A global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation

Abstract

The present invention provides a global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation. Based on a sample set of uncertain input variables of material parameters, a tower displacement set in the dynamic time-history response process of offshore wind turbines is obtained; further, based on a sample set of tower limit state function functions of offshore wind power, a support vector regression proxy model is established; then, through a new sample set obtained based on the Monte Carlo method, a predicted state function value based on the new sample set is obtained, and further, the failure probability of offshore wind power based on the new sample set is determined, thereby calculating the global reliability sensitivity index of the offshore wind turbine and completing the analysis of the global reliability sensitivity of offshore wind power. The present invention establishes a support vector regression proxy model by considering the uncertain input variables of material parameters, which is helpful for sensitivity analysis, identification of key design parameters, and optimization of structural performance. The calculation efficiency of reliability sensitivity is high, which is helpful for comprehensive reliability evaluation.

Description

Technical Field

[0001] The present invention relates to the technical field of offshore wind power reliability design, and in particular to a global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation. Background Art

[0002] Uncertainty analysis has been widely used in practical engineering. In the offshore wind power sector, most applications focus on the uncertainty output of model results, namely, the reliability problem. Few studies have explored how to allocate the uncertainty information of the model output to the uncertainty information of the model input, namely, the reliability sensitivity problem. Existing offshore wind power reliability sensitivity analysis mainly uses local reliability sensitivity analysis. However, for nonlinear models involving a large number of uncertain parameters, considering only the sensitivity calculated at a single reference point may result in the reference value being invalid within the range of the input variables.

[0003] Existing global reliability sensitivity analysis is based on explicit state function functions. However, in practical engineering, most state function functions are implicit, and global reliability sensitivity analysis requires a large number of finite element analysis samples, which is computationally inefficient and difficult to apply to practical engineering. Summary of the Invention

[0004] The present invention provides a global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation includes the following steps:

[0007] S1: Establish a finite element calculation model of a monopile offshore wind turbine based on finite element software;

[0008] S2: defining uncertainty input variables of material parameters to obtain a sample set of uncertainty input variables based on the material parameters, and then obtaining a tower displacement set during the dynamic time history response of the offshore wind turbine based on the finite element calculation model of the monopile offshore wind turbine;

[0009] S3: Determine the displacement failure threshold of the tower limit state to establish the tower limit state function for offshore wind power;

[0010] S4: obtaining a sample set of the tower limit state function function of the offshore wind turbine according to the tower displacement set during the dynamic time history response of the offshore wind turbine and the tower limit state function function of the offshore wind turbine, and establishing a support vector regression proxy model based on the sample set of the tower limit state function function of the offshore wind turbine;

[0011] S5: obtaining a new sample set based on the uncertainty input variables of the material parameters and the support vector regression agent model based on the Monte Carlo method, and obtaining a predicted state function value based on the new sample set;

[0012] S6: Obtaining a failure sample in the new sample set according to the predicted state performance function value based on the new sample set to obtain a failure probability of the offshore wind power based on the new sample set;

[0013] S7: According to the failure probability of offshore wind power based on the new sample set, a global reliability sensitivity index of the offshore wind turbine is obtained to complete the analysis of the global reliability sensitivity of the offshore wind power.

[0014] Furthermore, in S4, the method for establishing the support vector regression proxy model is as follows:

[0015] First, assume that the support vector regression surrogate model is:

[0016]

[0017] Where: Z(x) is the regression predictor variable of the support vector regression surrogate model; is the feature mapping function; ω is the weight vector; b is the intercept of the coefficient to be determined; ω T is the transpose of ω; x is the input sample independent variable;

[0018] Introduce slack variables, establish the optimization objective equation and constraints as follows:

[0019]

[0020] Where: ‖ω‖ represents the bi-norm of the weight vector; C represents the regularization parameter; N represents the total number of sample points; ξ n represents a positive slack variable; represents a negative slack variable; g(X n ) represents the nth sample point X n The tower limit state function of offshore wind power corresponding to the maximum tower displacement during the offshore wind turbine dynamic time history response process; Indicates that the nth sample point X n Function mapped to high-dimensional feature space; ε represents the difference between the predicted value and the nth sample point X n The maximum tower displacement d(X n ) between the allowable error; represents ω,ξ n , The optimization objective equation of

