Method and system for optimizing arrangement of nonlinear energy vibration absorbers based on particle swarm optimization

Abstract

The invention discloses a method and system for optimizing nonlinear energy vibration absorber arrangement based on a particle swarm optimization algorithm, and belongs to the technical field of nonlinear energy vibration absorber arrangement method.According to design parameters of a nonlinear vibration absorber, the mass, damping coefficient and nonlinear rigidity parameters of the vibration absorber are determined, and according to physical characteristics and stress conditions of a stand pipe, the nonlinear energy vibration absorber arrangement is optimized. Establishing a coupling kinetic equation of the riser and the vibration absorbers, describing vibration behaviors under the action of ocean currents and waves, setting initial values of the number, the position and the speed of particles, defining a fitness function for evaluating the position quality of each particle, and calculating vibration responses of the riser system under different vibration absorber arrangement conditions through a time domain minimum residual value method. Taking the minimum vibration amplitude as a target, calculating the fitness value of the position of each particle, iteratively updating the position and speed of each particle according to the updating rule of the particle swarm algorithm, and gradually approaching the optimal solution.

Description

Technical Field

[0001] The present invention relates to a method for arranging nonlinear vibration absorbers for marine risers, and in particular to a method and system for optimizing the arrangement of nonlinear energy vibration absorbers based on a particle swarm algorithm, belonging to the technical field of methods for arranging nonlinear vibration absorbers for marine risers. Background Art

[0002] Marine risers are important structures for exploiting marine oil and gas resources.

[0003] Deepwater risers connect the offshore floating platform and oil and gas resources, like a helicopter elevator, continuously transporting oil and gas resources.

[0004] Since the riser is a large-diameter pipeline of thousands of meters long and is placed in a complex and changeable marine environment, fluid-solid coupling occurs between the pipeline and the ocean current, resulting in large deformation phenomena such as large displacement and large overturning, causing fatigue and damage to the riser structure.

[0005] In order to solve this problem, it is considered to add a vibration absorber to the riser to reduce the amplitude of the riser through the vibration absorption effect of the vibration absorber.

[0006] The traditional vibration absorber arrangement method is difficult to achieve the best vibration reduction effect. Therefore, a method and system for optimizing the arrangement of nonlinear energy vibration absorbers based on particle swarm algorithm are designed to solve the above problem. Summary of the invention

[0007] The main purpose of the present invention is to provide a method and system for optimizing the arrangement of nonlinear energy absorbers based on a particle swarm algorithm.

[0008] The purpose of the present invention can be achieved by adopting the following technical solutions:

[0009] A method for optimizing the arrangement of nonlinear energy absorbers based on a particle swarm algorithm comprises the following steps:

[0010] S11: Determine the mass, damping coefficient and nonlinear stiffness parameters of the vibration absorber according to the design parameters of the nonlinear vibration absorber;

[0011] S12: According to the physical characteristics and stress conditions of the riser, the coupled dynamic equation of the riser and the vibration absorber is established to describe the vibration behavior under the action of current and waves;

[0012] S13: Set the initial values ​​of the number, position and speed of particles, and define the fitness function to evaluate the position of each particle;

[0013] S14: Calculate the vibration response of the riser system under different vibration absorber arrangements by using the time domain minimum residual method, and calculate the fitness value of each particle position with the goal of minimizing the vibration amplitude;

[0014] S15: According to the update rules of the particle swarm algorithm, the position and velocity of each particle are iteratively updated to gradually approach the optimal solution;

[0015] S16: When a predetermined number of iterations is reached or the fitness function meets the convergence condition, the vibration absorber is output as the optimal arrangement scheme.

[0016] Preferably, in step S15, the initialization of the particle swarm algorithm includes:

[0017] Set the number of particles in the particle swarm to ensure sufficient coverage of the search space;

[0018] Initialize the particle positions randomly in the search space of absorber placement options;

[0019] Randomly initialize the particle's velocity.

