Ship motion collaborative optimal control method based on multi-objective optimization

Abstract

The invention relates to a ship motion collaborative optimal control method based on multi-objective optimization, and belongs to the technical field of ship control. Comprising the following steps: constructing a ship operation cost target model and a ship motion equation, and solving a first rudder angle adjustment value corresponding to optimal operation cost; constructing a ship state space model and an environmental protection objective function, and solving to obtain a second rudder angle adjustment value corresponding to minimum gas emission; constructing a navigational speed stability objective function and a ship motion equation, and solving to obtain a third rudder angle adjustment value corresponding to the most stable navigational speed; constructing a steering frequency objective function and a steering engine physical model, and solving to obtain an optimal steering frequency; and determining an optimal rudder angle adjustment value based on the first, second and third rudder angle adjustment values and the optimal steering frequency. According to the method, multi-dimensional targets are comprehensively considered, environmental protection and energy conservation are achieved in the process of pursuing transportation time efficiency, steering engine abrasion is reduced as much as possible, the stability of ship navigation is maintained, and efficient collaborative optimal control over ship movement is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of ship control, and particularly to a cooperative optimal control method for ship motion based on multi-objective optimization. Background Art

[0002] With the rapid development of the modern shipping industry, the limitations of traditional ship control means have become increasingly prominent. Since traditional ship control means tend to focus on speed in pursuit of transportation timeliness, but lack a fine and systematic management mechanism for fuel consumption, ignoring the increase in economic costs brought about by fuel consumption and the negative impact of exhaust emissions on the environment. Moreover, frequent and unreasonable rudder operations in daily ship operation are extremely common, which not only cause serious mechanical wear to key equipment such as the rudder machine, shortening the equipment maintenance cycle and increasing costs significantly, but also the additional attitude adjustment and hydrodynamic consumption of the ship caused by each rudder operation will result in excessive fuel waste and may also damage the navigation stability of the ship. Summary of the Invention

[0003] In view of the above analysis, the present invention aims to disclose a cooperative optimal control method for ship motion based on multi-objective optimization, and find the optimal control strategy of the ship by considering multiple dimensions of objectives such as cost, environmental protection, speed stability, and reasonable rudder operation frequency. The specific steps are as follows:

[0004] Construct a ship operation cost target model based on speed, rudder angle, and main engine power, construct a ship motion equation based on the longitudinal speed, lateral speed, yaw angular velocity, and rudder angle of the ship, and solve for the first rudder angle adjustment value corresponding to the optimal operation cost based on the ship operation cost target model and the ship motion equation;

[0005] Construct a ship state space model based on the ship position, speed, gas emissions, and ship state, construct an environmental protection objective function based on the gas emissions, and solve for the second rudder angle adjustment value corresponding to the least gas emissions based on the ship state space model and the environmental protection objective function;

[0006] Construct a speed stability objective function based on the speed and the ideal speed, and solve for the third rudder angle adjustment value corresponding to the most stable speed based on the speed stability objective function and the ship motion equation;

[0007] Construct a rudder operation frequency objective function based on the change of the rudder angle, construct a rudder machine physical model based on the rudder angle, rudder machine rotation angular velocity, and speed, and solve for the optimal rudder operation frequency based on the rudder operation frequency objective function and the rudder machine physical model;

[0008] Determine the optimal rudder angle adjustment value based on the first, second, and third rudder angle adjustment values and the optimal rudder operation frequency.

[0009] Further, the determination of the optimal rudder angle adjustment value based on the first, second, and third rudder angle adjustment values and the optimal rudder operation frequency includes:

[0010] Normalize the optimal rudder operation frequency to obtain a normalized value;

[0011] Calculate a fourth rudder angle adjustment value based on a preset coefficient and the normalized value;

[0012] Calculate the optimal rudder angle adjustment value based on the first, second, third, and fourth rudder angle adjustment values.

