Parameter tuning method suitable for floating fan multiple tuned mass damper

Abstract

The invention relates to the technical field of floating fans, in particular to a parameter tuning method suitable for a multi-tuned mass damper of a floating fan, which sequentially comprises the following steps of: establishing a system dynamics model; defining an optimization variable and a constraint range; constructing a comprehensive fitness function; initializing a grey wolf population and algorithm parameters; executing a grey wolf position optimization updating mechanism; setting convergence judgment conditions; and outputting the optimal TMD parameter combination. According to the method, structural dynamic characteristics and an intelligent algorithm strategy are fully fused, particularly, spatial arrangement coordinates of the TMD are brought into an optimization variable domain, collaborative design of tuning parameters and arrangement space is achieved, the method is different from a single-parameter or fixed-point optimization mode, the limitation of artificial experience layout is avoided, overall suppression of structural multi-order modal response is achieved, and the method is suitable for large-scale popularization and application. The damping capacity and the stability margin of the fan structure under wind wave flow coupling excitation are improved, cross-modal and multi-source vibration cooperative treatment is achieved on the system response coordination and control strategy level, and the method has the adaptability to offshore wind power scenes.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of floating offshore wind turbines, in particular to a parameter tuning method suitable for a multiple tuned mass damper of a floating wind turbine. BACKGROUND

[0002] As a kind of offshore power generation equipment using floating structure to support wind turbine, the floating offshore wind turbine (floating wind turbine) realizes floating foundation through semi-submersible platform combined with anchor chain mooring system, breaks through the limitation of traditional fixed foundation, and is mainly deployed in deep sea area to obtain high-density wind energy resources, and is suitable for sea area development with water depth exceeding 60 meters. However, the evolution of wind turbine structure from traditional fixed type to floating type will increase the flexibility of wind turbine structure, and the wind, wave and flow coupling loads will be significantly affected, thereby causing multi-modal vibration (multi-modal and large amplitude vibration) of the floating wind turbine structure.

[0003] At present, passive control is mainly carried out by using tuned mass damper (TMD), and the arrangement mode of conventional TMD is mainly concentrated in a single point (such as the top of the tower or the bottom of the platform), which can only control the first wind mode, and has the disadvantages of narrow frequency band, limited arrangement space and parameter dependent empirical design, etc., and it is difficult to cope with the vibration response under complex multi-frequency excitation, and thus a multiple TMD system is derived in the field, that is, multiple TMDs are installed on the floating wind turbine to realize the control of multi-modal response of the structure, but there is still a lack of collaborative arrangement logic among multiple TMDs, and it is difficult to form an effective vibration reduction system, so it is necessary to tune the parameters of TMD to make the multiple TMD system reach the best working state.

[0004] At present, in the process of tuning the parameters of multiple TMDs, only a few specific wind, wave and flow conditions are considered, and the minimum response of the tower or platform is taken as the optimization target, so the vibration control effect under other conditions is limited, the comprehensive performance of the multiple TMD system is low, and it cannot meet the requirement of diversity of working conditions in deep sea area. SUMMARY

[0005] The present application aims to provide a parameter tuning method suitable for a multiple tuned mass damper of a floating wind turbine, which is different from the traditional empirical selection or common genetic algorithm optimization path, has stronger global search ability, faster convergence speed and better solution set stability, and is especially suitable for control strategy optimization of a multi-degree-of-freedom, nonlinear and strongly coupled response system in a floating wind power structure, and solves the problems in the prior art.

[0006] In order to achieve the above purpose, the present application adopts the following technical scheme: A parameter tuning method suitable for a multiple tuned mass damper of a floating wind turbine, comprising the following steps: S1) Establishing a system dynamics model; S2) Defining optimization variables and constraint ranges based on the numerical solution of the system dynamics model; S3) Constructing a comprehensive fitness function for comprehensive evaluation of TMD parameter combination control performance; S4) Initializing a grey wolf population and algorithm parameters within the constraint range based on the improved grey wolf optimization algorithm, each grey wolf individual in the grey wolf population representing a set of TMD parameter combinations, and calling the comprehensive fitness function to calculate the initial evaluation value of each grey wolf individual; S5) Performing a grey wolf position optimization process to adjust the TMD parameter combination; S6) Setting a convergence judgment condition, and stopping the grey wolf position optimization update process when the convergence condition is met during the execution of the grey wolf position optimization update process; S7) Obtaining the optimal TMD parameter combination to achieve optimal control effect; S8) After obtaining the optimal TMD parameter combination, verifying the parameter combination through a numerical simulation platform, if the index does not meet the standard, taking the optimal TMD parameter combination as a new initial value for secondary optimization until the engineering threshold is met.