[0020] 3. The method for optimizing the arrangement of nonlinear energy absorbers based on particle swarm algorithm according to claim 1, characterized in that: in step S16, the fitness function calculation is implemented by the following steps:

[0021] S21: Calculate the vibration response of the riser under the vibration absorber arrangement scheme corresponding to each particle by using the time domain minimum residual method;

[0022] S22: Calculate the fitness value of each particle position according to the vibration amplitude of the vibration response, with the goal of minimizing the vibration amplitude.

[0023] Preferably, the updating rules of the particle swarm algorithm include the following:

[0024] Update the velocity of each particle according to the inertia weight, individual learning factor and group learning factor;

[0025] υ i (t+1)=ω·υ i (t)+c1·r1·(pbest i -x i (t))+c2·r2·(gbest-x i (t));

[0026] υ i (t) is the velocity of particle i at time t;

[0027] x i (t) is the position of particle i at time t;

[0028] ω is the inertia weight, which controls the inertia of the particle moving forward;

[0029] c1, c2 are learning factors that adjust the speed at which particles move to the individual optimal and global optimal positions;

[0030] r1, r2 are random numbers between [0, 1];

[0031] pbest is the optimal position of the individual;

[0032] gbest is the global optimal position;

[0033] Update the position of each particle according to the updated velocity;

[0034] x i (t+1)=x i (t)+υ i (t+1);

[0035] After each iteration, the particle's best historical position and the global best historical position are updated.

[0036] Preferably, the convergence condition in S16 includes one of the following:

[0037] Reaching the predetermined maximum number of iterations;

[0038] The fitness function value reaches the set threshold;

[0039] After multiple consecutive iterations, the fitness value does not change significantly.

[0040] A particle swarm algorithm-based optimization system for nonlinear energy absorber placement includes a dynamic model module: used to establish and solve the dynamic model of the riser to describe the vibration behavior of the riser under the action of current and waves;

[0041] Parameter determination module: used to determine the mass, damping coefficient and nonlinear stiffness parameters of the vibration absorber;

[0042] Particle swarm algorithm module: used to perform initialization, fitness calculation and iterative update of particle swarm algorithm;

[0043] Result output module: used to output the optimal vibration absorber layout plan.

[0044] Preferably, the particle swarm algorithm module performs the particle swarm algorithm by the following steps:

[0045] S31: Initialize the particle swarm, including setting the number, position and speed of particles;

[0046] S32: Calculate the fitness function value of each particle, and calculate the vibration response of the riser under the corresponding vibration absorber arrangement scheme by using the time domain minimum residual method;

[0047] S33: Update the historical best position of each particle and the global historical best position;

[0048] S34: iteratively update the position and velocity of the particles according to the update rule of the particle swarm algorithm;

[0049] S35: Determine the convergence condition and output the optimal solution.

[0050] Preferably, the parameter determination module determines the mass, damping coefficient and nonlinear stiffness parameters of the nonlinear energy absorber according to the riser dynamics model to ensure the performance of the shock absorber under different layout schemes.

[0051] Preferably, the dynamic equation of the marine riser with multiple vibration absorbers is:

[0052]

[0053] ω(z,t) is the cross-flow lateral displacement;

[0054] z is the axial coordinate;

[0055] is the total mass per unit length, including the mass of the structure and the mass of the fluid;

[0056] C a is the mass coefficient of the fluid increase, ρ f is the density of the fluid being displaced, D is the outer diameter of the riser, EI is the bending stiffness, k is the spring stiffness of the absorber, d is the displacement of the absorber, c1 is the structural damping, and c2 is the damping of the shock absorber;

[0057] F ω =F D +F L It means that the fluid force is calculated as the sum of the damping and lift added by the fluid;

[0058] m NES represents the mass of the vibration absorber, q represents the amplitude of the wake oscillator;

[0059] ε ω is the van der Pol damping, A is the dimensionless coupling coefficient;

[0060] T(z,t) is the varying axial tension;

[0061] Ω f Indicates the vortex shedding frequency.

[0062] Further, the expression of the simplified model is as follows:

[0063]

[0064] υ is the dimensionless cross-flow lateral displacement; k, c are the dimensionless absorber stiffness and damping;

[0065] ξ is the damping ratio;

[0066] Ω R represents the dimensionless shedding frequency;

[0067] ω R1 is the natural frequency;

[0068] St is the Stovhal number;

[0069] β and are the dimensionless amplitude and dimensionless frequency of the tension change.