[0013] Further, the determination of the first rudder angle adjustment value corresponding to the optimal operation cost based on the ship operation cost target model and the ship motion equation includes:

[0014] Based on the ship operation cost target model and the ship motion equation, construct a Hamiltonian function using the variational method;

[0015] Based on the current ship speed, rudder angle, and main engine power collected by the ship sensors, iteratively solve the Hamiltonian function to obtain the first rudder angle adjustment value corresponding to the optimal operation cost.

[0016] Further, the ship operation cost target model is expressed as:

[0017]

[0018] where J e is the ship operation cost, q(t) is the fuel consumption rate, q(t) = a 1 v(t) 3 + a 2 δ(t) 2 + a 3 P(t) + a 4 ; v(t) is the current ship speed, δ(t) is the rudder angle, P(t) is the main engine power, C fuel is the real-time fuel unit price, T represents the total calculation duration, and the coefficients a 1 , a 2 , a 3 and a 4 are obtained by fitting historical data.

[0019] Further, the ship motion equation is expressed as:

[0020]

[0021] where represents the ship motion state obtained after rudder angle control; X is the current state quantity of the ship, X = [u, v, r] T, where u is the lateral speed of the ship, v is the longitudinal speed of the ship, r is the yaw angular velocity, M is the ship mass and inertia matrix, C(x) is the hydrodynamic coefficient matrix, and D(x) is the hydrodynamic damping coefficient matrix.

[0022] Further, the second rudder angle adjustment value corresponding to the least gas emissions obtained by solving based on the ship state space model and the environmental protection objective function includes:

[0023] Construct a ship state space model based on the ship's position, speed, gas emissions, and ship state;

[0024] Determine the control variables based on the speed adjustment amount, rudder angle adjustment value, and main engine power adjustment value;

[0025] Estimate the transition probability of the ship state variables under the action of different control variables;

[0026] Construct an environmental protection objective function based on gas emissions, speed, rudder angle, and main engine power;

[0027] With the goal of minimizing the total gas emissions within the calculated total duration, perform iterative solution based on the ship state space model and the environmental protection objective function to obtain the optimal value of the control variables, and obtain the second rudder angle adjustment value corresponding to the least gas emissions based on the optimal value of the control variables.

[0028] Further, the environmental protection objective function is expressed as:

[0029]

[0030] where J g is the total gas emissions, F(t) is the fuel consumption, are the emission factors of carbon dioxide, sulfur oxides, and nitrogen oxides respectively, and T represents the calculated total duration.

[0031] Further, the speed stability objective function constructed based on the speed and the ideal speed is expressed as:

[0032]

[0033] where J s is the speed stability target value, and the smaller the value, the more stable the speed; v ref is the preset ideal speed, v(t) is the current speed, and T is the calculated total duration.

[0034] Further, the rudder hitting frequency objective function constructed based on the change of the rudder angle is expressed as:

[0035]

[0036] where J rrepresents the rudder frequency, N is the number of sampling points, Δt is the sampling time interval, and δ(t i+1 ) is the rudder angle value at the (i + 1)-th sampling time, and δ(t i ) is the rudder angle value at the i-th sampling time.

[0037] Further, the physical model of the steering gear constructed based on the rudder angle, the angular velocity of the steering gear rotation, and the ship speed is expressed as:

[0038] M(δ, v, t) = W(δ, t) + F d (δ, v);

[0039] W(δ, t) = k 1 δ 2 (t) + k 2 δ(t)ω(t) + k 3 ω 2 (t);

[0040] F d (δ, v) = k 4 δ 2 (t)v(t) + k 5 δ(t)v 2 (t);

[0041] Among them, M(δ, v, t) represents the physical model of the steering gear; w(δ, t) is the wear model of the steering gear, which is used to calculate the wear degree of the steering gear; F d (δ, v) is the hydrodynamic model, which is used to describe the force of the hydrodynamic on the steering gear when the rudder angle and the ship speed change; δ(t) is the rudder angle, ω(t) is the angular velocity of the steering gear rotation, k 1 - k 3 is the wear coefficient determined according to the mechanical design parameters, material characteristics, and test data of the steering gear, v(t) represents the ship speed, k 4 and k 5 represent the hydrodynamic coefficients.

