An analysis method for the tension response of ship mooring ropes

Abstract

The present invention discloses an analysis method for the tension response of a mooring cable at a ship dock, which relates to the field of mooring cable tension modeling and analysis, and includes the following steps: S1, establishing a dynamic model of mooring cable tension and deformation; S2, recording mooring cable tension and monitoring the mooring cable deformation at the corresponding moment; S3, setting a safety factor, and performing early warning processing when the deformation exceeds the safety factor. The present invention provides a new modeling method for the tension deformation of a mooring cable at a ship dock, and the model in the present invention reflects the physical mechanism of the mooring cable, and the model is more accurate.

Description

Technical Field

[0001] The invention relates to a mooring cable tension modeling and analysis method, in particular to an analysis method for the tension response of a ship dock mooring cable. Background Art

[0002] Due to the effects of wind, current and waves, the tension of mooring cables changes randomly. Under the action of tension, mooring cables will deform. When the deformation exceeds a certain limit, they may break, causing serious marine damage and posing hidden dangers to the safe production of docks. Studying the relationship between the tension and response of dock mooring cables is the basis for the design and safe use of mooring cables. Therefore, establishing a dock mooring cable model and analyzing the response of the cable under tension are the key to the safety analysis of mooring cables and the basis for predicting the dynamic response of ships.

[0003] At present, a tension model based on Hooke's law has been proposed. By simulating the movement of an object within a certain range to make it close to the actual movement of the actual object, mathematical analysis can be performed. However, Hooke's law can only show that the displacement of an ideal elastic body is proportional to the force within the elastic limit. Based on this, the elastic body performs ideal simple harmonic motion after the external force is lost. However, due to uncertain factors such as materials, processes, and environment, ideal environments and ideal elastic bodies do not exist. For example, due to the influence of factors such as wind, flow, waves, and tides, the tension changes accordingly over time. Therefore, this model cannot accurately study the tension of moored ship cables and the corresponding deformation under tension. Summary of the invention

[0004] Purpose of the invention: In view of the above-mentioned prior art, a method for analyzing the tension response of ship dock mooring cables is proposed.

[0005] Technical solution: A method for analyzing the tension response of a ship dock mooring cable, comprising the following steps:

[0006] S1, establish a dynamic model of mooring cable tension and deformation;

[0007] S2, recording the tension of the mooring cable, and outputting the deformation of the mooring cable at the corresponding moment through the model;

[0008] S3, set the safety factor, and when the deformation exceeds the safety factor, perform early warning processing.

[0009] Furthermore, in step S1, the process of establishing the dynamic model includes the following steps:

[0010] S11, establish the mooring cable tension and deformation fractional differential model:

[0011]

[0012] Where f(t) represents the tension of the mooring cable at time t, δ(t) represents the deformation of the mooring cable under the tension f(t), and k represents an undetermined constant. represents the α-order Caputo fractional differential of f(t), and its definition expression is:

[0013]

[0014] Where Γ(·) represents the gamma function, is the integral independent variable;

[0015] S12, using the sampled data, identifying the parameter k and the parameter α in step S11, obtaining the optimal parameter values ​​of the parameter k and the parameter α, and obtaining the optimal model.

[0016] Furthermore, in step S12, the process of obtaining optimal parameter values ​​of mooring line tension and deformation includes the following steps:

[0017] S121, converting the fractional order differential model in step 11 into a fractional order integral model:

[0018]

[0019] in, represents the α-order fractional integral of δ(t);

[0020] Defined as:

[0021]

[0022] The symbol * represents the convolution operation;

[0023] S122, based on step S121, introduce the unit function B(t) and establish a vector expression of the unit function B(t):

[0024]

[0025] Where t∈(0,Ta], Ta represents the total duration, and the total duration Ta is divided into I time slices, and the duration of each time slice is The unit function B(t) is divided into B 0 (t),B 1 (t),B 2 (t),…,B I (t), F α is a matrix, and the symbol T represents matrix transpose;

[0026] matrix

[0027] in,

[0028] S123, based on step S122, establish Vector expression:

[0029]

