Method for obtaining mechanical parameters of multi-component mooring line

Abstract

The present application relates to a kind of acquisition methods of multi-component mooring cable mechanical parameters, belong to the technical field of anchoring system, especially suitable for known mooring cable composition, length, first position, the problem of solving target point load.This method is divided into four processes, respectively main process, load calculation sub-process, tangent catenary solution sub-process and general catenary solution sub-process.By modeling mooring line, after setting and input corresponding parameters, load calculation, tangent catenary solution and general catenary solution are carried out respectively, and finally the load of mooring cable and attachment connecting point is solved.Compared with existing methods, this method can consider factors such as floater, counterweight, elastic elongation, has wide application range, especially suitable for checking and verifying analysis of design scheme;Calculation process does not need to carry out a large number of formula derivation, and the theoretical method is simple and easy to understand;Calculation method has low requirement for computer resources.

Description

Technical Field

[0001] This invention relates to a method for obtaining the mechanical parameters of multi-component mooring cables, belonging to the technical field of mooring systems. Background Technology

[0002] As human exploration and utilization of the ocean deepens, the sea conditions become increasingly complex, posing significant technological challenges to the floating buoys upon which marine resource development relies. A common problem that must be solved before floating buoys can operate normally is their positioning at sea. Positioning at sea refers to ensuring that the movement of the floating buoy under the influence of wind, waves, and currents does not exceed certain limits, while simultaneously ensuring that the buoy's rolling motion meets the conditions for personnel and equipment operation, and that mooring loads do not damage the buoy's structure. Existing technologies include various methods of positioning at sea, such as anchoring and dynamic positioning. Anchoring is the earliest developed positioning method, and today it has spawned a wide variety of positioning schemes, with extremely broad applications in the field of marine engineering.

[0003] Anchoring and positioning technology involves deploying anchors on the seabed and connecting them to a floating hull using mooring cables. Under the gripping force of the anchors and the gravity of the mooring cables, the floating hull is confined within a certain range. The catenary mooring system is simple in structure, stable and reliable, and relatively less technically challenging, making it the mainstream form of mooring system. In a catenary mooring system, the mooring cable consists of a suspended section and a bottom section. When environmental conditions deteriorate, the floating hull drifts under the influence of wind, waves, and currents, causing the top of the mooring cable to move. This pulls up part of the bottom section's anchor chain, increasing the length and weight of the suspended section and changing its attitude. This leads to increased tension in the mooring cable, resulting in a corresponding increase in the horizontal component of the force acting on the floating hull—that is, an increased horizontal mooring force—to balance the increased environmental load.

[0004] Mooring systems are commonly used in shallow waters, but as marine resource development expands into deeper waters, their application depths are increasing, bringing a series of new challenges. In deep water, excessively long suspended sections lead to increased weight, and larger angles of depression at the top of the suspended section reduce the horizontal force. Therefore, deep-water mooring systems require minimizing the weight of the suspended section while maintaining positioning accuracy, and simultaneously adjusting its attitude. Against this backdrop, composite mooring cables have emerged, using steel or synthetic fiber cables to replace part of the anchor chain to reduce weight; buoys or counterweights are installed within them to adjust the mooring cable's attitude. Because anchor chains, steel cables, and synthetic fibers have different physical properties and therefore different catenary parameters, and because buoys and counterweights alter the catenary's mechanical equilibrium, the calculation and analysis of composite mooring cables are extremely complex.

[0005] With the continuous development of mooring technology, various methods have emerged to solve the computational analysis problems of mooring systems. The catenary model is the fundamental mathematical model for mooring systems, with key parameters including the catenary coefficient, the coordinates of the two connection points, and the linear density. Mooring systems composed of a single component can be simplified and solved analytically, generally meeting engineering requirements. However, for composite mooring cables, the different catenary parameters of each segment and the need for mechanical equilibrium at the connection points make analytical solutions difficult to derive. Currently, numerical methods are commonly used to solve this problem, with piecewise extrapolation being a frequently employed approach. The basic principle of piecewise extrapolation is: assuming the mooring cable is always in static equilibrium, the complete mooring cable is discretized into N elements. The parameters of each element are calculated from bottom to top, proceeding sequentially based on the connection relationships between elements until the endpoint is reached, yielding the final result. The accuracy of this method is related to the number of elements N, and error accumulation occurs during the extrapolation process.

[0006] Many existing commercial software programs have mooring cable analysis functions, but due to the limitations of the software's functional settings, users cannot perform model calculations of the mechanical parameters of mooring cables as needed. Summary of the Invention

[0007] In view of this, the present invention proposes a method for obtaining the mechanical parameters of a multi-component mooring cable. This method is applicable to solving the load at the connection point between the mooring cable and the float when the current state of the mooring cable is known.

