A method for rapid estimation of inherent frequency of offshore wind turbine structure and inversion of structural parameters

Abstract

The application provides a kind of offshore wind turbine structure inherent frequency fast estimation and structure parameter inversion method, belong to the ocean engineering structure monitoring technical field based on computer data processing;Establish offshore wind turbine structure finite element model, modal analysis is carried out to the structure parameter set to obtain inherent frequency, construct sample data set;Rely on data set to establish the initial polynomial proxy model of the first n order inherent frequency of offshore wind turbine;Significance test is carried out to each coefficient of initial polynomial proxy model, and significant sensitive item is screened, initial polynomial proxy model is simplified, and test inspection is carried out;Based on actual structure parameter, input proxy model, obtain the first n order inherent frequency;Linear equation set between the first n order inherent frequency and structure parameter is constructed;Equation set is solved into optimization solving problem, and the structure parameter of offshore wind turbine under measured inherent frequency is obtained.The method is used for real-time monitoring and safety evaluation of wind turbine structure health state under actual conditions, and operation is simple, precision is reliable.

Description

Technical Field

[0001] This invention belongs to the field of marine engineering structure monitoring technology based on computer data processing, and particularly relates to a method for rapid estimation of the natural frequency of offshore wind turbine structures and inversion of structural parameters. Background Technology

[0002] Offshore wind power, with its abundant wind energy resources, high utilization hours, and lack of onshore land occupation, has become a significant growth engine in the global renewable energy sector. The Global Wind Energy Council's "Global Offshore Wind Energy Report 2025" shows that by the end of 2024, the global cumulative grid-connected offshore wind power capacity had reached 83.2 GW, with an average annual growth rate of approximately 10% over the past decade. China has ranked first globally in cumulative offshore wind power capacity for four consecutive years.

[0003] Offshore wind turbines operate throughout their entire lifecycle in harsh marine environments characterized by strong winds, waves, and salt spray corrosion. They inevitably face structural degradation issues such as fatigue, corrosion, and loose connections. Furthermore, the difficulty of accessing offshore environments significantly increases maintenance costs compared to onshore wind power. Therefore, structural health monitoring of offshore wind turbines has become a crucial technical means to reduce maintenance costs and ensure their safe operation.

[0004] In structural monitoring and early warning indicators, natural frequency is one of the core parameters characterizing structural integrity. It is not only the basis for assessing the vibration characteristics of wind turbine structures, avoiding resonance failure, and conducting dynamic response analysis, but also a sensitive indicator reflecting changes in structural stiffness. Accurate and rapid acquisition of natural frequency is of great significance for assessing the in-service status of offshore wind turbines.

[0005] Currently, the mainstream method for calculating the natural frequency in the industry is to obtain the natural frequency of the offshore wind turbine structure by performing Fourier transform and modal identification on the monitoring acceleration time history data. This method has drawbacks such as being susceptible to measurement noise and environmental interference, complex modal identification process, and long calculation time. At the same time, it cannot accurately identify and assess the health status of the offshore wind turbine structure.

[0006] Therefore, there is an urgent need to propose a method for estimating the natural frequency and inverting the structural parameters of offshore wind turbines that is easy to calculate and has reliable accuracy. Summary of the Invention

[0007] To address the above problems, this invention provides a method for rapid estimation of the natural frequency and inversion of structural parameters of offshore wind turbines, comprising the following steps: S1. Establish a finite element model of the offshore wind turbine structure, perform modal analysis on multiple sets of structural parameters to obtain natural frequencies, and construct a sample dataset with structural parameters as input and the first n natural frequencies as output. S2, based on the sample dataset, establish an initial polynomial surrogate model for the first n natural frequencies of offshore wind turbines; S3. ANOVA was used to test the significance of the coefficients of the initial polynomial surrogate model. Coefficients with an absolute value of fit coefficients not less than 0.05 within the significance interval were selected as significant sensitive terms. The initial polynomial surrogate model was simplified based on the significant sensitive terms, and a test set was constructed for testing and verification to establish the simplified polynomial surrogate model. S4: Obtain the actual structural parameters of the offshore wind turbine, input the simplified polynomial surrogate model obtained in S3, and calculate the first n natural frequencies. S5. Based on the established simplified polynomial surrogate model and the measured structural natural frequency information, a linear equation system between the first n natural frequencies of the offshore wind turbine and the structural parameters is constructed. S6. The solution of the equation system is transformed into an optimization problem. The Fourier transform optimization algorithm is used to solve the above equation system to obtain the structural parameters of the offshore wind turbine at the measured natural frequency.

[0008] Preferably, the structural parameters in S1 specifically include: the elastic modulus of the offshore wind turbine material, the density of the offshore wind turbine material, the outer diameter of the offshore wind turbine central column, the outer diameter of the offshore wind turbine tower, the outer diameter of the offshore wind turbine diagonal brace, the outer diameter of the offshore wind turbine cross brace, the outer diameter of the offshore wind turbine pile support, the wall thickness of the offshore wind turbine components, and the concentrated mass of the top blade of the offshore wind turbine.