[0030] The deformation function δ(t) generated by the mooring cable under the action of the tension f(t) is divided into I time slices within the total time Ta, and the result is δ 0 (t),δ 1 (t),δ 2 (t),…,δ I (t), δ i (t) uses the sampled value of δ(t) Approximately, the vector δ = [δ 0 ,δ 1 ,δ 2 ,…,δ I ];

[0031] S124, based on step S123, establish a vectorized expression of the mooring cable tension f(t):

[0032]

[0033] The mooring cable tension f(t) is divided into I time slices within the total time Ta, and f is obtained. 0 (t),f 1 (t),f 2 (t),…,f I (t), δ i (t) uses f(t) to sample the value It means that the vector f=[f 0 ,f 1 ,f 2 ,…,f I ];

[0034] S125, using the cuckoo algorithm and gradient search, identify the undetermined parameters k and α in step S124.

[0035] Furthermore, in step S125, the cuckoo algorithm and gradient search are used to identify the parameter k and the parameter α, including the following steps:

[0036] S1251, generating N bird nest locations for identification parameter α:

[0037] α i,j =α min +r 1 (α max -α min )

[0038] Where i = 1, 2, ..., N, j = 1, 2, 3, ..., α i,j represents the value of the differential order α at the i-th bird's nest and the j-th generation; α min and α max Respectively represent the lower and upper bounds of the differential order α; r 1 ∈[0,1], is a random number;

[0039] S1252, according to the differential order α corresponding to the N bird's nest positions i,j ,design Iteration rule, get the value of parameter k corresponding to N differential orders α, the expression is as follows:

[0040]

[0041] in, It means that when the differential order is α i,j At the mth iteration The value of, set the maximum number of iterations M, output the final iteration result As when the differential order is α i,j When , the optimal identification result of parameter k;

[0042] S1253, introduce function represents the tension corresponding to the lth strain sampling obtained by parameter solution, f l represents the tension obtained by the lth sampling, l = 1, 2, ..., I; construct the tension measurement value f l and The mean square error is used as the objective function, and the formula is as follows:

[0043]

[0044] Among them, Meq i,j represents the mean square error obtained based on the parameters of the jth generation of the ith nest;

[0045] The differential order and the estimate of k corresponding to the minimum mean square error Pmeq in the jth generation are selected as the optimal differential order Pα and the estimate of the optimal k Pk.

[0046] Furthermore, the method further comprises the following steps:

[0047] S1254, introduce function α i,j =α i,j-1 +ξLe′vy(λ) updates the locations of N bird nests, where ξ represents the step length, Le′vy(λ) represents a random walk with a step length that follows the Le′vy distribution, and α i,j-1 represents the value of the previous generation of the i-th bird's nest, α i,jrepresents the value of the generation of the ith bird's nest;

[0048] S1255, according to the differential order α corresponding to the N bird's nest positions i,j , use the function identification parameters in step S1252; then solve the tension f corresponding to the lth strain sampling according to step S124 l , calculate Meq according to step S1253 i,j , take the parameters corresponding to the small mean square error, and update the parameters based on the following function:

[0049]

[0050] Among them, Pα, Pk are the parameter identification results, and Pmeq is the threshold for judging whether to end the iteration.

[0051] Beneficial effects: 1. The model of the present invention reflects the physical mechanism of the mooring cable and the model is accurate.

[0052] 2. The present invention utilizes block pulse functions to transform complex fractional-order calculations into vector calculations, thereby simplifying the computational complexity in the modeling process.

[0053] 3. The present invention provides a method for analyzing the tension of ship dock mooring cables, which takes into account the influence of the tension history on the deformation, reflects the dynamic process, and provides accurate analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flow chart for modeling a ship dock mooring cable of the present invention;

[0055] Figure 2 It is a parameter identification flow chart of the present invention. DETAILED DESCRIPTION

[0056] The present invention will be further explained below in conjunction with the accompanying drawings.