[0042] The present invention can at least achieve one of the following beneficial effects:

[0043] By considering the control of the ship from multiple dimensions, including the control of the ship from the dimensions of fuel consumption, exhaust emissions, mechanical wear, and navigation stability, finding the optimal ship control strategy that meets the requirements of low operating cost, low emissions, less mechanical wear, and stable ship speed, solving the problems in the prior art such as the increase in economic cost due to only pursuing transportation timeliness but ignoring fuel consumption, the negative impact of exhaust emissions on the environment, and the mechanical wear of the ship, and ensuring the smooth operation of the ship while ensuring the ship speed, environmental protection, and reducing mechanical wear.

[0044] By solving multiple objective functions to obtain the corresponding optimal control strategies, i.e., rudder angle adjustment values, and performing weighted fusion on multiple optimal control strategies, multi-objective collaborative optimization can be achieved, the comprehensive performance of the ship under complex working conditions can be improved, and the development needs of the shipping industry can be met.

[0045] Other features and advantages of the present invention will be described in the following specification, and some advantages can be made obvious from the specification or understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained from the content specifically pointed out in the specification, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The drawings are only for the purpose of showing specific embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference numerals represent the same components.

[0047] Figure 1 It is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] The following will specifically describe the preferred embodiments of the present invention with reference to the drawings, where the drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, rather than to limit the scope of the present invention.

[0049] An embodiment of the present invention discloses a cooperative optimal control method for ship motion based on multi-objective optimization, specifically including steps S01 to S05, where the order of steps S01 to S04 is not limited and they can also be implemented simultaneously.

[0050] It should be noted that the premise of the method discussed in this embodiment is that the ship speed has reached the minimum speed value required by the navigation task after the ship sets sail, that is, on the basis of meeting the navigation task, by considering multiple dimensions such as ship operating costs, environmental protection goals, speed stability, and equipment wear, the cooperative optimal control of ship motion is sought.

[0051] Step S01: Construct a ship operating cost target model based on ship speed, rudder angle, and main engine power, construct a ship motion equation based on the longitudinal speed, lateral speed, yaw angular velocity, and rudder angle of the ship, and solve for the first rudder angle adjustment value corresponding to the optimal operating cost based on the ship operating cost target model and the ship motion equation.

[0052] Specifically, the ship operating cost target model is expressed as:

[0053]

[0054] where J e is the ship operating cost, q(t) is the fuel consumption rate, and q(t) = a 1 v(t)3 +a 2 δ(t) 2 +a 3 P(t)+a 4 ; where \(v(t)\) is the current ship speed, \(\delta(t)\) is the rudder angle, \(P(t)\) is the main engine power, \(C\) fuel is the real-time fuel unit price, \(T\) represents the total calculation duration, and the coefficients \(a\) 1 、\(a\) 2 、\(a\) 3 and \(a\) 4 are obtained by fitting based on historical data.

[0055] Specifically, construct the ship motion equation. The current state variables of the ship are expressed as \(X = [u, v, r]\) T , where \(u\) is the lateral speed of the ship, \(v\) is the longitudinal speed of the ship, and \(r\) is the yaw angular velocity. Use the control input \(U=\delta\) (where \(\delta\) is the rudder angle at this moment) and the ship mass and inertia matrix \(M\), hydrodynamic coefficient matrix \(C(x)\), and hydrodynamic damping coefficient matrix \(D(x)\) to describe the ship motion state, which is expressed as:

[0056]

[0057] where represents the ship motion state obtained after rudder angle control.

[0058] Furthermore, solving for the first rudder angle adjustment value corresponding to the optimal operating cost based on the ship operating cost target model and the ship motion equation includes:

[0059] Based on the ship operating cost target model and the ship motion equation, use the variational method to construct the Hamiltonian function;

[0060] Based on the current ship speed, rudder angle, and main engine power collected by the ship sensors, iteratively solve the Hamiltonian function to obtain the first rudder angle adjustment value corresponding to the optimal operating cost.