[0021] Introduce the Lagrangian function, and obtain the Lagrangian function and partial derivatives as follows:

[0022]

[0023] Where, α, α * ,η,η * are all Lagrange multiplier matrices; represents the Lagrange equation; α n , η n Represent α, α respectively * ,η,η * The nth element in ;

[0024] According to the duality theorem, the Lagrangian function and partial derivatives are transformed into the saddle point problem of the Lagrangian function as follows:

[0025]

[0026] Then, according to the Lagrangian function and partial derivatives, the optimization objective equation and the constraint equation, the dual optimization equation is obtained as follows:

[0027]

[0028] Where: Z(X n ) represents the nth regression predictor variable of the support vector regression surrogate model; X nT Represents X n The transpose of ; n, j both represent the index numbers of the sample points;

[0029] Solve the dual optimization equation to get α n , The global optimal solution

[0030] Substituting the global optimal solution into formula (2), we can obtain the weight vector ω;

[0031] Then according to the dual optimization relationship, we can get:

[0032]

[0033] Substitute equation (3) into equation (6) and solve it to get b;

[0034] The final expression formula of the support vector regression proxy model is as follows:

[0035]

[0036] Among them, k(X n ,Xj ) represents the kernel function of support vector regression;

[0037] k(X n ,X j )=exp{-γ||X n -X j || 2} (8)

[0038] Where γ is the Gaussian kernel bandwidth; X n ,X j are the nth input sample independent variable and the jth input sample independent variable respectively; n and j are the index numbers of the sample points, and n≠j.

[0039] Furthermore, in S3, the tower limit state function of offshore wind power is established as follows:

[0040] g(X)=d allow -d(X n )

[0041] X n =(X1 n ,X2 n …X i n …X I n ) T

[0042] Where: g(X) represents the tower limit state function of offshore wind power. When g(X)>0, it means that the offshore wind power system is in a safe state. When g(X)≤0, it means that the offshore wind power system is in a failure state. allow Indicates the failure threshold of the set limit state; d(X n ) is the nth sample point X n The maximum tower displacement during the corresponding offshore wind turbine dynamic time history response process; X n represents the nth sample point; X i n represents the i-th uncertainty input variable of the n-th sample point; T represents transpose.

[0043] Furthermore, the method for obtaining the failure sample is as follows:

[0044] When the predicted state function value f(X (m) )<0, the mth new sample point is a failure sample.

[0045] Furthermore, in S6, the failure probability of offshore wind power is obtained as follows:

[0046]

[0047] Where: P f ′ is the failure probability of offshore wind power based on the new sample set; X (m′) is the failed sample; m' is the index number of the failed sample; M' is the total number of failed samples; M is the total number of sample points in the new sample set; f(X (m′) ) represents the predicted state function value of the m′th failure sample; I f Represents the indicator function.

[0048] Furthermore, in S7, the method for obtaining the global reliability sensitivity of the offshore wind turbine is as follows:

[0049]

[0050] Among them, f(X i ) is the i-th uncertainty input variable X i The probability density function of η i represents the reliability sensitivity index of the i-th uncertainty input variable;

[0051]

[0052] Where: f(X i |F) represents the i-th uncertainty input variable X i The probability density function under failure conditions; M' is the total number of failed samples; h is the bandwidth; m' is the index number of the failed sample; represents the i-th uncertainty input variable of the m′th failure sample point; K1(·) represents the kernel function of kernel density estimation; F is the failure event;

[0053] in,

[0054]

[0055] then,

[0056]

