A method for calibrating the design response spectrum of marine earthquake motion based on particle swarm optimization

Abstract

This scheme belongs to the research field of seismic design of marine structures, and specifically relates to a method for calibrating a marine earthquake design response spectrum based on a particle swarm algorithm, the steps of which include: processing marine earthquake records; calculating the dynamic amplification coefficient spectrum of marine earthquakes; adding adaptive parameters to the particle swarm algorithm to improve the high stability of the particle swarm algorithm; and then applying the particle swarm algorithm with high stability to the calibration of the marine earthquake design response spectrum, providing a high stability calibration method for the marine earthquake design spectrum. The present invention uses a particle swarm algorithm with high stability to accurately and quickly obtain the characteristic parameters of the marine earthquake calibration design response spectrum, so that the marine earthquake calibration design response spectrum is more consistent with the real marine earthquake response spectrum, and provides an efficient and accurate response spectrum calibration method for the calibration of the marine earthquake design response spectrum, solving the problem of instability and low efficiency in the calibration parameters of the marine earthquake design response spectrum.

Description

Technical Field

[0001] This scheme belongs to the research field of seismic design of marine structures, and specifically involves a method for calibrating the design response spectrum of marine earthquake motion based on particle swarm algorithm. Background Art

[0002] With the rapid development of marine engineering, the construction and operation of major marine projects such as offshore wind power generation, offshore oil drilling platforms, cross-sea bridges, submarine tunnels, submarine oil pipelines and submarine communication cables are increasing. These projects are often located in earthquake-prone areas. Therefore, it is particularly important to carry out reasonable structural seismic fortification for marine projects. However, due to the significant differences between the characteristics of sea and land seismic motions, traditional land-based seismic design standards are not fully applicable to marine projects.

[0003] Traditional seismic design of marine engineering mostly refers to the seismic fortification standards of land, such as the three-level two-stage seismic design method. However, this method lacks in-depth analysis of the seismic motion characteristics of the sea area, and it is difficult to ensure the rationality and accuracy of the design response spectrum. In addition, due to the lack of seismic response spectrum designed specifically for the seismic motion characteristics of the sea area, the rationality of the seismic design of marine engineering is questioned.

[0004] The design response spectrum of marine earthquake motion is an important basis for the seismic design and reinforcement evaluation of offshore building structures, and is also the main indicator for compiling marine earthquake zoning. It plays a key role in the synthesis of artificial seismic motions and the selection of seismic motions in marine sites. However, the existing calibration methods of the design response spectrum of marine earthquake motion have the problems of parameter instability and low efficiency, which makes it difficult to meet the accuracy and efficiency requirements of the seismic design of marine engineering. Therefore, it is particularly important to use a particle swarm algorithm with high stability to calibrate the design response spectrum of marine earthquake motion. A technology is needed to solve the problems of instability and low efficiency in the calibration parameters of the design response spectrum of marine earthquake motion. Summary of the invention

[0005] The purpose of this scheme is to provide a method for calibrating the design response spectrum of marine earthquake motion based on particle swarm algorithm, so as to solve the problems of instability and low efficiency in the calibration parameters of the design response spectrum of marine earthquake motion.

[0006] In order to achieve the above purpose, this scheme provides a method for calibrating the design response spectrum of marine earthquake motion based on particle swarm algorithm, including the following steps:

[0007] S1: Initialization particle swarm parameters of given particle swarm algorithm AGPSO: particle swarm size, particle dimension, number of iterations, inertia weight;

[0008] S2: Randomly initialize the position and velocity of each particle according to equations (1) and (2):

[0009] x i,d =(x max,d -x min,d )×rand(0,1)+x min,d (1)

[0010] v i,d =0.3×rand(0,1) (2)

[0011] Where: x min,d and x max,d Given by the range of characteristic parameter X; rand(0,1) is a random number uniformly distributed between 0 and 1; x i,d is the position of the ith particle; v i,d is the velocity of the ith particle; the expression of the characteristic parameter X is X=[T 0 , T g , T d , β max ,γ]; d is the particle dimension;

[0012] S3: Set the evaluation function. Assume that the initial value of the evaluation function is positive infinity. The evaluation function of the individual is Pbs(i) = +∞; the evaluation function value of the group is Gbs = +∞;

[0013] S4: At each iteration, the fitness function F(x i,d ):

[0014]

[0015] Where: β′(T) is the amplification coefficient spectrum of the calibrated sea area seismic motion; β(T) is the amplification coefficient spectrum of the real sea area seismic motion; T m is the maximum period of the amplification factor spectrum of sea ground motion.

