Semi-submerged ship ballast water distribution optimization method for exploring initial stability limit

Abstract

The invention provides a semi-submerged ship ballast water distribution optimization method for exploring an initial stability limit, and belongs to the technical field of ship and ocean engineering. Taking the proportion of ballast water loaded in each ballast tank as a decision variable, and taking the maximum initial stability height of the semi-submerged ship after free liquid level correction as an objective function; constructing a ballast water distribution and initial stability optimization model of the semi-submerged ship by taking displacement limitation, ship body forward floating, initial stability height limitation and rolling period limitation as constraints; performing linear conversion on a discontinuous piecewise function and a quadratic polynomial in the semi-submerged ship ballast water distribution and initial stability optimization model; solving the ballast water distribution and initial stability optimization model of the semi-submerged ship after linear conversion, and obtaining the initial stability height of the semi-submerged ship after free liquid level correction and a corresponding ballast water distribution scheme; the loading position of the goods on the deck of the semi-submerged ship is optimized through sensitivity analysis; and drawing a corresponding relation graph of the screened cargo loading position and the optimal initial stability height, and marking the optimal loading position of the cargo in the graph.

Description

Technical Field

[0001] The present invention relates to the technical field of ship and ocean engineering, and in particular to a ballast water distribution optimization method for a semi-submersible vessel for exploring the initial stability limit. Background Art

[0002] At present, in the actual operation of the ballast system equipped on semi-submersible ships, the staff adjusts the water volume in each ballast tank based on their professional knowledge and operating experience to ensure that the ship has a suitable buoyancy and stability. The working principle of this system is that the operator adjusts the ballast water volume in the ballast tank by controlling the time of the ballast tank water valve opening and closing, and the relevant information is fed back by the sensor, and the initial stability height of the ship is calculated and presented to the operator. This method consumes a lot of time, is inefficient, and the adjustment effect is greatly affected by the level of the operator. Or the function of automatically designing the ballast scheme is built into the ballast system, and the initial stability is used as a constraint condition. Through the heuristic algorithm, the initial stability of the ship is calculated by the formula under the condition of known ship cargo, ballast water distribution or free liquid surface influence, etc., as an indicator for checking or monitoring whether the ballast water distribution scheme meets the initial stability height constraint. However, the calculation time of the above method is long and it is impossible to obtain the optimal ballast scheme with the highest initial stability.

[0003] Therefore, a ballast water distribution method for a semi-submersible vessel that can efficiently obtain the highest initial stability is needed. Summary of the invention

[0004] In view of this, the present invention provides a semi-submersible vessel ballast water distribution optimization method for exploring the initial stability limit. The method can, under the premise of given cargo weight, center of gravity height and loading position, design a ballast water distribution plan with the highest initial stability for the semi-submersible vessel within ten seconds, and this plan is a global optimal precise solution rather than an optimized solution; and the method can select the best loading position for loading cargo on the deck of the semi-submersible vessel by calculating the maximum value of the initial stability.

[0005] To this end, the present invention provides the following technical solutions:

[0006] A ballast water distribution optimization method for a semi-submersible vessel for exploring the initial stability limit, comprising:

[0007] The proportion of ballast water in each ballast tank is taken as the decision variable, and the maximum initial stability height of the semi-submersible ship after free surface correction is taken as the objective function.

[0008] The ballast water distribution and initial stability optimization model of semi-submersible vessel is constructed with the constraints of displacement limit, ensuring the hull is floating, initial stability height limit and rolling period limit.

[0009] Performing linear transformation on the discontinuous piecewise function and the quadratic polynomial in the ballast water distribution and initial stability optimization model of the semi-submersible vessel;

[0010] The ballast water distribution and initial stability optimization model of the semi-submersible ship after linear transformation is solved, and the initial stability height of the semi-submersible ship after free surface correction and the corresponding ballast water distribution scheme are obtained.

