CN116859728A - Ship dynamic positioning system thrust distribution method based on improved multi-target particle swarm algorithm - Google Patents
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Abstract
The invention provides a ship dynamic positioning system thrust distribution method based on an improved multi-target particle swarm algorithm, which is characterized in that an objective function comprising a plurality of independent optimization targets is established, the improved multi-target particle swarm optimization algorithm is introduced into the solution of a multi-target thrust distribution optimization problem, rather than combining a plurality of optimization targets such as propeller power consumption, thrust distribution errors, propeller loss jitter and the like into a single-target optimization problem solution by a weighting coefficient mode, and more reliable and optimal thrust distribution results can be obtained under the condition of considering global property and flexibility, so that the thrust distribution precision is improved, the energy consumption is reduced, the thrust distribution errors, the propeller abrasion and the propeller jitter are reduced, the solution of the thrust distribution problem is more practical, the problems of difficulty in weight selection and conflict among the objective functions in the solution of the single-target thrust distribution problem are solved, and the physical significance of various performance indexes of the propeller is clarified.
Description
Technical Field
The invention relates to the technical field of thrust distribution of ship dynamic positioning systems, in particular to a ship dynamic positioning system thrust distribution method based on an improved multi-target particle swarm algorithm.
Background
The ship dynamic positioning system consists of a control system, a propulsion system and a measurement system, wherein the control system consists of a motion control system and a thrust distribution system. The motion control system adopts a certain control method to determine the control force and moment required by the ship to keep the set ship position and course according to the error between the current ship position and the set ship position. In order to ensure the safety of the ship in the running process, the ship is generally provided with a plurality of propellers, so that the ship provided with the dynamic positioning system is overdriven, the propulsion system is redundant, and a plurality of groups of propeller operation combinations meeting the required control force and moment exist, so that the optimal propeller operation combination mode, namely the actual running speed, rudder angle, azimuth angle and the like of each propeller is required to be determined through a thrust distribution system. The common propulsion system consists of propellers such as propellers, rudders, side thrusters, full-rotation propellers and the like, and is limited by physical characteristics, and the rotation speed, rudder angle and azimuth angle of the propellers are usually limited by an upper operation limit and a lower operation limit; meanwhile, in order to reduce the abrasion of the propeller during operation and prolong the service life, the change rate of the rotating speed and the azimuth angle (or rudder angle) of the propeller during operation cannot be too large; in addition, to reduce fuel costs, propulsion systems also need to be operated with as little energy consumption as possible. Therefore, the thrust distribution problem is to satisfy the control force and torque distribution (reduce thrust distribution error), the lowest energy consumption of the propeller, the smallest abrasion shake, and the constraint nonlinear optimization problem of numerical value and change rate constraint of the rotating speed, rudder angle and azimuth angle of the propeller.
The traditional thrust distribution problem solving method comprises a pseudo-inverse method, a quadratic programming algorithm, a sequential quadratic programming algorithm and the like, and the thrust distribution optimizing problem is often a non-convex problem due to the thrust and azimuth limitation generated by a propeller, so that the method is difficult to solve. With the development of computer technology, the intelligent optimization algorithm can well solve the constraint nonlinear optimization problem due to the characteristic of being free from the influence of the non-convexity of the problem, and is gradually introduced into the solution of the thrust distribution optimization problem of the ship dynamic positioning system. In addition, the thrust distribution problem is actually a multi-objective optimization problem of ensuring that the energy consumption of a propulsion system, the wear and shake of a propeller and the thrust distribution error are minimum on the premise of meeting control requirements. The Multi-objective particle swarm optimization (Multi-Objective Particle Swarm Optimization, MOPSO) algorithm is a population intelligent optimization algorithm proposed by Coello et al in 2004, and the algorithm is formed by introducing the concept of pareto domination into a basic particle swarm algorithm. The particle swarm algorithm is one of a plurality of swarm intelligent algorithms, and has the advantages of simple algorithm principle, few parameters to be adjusted, wide search range and high convergence rate. The particle swarm algorithm is simple in concept and structure and easy to realize, and is widely applied to optimization problems in many scientific fields, such as path planning, parameter identification, integer planning problems of tourists and the like. The particle swarm algorithm can be combined with other intelligent algorithms to make up for the advantages and make the usability of the algorithm stronger; in addition, the parameters in the machine learning methods such as an artificial neural network, a support vector machine and the like can be optimized. The multi-target particle swarm optimization algorithm (MOPSO) has the advantages of no requirement on a feasible domain (both convex and non-convex optimization problems), simple parameters, quick convergence and the like, and can be used for solving the problem of multi-target optimization of thrust distribution.
