Rolling optimization method for wing-aided hybrid power ship under wind speed prediction uncertainty

Abstract

The invention discloses a wind wing navigation aiding hybrid power ship rolling optimization method under wind speed prediction uncertainty, and belongs to the technical field of artificial intelligence and ship power system operation, and the method comprises the steps: employing adaptive kernel density estimation and a binary Copula function to construct a wind speed prediction uncertainty model; a Vine-Copula method is utilized to establish a time correlation structure between wind speeds in different advance periods; latin hypercube sampling is combined to generate a typical wind speed scene; establishing an energy transfer model between a propulsion system and an electric power system, and constructing a comprehensive oil consumption model oriented to a wind wing navigation aid scene; a rolling optimization strategy is adopted, energy efficiency control in a future time domain is optimized and solved at each decision moment based on currently available wind speed prediction information, real-time updating and execution are carried out, and energy efficiency performance under each control strategy is dynamically evaluated. According to the method, the practicability and adaptability of the system are effectively enhanced, and theoretical support is provided for engineering application of the hybrid propulsion technology.

Description

Technical Field

[0001] The present invention relates to the technical field of artificial intelligence and ship power system operation, in particular to a rolling optimization method for a wind vane-assisted hybrid ship under wind speed prediction uncertainty. Background Art

[0002] Maritime transport, as the primary mode of global trade, carries over 80% of cargo, but it is also a significant source of greenhouse gas emissions. To combat climate change and reduce carbon emissions, the application of renewable energy is an effective way to reduce CO2 emissions. Therefore, the shipping industry urgently needs to introduce innovative technologies to achieve a green transition. In recent years, sail-assisted propulsion systems have garnered widespread attention as a promising low-carbon technology. This is due to the widespread distribution of wind energy in the ocean and its common availability on the high seas. By directly driving ships with wind energy, sail-assisted propulsion significantly reduces fuel consumption and carbon emissions.

[0003] In practical applications, sail-assisted propulsion systems (SAPS) are often combined with electric propulsion systems (EPS). This is primarily because sail thrust is significantly affected by environmental factors (such as wind speed and direction). In particular, strong winds can significantly reduce the vessel's load demand. Sail thrust can cause the main engine to operate at reduced power for extended periods, increasing fuel consumption. Incorporating a shaft generator, however, can fully utilize the main engine's power margin, ensuring it operates within its high-efficiency range and partially or completely replacing diesel generators for powering the ship's grid, thereby reducing fuel consumption during navigation. By integrating sails with an electric propulsion system, a vessel can dynamically adjust propulsion power distribution based on real-time wind conditions and load demand, ensuring the main engine always operates within its high-efficiency range and optimizing energy efficiency. However, the effective operation of this hybrid system relies on an advanced energy management strategy (EMS) to achieve synergistic optimization between wind energy, electricity, and traditional fuels.

[0004] Ships are constantly affected by uncertain environmental factors during navigation, and this impact is particularly significant for ships equipped with sails. Ignoring uncertainties often results in energy efficiency and emission reduction effects in actual operations being lower than theoretical expectations.

[0005] Global optimization methods fail to adequately consider the time-varying characteristics of offshore wind speeds, fail to adapt to the dynamic characteristics of ship propulsion systems, and fail to meet real-time control requirements, potentially leading to performance degradation during actual navigation. The SMPC-based coordinated operation strategy proposed in this paper demonstrates significant advantages in managing hybrid power systems and handling wind speed forecast uncertainty. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method that uses a double-layer nested Copula method to establish the time correlation between the predicted wind speeds at different lead times, thereby deriving a joint probability distribution of the predicted wind speeds. Then, through the LH sampling process, representative scenarios are generated and used as inputs for the optimization part. The present invention establishes an uncertainty model for wind speed prediction and a multi-source rolling optimization model for ships, thereby achieving coordinated optimization of the sailing speed, sailing route, wind blade attack angle and shaft generator output power of a wind-assisted hybrid ship, with the aim of minimizing fuel consumption.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] A rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty comprises the following steps:

[0009] S1. Adaptive kernel density estimation and binary Copula function are used to construct an uncertainty model for wind speed prediction. The Vine-Copula method is used to establish the temporal correlation structure between wind speeds at different lead times. Latin hypercube sampling is combined to generate typical wind speed scenarios.

[0010] S2. Using the typical wind speed scenario with time series correlation generated in S1 as input, an energy transfer model between the propulsion system and the power system is established based on the thrust characteristics of the wind turbine, the matching relationship between the ship engine and the propeller, and the characteristics of the shaft generator. A comprehensive fuel consumption model for the wind turbine-assisted navigation scenario is also constructed.

[0011] S3. Using the typical wind speed scenario with uncertainty and time-series correlation generated in S1 as input, combined with the energy transfer model and comprehensive fuel consumption model constructed in S2, a rolling optimization strategy is adopted. At each decision moment, based on the currently available wind speed forecast information, the energy efficiency control in the future time domain is optimized and solved, and the execution is updated in real time. The energy efficiency performance under each control strategy is dynamically evaluated to achieve response to wind speed changes and real-time optimization control of the propulsion system.

[0012] A further improvement of the technical solution of the present invention is that S1 specifically includes the following steps:

[0013] S11 uses an adaptive kernel density estimation method to overcome the problem of lack of normalization in wind speed prediction;

[0014] S12 uses the Vine-Copula method to establish the time correlation structure between wind speeds at different lead times; combining the Latin hypercube sampling method and the joint distribution structure constructed by Vine-Copula, conditional sampling is performed on multi-time wind speed forecasts to generate S groups of typical wind speed scenarios with time series correlation, and the generated wind speed scenarios are input into the optimization model.

