A parameter tuning method suitable for a multiple tuned mass damper of a floating wind turbine

Abstract

The present application relates to the technical field of floating wind turbine, in particular to a parameter tuning method suitable for multiple tuned mass damper of floating wind turbine, sequentially comprising establishing system dynamics model; defining optimization variables and constraint range; constructing comprehensive fitness function; initializing grey wolf population and algorithm parameters; executing grey wolf position optimization updating mechanism; setting convergence judgment condition; outputting optimal TMD parameter combination. The present application fully integrates structural dynamics characteristics and intelligent algorithm strategy, especially by including the spatial arrangement coordinates of TMD into the optimization variable domain, realizing the collaborative design of tuning parameters and arrangement space, different from single parameter or fixed point optimization mode, avoiding the limitations of artificial experience arrangement, realizing the overall suppression of multi-order modal response of structure, improving the vibration reduction capacity and stability margin of wind turbine structure under the excitation of wind wave flow coupling, realizing the collaborative governance of cross-modal and multi-source vibration at the level of system response coordination and control strategy, and having the adaptability of offshore wind power scene.

Description

Technical Field

[0001] This invention relates to the field of floating offshore wind turbine technology, specifically to a parameter tuning method for multi-tuned mass dampers in floating wind turbines. Background Technology

[0002] As a type of offshore power generation equipment that uses a floating structure to support wind turbines, floating offshore wind turbines (floating wind turbines) achieve a floating foundation through a semi-submersible platform combined with an anchor chain mooring system, breaking through the limitations of traditional fixed foundations. They are mainly deployed in deep-sea areas to obtain high-density wind energy resources and are suitable for development in waters deeper than 60 meters. However, the evolution of wind turbine structures from traditional fixed to floating structures increases the flexibility of the turbine structure, making it significantly susceptible to multi-source coupled loads such as wind, waves, and currents. This, in turn, leads to multi-mode vibration (multi-mode, large-amplitude vibration) in the floating wind turbine structure.

[0003] Currently, passive control is mainly achieved using tuned mass dampers (TMDs). Conventional TMDs are often placed at a single point (such as the top of a tower or the bottom of a platform), which can only control the first-order downwind mode. They also have shortcomings such as narrow bandwidth, limited placement space, and parameter dependence on empirical design, making it difficult to cope with vibration responses under complex multi-frequency excitations. As a result, multiple TMD systems have emerged in the field, which involve installing multiple TMDs on a floating wind turbine to control the multi-order modal response of the structure. However, there is still a lack of coordinated deployment logic among multiple TMDs, which often just result in a number of superpositions and are difficult to form an effective vibration reduction system. Therefore, it is necessary to tune the TMD parameters to achieve the optimal working state of the multiple TMD system.

[0004] Currently, the tuning of multiple TMD parameters often only targets specific wind, wave and current conditions, with the optimization goal of minimizing a certain response of the tower or platform. The effect on vibration control under other conditions is limited, and the overall efficiency of the multiple TMD system is low, which cannot meet the requirements of the diverse operating conditions faced in deep-sea areas. Summary of the Invention

[0005] The purpose of this invention is to provide a parameter tuning method for multi-tuned mass dampers of floating wind turbines, which addresses the shortcomings of existing technologies. This method differs from traditional empirical selection or common genetic algorithm optimization paths, and has stronger global search capabilities, faster convergence speed, and better solution set stability. It is particularly suitable for the optimization of control strategies for multi-degree-of-freedom, nonlinear, and strongly coupled response systems in floating wind power structures, thus solving the problems existing in the above-mentioned existing technologies.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A parameter tuning method for multi-tuned mass dampers in floating wind turbines includes the following steps:

[0008] S1) Establish a system dynamics model;

[0009] S2) Based on the numerical solution of the system dynamics model, define the optimization variables and the range of constraints;

[0010] S3) Construct a comprehensive fitness function for comprehensively evaluating the performance of TMD parameter combination control;

[0011] 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.

[0012] S5) Perform the gray wolf position optimization process and adjust the TMD parameter combination;

[0013] 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.