[0008] A method for obtaining the mechanical parameters of a multi-component mooring cable includes the following steps:

[0009] Step 1: Treat the actual anchor chain and cable as homogeneous chains, and the float and weight as concentrated loads;

[0010] Step 2: Set the initial step size and allowable step size error, and select two initial feasible points;

[0011] Step 3: Based on the current step size, generate n test points within each range of the two initial feasible points. Select one test point from each range to form a group, resulting in a total of n groups of test points. Remove groups where the straight-line distance between two points is greater than the length of the homogeneous chain between them, thus obtaining multiple groups of valid test points. Use the two initial feasible points and each group of valid test points as homogeneous chain connection points, and calculate the load error of the two initial feasible points and each group of valid test points.

[0012] Step 4: Take the group corresponding to the minimum load error as the target group, and determine whether the minimum load error is less than the load error of the two initial feasible points. If it is less, the test point in the target group is taken as the new initial feasible point, and return to step 3; otherwise, proceed to step 5.

[0013] Step 5: Determine if the step size of the current target group is greater than the allowable step size error. If it is, reduce the step size and execute Step 3; otherwise, calculate the load at the current homogeneous chain connection point to obtain the mechanical parameters of the mooring cable.

[0014] Furthermore, the calculation of the load error includes the following steps:

[0015] Step 1: Divide the homogeneous chain into three segments according to the connection point of the homogeneous chain, calculate the catenary coefficient of the first, second and third segments of the homogeneous chain, and the coordinates of the bottom point of the first segment of the homogeneous chain. The first segment of the homogeneous chain is divided into two segments: the overhang segment and the bottom segment.

[0016] Step 2: Calculate the loads at the upper and lower connection points of each segment of the homogeneous chain based on the catenary coefficient and the coordinates of the bottom point of the first segment of the homogeneous chain.

[0017] Step 3: Based on the loads at the upper and lower connection points of each homogeneous chain segment, calculate the absolute value of the load difference between the upper and lower connection points, and add the load differences between the upper and lower connection points to obtain the load error.

[0018] Further, the coordinates of the bottom point and the catenary coefficient of the first homogeneous chain undercover segment are calculated, including the following steps:

[0019] Step 101: Calculate the catenary coefficient of the first homogeneous chain bottom section;

[0020] Set the allowable error of the tilt angle and the initial upper connection point coordinates of the first homogeneous chain. Establish a rectangular coordinate system with the anchor point of the homogeneous chain as the origin, the horizontal direction as the x-axis, and the direction perpendicular to the horizontal direction as the y-axis. Take any bottom point position coordinates in the positive x-axis direction, and satisfy the condition that the distance from the anchor point to the bottom point plus the straight-line distance from the bottom point to the upper connection point of the first homogeneous chain is less than the length of the first homogeneous chain. Calculate the catenary coefficient of the first homogeneous chain.

[0021] Step 102: Calculate the tilt angle of the bottom point of the first homogeneous chain based on the catenary coefficient;

[0022] According to the following formula:

[0023]

[0024] Where θ is the inclination angle of the undercover point, (x, y) are the coordinates of the undercover point, and a is the catenary coefficient. The inclination angle θ of the undercover point is calculated using the above formula.

[0025] Step 103: Determine the magnitude and sign of the tilt angle of the undercover point to obtain the coordinates of the undercover point;

[0026] Determine the magnitude and sign of the tilt angle of the undercover point. If the absolute value of the tilt angle is not less than the allowable tilt angle error and the sign of the tilt angle is negative, then reduce the coordinates of the undercover point by a fixed ratio of 80% and then execute steps 102 to 103. If the absolute value of the tilt angle is not less than the allowable tilt angle error and the sign of the tilt angle is positive, then increase the coordinates of the undercover point by a fixed ratio of 120% and then execute steps 102 to 103. If the absolute value of the tilt angle is less than the allowable angle error, then the current coordinates of the undercover point are the coordinates of the undercover point of the first mooring cable.

[0027] Furthermore, the catenary coefficient of the first, second, or third segment of the mooring cable is calculated, wherein the calculation of the catenary coefficient of each segment of the mooring cable includes the following steps:

[0028] Step 1) Calculate the horizontal and vertical relative distances between the two connection points based on the initial coordinates of the two connection points of this mooring cable segment. Set the allowable error for length, the allowable error for the length and position of this mooring cable segment, and arbitrarily select a catenary coefficient value 'a'.