[0057] Beneficial effect: The present invention provides a global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation. Based on a sample set of uncertain input variables of material parameters, a finite element calculation model of a single-pile offshore wind turbine is used to obtain a tower displacement set in the dynamic time-history response process of the offshore wind turbine. Then, according to the tower limit state function of the offshore wind turbine, a sample set of the tower limit state function function of the offshore wind turbine is obtained. Based on the sample set of the tower limit state function function of the offshore wind turbine, a support vector regression proxy model is established. Then, a new sample set of uncertain input variables based on material parameters is obtained based on the Monte Carlo method, and a predicted state function function value based on the new sample set is obtained. Then, a failure sample in the new sample set is determined, and the failure probability of the offshore wind turbine based on the new sample set is obtained. The global reliability sensitivity index of the offshore wind turbine is calculated, and the analysis of the global reliability sensitivity of the offshore wind turbine is completed. The present invention establishes a support vector regression proxy model by considering the uncertain input variables of material parameters. The use of the proxy model allows for easy modification of structural parameters, which is helpful for sensitivity analysis, identification of key design parameters, and optimization of structural performance. The calculation efficiency of the reliability sensitivity is high, which is helpful for comprehensive reliability evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0059] Figure 1 This is a flow chart of the global reliability sensitivity analysis method for offshore wind power of the present invention;

[0060] Figure 2 This is a finite element diagram of offshore wind power under static working conditions in an embodiment of the present invention;

[0061] Figure 3 Schematic diagram of the state function empirical distribution curve in an embodiment of the present invention;

[0062] Figure 4 Schematic diagram of the response surface regression plane in an embodiment of the present invention;

[0063] Figure 5 Schematic diagram of support vector regression plane in an embodiment of the present invention;

[0064] Figure 6 This is a finite element diagram of offshore wind power under wind, wave and earthquake conditions in an embodiment of the present invention;

[0065] Figure 7is a global sensitivity histogram of failure probability in an embodiment of the present invention;

[0066] Figure 8 Schematic diagram of the sensitivity analysis method in an embodiment of the present invention. DETAILED DESCRIPTION

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0068] This embodiment provides a global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation, such as Figure 1 and Figure 8 As shown, the following steps are included:

[0069] S1: Establish a finite element calculation model of a monopile offshore wind turbine based on finite element software;

[0070] Specifically, the team first determined the structural details, material properties, and analysis type (including dynamic and static analysis) of existing monopile offshore wind turbines. This information served as the foundation for establishing a finite element model of the monopile offshore wind turbine. Using the finite element software Plaxis, the finite element calculation model was established to effectively evaluate the turbine's structural response under various input conditions. Environmental conditions were then applied to the finite element calculation model, and boundary conditions were defined to conduct dynamic analysis.

[0071] S2: Define the uncertainty input variables of material parameters X=(X1,X2…X i …X I ), obtaining a sample set of uncertainty input variables based on material parameters, so as to obtain a tower displacement set during the dynamic time history response process of the offshore wind turbine according to the finite element calculation model of the monopile offshore wind turbine;

[0072] Where X represents the uncertainty input variable vector; X i represents the i-th uncertain input variable, i is the index number of the uncertain input variable; I represents the total number of uncertain input variables;

[0073] The material parameters in this embodiment are the mechanical parameters of the soil and the pile foundation.

[0074] Specifically, among the design variables, the input variables with high uncertainty should be statistically analyzed, and the uncertainty input variables of each group of materials should be used as a sample point. The hypercube sampling method is used to select N sample points (X 1 ,X 2 ,…,X n ,…,X N ), where the nth sample point X n =(X1 n ,X2 n …X i n …X I n ) T , X i n represents the i-th uncertainty input variable of the n-th sample point; the displacement set in the dynamic time history response process of the offshore wind turbine is solved by finite element analysis: (d(X 1 ),d(X 2 ),…,d(X n ),…,d(X N )), where d(X n ) is the nth sample point X n The corresponding maximum tower displacement during the offshore wind turbine dynamic time history response process; n is the index number of the sample point; N is the total number of sample points.