[0057] Based on the problems in the background technology, this embodiment provides a fractional-order modeling and analysis method for the tension response of mooring cables at a ship dock. The main process is as follows:

[0058] Step 1: Establish the mooring cable tension and deformation fractional differential order model according to the fractional order Hooke's law:

[0059]

[0060] Where f(t) represents the tension of the mooring cable at time t, δ(t) represents the deformation of the mooring cable under the tension f(t), and k represents an undetermined constant. represents the α-order Caputo fractional differential of f(t), and its definition expression is:

[0061]

[0062] In the above formula, Γ(·) represents the gamma function, The core of modeling is how to use sampling data to identify the optimal parameters of unknown parameters k and α.

[0063] Step 2: Convert the fractional-order differential model in step 1 into a fractional-order integral model:

[0064]

[0065] in, represents the α-order fractional integral of δ(t), Defined as:

[0066]

[0067] The symbol * represents a convolution operation.

[0068] Step 3: Establish the vector expression of the unit function B(t):

[0069] The unit function B(t) is divided into I time slices within the total duration Ta, and the duration of each time slice is Can be divided into B 0 (t),B 1 (t),B 2 (t),…,B I (t), any B i (t) can be used with B i express, Among them B i Defined as:

[0070]

[0071] exist The sampling time is recorded as According to the definition of fractional integral:

[0072]

[0073] in,

[0074] Define vector B = [B 0 ,B 1 ,B 2 ,…,B I ]and According to formula (3), we can get:

[0075]

[0076] The symbol T represents matrix transpose.

[0077] Remember the matrix

[0078] get:

[0079]

[0080] Step 4: Build Vector expression:

[0081] The deformation function δ(t) generated by the mooring cable under the action of the tension f(t) is divided into I time slices within the total time Ta, and the duration of each time slice is can be divided into δ 0 (t),δ 1 (t),δ 2 (t),…,δ I (t), any δ i (t)(0≤i≤I, the sampling value of δ(t) can be used Approximately, exist The sampling time is recorded as Define vector δ = [δ 0 ,δ 1 ,δ 2 ,…,δ I ]and

[0082]

[0083] Step 5: Establish a vector expression for the mooring line tension f(t).

[0084] The mooring cable tension f(t) is divided into I time slices within the total time Ta, and the duration of each time slice is Can be divided into f 0 (t),f 1 (t),f 2 (t),…,f I (t), any δ i (t) Available f(t) sampling value express, Define vector f = [f 0 ,f 1 ,f 2 ,…,f I ], obtained from steps 2 to 5:

[0085]

[0086] The parameter identification problem in the fractional-order model of the ship dock mooring cable formula (1) is transformed into the optimal estimation of the vector function in formula (6).

[0087] Step 6: Use the cuckoo algorithm combined with gradient search to identify the parameters k and α.

[0088] 6.1: Initialization

[0089] 1) Generate N bird nest locations for identification parameter α:

[0090] α i,j =α min +r 1 (α max -α min ) (7)

[0091] Where i = 1, 2, ..., N, j = 1, 2, 3, ..., α i,j represents the value of the differential order α of the jth generation of the ith bird's nest. When initialized, j = 1 represents the first generation, α min and α max Respectively represent the lower and upper bounds of the differential order α. 1 ∈[0,1] is a random number. Formula (7) indicates that N initial differential orders are randomly generated within the value range of the differential order α.

[0092] 2) According to the differential order α corresponding to the N bird's nest positions i,j design Iteration rules, Indicates the differential order α for the i-th nest and j-th generation i,j The estimation of parameter k at the next m-th iteration obtains the parameter k value corresponding to N differential orders α:

[0093]

[0094] Among them, α i,j represents the value of the differential order α at the i-th bird's nest and the j-th generation, It means that when the differential order is α i,j At the mth iteration The value of .

[0095] According to α i,j The experimentally measured tension and deformation can be obtained using formula (6): Take from formula (8) f(m) and δ(m) represent the mth sampling of f(t) and δ(t) respectively. Indicates the current order α i,j The tension calculated from the experimentally measured strain, η i>0 indicates the learning rate. When formula (8) holds true, we can get Indicates the estimated error of parameter k as the iteration continues The error between the experimentally measured tension and the calculated tension will gradually converge. Set the maximum number of iterations M, and the final iteration result That is, when the differential order is α i,j The optimal identification result of parameter k. The current order α i,j The following are the parameter identification results.