However, most of the current algorithms generally synthesize the above multiple thrust distribution optimization targets into a single target through a weighted summation mode, solve the single target problem, so that the objective function loses definite physical meaning, and the problem that the weight selection is difficult and the conflict among the targets is difficult to coordinate exists. Therefore, a method for solving the thrust distribution problem of the ship dynamic positioning system as a multi-objective optimization problem needs to be studied, so that the performance of the thrust distribution system is improved.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a ship dynamic positioning system thrust distribution method based on an improved multi-target particle swarm algorithm, which comprises the following steps:
s1, establishing a mathematical model tau for thrust distribution of a ship dynamic positioning system d ＝B(α)T；
wherein ,τd ＝[F x F y F n ] T To control the force and moment of the system output control, F x 、F y Respectively represent the control forces in the heave and heave directions, F n The moment of turning the bow is represented, representing the thrust produced by each propeller, +.>For azimuth angle of each propeller +>A configuration matrix for the propeller;
wherein ,(lxi ,l yi ) Indicating the installation position of the ith propeller, x indicating the longitudinal axis, taking the heading of the ship as positive; y is the transverse axis, and the starboard direction of the ship is positive;
s2, establishing an objective function and constraint conditions comprising five independent optimization targets;
wherein f is a compound comprising J p ,J e ,J α ,J δ ,J ω Multi-objective optimization function with five independent optimization objectives, the optimization objectives of which are to find the objective J p ,J e ,J α ,J δ ,J ω Minimum propeller speed, rudder angle and azimuth angle, J p ,J e ,J α ,J δ ,J ω Respectively representing the power consumption, thrust distribution error, rotating speed, rudder angle and azimuth angle change rate of the propeller; e, e i Constant, n number of propellers equipped for the ship, s= [ s ] x ，s y ，s n ] T Is the error value between the control command generated by the controller and the actual thrust after thrust distribution, q=diag (Q x ,Q y ,Q n ) The penalty weight for thrust errors in three degrees of freedom of heave, surge and heading,propeller component T x and Ty Is a function of the propeller rotational speed ω, rudder angle δ and azimuth angle α; alpha i ，δ i and ωi Represents azimuth angle, rudder angle and rotating speed omega of the ith propeller at the current moment 0i ，δ 0i and α0i The rotation speed, rudder angle and azimuth angle of the ith propeller at the previous moment; omega i,min (ω i,max )，δ i,min (δ i,max) and αi,min (α i,max ) Representing the minimum (maximum) values of the rotation speed, rudder angle and azimuth angle of the ith propeller, delta omega respectively i ，△δ i and △αi Respectively representing the variation of the rotation speed, rudder angle and azimuth angle of the ith propeller in unit time, and delta omega i,min (△ω i,max )，△δ i,min (△δ i,max) and △αi,min (△α i,max ) The minimum (maximum) values of the variation of the rotating speed, rudder angle and azimuth angle of the ith propeller in unit time are respectively;
s3, setting a multi-target particle swarm algorithmParameters: population scale N, maximum iteration number m, particle position boundary x min and xmax Boundary v of speed min and vmax Inertial weight and final inertial weight, individual learning factor c 1 And population learning factor c 2 Establishing an external archive set for initializing a population of particles in a feasible solution space, wherein the external archive set stores the locations of non-dominant solution particles generated in an iteration;
s4, according to a plurality of objective functions J p ,J e ,J α ,J δ ,J ω Respectively calculating fitness values of particles in the initial group, constructing a non-dominant solution set according to the Pareto dominant relationship, and updating an external archive set;