[0009] Preferably, the specific process of constructing the sample dataset in S1 includes: First, determine the reasonable engineering range of structural parameters. The range is the actual range of values ​​that the structure is safe and meets the design requirements in actual engineering, taking into account offshore wind power design specifications, steel structure design standards, and the actual engineering conditions. Secondly, generate no fewer than 100 sets of structural parameters using a simple random sampling method; Finally, modal analysis of the structural parameter set was performed using the finite element model of the offshore wind turbine structure, and a sample dataset was constructed with the structural parameters as input and the first n natural frequencies as output.

[0010] Preferably, before establishing the initial polynomial surrogate model of the first n natural frequencies of the offshore wind turbine in S2, the structural parameters in the sample dataset need to be Z-score standardized to eliminate the differences in the order of magnitude of each structural parameter. The formula for Z-score standardization is as follows: ; In the formula: For the required standardized structural parameter sample data, This is the mean of the sample data for this structural parameter. This represents the standard deviation of the sample data for this structural parameter.

[0011] Preferably, in step S3, the initial polynomial proxy model is simplified based on a significant sensitivity term. The specific process is as follows: S31. Using analysis of variance, the single-term significance test of the first-order, second-order, and interaction terms in the initial polynomial surrogate model established in S2 is performed to initially screen and obtain the set of significant terms of the first n-order natural frequency initial polynomial surrogate model. S32, For the set of significant items selected, the absolute value of their fitting coefficients is judged. The judgment threshold is 0.05. Items with an absolute value of fitting coefficient < 0.05 are defined as significant insensitive items, and items with an absolute value of fitting coefficient ≥ 0.05 are significant sensitive items. S33. Based on the judgment threshold, a second screening is performed within the set of significant items to obtain a set of significant and sensitive items with an absolute value of fitting coefficient ≥ 0.05. S34. Using the set of significant sensitive terms obtained by the second screening, the first n-order natural frequency polynomial surrogate model is re-established, which is the simplified polynomial surrogate model.

[0012] Preferably, the construction of a test set for testing and verification in step S3 specifically includes: First, two test sets are constructed. The first test set is obtained as follows: based on the structural parameter range determined in S1, at least 100 sets of structural parameters are generated again using simple random sampling. Then, modal analysis is performed on the structural parameter sets using the finite element model of the offshore wind turbine structure to construct the original structural parameter range test set. The second test set is obtained as follows: the structural parameter range in S1 is broadened, and at least 100 sets of structural parameters are generated again using simple random sampling. Then, modal analysis is performed on the structural parameter sets using the finite element model of the offshore wind turbine structure to construct the extended structural parameter range test set. Then, using the coefficient of determination R², mean absolute error (MAE), and mean relative error (MRE), if the simplified polynomial surrogate model has R² ≥ 0.90, MAE ≤ 0.50, and MRE ≤ 10% on the two test sets, its generalization and prediction capabilities are deemed satisfactory. If the simplified polynomial surrogate model has unsatisfactory generalization and prediction capabilities, the process returns to step S3 to reduce the threshold for the absolute value of the fitting coefficients and performs a second screening. Based on the newly obtained set of significant sensitive terms, a simplified polynomial surrogate model with the first n natural frequencies is re-established and tested again until the generalization and prediction capabilities of the simplified polynomial surrogate model meet the requirements.

[0013] Preferably, in S3, when constructing the second test set, widening the range of structural parameters in S1 specifically means: based on the reasonable engineering upper and lower limits of each structural parameter, a smaller expansion range is adopted for material parameters; and a larger expansion range is adopted for size parameters.

[0014] Preferably, in step S4, the actual structural parameters of the offshore wind turbine need to be normalized according to the normalization formula before they can be substituted into the verified simplified polynomial surrogate model to quickly calculate the first n natural frequencies of the offshore wind turbine structure.

[0015] Preferably, the linear equation system in S5 has the following specific form: ; In the formula: This is the matrix composed of the fitting coefficients of each term in the simplified polynomial surrogate model of the first n natural frequencies of the offshore wind turbine structure after verification, excluding constant terms; The structural parameters to be determined for the offshore wind turbine structure; It is obtained by subtracting the constant term in the simplified polynomial surrogate model from the measured first n natural frequencies of the offshore wind turbine structure.

