Intelligent optimization design method for parameters of offshore wind power damper

Abstract

The invention relates to the technical field of intelligent optimization of structural parameters of dampers of wind power generation equipment, and discloses an intelligent optimization design method for parameters of an offshore wind power damper. A damping coefficient, a rigidity coefficient and a piston stroke form a parameter vector, an upper bound and a lower bound are set, an input amplitude, frequency and an initial phase are recorded according to a harmonic sequence number, and multi-harmonic excitation is established. Enabling the device to be equivalent to a single degree of freedom, calculating the steady-state amplitude and phase difference of each order, and forming frequency-amplitude mapping; setting a unified target amplitude and being constrained by a stroke, and constructing frequency domain measurement based on full-order deviation square; calculating damping and rigidity gradients of the measurement to form vectors, performing updating, boundary and stroke projection, closed correction and resonance rejection in combination with the minimum step pitch and the threshold value, and defining minimum distinguishable change and convergence by tolerance; recalculating the step length and projection for the overrun order, and lowering the target when necessary; and finally, through step-by-step energy balance checking, outputting optimal damping, rigidity and stroke recorded values and a full-order response table.

Description

Technical Field

[0001] This invention relates to the field of intelligent optimization technology for structural parameters of wind power generation equipment dampers, specifically to an intelligent optimization design method for offshore wind power damper parameters. Background Technology

[0002] With the rapid development of the offshore wind power industry, the single-unit capacity and structural size of wind turbine generators are continuously increasing, posing severe challenges to the operational safety and reliability of the entire unit in the complex wind and wave environment at sea. As an important measure to ensure the structural stability of wind turbine generators and extend the life of key components, damping systems play a crucial role in absorbing structural vibration energy and reducing high-amplitude vibration response. However, the parameter design and optimization of offshore wind dampers still face many challenges.

[0003] In existing technologies, the selection of damper parameters typically relies on empirical methods, finite element simulation, or pre-defined mathematical models, such as equivalent linearization, modal analysis, or traditional resonant response analysis based on the time or frequency domain. These methods have several shortcomings: First, limited by empirical formulas and model structures, they often fail to accurately characterize the complex dynamic response of offshore wind turbines under strong multi-harmonic excitation and wind-wave coupling, resulting in insufficient adaptability and robustness of the damper parameters. Second, existing optimization methods often employ step-by-step adjustments and iterative trial-and-error approaches, lacking a globally consistent intelligent parameter optimization mechanism for frequency domain multi-harmonic responses, which easily leads to local optima or unbalanced frequency band responses. Furthermore, traditional parameter fitting and optimization processes generally rely on manually setting subjective parameters such as weights and proportional coefficients, which are difficult to dynamically determine in practical applications, resulting in damper parameter adjustments lacking adaptability and generalization capabilities for specific operating conditions. Under complex offshore conditions, wind turbines are subjected to coupled excitation from multiple sources of loads, including wind, waves, and currents. The actual dynamics of the system exhibit coupled resonance and amplitude transitions of multi-frequency energy. Single or low-order models often fail to accurately reflect the real operating conditions. Most existing frequency domain analysis methods only optimize the frequency response characteristics of the main harmonic or specific operating conditions, failing to achieve integrated modeling and global optimal control of the energy distribution and response across the entire frequency band and multiple harmonics. Furthermore, the weighting factors or harmonic coefficients used in spectral energy decomposition and fitting are often empirically selected, lacking physical basis and dynamic constraints, which can easily lead to optimization results deviating from actual requirements. Especially when adjusting the parameters of actual wind damping systems over a wide range, the lack of a verification mechanism based on physical boundaries and spectral energy balance can result in energy imbalances and discontinuous dynamic responses, affecting the stability and safety of damper performance.

[0004] Therefore, this case aims to propose an intelligent optimization design method for offshore wind damper parameters. Using external excitation with multiple harmonic superposition as the carrier, the damper is simplified into a single-degree-of-freedom vibration model. The parameter iteration is driven by frequency domain deviation measurement and gradient information. The reliability of parameter updates is ensured by combining closed constraints and feasible region projection. Error suppression and verification are carried out at both the stability and energy balance levels. Summary of the Invention

[0005] This invention provides an intelligent optimization design method for the parameters of offshore wind dampers, which helps to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: a method for intelligent optimization design of offshore wind damper parameters, comprising: Establish parameter vectors for damping coefficient, stiffness coefficient, and piston limit stroke, give the allowable upper and lower bounds for each parameter, record the input force amplitude, harmonic frequency, and initial phase according to the harmonic sequence number, and form an external excitation composed of multiple harmonic superpositions. The device is described as a single-degree-of-freedom model. The equivalent mass and displacement response are set, and the steady-state output displacement amplitude and force-displacement phase difference of each order are calculated to form a frequency-amplitude mapping. Set a uniform target amplitude, give a feasible upper bound in combination with the upper limit of the travel, and establish a frequency domain deviation metric based on the square of the difference between the full-order output and the target amplitude; The gradient components of the deviation metric are obtained for the damping coefficient and stiffness coefficient respectively, and then combined into a gradient vector. Set initial values ​​for parameter iteration, minimum adjustable step size and gradient threshold, calculate the quantization step size, perform parameter updates, boundary projection and feasible region projection, implement closed correction and resonance neighborhood derivation according to the out-of-bounds order, and give the minimum distinguishable response change and convergence criterion based on manufacturing tolerance. Calculate the order-wise relative error and the allowable upper limit, recalculate and update the parameters for the order that exceeds the limit according to the deterministic step size, complete the boundary and travel projection and closed constraints, and adjust the target amplitude until the criterion is met when the criterion cannot be met. Calculate the velocity components, single-cycle damping energy consumption and single-cycle input work step by step, check the step-by-step identities, and verify the substitution and root selection when there is inconsistency, and then check again. The system provides the recorded values ​​of the optimal damping coefficient, optimal stiffness coefficient, and piston limit stroke, and outputs the corresponding full-order frequency response table.

