Offshore wind turbine global reliability sensitivity analysis method based on kernel density estimation

Abstract

The invention discloses an offshore wind turbine global reliability sensitivity analysis method based on kernel density estimation, and the method comprises the steps: obtaining a tower displacement set in a power time history response process of an offshore wind turbine based on a sample set of uncertainty input variables of material parameters; establishing a support vector regression agent model based on a tower limit state performance function sample set of offshore wind power; then, through a new sample set obtained based on a Monte Carlo method, a predicted state function value based on the new sample set is obtained, and then the failure probability of offshore wind power based on the new sample set is determined, so that the global reliability sensitivity index of the offshore wind turbine is calculated; and completing the analysis of the global reliability sensitivity of the offshore wind power. According to the method, the support vector regression agent model is established by considering the uncertainty input variables of the material parameters, sensitivity analysis, key design parameter identification and structural performance optimization are facilitated, the calculation efficiency of reliability and sensitivity is high, and comprehensive reliability evaluation is facilitated.

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 field of offshore wind power, most applications focus on the uncertainty output of model result information, that is, the reliability solution problem. Few studies have explored how to allocate the uncertainty information of the model output to the uncertainty information of the model input, that is, 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, only considering the sensitivity calculated at a certain reference point may cause the reference value to fail within the range of the input variable.

[0003] The existing global reliability sensitivity theory analysis is based on explicit state function functions. However, in actual engineering, most state function functions are implicit, and global reliability sensitivity requires a large number of finite element analysis samples to be used, which has slow calculation efficiency and is difficult to apply to actual 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 material parameters, and then obtaining a tower displacement set in a dynamic time-history response process of the offshore wind turbine according to 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 function of offshore wind power;

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

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

[0012] S6: obtaining a failure sample in the new sample set according to the predicted state 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;

[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 agent model is:

[0016]

[0017] Where: Z(x) is the regression prediction 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 function of offshore wind power corresponding to the maximum tower displacement in 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 predicted value and the nth sample point X n The corresponding maximum tower displacement d(X n ) between the allowable error; Denote 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] In the formula, α, α * ,η,η * All are Lagrange multiplier matrices; represents the Lagrange equation; α n , η n Respectively represent α, α * ,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 number of the sample point;

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

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

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

[0032]

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

[0034] So 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 represents the failure threshold of the set limit state; 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; 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 failed 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] Further, 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 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 ith 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 effects: The global reliability sensitivity analysis method of offshore wind turbines based on kernel density estimation of the present invention obtains the tower displacement set in the dynamic time-history response process of offshore wind turbines through the finite element calculation model of single-pile offshore wind turbines based on the sample set of uncertain input variables of material parameters; then, according to the tower limit state function function of offshore wind power, obtain the sample set of the tower limit state function function of offshore wind power, and establish a support vector regression proxy model based on the sample set of the tower limit state function function of offshore wind power; then, by obtaining a new sample set of uncertain input variables based on material parameters based on the Monte Carlo method, obtain the predicted state function function value based on the new sample set, and then determine the failure sample in the new sample set, obtain the failure probability of offshore wind power based on the new sample set, and calculate the global reliability sensitivity index of the offshore wind turbine, and complete 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. The use of the proxy model allows 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 reliability sensitivity is high, which is helpful for comprehensive evaluation of reliability. 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 briefly introduces 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 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 It is a finite element diagram of offshore wind power under static working condition in an embodiment of the present invention;

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

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

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

[0064] Figure 6 It 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] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are 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, firstly, the structural details, material characteristics of the wind turbine, and analysis types (including dynamic analysis or static analysis) of the existing monopile offshore wind turbine are determined, and used as the basis for establishing the finite element model of the monopile offshore wind turbine. The finite element calculation model of the monopile offshore wind turbine is established using the finite element software Plaxis to effectively evaluate the response of the wind turbine structure under different input conditions. Environmental conditions are applied to the finite element calculation model, and boundary conditions are defined to perform dynamic analysis.

[0071] S2: Define the uncertainty input variables of material parameters X = (X1, X2…X i …X I ), obtaining a sample set of uncertain input variables based on material parameters, so as to obtain a tower displacement set in a 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 ith uncertainty input variable of the nth 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 function of offshore wind power;

[0076] Specifically, based on historical experience, when the horizontal displacement of wind turbines 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 wind turbines as 1.25% of the length of the wind turbine support structure as the displacement failure threshold of the tower limit state. Using the first-exceeding 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 calculation probability of offshore wind turbines 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 represents the failure threshold of the set limit state; 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; 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 tower limit state function of offshore wind power 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 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 functions of offshore wind power, a support vector regression proxy 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 agent model is:

[0086]

[0087] Where: Z(x) is the regression prediction 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 function of offshore wind power corresponding to the maximum tower displacement in 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 predicted value and the nth sample point X n The corresponding maximum tower displacement d(X n ) between the allowable error; Denote 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] In the formula, α, α, η, η * All are Lagrange multiplier matrices, and all are greater than 0; represents the Lagrange equation; α n , η n Respectively represent α, α * ,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 number of the sample point;

[0103] Solving the dual optimization equation (5), we 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] So 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 uncertain 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. The specific method is 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 proxy 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 function value based on the new sample set, so as to obtain the 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 failed 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 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 the unknown quantity. To solve f(X i |F), according to the failure sample f(X (m′) ), and perform kernel density estimation method, as follows;

[0127] Combined with the failure sample (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 ith uncertainty input variable of the m′th failure sample point; K1(·) represents the kernel function of kernel density estimation; F is a failure event; in this embodiment, the maximum displacement in the offshore wind turbine dynamic time history response process exceeds the set limit state failure threshold, which is 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 methods of the present invention are as follows:

[0135] The offshore wind turbine system is relatively complex. For the research object, in order to improve the calculation efficiency, the impeller-nacelle system (RNA) is considered as a whole and simplified as a mass block at the top of the tower, represented by a plate unit. The pile foundation uses large-diameter steel pipe piles, and the piles are 50m deep in the soil. The horizontal length of the soil is 150m, the total thickness of the soil layer is 100m, and the water depth is defined as 15m. The 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 power model was modeled using Plaxis3D, and the model parameters were constructed based on the geometric parameters and properties of the pile. The pile was constructed as a two-dimensional structural plate element with linear stiffness, and the thickness was specified to simulate the stiffness of the pile. The soil element was a three-dimensional 10-node tetrahedron element. An interface model was used to simulate the soil-structure interaction. The interface element consists of 12 nodes, which makes the soil structural element coordinated with the plate element. The contact surface element is used as an extension of the plate element at the pile end to avoid stress concentration. The boundary conditions are 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 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 it 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 compared with 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 4, 5 is the fitting of the two surrogate models. From the response surface fitting diagram, it can be found that when the plane is at zero state function function, the fitting condition near it is good, but the fitting condition far from the failure point is not good, which is not global. Therefore, it is not suitable for global failure probability sensitivity analysis. The support vector regression model has global fitting and does not have the disadvantage of local optimal fitting, so it is 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 failure probability of offshore wind power under wind, wave and earthquake conditions. The model is as follows Figure 6 The values ​​of random variables are shown in the following table.

[0152] Table 5 Random variables

[0153]

[0154]

[0155] The wave load is solved by the Morision equation using the Airy wave theory. The wind load takes into account the fluctuating wind and the average wind. The fluctuating wind uses the Davenport wind spectrum and is calculated using the harmonic superposition method. The ground peak acceleration of the seismic load is 0.2g.

[0156] The reliability is calculated by combining the response surface method and the support vector regression method. 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 can be 0 to 1.5 when based on the normal use limit state. In this case, 1.5 is taken, so this design meets the specifications.

[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. From the sampling, we can know the probability density curve of the conditional failure probability. Combined with formula (13), we can get the global sensitivity of the failure probability. The failure probability sensitivity is as follows: Figure 7 As can be seen from the figure, the uncertainty of the weight of the first layer of soil has a greater impact on the failure probability, followed by the internal friction angle of the first layer of soil, which is determined by the thickness of the first layer of soil. Therefore, increasing the resistance factor of the first layer of soil will help improve the service reliability of offshore wind power.

[0160] This embodiment solves the reliability of offshore wind power under dynamic loading based on the proxy model, and simplifies the regression of real data by establishing a proxy model, thereby significantly reducing the complexity and time of calculation. This enables the dynamic reliability analysis to obtain results quickly. The proxy model allows easy modification of structural parameters, which helps in sensitivity analysis, identification of key design parameters, and optimization of structural performance. It can also be easily integrated into uncertainty analysis, taking into account the uncertainty of various parameters, which helps to comprehensively evaluate reliability and take corresponding designs and decisions.

[0161] This embodiment performs parameter analysis on offshore wind power based on the global failure probability sensitivity of Bayes' rule. Compared with the local failure probability sensitivity analysis, the global failure probability sensitivity can analyze this parameter from the perspective of the entire distribution of the random variable, rather than the local sensitivity from a certain point. The global sensitivity analysis method adopts the Bayes' rule and the single-layer sampling method, which can effectively avoid the complexity and time-consuming shortcomings of the double-layer sampling method.

[0162] In addition, when using the Bayesian rule for analysis, a data-driven kernel density estimation method is proposed. Since the data-driven kernel density estimation method is a non-parametric estimation method, it is not necessary to make assumptions about the distribution type of random variables, that is, it can obtain its probability density function, which greatly improves the calculation accuracy. It solves the problem that due to the randomness of the state function function calculation for random variables, the failure sample may not conform to the assumed distribution, causing calculation errors.

[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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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 material parameters, and then obtaining a tower displacement set in a dynamic time-history response process of the offshore wind turbine according to 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 function of offshore wind power; S4: obtaining a sample set of the tower limit state function function of the offshore wind power plant according to the tower displacement set in the dynamic time history response process of the offshore wind turbine and the tower limit state function function of the offshore wind power plant, and establishing a support vector regression proxy model based on the sample set of the tower limit state function function of the offshore wind power plant; S5: according to the uncertainty input variables of the material parameters and the support vector regression proxy model, a new sample set based on the uncertainty input variables of the material parameters is obtained based on the Monte Carlo method, and a predicted state function value based on the new sample set is obtained; S6: obtaining a failure sample in the new sample set according to the predicted state 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; 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 agent model is: Where: Z(x) is the regression prediction 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 function of offshore wind power corresponding to the maximum tower displacement in 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 predicted value and the nth sample point X n The corresponding maximum tower displacement d(X n ) between the allowable error; Denote ω,ξ n , The optimization objective equation of Introduce the Lagrangian function, and obtain the Lagrangian function and partial derivatives as follows: In the formula, α, α * ,η,η * All are Lagrange multiplier matrices; represents the Lagrange equation; α n , η n Respectively represent α, α * ,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 number of the sample point; Solve the dual optimization equation to obtain α n , The global optimal solution Substituting the global optimal solution into equation (2), we can obtain the weight vector ω; Then according to the dual optimization relationship, we get: Substitute equation (3) into equation (6) and solve it to get b; So 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 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 represents the failure threshold of the set limit state; 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; 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 failed 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 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 ith 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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