[0016] Preferably, the specific process of S6 is as follows: Based on the linear equations obtained in S5, construct the objective function required for optimization and solution, which has the following specific form: ; In the formula: min represents the operation of finding the minimum value; f(x) is the objective function, representing the sum of squared residuals; It is the Euclidean norm; This is the matrix composed of the fitting coefficients of each term in the simplified polynomial surrogate model of the first n natural frequencies of the offshore wind turbine structure after verification, excluding constant terms; The structural parameters to be determined for the offshore wind turbine structure; The constant term in the simplified polynomial surrogate model is obtained by subtracting the first n natural frequencies of the offshore wind turbine structure from the measured natural frequencies. The process of solving the problem using the Fourier transform optimization algorithm requires setting search boundaries. The boundaries are set as follows: based on the reasonable engineering value range of the offshore wind turbine structural parameters, normalization is performed according to the normalization formula to determine the search boundaries of each structural parameter; after the solution is completed, the output optimal solution is inversely normalized according to the normalization formula to obtain the structural parameters of the offshore wind turbine.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. Precise simplification of the initial polynomial surrogate model: Through a dual screening mechanism of analysis of variance and fixed threshold, the coefficients of the initial polynomial surrogate model are screened. Compared with the traditional single sensitivity analysis or analysis of variance method, it can more accurately identify significant sensitive terms, thereby establishing a simplified polynomial surrogate model with both low complexity and high accuracy. 2. The simplified polynomial surrogate model is easy to calculate: Compared with the mainstream method for calculating the natural frequency of offshore wind turbine structures in the industry (which is complicated and time-consuming), the simplified polynomial surrogate model constructed in this invention has a concise and intuitive expression, which can quickly solve the natural frequency without complicated numerical calculations, thus significantly improving the efficiency of engineering applications. 3. Accurate Solution of Ill-conditioned Linear Equations: Addressing the severely ill-conditioned characteristics of the coefficient matrix in the structural parameter inversion of offshore wind turbines, this invention employs a Fourier transform optimization algorithm. Compared to classical algorithms such as particle swarm optimization, the Fourier transform optimization algorithm exhibits superior convergence accuracy and stability when handling ill-conditioned equations, thus effectively ensuring the accuracy of structural parameter inversion. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process flow of the present invention.

[0019] Figure 2 This is a schematic diagram of the finite element model of the tripod-type wind turbine structure used in this invention.

[0020] Figure 3 This is the distribution of fitting coefficients and the results of screening for significant sensitive terms in the first-order natural frequency polynomial model of this invention.

[0021] Figure 4 This is the distribution of fitting coefficients and the results of screening for significant sensitive terms in the second-order natural frequency polynomial model of this invention.

[0022] Figure 5 This is the distribution of fitting coefficients and the results of screening for significant sensitive terms in the third-order natural frequency polynomial model of this invention.

[0023] Figure 6 This is the distribution of fitting coefficients and the results of screening for significant sensitive terms in the fourth-order natural frequency polynomial model of this invention.

[0024] Figure 7 This is the distribution of fitting coefficients and the results of screening for significant sensitive terms in the fifth-order natural frequency polynomial model of this invention.

[0025] Figure 8 This is the fitting effect of the first-order natural frequency polynomial model of the present invention on the test set (original parameter range).

[0026] Figure 9 This is the fitting effect of the second-order natural frequency polynomial model of the present invention on the test set (original parameter range).

[0027] Figure 10 This is the fitting effect of the third-order natural frequency polynomial model of the present invention on the test set (original parameter range).

[0028] Figure 11This is the fitting effect of the fourth-order natural frequency polynomial model of the present invention on the test set (original parameter range).

[0029] Figure 12 This is the fitting effect of the fifth-order natural frequency polynomial model of the present invention on the test set (original parameter range).

[0030] Figure 13 This is the fitting effect of the first-order natural frequency polynomial model of the present invention on the test set (extension parameter range).

[0031] Figure 14 This is the fitting effect of the second-order natural frequency polynomial model of the present invention on the test set (extension parameter range).

[0032] Figure 15 This is the fitting effect of the third-order natural frequency polynomial model of the present invention on the test set (extension parameter range).

[0033] Figure 16 This is the fitting effect of the fourth-order natural frequency polynomial model of the present invention on the test set (extension parameter range).

[0034] Figure 17 This is the fitting effect of the fifth-order natural frequency polynomial model of this invention on the test set (extension parameter range). Detailed Implementation