[0029] Step 2) Coordinate system transformation: Establish a local coordinate system with the lowest point of the lower extension of this mooring cable as the origin, the horizontal direction as the x-axis, and the vertical direction as the y-axis. Transform the coordinates of each point to this local coordinate system, and take any point on the x-axis of this coordinate system as the first x-coordinate. L ;

[0030] Step 3) First x-coordinate L The lateral relative distance between the two connection points of this mooring cable segment is denoted as the second x-coordinate. R Substitute the first and second x-coordinates into the x-coordinate in the following formula:

[0031]

[0032] The solution is given by y. L and y R ;

[0033] Step 4) Calculate the longitudinal relative distance between the two initial connection points, and calculate y. L and y R The vertical relative distances are calculated, and the absolute value of the difference between the two relative distances is compared with the positional tolerance. If the absolute value of the difference between the two relative distances is not less than the positional tolerance, then the first horizontal coordinate x is reduced. L Then proceed to steps 3)-4); otherwise proceed to step 5.

[0034] Step 5) According to the formula:

[0035]

[0036] Where L represents (x L ,y L ) to (x R ,y R The arc length between L and the length of the mooring cable segment is compared with the absolute value of the difference between L and the length of the mooring cable segment. If the absolute value of the difference between L and the length of the mooring cable segment is not less than the length allowable error, the catenary coefficient value a is reduced. If the absolute value of the difference between L and the length of the homogeneous chain segment is less than the length allowable error, the current catenary coefficient value a is the catenary coefficient value of the homogeneous chain segment.

[0037] Furthermore, in step two, two initial feasible points are randomly selected within the initial coordinate system. The initial coordinate system is established with the anchor point of the homogeneous chain as the origin, the direction pointing horizontally towards the buoy as the positive x-axis, and the direction opposite to the direction of gravity as the positive y-axis.

[0038] Furthermore, the load at the homogeneous chain connection point includes the loads on the x-axis and y-axis of the connection point between the mooring cable and the float.

[0039] Furthermore, in step five, it is determined whether the step size of the current target group is greater than the allowable step size error. If it is, the step size is reduced. The step size is reduced by the golden section method or the bisection method.

[0040] Beneficial effects:

[0041] 1. In simplifying the model, this method treats both the float and the counterweight as concentrated loads. Compared with other existing methods, this method considers the forces on the float and the counterweight, which is closer to the actual stress situation of the mooring cable and has higher calculation accuracy.

[0042] 2. This method is simple in calculating the inclination angle of the bottom point and the arc length of the mooring cable, and does not require a lot of formula derivation. Compared with existing methods, this method has less computation and is simple to implement.

[0043] 3. This method involves relatively little computation and has a simple theoretical basis. When run on a computer, it consumes fewer computer resources and is more economical.

[0044] 4. This method uses the anchor point of the homogeneous chain as the origin when establishing the initial coordinate system, which reduces the amount of computation, simplifies the calculation process, and makes it easy to replicate. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of the three-segment combined mooring cable according to an embodiment of the present invention.

[0047] Figure 2 This is a schematic diagram of the force analysis at point P2 in an embodiment of the present invention.

[0048] Figure 3 This is a schematic diagram of the force analysis at point P3 in an embodiment of the present invention.

[0049] Figure 4 This is a schematic diagram of the main flow of the method for calculating the status parameters of mooring cables according to an embodiment of the present invention.

[0050] Figure 5 This is a schematic diagram of the load calculation sub-process of an embodiment of the present invention.

[0051] Figure 6 This is a schematic diagram of the sub-process for solving the tangent catenary in an embodiment of the present invention.

[0052] Figure 7 This is a schematic diagram of a typical catenary solution process in an embodiment of the present invention. Detailed Implementation

[0053] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0054] This embodiment presents a method for obtaining the mechanical parameters of multi-component mooring cables. This method is particularly suitable for solving problems involving mechanical parameters and attitude when the composition, length, and start and end positions of the mooring cable are known. (See attached diagram.) Figure 1 As shown, this embodiment uses a three-section combined mooring cable containing a float and a counterweight as an example to explain in detail the implementation steps of this calculation method. The force states of points P2 and P3 are shown in the attached figures. Figure 2 , Figure 3 As shown, in this embodiment, the process can be divided into four steps according to function and purpose: main process, load calculation subprocess, tangent catenary solution subprocess, and general catenary solution subprocess.

[0055] (I) Main process, as attached Figure 4 As shown, the main calculation steps are as follows:

[0056] Step 1: Modeling the mooring cable: Treat the actual anchor chain and cable as homogeneous chains, and the float and weight as concentrated loads;

[0057] By simplifying the floats and counterweights into either concentrated or distributed loads, and the actual anchor chains and cables into homogeneous chains, a simplified catenary model is obtained. The problem is simplified to: given the lengths and weights of each component of the combined mooring cable, and the coordinates of the anchor points and end positions of the mooring cable, solve for the coordinates of each connection point, the mechanical parameters of the end position, and determine the catenary attitude, then calculate the mechanical parameters of the end position.