[0075] S3: Determine the displacement failure threshold of the tower limit state and establish the tower limit state function for offshore wind power;

[0076] Specifically, based on historical experience, when the horizontal displacement of the wind turbine exceeds 1.25% of the length of the wind turbine support structure, it will cause an emergency drop in wind turbine efficiency or shutdown. Therefore, this embodiment uses the horizontal displacement of the wind turbine to be 1.25% of the length of the wind turbine support structure as the displacement failure threshold of the tower limit state. Using the first exceedance failure criterion, the reliability of the tower dynamic displacement response within the specified time can be described as:

[0077] P f =P r {d allow ≤d(X)}=P r {d allow -d(X)≤0}

[0078] Where: P f represents the failure probability of offshore wind power, P r represents the probability of offshore wind turbine calculation under the current distribution state of uncertain input variables; d allowrepresents the failure threshold of the set limit state; d(X) is the maximum displacement of the offshore wind turbine in the dynamic time history response process corresponding to the uncertain input variable;

[0079] According to formula (1), the tower limit state function of offshore wind power is established:

[0080] g(X)=d allow -d(X n )

[0081] Where: g(X) represents the tower limit state function of offshore wind power. When g(X)>0, it means that the offshore wind power system is in a safe state. When g(X)≤0, it means that the offshore wind power system is in a failure state. allow Indicates the failure threshold of the set limit state; d(X n ) is the nth sample point X n The maximum tower displacement during the corresponding offshore wind turbine dynamic time history response process; X n represents the nth sample point; X i n represents the i-th uncertainty input variable of the n-th sample point; T represents transpose.

[0082] Specifically, since the limit state performance function of the offshore wind power tower is an implicit expression, it needs to be represented by a proxy model.

[0083] S4: According to the tower displacement set in the offshore wind turbine dynamic time history response process and the tower limit state function function of the offshore wind power, the sample set (d(X 1 ),d(X 2 ),…,d(X n ),…,d(X N )) is substituted into the tower limit state function function of offshore wind power to obtain the tower limit state function function sample set of offshore wind power, that is, the sample set (g(X 1 ), g(X 2 )…g(X N )), based on the sample set of tower limit state function of offshore wind power, a support vector regression agent model is established to regress the sample set;

[0084] Preferably, the method for establishing the support vector regression proxy model is as follows:

[0085] First, assume that the support vector regression surrogate model is:

[0086]

[0087] Where: Z(x) is the regression predictor variable of the support vector regression surrogate model; is the feature mapping function; ω is the weight vector; b is the intercept of the coefficient to be determined; ω T is the transpose of ω; x is the input sample independent variable;

[0088] In order to calculate the weight vector ω, slack variables are introduced, and the optimization objective equation and constraints are established as follows:

[0089]

[0090] Where: ‖ω‖ represents the bi-norm of the weight vector; C represents the regularization parameter; N represents the total number of sample points; n represents the index number of the sample point; ξ n represents a positive slack variable; represents a negative slack variable; g(X n ) represents the nth sample point X n The tower limit state function of offshore wind power corresponding to the maximum tower displacement during the offshore wind turbine dynamic time history response process; Indicates that the nth sample point X n Function mapped to high-dimensional feature space; ε represents the difference between the predicted value and the nth sample point X n The maximum tower displacement d(X n ) between the allowable error; represents ω,ξ n , The optimization objective equation of

[0091] Specifically, the optimization objective equation and the constraint equation require that each sample point meets the conditions.

[0092] In order to solve the optimal ω and b, the Lagrangian function is introduced for solution, and the Lagrangian function and partial derivatives are obtained as follows:

[0093]

[0094] The partial derivatives of the Lagrangian function are as follows:

[0095]

[0096] Where, α, α, η, η * are all Lagrange multiplier matrices, and are all greater than 0; represents the Lagrange equation; α n , η n Represent α, α respectively * ,η,η * The nth element in ;

[0097] According to the duality theorem, the Lagrangian function and partial derivatives, that is, the original objective function (2), are transformed into the saddle point problem of the Lagrangian function as follows:

[0098]

[0099] Then, according to the Lagrangian function and partial derivatives, the optimization objective equation and the constraint equation, substitute equation (3) into equation (4) to obtain the dual optimization equation as shown in equation (5):

[0100]

[0101]