[0007] Further, in the step S1, the process of establishing the system dynamics model is as follows: Let the generalized displacement vector of the main structure be :

[0008] wherein, denotes the modal coordinate vector of the main structure in the real space dimension, is the modal degree of freedom number of the main structure; the relative displacement vector of the TMD is :

[0009] wherein, denotes the space dimension of the relative displacement vector of the TMD , is the number of TMDs arranged; The system dynamics model is:

[0010]

[0011]

[0012] wherein, is the modal mass matrix of the main structure, is the damping matrix of the main structure, is the stiffness matrix of the main structure, are the acceleration vector of the main structure modal coordinates, the velocity vector of the main structure modal coordinates, the displacement vector of the main structure modal coordinates, respectively, is the transpose of the coupling matrix, is the TMD placement matrix, is the modal shape matrix of the main structure, is the TMD installation placement matrix, is the mass of the TMD, is the damping of the TMD, is the stiffness diagonal matrix of the TMD, are the relative acceleration, relative velocity, relative displacement vector of the TMD, respectively, is the equivalent generalized force of the external load in modal coordinates.

[0013] Further, in the step S2, the optimization variables include the mass ratio, frequency ratio, damping ratio of the TMD, and the installation height of the TMD in the tower drum, and the constraint ranges thereof are set as follows:

[0014] wherein, is the mass ratio, is the frequency ratio, is the damping ratio, is the installation height of the TMD.

[0015] Further, in the step S3, the comprehensive fitness function is constructed as follows:

[0016] wherein, is the unified weighted single target, is the standard deviation of the tower top lateral displacement, is the maximum value of the platform pitch angle, is the modal energy participation factor, is the total penalty term, are the weights of each target, respectively; The standard deviation of the tower top lateral displacement The minimization function is:

[0017] wherein, is the modal shape value of the th mode at the height of the tower top, is the generalized coordinate response of the th mode, is the generalized coordinate response of the to include the optimized number of target modes, to simulate the total time length of the time domain integration, to the top displacement of the tower, to the mean value of the top displacement of the tower; the response amplitude of the platform pitch angle The minimization function is:

[0018] where, is the response of the platform pitch degree of freedom in the multi-degree of freedom dynamic model; the sum of modal energy participation factors The maximization function is:

[0019] where, denotes the mode number belongs to the target mode set, is the modal energy contribution ratio of the th mode, is the equivalent mass of the th mode, is the equivalent stiffness of the th mode, are the equivalent mass and the equivalent stiffness of all modes in the calculation of the total modal energy of the system, respectively, is the response of the generalized displacement of the th mode with time, is the velocity response of the th mode, is the modal potential energy term, is the modal kinetic energy term; total penalty term The minimization function is:

[0020] where, is the total penalty term, is the total mass of the main structure, is the weight coefficient of the mass term in the penalty function, is the weight coefficient of the frequency deviation term in the penalty function, is the TMD parameter tuning offset penalty term; total mass of TMD The calculation formula is as follows:

[0021] where, is the mass ratio of the th TMD; tuning offset penalty term The calculation formula is as follows:

[0022] Wherein, is the TMD tuning frequency of the th, is the target modal frequency.

[0023] Further, in the step S4, the process of initializing the grey wolf population and algorithm parameters is as follows: Randomly generate an initial grey wolf population within the constraint range, and each individual in the grey wolf population represents a set of TMD parameter combinations, and set the initial algorithm parameters including search factor , initial control factor , maximum weight factor , minimum weight factor , upper limit of iteration number , Levy disturbance intensity .

[0024] Further, in the step S5, the grey wolf position optimization process includes: S51) Adaptive convergence weight control S52) Grey wolf position update S53) Introducing Levy flight mechanism S54) Parent-child comparison and elite reservation Further, in the step S51, the process of adaptive convergence weight control is as follows: Calculate the nonlinear weight factor, and the calculation formula of the nonlinear weight factor is:

[0025] Wherein, is the weight factor of the th iteration, are the maximum and minimum weight factors respectively, is the current iteration number, is the maximum iteration number, is a nonlinear adjustment index; Generate a position update coefficient, including the following:

[0026]

[0027]

[0028] Wherein, is a contraction-dilation coefficient vector, is a weight modulation coefficient vector, They are random vector 1 and random vector 2, respectively. The dynamic convergence control factor is specifically expressed as:

[0029] In step S52, the gray wolf's position update process is as follows: All gray wolves update their positions using the control equations that simulate hunting behavior. The specific control equations are as follows:

[0030] in, The relative distance between the current individual and the leader. This is the solution with the best fitness in the population. For any individual in the population, For leaders The new candidate solutions given to the individual The three leaders with the best adaptability, The position of this individual after the iterative update represents the updated parameter combination. These represent the update results for the three leaders respectively; In step S53, the process of introducing the Levy flight mechanism includes: When the process is in its later stages or when signs of convergence appear, inject the following update formula into certain dimensions / individuals:

[0031] in, For each individual, the updated position calculated in this iteration. For the first The position vector of the optimal individual in the generation. This is the Levy step size coefficient. For random numbers that follow a Levy distribution, Defined as:

[0032] in, For a standard normally distributed random variable, Let be another independent standard normal random variable. For random variables variance is the exponential parameter of the Levy distribution; In step S54, the process of retaining elites and comparing parent-child relationships is as follows: The updated gray wolf individuals need to call the comprehensive fitness function again to calculate the evaluation value, and retain several gray wolf individuals with the best evaluation value and that meet the constraints from the current generation of gray wolf population as elite solutions. These elite solutions are then copied to the next generation of gray wolf population. For the remaining gray wolf individuals, the selection is carried out according to the parent-child comparison rule.