[0096] 3) According to formula (6), α i,j and calculate represents the tension corresponding to the lth strain sampling obtained by parameter solution, f l Represents the tension obtained by the l-th sampling, l = 1, 2,…, I.

[0097] 4) Define the objective function as the tension measurement value f l and the solution value The mean square error of , l = 1, 2, …, I:

[0098]

[0099] Meq i,j It represents the mean square error obtained according to the parameters of the i-th bird's nest and the j-th generation. The differential order and the estimate of k corresponding to the minimum mean square error Pmeq in the j-th generation are selected as the optimal differential order Pα and the optimal estimate of k Pk and retained to the next generation. j plus 1 indicates entering the next generation.

[0100] 6.2: Global Search

[0101] 1) Update the N bird's nest positions, i.e. the values ​​of the differential orders, according to the following formula:

[0102] α i,j =α i,j-1 +ξLe′vy(λ) (10)

[0103] Among them, ξ represents the step size, which can be taken as α i,j-1 represents the value of the previous generation of the i-th bird's nest, α i,j represents the value of the i-th nest in this generation, Le′vy(λ) represents the random walk whose step length follows the Le′vy distribution. Formula (10) represents the update of each nest based on the position of the previous generation plus a random walk.

[0104] 2) According to the differential order α corresponding to the N bird's nest positions i,jThe parameters are identified according to the parameter identification rule of formula (8).

[0105] 3) According to formula (6), α i,j and calculate It represents the tension corresponding to the lth strain sampling obtained by parameter solution.

[0106] 4) Calculate Meq according to formula (9) i,j :

[0107] 5) Update the parameters corresponding to the small mean square error:

[0108]

[0109] 6.3: Local Search

[0110] 1) Generate a new bird's nest location:

[0111] α i,j =α i,j +rand·H(υ)(α r1,j -α r2,j ) (12)

[0112] represents the positions of two random bird nests in the current population, rand and θ are random numbers uniformly distributed in the interval [0,1], and H(·) represents the Heaviside function.

[0113] 2) According to the differential order α corresponding to the N bird's nest positions i,j The parameters are identified according to the parameter identification rule of formula (8).

[0114] 3) According to formula (6), α i,j and calculate represents the tension corresponding to the lth strain sampling obtained by parameter solution, f l Represents the tension obtained by the lth sampling.

[0115] 4) Calculate Meq according to formula (9) i,j :

[0116] 5) Update the parameters corresponding to the small mean square error.

[0117]

[0118] Pα, Pk are the parameter identification results, and whether Pmeq is less than the threshold determines whether to end the iteration. If so, the global optimal solution is obtained, otherwise, enter the next generation and start the next generation global search.

[0119] Step 7: Mooring rope tension safety detection and analysis.

[0120] The parameter identification results Pα and Pk are used as the values ​​of α and k respectively. According to formula (5) and formula (6), we can get:

[0121]

[0122] We can further get:

[0123]

[0124] It can be seen that when α and k are determined, δ can be calculated if f is known. Since f is obtained by sampling f(t), δ is obtained by sampling δ(t). Therefore, by recording the tension of the mooring cable at the ship dock, the deformation of the mooring cable at the ship dock under tension can be obtained. This deformation takes into account the deformation under the historical force of the tension of the mooring cable at the ship dock. Taking into account the modeling error, a safety factor greater than 1 is set. As long as the deformation at any time is less than the quotient of the safe allowable deformation divided by the safety factor, the mooring cable is within the safety range, otherwise early warning processing is required.