[0007] Optionally, the step of establishing parameter vectors for damping coefficient, stiffness coefficient, and piston limit stroke, giving allowable upper and lower bounds for each parameter, and recording input force amplitude, harmonic frequency, and initial phase according to harmonic sequence number to form an external excitation composed of multiple harmonic superpositions specifically includes: Establish a damper structural parameter vector, which includes three terms in sequence: damping coefficient, stiffness coefficient, and piston limit stroke; Obtain the allowable range of variation for each parameter, and provide the lower and upper bounds respectively; Establish a multi-harmonic structure for external excitation: set the total number of harmonics and order index; register the input force amplitude, harmonic frequency and initial phase for each order. Forming the total external excitation: The sinusoidal inputs of all orders are superimposed one by one according to frequency and phase to obtain the total excitation record that changes with time.

[0008] Optionally, the step of representing the device using a single-degree-of-freedom model, setting equivalent mass and displacement response, calculating the steady-state output displacement amplitude and force-displacement phase difference for each order, and constructing a frequency-amplitude mapping specifically includes: The damper is described as a single-degree-of-freedom vibration system, and its equivalent mass and displacement response are set. Establish a second-order ordinary differential equation that includes inertial terms, damping terms, stiffness terms, and external excitation; For each input frequency, calculate the steady-state output displacement amplitude, and obtain it from the input amplitude, stiffness, equivalent mass, damping coefficient and angular frequency according to the standard frequency response relationship; Calculate the force-displacement phase difference for each order using the arctangent relationship; when the stiffness is equal to the square of the angular frequency multiplied by the equivalent mass, record the phase difference as ninety degrees. A frequency-response amplitude mapping set is established based on the correspondence between order and output amplitude.

[0009] Optionally, the setting of a unified target amplitude, combined with the upper limit of the travel range to provide a feasible upper bound, and the establishment of a frequency domain deviation metric based on the squared difference between the full-order output and the target amplitude, specifically includes: Set an ideal constant amplitude target, where all order targets have the same positive amplitude. The upper limit of the allowable amplitude is given by the piston's limit stroke and the total number of harmonics; when the initial target exceeds the upper limit, the target amplitude is adjusted to the upper limit. Construct the target deviation function: Sum the squares of the differences between the full-order output displacement amplitude and the target amplitude and normalize them to obtain the frequency domain deviation measure.

[0010] Optionally, the step of obtaining gradient components for the damping coefficient and stiffness coefficient for the deviation metric, and combining them into a gradient vector, specifically includes: The frequency domain deviation metric is differentiated with respect to the damping coefficient and the stiffness coefficient to obtain two partial derivative functions; The gradient vector is formed by the partial derivatives of the two terms; We introduce a sensitivity function for each order of output amplitude, and give the sensitivity expression relative to the damping coefficient and stiffness coefficient.

[0011] Optionally, the setting of initial values ​​for parameter iteration, minimum adjustable step size, and gradient threshold; calculation of quantization step size; parameter updates, boundary projection, and feasible region projection; implementation of closed-loop correction and resonance neighborhood derivation according to the out-of-bounds order; and provision of minimum distinguishable response change and convergence criteria based on manufacturing tolerances, specifically including: Set the initial value of the parameter iteration and the minimum adjustable step size, and give the minimum gradient threshold; Calculate the fractional step size and generate the step size components of damping and stiffness based on the current gradient and threshold; Perform parameter updates and boundary projection and travel feasible region projection; For the set of out-of-bounds orders, a deterministic selection is made: when updating the damping coefficient is better, the damping is corrected according to the closed relationship; when updating the stiffness coefficient is better, the stiffness is projected onto the interval within the single-order allowable interval. Perform boundary reprojection again on the updated parameters; Set a resonance neighborhood threshold, and for stiffness components close to resonance, expand the neighborhood by the minimum step size and immediately reproject it. The minimum adjustable step size is used to give the minimum discernible response change and the convergence threshold is calculated. When the difference between adjacent iterations of the objective function does not exceed the threshold or the objective magnitude needs to be lowered to the feasible upper bound, the conclusion of this iteration is given.

[0012] Optionally, the calculation of successive relative errors and allowable upper limits, recalculation and parameter updates for orders exceeding limits using deterministic step sizes, completion of boundary and travel projections and closed constraints, and adjustment of the target amplitude until the criterion is met when the constraints cannot be satisfied, specifically includes: Calculate the relative error for each order and give the upper limit of the error tolerance derived from the upper limit of the travel; when the upper limit of tolerance is negative, adjust the target amplitude to the feasible upper limit; Recalculate the quantization step size for out-of-limit orders and update the parameters according to the deterministic formula; Perform parameter boundary projection and travel feasible region projection; if it still exceeds the limit, use closed inverse constraint: modify the damping coefficient when the stiffness coefficient is fixed, or modify the stiffness coefficient within the single-order allowable range when the damping coefficient is fixed. After closed-form inverse kinematics, perform boundary projection again; if no real roots are found, give an infeasible conclusion and lower the target magnitude to a feasible upper bound. Define new and old objective function values ​​and give convergence criteria: when the difference does not exceed the threshold or the total relative error does not exceed the upper limit, it is determined to be spectrally stationary.

[0013] Optionally, the stepwise calculation of velocity components, single-cycle damping energy dissipation, and single-cycle input work, verifying the stepwise identities and, if inconsistent, re-verifying by substituting and root selection, specifically includes: Obtain velocity components step by step; Calculate the energy dissipation of each single-cycle damping and sum them to obtain the total energy dissipation. Calculate the input power for each single cycle and sum them to obtain the total input power; For each order, compare the input work and the damping energy consumption. When they are consistent, it is considered that the energy balance is achieved. If inconsistencies occur, check each item for speed, phase, output amplitude substitution, and root selection during travel projection, correct and check again until they are consistent step by step.

[0014] Optionally, the step of providing the recorded values ​​of the optimal damping coefficient, optimal stiffness coefficient, and piston limit stroke, and outputting the corresponding full-order frequency response table, specifically includes: Output the optimal parameter solution, including the recorded values ​​of the optimal damping coefficient, optimal stiffness coefficient, and piston limit stroke, where the piston limit stroke is consistent with the input record; For each order, a frequency response table is provided at the optimal parameter solution, listing the order, input frequency, output displacement amplitude, and phase difference.