[0102] Where: Z(X n ) represents the nth regression predictor variable of the support vector regression surrogate model; X nT Represents X n The transpose of ; n, j both represent the index numbers of the sample points;

[0103] Solve the dual optimization equation (5) and get α n , The global optimal solution

[0104] Specifically, the obtained global optimal solution is substituted into formula (2), and the weight vector ω can be obtained. Then, according to the dual optimization relationship of the Karush-Kuhn-Tucker (KKT) condition, the saddle point of the global optimal solution in the Lagrangian function satisfies:

[0105]

[0106] Substitute equation (3) into equation (6) and solve it to get b;

[0107] The final expression formula of the support vector regression proxy model is as follows:

[0108]

[0109] Among them, k(X n ,X j ) represents the kernel function of support vector regression, that is, Select Gaussian kernel as the kernel function, the formula is as follows:

[0110] k(X n ,X j )=exp{-γ||X n -X j || 2} (8)

[0111] Where γ is the Gaussian kernel bandwidth; X n ,X j are the nth input sample independent variable and the jth input sample independent variable, that is, the sample points in the feature space; n and j are the index numbers of the sample points, and n≠j.

[0112] At this point, the proxy model construction is completed.

[0113] S5: Input variable X=(X1, X2…X i …X d ), obtaining a new sample set of uncertainty input variables based on material parameters based on the Monte Carlo method, and obtaining a predicted state function value based on the new sample set according to the support vector regression proxy model;

[0114] Specifically, based on the completed support vector regression proxy model, the global reliability sensitivity calculation is performed as follows:

[0115] According to the uncertainty of material parameters, input variable X=(X1,X2…X i …X I ), based on the Monte Carlo method, a new set of samples (X (1) ,X (2) ,…,X (m) …,X (M) ),X (m) represents the mth sample point in the new sample set; m represents the index number of the sample in the new sample set; M represents the total number of samples in the new sample set; where the mth sample point X (m) =(X1 (m) ,X2 (m) …X i (m) …X I (m) ) T , X i (m) Represents the i-th uncertainty input variable of the m-th sample point in the new sample set; and then the new sample set (X (1) ,X (2) ,…,X (m) …,X (M) ) Input the support vector regression agent model, that is, formula (7), and output the predicted state function value (f(X (1) ), f(X (2) ),…f(X (m) )…f(X (M) )). Among them, f(X (m)) represents the predicted state function value corresponding to the mth new sample point;

[0116] S6: obtaining a failure sample set according to the predicted state performance function value based on the new sample set, so as to obtain a failure probability of the offshore wind power based on the new sample set;

[0117] Preferably, the method for obtaining the failure sample is as follows:

[0118] When the predicted state function value f(X (m) )<0, the mth new sample point is a failure sample.

[0119] Specifically, extract the predicted state function value f(X (m) ) is less than 0 as the failure sample f(x (m′) Then, the failure probability P of offshore wind power based on the new sample set is obtained according to the failure sample. f ′, as follows:

[0120]

[0121] Where: P f ′ is the failure probability of offshore wind power based on the new sample set; X (m′) is the failed sample; m' is the index number of the failed sample; M' is the total number of failed samples; M is the total number of sample points in the new sample set; f(X (m′) ) represents the predicted state function value of the m′th failure sample; I f represents the indicator function;

[0122] S7: According to the failure probability of offshore wind power based on the new sample set, a global reliability sensitivity index of the offshore wind turbine is obtained to complete the analysis of the global reliability sensitivity of the offshore wind power.