[0070] Furthermore, the pipeline amplitude is obtained by solving the problem through the time domain minimum residual method. The specific steps are as follows:

[0071] Set the basis function, use the basis function, and substitute the approximate solution represented by the basis function into the original equation.

[0072] Find the residual

[0073] Solving the construction objective function by response sensitivity method

[0074]

[0075] Furthermore, the step of optimizing the objective function and calculating the optimal solution based on the enhanced response sensitivity algorithm and determining the system parameters specifically includes:

[0076] Obtaining parameters to be identified according to the measurement data;

[0077] Tikhonov regularization and trust region restriction are introduced, and the iterative update amount is calculated in combination with the system response parameters;

[0078] Find the parameters to be identified that minimize the objective function according to the iterative update amount;

[0079] The iteration termination condition is met and the optimal solution is obtained;

[0080] Optionally, the objective function is to minimize the overall amplitude of the riser and apply a particle swarm algorithm to determine the optimal layout position of each vibration absorber in the key area.

[0081] Specifically, the objective function includes minimizing the amplitude of each node of the riser and minimizing the number of vibration absorbers;

[0082] Update the speed and position of each particle in the current particle swarm according to the speed update formula and position update formula;

[0083] Calculate the objective function value of each particle after the update, and update the optimal position of each particle and the optimal position of the population according to the updated objective function value of each particle;

[0084] Determine whether the current number of iterations has reached the maximum number of iterations;

[0085] If not, return to the step to update the speed and position of each particle in the current particle swarm according to the speed update formula and the position update formula;

[0086] If so, the current optimal position of each particle and the current optimal position of the population are output; the arrangement position of the riser vibration absorber is the current optimal position of the population.

[0087] On the second aspect, the present application provides a method and system for optimizing the layout of nonlinear energy vibration absorbers considering the vortex-induced vibration effect, and proposes a criterion for optimizing the configuration of vibration absorbers considering the vortex-induced vibration effect, so as to ensure that the vibration absorption effect of the riser is optimal with a limited number of vibration dampers.

[0088] Beneficial technical effects of the present invention:

[0089] The present invention provides a method and system for optimizing the arrangement of nonlinear energy absorbers based on a particle swarm algorithm. The use of intelligent algorithms for optimizing the arrangement has become a research hotspot. As an optimization algorithm, the particle swarm algorithm has the characteristics of fast convergence speed and strong global search capability, and is suitable for complex nonlinear system optimization problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 A flow chart of a method for optimizing the arrangement of vibration absorbers taking into account vortex-induced vibrations provided in Example 1 of the present invention.

[0091] Figure 2 is a schematic diagram of a method of a specific embodiment;

[0092] Figure 3 A schematic diagram of adding a nonlinear energy absorber to a marine riser according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0093] In order to make the technical solution of the present invention more clear and specific to those skilled in the art, the present invention is further described in detail below in conjunction with embodiments and drawings, but the implementation manner of the present invention is not limited thereto.

[0094] Reference Figure 1 , Figure 2 , Figure 3 The present invention provides a nonlinear energy absorber optimization arrangement method based on a particle swarm algorithm, the method comprising the following steps:

[0095] The dynamic equations of the marine riser with multiple shock absorbers are established and simplified to obtain a simplified model.

[0096] The displacement of the corresponding node is solved by TMRM method;

[0097] Taking the minimum amplitude response of each node of the riser as the objective function, the particle swarm algorithm is applied to determine the optimal layout position of each hydrogen sensor in the key area.

[0098] Furthermore, the dynamic equation of the multi-sensor marine riser is:

[0099]

[0100] Further, the expression of the simplified model is as follows:

[0101]

[0102] Furthermore, the pipeline amplitude is obtained by solving the problem through the time domain minimum residual method. The specific steps are as follows:

[0103] Set the basis functions of displacement, velocity, and acceleration, and intercept the first N items.