[0015] The present invention has the following beneficial effects: 1. By uniformly managing damper design parameters in vector form and defining external excitation as a multi-harmonic superposition signal, a refined simulation of complex offshore wind loads is achieved. Traditional methods often simplify the excitation to a single sine wave or random white noise, while this scheme uses harmonic indices to record the amplitude, frequency, and phase of each order, unfolding the wind load excitation step by step in the frequency domain and incorporating it along with the upper and lower bounds of the parameters into the design space, making the excitation model highly consistent with the actual operating environment. This excitation construction method, which is subdivided according to harmonic indices, can accurately capture the coupling effects of wind vibration loads at different frequency components, providing a solid foundation for subsequent frequency domain optimization and improving the consistency between design simulation and actual performance.

[0016] 2. The damper is simplified into a single-degree-of-freedom vibration system, and the steady-state displacement amplitude and phase difference at each excitation frequency are accurately solved, constructing a frequency-response amplitude mapping set. Compared to traditional methods that only focus on the displacement or acceleration response at the dominant frequency, this scheme calculates the output amplitude and phase difference for all excitation orders as a whole, ensuring the effectiveness of the design target across the entire frequency band. Simultaneously, the scheme automatically marks the phase difference as 90 degrees when resonance criticality is detected, providing a clear physical inflection point indication for subsequent parameter corrections. This achieves simultaneous analysis of multi-order responses, giving the design process a natural adaptability to multi-frequency coupling effects and avoiding system instability and fatigue damage caused by local resonance.

[0017] 3. By defining the design objective as a uniform amplitude and combining it with the upper limit constraint of the travel range, a frequency domain deviation metric function is formed, thereby quantifying the overall error between multi-order outputs and the target response. Unlike existing technologies that often use Pythagorean norm or weighted methods, this scheme directly measures the deviation based on the sum of the squares of the differences between each order output and the target value, achieving equal weighting across different orders through normalization. Furthermore, when the target amplitude exceeds the feasible region, it is automatically adjusted down to the travel limit boundary, ensuring optimization within the physically achievable range. This innovative method overcomes the problem of traditional objective settings being too abstract and difficult to implement, and reduces the instability caused by excessive reliance on subjectively set weights, improving the stability of optimization convergence and the feasibility of the results.

[0018] 4. The scheme calculates the gradient components of the damping coefficient and stiffness coefficient for the deviation metric function and constructs a complete gradient vector to reveal the sensitivity of parameter adjustments to frequency domain deviations. Unlike traditional parameter sensitivity analysis, which only provides a single sensitivity index, this method starts from the deviation function's derivation of each design parameter to obtain directional adjustment information for multi-frequency responses. It also introduces the frequency domain denominator as a unified evaluation variable, providing a consistent reference for step size calculation and feasible region determination. This allows for accurate parameter adjustments along the steepest descent direction during iterative updates, reducing blind searches, improving convergence rate, and optimizing overall performance while ensuring physical feasibility.

[0019] 5. This approach integrates multiple mechanisms, including parameter iteration, adaptive step size adjustment, boundary projection, feasible region projection, out-of-bounds closed-loop correction, and resonance neighborhood processing, into a single closed-loop control process. Unlike traditional fixed step size or single projection strategies, this scheme adaptively calculates the step size component based on the gradient lower bound and the minimum adjustable step size. After each update, it performs closed-loop feasibility correction on out-of-bounds stopping orders and implements neighborhood rejection for stiffness components near resonance points to avoid falling into resonance traps. The minimum discernible response change under manufacturing tolerances and the convergence criterion further ensure the verifiability of the results. This innovative process balances iteration speed and stability, improving both the predetermined convergence accuracy and the reliability of engineering implementation.

[0020] 6. To address potential out-of-limit output amplitudes during iteration, this solution employs sequential relative error calculation and threshold determination to achieve error suppression and dynamic adjustment of the target amplitude. Unlike existing techniques that often only perform simple convergence checks at the end of iterations, this method performs real-time quantization step size recalculation, parameter updates, and multi-level projection for out-of-limit situations in each iteration. When physical feasibility cannot be met, the target amplitude is automatically reduced until it becomes feasible before continuing iteration. This innovative process effectively avoids the risk of iteration deadlock or generating invalid solutions, while ensuring that a feasible optimal solution can still be found under manufacturing and travel constraints, thus improving the algorithm's robustness and practical usability.

[0021] 7. After spectrum optimization, the multi-order velocity components, single-cycle damping energy dissipation, and single-cycle input work are further compared and verified step by step to ensure that the input and energy dissipation are consistent at the mathematical and physical levels. Unlike existing technologies that only verify at the displacement or mode shape level, this scheme uses the identity judgment of energy balance, combined with the substitution verification during root selection and projection, to correct and verify any inconsistencies found until the identity is realized step by step. This not only ensures the physical rationality of the optimization results in theory, but also avoids design failures caused by potential energy deviations in practice, improving system safety and long-term reliability.

[0022] 8. The proposed solution outputs the converged optimal damping coefficient, stiffness coefficient, piston limit stroke, and corresponding full-frequency response table in a unified manner, forming a design data package that can be directly used in engineering. Unlike traditional design reports that typically only provide single-point characteristic values, this solution also provides the amplitude and phase difference information for each order of response, providing detailed information for subsequent verification tests and system debugging. This innovative output method balances the completeness of parameter settings with the operability of later verification, improving the efficiency of design delivery and ensuring the reliable performance of offshore wind dampers. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Example, refer to Figure 1 A method for intelligent optimization design of offshore wind damper parameters, comprising: Establish parameter vectors for damping coefficient, stiffness coefficient, and piston limit stroke, give the allowable upper and lower bounds for each parameter, record the input force amplitude, harmonic frequency, and initial phase according to the harmonic sequence number, and form an external excitation composed of multiple harmonic superpositions. The device is described as a single-degree-of-freedom model. The equivalent mass and displacement response are set, and the steady-state output displacement amplitude and force-displacement phase difference of each order are calculated to form a frequency-amplitude mapping. Set a uniform target amplitude, give a feasible upper bound in combination with the upper limit of the travel, and establish a frequency domain deviation metric based on the square of the difference between the full-order output and the target amplitude; The gradient components of the deviation metric are obtained for the damping coefficient and stiffness coefficient respectively, and then combined into a gradient vector. Set initial values ​​for parameter iteration, minimum adjustable step size and gradient threshold, calculate the quantization step size, perform parameter updates, boundary projection and feasible region projection, implement closed correction and resonance neighborhood derivation according to the out-of-bounds order, and give the minimum distinguishable response change and convergence criterion based on manufacturing tolerance. Calculate the order-wise relative error and the allowable upper limit, recalculate and update the parameters for the order that exceeds the limit according to the deterministic step size, complete the boundary and travel projection and closed constraints, and adjust the target amplitude until the criterion is met when the criterion cannot be met. Calculate the velocity components, single-cycle damping energy consumption and single-cycle input work step by step, check the step-by-step identities, and verify the substitution and root selection when there is inconsistency, and then check again. The system provides the recorded values ​​of the optimal damping coefficient, optimal stiffness coefficient, and piston limit stroke, and outputs the corresponding full-order frequency response table.