[0035] This invention proposes a method for rapid estimation of the natural frequency and inversion of structural parameters of offshore wind turbines. The overall process is as follows: Figure 1 As shown: S1. Using the structural design data and relevant dimensions of the offshore wind turbine, a finite element model of the offshore wind turbine structure is established. Modal analysis is performed on multiple sets of structural parameters to obtain the natural frequencies. A sample dataset is constructed with structural parameters as input and the first n natural frequencies as output. S2, based on the sample dataset, establish an initial polynomial surrogate model for the first n natural frequencies of offshore wind turbines; S3. ANOVA was used to test the significance of the coefficients of the initial polynomial surrogate model. Coefficients with an absolute value of fit coefficients not less than 0.05 within the significance interval were selected as significant sensitive terms. The initial polynomial surrogate model was simplified based on the significant sensitive terms, thus establishing a simplified polynomial surrogate model. A test set was constructed to test and verify the simplified polynomial surrogate model and evaluate its generalization and predictive ability. S4: Obtain the actual structural parameters of the offshore wind turbine, input the verified simplified polynomial surrogate model, and thus quickly calculate the first n natural frequencies; S5. Furthermore, based on the established simplified polynomial surrogate model and the measured structural natural frequency information, a linear equation system between the first n natural frequencies of the offshore wind turbine and the structural parameters is constructed. S6. The solution of the equation system is transformed into an optimization problem. The Fourier transform optimization algorithm is used to solve the above equation system to obtain the structural parameters of the offshore wind turbine at the measured natural frequency.

[0036] The present invention will be further described below with reference to embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0037] 1. Construction of Finite Element Model of Offshore Wind Turbine Structure This example constructs a finite element model of a tripod-type offshore wind turbine structure, such as... Figure 2 As shown. The model contains 18 nodes and 20 beam elements with uniform cross-sections. The specific components are divided as follows: 2 central columns (numbered 16~17), 3 tower tubes (numbered 18~20), 3 diagonal braces (numbered 13~15), 3 horizontal braces (numbered 10~12), and 9 pile braces (numbered 1~9).

[0038] In this wind turbine model, the outer diameters of the central column and tower are consistent. Dl Indicates that all supporting structures have the same outer diameter, using... Ds This indicates that all components have a uniform wall thickness, indicated by... t This indicates that a counterweight steel plate is installed at the top of the tower to simulate the concentrated mass of the blades. mass_ top express.

[0039] 2. Generation of sample data Determine the elastic modulus of the fan material E Fan material density density Wind turbine central column, tower outer diameter Dl , outer diameter of fan strut Ds Wind turbine component wall thickness t Weight of the counterweight steel plate at the top of the fan mass_top The reasonable engineering value ranges for these 6 structural parameters were determined by generating 100 sets of structural parameter sets using a simple random sampling method.

[0040] Table 1 Range of Structural Parameter Values

[0041] Using the finite element model of the tripod-type offshore wind turbine structure, modal analysis was performed on the 100 sets of structural parameters to obtain the natural frequencies. A sample dataset was constructed with 6 structural parameters as inputs and the first 5 natural frequencies as outputs. The dataset contains a total of 100 samples.

[0042] 3. Establishment of the initial second-order polynomial surrogate model for the first 5 natural frequencies Since the structural parameters differ significantly in magnitude, the sample dataset needs to be standardized before fitting the natural frequencies. This invention uses Z-score standardization, as shown in the following formula: ; In the formula: For the required standardized structural parameter sample data, This is the mean of the sample data for this structural parameter. This represents the standard deviation of the sample data for this structural parameter.

[0043] The initial second-order polynomial surrogate model was fitted using the least squares method. Each natural frequency corresponds to an independent second-order polynomial, whose general expression is: ; in, This is a certain natural frequency of the wind turbine. or For a specific structural parameter of the fan, For constant terms, The coefficients for the first-order term are the fitting coefficients. The fitting coefficients are quadratic terms. The coefficients are the fitting coefficients for the interaction term.

[0044] In this model, the number of structural parameters The number of terms in the 1st to 5th order natural frequency models is 28 each. A design matrix is ​​established based on the standardized sample dataset. Using the formula The 28 fitting coefficients in the initial second-order polynomial surrogate model of natural frequencies from the 1st to the 5th order can be solved respectively. The solution results are shown in Table 2.

[0045] Table 2. Fitting coefficients of the initial second-order polynomial surrogate model for the first to fifth natural frequencies of the wind turbine.

[0046] The initial second-order polynomial surrogate model constructed for the 1st to 5th natural frequencies has a coefficient of determination R. 2The values ​​are 0.999855, 0.999892, 0.999979, 0.999982, and 0.999999, respectively, indicating that the fully parameterized initial second-order polynomial surrogate model has a very high fit to the training sample data. However, the fully parameterized model contains a large number of interaction terms and quadratic terms, resulting in high model complexity.

[0047] 4. Significance analysis of the initial second-order polynomial surrogate model with the first 5 natural frequencies To simplify the complexity of the surrogate model of the initial second-order polynomials for the first to fifth natural frequencies, it is necessary to perform analysis of variance (partial F-test) on the coefficients of the model.

[0048] Null hypothesis: This term has no effect on the natural frequency and can be eliminated; Alternative hypothesis: This feature has a significant impact on the natural frequency and should be retained.

[0049] Calculate the F-value for each term in the initial second-order polynomial surrogate model of natural frequencies from order 1 to 5. The larger the F-value, the greater the contribution of the term and the more important it is. Based on the F-value and degrees of freedom, look up the F-distribution table to calculate the probability (P-value) of the current F-value assuming the null hypothesis is true. If P < 0.05, reject the null hypothesis, indicating that the term is significant to the natural frequencies.