[0011] Furthermore, the ratio of ballast water loaded into each ballast tank is used as the decision variable, and the maximum initial stability height of the semi-submersible ship after free surface correction is used as the objective function:

[0012] max GM(θ n )

[0013] Among them, the decision variable θ n is the ballast coefficient of the nth ballast tank, which expresses the ratio of the weight of the ballast water in the ballast tank to the full ballast capacity of the ballast tank; GM is the calculation function of the initial stability height of the semi-submersible ship after free surface correction.

[0014] Furthermore, the displacement limitation, ensuring the hull is upright, the initial stability height limitation and the rolling period limitation include:

[0015] Displacement Limitation:

[0016]

[0017] Balance constraints in the x and y directions to ensure the ship floats upright:

[0018]

[0019] The minimum limit constraint of initial stability value:

[0020] GM ≥ GM L

[0021] Characterize the relationship between the ship's rolling period and initial stability:

[0022]

[0023] Ship rolling period constraint:

[0024] T L ≤T≤T U

[0025] Decision variable constraints:

[0026]

[0027] Furthermore, the discontinuous piecewise function and the quadratic polynomial in the semi-submersible vessel ballast water distribution and initial stability optimization model are linearly transformed, including:

[0028] The outer approximation method is used to transform the quadratic polynomial associated with the ballast water volume and its center of gravity position in the objective function into multiple linear inequality constraints.

[0029] The discontinuous piecewise function that describes the influence of free surface on initial stability is transformed into a continuous piecewise function through a conversion method combining continuous piecewise function and inequality, and then the linearized constraint is obtained.

[0030] Furthermore, the outer approximation method is used to convert the quadratic polynomial associated with the ballast water volume and its center of gravity position in the objective function into multiple linear inequality constraints, including:

[0031] Extract the nonlinear part U n :

[0032]

[0033] Transform the nonlinear part U by the outer approximation method n , we obtain the linear constraints:

[0034]

[0035] in, Respectively represent the slope, intercept and horizontal coordinate values ​​of the tangent point of the line segment; K n For U n The number of line segments is obtained after linear transformation.

[0036] Furthermore, the conversion method combining continuous piecewise function with inequality to describe the effect of free surface on initial stability is converted into a continuous piecewise function to obtain linearized constraints, including:

[0037] Introducing the continuous piecewise function β n With inequality constraints, we can characterize the discontinuous piecewise function in FR:

[0038]

[0039] When 0<θ n <1, β n >0, limiting α n Only 1 can be selected;

[0040] When θ n = 0 or 1, β n =0, under the constraint α n It can be 0 or 1, combined with the requirement of finding the maximum value of the objective function, α n It will tend to be 0.

[0041] Furthermore, the input parameters of the semi-submersible vessel ballast water distribution and initial stability optimization model include:

[0042] Semi-submersible vessel’s empty ship weight w s and its centroid coordinates (x s ,y s ,z s);

[0043] Loading weight w c and its centroid coordinates (x c ,y c ,z c );

[0044] The displacement of the semi-submersible ship when loaded with cargo is Δ, the buoyancy center height KB and the x coordinate x F , transverse metacentric radius BM;

[0045] Total number of ballast tanks N, maximum ballast water volume of the nth ballast tank B n , Coordinates of the center of gravity of a full ballast tank Bilge z coordinate The lateral moment of inertia of the free liquid surface area about its tilt axis is m n ;

[0046] Rolling rotation radius R, rolling period T and its lower limit T of semi-submersible ship L , Upper limit T U ;

[0047] Minimum initial stability limit GM of semi-submersible vessel when loaded with cargo L .