[0026] First, by centrally managing the three parameters—damping coefficient, stiffness coefficient, and piston stroke—in a vector form and clearly defining the upper and lower limits of each parameter, the problem of unclear parameter coupling identification and easy omission of key parameter ranges in the original technology is solved. Second, the actual marine wind vibration load is accurately reproduced using a multi-harmonic model, overcoming the simulation deviations caused by simplification to single frequency or random excitation in the past. Third, by using the sum of squared frequency domain deviations as a metric, multiple-order responses are simultaneously included in the target evaluation, avoiding local optimal failures caused by focusing only on the dominant frequency or improper weighting. Then, by calculating directional gradients for damping and stiffness respectively based on the deviation metric, a multi-dimensional gradient vector is constructed to guide parameter adjustments to evolve along the optimal direction, improving the convergence rate and reducing blind searches. Subsequently, closed projection and resonance neighborhood exclusion are adaptively performed within the true boundary and feasible stroke domain to prevent iterations from exceeding the feasible range and falling into the danger of resonance. Finally, by calculating the order-wise relative error in real time and adjusting the target when necessary, the parameter updates always meet physical feasibility, avoiding iterative deadlock and invalid loops. Finally, by checking the energy balance identity step by step, the physical rationality and stability of the design results at the energy level are verified, ensuring the safety and long-term reliability of the design.

[0027] The establishment of parameter vectors for damping coefficient, stiffness coefficient, and piston limit stroke, providing allowable upper and lower bounds for each parameter, and recording the input force amplitude, harmonic frequency, and initial phase according to harmonic sequence number, forms an external excitation composed of superimposed multi-order harmonics, specifically including: Establish a damper structural parameter vector, which includes three terms in sequence: damping coefficient, stiffness coefficient, and piston limit stroke; Obtain the allowable range of variation for each parameter, and provide the lower and upper bounds respectively; Establish a multi-harmonic structure for external excitation: set the total number of harmonics and order index; register the input force amplitude, harmonic frequency and initial phase for each order. Forming the total external excitation: The sinusoidal inputs of all orders are superimposed one by one according to frequency and phase to obtain the total excitation record that changes with time.

[0028] Further specific implementation steps include: The damper structure parameter vector is constructed as follows: ;in, An ordered triplet for damper design parameters; This is the damping coefficient, in units of... ; Stiffness coefficient, unit: ; This refers to the piston's limit stroke, measured in units of... ; Obtain the allowed range of parameter variation: , , ;in, , These are the lower and upper limits of the allowable damping coefficient, respectively; , These are the lower and upper limits of the allowable stiffness coefficient, respectively; , These are the lower and upper limits of the allowable piston stroke, respectively; these ranges are determined by the physical structure materials and the actual stroke of the equipment. The external excitation force is constructed as an excitation function composed of multiple harmonics, specifically as follows: ;in, These are continuous time intervals, measured in seconds. For a moment Total external incentives; For harmonic indexing; This represents the total number of harmonics. For the first Step input force amplitude; For the first First harmonic frequency; No. The initial phase of the input.

[0029] First, the damping coefficient, stiffness coefficient, and piston limit stroke in the damper design are organized into ordered triplets according to engineering dimensions and centrally registered in vector form, effectively avoiding errors in results caused by inconsistent parameter definitions between experiments and simulations. Second, a precisely defined allowable variation range is given for each parameter, ensuring that subsequent optimization is constrained by the physical limits of engineering manufacturability and actual stroke. This step completely solves the non-physical interpretation or meaningless jitter caused by simple truncation in boundary treatment of common optimization algorithms. Third, by constructing the external excitation force using a multi-order harmonic superposition method and assigning independent amplitude, frequency, and phase to each harmonic, the random and multi-frequency vibration characteristics of actual sea wind are accurately reproduced, far superior to the traditional single specification that only takes the dominant frequency or white noise. This multi-order decomposition not only enhances the correspondence between the simulation model and the real working conditions but also provides rich input information for subsequent frequency domain response mapping, realizing the organic combination of load source and parameter space.

[0030] The process of describing the device using a single-degree-of-freedom model, setting equivalent mass and displacement response, calculating the steady-state output displacement amplitude and force-displacement phase difference for each order, and constructing a frequency-amplitude mapping specifically includes: The damper is described as a single-degree-of-freedom vibration system, and its equivalent mass and displacement response are set. Establish a second-order ordinary differential equation that includes inertial terms, damping terms, stiffness terms, and external excitation; For each input frequency, calculate the steady-state output displacement amplitude, and obtain it from the input amplitude, stiffness, equivalent mass, damping coefficient and angular frequency according to the standard frequency response relationship; Calculate the force-displacement phase difference for each order using the arctangent relationship; when the stiffness is equal to the square of the angular frequency multiplied by the equivalent mass, record the phase difference as ninety degrees. A frequency-response amplitude mapping set is established based on the correspondence between order and output amplitude.

[0031] Further specific implementation steps include: Simplify the damper into a single-degree-of-freedom vibration system, and assume its equivalent mass is . The response displacement is The dynamic differential equation is obtained as follows: ;in, Equivalent mass, unit is kilogram; The displacement response is a function of time; , These are the first and second time derivatives, respectively; For any order Input excitation frequency Calculate its response amplitude under steady-state conditions: ;in, For the first Output displacement amplitude; And construct angular frequency Phase difference The closed relation is: , ;in, For the first angular frequency; For the first Step force-displacement phase difference; like Then let ; Therefore, the displacement response can be expressed as: ; Establish a frequency-response amplitude mapping set: ;in, To include all harmonic numbers The set of output amplitudes.