[0033] Furthermore, in step S6, the convergence criterion includes the maximum number of iterations. and fitness convergence threshold ; Fitness convergence threshold The formula for determining this is:

[0034] in, For the first The global optimal fitness is determined. It is a continuous algebra; When the The global optimal fitness improves by less than the fitness convergence threshold over several consecutive generations. Or the number of iterations reaches the maximum value. If the algorithm converges, the iteration is considered to have terminated.

[0035] Furthermore, in step S7, the process of outputting the optimal TMD parameter combination includes: For single-objective optimization problems, output the TMD parameter configuration of the globally optimal individual at convergence; For multi-objective optimization problems, the Pareto sorting method is used to sort the population using non-dominated sorting to select the first frontier non-dominated solution set. The output includes the corresponding TMD parameters and TMD placement positions. , values ​​of each objective function.

[0036] Compared with the prior art, the beneficial effects of the present invention are: The application fully integrates structural dynamic characteristics and intelligent algorithm strategies, especially by including the spatial arrangement coordinates of the TMD into the optimization variable domain, realizing the collaborative design of the tuning parameters and the arrangement space, which is different from the traditional single parameter or fixed point optimization method, avoiding the limitations of artificial experience arrangement, realizing the overall suppression of the multi-order modal response of the structure, significantly improving the vibration reduction capacity and stability margin of the fan structure under the coupling excitation of wind, wave and flow, realizing the collaborative management of cross-modal and multi-source vibration at the system response coordination and control strategy level, and having adaptability to offshore wind power scenarios. Specifically, the application simultaneously includes TMD parameters (mass ratio, frequency ratio, damping ratio) and TMD arrangement positions into optimization variables, tunes the spatial position according to the structural modal characteristics, and improves the adaptability and performance coverage of the control system; a joint optimization model including mass ratio, frequency ratio, damping ratio and TMD arrangement position is constructed, and the adaptive modal response area is constructed; an improved grey wolf optimization algorithm (I-GWO) introducing Levy flight mechanism and dynamic weight adjustment is used to enhance search accuracy and diversity; a comprehensive fitness function is constructed to comprehensively consider tower top displacement, platform pitch and modal energy factors, realize the collaborative optimization of TMD parameters and spatial layout, and improve the tuning accuracy and response robustness of the system under complex sea conditions; and finally, the optimal solution set is output, which has strong practical engineering flexibility. DETAILED DESCRIPTION

[0037] In order for those skilled in the art to better understand the scheme of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below. Obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0038] The embodiment of the application provides a parameter tuning method suitable for a multiple tuned mass damper of a floating wind turbine. In order to realize the optimal configuration of the system parameters and arrangement positions of the multiple tuned mass damper (MTMD), an improved grey wolf optimization algorithm (Improved Grey Wolf Optimizer, I-GWO) is used for multi-objective joint optimization of the system, specifically including the following steps: S1) Establish a system dynamics model First, a multi-degree-of-freedom dynamics model of the coupling of the main structure of the floating wind turbine (including six rigid body degrees of freedom of the platform and the first several bending modes of the tower) and the TMD is established, which is used to represent the coupling motion relationship between the tower, the platform and the multiple TMDs.

[0039] In order to simulate the multi-order modal response of the floating wind turbine under the coupling action of wind, wave and flow, the following main structure and TMD coupling dynamics model is established: Let the generalized displacement vector of the main structure be

[0040] where, is the modal coordinate vector of the main structure is the dimension of the real space where is the number of modal degrees of freedom of the main structure.

[0041] Let the relative displacement vector of the TMD be is given by:

[0042] where, is the relative displacement vector of the TMD is the dimension of the space where is the number of TMDs arranged.

[0043] The system dynamics model is given by:

[0044] where, is the modal mass matrix of the main structure; is the damping matrix of the main structure; is the stiffness matrix of the main structure; are the acceleration vector of the modal coordinates of the main structure, the velocity vector of the modal coordinates of the main structure, and the displacement vector of the modal coordinates of the main structure, respectively; is the transpose of the coupling matrix, i.e. is the transpose matrix of is the modal shape matrix of the main structure, with each column being a first-order modal shape function, is the TMD installation arrangement matrix used to select the modal response at different tower heights, and their product is to establish the modal coupling relationship between the TMD and the main structure; is the mass of the TMD; is the damping of the TMD; is the stiffness diagonal matrix of the TMD; are the relative acceleration, relative velocity, and relative displacement vectors of the TMD, respectively; is the equivalent generalized force of the external load (wind, wave, flow, etc.) in the modal coordinates;​​ TMD arrangement matrix may be expressed as:

[0045] its first row is determined by the modal displacement value of the main structure at the installation height , wherein, represents the number index of the TMD, and the value range is ; represents the installation height of the first TMD.