[0104]

[0105] Using the basis function, substitute the approximate solution represented by the basis function into the original equation. Calculate the residual

[0106]

[0107] In order to make the residual as small as possible, find a set of coefficients a i ∈a makes R(a,t) minimum in time [0,T], that is,

[0108]

[0109] in is the nonlinear objective function, A is the feasible domain of the unknown coefficient a, and R(a,t) is the residual vector of the system.

[0110] Solved by the response sensitivity method.

[0111] According to the coefficient traversal principle, the objective function At discrete time nodes {t k ∈[0,T]k=1,2...l} to linearize the original nonlinear objective function is transformed into an approximate linear objective function Right now

[0112]

[0113] Theoretically, the infinite series of equation (3-2) can make the objective function is equal to 0, so in The first-order response sensitivity matrix is ​​as follows

[0114]

[0115] It should be noted that the approximate linear objective function It may be pathological, for example, when the number of unknowns is greater than the data, Tikhonov regularization is usually introduced to solve such problems. After introducing Tikhonov regularization, the problem can be transformed into

[0116]

[0117] In equation (3-10), I is the identity matrix, λ is called the regularization parameter and λ≥0. ||·|| represents l 2 Norm.

[0118] Particle swarm optimization is an optimization algorithm based on swarm intelligence. It simulates the foraging behavior of bird flocks to find the optimal solution. Particle swarm optimization algorithm performs well in solving nonlinear and complex optimization problems. The following is a detailed description of the optimization process of offshore riser vibration absorber layout based on particle swarm optimization.

[0119] (1) A particle group is composed of multiple particles, each of which represents a possible solution. In the present invention, the position of each particle represents a layout of a nonlinear energy absorber (NES).

[0120] Set the parameters of the particle swarm algorithm, including the number of particles N, the maximum number of iterations T, the inertia weight ω, the learning factors c1 and c2, and the initial values ​​of the particle speed and position.

[0121] The initial position and velocity of each particle are randomly generated. The initial position represents the initial arrangement position of the NES on the riser, and the velocity represents the rate of change of the position.

[0122] (2) A fitness function is introduced to evaluate the quality of each particle position. In the present invention, the fitness function takes the minimum vibration amplitude as the goal. Specifically defined as: the smaller the fitness value, the better the NES layout scheme.

[0123] f(x i )=R(x i )

[0124] The NES layout scheme corresponding to the current position of each particle is solved to calculate the vibration response of the riser under the action of current and waves. Based on the calculation results, the fitness value of the current position of each particle is calculated.

[0125] (3) During the search process, each particle will remember its best position in history, that is, the position with the smallest fitness value, which is called the individual optimal position (pbesti).

[0126] Among all particles, the position with the smallest fitness value is the global optimal position (gbest).

[0127] Velocity and position update formula:

[0128] υ i (t+1)=ω·υ i (t)+c1·r1·(pbest i -x i (t))+c2·r2·(gbest-x i (t))

[0129] x i (t+1)=x i (t)+υ i (t+1)

[0130] in:

[0131] υ i (t): velocity of particle i at time t; x i (t): the position of particle i at time t; ω: inertia weight, controlling the inertia of the particle; c1, c2: learning factors, adjusting the speed at which the particle moves to the individual optimal and global optimal positions; r1, r2: random numbers between [0, 1].

[0132] (4) If the number of iterations reaches the predetermined maximum value T, the algorithm is terminated. If the fitness value of the global optimal position changes very little in several consecutive iterations, the algorithm is considered to have converged and terminated.

[0133] (5) When the algorithm terminates, the global optimal position gbest is output as the optimal arrangement of the vibration absorber. At this point, the vibration response of the riser system is minimized, achieving the best vibration reduction effect.

[0134] In this embodiment, the amplitude of the riser caused by the vortex-induced vibration is taken into consideration, and a vibration damper optimization configuration criterion is proposed in consideration of the vortex-induced vibration.