[0123] Preferably, the formula used to obtain the global reliability sensitivity index of the offshore wind turbine is as follows:

[0124]

[0125] Among them, f(X i ) is the i-th uncertainty input variable X i The probability density function of η i represents the reliability sensitivity index of the i-th uncertainty input variable;

[0126] From the above formula, we can see that P′ f and f(X i ) is the known quantity, and f(Xi |F) is an unknown quantity. To solve f(X i |F), according to the failure sample f(X (m′) ), perform kernel density estimation, as follows;

[0127] Combined failure samples (X i (1′) ,X i (2′) ,…X i (m′) ,…X i (M′) ) where X i (m′) is the i-th uncertainty input variable of the m′th failure sample point. According to the kernel density estimation method, the probability density function is:

[0128]

[0129] f(x i |F) represents the i-th uncertainty input variable X i Probability density function under failure conditions; M′ is the total number of failed samples; h is the bandwidth, h = 2; m′ is the index number of the failed sample; represents the i-th uncertainty input variable of the m′-th failure sample point; K1(·) represents the kernel function of kernel density estimation; F is the failure event; in this embodiment, the maximum displacement of the offshore wind turbine in the dynamic time history response process exceeds the set limit state failure threshold, which is considered a failure event;

[0130] Among them, the kernel function selects the Gaussian kernel function which is most commonly used in practice:

[0131]

[0132] then,

[0133]

[0134] The specific implementation of the present invention is as follows:

[0135] Offshore wind turbine systems are relatively complex. To improve computational efficiency, the rotor-nacelle system (RNA) was considered as a single unit, simplified as a mass at the top of the tower and represented using plate elements. Large-diameter steel pipe piles were used for the pile foundation, embedded to a depth of 50 m. The horizontal length of the soil was 150 m, the total soil thickness was 100 m, and the water depth was defined as 15 m. Wind turbine and soil parameters are shown in Tables 1 and 2, respectively.

[0136] Table 1 Offshore wind turbine parameters

[0137]

[0138] Table 2 Soil parameters

[0139]

[0140] The offshore wind turbine model was constructed using Plaxis3D, with model parameters constructed based on the pile geometry and properties. The piles were constructed as two-dimensional structural plate elements with linear stiffness, with a specified thickness to simulate the pile stiffness. The soil elements were three-dimensional, 10-node tetrahedral elements. An interface model was used to simulate soil-structure interaction. The interface elements consisted of 12 nodes, allowing for coordination between the soil structural elements and the plate elements. Contact surface elements were used at the pile ends as extensions of the plate elements to avoid stress concentrations. Boundary conditions were modeled to avoid boundary effects.

[0141] Case 1: Static Verification Conditions

[0142] In order to verify the accuracy of the proposed method, the Monte Carlo method is compared with the proposed method. The model simulates the static working condition by applying static force at the top of the tower, such as Figure 2 As shown, the displacement of the top of the tower in the ultimate limit state is assumed to be 0.375m (Note: The purpose of this assumption is to verify the definition of the accuracy of the reliability of the method and has nothing to do with the actual stress limit state). The random variables are shown in the following table

[0143] Table 3 Random variables

[0144]

[0145] Plaxis is driven by Python to run static calculations. Figure 3 The empirical distribution curves of the state function functions of the three methods are shown in the following table.

[0146] Table 4 Reliability results

[0147]

[0148] From the data in the table, it can be found that the reliability of the two methods is lower than that of the Monte Carlo method. However, the difference in the reliability estimated by the two methods is always small. Therefore, although there are differences among the three methods, considering that the two surrogate model methods have a shorter running time than the Monte Carlo method, it can be concluded that the two surrogate model methods have a certain degree of accuracy and the solution framework can be used.

[0149] Figure 4Figure 5 shows the fit of the two surrogate models. The response surface fit plot shows that the plane fits well near the zero state function, but the fit is poor beyond the failure point, indicating a lack of global consistency. Therefore, it is not suitable for global failure probability sensitivity analysis. The support vector regression model offers global consistency and does not suffer from the drawback of local optimality, making it suitable for global reliability sensitivity analysis.

[0150] Case 2: Wind-Wave-Earthquake Conditions

[0151] The accuracy of the method in this embodiment and its applicability in global sensitivity analysis of failure probability can be seen from Case 1. This case calculates the reliability and global reliability sensitivity of offshore wind power under wind, wave and earthquake conditions. The model is as follows: Figure 6 The values ​​of the random variables are shown in the following table.