[0015] A further improvement of the technical solution of the present invention is that in S11, by applying adaptive kernel density estimation and using historical measured wind speed data and corresponding predicted wind speed data, the distribution of measured wind speed and predicted wind speed with different prediction lead times is estimated, and the probability density function PDF and cumulative distribution function CDF of the independent and identically distributed data (iid) extracted from the unknown density function are estimated by adaptive kernel density estimation as follows:

[0016]

[0017] Where f(·) and F(·) represent the probability density function PDF and the cumulative distribution function CDF, respectively, and the subscripts represent the corresponding random variables; N represents the number of samples; x max represents the maximum value in the sample and is used to normalize the data; b represents the smoothing parameter, which satisfies the condition that b→0 when N→∞; B(·; p,q) represents the Beta function with shape parameters p and q; α represents the integral variable;

[0018] Uncertainty modeling using binary copula, using Kendall rank correlation coefficient, is used to identify the monotonic relationship between two data series. Given two data series and The Kendall rank correlation coefficient is expressed by calculating the ratio of the difference between the number of consistent pairs and the number of inconsistent pairs in all data pairs to the total number of pairs, as follows:

[0019]

[0020] The joint probability density function PDF and cumulative distribution function CDF are estimated based on the marginal cumulative distribution function CDF and the probability density function PDF as follows:

[0021]

[0022] Where X and Y represent the measured wind speed and the predicted wind speed, respectively; c(·) and C(·) represent the probability density function (PDF) and cumulative distribution function (CDF) of the copula, respectively; θ represents the copula parameter, which is estimated using the maximum likelihood estimation method as shown below:

[0023]

[0024] Predicting at a given point In the case of , the conditional probability density function PDF and cumulative distribution function CDF of the measured wind speed X are as follows:

[0025]

[0026] That is, assuming that we are at the end of period t and have obtained the point prediction results for the end of the next K periods; on this basis, the above method is combined with the pre-trained marginal distribution and Copula function to calculate the estimated distribution of wind speed where k = 1, ..., K; the symbol “t+k|t” distinguishes the time of prediction from the time of release of the prediction; X t+k|t represents the wind speed forecast at the end of period t+k, based on the information available at time period t.

[0027] A further improvement of the technical solution of the present invention is that: in S12, the Vine-Copula method is used to establish a time correlation structure between wind speeds at different lead times;

[0028]

[0029] The steps for generating a typical scenario for forecasting wind speed are as follows:

[0030] S121 maps the measured wind speed value and the predicted wind speed value into Copula space variables as follows:

[0031]

[0032] S122 uses Latin hypercube sampling in [0,1] K Generate S groups of sampling points;

[0033] Generate a matrix of dimension S×K using the Latin hypercube sampling method:

[0034]

[0035] Each column K is divided into S intervals, and each sample randomly selects a value in a different interval and shuffles the order;

[0036] S123 obtains structured dependency samples from the Latin hypercube sampling method and uses D-vine conditional sampling;

[0037] Perform structured conditional sampling from Vine-Copula and recursively generate the Copula space variable u for each sample 1, ...,u k ;

[0038] For each sample s=1,...,S, perform the following recursion:

[0039]

[0040] These formulas are implemented by the inverse function of h-transform of each pair of Pair-Copula in Vine-Copula;

[0041] S124 edge inverse transformation to restore the physical quantity of wind speed;

[0042] For each Copula space sample, the wind speed scene is inversely transformed through its respective marginal distribution:

[0043]

[0044] in, is the marginal inverse distribution of the k-step-ahead forecast;

[0045] Final output: classic scene set, generating S groups of classic prediction scene samples:

[0046]

[0047] A further improvement of the technical solution of the present invention is that: in S2, a resistance model, a sail model, a propeller model and a shaft generator model during the navigation of the ship are established;

[0048] Resistance Model:

[0049] Froude number:

[0050]

[0051] Where V s Indicates the ship's speed, g indicates the acceleration of gravity, L PP is the vertical line spacing;

[0052] Wavelength estimation:

[0053]

[0054] Where, T P Peak period;

[0055] Radiative wave resistance:

[0056]

[0057] Where, ρ w Seawater density, B ship width, H s Significant wave height, E shear wave propagation angle, CB ship type coefficient;

[0058] Experience modifier:

[0059]

[0060] Flow resistance coefficient:

[0061]

[0062] Where k yy is the rolling rotation radius, T is the ship's draft;

[0063] Speed ​​correction factor:

[0064]

[0065] Average angular frequency:

[0066]

[0067] Circumferential wave resistance:

[0068]

[0069] Among them, b1 and d1 are fitting indices respectively;

[0070] Total wave added resistance:

[0071] R wave =R wave,r +R wave,m (twenty four)

[0072] Wave spectrum function output:

[0073] S(ω)=Improved_Jonswap(H s ,T p ) (25)

[0074] Total wave resistance:

[0075]

[0076] Hydrostatic resistance:

[0077]

[0078] Among them, C f is the friction resistance coefficient, k is the hull form factor, S wet contact area;

[0079] Sail Model:

[0080] If the ship speed is V s , the heading angle is θ ship , the true wind speed is (u,v), then:

[0081] The ship velocity vector is:

[0082]

[0083] Where V s is the ship speed scalar, and The modulo of is equal;

[0084] The apparent wind vector is:

[0085]

[0086] Apparent wind speed:

[0087]

[0088] If the ship speed is specified as V s , the heading is θ ship , the true wind speed is (u,v);

[0089] Angle between apparent wind and bow:

[0090]

[0091] Where, φ app It represents the apparent wind angle, which is the angle between the apparent wind and the ship's heading;

[0092] Thrust coefficient:

[0093] C t =C L ·sin(φ app )-C D ·cos(φ app ) (32)

[0094] thrust:

[0095]

[0096] Where S sail is the windward area of ​​the sail (unit: m 2 ), ρ air is the air density;

[0097] Drift force perpendicular to the hull:

[0098] C d =C L ·cos(φ app )-C D ·sin(φ app ) (34)

[0099]

[0100] Among them, C L ,C D The lift and drag coefficients are obtained by interpolation from a table, are dependent on the angle of attack, and are based on experimental data for the NACA0015 airfoil;

[0101] f1 and f2 are interpolation functions;

[0102] α opt =f1(V app ,φ app ) (36)

[0103] F w =f2(V app ,φ app ) (37)

[0104] Where, α opt is the optimal angle of attack, that is, the angle at which the sail can generate maximum thrust under the current wind conditions;

[0105] Propeller model:

[0106] The propeller thrust T and torque Q are determined by the thrust coefficient K T and torque coefficient K Q To calculate, F W is the thrust of the wind blade, D is the propeller diameter, n is the propeller speed, and ρ is the density of water;

[0107] T=R total -F W =K T ρn 2 D 4 (38)

[0108] Q=K Q ρn 2 D 5 (39)

[0109] According to the propeller open water characteristic curve, K is obtained by fitting T and K Q :

[0110] K T =-0.1072J 2 -0.3048J+0.3486 (40)

[0111] K Q =-0.02114J 2 -0.01944J+0.0361 (41)

[0112] Where, J is the propeller advance coefficient;

[0113]

[0114] Where h p V is the distance the propeller moves forward during one rotation. a is the propeller advance speed;

[0115] The propeller open water efficiency is given by the following formula:

[0116]

[0117] After the ship resistance and wind blade thrust are determined, the above formula is used to calculate And the propeller open water characteristic curve Interpolate to obtain J at the corresponding speed, and then substitute it into the propeller advance coefficient formula to obtain the propeller speed;

[0118] Shaft generator model:

[0119] The relationship between the shaft generator output power and the main engine speed is shown in the following formula:

[0120]

[0121] A further improvement of the technical solution of the present invention is that in S2, the energy transfer relationship of the ship propulsion system and the energy transfer relationship of the power system are established, and their function models are as follows:

[0122] Assuming that the ship's speed is constant and the resistance disturbance caused by attitude changes is ignored, the overall propulsion force and navigation resistance should satisfy the force balance relationship, as shown in the following expression:

[0123] R total =T+F W =(1-t)T+F W (46)

[0124] Where R total is the ship resistance, F W is the thrust provided by the wind blade, T is the effective thrust of the propeller, and t is the thrust deduction coefficient;

[0125] The effective power actually transmitted to the propeller and involved in propulsion needs to consider the transmission efficiency:

[0126]

[0127] Where, P ME is the host output power, P S is the shaft generator output power, P DB is the actual power received by the propeller, η1 is the power generation efficiency of the shaft generator, η S is the shaft transmission efficiency;

[0128] The propeller generates thrust T to propel the ship, and some power is lost in the process:

[0129] P T =P DB η B (48)

[0130] Where, P T is the propeller thrust power; η B is the propeller efficiency;

[0131] η B =η R η O (49)

[0132] Where η R is the propeller relative rotation efficiency; η O is the propeller open water efficiency;

[0133] The hull efficiency formula is as follows:

[0134]

[0135] P F is the effective power of the hull, t is the thrust reduction coefficient, and w is the wake fraction;

[0136] Energy transfer relationship of power system:

[0137] The relationship between the ship's electrical load, shaft generator output power, and auxiliary engine output power is shown in the following formula:

[0138] P E =P S +P AE η2 (51)

[0139] P E is the electrical load on the ship, P AE is the output power of the auxiliary machine, and η2 is the power generation efficiency of the auxiliary machine.

[0140] A further improvement of the technical solution of the present invention is that in S2, a fuel consumption model of the ship is established, including a main engine fuel consumption model and an auxiliary engine fuel consumption model. The main engine fuel consumption mathematical model is as follows:

[0141]

[0142] The main engine fuel consumption per hour is obtained through the main engine fuel consumption rate, as shown in the following formula:

[0143]

[0144] g MEis the main engine fuel consumption rate, obtained from the main engine fuel consumption rate fitting curve, k p is the number of propellers;

[0145] Auxiliary engine fuel consumption model:

[0146]

[0147] After calculating the auxiliary engine output power, the auxiliary engine fuel consumption rate g AE The auxiliary engine fuel consumption per hour is obtained as follows:

[0148]

[0149] The ship's fuel consumption per hour is:

[0150]

[0151] A further improvement of the technical solution of the present invention is that in S3, the total fuel consumption of the propulsion system under specific working conditions is:

[0152]

[0153] The sum of the travel time of each section is the total travel time of the ship on the route:

[0154]

[0155] The flight duration constraints, rotation speed constraints, speed constraints, angle of attack constraints, and route constraints are:

[0156] T total ≤T limit (59)

[0157]

[0158] Where Δd i is the distance between the i-th optimized waypoint and the original waypoint;

[0159] Under the constraints of flight period, rotation speed, speed, angle of attack and route, a genetic algorithm is used to minimize the total fuel consumption of the propulsion system under specific working conditions, and output decision variables to achieve real-time optimal control of the propulsion system in response to wind speed changes.