[0135] The offshore riser vibration absorber placement system based on particle swarm algorithm includes multiple modules, each of which works together to achieve the optimal placement of nonlinear energy absorbers (NES) on offshore risers. The specific composition and functions of the system are as follows:

[0136] A marine riser vibration absorber placement system based on particle swarm algorithm is designed to optimize the placement of vibration absorbers to improve the vibration reduction effect of marine risers. The system integrates functional modules such as dynamic modeling, parameter setting, optimization calculation and result output, and realizes the automation of the entire process from riser vibration analysis to vibration absorber placement optimization.

[0137] First, the system includes a dynamic model module, which is used to establish and solve the dynamic model of the marine riser. By inputting the physical characteristics and environmental parameters of the riser, such as the length, diameter, material properties of the riser, and external excitation factors such as currents and waves, the dynamic model module can generate a mathematical model that accurately describes the vibration behavior of the riser.

[0138] Secondly, the parameter determination module is used to set and adjust the relevant parameters of the nonlinear energy absorber (NES). These parameters include the mass, damping coefficient and nonlinear stiffness of the vibration absorber. By setting these parameters reasonably, it can be ensured that the vibration absorber can effectively absorb and dissipate the vibration energy of the riser in actual application.

[0139] The particle swarm algorithm module is the core of the system. This module is responsible for executing the particle swarm optimization algorithm to find the best layout of the vibration absorber. The particle swarm algorithm module first initializes the particle swarm, including setting the initial values ​​of the number of particles, positions and velocities. Then, the vibration response of the vibration absorber layout corresponding to each particle position is calculated through numerical simulation, and the fitness value of each particle position is calculated according to the goal of minimizing the vibration amplitude. During the iteration process, the particle swarm algorithm module continuously updates the position and velocity of the particles, gradually approaching the optimal solution until the predetermined convergence conditions are met.

[0140] The system also includes a result output module for displaying and outputting the optimal vibration absorber layout. After the particle swarm optimization algorithm is completed, the result output module will use the global optimal position as the optimal layout of the vibration absorber and generate a detailed optimization report. The report includes the specific layout position of the vibration absorber, the convergence curve of the optimization process, and the numerical simulation results of the riser vibration response.

[0141] The above are only further embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solutions and concepts of the present invention within the scope disclosed by the present invention, which belong to the protection scope of the present invention.

Claims

1. A method for optimizing the arrangement of nonlinear energy absorbers based on particle swarm optimization, characterized in that: The steps include: S11: According to the design objectives and constraints of the nonlinear vibration absorber, the mass, damping coefficient and nonlinear stiffness parameters of the vibration absorber are determined through dynamic characteristics analysis, experimental analysis and nonlinear characteristics analysis; S12: According to the length, stiffness, diameter and other properties of the riser, as well as the magnitude of the current force, the coupled dynamic equation of the riser and the vibration absorber is established to describe the vibration behavior under the action of current and waves; S13: Set the initial values ​​of the number, position and speed of particles, and define the fitness function to evaluate the position of each particle; S14: Calculate the vibration response of the riser system under different vibration absorber arrangements by using the time domain minimum residual method, and calculate the fitness value of each particle position with the goal of minimizing the vibration amplitude; S15: According to the update rules of the particle swarm algorithm, the position and velocity of each particle are iteratively updated to gradually approach the optimal solution; S16: Setting a predetermined number of iterations or setting a fitness function, when the predetermined number of iterations is reached or the fitness function meets a convergence condition, outputting the vibration absorber as an optimal arrangement solution.

2. The method for optimizing the arrangement of nonlinear energy absorbers based on particle swarm algorithm according to claim 1, characterized in that: In step S15, the initialization of the particle swarm algorithm includes: By comprehensively considering the spatial dimension and the complexity of the problem, the number of particles in the particle swarm is set to ensure sufficient coverage of the search space. The number of particles is set between 20 and 50. According to the number of set particle groups, the upper and lower bounds of each particle's activity are determined so that each particle is randomly distributed within the bounds. Determine the upper and lower bounds for each particle's velocity, and randomly initialize the particle's velocity within each bound.