[0058] The combined mooring cable calculated in this embodiment consists of three segments with different characteristics. The first segment is divided into a bottom section and a suspended section, while the second and third segments are both suspended sections. A coordinate system is established with the anchor point as the origin, the horizontal direction pointing towards the float as the positive x-axis, and the direction opposite to the direction of gravity as the positive y-axis. The bottom point is denoted as P1(x1, 0), the connection point between the first and second segments is denoted as P2(x2, y2), the connection point between the second and third segments is denoted as P3(x3, y3), and the connection point between the third segment and the float is denoted as P4(x4, y4). The linear density (mass per unit length) and segment lengths of the three segments are represented as m1, S1, m2, S2, m3, and S3, respectively. A counterweight is installed at point P2, and the force exerted by the counterweight is denoted as F2; ​​a float is installed at point P3, and the force exerted by the float is denoted as F3. The force states at points P2 and P3 are as follows: Figure 2 , Figure 3 As shown. Since the counterweight and float do not require separate sections, the catenary is divided into three sections in total.

[0059] Step 2: Set the initial step size and allowable step size error, and select two initial feasible points;

[0060] This method sets an initial step size value st and a step size allowable error [st]. The step size allowable error is used to determine whether to end the search. It can be determined according to the accuracy requirements of the position coordinate calculation. In order to reduce the computational burden, the step size is generally set to be large and greater than the step size allowable error. Then, by narrowing the search range, the final solution to the problem is obtained.

[0061] The load at a point (x, y) on the catenary is:

[0062] F x =a·ρ·g

[0063]

[0064] Step 3: Based on the current step size, generate n test points within each range of the two initial feasible points. Select one test point from each range to form a test point group, resulting in a total of n test point groups. Remove groups where the straight-line distance between two points is greater than the length of the homogeneous chain between the two points, resulting in multiple effective test point groups. Use each group of test points as the connection point of the homogeneous chain and calculate the load error of the test points within each group.

[0065] Based on the geometric relationship of the three mooring cable segments, arbitrarily select a set of data from the feasible region as the position coordinates of points P2 (x2, y2) and P3 (x3, y3). Calculate the load difference under this state, denoted as the current load error dF. The current load error is used to determine whether mechanical equilibrium has been reached. For details on the load error calculation steps, please refer to the load calculation sub-flow.

[0066] Centered on P2(x2, y2) and P3(x3, y3) respectively, n test points are generated according to a step size st and certain rules. Based on geometric constraints, invalid test points are eliminated, retaining only valid ones. The rules for generating test points can be random number generation, the golden section method, etc. The distribution range of the generated test points should be directly related to the step size; therefore, the step size can be used as a basis for judging the distribution range of the test points.

[0067] Each test point is used as the position coordinate of point P2 and P3, respectively, and the load error {dF} under the corresponding state is calculated. The load error calculation steps are detailed in the load calculation sub-flow.

[0068] Step 4: Take the group corresponding to the minimum load error as the target group, and determine whether the minimum load error is less than the load error of the two initial feasible points. If it is less, the test point in the target group is taken as the new initial feasible point, and return to step 3; otherwise, proceed to step 5.

[0069] Based on the mechanical equilibrium conditions, determine whether the current calculation results meet the requirements and decide on the next step. Check if the minimum load error min({dF}) calculated from each set of test points is less than the current load error dF. If it is less, it means that at least one set of data among the test points is closer to the correct result than the determined position coordinates of points P2 and P3. The test point corresponding to the minimum load error should be used as the new position coordinates of points P2 and P3, and the minimum load error should be recorded as the new current load error, i.e., dF = min({dF}). Then proceed to step three. If it is not less, it means that no result more accurate than the determined position coordinates of points P2 and P3 was found within the search range. Proceed to step five.

[0070] Step 5: Determine if the step size of the current target group is greater than the allowable step size error. If it is, reduce the step size and execute Step 3; otherwise, calculate the load at the current homogeneous chain connection point to obtain the mechanical parameters of the mooring cable.

[0071] Determine if the current step size value st is greater than the allowable step size error [st]. If it is, it means that the distribution range of the test points is greater than the allowable accuracy and does not meet the calculation requirements. The next step is to reduce the step size value according to certain rules and then execute step three. The rules for reducing the step size value can be the bisection method, the golden section method, etc.

[0072] If the step size value st is not greater than the step size allowable error [st], it means that the distribution range of the test points is not greater than the allowable accuracy, which can meet the calculation requirements. The current position coordinates P2(x2, y2) and P3(x3, y3) are the final coordinates of points P2 and P3.

[0073] Based on the final coordinates of points P2 and P3, the state parameters of each segment of the mooring cable are further calculated to complete the calculation process.

[0074] (II) Load calculation sub-process, as shown in the appendix Figure 5 As shown, the detailed calculation steps are as follows:

[0075] The load calculation sub-process calculates the load at the connection points of each segment based on the parameters and coordinates of each segment, analyzes the load error at points P2 and P3, and outputs the load error for use in the main process steps.