[0046] The dynamic model not only describes the dynamic response of the structure under the action of wind, wave, flow and other loads, but also provides a calculation basis for subsequent optimization. The numerical solution of the above dynamic equation can output the tower top displacement, platform pitch angle, modal energy and other response quantities, which will be used as the input basis of optimization variables and constraints in the next step.

[0047] S2) Based on the numerical solution of the system dynamics model, define the optimization variables and constraint range The optimization variables include the mass ratio, frequency ratio, damping ratio of the TMD, and the arrangement position coordinates of the TMD in the tower cylinder, i.e. the installation height of the TMD, and the value range and engineering constraint conditions are set as follows: Initial constraint range:

[0048] wherein, is the mass ratio, which represents the proportion of the mass of the first TMD to the reference mass of the main structure; is the frequency ratio, which represents the ratio of the tuning frequency of the first TMD to the target modal frequency; is the damping ratio, which represents the equivalent damping ratio of the first TMD; is the TMD installation height, which represents the installation position coordinates of the first TMD in the tower cylinder.

[0049] The above range can be determined according to the total mass of the floating wind turbine tower, TMD design experience, structural bearing capacity and modal analysis results, the natural frequency of the target control mode, and the actual parameters of the damper material and installation form as follows:

[0050] wherein, This represents the total height of the tower.

[0051] The above optimization variables are used to calculate the response behavior under different combinations through dynamic equations, and their constraints provide a feasible boundary for the next step of calculating the fitness function.

[0052] S3) Construct the comprehensive fitness function The comprehensive fitness function is constructed as follows:

[0053] in, To unify the weighted single objective and facilitate subsequent I-GWO iterations; The standard deviation of the lateral displacement at the top of the tower; This represents the maximum platform pitch angle. Modal energy participation factor; This is the total penalty item; These are the weights for each objective (e.g., each is 0.25).

[0054] The indices in the above-mentioned comprehensive fitness function are calculated from the response results obtained from the dynamic model and constrained within the defined variable range. This comprehensive fitness function is used to comprehensively evaluate the control performance of each set of TMD parameters.

[0055] Specifically, the standard deviation of the lateral displacement at the top of the tower. The minimization function is:

[0056] in, For the first First mode at the top height of the tower The mode shape value; For the first The generalized coordinate response of the first mode; To include the target number of modes in the optimization, let's assume the platform pitch mode plus the first two bending modes of the tower. Then, at this point... Take 3; This is the total time length of the simulation time-domain integration, used to calculate statistics (such as standard deviation and energy integral). This refers to the displacement at the top of the tower. This represents the average displacement at the top of the tower.

[0057] Platform pitch response amplitude The minimization function is:

[0058] where, is the platform pitch degree of freedom response in the multi-degree of freedom dynamic model; the sum of modal energy participation factors The maximization function is:

[0059]

[0060] where, is the modal number belongs to the target modal set (target); is the modal energy contribution ratio of the th mode, which is used to reflect the importance of the mode in the total response energy; is the equivalent mass of the th mode; is the equivalent stiffness of the th mode; are the equivalent mass and equivalent stiffness of all modes in the total modal energy calculation of the system, respectively; are the generalized displacement response of the th mode with time and the velocity response of the th mode, respectively; are the modal kinetic energy term and the modal potential energy term, respectively, representing the velocity energy of each mode with time and the displacement energy of each mode with time.

[0061] Total penalty term The minimization function is:

[0062] where, is the total penalty term; is the total mass of the main structure; is the weight coefficient of the mass term in the penalty function, which is used to constrain the total mass of the TMD within the allowable range, and the commonly used range is 0.2 to 0.5; is the TMD parameter tuning offset penalty term; is the weight coefficient of the frequency deviation term in the penalty function, which is used to penalize the TMD tuning frequency deviating too much from the target modal frequency, and the commonly used range is 0.3 to 0.7.

[0063] TMD total mass The calculation formula is as follows:

[0064] in, For the first The quality ratio of each TMD.

[0065] Tuning offset penalty The calculation formula is as follows:

[0066] For the first One TMD tuning frequency; The target modal frequency.

[0067] The value of the above comprehensive fitness function is used as the criterion for judging the quality of individuals and will be directly input into the initialization and iteration steps of the optimization algorithm.

[0068] S4) Based on the improved gray wolf optimization algorithm, the gray wolf population and algorithm parameters are initialized within the constraints, and the comprehensive fitness function is called to calculate the initial evaluation value of each gray wolf individual. Within the constraints, an initial gray wolf population is randomly generated, consisting of multiple initial gray wolf individuals, each representing a set of TMD parameter combinations.

[0069] The initial control parameters for the algorithm include the following: Search factors

[0070] Initial control factor

[0071] Maximum weight factor

[0072] Minimum weight factor

[0073] Population size (In subsequent iterations, all computational steps are performed on the population) (each individual executes in parallel) Maximum number of iterations (Determined based on experiment and time budget) perturbation step size Generated according to the Mantegna algorithm, specifically represented as follows:

[0074] in, To control the numerator random variable the standard deviation of the normal distribution, such that the generated random step obeys a stable Levy distribution, in particular, , is a gamma function; is a random variable the variance of the normal distribution; is a standard normal distribution random number, = 1.5; Levy disturbance coefficient .