s5, selecting an individual optimal solution Pbest according to the Pareto dominance relation, selecting a global optimal solution Gbest from the external archive set, wherein the individual optimal solution Pbest is generated according to a non-dominance solution obtained by comparing a current generation individual optimal solution with a previous generation individual optimal solution according to the Pareto dominance relation, and the global optimal solution Gbest is obtained by evaluating the individual density of each particle in the external archive set and selecting the Pareto optimal solution with small particle density as the global optimal solution;
s6, updating the speed and the position of the particles, judging whether the updated speed and position are within the range of the speed boundary and the position boundary, and determining that the speed updating formula and the position updating formula are as follows:
wherein ,representing the speed, position, individual optimum position and population optimum position of the ith particle in d-dimension at the t-th iteration,/->Representing the speed and position of the ith particle in d dimension at the t+1st iteration, rand 1 and rand2 Is [0,1]Random numbers uniformly distributed among them
S7, updating inertia weight kappa and individual learning factor c 1 And population learning factor c 2 The formula is as follows:
wherein ,κ1 Kappa for initial inertial weight 2 Is the final inertial weight; c 1s ,c 1e and c2s ,c 2e Learning factor c for individual 1 And population learning factor c 2 T is the current iteration number;
s8, judging whether the current iteration times meet the termination condition, if the current iteration times are greater than the maximum iteration times m, stopping iteration, and outputting an optimal solution; if the current iteration number is smaller than the maximum iteration number m, turning to step S4 to continue searching the optimal solution;
s9, outputting an optimal solution (omega, delta, alpha) meeting the multi-objective optimization function, wherein the optimal solution comprises propeller rotating speed omega= [ omega ] 1 *,ω 2 *,...,ω n *] T Rudder angle delta = [ delta ] 1 *,δ 2 *,...,δ n *] T Azimuth angle α= [ α ] 1 *,α 2 *,...,α n *] T And sending an instruction to each propeller of the ship to complete the thrust distribution task.
In an alternative embodiment, the updating the external archive set in step S4 uses a congestion distance-based sorting method, where the formula is as follows:
wherein ,di Indicating the degree of crowding of the ith particle,function value of the i-1 th particle representing the j-th objective function,/and/or>Function value of the (i+1) th particle representing the jth objective function,/for the (j) th particle>Representing the maximum of the jth objective function,representing the minimum of the jth objective function.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention solves the thrust distribution optimization problem by utilizing an improved multi-objective particle swarm algorithm, and the main difference between single-objective optimization and multi-objective optimization is that the single-objective optimization and the multi-objective optimization only comprise one objective function, only one optimal solution exists when the solution is performed, the optimal solution is unique and determined, a plurality of objective functions exist in the multi-objective optimization problem, two or more mutually conflicting targets are needed to be weighed simultaneously when the solution is performed to obtain a group of mutually independent optimal solution sets, and a certain solution is selected as a solution of the optimization problem according to actual conditions. The traditional thrust distribution problem is that a multi-target problem is converted into a single-target problem to be solved by a weighting coefficient method, and the conversion can simplify the solution of the problem, but can also lead each performance index of the propeller to lose definite physical significance.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings which are used in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained according to these drawings without inventive faculty for a person skilled in the art.