[0152] Table 5 Random variables

[0153]

[0154]

[0155] Wave loads are calculated using the Airy wave theory and the Morision equation. Wind loads consider both fluctuating and average winds. Fluctuating winds are calculated using the Davenport wind spectrum and the harmonic superposition method. The peak ground acceleration for seismic loads is 0.2g.

[0156] Reliability was calculated using a combination of response surface methodology and support vector regression. The reliability results are shown in Table 6. According to the "Uniform Standard for Reliability Design of Building Structures," the reliability index of structural components based on the serviceability limit state can range from 0 to 1.5. In this case, the value was 1.5, indicating that the design complies with the standard.

[0157] Table 6 Reliability results

[0158]

[0159] Combined with the support vector regression model, the single-layer sampling method based on the Bayesian rule is used to analyze the global sensitivity of the failure probability. The probability density curve of the conditional failure probability can be obtained by sampling. Combined with formula (13), the global sensitivity of the failure probability can be obtained. The failure probability sensitivity is as follows: Figure 7 As can be seen from the figure, the uncertainty of the first soil layer's mass has the greatest impact on the failure probability, followed by the first soil layer's internal friction angle, which is determined by the first soil layer's thickness. Therefore, increasing the first soil layer's resistance factor can help improve offshore wind turbine service reliability.

[0160] This embodiment uses a proxy model to solve the reliability of offshore wind power under dynamic loading. By establishing a proxy model and performing a simplified regression on real data, the computational complexity and time are significantly reduced. This allows for rapid results in dynamic reliability analysis. The proxy model allows for easy modification of structural parameters, which facilitates sensitivity analysis, identification of key design parameters, and optimization of structural performance. Furthermore, it can be easily integrated into uncertainty analysis, accounting for the uncertainty of various parameters, facilitating a comprehensive reliability assessment and enabling appropriate design and decision-making.

[0161] This embodiment uses Bayesian global failure probability sensitivity to analyze offshore wind turbine parameters. Compared to local failure probability sensitivity analysis, global failure probability sensitivity analyzes parameters from the perspective of the entire distribution of random variables, rather than analyzing them from a single point like local sensitivity. Global sensitivity analysis employs Bayesian and single-layer sampling, effectively avoiding the complexity and time-consuming nature of double-layer sampling.

[0162] Furthermore, when applying Bayesian analysis, a data-driven kernel density estimation method is proposed. Because this method is a nonparametric estimation method, it does not require assumptions about the distribution type of the random variable and can obtain its probability density function, significantly improving computational accuracy. This method addresses the problem of computational errors caused by failure samples not conforming to the assumed distribution due to the random nature of the state function calculation for random variables.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation, characterized in that: The steps include: S1: Establish a finite element calculation model of a monopile offshore wind turbine based on finite element software; S2: defining uncertainty input variables of material parameters to obtain a sample set of uncertainty input variables based on the material parameters, and then obtaining a tower displacement set during the dynamic time history response of the offshore wind turbine based on the finite element calculation model of the monopile offshore wind turbine; S3: Determine the displacement failure threshold of the tower limit state to establish the tower limit state function for offshore wind power; S4: obtaining a sample set of the tower limit state function function of the offshore wind turbine according to the tower displacement set during the dynamic time history response of the offshore wind turbine and the tower limit state function function of the offshore wind turbine, and establishing a support vector regression proxy model based on the sample set of the tower limit state function function of the offshore wind turbine; S5: obtaining a new sample set based on the uncertainty input variables of the material parameters and the support vector regression agent model based on the Monte Carlo method, and obtaining a predicted state function value based on the new sample set; S6: Obtaining a failure sample in the new sample set according to the predicted state performance function value based on the new sample set to obtain a failure probability of the offshore wind power based on the new sample set; S7: According to the failure probability of offshore wind power based on the new sample set, a global reliability sensitivity index of the offshore wind turbine is obtained to complete the analysis of the global reliability sensitivity of the offshore wind power.