[0016] S5: Update the individual optimal fitness and position of each particle. In each iteration, if the individual evaluation function value Pbs(i) is greater than the fitness function value F(x i,d ), then the individual evaluation function value Pbs(i) is equal to the fitness function value F(x i,d ), which is the individual optimal fitness of each particle, and this position is the individual optimal position of each particle, namely Pbest i,d =x i,d ;

[0017] S6: Update the optimal fitness and position of the group; in each iteration, if the evaluation function value Gbs of the group is greater than the fitness function value F(x i,d), then the evaluation function value Gbs of the group is equal to the fitness function value F(x i,d ), which is the optimal fitness of the group, and this position is the optimal position of the group, that is, Gbest = x i,d ;

[0018] S7: Adaptive parameter adjustment to improve the local and global search capabilities of particles;

[0019] S8: Update velocity and position; the velocity and position of the particle will be updated so that it moves in the search space:

[0020]

[0021] Where: t is the current iteration step; w is the weight coefficient.

[0022] S9: Boundary processing; if the particle moves beyond the defined search space boundary, the adjacent boundary value is taken; according to the logical terminology, it is judged whether it exceeds the defined search space boundary, that is:

[0023]

[0024] Furthermore, before step S1, the selected sea area earthquake records are processed to calculate the acceleration response spectrum of the sea area earthquake.

[0025] Furthermore, the steps of processing the sea area seismic records are: A1: processing the sea area seismic records.

[0026]

[0027] Where: a X (t i ), a Y (t i ), a Z (t i) are the X, Y, and Z components of the original record; R is the recorded rotation matrix; a E (t i ), a N (t i ), a U (t i) are the original recorded EW, NS, and UD components; t i is the step length of the record.

[0028] The rotated records were de-meaned, baseline corrected, de-peaked, zero-filled and filtered using a fourth-order Butterworth bandpass filter.

[0029] A2: Calculate the dynamic amplification coefficient spectrum of sea ground motion.

[0030] Furthermore, the first inflection point period T 0 , site characteristic period T g , attenuation change period T d , the platform value of the amplification factor spectrum β max , the range of characteristic parameters such as the attenuation index γ, that is, the upper limit value is x max,d =[1, 3, 6, 10, 2], the lower limit is x min,d =[0.02, 0.1, 1.5, 1, 0.1].

[0031] Furthermore, in step S4, it is necessary to determine the spectral form of the amplification factor of the calibrated sea area earthquake motion:

[0032]

[0033] Further, in step S7, the adaptive parameters, weight coefficient w and learning factor c are adjusted 1 and c 2 , at each iteration, the weight coefficient w is adaptively updated as follows:

[0034]

[0035] Where: t is the current iteration step; T is the total number of steps required for iteration; w max and w min The maximum and minimum weight values ​​are given initially. Learning factor c 1 and c 2 It is necessary to control local and global search capabilities in different groups, namely:

[0036] Group 1: c 1 =1.95-2t 1 / 3 T 1 / 3 ;c 2 =2t 1 / 3 T 1 / 3 +0.05;

[0037] Group 2: c 1 =(-2t 3 / T 3 )+2.5;c 2 =(2t 3 / T 3 )+0.5;

[0038] Group 3: c 1 =1.95-2t 1 / 3 / T 1 / 3 ;c 2 =(2t 3 / T 3 )+0.5;

[0039] Group 4: c 1 =(-2t 3 / T 3 )+2.5;c 2 =2t 1 / 3 / T 1 / 3 +0.05;

[0040] At each iteration, when c 1 Greater than c 2 When c 2 Greater than c 1 When , the particle has better global search ability. 1 and c 2 A good balance is sought between them and they are considered as dynamic coefficients to improve the high stability and robustness of the response spectrum calibration algorithm.

