0; det(·) represents the determinant calculation; i represents the index number of the propeller; I represents the total number of propellers; P i represents the power consumption of the i-th propeller; τ is the theoretical control force of the three degrees of freedom of the ship; X V ,Y V ,N V They represent the longitudinal force, transverse force and turning moment required for ship motion respectively; B(α) represents the propeller configuration matrix; P 0i represents the power consumption of the i-th propeller in the previous allocation cycle; (α-α0) represents the difference between the azimuth angle of each propeller in the current allocation cycle and the azimuth angle of each propeller in the previous cycle; is the power change rate of other electrical equipment on board; C i Indicates the correction factor; T i represents the thrust of the i-th thruster; T 0i represents the thrust of the i-th thruster in the previous distribution cycle; G represents the weight coefficient of the thruster load balancing item; Represents the average thrust of all thrusters.

3. The method for dynamically weighted ship thrust distribution based on the parallel Sand Cat Seagull optimization algorithm according to claim 1, characterized in that: The formulas used to obtain the longitudinal force, lateral force, and turning moment required for the ship's movement are as follows: Where: X V ,Y V ,N V They represent the longitudinal force, transverse force and turning moment required for ship motion respectively; Θ PID represents a PID controller; represents environmental feedforward compensation; D V represents dynamic damping; Where, e=η d -or Where: K p ,K d ,K i Respectively represent the proportional coefficient, differential coefficient, and integral coefficient in the PID controller; e represents the ship attitude error; represents the first-order differential of e; k represents time; η d represents the target position and heading in the northeast coordinate system; η represents the current position and heading of the ship in the northeast coordinate system.

4. The method for dynamically weighted ship thrust distribution based on the parallel Sand Cat Seagull optimization algorithm according to claim 1, characterized in that: Obtain the local optimal individual solution X of the thrust distribution mathematical model SOA The method is as follows: S321: Initialize the seagull population using the Latin hypercube distribution; S322: Generate a random number p for the seagull individual in the seagull population to obtain the updated position of the seagull individual; Among them, when the seagull behavior random number p>ρ H When , the formula used to obtain the updated position of the seagull individual is as follows: D x (t H )=|C x (t H )+M x (t H )| C x (t H )=A×p x (t H ) A=2-(t H ×(2 / T Hmax )) M x (t H )=B×(p bs (t H )-p x (t H )) B=2×A 2 ×r d Where: D x (t H ) is the distance between the individual seagull and the best individual seagull; M x (t H ) is the convergence direction of the best seagull individual, that is, the direction of the optimal seagull; C x (t H ) is the new position that can be moved without conflict; |·| is the absolute value; T Hmax The maximum number of iterations for the Seagull optimization algorithm; p x (t H ) is the updated position of the individual seagull; p bs (t H ) is the position of the best seagull individual in the population; A is the control factor of seagull migration behavior; r d is a uniformly distributed random number; B is the search balance factor, which is used to weigh the Seagull algorithm; ρ H represents the seagull behavior judgment index; t H Indicates the iteration number of the Seagull optimization algorithm; When the seagull behavior random number p≤ρ H When , the formula used to obtain the updated position of the seagull individual is as follows: x=r×cos(θ H ) y=r×sin(θ H ) z=r×θ H p x (t H )=p bs (t H )+D x (t H )×x×y×z Where r is the flight radius; x, y, z are the coordinates of the seagull in the geographic coordinate system; θ H is a random number between [0,2]; u and v are constants used to define the spiral shape; p x (t H ) is the updated position of the individual seagull; S323: Based on the thrust distribution mathematical model, obtain the fitness of the updated seagull individual position to obtain the local optimal individual solution X of the thrust distribution mathematical model. SOA .

5. The method for dynamically weighted ship thrust distribution based on the parallel Sand Cat Seagull optimization algorithm according to claim 1, characterized in that: The formula used to obtain the hybrid optimal solution of the thrust allocation mathematical model: X=W1·X SCO +W2·X SOA W1 + W2 = 1 Where: X represents the hybrid optimal solution; W1 represents the weight of the solution of the sand cat optimization algorithm; W2 represents the weight of the solution of the seagull optimization algorithm; X SCO represents the global optimal individual solution of the thrust distribution mathematical model; X SOA Represents the local optimal individual solution of the thrust distribution mathematical model.

6. The method for dynamically weighted ship thrust distribution based on the parallel Sand Cat Seagull optimization algorithm according to claim 5, characterized in that: The method for dynamically adjusting the weights of the solutions of the sand cat optimization algorithm and the weights of the solutions of the seagull optimization algorithm is as follows: S41: Obtain the evaluation function value of the weight; E=W1×Δf norm +W2×Var norm Where: W represents the evaluation function value of the weight; Δf norm Indicates the standardized fitness change value; Var norm represents the standardized variance of the search variable; Where, Δf=|f best -f best-prev | Where: Δf represents the fitness change value; f best is the fitness value of the optimal solution in the current iteration, f best-prev is the fitness value of the optimal solution in the previous iteration; Var X is the variance of the search variable; U represents the number of search solutions; u represents the index number of the search solution; ub represents the maximum upper bound of the global search space; lb represents the minimum lower bound of the global search space; x u is the value of the u-th search solution, μ X is the mean of the search solution, and ε is a constant used to avoid the denominator being zero; S42: Obtain the fitness threshold of the hybrid solution; tol(t)=tol min +(tol max -tol min )·e (-λt) Where: tol(t) represents the fitness threshold at the current iteration step; tol min , tol max are the minimum fitness threshold and the maximum fitness threshold respectively; t represents the iteration step index; λ is the decay rate; S43: When E < tol(t), reduce the weight W1 of the solution of the sand cat optimization algorithm and increase the weight W2 of the solution of the seagull optimization algorithm; When E > tol(t), increase the weight W1 of the solution of the sand cat optimization algorithm and reduce the weight W2 of the solution of the seagull optimization algorithm; When E = tol(t), both the weight W1 of the solution of the sand cat optimization algorithm and the weight W2 of the solution of the seagull optimization algorithm remain unchanged.

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