[0061] Furthermore, the Hamiltonian function is:

[0062] \(H(X,U,\lambda,t)=C\) fuel *(\(a\) 1 \(v(t)\) 3 +\(a\) 2 \(\delta(t)\) 2 +\(a\) 3 \(P(t)+a\) 4 )+\(\lambda\) T \(f(X,U)\);

[0063] where, is the co-state variable vector, with the same dimension as X. The construction of the Hamiltonian function closely combines the ship operation cost objective with the ship motion state, enabling the optimization process to find the optimal control strategy for fuel expenditure based on considering the actual ship motion.

[0064] Furthermore, according to the optimality conditions of the calculus of variations Take the partial derivative of the Hamiltonian function H with respect to the control input δ.

[0065] Furthermore, substitute the ship speed, rudder angle, and main engine power at the current moment collected by the ship sensors into the Hamiltonian function, and use the Newton-Raphson iteration method to solve for the rudder angle at the next moment. The iteration formula is where n represents the number of iterations.

[0066] It should be noted that the strategies for controlling the ship mainly include the control and adjustment of the rudder angle, ship speed, and main engine power. When the rudder angle δ(t) changes, the ship speed v(t) and the main engine power P(t) will both change accordingly. During the process of solving the Hamiltonian function in step S01, we mainly focus on the changes in the ship motion state caused by the iterative relationship of the rudder angle δ(t).

[0067] Furthermore, in each iteration process, it is necessary to recalculate and values.

[0068] Furthermore, in each iteration process, use the Runge-Kutta method to solve the ship motion state equation to obtain the state changes of the ship under different control inputs. The general form of the Runge-Kutta method is where h is the step size, k 4 = f(X n + h k3 , U n + h k3 ).

[0069] Furthermore, continuously iterate until the preset convergence condition is met. The convergence condition is that the change value of the rudder angle obtained from two adjacent iterations is less than the set threshold (exemplarily, such as 1°). At this time, the difference between the obtained rudder angle value and the current rudder angle value is the first rudder angle adjustment value corresponding to the optimal operation cost.

[0070] Step S02: Construct a ship state space model based on the ship position, ship speed, gas emissions, and ship state, construct an environmental protection objective function based on the gas emissions, and solve to obtain the second rudder angle adjustment value corresponding to the least gas emissions based on the ship state space model and the environmental protection objective function. Specifically include:

[0071] S021. Constructing a ship state space model based on ship position, speed, gas emissions, and ship status includes:

[0072] Define the state variable s = (l, v, e), where l represents the ship's operating position, v represents the current speed, i.e., v(t), and e represents the gas emission level. The state variable s at each moment t constitutes a discretized ship state space model.

[0073] S022. Determine the control variable based on the speed adjustment amount, rudder angle adjustment value, and main engine power adjustment value. The control variable is expressed as: a = (Δv, Δδ, ΔP), where Δv represents the speed adjustment amount, Δδ represents the rudder angle adjustment value, and ΔP represents the main engine power adjustment amount.

[0074] S023. Estimate the transition probability of the ship state variable under the action of different control variables.

[0075] Based on the ship sensors, obtain l, v, and e at the current moment to get the current value s of the state variable s t . Based on different control variables a t Simulate the change of the ship's motion state according to the ship's motion characteristics. Based on the results of multiple simulations, count the frequency P(s t+1 |s t , a t ) of the ship transferring from the current state to the next state. For example, if in multiple simulations, the ship has an 80% probability of reaching the expected speed and position after adjusting the speed, the transition probability is 80%. It should be noted that the simulation process can be realized by pre-simulation calculation. In practical applications, based on the pre-calculation results of the inverse calculation, the transition probability of the ship state variable can be obtained based on the current value of the state variable s and different control variables.

[0076] S024. Construct an environmental protection objective function based on gas emissions, speed, rudder angle, and main engine power.

[0077] Specifically, the environmental protection objective function is expressed as:

[0078]

[0079] where J g is the total gas emission, F(t) is the fuel consumption, are the emission factors of carbon dioxide, sulfur oxides, and nitrogen oxides respectively, T represents the total calculation duration. For the time T, the fuel consumption (τ is the integration variable used to distinguish time), q(t) = a 1 v(t) 3 + a2 δ(t) 2 + a 3 P(t) + a 4 。

[0080] S025. With the goal of minimizing the total gas emissions within the calculated total duration, iterative solution is carried out based on the ship state space model and the environmental protection objective function to obtain the optimal value of the control variable, and the second rudder angle adjustment value corresponding to the least gas emissions is obtained based on the optimal value of the control variable.