[0041] The sea area seismic response spectrum calibrated by this method has the characteristics of high stability and high efficiency. This method uses learning factors c1 and c2 of different groups to control the local and global search capabilities of particles, which not only improves stability, but also reduces the number of transport iterations, effectively reduces the calculation time, and makes the calibrated sea area seismic design spectrum more consistent with the real sea area seismic response spectrum.

[0042] This scheme has high stability. Through adaptive parameter adjustment and optimized particle swarm algorithm, the stability of the algorithm in the search process is improved, and the impact of parameter fluctuations on the results is reduced. The algorithm in this scheme can quickly converge to the optimal solution, improve the efficiency of the calibration process, and ensure the accuracy of the results. The algorithm can adapt to different sea earthquake characteristics and has good generalization ability. By dynamically adjusting the weight coefficient and learning factor, the algorithm shows good robustness in the face of complex and changeable search space. The optimized particle swarm algorithm reduces the number of iterations, effectively reduces the calculation time, and improves the efficiency of the calibration process. Through the design response spectrum that is more in line with the actual sea earthquake characteristics, the rationality and reliability of the seismic design of marine engineering are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of the calibration results of 100 calibrations of a seismic response spectrum. This scheme is marked with AGPSO, the particle swarm algorithm is marked with PSO, and the differential evolution algorithm is marked with DE;

[0044] Figure 2 A flow chart for calibrating the design response spectrum of sea-area earthquake motion for the present invention.

[0045] The following is further described in detail through specific implementation methods: DETAILED DESCRIPTION

[0046] The embodiment is basically as shown in the attached Figure 1 As shown: A method for calibrating the design response spectrum of marine earthquake motion based on particle swarm algorithm, comprising the following steps:

[0047] A1: Process the sea area seismic records.

[0048]

[0049] Where: a X (t i ), a Y (t i ), a Z (t i) are the X, Y, and Z components of the original record; R is the recorded rotation matrix; a E (t i ), a N (t i ), a U (t i) are the original recorded EW, NS, and UD components; t i is the step length of the record.

[0050] The rotated records were de-meaned, baseline corrected, de-peaked, zero-filled and filtered using a fourth-order Butterworth bandpass filter.

[0051] A2: Calculate the dynamic amplification coefficient spectrum of sea ground motion.

[0052] A3: Determine the first inflection point period T 0 , site characteristic period T g , attenuation change period T d , the platform value of the amplification factor spectrum β max , attenuation index γ and other characteristic parameters. That is, the upper limit value is x max,d =[1, 3, 6, 10, 2], the lower limit is x min,d =[0.02, 0.1, 1.5, 1, 0.1].

[0053] S1: Initialization particle swarm parameters of the particle swarm algorithm AGPSO with given high stability: particle swarm size, particle dimension, number of iterations, inertia weight;

[0054] S2: Randomly initialize the position and velocity of each particle according to equations (1) and (2):

[0055] x i,d =(x max,d -x min,d )×rand(0,1)+x min,d (1)

[0056] v i,d =0.3×rand(0,1) (2)

[0057] Where: x min,d and x max,d Given by the range of characteristic parameter X; rand(0,1) is a random number uniformly distributed between 0 and 1; x i,d is the position of the ith particle; v i,d is the velocity of the ith particle; the expression of the characteristic parameter X is X=[T 0 , T g , T d , β max ,γ]; d is the particle dimension;

[0058] S3: Set the evaluation function. Assume that the initial value of the evaluation function is positive infinity, that is, the evaluation function of the individual is Pbs(i) = +∞; the evaluation function value of the group is Gbs = +∞;

[0059] S4: Determine the spectral form of the calibrated sea area ground motion amplification factor:

[0060]

[0061] In each iteration, the fitness function F(x i,d ):

[0062]

[0063] Where: β′(T) is the amplification coefficient spectrum of the calibrated sea area seismic motion; β(T) is the amplification coefficient spectrum of the real sea area seismic motion; T m is the maximum period of the amplification factor spectrum of sea ground motion.