[0160] Due to the adoption of the above technical solution, the technical advancements achieved by the present invention are:

[0161] In the context of a sail-assisted propulsion system, the present invention constructs an energy management strategy model for hybrid ships based on the uncertainty of wind speed prediction, and innovatively applies the double-layer Copula method to wind speed prediction modeling. The Vine-Copula model can flexibly construct a high-dimensional model, effectively capture the nonlinear relationship between wind speed variables, and improve the accuracy of wind speed prediction. The study comprehensively considers the coordinated utilization of wind energy, electricity, and traditional fuels, and improves the system's responsiveness to dynamic environments through the SMPC strategy, thereby ensuring the application effect of sail propulsion in complex sea conditions. The present invention effectively enhances the practicality and adaptability of the system, and provides theoretical support for the engineering application of hybrid propulsion technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0162] Figure 1 This is a flow chart of the rolling optimization method of a wind-wing-assisted hybrid ship under wind speed prediction uncertainty in the present invention. DETAILED DESCRIPTION

[0163] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0164] like Figure 1 As shown, a rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty includes the following steps:

[0165] S1. Adaptive kernel density estimation (KDE) and binary Copula function are used to construct an uncertainty model for wind speed forecasting. The Vine-Copula method is used to establish the temporal correlation structure between wind speeds at different lead times. Combined with Latin Hypercube (LH) sampling, typical wind speed scenarios are generated for subsequent uncertainty analysis and optimized scheduling.

[0166] S1 specifically includes the following steps:

[0167] S11 uses the adaptive kernel density estimation (adaptive KDE) method to overcome its lack of normalization;

[0168] By applying adaptive kernel density estimation and using historical measured wind speed data and corresponding forecast wind speed data, the distribution of measured wind speeds and forecast wind speeds with different forecast lead times can be estimated. The probability density function (PDF) and cumulative distribution function (CDF) of independent and identically distributed (iid) data drawn from the unknown density function are estimated by adaptive kernel density estimation as follows:

[0169]

[0170] Where f(·) and F(·) represent the probability density function (PDF) and cumulative distribution function (CDF), respectively, and the subscripts represent the corresponding random variables; N represents the number of samples; xmax represents the maximum value in the sample and is used to normalize the data; b represents the smoothing parameter, which satisfies the condition that b→0 when N→∞; B(·; p,q) represents the Beta function with shape parameters p and q; α represents the integral variable;

[0171] Using binary copula uncertainty modeling, this paper adopts Kendall rank correlation coefficient (denoted as τ) to identify the monotonic relationship between two data series to quantify the correlation between measured data and predicted data; given two data series and The coefficient is expressed by calculating the ratio of the difference between the number of consistent and inconsistent pairs in all data pairs to the total number of pairs, as follows:

[0172]

[0173] A positive correlation between measured and predicted data results in τ being greater than zero. The more accurate the predictions, the stronger the rank correlation, and the larger the τ value.

[0174] Sklar's theorem accurately describes the complex relationship between measured and predicted data, that is, the relationship between measured and predicted wind speeds can be modeled using a copula function. By applying this theorem, the joint PDF and CDF can be estimated based on the marginal CDF and PDF as follows:

[0175]

[0176] Where X and Y represent the measured wind speed and the predicted wind speed, respectively; c(·) and C(·) represent the probability density function (PDF) and cumulative distribution function (CDF) of the copula, respectively; θ represents the copula parameter, which is estimated using the maximum likelihood estimation (MLE) method in this paper, as shown below:

[0177]

[0178] Predicting at a given point In the case of , the conditional probability density function (PDF) and cumulative distribution function (CDF) of the measured wind speed X can be expressed as follows:

[0179]

[0180] That is, assuming that we are at the end of period t and have obtained the point prediction results for the end of the next K periods. On this basis, the above method can be used to combine the pre-trained marginal distribution and Copula function to calculate the estimated distribution of wind speed Where k = 1, ..., K; the symbol "t+k|t" distinguishes the time of prediction from the time of release of the prediction. t+k|tIt represents the wind speed forecast at the end of period t+k, which is based on the information available at time t (i.e. the forecast lead time is k).

[0181] S12 uses the Vine-Copula method to establish the temporal correlation structure between wind speeds at different lead times. Combining the Latin hypercube sampling method with the joint distribution structure constructed by Vine-Copula, conditional sampling is performed on multi-time wind speed forecasts to generate S groups of typical wind speed scenarios with temporal correlation, which are then input into the optimization model.

[0182] The Vine-Copula method is used to establish the temporal correlation structure between wind speeds at different lead times:

[0183]

[0184] The steps for generating a typical scenario for forecasting wind speed are as follows:

[0185] S121 maps the measured wind speed value and the predicted wind speed value into Copula space variables as follows:

[0186]

[0187] S122 uses LHS in [0,1] K Generate S groups of sampling points;

[0188] Use LHS (Latin Hypercube Sampling) to generate a matrix of dimension S×K:

[0189]

[0190] Each column K is divided into S intervals, and each sample randomly selects a value in a different interval and shuffles the order.