[0032] First, the three major physical quantities in the system—inertia, damping, and elasticity—are summarized as equivalent mass, damping coefficient, and stiffness coefficient. Based on this, the steady-state output displacement amplitude and phase deviation are calculated step-by-step, achieving accurate closed-form solutions for each excitation order across the entire frequency spectrum. Unlike existing techniques that often rely on numerical integration or chain-like sensitivity analysis in simulation software, this method, for the first time, solidifies the frequency response mapping for each order as an integrated "frequency-amplitude" set, reducing the computational burden of numerical integration and avoiding numerical noise introduced by discretization. Furthermore, when resonance criticality is detected, the phase difference is automatically set to a fixed value, providing a clear physical trigger point for subsequent closed-form corrections.

[0033] The process involves setting a unified target amplitude, providing a feasible upper bound based on the upper limit of the travel range, and establishing a frequency domain deviation metric based on the squared difference between the full-order output and the target amplitude. Specifically, this includes: Set an ideal constant amplitude target, where all order targets have the same positive amplitude. The upper limit of the allowable amplitude is given by the piston's limit stroke and the total number of harmonics; when the initial target exceeds the upper limit, the target amplitude is adjusted to the upper limit. Construct the target deviation function: Sum the squares of the differences between the full-order output displacement amplitude and the target amplitude and normalize them to obtain the frequency domain deviation measure.

[0034] Further specific implementation steps include: The ideal target response is set to a constant amplitude ideal value: , ;in, For the first First-order reference target amplitude; To standardize the target response amplitude; And satisfy: , , ; If the above conditions are not met, then let ; The sum of frequency domain response deviations is calculated as follows: ;in, The objective function is to quantize the mean square deviation of the output spectrum from the ideal equal-weighted spectrum, which is then minimized in the optimization.

[0035] By defining the ideal response target as a uniform amplitude ideal value across all orders and combining it with the upper limit of piston stroke to form a dynamic feasible upper bound, this method effectively solves the problems of ambiguous target setting and frequent occurrences of infeasibility due to exceeding limits during the optimization process. In existing technologies, designers typically need to set targets for each frequency point or weighted bias reduction based on experience. This solution, however, achieves automatic correction and feasibility assurance of the target value by explicitly defining a unified ideal amplitude and directly comparing it with the physical stroke limit. Specifically, if the initial target exceeds the physical stroke limit, the target is immediately lowered to an achievable boundary value without manual intervention, avoiding optimization from falling into invalid intervals or generating meaningless high-amplitude responses. Subsequently, a metric function is established based on the squared deviation between the full-order output and the target, quantifying and uniformly evaluating multi-order errors, thus eliminating the drawbacks of excessive focus on a single frequency point leading to local optima or neglecting other frequency bands. This innovation ensures that the optimization process has clear physical constraints and does not rely on subjective weight settings, guaranteeing that iterations always revolve around a consistent target across all frequency bands within the feasible range, improving the algorithm's stability and industrial applicability.

[0036] The deviation metric obtains gradient components for the damping coefficient and stiffness coefficient respectively, and combines them into a gradient vector, specifically including: The frequency domain deviation metric is differentiated with respect to the damping coefficient and the stiffness coefficient to obtain two partial derivative functions; The gradient vector is formed by the partial derivatives of the two terms; We introduce a sensitivity function for each order of output amplitude, and give the sensitivity expression relative to the damping coefficient and stiffness coefficient.

[0037] Further specific implementation steps include: Calculate the deviation function with respect to The gradient is: ; Calculate the deviation function with respect to The gradient is: ; in, , For partial derivative functions, quantize them separately. right , Sensitivity; The gradient vector is constructed as follows: ;in, For vector functions, corresponding to The gradient of the three components, the third component being 0. It does not affect the linear frequency response; Set the first The denominator of the frequency domain is ; get: , ;in, , This is the sensitivity function to the output amplitude.

[0038] By calculating the directional derivatives of the full-order deviation metric function along the damping and stiffness directions respectively, this method quantifies the specific influence of each parameter on the full-frequency deviation, providing accurate directional information for subsequent step size calculation and parameter correction. Compared with existing single sensitivity indices or overall gradient approximations, this method can capture the personalized contribution of parameters to different-order responses under multi-frequency coupling, effectively avoiding overshoot or slow convergence caused by blind adjustments. By incorporating the response denominator into a unified factor and introducing the frequency domain denominator as a unified evaluation quantity, different frequency responses are more standardized into the same metric system, making the gradient vector consistent across multiple physical dimensions. This not only improves the effectiveness of parameter updates but also provides a solid numerical foundation for subsequent adaptive step size calculations, promoting the efficiency and stability of the overall optimization process.

[0039] The process involves setting initial values ​​for parameter iteration, minimum adjustable step size, and gradient threshold; calculating the quantization step size; updating parameters; boundary projection and feasible region projection; implementing closed-loop correction and resonance neighborhood derivation according to the out-of-bounds order; and providing minimum distinguishable response change and convergence criteria based on manufacturing tolerances. Specifically, this includes: Set the initial value of the parameter iteration and the minimum adjustable step size, and give the minimum gradient threshold; Calculate the fractional step size and generate the step size components of damping and stiffness based on the current gradient and threshold; Perform parameter updates and boundary projection and travel feasible region projection; For the set of out-of-bounds orders, a deterministic selection is made: when updating the damping coefficient is better, the damping is corrected according to the closed relationship; when updating the stiffness coefficient is better, the stiffness is projected onto the interval within the single-order allowable interval. Perform boundary reprojection again on the updated parameters; Set a resonance neighborhood threshold, and for stiffness components close to resonance, expand the neighborhood by the minimum step size and immediately reproject it. The minimum adjustable step size is used to give the minimum discernible response change and the convergence threshold is calculated. When the difference between adjacent iterations of the objective function does not exceed the threshold or the objective magnitude needs to be lowered to the feasible upper bound, the conclusion of this iteration is given.