[0048] Furthermore, the calculation function of the initial stability height of the semi-submersible vessel after free surface correction includes:

[0049] When a semi-submersible vessel is loaded with cargo, the center of gravity height of the vessel, cargo, and ballast water as a whole is KG:

[0050]

[0051] Correction value FR of the free liquid surface in the ballast tank for initial stability:

[0052]

[0053] Where ρ is the density of seawater, α n For auxiliary variables:

[0054]

[0055] When θ n = 0 or 1, that is, the nth ballast tank is not loaded with ballast water or is full of ballast water, and there is no free liquid surface in the tank;

[0056] When 0<θ n When <1, the nth ballast tank is partially filled with ballast water but not full. When the ship tilts, there is a free liquid surface in the tank, which generates an additional tilting moment and reduces the initial stability of the ship.

[0057] The initial stability height GM of the semi-submersible vessel corrected by free surface:

[0058] GM=KB+BM-KG-FR

[0059] Among them, KB and BM are determined by the center of buoyancy and metacenter of the hull model at the corresponding displacement.

[0060] Furthermore, the ballast water distribution and initial stability optimization model of the semi-submersible vessel after the linear transformation is solved by a linear solver to obtain the initial stability height of the semi-submersible vessel after free surface correction and the corresponding ballast water distribution scheme.

[0061] Furthermore, the method of solving the ballast water distribution and initial stability optimization model of the semi-submersible vessel after linear transformation to obtain the initial stability height of the semi-submersible vessel after free surface correction and the corresponding ballast water distribution scheme also includes:

[0062] The initial stability height of the semi-submersible ship after free surface correction corresponding to different loading positions of cargo on the semi-submersible ship is solved, and the loading position with the largest initial stability height of the semi-submersible ship after free surface correction is recommended as the optimal loading position, and the corresponding ballast water distribution plan is obtained.

[0063] Advantages and positive effects of the present invention:

[0064] The present invention aims to maximize the initial stability height corrected by the free liquid surface, and establishes a ballast water distribution and initial stability optimization model for a semi-submersible vessel. It can solve the optimal ballast water distribution scheme and the limit of its initial stability height when the semi-submersible vessel is loaded with heavy cargo while ensuring the reasonable draft, buoyancy and rolling period of the ship, and explore the adaptability limit of the semi-submersible vessel to loading heavy cargo.

[0065] The present invention designs a linearization technology of hybrid discontinuous piecewise function and quadratic polynomial for the nonlinear part of the initial stability of the objective function, so that the model can use a linear solver to quickly obtain an accurate solution within seconds, significantly improving the solution speed and solution quality. Embedding this algorithm in the ballast system of a semi-submersible vessel can significantly improve its real-time dynamic response capability to cope with emergencies.

[0066] The present invention can quickly obtain the maximum initial stability height of a semi-submersible vessel and the corresponding ballast water solution for different cargoes at different loading positions, thereby quickly recommending the optimal loading position of the cargo with the maximum initial stability height as the goal, thereby improving the intelligent decision-making level of the semi-submersible vessel for the design of the cargo loading position.

[0067] The method is also applicable to various ships such as floating docks, crane ships, and ro-ro ships that have ballast tanks and adjust the initial stability of the ship through ballast water. Based on the above reasons, the present invention can be widely promoted in the technical field of ship ballast water distribution and initial stability optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0069] Figure 1 A flow chart of a method in an embodiment of the present invention;

[0070] Figure 2 Establishing a diagram for the ship coordinate system in an embodiment of the present invention;

[0071] Figure 3 It is a schematic diagram of the convergence of the linearized center of gravity height KG of the internal and external approximation method in an embodiment of the present invention;

[0072] Figure 4 Schematic diagram of the process of linearizing the center of gravity height KG using the external and internal approximation method in an embodiment of the present invention;

[0073] Figure 5 Schematic diagram of a ballast water distribution scheme for a single-layer ballast tank of a semi-submersible vessel in an embodiment of the present invention;

[0074] Figure 6 A panoramic view of the ballast water distribution scheme of a semi-submersible vessel in an embodiment of the present invention;

[0075] Figure 7 This is a schematic diagram of the recommended optimal loading position for cargo in an embodiment of the present invention. DETAILED DESCRIPTION