[0050] The F-values, P-values, and significance of the initial second-order polynomial surrogate models of the first to fifth natural frequencies calculated using MATLAB are shown in Tables 3 to 7 (the fitting coefficients before the characteristic terms in the tables represent the characteristic terms).

[0051] Table 3. Analysis of variance results for the initial second-order polynomial surrogate model with first-order natural frequencies.

[0052] Table 4. Analysis of variance results for the initial second-order polynomial surrogate model with second-order natural frequencies.

[0053] Table 5. Analysis of variance results for the initial second-order polynomial surrogate model with third-order natural frequencies.

[0054] Table 6. Analysis of variance results for the initial second-order polynomial surrogate model with fourth-order natural frequencies.

[0055] Table 7. Analysis of variance results for the initial second-order polynomial surrogate model with fifth-order natural frequencies.

[0056] The analysis results in Tables 2-7 show that in the initial second-order polynomial surrogate models of natural frequencies from order 1 to 5, the vast majority of feature terms meet the statistical significance requirement. However, the fitting coefficients of some significant terms are relatively small, indicating that although these terms have a significant impact on the natural frequencies, their parameter sensitivity is low. Therefore, insignificant terms and significant but low-sensitivity redundant terms in the model can be selectively removed, retaining only the core terms that are significant and highly sensitive to changes in natural frequencies, thereby simplifying the initial second-order polynomial surrogate model.

[0057] This invention sets a fixed discrimination threshold to remove redundant terms, defining terms with an absolute fitting coefficient less than 0.05 as significantly insensitive terms within the significant feature terms. By retaining significantly sensitive terms with an absolute fitting coefficient not less than 0.05, model dimensionality reduction and simplification are achieved. The screening results are shown below. Figures 3-7 .

[0058] The screening results show that: the surrogate models of the first and second order natural frequencies with initial second-order polynomials retain five feature terms: E, Dl, Ds, t, and mass_top; the surrogate models of the third and fourth order natural frequencies with initial second-order polynomials retain seven feature terms: E, density, Dl, Ds, t, E·Ds, and Dl·Ds; and the surrogate models of the fifth order natural frequencies with initial second-order polynomials retain six feature terms: E, density, Dl, Ds, t, and E·Ds.

[0059] 5. Establishment of the simplified polynomial surrogate model for the first 5 natural frequencies Based on the above feature selection results, the surrogate models of natural frequencies of orders 1 to 5 are re-established, and the simplified surrogate models of natural frequencies of orders 1 to 5 are obtained. The fitting coefficients of each simplified model are shown in Table 8.

[0060] Table 8. Fitting coefficients of the simplified polynomial surrogate models of natural frequencies from order 1 to 5.

[0061] Based on significance analysis and parameter sensitivity screening, after removing redundant terms that have no significant impact on the intrinsic frequency, a simplified polynomial surrogate model was constructed, with a determination coefficient R0. 2 The values ​​are 0.9927, 0.9935, 0.9997, 0.9998, and 0.99996, respectively.

[0062] Compared to the fully parameterized initial second-order polynomial surrogate model, the simplified polynomial surrogate model shows a slight decrease in fitting accuracy, but the R-values ​​for all orders are higher. 2 All values ​​are above 0.99, indicating that the simplified polynomial surrogate model can still accurately represent the mapping relationship between structural parameters and natural frequencies, while significantly reducing model complexity.

[0063] 6. Validation of the simplified polynomial surrogate model with the first 5 natural frequencies First, based on the value range of each structural parameter in Table 1, 100 sets of structural parameters were generated again by simple random sampling. Then, modal analysis was performed using the finite element model of the tripod-type offshore wind turbine structure to calculate 100 sets of sample data, which were used to test the predictive ability of the simplified polynomial surrogate model.

[0064] Secondly, the range of values ​​for each structural parameter in Table 1 is broadened to form an extension parameter range, the specific values ​​of which are shown in Table 9.

[0065] In this embodiment, a smaller expansion ratio (1%~5%) is used for material parameters (elastic modulus, density) because the range of variation of material properties is relatively narrow in actual engineering; while a larger expansion ratio (10%~35%) is used for dimensional parameters (outer diameter and wall thickness of central column, tower, strut, and mass of top counterweight steel plate) because processing errors, assembly gaps, etc. are more likely to fluctuate significantly in practice.

[0066] Based on the updated range of structural parameters, 100 sets of structural parameters were generated by simple random sampling. Then, modal analysis was performed using the finite element model of the tripod-type offshore wind turbine structure to calculate 100 sets of sample data, which were used to test the generalization ability of the simplified polynomial surrogate model.