[0040] Further specific implementation steps include: Set the initial value for iteration to... The minimum adjustable step distance for manufacturing is given as: , And construct the minimum gradient threshold as: , ;in, ; For iterative indexing; , Minimum adjustable step size; , This is the lower bound of the gradient; In the first Evaluation at the next iteration parameter; Calculate the quantization step size vector: , , ;in, Let be the step size vector, at the th... Three-component step size under the next iteration index; , Scalar step size; Update parameters: ; Perform constraint projection, specifically: S501, Parametric Boundary Projection: , ; S502, Formation of Feasible Region Determination and Projection: make , ; If it exists Then cut off to the feasible boundary: ;in, This represents the output amplitude after the stage. The deterministic parameter selection and closed-form inverse solution are performed as follows: , ;in, , The criterion is chosen for determinism; when When, select update Specifically: , ;in, , They are respectively the set of out-of-bounds orders and the set of orders that can be delimited. A closed-form feasible out-of-bounds subset; like ; like If so, it is deemed infeasible and will be... Downgraded to And continue to update and project at the current parameters until convergence; when When, select update Specifically: , ;in, The constraint radius; It is a single-order allowed interval; Let this round of pre-update values If they intersect If not empty, then: ;in, for The lower endpoint; for The upper endpoint; like If so, it will be deemed infeasible and will be... Downgraded to And continue to update and project at the current parameters until convergence; The strategy for selecting numbers is as follows: For the equation The plus sign corresponds to the minus sign. The actual values ​​of the two endpoints are determined by the interval projection formula. The boundary reprojection after closed-loop inverse kinematics is as follows: , ; Set the resonance neighborhood threshold If it exists Then Determine the neighborhood based on the minimum step size: like ,but ; like ,but ; Then immediately perform boundary reprojection: ; Construct the minimum distinguishable response change induced by manufacturing tolerances, specifically as follows: , ;in, For the first The smallest distinguishable amplitude change; This is the convergence threshold; when When convergence is reached, it is determined that the convergence has occurred. If there is no real root or Then it is determined to be the current Not feasible, and the target amplitude is lowered to Subsequently in the current Continue calculating, updating, and projecting until convergence.

[0041] First, by setting initial parameter values ​​and specifying the minimum adjustable step size and gradient lower bound under manufacturing tolerances, each update is performed within a range that can be identified by physical manufacturing, avoiding invalid iterations caused by small step sizes. Second, for out-of-bounds situations that occur after parameter updates, the solution implements closed-loop feasible correction or interval projection according to the out-of-bounds order, which can directly restore parameter validity within the physically feasible region without discarding the iteration path. Third, minimum neighborhood repulsion is applied to parameter components that are close to resonance to prevent optimization from falling into resonance valleys and ensure system stability. Finally, a convergence criterion is constructed by manufacturing the minimum identifiable response change, realizing convergence judgment based on engineering-verifiable physical differences, avoiding the disconnect between traditional convergence criteria and actual manufacturability. This fusion of multiple constraints and adaptive mechanisms not only accelerates the convergence speed but also ensures that the entire optimization process remains within feasible physical constraints, greatly improving engineering practicality.

[0042] The calculation of successive relative errors and allowable upper limits, recalculation and parameter updates for orders exceeding limits using deterministic step sizes, completion of boundary and travel projections and closed constraints, and adjustment of target amplitudes until the criteria are met when they cannot be satisfied, specifically includes: Calculate the relative error for each order and give the upper limit of the error tolerance derived from the upper limit of the travel; when the upper limit of tolerance is negative, adjust the target amplitude to the feasible upper limit; Recalculate the quantization step size for out-of-limit orders and update the parameters according to the deterministic formula; Perform parameter boundary projection and travel feasible region projection; if it still exceeds the limit, use closed inverse constraint: modify the damping coefficient when the stiffness coefficient is fixed, or modify the stiffness coefficient within the single-order allowable range when the damping coefficient is fixed. After closed-form inverse kinematics, perform boundary projection again; if no real roots are found, give an infeasible conclusion and lower the target magnitude to a feasible upper bound. Define new and old objective function values ​​and give convergence criteria: when the difference does not exceed the threshold or the total relative error does not exceed the upper limit, it is determined to be spectrally stationary.

[0043] Further specific implementation steps include: Constructing the stationarity error factor: , ;in, For the first order relative error; The relative error limit is calculated from the equivalent upper bound determined by the travel, specifically as follows: , ;in, This represents the upper limit of the relative error tolerance. like Then let ; If it exists Then, a deterministic modification will be made, specifically: S601, Recalculate the quantization step size: , ; S602. Update parameters using a deterministic formula: , ; S603, Projection of Execution Boundary and Travel Feasible Region: Parameter boundary projection: , ; Projection of feasible region: Let , ; If it still exists after projection onto the parameter boundary Then, the constraints are solved by closed-form inverse problem: fixed hour: ; fixed hour: , ; If the intersection If not empty, then ; like Then let ; Boundary reprojection after closed-form inverse kinematics: , ; If the square root term is negative, then the conclusion that it is impossible to have no real roots is given, and the following is also given. Downgraded to Continue according to the aforementioned modified rules until the criteria are met; S604. Define and determine convergence criteria: , ;in, , These are the objective function values ​​before and after the correction, respectively. when or all If the spectral stationarity is satisfied, a conclusion is given; otherwise, the aforementioned correction rules are continuously executed and calculated until the criterion is satisfied.

[0044] During the iteration process, this scheme further constructs a relative error factor in real time for outputs in frequency bands exceeding the allowable amplitude and provides an upper bound for the relative error calculated from the upper limit of the travel range, thus achieving closed-loop control of error suppression and target reduction. Specifically, when an output response of a certain order is detected to exceed the physical feasible upper bound, the scheme recalculates the quantization step size for the order exceeding the limit based on the pre-calculated relative error limit, and performs multiple rounds of projection and closed constraints within the boundary and travel domain to ensure that each update strictly adheres to the physical upper limit. If the exceedance cannot be eliminated after closed constraints, the overall target amplitude is automatically reduced to a feasible value, and iteration continues under the current parameter conditions, completely avoiding the algorithm from falling into a state of no solution or oscillation under high targets. Unlike existing technologies that only uniformly determine convergence in the final round, this method achieves real-time correction of errors and targets in each iteration, making the optimization process more robust, adaptable to dynamically changing physical constraints, and ensuring that the final solution satisfies the design target without exceeding the actual travel range or manufacturing tolerance limits.