[0076] Step 1: Divide the mooring cable model into three segments based on the homogeneous chain connection points. Calculate the coordinates of the bottom point and the catenary coefficient of the first segment of the mooring cable, and the catenary coefficients and connection point coordinates of the second and third segments of the mooring cable. The first segment is divided into a bottom segment and a suspended segment. Based on the input parameters, calculate the attitude of the suspended segment of the mooring cable between the bottom point P1 and P2. For details of the calculation steps, please refer to the tangent catenary solver sub-flow. The second and third segments are suspended segments. Based on the input parameters, calculate the attitude of the mooring cable for each suspended segment in sequence. For details of the calculation steps, please refer to the general catenary solver sub-flow.

[0077] Step 2: Calculate the loads at the upper and lower connection points of each mooring cable segment based on the catenary coefficient and the coordinates of the bottom point of the first homogeneous chain segment.

[0078] Calculate the load at each connection point based on the attitude of each mooring cable segment:

[0079] The x-direction and y-direction loads at connection point P2 on the first mooring cable are denoted as Fx2-s1 and Fy2-s1, respectively.

[0080] The x-direction and y-direction loads at the lower connection point P2 of the second mooring cable are denoted as Fx2-s2 and Fy2-s2, respectively.

[0081] The x-direction and y-direction loads at connection point P3 on the second mooring cable are denoted as Fx3-s2 and Fy3-s2, respectively.

[0082] The x-direction and y-direction loads at the lower connection point P3 of the third mooring cable are denoted as Fx3-s3 and Fy3-s3, respectively.

[0083] Step 3: Based on the loads at the upper and lower connection points of each mooring cable segment, calculate the absolute value of the load difference between each upper and lower connection point, and add the load differences between each upper and lower connection point to obtain the load error.

[0084] Since the results obtained in the current calculation steps are inaccurate, points P2 and P3 cannot reach the mechanical equilibrium condition, and the load error needs to be calculated.

[0085] Subtract the loads acting on the same point in different directions from each other, and subtract the counterweight load F2 and the buoyancy load F3. Sum the absolute values ​​of the load differences to get the load difference at each point, i.e.:

[0086] Load difference at point P2: dF2=|Fx2-s1-Fx2-s2|+|Fy2-s1-Fy2-s2-F2|;

[0087] Load difference at point P3: dF3=|Fx3-s2-Fx3-s3|+|Fy3-s2-Fy3-s3+F3|.

[0088] The sum of the load differences between points P2 and P3, dF = dF2 + dF3, is taken as the final output of this process.

[0089] (III) Sub-process for solving tangent catenary curves, as shown in the appendix. Figure 6 As shown, the detailed calculation steps are as follows:

[0090] The tangent catenary solver can be used to calculate the coordinates of the bottom point and the catenary coefficient of the suspended section of the mooring cable. Since the first section of the mooring cable is divided into a bottom section and a suspended section, the bottom section between the anchor point and the bottom point is considered to be laid flat on the seabed and does not need to be calculated. The suspended section between the bottom point and point P2 needs to be calculated according to the catenary model, so the position of the bottom point P1 needs to be determined first.

[0091] Step 101: Calculate the catenary coefficient of the first mooring cable segment;

[0092] Set the allowable error of the tilt angle and the initial upper connection point coordinates of the first mooring cable. Establish a rectangular coordinate system with the anchor point of the mooring cable model as the origin, the horizontal direction as the x-axis, and the direction perpendicular to the horizontal direction as the y-axis. Take any bottom point position coordinates in the positive x-axis direction, and satisfy the condition that the distance from the anchor point to the bottom point plus the straight-line distance from the bottom point to the upper connection point of the first mooring cable is less than the length of the first mooring cable. Calculate the catenary coefficient of the first mooring cable.

[0093] Establish a coordinate system with the lowest point of the catenary as the origin. The standard equation of the catenary can be written as:

[0094]

[0095] 'a' is the catenary coefficient, which determines the shape of the catenary;

[0096] In this calculation, an arbitrary coordinate of the bottom point is selected in the positive x-axis direction. The first segment of the mooring cable should smoothly transition to the seabed mud surface in a tangential manner. Therefore, the calculated angle at the bottom point can be used as the basis for judging whether the result meets the error requirements. An appropriate value is taken as the allowable error for the calculated angle of the bottom point, such as 0.01°. In the calculation, an initial value needs to be determined first. Based on the coordinates of the anchor point and point P2, an appropriate bottom point coordinate P1(x1, 0) is estimated to ensure that the mooring cable is continuous and meets the conditions for catenary calculation. The length of the suspended segment is calculated as: S = S1 - x1. The attitude of the suspended mooring cable is calculated. For the calculation steps, please refer to the general catenary solution sub-flow.