[0067] Table 9. Range of values ​​for structural parameters after extension

[0068] Calculate the coefficients of determination (R²) of the simplified polynomial surrogate model on both test sets. 2 The root mean square error (RMSE), mean absolute error (MAE), and mean relative error (MRE) are calculated using the following formulas: ; ; ; ; In the formula: To test the values ​​of the inherent frequencies in the set, To simplify the natural frequency values ​​calculated by the polynomial surrogate model, This represents the number of samples.

[0069] Finally, the fitted images of the simplified multinomial surrogate model on the two test sets are shown in [link to image]. Figures 8-17 The calculated evaluation index results are shown in Table 10.

[0070] Table 10 Evaluation metrics of the simplified polynomial surrogate model on the two test sets

[0071] By comparing the generalization and prediction capabilities of the simplified multinomial surrogate model on the original parameter range test set and the extended parameter range test set, the following conclusions are drawn: (1) Original parameter range test set R of simplified polynomial surrogate models of natural frequencies from order 1 to 5 2 All values ​​are greater than 0.99, RMSE and MAE are between 0.02 and 0.06, and MRE is between 0.08% and 1.05%. The model error is extremely small, the curves almost completely overlap, and the model's predictive ability is excellent.

[0072] (2) Extensional parameter range test set The fitting accuracy of the simplified polynomial surrogate model with first and second order natural frequencies decreases: R 2 The decrease from 0.99 to 0.91-0.93 indicates that the model's mapping law for low-order modes deviated to some extent during extrapolation; RMSE, MAE, and MRE increased significantly, but the overall trend of the curves remained consistent with the true values, and there was no complete deviation.

[0073] The fitting accuracy of the simplified polynomial surrogate model with natural frequencies of orders 3-4 remains good: R 2 The value remains above 0.99, and the model's fitting stability has hardly changed. Although the increases in RMSE and MAE are significant, considering the magnitude of the 3-4 frequency, the increase in MRE of the 3-4 order model is less than that of the 1-2 order model.

[0074] The fitting accuracy of the 5th-order natural frequency simplified polynomial surrogate model is generally at a reasonable level: R 2 The value decreased by about 0.02 to 0.9793, and the model fitting effect was still good. The RMSE increased from 0.0390 to 1.6164, and the MAE increased from 0.0285 to 0.4286, which was also a large increase. However, the reason is that the numerical magnitude of the 5th order frequency is higher than that of other orders, which amplifies the absolute error. The average relative error (MRE) of the model itself is only 1.09%, which is the smallest among the simplified polynomial surrogate models of the 1st to 5th order natural frequencies.

[0075] 7. Estimation formulas for the first five natural frequencies of offshore wind turbine structures Finally, the estimation formulas for the 1st to 5th natural frequencies of this tripod-type offshore wind turbine structure are as follows: Formula for estimating the first-order natural frequency: ; Formula for estimating the second-order natural frequency: ; Formula for estimating the third-order natural frequency: ; Formula for estimating the fourth-order natural frequency: ; Formula for estimating the 5th natural frequency: ; In the above formula: ; ; ; ; ; ; In the formula: E The elastic modulus (Pa) of the wind turbine material. density The density of the fan material (kg / m³) 3 ), Dl The outer diameter (m) of the wind turbine's central column and tower. Ds The outer diameter (m) of the wind turbine support structure. t The wall thickness of the wind turbine components (m) mass_top The mass (kg) of the steel plate used as a counterweight at the top of the wind turbine.

[0076] 8. Solving for the structural parameters of offshore wind turbines using a simplified polynomial surrogate model. After constructing a sample set and establishing an initial second-order polynomial surrogate model, significant sensitive terms were obtained through dual screening using "analysis of variance + fixed threshold". A simplified polynomial surrogate model was then established and tested. In this example, the surrogate models for the first five natural frequencies of the tripod-type offshore wind turbine structure were finally obtained. The specific fitting coefficients of each model are shown in Table 8.

[0077] Based on the surrogate model, the mapping relationship between the first five natural frequencies of the tripod-type offshore wind turbine structure and the structural parameters can be expressed as a matrix product:

[0078] In the formula: ; ; ; Therefore, it is also possible to solve the structural parameter vector x of a tripod-type offshore wind turbine from the measured frequency, thereby achieving structural parameter identification based on the measured natural frequency. Considering that the constant terms are known, the actual system of equations to be solved is: ; In the formula: ; ; ; ; ; Further calculation of the coefficient matrix condition number The system of equations was found to exhibit severe ill-conditioned characteristics. Although traditional solution methods (such as pseudo-inverses) can obtain least-squares solutions, there are inherent deviations between the surrogate model and the actual physical process. When using the surrogate model to invert structural parameters, data noise will inevitably be introduced, which will lead to a significant amplification of the error in the calculation results.