3. The method for optimizing the arrangement of nonlinear energy absorbers based on particle swarm algorithm according to claim 1, characterized in that: In step S16, the fitness function calculation is implemented by the following steps: S21: Calculate the vibration response of the riser under the vibration absorber arrangement scheme corresponding to each particle by using the time domain minimum residual method; S22: Calculate the fitness value of each particle position according to the vibration amplitude of the vibration response, with the goal of minimizing the vibration amplitude.

4. The method for optimizing the arrangement of nonlinear energy absorbers based on particle swarm algorithm according to claim 2, characterized in that: The update rules of the particle swarm algorithm include the following: According to the inertia weight ω, the individual learning factor c1 and the group learning factor c2, the speed of each particle is updated to continuously approach the optimal solution; υ i (t+1)=ω·υ i (t)+c1·r1·(pbest i -x i (t))+c2·r2·(gbest-x i (t)); υ i (t) is the velocity of particle i at time t; x i (t) is the position of particle i at time t; ω is the inertia weight, which controls the inertia of the particle moving forward; c1, c2 are learning factors that adjust the speed at which particles move to the individual optimal and global optimal positions; r1, r2 are random numbers between [0, 1]; pbest is the optimal position of the individual; gbest is the global optimal position; Update the position of each particle according to the updated velocity; x i (t+1)=x i (t)+υ i (t+1); After each iteration, the particle's best historical position and the global best historical position are updated.

5. The method for optimizing the arrangement of nonlinear energy absorbers based on particle swarm algorithm according to claim 2, characterized in that: In S16, the convergence conditions include any of the following: Reaching the predetermined maximum number of iterations; The fitness function value reaches the set threshold; After multiple consecutive iterations, the fitness value does not change significantly.

6. A particle swarm algorithm based optimization system for nonlinear energy absorber arrangement, a particle swarm algorithm based optimization method for nonlinear energy absorber arrangement according to any one of claims 1 to 5, characterized in that: Includes dynamic model module: used to establish and solve the dynamic model of the riser to describe the vibration behavior of the riser under the action of current and waves; Parameter determination module: used to determine the mass, damping coefficient and nonlinear stiffness parameters of the vibration absorber; Particle swarm algorithm module: used to perform initialization, fitness calculation and iterative update of particle swarm algorithm; Result output module: used to output the optimal vibration absorber layout plan.

7. The particle swarm algorithm based optimization nonlinear energy absorber arrangement system according to claim 6, characterized in that: The particle swarm algorithm module performs the particle swarm algorithm through the following steps: S31: Initialize the particle swarm, including setting the number, position and speed of particles; S32: Calculate the fitness function value of each particle, and calculate the vibration response of the riser under the corresponding vibration absorber arrangement scheme by using the time domain minimum residual method; S33: Update the historical best position of each particle and the global historical best position; S34: iteratively update the position and velocity of the particles according to the update rule of the particle swarm algorithm; S35: Determine the convergence condition and output the optimal solution.

8. The particle swarm algorithm-based optimization system for nonlinear energy absorber placement according to claim 7, characterized in that: The parameter determination module determines the mass, damping coefficient and nonlinear stiffness parameters of the nonlinear energy absorber according to the riser dynamics model to ensure the performance of the shock absorber under different layout schemes.

9. The particle swarm algorithm based optimization nonlinear energy absorber arrangement system according to claim 8, characterized in that: Dynamic equations of marine riser with multiple vibration absorbers: ω(z,t) is the cross-flow lateral displacement; z is the axial coordinate; is the total mass per unit length, including the mass of the structure and the mass of the fluid; C a is the mass coefficient of the fluid, ρ f is the density of the fluid being displaced, D is the outer diameter of the riser, EI is the bending stiffness, k is the spring stiffness of the absorber, d is the displacement of the absorber, c1 is the structural damping, and c2 is the damping of the shock absorber; F ω =F D +F L It means that the fluid force is calculated as the sum of the damping and lift added by the fluid; m NES represents the mass of the vibration absorber, q represents the amplitude of the wake oscillator; ε ω is the van der Pol damping, A is the dimensionless coupling coefficient; T(z,t) is the varying axial tension; Ω f Indicates the vortex shedding frequency.

Images