[0014] S7) Obtain the optimal TMD parameter combination to achieve the optimal control effect;

[0015] 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.

[0016] Furthermore, in step S1, the process of establishing the system dynamics model is as follows:

[0017] Let the generalized displacement vector of the main structure be... for:

[0018]

[0019] 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;

[0020] The relative displacement vector of each TMD for:

[0021]

[0022] in, Represents the relative displacement vector of TMD Spatial dimension, The number of TMDs deployed;

[0023] The system dynamics model is as follows:

[0024]

[0025]

[0026]

[0027] 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.

[0028] Furthermore, in step S2, the optimization variables are defined as follows: the mass ratio, frequency ratio, damping ratio of the TMD, and the installation height of the TMD in the tower. The constraints are set as follows:

[0029]

[0030] in, For mass ratio, For frequency ratio, For the damping ratio, This refers to the installation height of the TMD.

[0031] Furthermore, in step S3, the comprehensive fitness function is constructed as follows:

[0032]

[0033] 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;

[0034] Standard deviation of lateral displacement at the top of the tower The minimization function is:

[0035]

[0036] 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.

[0037] Platform pitch response amplitude The minimization function is:

[0038]

[0039] in, The platform pitch degree of freedom response in a multi-degree-of-freedom dynamic model;

[0040] Sum of modal energy participation factors The maximization function is:

[0041]

[0042] 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, For the model state energy item, This is the modal kinetic energy term;

[0043] Total penalty items The minimization function is:

[0044]

[0045] 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;

[0046] TMD total mass The calculation formula is as follows:

[0047]

[0048] in, For the first TMD quality ratio;

[0049] Tuning offset penalty The calculation formula is as follows:

[0050]

[0051] in, For the first A TMD tuning frequency The target modal frequency.

[0052] Furthermore, in step S4, the process of initializing the gray wolf population and algorithm parameters is as follows:

[0053] Within the constraints, an initial gray wolf population is randomly generated. Each individual in the gray wolf population represents a set of TMD parameter combinations, and the initial algorithm parameters, including the search factor, are set. Initial control factor Maximum weight factor Minimum weight factor Maximum number of iterations Levy disturbance intensity .

[0054] Furthermore, in step S5, the gray wolf position optimization process includes:

[0055] S51) Adaptive convergence weight control

[0056] S52) Gray Wolf Location Update

[0057] S53) Introduces Levy flight mechanism

[0058] S54) Father-Son Comparison and Elite Retention

[0059] Furthermore, in step S51, the adaptive convergence weight control process is as follows:

[0060] The formula for calculating the nonlinear weighting factor is as follows:

[0061]

[0062] 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;

[0063] Generate position update coefficients, including the following:

[0064]

[0065]

[0066]

[0067] 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:

[0068]

[0069] In step S52, the gray wolf's position update process is as follows:

[0070] All gray wolves update their positions using the control equations that simulate hunting behavior. The specific control equations are as follows:

[0071]

[0072] 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;

[0073] In step S53, the process of introducing the Levy flight mechanism includes:

[0074] When the process is in its later stages or when signs of convergence appear, inject the following update formula into certain dimensions / individuals:

[0075]

[0076] 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:

[0077]

[0078] 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;

[0079] In step S54, the process of retaining elites and comparing parent-child relationships is as follows:

[0080] 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.

[0081] Furthermore, in step S6, the convergence criterion includes the maximum number of iterations. and fitness convergence threshold ;

[0082] Fitness convergence threshold The formula for determining this is:

[0083]

[0084] in, For the first The global optimal fitness is determined. It is a continuous algebra;

[0085] 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.

[0086] Furthermore, in step S7, the process of outputting the optimal TMD parameter combination includes:

[0087] For single-objective optimization problems, output the TMD parameter configuration of the globally optimal individual at convergence;

[0088] 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.