[0079] To address the aforementioned problems, this invention employs a numerical solution method based on the Fourier Transform Optimizer (FTO). This method first utilizes variational principles to transform the ill-conditioned equation system... The solution is transformed into the following unconstrained optimization problem, and then the FTO optimization algorithm is used to search for the optimal solution.

[0080] ; FTO is a swarm intelligence optimization algorithm based on frequency domain transform. The algorithm initialization includes... The population consists of individuals, each represented by an 8-dimensional row vector x (corresponding to the 8 normalized variables in Table 8). The FTO treats each individual as a time-domain signal, maps it to the frequency domain through Fast Fourier Transform, and sequentially performs operations such as differential frequency mixing, Lévy flight, adaptive low-pass filtering, orthogonal learning, and local search based on the Runge-Kutta method to achieve a dynamic balance between global exploration and local exploitation.

[0081] After each iteration, the individual is returned from the frequency domain to the time domain via inverse Fourier transform, and boundary constraints are applied to ensure the physical feasibility of the solution. The boundaries are calculated based on the structural parameter range of the tripod-type offshore wind turbine and its normalization formula.

[0082] Furthermore, the algorithm retains the top 10% of elite individuals in the population and replaces the worst individuals with elites after each iteration to prevent population degradation. After several generations of iteration, the globally optimal solution output by the algorithm needs to be denormalized to obtain the six structural parameters of the tripod-type offshore wind turbine: elastic modulus E, material density, wind turbine central column, tower outer diameter Dl, wind turbine strut outer diameter Ds, wind turbine component wall thickness t, and the mass_top of the wind turbine top counterweight steel plate.

[0083] Using the FTO optimization algorithm and a proxy model of the first five natural frequencies of the tripod-type offshore wind turbine structure, and following the aforementioned procedure, the six structural parameters of the structure were solved in both the original parameter range test set and the extended parameter range test set. The results are shown in Tables 11 and 12. The solution parameters for the original parameter range test set were: population size 100, iteration count 400; the solution parameters for the extended parameter range test set were: population size 80, iteration count 200.

[0084] Table 11 shows the solution performance of the FTO optimization algorithm on the test set with the original parameter range.

[0085] Table 12 Solution performance of the FTO optimization algorithm on the extrapolation parameter range test set.

[0086] The results show that, on the original parameter range test set, the average relative error of the six structural parameters obtained by the FTO algorithm is less than 10%, and the inversion accuracy is quite ideal. On the extensional parameter range test set, the average relative error of each structural parameter is larger than that on the original parameter range test set, but it is still within a reasonable range, which verifies the effectiveness and generalization ability of the method in different parameter spaces.

[0087] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0088] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for rapid estimation of the natural frequency and inversion of structural parameters of an offshore wind turbine, characterized in that, The process includes the following: S1. Establish a finite element model of the offshore wind turbine structure, perform modal analysis on multiple sets of structural parameters to obtain natural frequencies, and construct a sample dataset with structural parameters as input and the first n natural frequencies as output. S2, based on the sample dataset, establish an initial polynomial surrogate model for the first n natural frequencies of offshore wind turbines; S3. ANOVA was used to test the significance of the coefficients of the initial polynomial surrogate model. Coefficients with an absolute value of fit coefficients not less than 0.05 within the significance interval were selected as significant sensitive terms. The initial polynomial surrogate model was simplified based on the significant sensitive terms, and a test set was constructed for testing and verification to establish the simplified polynomial surrogate model. S4: Obtain the actual structural parameters of the offshore wind turbine, input the simplified polynomial surrogate model obtained in S3, and calculate the first n natural frequencies. S5. Based on the established simplified polynomial surrogate model and the measured structural natural frequency information, a system of linear equations relating the first n natural frequencies of the offshore wind turbine to the structural parameters is constructed; the specific form of the system of linear equations is as follows: ； In the formula: This is the matrix composed of the fitting coefficients of each term in the simplified polynomial surrogate model of the first n natural frequencies of the offshore wind turbine structure after verification, excluding constant terms; The structural parameters to be determined for the offshore wind turbine structure; The constant term in the simplified polynomial surrogate model is obtained by subtracting the first n natural frequencies of the offshore wind turbine structure from the measured natural frequencies. S6. The solution to the system of equations is transformed into an optimization problem. The Fourier transform optimization algorithm is used to solve the above system of equations to obtain the structural parameters of the offshore wind turbine at the measured natural frequency. The specific process is as follows: Based on the linear equations obtained in S5, construct the objective function required for optimization and solution, which has the following specific form: ； In the formula: min represents the operation of finding the minimum value; f(x) is the objective function, representing the sum of squared residuals; It is the Euclidean norm; This is the matrix composed of the fitting coefficients of each term in the simplified polynomial surrogate model of the first n natural frequencies of the offshore wind turbine structure after verification, excluding constant terms; The structural parameters to be determined for the offshore wind turbine structure; The constant term in the simplified polynomial surrogate model is obtained by subtracting the first n natural frequencies of the offshore wind turbine structure from the measured natural frequencies. The process of solving the problem using the Fourier transform optimization algorithm requires setting search boundaries. The boundaries are set as follows: based on the reasonable engineering value range of the offshore wind turbine structural parameters, normalization is performed according to the normalization formula to determine the search boundaries of each structural parameter; after the solution is completed, the output optimal solution is inversely normalized according to the normalization formula to obtain the structural parameters of the offshore wind turbine.