[0081] Specifically, based on the current value s t of the state variable s in step S023, iterative update is carried out according to the Bellman optimal performance equation based on the transition probability of the ship state variable under the action of the same control variable a; where V(s) is the value function corresponding to s t , where C(s, a) is the cost of taking the control variable a in the state s t (i.e., the fuel consumption F(t)), γ is the discount factor (the value range is between 0 and 1), s′ represents the next possible state, and P(s′|s, a) represents the corresponding transition probability.

[0082] Since the environmental protection objective function is determined based on F(t), iterative update is carried out on the Bellman optimal performance equation, and the control variable that minimizes the value function V(s) is selected as the optimal value of the control variable in the current state, that is, the minimum value of the environmental protection objective function J g can be achieved.

[0083] The rudder angle adjustment value in the optimal value of the control variable is the second rudder angle adjustment value corresponding to the least gas emissions

[0084] Step S03. Based on the ship speed and the ideal ship speed, a ship speed stability objective function is constructed, and the third rudder angle adjustment value corresponding to the most stable ship speed is obtained by solving based on the ship speed stability objective function and the ship motion equation.

[0085] Specifically, the ship speed stability objective function is expressed as:

[0086]

[0087] where, J s is the ship speed stability target value, and the smaller the value, the more stable the ship speed; v ref is the preset ideal ship speed, v(t) is the current ship speed, and T is the calculated total duration.

[0088] The ship motion equation is expressed as:

[0089]

[0090] It should be noted that the strategies for controlling a ship mainly include the control and adjustment of the rudder angle, ship speed, and main engine power. In step S03, since the goal is to maintain a stable target ship speed, the strategies for controlling the ship include adjusting the rudder angle and main engine power.

[0091] Furthermore, in order to solve the optimal control strategy, the linear quadratic regulator (LQR) in the optimal control algorithm is used to solve the optimal control gain matrix K. The quadratic performance index function is designed as where Q is the state weight matrix, which is used to balance the importance of state variables such as speed deviation in the objective function, and R is the control weight matrix, which is used to represent the operating cost caused by the control input, i.e., the rudder angle input. When R = 1, it represents the unit control cost.

[0092] Furthermore, the Riccati equation is used to solve the solution matrix P required for the quadratic performance index function:

[0093] PA + A T P - PBR -1 B T P + Q = 0; where

[0094] Furthermore, the optimal control gain matrix K = R -1 B T P.

[0095] Furthermore, during the ship's navigation, the state data of the ship is collected in real time, including the longitudinal speed u, lateral speed v, and yaw angular velocity r, which form the state vector X.

[0096] Furthermore, based on the current longitudinal speed u and lateral speed v, the current ship speed v(t) is obtained.

[0097] Furthermore, the deviation vector e = v(t) - v of the current ship speed v(t) from the preset ideal ship speed v ref is calculated. The deviation vector e is multiplied by the optimal control gain matrix K, i.e., [Δδ ref , ΔP * , * T = Ke. Here, [Δδ * , ΔP * T represents the optimal control strategy, which is a column vector composed of the rudder angle adjustment value and the main engine power adjustment value. Δδ * is the third rudder angle adjustment value, denoted as

[0098] ​​Step S04: Construct a target function for the rudder operation frequency based on the rudder angle change, construct a physical model of the rudder actuator based on the rudder angle, the rotational angular velocity of the rudder actuator, and the ship speed, and solve for the optimal rudder operation frequency based on the target function for the rudder operation frequency and the physical model of the rudder actuator.

[0099] Specifically, the target function for the rudder operation frequency is expressed as:

[0100]

[0101] where J r represents the rudder operation frequency, N is the number of sampling points, Δt is the sampling time interval, δ(t i+1 ) is the rudder angle value at the (i + 1)-th sampling time, and δ(t i ) is the rudder angle value at the i-th sampling time.