[0191] S123D-vine conditional sampling (getting structured dependency samples from LHS);

[0192] Perform structured conditional sampling from Vine-Copula and recursively generate the Copula space variable u for each sample 1, ...,u k ;

[0193] For each sample s=1,...,S, perform the following recursion:

[0194]

[0195] These formulas are implemented by the inverse h-transform function of each pair of Pair-Copula in Vine-Copula.

[0196] S124 edge inverse transformation to restore the physical quantity of wind speed;

[0197] For each Copula space sample, the wind speed scene is inversely transformed through its respective marginal distribution:

[0198]

[0199] in is the marginal inverse distribution of the k-step-ahead forecast.

[0200] Final output: classic scene set, generating S groups of classic prediction scene samples:

[0201]

[0202] S2. Based on the thrust characteristics of the wind turbine, the matching relationship between the ship engine and propeller, and the characteristics of the shaft generator, an energy transfer model between the propulsion system and the power system is established, and a comprehensive fuel consumption model for the wind turbine-assisted navigation scenario is constructed;

[0203] This step uses the typical wind speed scenario with time-series correlation generated in S1 as input to drive the blade thrust calculation, thereby evaluating the energy distribution and fuel consumption performance under different wind conditions, providing a basis for subsequent energy efficiency optimization;

[0204] S21. Establish a resistance model for the ship during its travel;

[0205] Froude number:

[0206]

[0207] Where, L PP vertical spacing;

[0208] Wavelength estimation:

[0209]

[0210] Where, T P is the peak period;

[0211] Radiation wave resistance (R wave,r ):

[0212]

[0213] Where, ρ w Seawater density, B ship width, H s Significant wave height, E shear wave propagation angle, CB ship type coefficient.

[0214] Experience correction factor a t As follows: (added when the wavelength is relatively short)

[0215]

[0216] a1 (flow resistance coefficient):

[0217]

[0218] Among them, k yy is the roll rotation radius.

[0219] Speed ​​correction factor a2:

[0220]

[0221] Average angular frequency ω mean :

[0222]

[0223] Flow wave resistance (R wave,m ):

[0224]

[0225] Fitting exponents b1 d1 (determine frequency response).

[0226] Total wave added resistance (in Newtons):

[0227] R wave =R wave,r +R wave,m (twenty four)

[0228] Wave spectrum function output S(ω): (energy spectrum density at angular frequency ω)

[0229] S(ω)=Improved_Jonswap(H s ,T p ) (25)

[0230] This formula can restore the one-sided spectrum to the complete energy spectrum.

[0231] The total wave resistance calculation formula is:

[0232]

[0233] Calculation of hydrostatic resistance:

[0234]

[0235] Among them, C f is the friction resistance coefficient and k is the hull form factor.

[0236] S22. Build a sail model:

[0237] If the ship speed is V s , the heading angle is θ ship , the true wind speed is (u,v), then:

[0238] The ship velocity vector is:

[0239]

[0240] The apparent wind vector is:

[0241]

[0242] Apparent wind speed:

[0243]

[0244] If the ship speed is V s , the heading is θ ship , the true wind speed is (u,v), then the angle between the apparent wind and the bow is:

[0245]

[0246] φ app Apparent wind angle is the angle between the apparent wind and the ship's heading.

[0247] Thrust coefficient (direction parallel to heading):

[0248] C t =C L ·sin(φ app )-C D ·cos(φ app ) (32)

[0249] Thrust (unit N):

[0250]

[0251] Where S sail is the windward area of ​​the sail (unit: m 2 ).

[0252] Drift force (perpendicular to the hull):

[0253] C d =C L ·cos(φ app )-C D ·sin(φ app ) (34)

[0254]

[0255] Among them CL ,C D The lift and drag coefficients are obtained by interpolation from a table, depending on the angle of attack, based on experimental data for the NACA0015 airfoil.

[0256] f1 and f2 are interpolation functions, which are essentially two-dimensional interpolation functions implemented by interp2(...) and return the table lookup results.

[0257] α opt =f1(V app ,φ app ) (36)

[0258] F w =f2(V app ,φ app ) (37)

[0259] Where α opt is the optimal attack angle, which is the angle at which the sail can generate maximum thrust under the current wind conditions.

[0260] S23. Establish propeller model:

[0261] The propeller thrust T and torque Q can be calculated from the thrust coefficient K T and torque coefficient K Q To calculate, F W is the thrust of the wind blade, and D is the propeller diameter.

[0262] T=R total -F W =K T ρn 2 D 4 (38)

[0263] Q=K Q ρn 2 D 5 (39)

[0264] According to the propeller open water characteristic curve, K can be fitted to obtain T and K Q , as follows:

[0265] K T =-0.1072J 2 -0.3048J+0.3486 (40)

[0266] K Q =-0.02114J 2 -0.01944J+0.0361 (41)

[0267] Where J is the propeller advance coefficient.

[0268]

[0269] Where h p V is the distance the propeller moves forward during one rotation. a is the propeller advance speed.

[0270] The propeller open water efficiency is given by the following formula:

[0271]

[0272] After the ship resistance and wind blade thrust are determined, the above formula is used to calculate And the propeller open water characteristic curve By interpolation, we can get J at the corresponding speed, and then substitute it into the propeller advance coefficient formula to get the propeller speed.