[0075] In this embodiment, first set the population size , the upper limit of the number of iterations and other parameters, then randomly generate initial population individuals within the defined variable constraint range, and call the fitness function to calculate their initial evaluation value. This initialization step ensures that all individuals have obtained an initial fitness score (i.e. initial evaluation value), providing a benchmark for subsequent position updates and iterations.

[0076] S5) Perform grey wolf position optimization process to adjust TMD parameter combination The grey wolf position optimization process specifically includes the following steps: S51) Adaptive convergence weight control Calculate the nonlinear weight factor, and the calculation formula is:

[0077] wherein, is the weight factor of the th iteration; are the maximum and minimum weight factors, respectively; is the current iteration number; is the maximum iteration number; is a nonlinear adjustment index, which can be .

[0078] Generating position update coefficients (vector independent) includes the following:

[0079] wherein, is a contraction-expansion coefficient vector; is a weight modulation coefficient vector; are random vector 1 and random vector 2, respectively; is a dynamic convergence control factor, which decreases linearly with the number of iterations, which can be specifically expressed as:

[0080] By introducing a nonlinear weighting factor For dynamic convergence control factors A dynamic adaptive adjustment is performed, causing the algorithm to decrease non-linearly and smoothly during the iteration process. This mechanism maintains a large convergence step size in the early stages of the algorithm to enhance global search capabilities, and gradually reduces the step size in the later stages to achieve smooth approximation. This improves the stability and smoothness of the algorithm during the convergence phase and effectively avoids premature convergence and getting trapped in local optima due to excessively fast convergence speed.

[0081] S52) Gray Wolf Location Update (Leadership guidance) Let the current three leaders be... All gray wolves update their positions using the control equations that simulate hunting behavior. The specific control equations are as follows:

[0082]

[0083] in, The relative distance between the current individual and the leader individual; This is a weighted modulation coefficient vector used to dynamically change the attractiveness of the leader's position to individuals, thereby increasing diversity. Specifically, ; The solution with the best fitness in the population (including (Three levels of "alpha wolves") For any individual in the population; For leaders The proposed new solutions for each individual; This is a contraction-expansion coefficient vector used to determine the degree of "closeness" or "distance" between an individual and a leader. Specifically, More specifically, ; The three leaders with the best adaptability; This represents the position of the individual after the iterative update, and signifies the updated parameter combination. These represent the updated results for the three leaders, and the average of these results yields the new positions.

[0084] The search method is determined as follows: when At that time, individuals tend to withdraw towards the leader and focus on localized development; when At that time, individuals tend to distance themselves from the leader's perspective and focus on exploring the overall picture.

[0085] S53) Introduces the Levy flight mechanism to improve jump-out capability (avoiding premature convergence). To enhance the global search capability of the optimization process and reduce the risk of getting trapped in local optima, the Levy flight mechanism is introduced into the position update formula of I-GWO.

[0086] Specifically, in the later stages or when convergence signs appear, the update formula is injected into certain dimensions / individuals as follows:

[0087] in, This refers to the updated position of the individual calculated in this iteration; For the first The position vector of the optimal individual in the generation; This is the Levy step size control coefficient, used to control the search amplitude and adjust the disturbance intensity. Its value typically ranges from [value range missing]. ; Let random numbers follow a Levy distribution, defined as:

[0088] in, It is a standard normal random variable (zero-mean normal random variable) and is only enabled when the triggering condition is met (such as multi-generation improvement < threshold); For another independent standard normal random variable (zero-mean normal random variable), it is only enabled when the triggering condition is met (such as multi-generation improvement < threshold); For random variables The variance; The exponential parameter of the Levy distribution is typically taken as... It is used to control the ratio of long jumps to short jumps.

[0089] S54) Father-Son Comparison and Elite Retention In each generation of iterations, ordinary individuals are based on Three types of leaders guide the process, adjusting parameter combinations according to the position update formula. When the group shows an early convergence trend, Levy flight perturbation is introduced to enhance the ability to escape local optima. The updated individuals need to call the fitness function again to calculate their evaluation value, and are then filtered through parent-child comparison and elite retention mechanisms. The updated and filtered fitness evaluation values ​​are input into the following convergence judgment formula to determine whether to enter the next iteration or terminate.

[0090] Specifically, after each generation is completed, the fitness of the new solution is updated. (Optimal) Individuals are selected, and elite solutions are retained for the next iteration. After each generation, the fitness score of all individuals in the current population is calculated, and they are ranked according to their fitness scores as follows: Individual: The individual with the best fitness serves as the main guiding direction for the search of the next generation of the population; Individual: The individual ranked second in fitness, used to guide the search for suboptimal solutions; Individual: The third-ranked individual in terms of fitness increases search diversity and prevents getting trapped in local optima.