[0102] The physical model of the rudder actuator constructed based on the rudder angle, the rotational angular velocity of the rudder actuator, and the ship speed is expressed as:

[0103] M(δ, v, t) = W(δ, t) + F d (δ, v);

[0104] W(δ, t) = k 1 δ 2 (t) + k 2 δ(t)ω(t) + k 3 ω 2 (t);

[0105] F d (δ, v) = k 4 δ 2 (t)v(t) + k 5 δ(t)v 2 (t);

[0106] where M(δ, v, t) represents the physical model of the rudder actuator; W(δ, t) is the rudder actuator wear model for calculating the wear degree of the rudder actuator; F d (δ, v) is the hydrodynamic model for describing the force exerted by the hydrodynamic force on the rudder actuator when the rudder angle and the ship speed change; δ(t) is the rudder angle, ω(t) is the rotational angular velocity of the rudder actuator, k 1 -k 3 are wear coefficients determined according to the mechanical design parameters, material properties, and test data of the rudder actuator, v(t) represents the ship speed, k 4 and k 5 represent hydrodynamic coefficients.

[0107] Furthermore, the sampling gradient descent method is used for iterative optimization, and the formula is where δ f,nis the rudder angle change frequency at the nth iteration, and α is the learning rate, whose value is set according to the control accuracy requirements.

[0108] Calculate the objective function J r with respect to the rudder angle change frequency δ f gradient At each iteration, according to the current rudder angle change frequency δ f,n , use the physical model of the steering gear to calculate the corresponding equipment loss, and evaluate it according to the preset constraint conditions (such as the maximum allowable wear of the equipment). If the constraint conditions are met, continue the iterative optimization; if not, adjust the iteration step size or adopt other optimization strategies.

[0109] Continue the iterative process until the objective function of the rudder frequency converges, that is, the change in the objective function values obtained from two adjacent iterations is less than the set threshold. At this time, the obtained rudder angle change frequency is the reasonable rudder frequency range, recorded as

[0110] Step S05, determine the optimal rudder angle adjustment value based on the first, second, and third rudder angle adjustment values and the optimal rudder frequency.

[0111] Specifically include:

[0112] Normalize the optimal rudder frequency to obtain a normalized value;

[0113] Calculate the fourth rudder angle adjustment value based on the preset coefficient and the normalized value;

[0114] Calculate the optimal rudder angle adjustment value based on the first, second, third, and fourth rudder angle adjustment values.

[0115] Further, normalizing the optimal rudder frequency to obtain a normalized value includes:

[0116] Assume The value range is [0, f max (f max is the maximum rudder frequency), and convert it to In this way the value range becomes [0, 1];

[0117] Further, based on the preset coefficient λ and the normalized value calculate the fourth rudder angle adjustment value

[0118] where the value of λ is determined according to the specific characteristics of the ship and actual operation experience. Exemplarily, when a large ship is sailing in a straight line normally, the maximum rudder frequency is generally set to 10 times per minute, and the value range of λ can be taken in the interval of 1 - 10 degrees, for example, 5 degrees. Further, for example, when When it is 6 times per minute, the normalized value The fourth rudder angle adjustment value

[0119] It should be noted that due to the different characteristics of different ships, the value of λ is different. For large ships, due to their large inertia, the influence of the rudder angle change on the course is relatively gentle, and the steering response is slow. Therefore, the maximum rudder operation frequency is relatively low. At the maximum rudder operation frequency, to ensure that the equivalent rudder angle change rate will not be too large, λ needs to take a smaller value. This is because if λ is too large, the influence of the rudder operation frequency on the comprehensive rudder angle adjustment value will be too significant, which does not conform to the characteristics of large ships with large inertia and relatively stable rudder angle change. Different from the situation of large ships, for small and medium-sized ships, considering their relatively flexible steering characteristics, the value of λ can be relatively large.