[0076] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0077] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0078] The present invention provides a ballast water distribution optimization method for a semi-submersible vessel for exploring the initial stability limit, and the concept is as follows: constructing a semi-submersible vessel initial stability height measurement function after free surface correction; establishing a ballast water distribution and initial stability optimization model for a semi-submersible vessel with the proportion of ballast water loaded into each ballast tank as a decision variable; designing a linearization method of a nonlinear objective function of a mixed discontinuous piecewise function and a quadratic polynomial to achieve rapid and accurate solution of the optimization model; exploring the initial stability limit of a semi-submersible vessel, providing a determination method for the feasibility of loading heavy cargo on a semi-submersible vessel, and recommending a loading position with the maximum initial stability height.

[0079] The method steps of the present invention include: obtaining relevant data such as the hull, buoyancy, and ballast tanks of the semi-submersible vessel, as well as data such as cargo weight, center of gravity height, and loading position. The information of the semi-submersible vessel and the loaded cargo is used as input parameters to construct a semi-submersible vessel initial stability height measurement function after free surface correction. Taking the maximum initial stability height as the goal, the proportion of ballast water loaded into each ballast tank as the decision variable, and the displacement limit, ensuring the positive buoyancy of the hull, the initial stability height limit, and the roll period limit as constraints, a semi-submersible vessel ballast water distribution and initial stability optimization model is established. This is a nonlinear model that contains a discontinuous piecewise function and a quadratic polynomial in the objective function. For the quadratic polynomial caused by the correlation between the ballast water volume and its center of gravity position in the objective function, the outer approximation method is used to characterize it as a linear piecewise function, thereby converting the quadratic polynomial into multiple linear inequality constraints. For the discontinuous piecewise function caused by the free surface correction of initial stability in the objective function, a conversion method combining continuous piecewise function and inequality is designed to characterize its lower bound, convert it into a continuous piecewise function, and then further linearize it. After converting the semi-submersible ship ballast water distribution and initial stability optimization model into a linear model, the optimal ballast water distribution solution and the corresponding maximum initial stability height can be quickly obtained using linear solvers such as Gurobi. A sensitivity analysis is conducted on the loading position of cargo on the deck of the semi-submersible ship to explore the cargo loading position with the maximum initial stability of the semi-submersible ship.

[0080] Combination Figure 1The method flow chart shown further illustrates the method of the present invention:

[0081] Step 1: Establish the semi-submersible vessel coordinate system, such as Figure 2 As shown, including:

[0082] The intersection of the vertical line at the stern of the semi-submersible ship and the base plane is taken as the coordinate origin o, the intersection of the base plane and the midline plane is taken as the x-axis, and the direction pointing to the bow is positive;

[0083] The tail vertical line is the z-axis, with upward being positive;

[0084] The straight line passing through the origin and perpendicular to xoz is the y-axis, and the positive direction is to the starboard.

[0085] Step 2: Obtain data related to the semi-submersible vessel and cargo, including:

[0086] Semi-submersible vessel’s empty ship weight w s and its centroid coordinates (x s ,y s ,z s ), Loading weight w c and its centroid coordinates (x c ,y c ,z c );

[0087] The displacement of the semi-submersible ship when loaded with cargo is Δ, the buoyancy center height KB and the x coordinate x F , transverse metacentric radius BM;

[0088] The total number of ballast tanks is N, and the maximum amount of ballast water that can be loaded into the nth ballast tank is B n , Coordinates of the center of gravity of a full ballast tank Bilge z coordinate The lateral moment of inertia of the free liquid surface area about its tilt axis is m n ;

[0089] Rolling rotation radius R, rolling period T and its lower limit T of semi-submersible ship L , Upper limit T U ;

[0090] Minimum initial stability limit GM of semi-submersible vessel when loaded L .

[0091] Step 3: Set decision variables, including:

[0092] θ n It is the ballast coefficient of the nth ballast tank, that is, the ratio of the weight of the ballast water in the ballast tank to the full ballast capacity of the ballast tank.