[0097] Step 102: Calculate the inclination angle of the bottoming point of the first mooring cable segment based on the catenary coefficient;

[0098] According to the following formula:

[0099]

[0100] Where θ is the inclination angle of the undercover point, (x, y) are the coordinates of the undercover point, and a is the catenary coefficient. The inclination angle θ of the undercover point is calculated using the above formula.

[0101] Step 103: Determine the magnitude and sign of the tilt angle of the undercover point to obtain the coordinates of the undercover point;

[0102] Determine the magnitude and sign of the tilt angle of the undercover point. If the absolute value of the tilt angle is not less than the allowable tilt angle error and the sign of the tilt angle is negative, then reduce the coordinates of the undercover point by a fixed ratio of 80% and then execute steps 2-3. If the absolute value of the tilt angle is not less than the allowable tilt angle error and the sign of the tilt angle is positive, then increase the coordinates of the undercover point by a fixed ratio of 120% and then execute steps 2-3. If the absolute value of the tilt angle is less than the allowable angle error, then the current coordinates of the undercover point are the coordinates of the undercover point of the first mooring cable.

[0103] The coordinates of the undercover point used in the current calculation are inaccurate, so the calculated lower end of the suspended section is not tangent to the undercover point. Furthermore, since the sign of the inclination angle at the lower connection point of the suspended section corresponds to the direction of correction of the undercover point's coordinates, the next step to be performed needs to be determined based on the magnitude and sign of the inclination angle at the lower connection point.

[0104] 1) If the absolute value of the tilt angle is not less than the allowable angle error, it means that the calculation result error is greater than the allowable angle error, and the coordinates of the undercover point need to be corrected. The correction method is as follows:

[0105] a) If the tilt angle is negative, it indicates that the suspended section is too short, and the lower end of the suspended section forms an obtuse angle with the bottom section, which does not meet the mechanical equilibrium conditions. The coordinates of the bottom point need to be reduced according to certain rules to obtain the corrected x1, and then step 3 can be executed. The reduction rule can be to reduce by a fixed ratio, such as the current coordinate value × 80%, or to use methods such as Newton's method or the bisection method.

[0106] b) If the tilt angle sign is positive, it indicates that the suspended section is too long, and part of the mooring cable has fallen below the seabed mud surface. The coordinates of the bottom point need to be increased according to certain rules to obtain the corrected x1, and then step 3 can be executed. The increase rule can be to increase by a fixed ratio, such as the current coordinate value × 120%, or by using Newton's method, the dichotomy method, etc.

[0107] 2) If the absolute value of the tilt angle is less than the allowable angle error, it means that the error of the calculation result is less than the allowable angle error. The current position coordinates of the undercover point and the corresponding catenary coefficient are the final results under this input condition.

[0108] (iv) General catenary solution process, as shown in the appendix. Figure 7 As shown, the detailed calculation steps are as follows:

[0109] The general catenary calculation method is based on this approach. It is used to solve for the catenary attitude parameters, i.e., the catenary coefficients, when the coordinates of two points and the length of the catenary between them are known. The input parameters for this process are: the x and y coordinates of the two points, and the actual length s of the catenary between the two points.

[0110] Step 1: Calculate the horizontal and vertical relative distances between the two connection points based on the initial coordinates of the first, second, or third mooring cable segments. Set the allowable error for length, the allowable error for the length and position of this mooring cable segment, and arbitrarily select a catenary coefficient value 'a'.

[0111] The calculation uses the catenary length and the coordinates of the two connection points as the basis for convergence judgment. Therefore, the allowable error of the catenary length [s] and the allowable error of the position [y] must be input first, and an arbitrary feasible catenary coefficient a can be selected as the initial value for the calculation.

[0112] Step 2: Transform the coordinate system: Take the lowest point of the lower extension line of the first, second or third mooring cable as the origin, establish a local coordinate system with the x-axis in the horizontal direction and the y-axis in the vertical direction, and take any point on the x-axis in this coordinate system as the first abscissa xL;

[0113] The parameters defined in the above calculation steps are all values ​​in the global coordinate system. To reduce the number of calculation variables, a coordinate transformation is required: A coordinate system is established with the lowest point of the extended lower end of the suspended mooring cable as the origin, and the horizontal and vertical directions as the x-axis and y-axis, respectively. The input parameters are transformed from the original global coordinate system to this local coordinate system. All subsequent calculation steps are performed in this local coordinate system. An arbitrary x-coordinate xL is selected in the local coordinate system as the initial value for calculating the x-coordinate of the left-side point.