[0089] Compared with the prior art, the beneficial effects of the present invention are:

[0090] This invention fully integrates structural dynamics characteristics with 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. Unlike traditional single-parameter or fixed-point optimization methods, it avoids the limitations of manual experience in layout and achieves overall suppression of multi-mode responses of the structure. It significantly improves the vibration reduction capability and stability margin of the wind turbine structure under wind, wave and current coupled excitation. At the level of system response coordination and control strategy, it achieves collaborative management of cross-modal and multi-source vibrations and has adaptability to offshore wind power scenarios. Specifically, this invention incorporates TMD parameters (mass ratio, frequency ratio, damping ratio) and TMD placement location into the optimization variables simultaneously, and performs spatial position tuning based on structural modal characteristics to improve the adaptability and performance coverage of the control system. A joint optimization model including mass ratio, frequency ratio, damping ratio, and TMD placement location is constructed to adaptively optimize the modal response region. An improved Grey Wolf Optimization Algorithm (I-GWO) incorporating the Levy flight mechanism and dynamic weight adjustment is adopted to enhance search accuracy and diversity. A comprehensive fitness function is constructed to fully consider tower top displacement, platform pitch, and modal energy factors, achieving coordinated optimization of TMD parameters and spatial layout, thus improving the system's tuning accuracy and response robustness under complex sea conditions. Finally, the optimal solution set is output, demonstrating strong flexibility in practical engineering selection. Detailed Implementation

[0091] To enable those skilled in the art to better understand 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 a part of the embodiments of the present application, and not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0092] This invention provides a parameter tuning method for multi-tuned mass dampers (MTMDs) in floating wind turbines. To achieve optimal configuration of MTMD system parameters and placement, an improved Grey Wolf Optimizer (I-GWO) algorithm is used to perform multi-objective joint optimization of the system, specifically including the following steps:

[0093] S1) Establish the system dynamics model

[0094] First, a multi-degree-of-freedom dynamic model of the main structure of the floating wind turbine (including six rigid body degrees of freedom of the platform and several bending modes in front of the tower) coupled with the TMD is established to characterize the coupled motion relationship between the tower, the platform and multiple TMDs.

[0095] To simulate the multi-mode response of a floating wind turbine under the coupled action of low-frequency loads such as wind, waves, and current, the following dynamic model of the main structure coupled with the TMD is established:

[0096] Let the generalized displacement vector of the main structure be... for:

[0097]

[0098] 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.

[0099] The relative displacement vector of each TMD Represented as:

[0100]

[0101] in, Represents the relative displacement vector of TMD Spatial dimension, The number of TMDs deployed.

[0102] The system dynamics model is expressed as:

[0103]

[0104] in, The modal mass matrix of the main structure;

[0105] Damping matrix of the main structure;

[0106] The stiffness matrix of the main structure;

[0107] These represent the acceleration vector, velocity vector, and displacement vector of the main structure modal coordinates, respectively.

[0108] This represents the transpose of the coupling matrix, i.e. for The transpose of the matrix, This represents the modal shape matrix of the main structure, with each column being a first-order modal shape function. The TMD installation layout matrix is ​​used to select the modal response at different tower heights; multiplying the two matrices yields the result. In order to establish a modal coupling relationship between the TMD and the main structure;

[0109] For the quality of TMD;

[0110] Damping for TMD;

[0111] Let TMD be the stiffness diagonal matrix;

[0112] These represent the relative acceleration, relative velocity, and relative displacement vectors of the TMD, respectively.

[0113] The equivalent generalized force of external loads (wind, waves, currents, etc.) in modal coordinates;

[0114] TMD Arrangement Matrix It can be represented as:

[0115]

[0116] its first Line by installation height The modal displacement values ​​of the main structure are determined, where, This represents the index of the TMD number, with a value range of 100. ; Indicates the first The installation height of each TMD.

[0117] This dynamic model not only describes the dynamic response of the structure under loads such as wind, waves, and currents, but also provides a computational basis for subsequent optimization. The numerical solution of the above dynamic equations can output response quantities such as tower top displacement, platform pitch angle, and modal energy. These results will be used as inputs for optimization variables and constraints in the next step.

[0118] S2) Based on the numerical solution of the system dynamics model, define the optimization variables and the range of constraints.