Fig. 1 is a schematic flow chart of a thrust distribution method of a ship dynamic positioning system based on an improved multi-target particle swarm algorithm according to an embodiment of the present disclosure;
FIG. 2 is a schematic view of a CS II ship model propeller configuration;
FIG. 3 is a schematic diagram of a closed loop control system for dynamic positioning of a vessel;
FIG. 4 is a graph showing the force component variation of each propeller during thrust force distribution;
FIG. 5 is a graph showing the variation of the rotational speed and rudder angle of each propeller during thrust distribution;
FIG. 6 is a graph showing the variation of thrust distribution errors during thrust distribution;
fig. 7 is a graph showing the overall power consumption of the propeller during thrust distribution.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the present embodiment proposes a ship dynamic positioning system thrust distribution method based on an improved multi-target particle swarm algorithm, including:
s1, establishing thrust distribution mathematics of ship dynamic positioning systemModel τ d ＝B(α)T；
wherein ,τd ＝[F x F y F n ] T To control the force and moment of the system output control, F x 、F y Respectively represent the control forces in the heave and heave directions, F n The moment of turning the bow is represented, representing the thrust produced by each propeller, +.>For azimuth angle of each propeller +>A configuration matrix for the propeller;
wherein ,(lxi ,l yi ) Indicating the installation position of the ith propeller, x indicating the longitudinal axis, taking the heading of the ship as positive; y is the transverse axis, and the starboard direction of the ship is positive;
s2, establishing an objective function and constraint conditions comprising five independent optimization targets;
wherein f is a compound comprising J p ,J e ,J α ,J δ ,J ω Multi-objective optimization function with five independent optimization objectives, the optimization objectives of which are to find the objective J p ,J e ,J α ,J δ ,J ω Minimum propeller speed, rudder angle and azimuth angle, J p ,J e ,J α ,J δ ,J ω Respectively representing the power consumption, thrust distribution error, rotating speed, rudder angle and azimuth angle change rate of the propeller; e, e i Constant, n number of propellers equipped for the ship, s= [ s ] x ，s y ，s n ] T Is the error value between the control command generated by the controller and the actual thrust after thrust distribution, q=diag (Q x ,Q y ,Q n ) The penalty weight for thrust errors in three degrees of freedom of heave, surge and heading,propeller component T x and Ty Is a function of the propeller rotational speed ω, rudder angle δ and azimuth angle α; alpha i ，δ i and ωi Represents azimuth angle, rudder angle and rotating speed omega of the ith propeller at the current moment 0i ，δ 0i and α0i The rotation speed, rudder angle and azimuth angle of the ith propeller at the previous moment; omega i,min (ω i,max )，δ i,min (δ i,max) and αi,min (α i,max ) Representing the minimum (maximum) values of the rotation speed, rudder angle and azimuth angle of the ith propeller, delta omega respectively i ，△δ i and △αi Respectively representing the variation of the rotation speed, rudder angle and azimuth angle of the ith propeller in unit time, and delta omega i,min (△ω i,max )，△δ i,min (△δ i,max) and △αi,min (△α i,max ) The rotation speed, rudder angle and azimuth angle of the ith propeller are respectively the most variable in unit timeSmall (maximum) value;
s3, setting parameters of a multi-target particle swarm algorithm: population scale N, maximum iteration number m, particle position boundary x min and xmax Boundary v of speed min and vmax Inertial weight and final inertial weight, individual learning factor c 1 And population learning factor c 2 Establishing an external archive set for initializing a population of particles in a feasible solution space, wherein the external archive set stores the locations of non-dominant solution particles generated in an iteration;
s4, according to a plurality of objective functions J p ,J e ,J α ,J δ ,J ω Respectively calculating fitness values of particles in the initial group, constructing a non-dominant solution set according to the Pareto dominant relationship, and updating an external archive set;
pareto dominance is defined as: for the objective function f (x), x= [ ω, δ, α] T ，ω＝[ω 1 ,ω 2 ,...,ω n ] T ,δ＝[ω 1 ,δ 2 ,...,δ n ] T ,α＝[α 1 ,α 2 ,...,α n ] T Any two solutions x in a feasible solution set 1 、x 2 The dominance relationship is defined as:
wherein: < mean dominance, x 1 Dominant x 2 Then x 1 At least one objective function value ratio x 2 Good, and x 1 Not all objective function values of (2) are not greater than x 2 And (3) difference.