[0114] Step 3, First x-coordinate L Add the lateral relative distance between the two connection points of the mooring cable segment, denoted as the second abscissa xR, and substitute the first and second abscissas into x in the following formula:

[0115]

[0116] The solution is given by y. L and y R ;

[0117] Step 4: Calculate the longitudinal relative distance between the two initial connection points, and calculate y. L and y R The vertical relative distance is compared with the absolute value of the difference between the two relative distances and the positional error. If the absolute value of the difference between the two relative distances is not less than the positional error, the first horizontal coordinate xL is reduced by the golden section method or the bisection method, and then steps 3-4 are executed. If the absolute value of the difference between the two relative distances is less than the positional error, then step 5 is executed.

[0118] The longitudinal relative positions of the two points obtained in the previous step were calculated based on the current catenary coefficient, which is inaccurate. It is necessary to determine the relative error and decide on the next step. Calculate the longitudinal relative distance between the two points obtained in the previous step, the initial longitudinal relative distance between the two points input for this process, and calculate the absolute value of the difference between the two relative distances, which is recorded as the current position error.

[0119] 1) Determine if the current position error is less than the allowable position error [y]. If it is not less, it means that the x-coordinate of the current left point is unreasonable and needs to be corrected. After correction, proceed to step 4. Correction methods can include the golden section method, Newton's method, or the bisection method, etc.

[0120] 2) Determine if the current position error is less than the position allowable error [y]. If it is less, it means that the value of the horizontal coordinate of the current left point is reasonable and the relative position of the two points is consistent with the relative position of the two points initially input into the process. Step 5 can then be executed.

[0121] Step 5: According to the formula:

[0122] The formula for calculating the arc length between a point (x, y) on a catenary and the origin is:

[0123]

[0124]

[0125] Where L represents (x L ,y L ) to (x R ,y R The arc length between ); ρ is the linear density, that is, the mass per unit length of the catenary. Compare the absolute value of the difference between L and the length of the current mooring cable segment with the length allowable error. If the absolute value of the difference between L and the length of the current mooring cable segment is not less than the length allowable error, then the catenary coefficient value a is reduced by the golden section method or the bisection method. If the absolute value of the difference between L and the length of the current mooring cable segment is less than the length allowable error, then the current catenary coefficient value a is the catenary coefficient value of the first, second or third mooring cable segment, and then proceed to step 6.

[0126] Once the relative positions of the two points are determined, the length of the catenary between them depends only on the catenary coefficient. Therefore, the catenary length can be compared with the actual length to determine the next step. Calculate the catenary length L between the two points based on the catenary coefficient. Determine whether the absolute value of the difference between the catenary length L and the actual length s is less than the allowable length error [s].

[0127] 1) If it is not less than, it means that the deviation between the catenary length L and the actual length s between the two points is large, the catenary coefficient is inaccurate, the catenary coefficient needs to be corrected, and then step 4 is executed; the correction method can be the golden section method, Newton's method or the bisection method.

[0128] 2) If it is less than, it means that the deviation between the catenary length L and the actual length s between the two points is small, which meets the calculation requirements, the catenary coefficient is accurate, and the current catenary coefficient a and the coordinates of the two points (x, s, s) are... L ,y L ) and (x R ,y R The result is the calculation result.

[0129] Step 6, (x) L ,y L ) and (x R ,y R Once the coordinates of the two points are transformed to the original coordinate system, the transformed coordinates will be the coordinates of the two connection points of the first, second, or third mooring cable segment.