[0119] The optimization variables include the TMD's mass ratio, frequency ratio, damping ratio, and the TMD's position coordinates within the tower, i.e., the TMD's placement height. Their value ranges and engineering constraints are set as follows:

[0120] Initial constraint range:

[0121]

[0122] in, Let be the mass ratio, representing the first . The proportion of the mass of each TMD to the reference mass of the main structure;

[0123] The frequency ratio represents the first... The ratio of the tuning frequency of a TMD to the target modal frequency;

[0124] Let be the damping ratio, indicating the first . The equivalent damping ratio of a TMD;

[0125] The installation height of the TMD indicates the number of... The coordinates of the installation position of each TMD inside the tower.

[0126] The above range can be based on the total mass of the floating wind turbine tower. TMD design experience, structural bearing capacity and modal analysis results, natural frequencies of the target control modes. The actual parameters of the damper material and installation method are determined as follows:

[0127]

[0128] in, This represents the total height of the tower.

[0129] 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.

[0130] S3) Construct the comprehensive fitness function

[0131] The comprehensive fitness function is constructed as follows:

[0132]

[0133] in, To unify the weighted single objective and facilitate subsequent I-GWO iterations;

[0134] The standard deviation of the lateral displacement at the top of the tower;

[0135] This represents the maximum platform pitch angle.

[0136] Modal energy participation factor;

[0137] This is the total penalty item;

[0138] These are the weights for each objective (e.g., each is 0.25).

[0139] 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.

[0140] Specifically, the standard deviation of the lateral displacement at the top of the tower. The minimization function is:

[0141]

[0142] in, For the first First mode at the top height of the tower The mode shape value;

[0143] For the first The generalized coordinate response of the first mode;

[0144] 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;

[0145] This is the total time length of the simulation time-domain integration, used to calculate statistics (such as standard deviation and energy integral).

[0146] This refers to the displacement at the top of the tower.

[0147] This represents the average displacement at the top of the tower.

[0148] Platform pitch response amplitude The minimization function is:

[0149]

[0150] in, The platform pitch degree of freedom response in a multi-degree-of-freedom dynamic model;

[0151] Sum of modal energy participation factors The maximization function is:

[0152]

[0153]

[0154] in," "Indicates the modal number" It belongs to the target modality set (target);

[0155] For the first The energy contribution ratio of each mode is used to reflect the importance of that mode in the total response energy;

[0156] For the first The equivalent mass of the first mode;

[0157] For the first Equivalent stiffness of the first mode;

[0158] These represent the equivalent mass and equivalent stiffness of all modes in the calculation of the total modal energy of the system;

[0159] The first The response of the generalized displacement of the first mode over time, the response of the second mode to the generalized displacement over time, the response of the third mode to the generalized displacement over the generalized displacement to ... Velocity response of first mode;

[0160] These are the modal kinetic energy term and the modal dynamic energy term, respectively, representing the velocity energy of each mode over time and the displacement energy of each mode over time.

[0161] Total penalty items The minimization function is:

[0162]

[0163] in, This is the total penalty item;

[0164] Total mass of the main structure;

[0165] This is the weighting coefficient of the quality term in the penalty function, used to constrain the total quality of the TMD from exceeding the allowable range. The commonly used range is 0.2 to 0.5.

[0166] This is a penalty term for the tuning offset of the TMD parameters;

[0167] This is the weighting coefficient for the frequency deviation term in the penalty function, used to penalize excessive deviations between the TMD tuning frequency and the target modal frequency. The commonly used range is 0.3 to 0.7.

[0168] TMD total mass The calculation formula is as follows:

[0169]

[0170] in, For the first The quality ratio of each TMD.

[0171] Tuning offset penalty The calculation formula is as follows:

[0172]

[0173] For the first One TMD tuning frequency;

[0174] The target modal frequency.

[0175] 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.

[0176] 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.

[0177] 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.

[0178] The initial control parameters for the algorithm include the following:

[0179] Search factors

[0180] Initial control factor

[0181] Maximum weight factor

[0182] Minimum weight factor

[0183] Population size (In subsequent iterations, all computational steps are performed on the population) (each individual executes in parallel)

[0184] Maximum number of iterations (Determined based on experiment and time budget)

[0185] perturbation step size Generated according to the Mantegna algorithm, specifically represented as follows:

[0186]

[0187] in, To control the numerator random variable The standard deviation of ensures that the generated random step size follows a stable Levy distribution. Specifically, , For gamma function;

[0188] For random variables The variance;

[0189] These are random numbers from a standard normal distribution. =1.5;

[0190] Levy perturbation coefficient .