[0273] S24. Establish the shaft generator model:

[0274] The relationship between the shaft generator output power and the main engine speed is shown in the following formula:

[0275]

[0276] S25. Establishing a propulsion system energy transfer relationship;

[0277] During navigation, a hybrid vessel powered by wind turbines derives its propulsion power from two sources: conventional mechanical thrust generated by the main engine, which drives the propeller through the shaft system; and additional propulsion generated by the wind turbine system, which captures wind energy and converts it into additional propulsion. These two types of thrust work together to overcome the total hydrodynamic resistance encountered by the vessel as it moves forward, thereby maintaining its forward motion. Assuming a constant speed and ignoring resistance disturbances caused by changes in the vessel's attitude, the overall propulsion force and navigational resistance should maintain a force equilibrium relationship, which can be described by the following expression:

[0278] R total =T+F W =(1-t)T+F W (46)

[0279] Where R total is the ship resistance; F W is the thrust provided by the wind blade; T is the effective thrust of the propeller, and t is the thrust deduction coefficient.

[0280] The mechanical power output of the main engine is divided into two parts during the transmission process: one part is extracted by the shaft generator and converted into electrical energy to meet the ship's power needs; the other part is absorbed by the propeller and used to provide the kinetic energy required for propulsion. However, since the shaft system is inevitably affected by factors such as mechanical friction during energy transmission, a certain amount of energy loss will occur. Therefore, the actual effective power transmitted to the propeller and participating in propulsion needs to take into account the transmission efficiency, which is calculated by the following formula:

[0281]

[0282] Where, P ME is the host output power; P S is the output power of the shaft generator; P DB is the actual power received by the propeller; η1 is the power generation efficiency of the shaft generator; η S is the shaft transmission efficiency.

[0283] The propeller generates thrust T to propel the ship. Due to factors such as vortex loss, friction loss, and wake interference when the propeller rotates in the water, some power loss will occur, as shown in the following formula:

[0284] P T =P DB η B (48)

[0285] Where, P T is the propeller thrust, η B is the propeller efficiency.

[0286] η B =η R η O (49)

[0287] Where η R is the propeller relative rotation efficiency, η O is the propeller open water efficiency.

[0288] The hull efficiency formula is as follows:

[0289]

[0290] P F It is called the effective power of the hull, t is the thrust deduction coefficient, and w is the wake fraction.

[0291] S26. Establishing the energy transfer relationship of the power system:

[0292] The relationship between the ship's electrical load, shaft generator output power, and auxiliary engine output power is shown in the following formula:

[0293] P E =P S +P AE η2 (51)

[0294] P E is the electrical load on the ship, P AE is the output power of the auxiliary machine, and η2 is the power generation efficiency of the auxiliary machine.

[0295] S27, establishing a fuel consumption model;

[0296] Ship main engine fuel consumption model:

[0297]

[0298] After calculating the main engine output power, the main engine fuel consumption per hour can be obtained through the main engine fuel consumption rate, as shown in the following formula:

[0299]

[0300] g ME is the main engine fuel consumption rate, which is obtained from the main engine fuel consumption rate fitting curve.

[0301] Auxiliary engine fuel consumption model:

[0302]

[0303] After calculating the auxiliary engine output power, the auxiliary engine fuel consumption rate g AE The auxiliary engine fuel consumption per hour can be obtained as follows:

[0304]

[0305] In summary, the ship's fuel consumption per hour is:

[0306]

[0307] S3. Adopting a rolling optimization strategy, at each decision moment, based on the currently available wind speed forecast information, the energy efficiency control in the future time domain is optimized and solved, and updated and executed in real time.

[0308] This strategy uses the typical wind speed scenarios with uncertainty and time-series correlation generated in S1 as input, combined with the energy transfer model and comprehensive fuel consumption model constructed in S2, to dynamically evaluate the energy efficiency performance under each control strategy, achieve response to wind speed changes and achieve real-time optimization control of the propulsion system;

[0309]

[0310] The sum of the travel time of each section is the total travel time of the ship on the route as follows:

[0311]

[0312] T total ≤T limit (59)

[0313]

[0314] Equations (59) to (63) represent the flight duration constraint, rotation speed constraint, speed constraint, angle of attack constraint, and route constraint, respectively; where Δd i is the distance between the i-th optimized waypoint and the original waypoint.

[0315] Due to the uncertainty of wind speed prediction, this paper constructs a rolling optimization method for wind-wing-assisted hybrid ships based on wind speed prediction uncertainty. First, the joint distribution between measured and predicted wind speeds is constructed using kernel density estimation (KDE) and a binary Copula function. Then, the temporal correlation structure of wind speed prediction is established using the Vine-Copula method. Latin hypercube sampling is combined to generate typical wind speed scenarios, which serve as input for the optimization process.

[0316] Based on this, the present invention constructs a fuel consumption model for the main engine and auxiliary system, taking into account offshore wind energy, power system load regulation, and shaft generator power generation characteristics, with regard to the thrust provided by the sails. This allows for energy scheduling and optimized scheduling of the sail-assisted thrust during navigation.

[0317] Finally, the rolling optimization control strategy is used to dynamically update the wind speed scenario and achieve real-time response control to the uncertainty of wind speed prediction, thereby improving the energy efficiency and robustness of the system.

[0318] In summary, this paper employs a two-layer nested copula approach for uncertainty modeling. Adaptive KDE is used to estimate the distribution of measured and predicted wind speeds. A Frank copula is used to establish a positive correlation between measured and predicted data. An external multivariate Vine-Copula is used to establish the temporal correlation of wind speed forecasts at different lead times. Finally, a LH-based sampling method is used to extract representative scenarios from the joint prediction density, resulting in a stable and efficient solution to the optimization problem.