Pareto optimal solution definition: if the decision vector x 1 For Pareto optimal decision vector, there is no x 2 ∈X:x 2 ＜x 1 E X, i.e. there is no ratio X within set X 1 Better solution, x 1 Is the optimal solution in X, and the Pareto optimal solution also becomes the non-dominant solution.
Pareto optimal solution set: the set of Pareto optimal solutions is referred to as the Pareto optimal solution set,denoted as P * 。
In this embodiment, the updating of the external archive set is based on the crowding distance sorting method, and the formula is as follows:
wherein ,di Indicating the degree of crowding of the ith particle,function value of the i-1 th particle representing the j-th objective function,/and/or>Function value of the (i+1) th particle representing the jth objective function,/for the (j) th particle>Representing the maximum of the jth objective function,representing the minimum of the jth objective function.
The last step is to obtain a group of mutually independent Pareto optimal solution sets, so that the problems of difficult weight selection and conflict among objective functions in the single-objective thrust distribution problem solving are solved, and the physical significance of various performance indexes of the propeller is clarified.
S5, selecting an individual optimal solution Prest according to the Pareto dominant relationship, and selecting a global optimal solution Gbest from the external archive set;
the method comprises the steps that an individual optimal solution Prest is generated according to a non-dominant solution obtained by comparing a current-generation individual optimal solution with a previous-generation individual optimal solution according to a Pareto dominant relationship, the newly generated individual optimal solution does not have a dominant relationship with an original individual optimal solution, the individual optimal solution Prest can be obtained by comparing crowding distances or one of the individual optimal solutions Prest is randomly selected, a global optimal solution Gbest is used for evaluating the individual density of each particle in an external archive set, the Pareto optimal solution with small particle density is selected as the global optimal solution, and the algorithm is prevented from being trapped into local optimal in iteration;
s6, updating the speed and the position of the particles, judging whether the updated speed and position are within the range of the speed boundary and the position boundary, and determining that the speed updating formula and the position updating formula are as follows:
wherein ,representing the speed, position, individual optimum position and population optimum position of the ith particle in d-dimension at the t-th iteration,/->Representing the speed and position of the ith particle in d dimension at the t+1st iteration, rand 1 and rand2 Is [0,1]Random numbers uniformly distributed among the two;
s7, updating inertia weight kappa and individual learning factor c 1 And population learning factor c 2 The formula is as follows:
wherein ,κ1 Kappa for initial inertial weight 2 Is the final inertial weight; c 1s ,c 1e and c2s ,c 2e Learning factor c for individual 1 And population learning factor c 2 T is the current iteration number;
the inertia weight kappa mainly controls the influence of the speed of the t generation particles on the speed of the t+1 generation particles, when the kappa value is very large, the speed of the t+1 generation particles is mainly influenced by the speed of the t generation particles, the influence of the self part and the social part is small, the population searching range is wide, the global searching capability is strong, but the flying direction of the particles is not easy to change, and the algorithm convergence is not facilitated. When kappa takes smaller value, the speed of t+1 generation particles is mainly influenced by the second part and the third part in the speed updating formula, and is less influenced by the speed of t generation particles, at the moment, the algorithm convergence speed is accelerated and the local searching capability is strong, so that the global or local searching capability of the algorithm can be controlled by adjusting the value of kappa, and the convergence speed, the precision and the searching range of the multi-target particle swarm algorithm are improved. In practical applications, it is generally desirable that the algorithm has strong global search at the beginning and then gradually changes to local fine search according to the situation of global search, so that the running time and the iteration number of the algorithm are reduced, which requires that κ can linearly decrease with the increase of the iteration number.