[0093] Step 4: Construct the initial stability calculation function of the semi-submersible ship corrected by free surface, including:

[0094] When a semi-submersible vessel is loaded with cargo, the formula for the center of gravity height KG of the vessel, cargo, and ballast water as a whole is as follows:

[0095]

[0096] The formula for the correction value FR of the free liquid surface in the ballast tank to the initial stability is as follows:

[0097]

[0098] Where ρ is the density of seawater, α n is an auxiliary variable, and its formula is as follows:

[0099]

[0100] When θ n = 0 or 1, that is, the nth ballast tank is not filled with ballast water or is full of ballast water, and there is no free liquid surface in the tank, which will not cause adverse effects on the stability of the ship;

[0101] When 0<θ n <1, that is, the nth ballast tank is partially filled with ballast water but not full. When the ship tilts, there will be a free liquid surface in the tank, which will generate an additional tilting moment and reduce the initial stability of the ship.

[0102] The formula for the initial stability height GM of a semi-submersible vessel corrected by free surface is as follows:

[0103] GM=KB+BM-KG-FR (4)

[0104] Among them, KB and BM can be determined by the center of buoyancy and metacenter of the hull model at the corresponding displacement.

[0105] Step 5: Establish a ballast water distribution and initial stability optimization model for semi-submersible vessels, including:

[0106] Construct an objective function to maximize the initial stability of special ships in specific operating scenarios:

[0107] max GM(θ n ) (5)

[0108] Limit the displacement of the ship, that is, the sum of the ballast water weight, cargo weight and empty ship weight cannot exceed the displacement of the ship:

[0109]

[0110] Construct the balance constraints in the x and y directions to ensure that the hull floats upright:

[0111]

[0112] The minimum limit constraint of initial stability value:

[0113] GM ≥ GM L (9)

[0114] Characterize the relationship between the ship's rolling period and initial stability:

[0115]

[0116] Ship rolling period constraint:

[0117] T L ≤T≤T U (11)

[0118] Decision variable constraints:

[0119]

[0120] Step 6: Design an efficient and accurate solution method, including the following steps:

[0121] Step 6.1: Linearize KG using the outer approximation method and extract the nonlinear part U from it n :

[0122]

[0123] Will U n The process of converting to a linear piecewise function is as follows. The meanings of the parameters involved in the process are: u n For U n The derivative of They are θ n The maximum and minimum values ​​of ; U n exist and The function value at ; for u n exist The function value at Ψ is U n The set of line segment parameters after conversion into a linear piecewise function; Respectively represent the slope, intercept and horizontal coordinate values ​​of the tangent point of the line segment; K n For U n The number of line segments obtained after linear transformation of Ψ; is the U of the algorithm at the kth iteration n ; is the θ of the kth iteration of the algorithm n ; ε KH is the absolute error of KG; u For U n The absolute error of .

[0124] S1 input U n with un , and make

[0125] S2 judges, if See Figure 3 ,make Go to S6, otherwise go to S3;

[0126] S3 Calculation U n With the point The tangent point between the straight lines is obtained by See formula (14), then Go to S4;

[0127]

[0128] S4 judges, if See Figure 4 , let k=k+1, go to S5, otherwise go to S6;

[0129] S5 Solving get See formula (15). Go to S3;

[0130]

[0131] S6 outputs ψ and ends.

[0132] From the above process, we can get U n The linear piecewise function expression of realizes the linearization of KG:

[0133]

[0134] Among them, the absolute error of KG is ε KG , then U n The allowable deviation is When U n The deviations are all less than ε u When , it can be ensured that the deviation of KG does not exceed ε KG .

[0135] Step 6.2: Linearize FR using piecewise function.