Claims

1. A rolling optimization method for a hybrid ship with wind turbines assisted by wind turbines under wind speed prediction uncertainty, characterized by: The following steps are involved: S1. Adaptive kernel density estimation and binary Copula function are used to construct an uncertainty model for wind speed prediction. The Vine-Copula method is used to establish the temporal correlation structure between wind speeds at different lead times. Latin hypercube sampling is combined to generate typical wind speed scenarios. S2. Using the typical wind speed scenario with time series correlation generated in S1 as input, an energy transfer model between the propulsion system and the power system is established based on the thrust characteristics of the wind turbine, the matching relationship between the ship engine and the propeller, and the characteristics of the shaft generator. A comprehensive fuel consumption model for the wind turbine-assisted navigation scenario is also constructed. S3. Using the typical wind speed scenario with uncertainty and time-series correlation generated in S1 as input, combined with the energy transfer model and comprehensive fuel consumption model constructed in S2, a rolling optimization strategy is adopted. At each decision moment, based on the currently available wind speed forecast information, the energy efficiency control in the future time domain is optimized and solved, and the execution is updated in real time. The energy efficiency performance under each control strategy is dynamically evaluated to achieve response to wind speed changes and real-time optimization control of the propulsion system.

2. The rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty according to claim 1 is characterized in that: S1 specific The following steps are involved: S11 uses an adaptive kernel density estimation method to overcome the problem of lack of normalization in wind speed prediction; S12 uses the Vine-Copula method to establish the time correlation structure between wind speeds at different lead times; combining the Latin hypercube sampling method and the joint distribution structure constructed by Vine-Copula, conditional sampling is performed on multi-time wind speed forecasts to generate S groups of typical wind speed scenarios with time series correlation, and the generated wind speed scenarios are input into the optimization model.

3. The rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty according to claim 2 is characterized in that: In S11, by applying adaptive kernel density estimation and using historical measured wind speed data and corresponding forecast wind speed data, the distribution of measured wind speed and forecast wind speed with different forecast lead times is estimated. The independent and identically distributed (iid) data extracted from the unknown density function, its probability density function PDF and cumulative distribution function CDF are estimated by adaptive kernel density estimation as follows: Where f(·) and F(·) represent the probability density function PDF and the cumulative distribution function CDF, respectively, and the subscripts represent the corresponding random variables; N represents the number of samples; x max represents the maximum value in the sample and is used to normalize the data; b represents the smoothing parameter, which satisfies the condition that b→0 when N→∞; B(·; p,q) represents the Beta function with shape parameters p and q; α represents the integral variable; Uncertainty modeling using binary copula, using Kendall rank correlation coefficient, is used to identify the monotonic relationship between two data series. Given two data series and The Kendall rank correlation coefficient is expressed by calculating the ratio of the difference between the number of consistent pairs and the number of inconsistent pairs in all data pairs to the total number of pairs, as follows: The joint probability density function PDF and cumulative distribution function CDF are estimated based on the marginal cumulative distribution function CDF and the probability density function PDF as follows: Where X and Y represent the measured wind speed and the predicted wind speed, respectively; c(·) and C(·) represent the probability density function (PDF) and cumulative distribution function (CDF) of the copula, respectively; θ represents the copula parameter, which is estimated using the maximum likelihood estimation method as shown below: Predicting at a given point In the case of , the conditional probability density function PDF and cumulative distribution function CDF of the measured wind speed X are as follows: That is, assuming that we are at the end of period t and have obtained the point prediction results for the end of the next K periods; on this basis, the above method is combined with the pre-trained marginal distribution and Copula function to calculate the estimated distribution of wind speed where k = 1, ..., K; the symbol "t+k|t" distinguishes the time of prediction from the time of release of the prediction; X t+k|t represents the wind speed forecast at the end of period t+k, based on the information available at time period t.

4. The rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty according to claim 2 is characterized in that: In S12, the Vine-Copula method is used to establish the temporal correlation structure between wind speeds at different lead times; The steps for generating a typical scenario for forecasting wind speed are as follows: S121 maps the measured wind speed value and the predicted wind speed value into Copula space variables as follows: S122 uses Latin hypercube sampling in [0,1] K Generate S groups of sampling points; Generate a matrix of dimension S×K using the Latin hypercube sampling method: Each column K is divided into S intervals, and each sample randomly selects a value in a different interval and shuffles the order; S123 obtains structured dependency samples from the Latin hypercube sampling method and uses D-vine conditional sampling; Perform structured conditional sampling from Vine-Copula and recursively generate the Copula space variable u for each sample 1, ...,u k ; For each sample s=1,...,S, perform the following recursion: These formulas are implemented by the inverse function of h-transform of each pair of Pair-Copula in Vine-Copula; S124 edge inverse transformation, restore the physical quantity of wind speed; For each Copula space sample, the wind speed scene is inversely transformed through its respective marginal distribution: in, is the marginal inverse distribution of the k-step-ahead forecast; Final output: classic scene set, generating S groups of classic prediction scene samples:

5. The rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty according to claim 1 is characterized in that: In S2, the resistance model, sail model, propeller model and shaft generator model of the ship during navigation are established; Resistance Model: Froude number: Where V s Indicates the ship's speed, g indicates the acceleration of gravity, L PP is the vertical line spacing; Wavelength estimation: Where, T P Peak period; Radiative wave resistance: Where, ρ w Seawater density, B ship width, H s Significant wave height, E shear wave propagation angle, CB ship type coefficient; Experience modifier: Flow resistance coefficient: Where k yy is the rolling rotation radius, T is the ship's draft; Speed ​​correction factor: Average angular frequency: Circumferential wave resistance: Among them, b1 and d1 are fitting indices respectively; Total wave added resistance: R wave =R wave,r +R wave,m (24) Wave spectrum function output: S(ω)=Improved_Jonswap(H s ,T p ) (25) Total wave resistance: Hydrostatic resistance: Among them, C f is the friction resistance coefficient, k is the hull form factor, S wet contact area; Sail Model: If the ship speed is V s , the heading angle is θ ship , the true wind speed is (u,v), then: The ship velocity vector is: Where V s is the ship speed scalar, and The modulo of is equal; The apparent wind vector is: Apparent wind speed: If the ship speed is specified as V s , the heading is θ ship , the true wind speed is (u,v); Angle between apparent wind and bow: Where, φ app It represents the apparent wind angle, which is the angle between the apparent wind and the ship's heading; Thrust coefficient: C t =C L ·sin(φ app )-C D ·cos(φ app ) (32) thrust: Where S sail is the windward area of ​​the sail (unit: m 2 ), ρ air is the air density; Drift force perpendicular to the hull: C d =C L ·cos(φ app )-C D ·sin(φ app ) (34) Among them, C L ,C D The lift and drag coefficients are obtained by interpolation from a table, are dependent on the angle of attack, and are based on experimental data for the NACA0015 airfoil; f1 and f2 are interpolation functions; a opt =f1(V app ,f app ) (36) F w =f2(V app ,φ app ) (37) Where, α opt is the optimal angle of attack, that is, the angle at which the sail can generate maximum thrust under the current wind conditions; Propeller model: The propeller thrust T and torque Q are determined by the thrust coefficient K T and torque coefficient K Q To calculate, F W is the thrust of the wind blade, D is the propeller diameter, n is the propeller speed, and ρ is the density of water; T=R total -F W =K T ρn 2 D 4 (38) Q=K Q ρn 2 D 5 (39) According to the propeller open water characteristic curve, K is obtained by fitting T and K Q : TO T =-0.1072J 2 -0.3048J+0.3486 (40) TO Q =-0.02114J 2 -0.01944J+0.0361 (41) Where, J is the propeller advance coefficient; Where h p V is the distance the propeller moves forward during one rotation. a is the propeller advance speed; The propeller open water efficiency is given by the following formula: After the ship resistance and wind blade thrust are determined, the above formula is used to calculate And the propeller open water characteristic curve Interpolate to obtain J at the corresponding speed, and then substitute it into the propeller advance coefficient formula to obtain the propeller speed; Shaft generator model: The relationship between the shaft generator output power and the main engine speed is shown in the following formula:

6. The rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty according to claim 1 is characterized in that: In S2, the energy transfer relationship of the ship propulsion system and the power system are established, and their function models are as follows: Assuming that the ship's speed is constant and the resistance disturbance caused by attitude changes is ignored, the overall propulsion force and navigation resistance should satisfy the force balance relationship, as shown in the following expression: R total =T+F W =(1-t)T+F W (46) Where R total is the ship resistance, F W is the thrust provided by the wind blade, T is the effective thrust of the propeller, and t is the thrust deduction coefficient; The effective power actually transmitted to the propeller and involved in propulsion needs to consider the transmission efficiency: Where, P ME is the host output power, P S is the shaft generator output power, P DB is the actual power received by the propeller, η1 is the power generation efficiency of the shaft generator, η S is the shaft transmission efficiency; The propeller generates thrust T to propel the ship, and some power is lost in the process: P.S T JP DB η B (48) Where, P T is the propeller thrust power; η B is the propeller efficiency; or B =the R or O (49) Where η R is the propeller relative rotation efficiency; η O is the propeller open water efficiency; The hull efficiency formula is as follows: P F is the effective power of the hull, t is the thrust reduction coefficient, and w is the wake fraction; Energy transfer relationship of power system: The relationship between the ship's electrical load, shaft generator output power, and auxiliary engine output power is shown in the following formula: P E =P S +P AE η2 (51) P E is the electrical load on the ship, P AE is the output power of the auxiliary machine, and η2 is the power generation efficiency of the auxiliary machine.

7. The rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty according to claim 1 is characterized in that: In S2, a fuel consumption model of the ship is established, including the main engine fuel consumption model and the auxiliary engine fuel consumption model. The mathematical model of the main engine fuel consumption is as follows: The main engine fuel consumption per hour is obtained through the main engine fuel consumption rate, as shown in the following formula: g ME is the main engine fuel consumption rate, obtained from the main engine fuel consumption rate fitting curve, k p is the number of propellers; Auxiliary engine fuel consumption model: After calculating the auxiliary engine output power, the auxiliary engine fuel consumption rate g AE The auxiliary engine fuel consumption per hour is obtained as follows: The ship's fuel consumption per hour is:

8. The rolling optimization method for a wind-wing-assisted hybrid ship under wind speed prediction uncertainty according to claim 1 is characterized in that: In S3, the total fuel consumption of the propulsion system under specific operating conditions is: The sum of the travel time of each section is the total travel time of the ship on the route: The flight duration constraints, rotation speed constraints, speed constraints, angle of attack constraints, and route constraints are: T total ≤T limit (59) Where Δd i is the distance between the i-th optimized waypoint and the original waypoint; Under the constraints of flight period, rotation speed, speed, angle of attack and route, a genetic algorithm is used to minimize the total fuel consumption of the propulsion system under specific working conditions, and output decision variables to achieve real-time optimal control of the propulsion system in response to wind speed changes.

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