2. The method for rapid estimation of the natural frequency and inversion of structural parameters of an offshore wind turbine as described in claim 1, characterized in that: The structural parameters in S1 specifically include: the elastic modulus of the offshore wind turbine material, the density of the offshore wind turbine material, the outer diameter of the offshore wind turbine central column, the outer diameter of the offshore wind turbine tower, the outer diameter of the offshore wind turbine diagonal brace, the outer diameter of the offshore wind turbine cross brace, the outer diameter of the offshore wind turbine pile support, the wall thickness of the offshore wind turbine components, and the concentrated mass of the top blade of the offshore wind turbine.

3. The method for rapid estimation of the natural frequency and inversion of structural parameters of an offshore wind turbine as described in claim 1, characterized in that: The specific process of constructing the sample dataset in S1 includes: First, determine the reasonable engineering range of structural parameters. The range is the actual range of values ​​that the structure is safe and meets the design requirements in actual engineering, taking into account offshore wind power design specifications, steel structure design standards, and the actual engineering conditions. Secondly, generate no fewer than 100 sets of structural parameters using a simple random sampling method; Finally, modal analysis of the structural parameter set was performed using the finite element model of the offshore wind turbine structure, and a sample dataset was constructed with the structural parameters as input and the first n natural frequencies as output.

4. The method for rapid estimation of the natural frequency and inversion of structural parameters of an offshore wind turbine as described in claim 1, characterized in that: Before establishing the initial polynomial surrogate model of the first n natural frequencies of the offshore wind turbine in S2, it is necessary to perform Z-score standardization on the structural parameters in the sample dataset to eliminate the differences in the order of magnitude of each structural parameter. The formula for Z-score standardization is as follows: ； In the formula: For the required standardized structural parameter sample data, This is the mean of the sample data for this structural parameter. This represents the standard deviation of the sample data for this structural parameter.

5. The method for rapid estimation of the natural frequency and inversion of structural parameters of an offshore wind turbine as described in claim 1, characterized in that: The process of simplifying the initial polynomial proxy model based on significant sensitivity terms in S3 is as follows: S31. Using analysis of variance, the single-term significance test of the first-order, second-order, and interaction terms in the initial polynomial surrogate model established in S2 is performed to initially screen and obtain the set of significant terms of the first n-order natural frequency initial polynomial surrogate model. S32, For the set of significant items selected, the absolute value of their fitting coefficients is judged. The judgment threshold is 0.

05. Items with an absolute value of fitting coefficient < 0.05 are defined as significant insensitive items, and items with an absolute value of fitting coefficient ≥ 0.05 are significant sensitive items. S33. Based on the judgment threshold, a second screening is performed within the set of significant items to obtain a set of significant and sensitive items with an absolute value of fitting coefficient ≥ 0.

05. S34. Using the set of significant sensitive terms obtained by the second screening, the first n-order natural frequency polynomial surrogate model is re-established, which is the simplified polynomial surrogate model.

6. The method for rapid estimation of the natural frequency and inversion of structural parameters of an offshore wind turbine as described in claim 1, characterized in that: The S3 section describes the construction of a test set for testing and verification, specifically including: First, two test sets are constructed. The first test set is obtained as follows: based on the structural parameter range determined in S1, at least 100 sets of structural parameters are generated again using simple random sampling. Then, modal analysis is performed on the structural parameter sets using the finite element model of the offshore wind turbine structure to construct the original structural parameter range test set. The second test set is obtained as follows: the structural parameter range in S1 is broadened, and at least 100 sets of structural parameters are generated again using simple random sampling. Then, modal analysis is performed on the structural parameter sets using the finite element model of the offshore wind turbine structure to construct the extended structural parameter range test set. Then, using the coefficient of determination R², mean absolute error (MAE), and mean relative error (MRE), if the simplified polynomial surrogate model has R² ≥ 0.90, MAE ≤ 0.50, and MRE ≤ 10% on the two test sets, its generalization and prediction capabilities are deemed satisfactory. If the simplified polynomial surrogate model has unsatisfactory generalization and prediction capabilities, the process returns to step S3 to reduce the threshold for the absolute value of the fitting coefficients and performs a second screening. Based on the newly obtained set of significant sensitive terms, a simplified polynomial surrogate model with the first n natural frequencies is re-established and tested again until the generalization and prediction capabilities of the simplified polynomial surrogate model meet the requirements.

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