[0125] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for analyzing the tension response of a ship mooring rope, characterized in that: The following steps are involved: S1, establish a dynamic model of mooring cable tension and deformation; S2, recording the tension of the mooring cable, and outputting the deformation of the mooring cable at the corresponding moment through the model; S3, set the safety factor, and when the deformation exceeds the safety factor, perform warning processing; In step S1, the process of establishing a dynamic model includes the following steps: S11, establish the mooring cable tension and deformation fractional differential model: Where f(t) represents the tension of the mooring cable at time t, δ(t) represents the deformation of the mooring cable under the tension f(t), and k represents an undetermined constant. represents the α-order Caputo fractional differential of f(t), and its definition expression is: Where Γ(·) represents the gamma function, is the integral independent variable; S12, using the sampled data, identifying the parameter k and the parameter α in step S11, obtaining the optimal parameter values ​​of the parameter k and the parameter α, and obtaining the optimal model; In step S12, the process of obtaining optimal parameter values ​​of mooring line tension and deformation includes the following steps: S121, converting the fractional order differential model in step 11 into a fractional order integral model: in, represents the α-order fractional integral of δ(t); Defined as: The symbol * represents the convolution operation; S122, based on step S121, introduce the unit function B(t) and establish a vector expression of the unit function B(t): Where t∈(0,Ta], Ta represents the total duration, and the total duration Ta is divided into I time slices, and the duration of each time slice is The unit function B(t) is divided into B0(t), B1(t), B2(t),…, B I (t), F α is a matrix, and the symbol T represents matrix transpose; matrix in, S123, based on step S122, establish Vector expression: The deformation function δ(t) generated by the mooring cable under the tension f(t) is divided into I time slices within the total time Ta, and we get δ0(t), δ1(t), δ2(t), …, δ I (t), δ i (t) uses the sampled value of δ(t) Approximately, the vector δ = [δ0, δ1, δ2, …, δ I ]; S124, based on step S123, establish a vectorized expression of the mooring cable tension f(t): The mooring cable tension f(t) is divided into I time slices within the total time Ta, and we get f0(t),f1(t),f2(t),…,f I (t), δ i (t) uses f(t) to sample the value It means that the vector f=[f0,f1,f2,…,f I ]; S125, using the cuckoo algorithm and gradient search, identify the undetermined parameters k and α in step S124.

2. The method for analyzing the tension response of a ship dock mooring rope according to claim 1, characterized in that: In step S125, the cuckoo algorithm and gradient search are used to identify the parameters k and α, including the following steps: S1251, generating N bird nest locations for identification parameter α: α i,j ＝α min +r1(α max -α min ) Where i = 1, 2, ..., N, j = 1, 2, 3, ..., α i,j represents the value of the differential order α at the i-th bird's nest and the j-th generation; α min and α max They represent the lower and upper bounds of the differential order α respectively; r1∈[0,1] is a random number; S1252, according to the differential order α corresponding to the N bird's nest positions i,j ,design Iteration rule, get the value of parameter k corresponding to N differential orders α, the expression is as follows: in, It means that when the differential order is α i,j At the mth iteration The value of, set the maximum number of iterations M, output the final iteration result As when the differential order is α i,j When , the optimal identification result of parameter k; S1253, introduce function represents the tension corresponding to the lth strain sampling obtained by parameter solution, f l represents the tension obtained by the lth sampling, l = 1, 2, ..., I; construct the tension measurement value f l and The mean square error is used as the objective function, and the formula is as follows: Among them, Meq i,j represents the mean square error obtained based on the parameters of the jth generation of the ith nest; The differential order and the estimate of k corresponding to the minimum mean square error Pmeq in the jth generation are selected as the optimal differential order Pα and the estimate of the optimal k Pk.

3. The method for analyzing the tension response of a ship dock mooring rope according to claim 2, characterized in that: The following steps are also included: S1254, introduce function α i,j =α i,j-1 +ξLe′vy(λ) updates the locations of N bird nests, where ξ represents the step length, Le′vy(λ) represents a random walk with a step length that follows the Le′vy distribution, and α i,j-1 represents the value of the previous generation of the i-th bird's nest, α i,j represents the value of the generation of the ith bird's nest; S1255, according to the differential order α corresponding to the N bird's nest positions i,j , use the function identification parameters in step S1252; then solve the tension f corresponding to the lth strain sampling according to step S124 l , calculate Meq according to step S1253 i,j , take the parameters corresponding to the small mean square error, and update the parameters based on the following function: Among them, Pα, Pk are the parameter identification results, and Pmeq is the threshold for judging whether to end the iteration.

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