[0120] Furthermore, the optimal rudder angle adjustment value is calculated based on the first, second, third, and fourth rudder angle adjustment values:

[0121]

[0122] where w 1 、w 2 、w 3 and w 4 are weight coefficients, and their sum is 1. The values of each weight coefficient are determined according to user needs. Among them, the magnitude of w 1 represents the weight of the ship operation cost affecting the rudder angle adjustment value, the magnitude of w 2 represents the weight of the environmental protection emissions affecting the rudder angle adjustment value, the magnitude of w 3 represents the weight of the speed stability affecting the rudder angle adjustment value, and the magnitude of w 4 represents the weight of the physical wear of the steering gear affecting the rudder angle adjustment value. Exemplarily, when the shipping task is a passenger transportation task, increase the value of w 3 ; when the navigation task needs to enter the emission control area, increase the value of w 2 ; when encountering bad sea conditions, increase the values of w 3 、w 4 ; in the sea area with smooth navigation, increase the value of w 1 .

[0123] It should be noted that after calculating the optimal rudder angle adjustment value δ * (t) through steps S01 - S05, the ship is controlled to adjust the rudder angle based on δ * (t). Furthermore, the main engine system of the ship updates the main engine power based on the adjusted rudder angle. During the ship's navigation, steps S01 - S05 are executed within each set time period T to achieve continuous optimal control of ship motion coordination during navigation.

[0124] The present embodiment discloses a method for coordinated optimal control of ship motion based on multi-objective optimization. The method considers the control of the ship from multiple dimensions, including fuel consumption, exhaust emissions, mechanical wear and navigation stability, and seeks the optimal ship control strategy that satisfies low operating costs, low emissions, low mechanical wear and stable speed. The method solves the problems in the prior art of only pursuing transportation timeliness while ignoring the increased economic costs caused by fuel consumption, the negative impact of exhaust emissions on the environment and the mechanical wear of the ship. The method ensures the smooth operation of the ship while ensuring the speed, environmental protection and reducing mechanical wear.

[0125] By solving multiple objective functions to obtain the corresponding optimal control strategy, i.e., the rudder angle adjustment value, and performing weighted fusion on multiple optimal control strategies, multi-objective collaborative optimization can be achieved, thus improving the comprehensive performance of the ship under complex working conditions and meeting the needs of shipping development.

[0126] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A ship motion coordinated optimal control method based on multi-objective optimization, characterized in that: The steps include: A ship operation cost target model is constructed based on the ship speed, rudder angle and main engine power, a ship motion equation is constructed based on the ship's longitudinal speed, lateral speed, bow angular velocity and rudder angle, and a first rudder angle adjustment value corresponding to the optimal operation cost is solved based on the ship operation cost target model and the ship motion equation; A ship state space model is constructed based on the ship position, speed, gas emissions and ship state, an environmental protection objective function is constructed based on gas emissions, and a second rudder angle adjustment value corresponding to the minimum gas emissions is obtained based on the ship state space model and the environmental protection objective function; A speed stability objective function is constructed based on the ship speed and the ideal speed, and the third rudder angle adjustment value corresponding to the most stable speed is obtained based on the speed stability objective function and the ship motion equation. Based on the change of rudder angle, a steering frequency objective function is constructed. Based on the rudder angle, the rudder rotation angular velocity and the ship speed, a steering gear physical model is constructed. Based on the steering frequency objective function and the steering gear physical model, the optimal steering frequency is obtained. An optimal rudder angle adjustment value is determined based on the first, second, third rudder angle adjustment values ​​and the optimal steering frequency.

2. The ship motion coordinated optimal control method according to claim 1, characterized in that: Determining the optimal rudder angle adjustment value based on the first, second, and third rudder angle adjustment values ​​and the optimal steering frequency comprises: The optimal steering frequency is normalized to obtain a normalized value; Calculating a fourth rudder angle adjustment value based on a preset coefficient and a normalized value; An optimal rudder angle adjustment value is calculated based on the first, second, third and fourth rudder angle adjustment values.