[0136] FR contains discontinuous piecewise functions and introduces continuous piecewise functions β n Characterize discontinuous piecewise functions with inequality constraints:

[0137]

[0138] When 0<θn <1, β n >0, then equation (18) limits α n Only 1 can be selected;

[0139] When θ n =0 or 1, β n = 0, then under the constraint of formula (18) n It can be 0 or 1, combined with the objective function to find the maximum value of formula (3), α n It will tend to be 0.

[0140] For β n , introduce three continuous variables λ n,r (r=1,2,3) and 2 01 variables Convert it to a linear constraint consisting of:

[0141] Building Beta n ,θ n Relationship with newly introduced variables:

[0142]

[0143] Limiting λ n,r The sum is 1:

[0144]

[0145] Requires only one is 1:

[0146]

[0147] Building Lambda n,r and Relationship:

[0148]

[0149]

[0150] Determine the continuous variable λ n,r The range constraints are:

[0151]

[0152] Constrain the value range of the variable:

[0153]

[0154] Step 6.3: Linearize GM constraints.

[0155] When GM<0, there is no feasible solution for the ship's rolling period and initial stability. At this time, the ship has negative stability and is very likely to capsize once disturbed by external forces.

[0156] When GM ≥ 0, constraints (10) and (11) are transformed into linear constraints:

[0157] (2R / T U ) 2 ≤GM≤(2R / T L ) 2 (28)

[0158] Step 6.4: Convert the semi-submersible vessel ballast water distribution and initial stability optimization model into a linear optimization model, including:

[0159] maxGM=KB+BM-KG-FR (29)

[0160]

[0161] Formula (2), (6)-(9), (12), (16), (18)-(28)

[0162] Step 6.5: Call the linear solver to solve the linear optimization model in Step 6.4. In this embodiment, preferably, Gurobi is used to solve the linear optimization model to quickly obtain the optimal solution for ballast water distribution, such as Figure 5 , 6 As shown in Figure 3, and the corresponding maximum initial stability height.

[0163] Step 7: Conduct sensitivity analysis on cargo loading positions, list possible cargo loading positions, optimize the initial stability height of the semi-submersible vessel using Step 4 to Step 6 for each position, and draw a corresponding relationship diagram between cargo loading positions and optimal initial stability height, such as Figure 7 As shown, the optimal loading position of the cargo is marked in the figure.

[0164] The effects of the present invention are further described below through specific application examples.

[0165] In this embodiment, the semi-submersible vessel has a deadweight of 50,000 tons, a length of 228m, a width of 43m, a draft of 13m, an empty ship and various loads weighing 28,900t, and its center of gravity coordinates are (120m, 0m, 11m). There are 85 ballast tanks in the ship, and two stern pontoons at the stern. The displacement of the semi-submersible ship under the designed draft is 82,200t, and the center of buoyancy coordinates are (113m, 0m, 5m); the displacement of the marine platform is 30,000t, and the center of gravity height is 5m. When loaded on the semi-submersible ship, its center of gravity is on the same plumb line as the center of buoyancy of the semi-submersible ship; the upper and lower limits of the semi-submersible ship's rolling period are 9s and 20s, respectively. Solve the initial stability of the semi-submersible ship loaded with the marine platform under the designed draft. The linear solver Gurobi is called by the method of the present invention, and the optimal solution for the ballast water distribution of the semi-submersible ship can be quickly obtained within a few seconds as shown in Table 1; and the maximum value of the initial stability height, as shown in Figure 5 , 6 shown.

[0166] Table 1

[0167]

[0168] The open source nonlinear solver SCIP is selected as a comparison. The method of the present invention is used to call SCIP for solution, and SCIP is used to directly solve the global optimal solution of the nonlinear model in Step 5. The comparison results of the optimization solution quality and efficiency are shown in Table 2. It can be seen from the comparison results that:

[0169] (1) In terms of optimization quality, the difference between the GM obtained by the method of the present invention and the GM obtained by directly solving the nonlinear model is less than 1%, and as the accuracy increases, the difference quickly narrows to be exactly the same.