There is c in the velocity update formula 1 and c2 Two learning factors, namely, a learning factor c, are respectively used for adjusting the proportion of the self part and the social part in a speed formula 1 According to the historical optimal position searched by the particle, the flying speed of the next generation particle is adjusted, and the factor c is learned 2 The flying speed of the next generation of particles is regulated according to the optimal position of the particle population, the speed of the particles flying to the optimal position of the particle population is controlled, the learning factor is as important as the inertia weight, and the learning factor c can be regulated 1 and c2 The value of (2) controls the search ability of the particles in the solution space. When c 1 and c2 At 0 or less, the particles are mainly affected by the current speed, the particles may be far away from the target area, and no better solution is searched; when c 1 When the particles are larger, the positions of the particles in the space are more dispersed, which is unfavorable for information sharing among individualsSharing, wherein the algorithm convergence speed is lower; when c 2 When the algorithm is larger, the algorithm convergence speed is high, but the local searching capability is lost; c 1 and c2 The greater the speed, the greater the particle speed may be and the optimal solution may be skipped. If the population extremum is to be found, a larger c can be selected 2 Value and smaller c 1 If the value is contrary, if the individual extremum is to be found, a larger c can be selected 1 Value and smaller c 2 Values. It follows that a reasonable choice of the value of the learning factor has an important effect on the performance of the algorithm, and therefore a linearly decreasing learning factor c can be used in the iterative process of the algorithm 1 And a learning factor c that increases linearly 2 The optimizing capability of the algorithm is improved.
S8, judging whether the current iteration times meet the termination condition, if the current iteration times are greater than the maximum iteration times m, stopping iteration, and outputting an optimal solution; if the current iteration number is smaller than the maximum iteration number m, turning to step S4 to continue searching the optimal solution;
s9, outputting an optimal solution (omega, delta, alpha) meeting the multi-objective optimization function, wherein the optimal solution comprises propeller rotating speed omega= [ omega ] 1 *,ω 2 *,...,ω n *] T Rudder angle delta = [ delta ] 1 *,δ 2 *,...,δ n *] T Azimuth angle α= [ α ] 1 *,α 2 *,...,α n *] T And sending an instruction to each propeller of the ship to complete the thrust distribution task.
In an alternative embodiment, the updating the external archive set in step S4 uses a congestion distance-based sorting method, where the formula is as follows:
wherein ,di Indicating the degree of crowding of the ith particle,function value of the i-1 th particle representing the j-th objective function,/and/or>Function value of the (i+1) th particle representing the jth objective function,/for the (j) th particle>Representing the maximum of the jth objective function,representing the minimum of the jth objective function.
The following specific examples are presented in conjunction with the above embodiments, and it will be understood that the following specific examples merely exemplify the implementation of the above embodiments, and are not intended to limit the technical solutions of the above embodiments.
As shown in FIG. 2, the method of the invention is illustrated by taking a 1:70 scaled down Ship model Cyber-clip II (CSII) as a calculation object, wherein the Ship has a length of 1.2555m and a width of 0.29m, the Ship model is provided with three propellers in total, a Ship bow is provided with a lateral channel propeller, a main propeller of two propeller and rudder combinations (abbreviated as rudder propeller combinations) is positioned at the Ship stern, and the three propellers together provide the force and moment required by advancing and retreating, drifting and swaying of the Ship in the horizontal plane, and the parameter values of the propellers are shown in the following table:
the thrust generated by the rudder propeller combined propeller consists of two parts, wherein the first part is the propeller thrust as follows:
the second part is the lift and drag generated by the rudder:
lift of rudder:
resistance of rudder:
the heave and heave forces generated by the rudder propeller device in the propeller can be expressed as:
wherein ,k iTn and kiLn 、/>k iDn 、/>The parameters of the propeller and rudder are shown in the following table.
Based on the principle shown in fig. 3, a Matlab model is established to simulate and verify the thrust distribution of the ship propeller, and algorithm parameters are set as follows: population size n=250, maximum iteration number m=100, initial value c of learning factor 1s ＝2.5，c 2s End value c of learning factor =0.5 1e ＝0.5，c 2e =2.5, initial inertial weight κ 1 =0.4, final inertial weight κ 2 =0.9. Setting relevant parameters in an objective function: constant h= [9×10 ] in power consumption term -4 9×10 -4 4×10 -5 ]Relaxation variable weight matrix q=diag (10 in the equality constraint 3 10 3 10 4 )。
Fig. 4-7 show corresponding simulation result curves in the reasoning and dividing process, and as can be seen from fig. 4, the decomposition force change of each propeller in the direction of the heave and the heave is relatively stable, the change amplitude is small, and the abrasion of the propeller is reduced.