[0045] The stepwise calculation of velocity components, single-cycle damping energy dissipation, and single-cycle input work involves verifying the stepwise identities and, if inconsistent, re-verifying the substitution and root selection processes before final verification. Specifically, this includes: Obtain velocity components step by step; Calculate the energy dissipation of each single-cycle damping and sum them to obtain the total energy dissipation. Calculate the input power for each single cycle and sum them to obtain the total input power; For each order, compare the input work and the damping energy consumption. When they are consistent, it is considered that the energy balance is achieved. If inconsistencies occur, check each item for speed, phase, output amplitude substitution, and root selection during travel projection, correct and check again until they are consistent step by step.

[0046] Further specific implementation steps include: Obtain the velocity components by performing closed-form differentiation. ; Construct a closed-form expression for single-cycle damping energy dissipation, specifically as follows: , , ;in, For the first Single-cycle damping energy consumption; For the first First period; Total energy consumption; Constructing a closed-form expression for single-cycle input power, specifically: , ;in, For the first Single-cycle input power; Total input power; If each step is identical If the calculations are correct, then the energy balance and spectral stability are considered valid; if discrepancies occur, the conclusion is that the calculations are inconsistent and each item needs to be verified. , Substituting the values ​​and selecting the roots of the path projection, then correcting and substituting them again into the closed-form check, until successive identity is achieved; where, It represents the identity sign.

[0047] First, the velocity component is obtained by closed-form differentiation of the output amplitude and phase difference at each order. Then, the energy values ​​of dissipation and input are calculated according to the closed-form expressions of damped energy dissipation and input work, and the two are compared step by step to see if they are strictly equal. If there is an inconsistency, the scheme automatically initiates the substitution correction and root selection verification process until the energy balance is achieved. This verification mechanism makes up for the common deficiency of only focusing on displacement or displacement amplitude difference, and further elevates the design from the mode shape level to the energy conservation level, avoiding design failure or equipment damage caused by potential energy deviation. Unlike traditional schemes that only perform coarse safety factor assessment at the system level, this method can accurately guarantee energy conservation under multi-spectral coupling conditions, improving the safety and reliability of the optimization results during on-site installation and long-term operation.

[0048] The document provides recorded values ​​for the optimal damping coefficient, optimal stiffness coefficient, and piston limit stroke, and outputs the corresponding full-order frequency response table, specifically including: Output the optimal parameter solution, including the recorded values ​​of the optimal damping coefficient, optimal stiffness coefficient, and piston limit stroke, where the piston limit stroke is consistent with the input record; For each order, a frequency response table is provided at the optimal parameter solution, listing the order, input frequency, output displacement amplitude, and phase difference.

[0049] Further specific implementation steps include: Output the final optimal parameter solution ;in, , This represents the optimal value for the final damping coefficient; This represents the optimal value for the final stiffness coefficient; This is the recorded value for the final piston limit stroke; Output the corresponding frequency response table: , .

[0050] The optimal damping coefficient, stiffness coefficient, and piston limit stroke after convergence are summarized, and a full-order frequency response table containing the output amplitude and phase difference for each excitation order is generated. This response table not only encompasses complete verification data for multiple frequency bands and physical quantities, but can also be directly imported into simulation platforms and test benches for verification, effectively shortening the design-testing-debugging cycle. Furthermore, engineers can use this response table to adjust the damper structure or control strategy on-site to achieve precise matching of the expected response. Compared with the single-frequency parameter tables or main frequency response reports commonly used in existing technologies, the full-frequency response data package output by this method improves the transparency and operability of parameter application, making the overall design delivery more efficient and reliable, and providing detailed basic data for subsequent vibration control strategies and performance monitoring.

[0051] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0052] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An offshore wind power damper parameter intelligent optimization design method, characterized in that, The method comprises the following steps: A parameter vector of damping coefficient, stiffness coefficient and piston limit stroke is established, the allowed upper and lower bounds of each parameter are given, the input force amplitude, harmonic frequency and initial phase are recorded according to the harmonic order, and an external excitation formed by superposition of multiple harmonics is formed; The device is expressed according to a single degree of freedom model, the equivalent mass and displacement response are set, the steady-state output displacement amplitude and force-displacement phase difference of each order are calculated, and a frequency-amplitude mapping is constructed; A unified target amplitude is set, a feasible upper bound is given in combination with the stroke upper limit, a frequency domain deviation measure based on the square of the difference between the full order output and the target amplitude is established; The gradient components of the deviation measure are obtained with respect to the damping coefficient and the stiffness coefficient, and are combined into a gradient vector; The parameter iteration initial value, the minimum adjustable step and the gradient threshold are set, the componentized step is calculated, the parameter update, boundary projection and stroke feasible region projection are performed, the closed-form correction and resonance neighborhood push-out are implemented according to the out-of-bound order, and the minimum identifiable response change and convergence criterion are given according to the manufacturing tolerance; The relative error of each order and the allowed upper limit are calculated, the parameters of the orders exceeding the limit are recalculated and updated according to the determined step, the boundary and stroke projection and closed constraint are completed, and when the criterion cannot be met, the target amplitude is lowered until the criterion is met; The velocity component, single-cycle damping energy and single-cycle input work of each order are calculated, the consistency of each order is checked, and when the consistency is inconsistent, the substitution and root selection are rechecked. The recorded values of the optimal damping coefficient, the optimal stiffness coefficient and the piston limit stroke are given, and the corresponding full-order frequency response table is output.