[0191] In this embodiment, the population size is first set. Maximum number of iterations Parameters are defined, and then, within the defined variable constraints, initial population individuals are randomly generated, and the fitness function is called to calculate their initial evaluation value. This initialization step ensures that all individuals have obtained an initial fitness score (i.e., an initial evaluation value), providing a benchmark for subsequent position updates and iterations.

[0192] S5) Perform the gray wolf position optimization process and adjust the TMD parameter combination.

[0193] The gray wolf's location optimization process includes the following steps:

[0194] S51) Adaptive convergence weight control

[0195] The formula for calculating the nonlinear weighting factor is as follows:

[0196]

[0197] in, For the first The weighting factor for the next iteration;

[0198] These are the maximum and minimum weight factors, respectively;

[0199] This represents the current iteration number;

[0200] This represents the maximum number of iterations.

[0201] For non-linear adjustment exponents, the following can be taken: .

[0202] The generation of position update coefficients (vectors are independent in each dimension) includes the following:

[0203]

[0204] in, This is a vector of contraction-expansion coefficients; This is the weighted modulation coefficient vector; These are random vector 1 and random vector 2, respectively. This is a dynamic convergence control factor that decreases linearly with algebraic progression. Specifically, it can be expressed as:

[0205]

[0206] 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.

[0207] S52) Gray Wolf Location Update (Leadership guidance)

[0208] 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:

[0209]

[0210]

[0211] in, The relative distance between the current individual and the leader individual;

[0212] This is a weighted modulation coefficient vector used to dynamically change the attractiveness of the leader's position to individuals, thereby increasing diversity. Specifically, ;

[0213] The solution with the best fitness in the population (including (Three levels of "alpha wolves")

[0214] For any individual in the population;

[0215] For leaders The proposed new solutions for each individual;

[0216] 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, ;

[0217] The three leaders with the best adaptability;

[0218] This represents the position of the individual after the iterative update, and signifies the updated parameter combination.

[0219] These represent the updated results for the three leaders, and the average of these results yields the new positions.

[0220] The search method is determined as follows:

[0221] when At that time, individuals tend to withdraw towards the leader and focus on localized development;

[0222] when At that time, individuals tend to distance themselves from the leader's perspective and focus on exploring the overall picture.

[0223] S53) Introduces the Levy flight mechanism to improve jump-out capability (avoiding premature convergence).

[0224] 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.

[0225] Specifically, in the later stages or when convergence signs appear, the update formula is injected into certain dimensions / individuals as follows:

[0226]

[0227] in, This refers to the updated position of the individual calculated in this iteration;

[0228] For the first The position vector of the optimal individual in the generation;

[0229] 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]. ;

[0230] Let random numbers follow a Levy distribution, defined as:

[0231]

[0232] 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);

[0233] 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);

[0234] For random variables The variance;

[0235] The exponential parameter of the Levy distribution is typically taken as... It is used to control the ratio of long jumps to short jumps.

[0236] S54) Father-Son Comparison and Elite Retention

[0237] 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.

[0238] 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:

[0239] Individual: The individual with the best fitness serves as the main guiding direction for the search of the next generation of the population;

[0240] Individual: The individual ranked second in fitness, used to guide the search for suboptimal solutions;

[0241] Individual: The third-ranked individual in terms of fitness increases search diversity and prevents getting trapped in local optima.

[0242] More specifically, to ensure the stability and feasibility of the solution, the elite retention strategy is adopted as follows:

[0243] 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;

[0244] 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;

[0245] 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.

[0246] 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.

[0247] S6) Set convergence criteria. During the gray wolf position optimization and update process, the algorithm terminates the iteration when the convergence criteria are met.

[0248] Two types of convergence criteria are set as follows:

[0249] a. Maximum number of iterations

[0250] 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 determined 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.