As can be seen from fig. 5, the variation of the rotation speed and rudder angle of each propeller is within the limit of the constraint condition of the thrust distribution optimization model.
Fig. 6 is a graph showing a change in thrust force distribution error during thrust force distribution.
Fig. 7 is a graph showing the overall power consumption of the propeller during thrust distribution.
Simulation results show that the ship dynamic positioning thrust distribution optimization method based on the multi-target particle swarm algorithm can meet the comprehensive requirements of small energy consumption, small thrust distribution error and small abrasion and shake of the propeller, and the optimal propeller combination is selected through thrust distribution to meet the operation requirements of the ship, so that the effectiveness of the algorithm is verified. As can be seen from fig. 4-7, the thrust distribution error of the multi-target particle swarm optimization algorithm is smaller, the total power consumption of the propeller is smaller, and the thrust distribution task can be completed.
Although the invention has been described with reference to the above embodiments, it should be understood that the invention is not limited thereto, but rather may be modified or altered somewhat by persons skilled in the art without departing from the spirit and scope of the invention.
Claims (2)
1. The thrust distribution method of the ship dynamic positioning system based on the improved multi-target particle swarm algorithm is characterized by comprising the following steps of:
s1, establishing a mathematical model tau for thrust distribution of a ship dynamic positioning system d ＝B(α)T；
wherein ,τd ＝[F x F y F n ] T To control the force and moment of the system output control, F x 、F y Respectively represent the control forces in the heave and heave directions, F n The moment of turning the bow is represented, representing the thrust forces generated by the respective propellers,for azimuth angle of each propeller +>A configuration matrix for the propeller;
wherein ,(lxi ,l yi ) Indicating the installation position of the ith propeller, x indicating the longitudinal axis, taking the heading of the ship as positive; y is the transverse axis, and the starboard direction of the ship is positive;
s2, establishing an objective function and constraint conditions comprising five independent optimization targets;
wherein f is a compound comprising J p ,J e ,J α ,J δ ,J ω Multi-objective optimization function with five independent optimization objectives, the optimization objectives of which are to find the objective J p ,J e ,J α ,J δ ,J ω Minimum propeller speed, rudder angle and azimuth angle, J p ,J e ,J α ,J δ ,J ω Respectively representing the power consumption, thrust distribution error, rotating speed, rudder angle and azimuth angle change rate of the propeller; e, e i Constant, n number of propellers equipped for the ship, s= [ s ] x ，s y ，s n ] T Is the error value between the control command generated by the controller and the actual thrust after thrust distribution, q=diag (Q x ,Q y ,Q n ) The penalty weight for thrust errors in three degrees of freedom of heave, surge and heading,propeller component T x and Ty Is a function of the propeller rotational speed ω, rudder angle δ and azimuth angle α; alpha i ，δ i and ωi Represents azimuth angle, rudder angle and rotating speed omega of the ith propeller at the current moment 0i ，δ 0i and α0i The rotation speed, rudder angle and azimuth angle of the ith propeller at the previous moment; omega i,min (ω i,max )，δ i,min (δ i,max) and αi,min (α i,max ) Representing the minimum (maximum) values of the rotation speed, rudder angle and azimuth angle of the ith propeller, delta omega respectively i ，△δ i and △αi Respectively representing the variation of the rotation speed, rudder angle and azimuth angle of the ith propeller in unit time, and delta omega i,min (△ω i,max )，△δ i,min (△δ i,max) and △αi,min (△a i,max ) The minimum (maximum) values of the variation of the rotating speed, rudder angle and azimuth angle of the ith propeller in unit time are respectively;
s3, setting parameters of a multi-target particle swarm algorithm: population scale N, maximum iteration number m, particle position boundary x min and xmax Boundary v of speed min and vmax Inertial weight and final inertial weight, individual learning factor c 1 And population learning factor c 2 Initial and final values of (a), creating an external archive set, and de-empting in the feasible mannerInitializing a population of particles in a middle, wherein the external archive set stores locations of non-dominant solution particles generated in an iteration;