[0064] S5: Update the individual optimal fitness and position of each particle. In each iteration, if the individual evaluation function value Pbs(i) is greater than the fitness function value F(x i,d ), then the individual evaluation function value Pbs(i) is equal to the fitness function value F(x i,d ), which is the individual optimal fitness of each particle, and this position is the individual optimal position of each particle, namely Pbest i,d =x i,d .

[0065] S6: Update the optimal fitness and position of the group. In each iteration, if the evaluation function value Gbs of the group is greater than the fitness function value F(x i,d ), then the evaluation function value Gbs of the group is equal to the fitness function value F(xi,d ), which is the optimal fitness of the group, and this position is the optimal position of the group, that is, Gbest = x i,d .

[0066] S7: Adaptive parameter adjustment, weight coefficient w and learning factor c 1 and c 2 At each iteration, the weight coefficient w is adaptively updated as follows:

[0067]

[0068] Where: t is the current iteration step; T is the total number of steps required for iteration; w max and w min The maximum and minimum weight values ​​are given initially. Learning factor c 1 and c 2 It is necessary to control local and global search capabilities in different groups, namely:

[0069] Group 1: c 1 =1.95-2t 1 / 3 T 1 / 3 ;c 2 =2t 1 / 3 T 1 / 3 +0.05;

[0070] Group 2: c 1 =(-2t 3 / T 3 )+2.5;c 2 =(2t 3 / T 3 )+0.5;

[0071] Group 3: c 1 =1.95-2t 1 / 3 / T 1 / 3 ;c 2 =(2t 3 / T 3 )+0.5;

[0072] Group 4: c 1 =(-2t 3 / T 3 )+2.5;c 2 =2t 1 / 3 / T 1 / 3 +0.05;

[0073] At each iteration, when c 1 Greater than c 2 When c 2 Greater than c 1When , the particle has better global search ability. 1 and c 2 A good balance is sought between them and they are considered as dynamic coefficients to improve the high stability and robustness of the response spectrum calibration algorithm.

[0074] The speed and position of the next particle update are determined by dividing the particle population size by 4 and taking the remainder. When the remainder is 0, the learning factor c of the first group is used. 1 and c 2 To update the speed and position; when the remainder is 1, use the learning factor c of the second group 1 and c 2 To update the speed and position; when the remainder is 2, use the learning factor c of the third group 1 and c 2 To update the speed and position; when the remainder is 3, use the learning factor c of the fourth group 1 and c 2 to update the speed and position.

[0075] S8: Update velocity and position. The velocity and position of the particle will be updated as it moves in the search space:

[0076]

[0077] S9: Boundary processing. If the particle moves beyond the defined search space boundary, the adjacent boundary value is taken. According to the logical terms, it is judged whether it exceeds the defined search space boundary, that is:

[0078]

[0079] The above steps S4-S9 are executed repeatedly until the number of iterations t reaches the maximum number of iterations T or the convergence condition is met, then the calculation is stopped. Calculate the first inflection point period T 0 , site characteristic period T g , attenuation change period T d , the platform value of the amplification factor spectrum β max , the optimal solution of the decay exponent γ.

[0080] The design response spectrum of sea earthquake motion is obtained by fitting according to the optimal solution of characteristic parameters.