[0170] (2) In terms of solution efficiency, when SCIP is used, the method of the present invention can shorten the solution time by more than 90%. Using the method of the present invention to call Gurobi can further improve the solution efficiency, shortening the time to less than 2 seconds when the error is less than 0.1%.

[0171] Table 2

[0172]

[0173] A sensitivity analysis was conducted on the loading position of the cargo on the deck of the semi-submersible vessel. The x-coordinate of the cargo was 80 to 140 m, the y-coordinate was -6 to 6 m, and other parameters were the same. The optimization results are shown in Figure 7 Therefore, the recommended loading position is the one with the x-coordinate value of the cargo gravity center of 101.5m and the y-coordinate value of 0m, which can obtain the maximum initial stability value of 3.93m.

[0174] Combined with the above embodiments, the present invention can efficiently explore the initial stability height limit of semi-submersible ships loading heavy items, as well as the optimal ballast water distribution scheme, which is significantly improved in terms of optimization quality and efficiency compared to the prior art. The method of the present invention is also applicable to various types of ships such as floating docks, crane ships, and roll-on / roll-off ships that have ballast tanks and adjust initial stability through ballast water.

[0175] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing ballast water distribution of a semi-submersible vessel for exploring the initial stability limit, characterized in that: include: The proportion of ballast water in each ballast tank is taken as the decision variable, and the maximum initial stability height of the semi-submersible ship after free surface correction is taken as the objective function. The ballast water distribution and initial stability optimization model of semi-submersible vessel is constructed with the constraints of displacement limit, ensuring the hull is floating, initial stability height limit and rolling period limit. Performing linear transformation on the discontinuous piecewise function and the quadratic polynomial in the ballast water distribution and initial stability optimization model of the semi-submersible vessel; The ballast water distribution and initial stability optimization model of the semi-submersible ship after linear transformation is solved, and the initial stability height of the semi-submersible ship after free surface correction and the corresponding ballast water distribution scheme are obtained.

2. The method for optimizing ballast water distribution of a semi-submersible vessel for exploring the initial stability limit according to claim 1, characterized in that: The ratio of ballast water in each ballast tank is used as the decision variable, and the maximum initial stability height of the semi-submersible ship after free surface correction is used as the objective function: max GM(θ n ) Among them, the decision variable θ n is the ballast coefficient of the nth ballast tank, which expresses the ratio of the weight of the ballast water in the ballast tank to the full ballast capacity of the ballast tank; GM is the calculation function of the initial stability height of the semi-submersible ship after free surface correction.

3. The method for optimizing ballast water distribution of a semi-submersible vessel for exploring the initial stability limit according to claim 1, characterized in that: The above-mentioned displacement limitation, ensuring the upright buoyancy of the hull, initial stability height limitation and rolling period limitation include: Displacement Limitation: Balance constraints in the x and y directions to ensure the ship floats upright: The minimum limit constraint of initial stability value: GM≥GM L Characterize the relationship between the ship's rolling period and initial stability: Ship rolling period constraint: T L ≤T≤T U Decision variable constraints:

4. The method for optimizing ballast water distribution of a semi-submersible vessel for exploring the initial stability limit according to claim 1, characterized in that: The non-continuous piecewise function and the quadratic polynomial in the semi-submersible vessel ballast water distribution and initial stability optimization model are linearly transformed, including: The outer approximation method is used to transform the quadratic polynomial associated with the ballast water volume and its center of gravity position in the objective function into multiple linear inequality constraints. The discontinuous piecewise function that describes the influence of free surface on initial stability is transformed into a continuous piecewise function through a conversion method combining continuous piecewise function and inequality, and then the linearized constraint is obtained.