[0251] b. Fitness convergence threshold

[0252] 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:

[0253]

[0254] in, For the first The global optimal fitness;

[0255] For continuous algebra (e.g., 10 algebras);

[0256] 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.

[0257] 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.

[0258] S7) Output the optimal TMD parameter combination to achieve the best control effect.

[0259] For single-objective optimization problems, directly output the globally optimal individual at convergence (i.e., ...). TMD parameter configuration for individuals.

[0260] 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:

[0261] 1. Corresponding TMD parameters (including mass ratio) Damping ratio Frequency ratio );

[0262] 2. TMD placement location in the tower ;

[0263] 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).

[0264] 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.

[0265] 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.

[0266] 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.

[0267] S8) Result Verification and Simulation Feedback

[0268] 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:

[0269] 1. Input data preparation

[0270] Structural model parameters, such as tower mass distribution, stiffness, damping, platform mass and moment of inertia, are obtained through experimental measurements or design drawings.

[0271] TMD parameter combination: given by the optimization results, including mass ratio Damping ratio Frequency ratio Arrangement ;

[0272] 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;

[0273] Boundary and constraint conditions: anchoring method of floating wind turbine, setting of degree of freedom constraints, initial displacement / velocity conditions, etc.

[0274] 2. Simulation Modeling and Execution

[0275] In the dynamic simulation platform, the optimized TMD parameters and position coordinates are directly written into the tower model node attributes;

[0276] 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;

[0277] 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.

[0278] 3. Output Results and Index Calculation

[0279] 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.

[0280] Recalculate the four indicators based on the definition of the objective function:

[0281] Standard deviation of lateral displacement at the top of the tower

[0282] Platform pitch response amplitude

[0283] Sum of modal energy participation factors

[0284] Penalty items (total TMD mass and tuning offset)

[0285] 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.

[0286] 4. Verification Methods and Evaluation

[0287] Time-domain simulation of the dynamic model for backfilling the optimal solution / representative non-dominated solution:

[0288] 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.

[0289] Frequency domain verification: Perform FFT analysis to verify the response suppression effect at the target modal frequency;

[0290] Energy analysis: Calculate the energy dissipation of the TMD and the change in the total system energy to ensure stable operation of the controller.

[0291] 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.

[0292] 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.

[0293] 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:

[0294] Parameters and layout are optimized in an integrated manner, and the variable-parameter mapping is clear, avoiding the limitations of manual experience in layout.

[0295] Energy participation factor-driven layout scheme, adaptive modal response region;

[0296] The multi-objective fitness function comprehensively considers peak response, energy consumption, and robustness.

[0297] Levy flight and dynamic convergence strategies are introduced to enhance search accuracy and diversity;

[0298] Boundary / feasibility and elite retention ensure project feasibility and stable convergence;

[0299] It outputs a non-dominated solution set, providing greater flexibility in selecting solutions for practical engineering projects.

[0300] 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. 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 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 lateral displacement of the tower top, This represents the average lateral displacement at the top of the tower. Platform pitch response amplitude The 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 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 velocity response of the first mode, For the model state energy item, This is the modal kinetic energy term.

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, Generalized displacement vector representing the main structure 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 the TMD Spatial dimension; 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 modal coupling matrix. The modal coupling matrix is... The main structural mode shape matrix, Install and deploy the mapping matrix for TMD. The mass diagonal matrix of TMD. This is the damping diagonal matrix of the 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, The mass ratio of TMD. The frequency ratio of TMD, The damping ratio of the TMD. This refers to the installation height of the TMD within the tower.

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 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 .

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 S5, the gray wolf position optimization process includes: S51) Adaptive convergence weight control; S52) Gray Wolf location updated; S53) introduces the Levy flight mechanism; S54) Father-son comparison and elite preservation.

6. The parameter tuning method for a multi-tuned mass damper of a floating wind turbine according to claim 5, 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.

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 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.

8. 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 the non-dominated sorting method, and the first frontier non-dominated solution set is selected. The output includes the corresponding TMD parameters, TMD placement positions, and the values ​​of each objective function.

Images