[0091] More specifically, to ensure the stability and feasibility of the solution, the elite retention strategy is adopted as follows: 1. Retain from the current generation population The individual with the best fitness that meets the constraints (physical range of TMD parameters, feasible range of tower layout location), Population size; 2. Directly copy these elite solutions to the next generation of the population to avoid losing high-quality solutions that have been found during the iteration process; 3. For the remaining individuals, the selection is carried out according to the parent-child comparison rule: if the child individual is better than the parent and meets the constraints, the parent is replaced; otherwise, the parent is retained.

[0092] This process ensures global search capability while maintaining local convergence accuracy and physical feasibility of the solution, thereby improving the overall effect of TMD placement and parameter optimization.

[0093] S6) Set convergence criteria. During the gray wolf position optimization and update process, the algorithm terminates the iteration when the convergence criteria are met. Two types of convergence criteria are set as follows: a. Maximum number of iterations

[0094] The fitness level is determined based on a combination of the convergence characteristics of the optimization algorithm and the time cost allowed by engineering calculations. Through multiple rounds of pre-experiments on the simplified model, the fitness trend is statistically analyzed. When the fitness stabilizes after a certain number of iterations and the improvement is minimal, this number of iterations is used as a reference, and further set in conjunction with the real-time requirements of the engineering project. (e.g., 200-500 generations), when reaching The iteration terminates when the time is right.

[0095] b. Fitness convergence threshold

[0096] Based on the sensitivity setting of the optimization objective, a judgment formula is used to determine whether the improvement of the global optimal fitness over several consecutive generations is lower than a threshold:

[0097] in, For the first The global optimal fitness; For continuous algebras (e.g., 10 algebras); Fitness convergence threshold Usually taken It can be flexibly adjusted according to the accuracy requirements of engineering calculations. Used to determine whether the algorithm has entered a convergent state; if the change in the optimal solution is less than [value missing] over several consecutive generations. If the algorithm converges, the iteration is considered to have terminated.

[0098] When any of the above convergence conditions is met, that is, when the th... The improvement of the optimal fitness over several consecutive generations is less than the fitness convergence threshold. Or the number of iterations reaches the maximum value. When the algorithm has converged, the iteration is considered to have terminated, and the algorithm enters the result output stage.

[0099] S7) Output the optimal TMD parameter combination to achieve the best control effect. For single-objective optimization problems, directly output the globally optimal individual at convergence (i.e., ...). TMD parameter configuration for individuals.

[0100] For multi-objective optimization problems, the non-dominated sorting method (NSGA-II mechanism) is used to perform Pareto sorting on the population, and the first front (Front1) non-dominated solution set is selected. The output includes: 1. Corresponding TMD parameters (including mass ratio) Damping ratio Frequency ratio ); 2. Location of TMD within the tower ; 3. Values ​​of each objective function (including standard deviation of tower top displacement, amplitude of platform pitch angle response, sum of modal energy participation factors, and penalty term value).

[0101] This convergence determination and solution set output method ensures that the optimization results converge within a reasonable computation time and provides the global optimal solution and multiple feasible trade-off solutions for engineering design.

[0102] When the optimal value of the fitness function improves by less than a set threshold over several consecutive generations. Or the number of iterations reaches the maximum value. If the condition is met, then convergence is determined. The final output is a set of TMD parameter combinations, which includes the global optimal solution (…). The output TMD parameter combination, along with the Pareto front undominated solution set, enables the structural critical response comprehensive fitness function. Minimize to achieve optimal control.

[0103] Furthermore, the output solution set (TMD parameter combination) can be backfilled into the dynamic equation for simulation verification, forming a complete optimization-verification closed loop.

[0104] S8) Result Verification and Simulation Feedback After obtaining the optimization results, this embodiment uses a numerical simulation platform (such as MATLAB / Simulink or Python (NumPy / SciPy) + OpenFAST / ANSYS (choose one for structure / modal and load coupling), and the time integration can use Newmark-β or fourth-order Runge-Kutta) to verify and adjust the selected parameter scheme. The specific process is as follows: 1. Input data preparation Structural model parameters, such as tower mass distribution, stiffness, damping, platform mass and moment of inertia, are obtained through experimental measurements or design drawings. TMD parameter combination: given by the optimization results, including mass ratio Damping ratio Frequency ratio Arrangement ; Environmental load time history: wind speed spectrum (Kaimal or IEC standard), wave spectrum (JONSWAP or Pierson–Moskowitz), and the phase relationship between the flow field and the waves, generated by the wind-wave-flow joint environmental model; Boundary and constraint conditions: anchoring method of floating wind turbine, setting of degree of freedom constraints, initial displacement / velocity conditions, etc.

[0105] 2. Simulation Modeling and Execution In the dynamic simulation platform, the optimized TMD parameters and position coordinates are directly written into the tower model node attributes; Set the simulation time step (e.g.) The total simulation duration (e.g., 600–1800 s) is adjusted to ensure the capture of low-frequency modal responses; Synchronously load wind, wave, and current coupled excitations, and call a numerical integrator (such as Newmark-β or Runge-Kutta) to solve for the response.