[0081] The above is only an embodiment of the present invention, and the common knowledge such as the known specific structure and characteristics in the scheme is not described in detail here. It should be pointed out that for those skilled in the art, several deformations and improvements can be made without departing from the structure of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for calibrating the design response spectrum of marine earthquake motion based on particle swarm algorithm, characterized in that: The following steps are involved: S1: Initialization particle swarm parameters of given particle swarm algorithm AGPSO: particle swarm size, particle dimension, number of iterations, inertia weight; S2: Randomly initialize the position and velocity of each particle according to equations (1) and (2): x i,d =(x max,d -x min,d )×rand(0,1)+x min,d (1) in i,d =0.3×rand(0,1) (2) Where: x min,d and x max,d Given by the range of characteristic parameter X; rand(0,1) is a random number uniformly distributed between 0 and 1; x i,d is the position of the ith particle; v i,d is the velocity of the ith particle; the expression of the characteristic parameter X is X=[T0,T g , T d , β max ,γ]; d is the particle dimension; S3: Set the evaluation function. Assume that the initial value of the evaluation function is positive infinity. The evaluation function of the individual is Pbs(i) = +∞; the evaluation function value of the group is Gbs = +∞; S4: At each iteration, the fitness function F(x i,d ): Where: β′(T) is the amplification coefficient spectrum of the calibrated sea area seismic motion; β(T) is the amplification coefficient spectrum of the real sea area seismic motion; T m is the maximum period of the amplification factor spectrum of sea-area earthquake motion; S5: Update the individual optimal fitness and position of each particle; in each iteration, if the individual evaluation function value Pbs(i) is greater than the fitness function value F(x i,d ), then the individual evaluation function value Pbs(i) is equal to the fitness function value F(x i,d ), which is the individual optimal fitness of each particle, and this position is the individual optimal position of each particle, namely Pbest i,d =x i,d ; S6: Update the optimal fitness and position of the group; in each iteration, if the evaluation function value Gbs of the group is greater than the fitness function value F(x i,d ), then the evaluation function value Gbs of the group is equal to the fitness function value F(x i,d ), which is the optimal fitness of the group, and this position is the optimal position of the group, that is, Gbest = x i,d ; S7: Adaptive parameter adjustment to improve the local and global search capabilities of particles; S8: Update velocity and position; the velocity and position of the particle will be updated so that it moves in the search space: Where: t is the current iteration step; w is the weight coefficient. S9: Boundary processing; If the particle moves beyond the defined search space boundary, the adjacent limit value is taken; according to the logical terms, it is judged whether it exceeds the defined search space boundary, that is:

2. The method for calibrating the design response spectrum of sea earthquake motion based on particle swarm algorithm according to claim 1 is characterized by: Before step S1, the selected sea area earthquake records are processed to calculate the acceleration response spectrum of the sea area earthquake.

3. The method for calibrating the design response spectrum of sea earthquake motion based on particle swarm algorithm according to claim 2 is characterized in that: The steps of processing the sea area seismic records are: A1: processing the sea area seismic records; Where: a X (t i ), a Y (t i ), a Z (t i) are the X, Y, and Z components of the original record; R is the recorded rotation matrix; a E (t i ), a N (t i ), a U (t i) are the original recorded EW, NS, and UD components; t i is the recorded step length; The rotated records were de-meaned, baseline corrected, de-peaked, zero-filled, and filtered using a fourth-order Butterworth bandpass filter; A2: Calculate the dynamic amplification coefficient spectrum of sea ground motion.

4. The method for calibrating the design response spectrum of sea earthquake motion based on particle swarm algorithm according to claim 3 is characterized by: The step A3 is also included: determining the first inflection point period T0, the site characteristic period T g , attenuation change period T d , the platform value of the amplification factor spectrum β max , the range of characteristic parameters such as the attenuation index γ, that is, the upper limit value is x max,d =[1, 3, 6, 10, 2], the lower limit is x min,d =[0.02, 0.1, 1.5, 1, 0.1].

5. The method for calibrating the design response spectrum of sea earthquake motion based on particle swarm algorithm according to claim 1 is characterized in that: In step S4, it is necessary to determine the spectral form of the amplification factor of the calibrated sea area ground motion:

6. The method for calibrating the design response spectrum of sea earthquake motion based on particle swarm algorithm according to claim 1 is characterized by: In step S7, the adaptive parameters, weight coefficient w and learning factors c1 and c 2， At each iteration, the weight coefficient w is adaptively updated as follows: Where: t is the current iteration step; T is the total number of steps required for iteration; w max and w min The maximum and minimum weight values ​​are given initially; the learning factors c1 and c2 need to be in different groups to control the local and global search capabilities, that is: The first group: c1 = 1.95-2t 1 / 3 T 1 / 3 ; c2=2t 1 / 3 T 1 / 3 +0.05; The second group: c1 = (-2t 3 / T 3 )+2.5; c2=(2t 3 / T 3 )+0.5; Group 3: c1 = 1.95-2t 1 / 3 / T 1 / 3 ; c2=(2t 3 / T 3 )+0.5; Group 4: c1=(-2t 3 / T 3 )+2.5; c2=2t 1 / 3 / T 1 / 3 +0.05.

Images