2. The global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation according to claim 1 is characterized in that: In S4, the method for establishing the support vector regression proxy model is as follows: First, assume that the support vector regression surrogate model is: Where: Z(x) is the regression predictor variable of the support vector regression surrogate model; is the feature mapping function; ω is the weight vector; b is the intercept of the coefficient to be determined; ω T is the transpose of ω; x is the input sample independent variable; Introduce slack variables, establish the optimization objective equation and constraints as follows: Where: ‖ω‖ represents the bi-norm of the weight vector; C represents the regularization parameter; N represents the total number of sample points; ξ n represents a positive slack variable; represents a negative slack variable; g(X n ) represents the nth sample point X n The tower limit state function of offshore wind power corresponding to the maximum tower displacement during the offshore wind turbine dynamic time history response process; Indicates that the nth sample point X n Function mapped to high-dimensional feature space; ε represents the difference between the predicted value and the nth sample point X n The maximum tower displacement d(X n ) between the allowable error; represents ω,ξ n , The optimization objective equation of Introduce the Lagrangian function, and obtain the Lagrangian function and partial derivatives as follows: Where, α, α * ,η,η * are all Lagrange multiplier matrices; represents the Lagrange equation; α n , η n Represent α, α respectively * ,η,η * The nth element in ; According to the duality theorem, the Lagrangian function and partial derivatives are transformed into the saddle point problem of the Lagrangian function as follows: Then, according to the Lagrangian function and partial derivatives, the optimization objective equation and the constraint equation, the dual optimization equation is obtained as follows: Where: Z(X n ) represents the nth regression predictor variable of the support vector regression surrogate model; X nT Represents X n The transpose of ; n, j both represent the index numbers of the sample points; Solve the dual optimization equation to get α n , The global optimal solution Substituting the global optimal solution into formula (2), we can obtain the weight vector ω; Then according to the dual optimization relationship, we can get: Substitute equation (3) into equation (6) and solve it to get b; The final expression formula of the support vector regression proxy model is as follows: Among them, k(X n ,X j ) represents the kernel function of support vector regression; k(X n ,X j )=exp{-γ||X n -X j || 2 } (8) Where γ is the Gaussian kernel bandwidth; X n ,X j are the nth input sample independent variable and the jth input sample independent variable respectively; n and j are the index numbers of the sample points, and n≠j.

3. The global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation according to claim 1 is characterized in that: In S3, the tower limit state function of offshore wind power is established as follows: g(X)=d allow -d(X n ) X n (X1 n ,X2 n …X i n …X I n ) T Where: g(X) represents the tower limit state function of offshore wind power. When g(X)>0, it means that the offshore wind power system is in a safe state. When g(X)≤0, it means that the offshore wind power system is in a failure state. allow Indicates the failure threshold of the set limit state; d(X n ) is the nth sample point X n The maximum tower displacement during the corresponding offshore wind turbine dynamic time history response process; X n represents the nth sample point; X i n represents the i-th uncertainty input variable of the n-th sample point; T represents transpose.

4. The global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation according to claim 1 is characterized in that: The method for obtaining the failure sample is as follows: When the predicted state function value f(X (m) )<0, the mth new sample point is a failure sample.

5. The global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation according to claim 1 is characterized in that: In S6, the failure probability of offshore wind power is obtained as follows: Where: P f ′ is the failure probability of offshore wind power based on the new sample set; X (m′) is the failed sample; m' is the index number of the failed sample; M' is the total number of failed samples; M is the total number of sample points in the new sample set; f(X (m′) ) represents the predicted state function value of the m′th failure sample; I f Represents the indicator function.

6. The global reliability sensitivity analysis method for offshore wind turbines based on kernel density estimation according to claim 1 is characterized in that: In S7, the method for obtaining the global reliability sensitivity of the offshore wind turbine is as follows: Among them, f(X i ) is the i-th uncertainty input variable X i The probability density function of η i represents the reliability sensitivity index of the i-th uncertainty input variable; Where: f(X i |F) represents the i-th uncertainty input variable X i The probability density function under failure conditions; M' is the total number of failed samples; h is the bandwidth; m' is the index number of the failed sample; represents the i-th uncertainty input variable of the m′th failure sample point; K1(·) represents the kernel function of kernel density estimation; F is the failure event; in, then,

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