3. The ship motion coordinated optimal control method according to claim 1, characterized in that: The first rudder angle adjustment value corresponding to the optimal operation cost is solved based on the ship operation cost target model and the ship motion equation, including: Based on the ship operation cost target model and the ship motion equation, the Hamiltonian function is constructed using the calculus of variation. Based on the current speed, rudder angle, and main engine power collected by the ship's sensors, the Hamiltonian function is iteratively solved to obtain the first rudder angle adjustment value corresponding to the optimal operating cost.

4. The ship motion coordinated optimal control method according to claim 3, characterized in that: The ship operation cost target model is expressed as: Among them, J e is the ship operation cost, q(t) is the fuel consumption rate, q(t)=a1v(t) 3 +a2δ(t) 2 +a3P(t)+a4; v(t) is the current speed, δ(t) is the rudder angle, P(t) is the main engine power, C fuel is the real-time unit price of fuel, T represents the total calculation time, and the coefficients a1, a2, a3, and a4 are fitted based on historical data.

5. The ship motion coordinated optimal control method according to claim 1, characterized in that: The ship motion equation is expressed as: in Indicates the motion state of the ship after rudder angle control; X is the current state of the ship, X = [u, v, r] T , where u is the ship's lateral velocity, v is the ship's longitudinal velocity, r is the bow angular velocity, M is the ship's mass and inertia matrix, C(x) is the hydrodynamic coefficient matrix, and D(x) is the hydrodynamic damping coefficient matrix.

6. The ship motion coordinated optimal control method according to claim 1, characterized in that: The second rudder angle adjustment value corresponding to the minimum gas emission obtained by solving the ship state space model and the environmental protection objective function includes: Construct a ship state space model based on ship position, speed, gas emissions and ship status; Determine the control variable based on the speed adjustment value, the rudder angle adjustment value, and the main engine power adjustment value; Estimate the transition probability of ship state variables under the influence of different control variables; Construct environmental protection objective function based on gas emissions and ship speed, rudder angle, and main engine power; With the goal of minimizing the total gas emissions within the calculated total time, an iterative solution is performed based on the ship state space model and the environmental protection objective function to obtain the optimal value of the control variable. Based on the optimal value of the control variable, the second rudder angle adjustment value corresponding to the minimum gas emissions is obtained.

7. The ship motion coordinated optimal control method according to claim 6, characterized in that: The environmental protection objective function is expressed as: Among them, J g is the total gas emission, F(t) is the fuel consumption, are the emission factors of carbon dioxide, sulfur oxides and nitrogen oxides respectively, and T represents the total calculation time.

8. The ship motion coordinated optimal control method according to claim 1, characterized in that: The speed stability objective function constructed based on the speed and the ideal speed is expressed as: Among them, J s is the target value of speed stability, the smaller the value, the more stable the speed; v ref is the preset ideal speed, v(t) is the current speed, and T is the total calculation time.

9. The ship motion coordinated optimal control method according to claim 1, characterized in that: The objective function of building the steering frequency based on the rudder angle change is expressed as: Among them, J r represents the steering frequency, N is the number of sampling points, Δt is the sampling time interval, δ(t i+1 ) is the rudder angle value at the i+1th sampling time, δ(t i ) is the rudder angle value at the i-th sampling time.

10. The ship motion coordinated optimal control method according to claim 1, characterized in that: The physical model of the steering gear constructed based on the rudder angle, the angular velocity of the steering gear rotation and the ship speed is expressed as: M(δ,v,t)=W(δ,t)+F d (δ,v); W(δ,t)=k1δ 2 (t)+k2δ(t)ω(t)+k3ω 2 (t); F d (δ,v)=k4δ 2 (t)v(t)+k5δ(t)v 2 (t); Where, M(δ, v, t) represents the physical model of the servo; W(δ, t) is the servo wear model, which is used to calculate the degree of wear of the servo; F d (δ, v) is the hydrodynamic model, which is used to describe the force of hydrodynamic force on the steering gear when the rudder angle and ship speed change; δ(t) is the rudder angle, ω(t) is the angular velocity of the steering gear, k1-k3 are the wear coefficients determined according to the mechanical design parameters, material properties and test data of the steering gear, v(t) represents the ship speed, and k4 and k5 represent the hydrodynamic coefficients.

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