[0106] 3. Output Results and Index Calculation The lateral displacement at the top of the tower, the platform pitch angle time history, the modal energy participation factor, and the relative displacement of the TMD are directly extracted from the simulation results. Recalculate the four indicators based on the definition of the objective function: Standard deviation of lateral displacement at the top of the tower Platform pitch response amplitude Sum of modal energy participation factors Penalty items (total TMD mass and tuning offset) If all indicators meet or exceed expectations when compared with the optimization objective, the final result is output; if there is a deviation, the set of parameters is fed back to the optimization algorithm as new initial values ​​for a second iteration of optimization.

[0107] 4. Verification methods and evaluation Time-domain simulation of the dynamic model for backfilling the optimal solution / representative non-dominated solution: Time-domain verification: Analyze the time history response curve, impact response decay rate, residual vibration level, and compare the tower top displacement time history standard deviation, platform pitch peak value, and TMD relative displacement acceptability. Frequency domain verification: Perform FFT analysis to verify the response suppression effect at the target modal frequency; Energy analysis: Calculate the energy dissipation of the TMD and the change in the total system energy to ensure stable operation of the controller.

[0108] If the target is not met, the solution (i.e., the optimal solution / representative non-dominated solution) is used as a new initial value for secondary optimization (closed-loop feedback) until the engineering threshold is met.

[0109] This verification and feedback mechanism ensures that the optimization results not only perform well in algorithmic calculations but also exhibit stability and engineering feasibility under actual environmental load conditions. This forms a complete closed-loop process of "dynamic model—fitness function—optimization iteration—convergence determination—result verification," ensuring the technical solution possesses logical consistency and engineering operability.

[0110] The parameter tuning method provided in this embodiment fully integrates structural dynamics characteristics and intelligent algorithm strategies. In particular, by incorporating the spatial layout coordinates of the TMD into the optimization variable domain, it achieves the collaborative design of tuning parameters and layout space. This method differs from traditional single-parameter or fixed-point optimization methods and has the following significant innovative advantages: Parameters and layout are optimized in an integrated manner, and the variable-parameter mapping is clear, avoiding the limitations of manual experience in layout. Energy participation factor-driven layout scheme, adaptive modal response region; The multi-objective fitness function comprehensively considers peak response, energy consumption, and robustness. Levy flight and dynamic convergence strategies are introduced to enhance search accuracy and diversity; Boundary / feasibility and elite retention ensure project feasibility and stable convergence; It outputs a non-dominated solution set, providing greater flexibility in selecting solutions for practical engineering projects.

[0111] Although the present invention has been described using the above preferred embodiments, it is not intended to limit the scope of protection of the present invention. Any changes and modifications made by those skilled in the art to the above embodiments without departing from the spirit and scope of the present invention shall still fall within the scope of protection of the present invention.

Claims

1. A parameter tuning method for a multi-tuned mass damper suitable for floating wind turbines, characterized in that, Includes the following steps: S1) Establish a system dynamics model; S2) Based on the numerical solution of the system dynamics model, define the optimization variables and the range of constraints; S3) Construct a comprehensive fitness function for comprehensively evaluating the performance of TMD parameter combination control; S4) Based on the improved gray wolf optimization algorithm, the gray wolf population and algorithm parameters are initialized within the constraints. Each gray wolf in the gray wolf population represents a set of TMD parameter combinations. The comprehensive fitness function is called to calculate the initial evaluation value of each gray wolf. S5) Perform the gray wolf position optimization process and adjust the TMD parameter combination; S6) Set convergence criteria. When the convergence criteria are met during the gray wolf position optimization and update process, stop the gray wolf position optimization and update process. S7) Obtain the optimal TMD parameter combination to achieve the optimal control effect; S8) After obtaining the optimal TMD parameter combination, the parameter combination is verified through a numerical simulation platform. If the index does not meet the standard, the optimal TMD parameter combination is used as a new initial value for secondary optimization until the engineering threshold is met.

2. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 1, characterized in that, In step S1, the process of establishing the system dynamics model is as follows: Let the generalized displacement vector of the main structure be... for: ; in, Represents the principal structural modal coordinate vector The dimension of the real number space in which it resides. The number of modal degrees of freedom of the main structure; The relative displacement vector of each TMD for: ; in, Represents the relative displacement vector of TMD Spatial dimension, The number of TMDs deployed; The system dynamics model is as follows: ； ； ； in, The modal mass matrix of the main structure, The damping matrix of the main structure, The stiffness matrix of the main structure, Let represent the acceleration vector, velocity vector, and displacement vector of the main structure modal coordinates, respectively. This represents the transpose of the coupling matrix. Arrange the matrix for TMD. The main structural mode shape matrix, Install and arrange the matrix for TMD. For the quality of TMD, For the damping of TMD, Let TMD be the stiffness diagonal matrix. These represent the relative acceleration, relative velocity, and relative displacement vectors of the TMD, respectively. It is the equivalent generalized force of the external load in modal coordinates.

3. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 1, characterized in that, In step S2, the optimization variables are defined as follows: the mass ratio, frequency ratio, damping ratio, and installation height of the TMD in the tower. The constraints are set as follows: ; ; ； ； in, For mass ratio, For frequency ratio, For the damping ratio, This refers to the installation height of the TMD.

4. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 1, characterized in that, In step S3, the comprehensive fitness function is constructed as follows: ； in, To unify weighted single objectives, The standard deviation of the lateral displacement at the top of the tower. This represents the maximum platform pitch angle. For modal energy participation factors, For the total penalty item, These are the weights for each objective; Standard deviation of lateral displacement at the top of the tower The minimization function is: ； ； in, For the first First mode at the top height of the tower The mode shape value, For the first The generalized coordinate response of the first mode. To include the target number of modes in the optimization, This represents the total time length of the time-domain integration in the simulation. For the displacement of the tower top, This represents the average displacement at the top of the tower. Platform pitch response amplitude The minimization function is: ; in, The platform pitch degree of freedom response in a multi-degree-of-freedom dynamic model; Sum of modal energy participation factors The maximization function is: ； ； in, Indicates the modal number Belongs to the target modality set. For the first The proportion of energy contribution of each mode. For the first The equivalent mass of the first mode, For the first The equivalent stiffness of the first mode, These represent the equivalent mass and equivalent stiffness of all modes in the calculation of the total modal energy of the system. For the first The response of the generalized displacement of the first mode over time. For the first The velocity response of the first mode, As a model of potential energy, This is the modal kinetic energy term; Total penalty items The minimization function is: ; in, For the total penalty item, Total mass of the main structure. The weighting coefficients for the quality term in the penalty function. The weighting coefficients for the frequency deviation term in the penalty function. This is a penalty term for the tuning offset of the TMD parameters; TMD total mass The calculation formula is as follows: ； in, For the first TMD quality ratio; Tuning offset penalty The calculation formula is as follows: ； in, For the first A TMD tuning frequency The target modal frequency.

5. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 1, characterized in that, In step S4, the process of initializing the gray wolf population and algorithm parameters is as follows: An initial gray wolf population is randomly generated within the constraints, and initial algorithm parameters are set, including search factors. Initial control factor Maximum weight factor Minimum weight factor Maximum number of iterations Levy disturbance intensity .

6. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 1, characterized in that, In step S5, the gray wolf position optimization process includes: S51) Adaptive convergence weight control S52) Gray Wolf Location Update S53) Introduces Levy flight mechanism S54) Father-son comparison and elite preservation.

7. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 6, characterized in that, In step S51, the adaptive convergence weight control process is as follows: The formula for calculating the nonlinear weighting factor is as follows: ; in, For the first Weighting factor for the next iteration These are the maximum and minimum weight factors, respectively. This represents the current iteration number. The maximum number of iterations, It is a non-linear adjustment index; Generate position update coefficients, including the following: ; ; ； in, For the contraction-expansion coefficient vector, The weighted modulation coefficient vector, They are random vector 1 and random vector 2, respectively. The dynamic convergence control factor is specifically expressed as: ; In step S52, the gray wolf's position update process is as follows: All gray wolves update their positions using the control equations that simulate hunting behavior. The specific control equations are as follows: ； ； ; ； in, The relative distance between the current individual and the leader. This is the solution with the best fitness in the population. For any individual in the population, For leaders The new candidate solutions given to the individual The three leaders with the best adaptability, The position of this individual after the iterative update represents the updated parameter combination. These represent the update results for the three leaders respectively; In step S53, the process of introducing the Levy flight mechanism includes: When the process is in its later stages or when signs of convergence appear, inject the following update formula into certain dimensions / individuals: ; in, For each individual, the updated position calculated in this iteration. For the first The position vector of the optimal individual in the generation. This is the Levy step size coefficient. For random numbers that follow a Levy distribution, Defined as: ; ; ; in, For a standard normally distributed random variable, Let be another independent standard normal random variable. For random variables variance is the exponential parameter of the Levy distribution; In step S54, the process of retaining elites and comparing parent-child relationships is as follows: The updated gray wolf individuals need to call the comprehensive fitness function again to calculate the evaluation value, and retain several gray wolf individuals with the best evaluation value and that meet the constraints from the current generation of gray wolf population as elite solutions. These elite solutions are then copied to the next generation of gray wolf population. For the remaining gray wolf individuals, the selection is carried out according to the parent-child comparison rule.

8. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 7, characterized in that, In step S6, the convergence criterion includes the maximum number of iterations. and fitness convergence threshold ; Fitness convergence threshold The formula for determining this is: ; in, For the first The global optimal fitness is determined. It is a continuous algebra; When the The global optimal fitness improves by less than the fitness convergence threshold over several consecutive generations. Or the number of iterations reaches the maximum value. If the algorithm converges, the iteration is considered to have terminated.

9. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 1, characterized in that, In step S7, the process of outputting the optimal TMD parameter combination includes: For single-objective optimization problems, output the TMD parameter configuration of the globally optimal individual at convergence; For multi-objective optimization problems, the Pareto sorting method is used to sort the population using non-dominated sorting to select the first frontier non-dominated solution set. The output includes the corresponding TMD parameters and TMD placement positions. , values ​​of each objective function.

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