5. A method for optimizing ballast water distribution of a semi-submersible vessel for exploring the initial stability limit according to claim 4, characterized in that: The outer approximation method is used to convert the quadratic polynomial associated with the ballast water volume and its center of gravity position in the objective function into multiple linear inequality constraints, including: Extract the nonlinear part U n : Transform the nonlinear part U by the outer approximation method n , we obtain the linear constraints: in, Respectively represent the slope, intercept and horizontal coordinate values ​​of the tangent point of the line segment; K n For U n The number of line segments is obtained after linear transformation.

6. A method for optimizing ballast water distribution of a semi-submersible vessel for exploring initial stability limits according to claim 4, characterized in that: The conversion method combining continuous piecewise function and inequality to describe the discontinuous piecewise function of the influence of free surface on initial stability is converted into a continuous piecewise function, and then the linearized constraint is obtained, including: Introducing the continuous piecewise function β n With inequality constraints, we can characterize the discontinuous piecewise function in FR: When 0<θ n <1, β n >0, limiting α n Only 1 can be selected; When θ n = 0 or 1, β n =0, under the constraint α n It can be 0 or 1, combined with the requirement of finding the maximum value of the objective function, α n It will tend to be 0.

7. A method for optimizing ballast water distribution of a semi-submersible vessel for exploring initial stability limits according to claim 1, characterized in that: The input parameters of the semi-submersible vessel ballast water distribution and initial stability optimization model include: Semi-submersible vessel’s empty ship weight w s and its centroid coordinates (x s ,y s ,z s ); Loading weight w c and its centroid coordinates (x c ,y c ,z c ); The displacement of the semi-submersible ship when loaded with cargo is Δ, the buoyancy center height KB and the x coordinate x F , transverse metacentric radius BM; Total number of ballast tanks N, maximum ballast water volume of the nth ballast tank B n , Coordinates of the center of gravity of a full ballast tank Bilge z coordinate The lateral moment of inertia of the free liquid surface area about its tilt axis is m n ; Rolling rotation radius R, rolling period T and its lower limit T of semi-submersible ship L , Upper limit T U ; Minimum initial stability limit GM of semi-submersible vessel when loaded with cargo L .

8. A method for optimizing ballast water distribution of a semi-submersible vessel for exploring initial stability limits according to claim 2, characterized in that: The calculation function of the initial stability height of the semi-submersible vessel after free surface correction includes: When a semi-submersible vessel is loaded with cargo, the center of gravity height of the vessel, cargo, and ballast water as a whole is KG: Correction value FR of the free liquid surface in the ballast tank for initial stability: Where ρ is the density of seawater, α n For auxiliary variables: When θ n = 0 or 1, that is, the nth ballast tank is not loaded with ballast water or is full of ballast water, and there is no free liquid surface in the tank; When 0<θ n When <1, the nth ballast tank is partially filled with ballast water but not full. When the ship tilts, there is a free liquid surface in the tank, which generates an additional tilting moment and reduces the initial stability of the ship. The initial stability height GM of the semi-submersible vessel corrected by free surface: GM=KB+BM-KG-FR Among them, KB and BM are determined by the center of buoyancy and metacenter of the hull model at the corresponding displacement.

9. The method for optimizing ballast water distribution of a semi-submersible vessel for exploring the initial stability limit according to claim 1, characterized in that: The ballast water distribution and initial stability optimization model of the semi-submersible ship after the linear transformation is solved by a linear solver to obtain the initial stability height of the semi-submersible ship after free surface correction and the corresponding ballast water distribution plan.

10. The method for optimizing ballast water distribution of a semi-submersible vessel for exploring the initial stability limit according to claim 1, characterized in that: The method of solving the ballast water distribution and initial stability optimization model of the semi-submersible ship after linear transformation to obtain the initial stability height of the semi-submersible ship after free surface correction and the corresponding ballast water distribution scheme also includes: The initial stability height of the semi-submersible ship after free surface correction corresponding to different loading positions of cargo on the semi-submersible ship is solved, and the loading position with the largest initial stability height of the semi-submersible ship after free surface correction is recommended as the optimal loading position, and the corresponding ballast water distribution plan is obtained.

Images