[0130] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for obtaining the mechanical parameters of a multi-component mooring cable, characterized in that, Includes the following steps: Step 1: Treat the actual anchor chain and cable as homogeneous chains, and the float and weight as concentrated loads; Step 2: Set the initial step size and allowable step size error, and select two initial feasible points; Step 3: According to the current step size, generate n test points within each range centered on the two initial feasible points. Select one test point from each range to form a group, resulting in a total of n groups of test points. Remove groups where the straight-line distance between two points is greater than the length of the homogeneous chain between the two points, thus obtaining multiple groups of valid test points; Using two initial feasible points and each group of effective test points as homogeneous chain connection points, calculate the load error of the two initial feasible points and each group of effective test points; Step 4: Take the group corresponding to the minimum load error as the target group, and determine whether the minimum load error is less than the load error of the two initial feasible points. If it is less, the test point in the target group is taken as the new initial feasible point, and return to step 3; otherwise, proceed to step 5. Step 5: Determine if the step size of the current target group is greater than the allowable step size error. If it is, decrease the step size and execute Step 3; otherwise, calculate the load at the current homogeneous chain connection point to obtain the mechanical parameters of the mooring cable. The calculation of the load error includes the following steps: Step 1: Divide the homogeneous chain into three segments according to the connection point of the homogeneous chain, calculate the catenary coefficient of the first, second and third segments of the homogeneous chain, and the coordinates of the bottom point of the first segment of the homogeneous chain. The first segment of the homogeneous chain is divided into two segments: the overhang segment and the bottom segment. Step 2: Calculate the loads at the upper and lower connection points of each segment of the homogeneous chain based on the catenary coefficient and the coordinates of the bottom point of the first segment of the homogeneous chain. Step 3: Based on the loads at the upper and lower connection points of each homogeneous chain segment, calculate the absolute value of the load difference at each upper and lower connection point, and add the load differences at each upper and lower connection point to obtain the load error. Calculate the catenary factor for the first, second, or third segment of the mooring cable. The calculation of the catenary factor for each segment of the mooring cable includes the following steps: Step 1) Calculate the horizontal and vertical relative distances between the two connection points based on the initial coordinates of the two connection points of this mooring cable segment. Set the allowable error for length, the allowable error for the length and position of this mooring cable segment, and arbitrarily select a catenary coefficient value. ; Step 2) Coordinate system transformation: Establish a local coordinate system with the lowest point of the lower extension of this mooring cable as the origin, the horizontal direction as the x-axis, and the vertical direction as the y-axis. Transform the coordinates of each point to this local coordinate system, and take any point on the x-axis of this coordinate system as the first abscissa xL; Step 3) Add the first horizontal coordinate xL to the lateral relative distance between the two connection points of this mooring cable segment, and denote the second horizontal coordinate xR. Substitute the first and second horizontal coordinates into the x in the following formula: The solutions are denoted as yL and yR respectively. Step 4): Calculate the initial longitudinal relative distance between the two connection points. Calculate the longitudinal relative distances yL and yR. Compare the absolute value of the difference between the two relative distances with the positional error. If the absolute value of the difference between the two relative distances is not less than the positional error, then reduce the first abscissa xL and execute steps 3)-4); otherwise, execute step 5). Step 5) According to the formula: in, express arrive Compare The absolute value of the difference between the length of this section of the mooring cable and the allowable length error, if If the absolute value of the difference between the length of this section of the mooring cable and the length of the current section is not less than the allowable length error, then the catenary coefficient value should be reduced. ,like If the absolute value of the difference between the current homogeneous chain segment and the current catenary coefficient is less than the allowable length error, then the current catenary coefficient value is... This is the catenary coefficient value of the homogeneous chain in this segment.

2. The method as described in claim 1, characterized in that, The calculation of the coordinates of the bottom point and the catenary coefficient of the first homogeneous chain bottom segment includes the following steps: Step 101: Calculate the catenary coefficient of the first homogeneous chain bottom section; Set the allowable error of the tilt angle and the initial upper connection point coordinates of the first homogeneous chain. Establish a rectangular coordinate system with the anchor point of the homogeneous chain as the origin, the horizontal direction as the x-axis, and the direction perpendicular to the horizontal direction as the y-axis. Take any bottom point position coordinates in the positive x-axis direction, and satisfy the condition that the distance from the anchor point to the bottom point plus the straight-line distance from the bottom point to the upper connection point of the first homogeneous chain is less than the length of the first homogeneous chain. Calculate the catenary coefficient of the first homogeneous chain. Step 102: Calculate the tilt angle of the bottom point of the first homogeneous chain based on the catenary coefficient; According to the following formula: in, Let (x, y) be the inclination angle of the undercover point, and (x, y) be the coordinates of the undercover point. The catenary coefficient is used to calculate the inclination angle of the base point using the above formula. ; Step 103: Determine the magnitude and sign of the tilt angle of the undercover point to obtain the coordinates of the undercover point; Determine the magnitude and sign of the tilt angle of the undercover point. If the absolute value of the tilt angle is not less than the allowable tilt angle error and the sign of the tilt angle is negative, then reduce the coordinates of the undercover point by a fixed ratio of 80% and then execute steps 102 to 103. If the absolute value of the tilt angle is not less than the allowable tilt angle error and the sign of the tilt angle is positive, then increase the coordinates of the undercover point by a fixed ratio of 120% and then execute steps 102 to 103. If the absolute value of the tilt angle is less than the allowable angle error, then the current coordinates of the undercover point are the coordinates of the undercover point of the first mooring cable.

3. The method as described in claim 1, characterized in that, In step two, two initial feasible points are randomly selected within the initial coordinate system. The initial coordinate system is established with the anchor point of the homogeneous chain as the origin, the direction pointing horizontally towards the buoy as the positive x-axis, and the direction opposite to the direction of gravity as the positive y-axis.

4. The method according to any one of claims 1-3, characterized in that, The load at the homogeneous chain connection point includes the loads on the x-axis and y-axis of the connection point between the mooring cable and the float.

5. The method as described in claim 1, characterized in that, In step five, it is determined whether the step size of the current target group is greater than the allowable step size error. If it is, the step size is reduced. The step size is reduced by the golden section method or the bisection method.

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