s4, according to a plurality of objective functions J p ,J e ,J a ,J δ ,J ω Respectively calculating fitness values of particles in the initial group, constructing a non-dominant solution set according to the Pareto dominant relationship, and updating an external archive set;
s5, selecting an individual optimal solution Pbest according to the Pareto dominance relation, selecting a global optimal solution Gbest from the external archive set, wherein the individual optimal solution Pbest is generated according to a non-dominance solution obtained by comparing a current generation individual optimal solution with a previous generation individual optimal solution according to the Pareto dominance relation, and the global optimal solution Gbest is obtained by evaluating the individual density of each particle in the external archive set and selecting the Pareto optimal solution with small particle density as the global optimal solution;
s6, updating the speed and the position of the particles, judging whether the updated speed and position are within the range of the speed boundary and the position boundary, and determining that the speed updating formula and the position updating formula are as follows:
wherein ,representing the speed, position, individual optimum position and population optimum position of the ith particle in d-dimension at the t-th iteration,/->Representing the speed and position of the ith particle in d dimension at the t+1st iteration, rand 1 and rand2 Is [0,1]Random numbers uniformly distributed among the two;
S7updating inertia weight kappa and individual learning factor c 1 And population learning factor c 2 The formula is as follows:
wherein ,κ1 Kappa for initial inertial weight 2 Is the final inertial weight; c 1s ,c 1e and c2s ,c 2e Learning factor c for individual 1 And population learning factor c 2 T is the current iteration number;
s8, judging whether the current iteration times meet the termination condition, if the current iteration times are greater than the maximum iteration times m, stopping iteration, and outputting an optimal solution; if the current iteration number is smaller than the maximum iteration number m, turning to step S4 to continue searching the optimal solution;
s9, outputting an optimal solution (omega) meeting the multi-objective optimization function * ，δ * ，α * ) Comprising propeller rotational speed omega * ＝[ω 1 * ,ω 2 * ,...,ω n * ] T Rudder angle delta * ＝[δ 1 * ,δ 2 * ,...,δ n * ] T Azimuth angle alpha * ＝[α 1 * ,α 2 * ,...,α n * ] T And sending an instruction to each propeller of the ship to complete the thrust distribution task.
2. The method for distributing thrust of a ship dynamic positioning system based on an improved multi-objective particle swarm algorithm according to claim 1, wherein the updating of the external archive set in step S4 uses a crowding-distance-based sorting method according to the following formula:
wherein ,di Indicating the degree of crowding of the ith particle,the function value of the i-1 th particle representing the j-th objective function,function value of the (i+1) th particle representing the jth objective function,/for the (j) th particle>Represents the maximum of the jth objective function, +.>Representing the minimum of the jth objective function. />
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| CN117111449A (en) * | 2023-10-19 | 2023-11-24 | 哈尔滨工程大学 | Dam defect detection ROV approaching sailing thrust distribution system and method |
| CN118014168A (en) * | 2024-04-10 | 2024-05-10 | 沈阳德成软件技术有限公司 | Particle swarm optimization-based enterprise operation management optimization method |
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| CN117111449A (en) * | 2023-10-19 | 2023-11-24 | 哈尔滨工程大学 | Dam defect detection ROV approaching sailing thrust distribution system and method |
| CN117111449B (en) * | 2023-10-19 | 2024-01-09 | 哈尔滨工程大学 | Dam defect detection ROV approaching sailing thrust distribution system and method |
| CN118014168A (en) * | 2024-04-10 | 2024-05-10 | 沈阳德成软件技术有限公司 | Particle swarm optimization-based enterprise operation management optimization method |
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