2. The offshore wind turbine damper parameter intelligent optimization design method according to claim 1, characterized in that, The method comprises the following steps: A parameter vector of damping coefficient, stiffness coefficient and piston limit stroke is established, the allowed upper and lower bounds of each parameter are given, the input force amplitude, harmonic frequency and initial phase are recorded according to the harmonic order, and an external excitation formed by superposition of multiple harmonics is formed, which specifically comprises: A damper structure parameter vector is established, which sequentially contains three items of damping coefficient, stiffness coefficient and piston limit stroke; The allowed variation range of each parameter is obtained, and the lower bound and the upper bound are given respectively; A multi-harmonic composition is established for the external excitation: the total number of harmonics and the order index are set; the input force amplitude, harmonic frequency and initial phase are registered for each order; 3. The offshore wind turbine damper parameter intelligent optimization design method according to claim 2, characterized in that, The total external excitation is formed: the sinusoidal inputs of all orders are superimposed item by item according to the frequency and phase to obtain the total excitation record varying with time. The device is expressed according to a single degree of freedom model, the equivalent mass and displacement response are set, the steady-state output displacement amplitude and force-displacement phase difference of each order are calculated, and a frequency-amplitude mapping is constructed, which specifically comprises: The damper is expressed according to a single degree of freedom vibration system, and the equivalent mass and displacement response are set; A second-order ordinary differential equation containing inertia term, damping term, stiffness term and external excitation is established; For each input frequency, the steady-state output displacement amplitude is calculated, and the input amplitude, stiffness, equivalent mass, damping coefficient and angular frequency are obtained according to the standard frequency response relationship; The force-displacement phase difference of each order is calculated, and is obtained according to the inverse tangent relationship; when the stiffness and the square of the angular frequency multiplied by the equivalent mass are equal, the phase difference is recorded as ninety degrees; 4. The offshore wind turbine damper parameter intelligent optimization design method according to claim 3, characterized in that, A frequency-response amplitude mapping set is established according to the correspondence between the order and the output amplitude. The method comprises the following steps: Setting ideal constant-amplitude target, all order target amplitudes are equal and positive; Giving amplitude upper bound by piston limit stroke and total harmonic number; when initial target exceeds the upper bound, adjusting target amplitude to the upper bound; Constructing target deviation function: squaring and summing the difference between all order output displacement amplitudes and target amplitudes, and normalizing to get frequency domain deviation measure.

5. The offshore wind turbine damper parameter intelligent optimization design method according to claim 4, characterized in that, The gradient components of the deviation measure with respect to damping coefficient and stiffness coefficient are obtained respectively, and combined into a gradient vector, specifically including: Taking the derivative of the frequency domain deviation measure with respect to the damping coefficient and the stiffness coefficient respectively, two partial derivatives are obtained; The two partial derivatives form a gradient vector; Introducing the sensitivity function of each order to the output amplitude, and giving the sensitivity expression with respect to the damping coefficient and the stiffness coefficient.

6. The offshore wind turbine damper parameter intelligent optimization design method according to claim 5, characterized in that, Setting parameter iteration initial value, minimum adjustable step size and gradient threshold, calculating component step size, performing parameter update, boundary projection and stroke feasible region projection, implementing closed-form correction and resonance neighborhood push-out for out-of-bound orders, and giving minimum identifiable response change and convergence criterion according to manufacturing tolerance, specifically including: Setting parameter iteration initial value and minimum adjustable step size, and giving minimum gradient threshold; Calculating component step size, and generating damping and stiffness step components according to current gradient and threshold; Performing parameter update and executing boundary projection and stroke feasible region projection; Determining the selection of out-of-bound order set: when the updated damping coefficient is better, correcting the damping according to the closed-form relationship; when the updated stiffness coefficient is better, performing interval projection on the stiffness within the single-order allowed interval; Performing boundary re-projection on the updated parameters again; Setting resonance neighborhood threshold, and pushing out the neighborhood of the stiffness component close to resonance according to the minimum step size and immediately re-projecting; Giving the minimum identifiable response change according to the minimum adjustable step size of manufacturing, and calculating the convergence threshold; When the difference between adjacent iterations of the target function does not exceed the threshold or the target amplitude needs to be lowered to the feasible upper bound, giving the conclusion of this round of iteration.

7. The offshore wind turbine damper parameter intelligent optimization design method according to claim 6, characterized in that, Calculating the relative error of each order and the allowed upper limit, recalculating and updating the parameters according to the determined step size for the out-of-limit orders, completing boundary and stroke projection and closed-form constraint, and lowering the target amplitude until the criterion is met when it cannot be met, specifically including: Calculating the relative error of each order and giving the error allowed upper limit derived from the stroke upper limit; when the allowed upper limit is negative, adjusting the target amplitude to the feasible upper bound; Recalculating the component step size for the out-of-limit orders and updating the parameters according to the determined formula; Performing parameter boundary projection and stroke feasible region projection; still out of bounds, using closed-form inverse solution constraint: correcting the damping coefficient while fixing the stiffness coefficient, or correcting the stiffness coefficient within the single-order allowed interval while fixing the damping coefficient; Performing boundary projection again after closed-form inverse solution; if there is no real root situation, giving an infeasible conclusion and lowering the target amplitude to the feasible upper bound; Defining new and old target function values and giving convergence criterion: when the difference does not exceed the threshold or all relative errors do not exceed the upper limit, it is determined that the frequency spectrum is stable.

8. The offshore wind turbine damper parameter intelligent optimization design method according to claim 7, characterized in that, Calculating the velocity component of each order, the single-cycle damping energy and the single-cycle input work, checking the identity of each order, and rechecking after reselecting the substitution and roots when they are inconsistent, specifically including: Obtaining the velocity component of each order; Calculating the single-cycle damping energy of each order and summing to get the total energy; Calculate each order single period input work and sum up to get total input work; Compare input work with damping energy dissipation for each order respectively, and record as energy balance is established when consistent; If inconsistent, review each item of speed, phase, output amplitude substitution and root selection when stroke projection, correct and check again until consistent step by step.

9. The offshore wind turbine damper parameter intelligent optimization design method according to claim 8, characterized in that, The record value of the optimal damping coefficient, the optimal stiffness coefficient and the piston limit stroke is given, and the corresponding full order frequency response table is output, specifically including: The optimal parameter solution is output, including the record value of the optimal damping coefficient, the optimal stiffness coefficient and the piston limit stroke, wherein the piston limit stroke is consistent with the input record; The frequency response table at the optimal parameter solution is given for each order, listing the order, input frequency, output displacement amplitude and phase difference.

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