Offshore wind turbine generator stochastic dynamics analysis method capable of processing high-dimensional random factors

Abstract

The invention discloses an offshore wind turbine generator stochastic dynamics analysis method capable of processing high-dimensional stochastic factors, which comprises the following steps of: establishing a self-adaptive weight factor-based uniform subdivision technology, and obtaining a high-dimensional stochastic input variable of a structure in a complex environment; deriving a probability density integral equation of the offshore wind turbine generator with high-dimensional random factors, and depicting a structural uncertainty propagation process; solving the probability density integral equation by adopting a direct probability integral method based on a uniform subdivision technology to obtain a probability density function of the structural response of the wind turbine generator; and in combination with equivalent extreme value mapping, a direct probability integral method based on a uniform subdivision technology is further used for solving the fatigue reliability of the wind turbine generator. According to the self-adaptive uniform subdivision technology based on the weight factors, the weight factor solving process and the representative point selecting process are decoupled, the representative points of the high-dimensional probability space can be generated in a self-adaptive mode, the assignment probability of the representative points is calculated based on the weight factors, and the random factors of the structure in the complex environment are obtained.

Description

Technical Field

[0001] This invention relates to structural uncertainty quantification technology, and more particularly to a stochastic dynamics analysis method for offshore wind turbines that can handle high-dimensional random factors. Background Technology

[0002] Compared to traditional onshore wind power, which faces constraints such as geographical limitations and ecological impacts, offshore wind power, with its vast resource reserves and fewer environmental constraints, has become an important direction for the future development of wind energy. As offshore wind power projects gradually move into deeper operating areas, the marine dynamic environment in which wind turbines operate is becoming increasingly complex, and the impact of multiple stochastic excitations must inevitably be considered. Against this backdrop, fatigue reliability analysis of wind turbines is crucial for ensuring the stable, safe, and efficient operation of the power system. However, how to efficiently and accurately assess the fatigue reliability of offshore wind turbines under multiple stochastic excitations, especially for structures with high-dimensional probability spaces, remains a challenging problem that urgently needs to be solved.

[0003] The direct probability integral method, based on the principle of probability conservation, decouples the calculation of physical evolution and probability density evolution, enabling efficient and accurate analysis of structural stochastic responses and reliability. However, traditional Voronoi element-based partitioning techniques limit the dimensionality of the structures solved by this method. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to propose a stochastic dynamics analysis method for offshore wind turbines that can handle high-dimensional random factors, enabling a comprehensive analysis of the stochastic response and structural fatigue reliability of wind turbines in complex marine environments.

[0005] Technical solution: This invention includes the following steps:

[0006] S1: High-dimensional probability space adaptive uniform partitioning: Establish an adaptive uniform partitioning technique based on weight factors. Through representative point generation, weight factor calculation and correction, pruning strategy execution and probability normalization, high-dimensional random input variables of structures in complex environments are obtained.

[0007] S2: Constructing a high-dimensional probability density integral equation: Deriving the probability density integral equation of offshore wind turbines with high-dimensional random factors to characterize the propagation process of structural uncertainty;

[0008] S3: Efficient solution of probability density integral equation: The probability density integral equation is solved by using the direct probability integral method based on uniform partitioning technology to obtain the probability density function of the wind turbine structural response;

[0009] S4: High-dimensional stochastic fatigue reliability assessment: Combining equivalent extreme value mapping and Miner's linear cumulative damage criterion, the direct probability integral method is used to solve the fatigue reliability of wind turbine units.

[0010] The generation of representative points specifically involves: determining the dimension s and spatial range R of the structural probability space based on the actual requirements of the wind turbine project, and generating the basic random variables required for structural stochastic dynamics analysis. At this point, the sample space is represented as B. s = {(r, η1, η2, …, η s−1 | 0 ≤ r ≤ R, 0 ≤ η1 ≤ 2π, 0 ≤ η2 ≤ 2π, …, 0 ≤η s−1 ≤ 2π); The random variable R follows a chi-square distribution;

[0011] In the s-dimensional spherical coordinate sample space B s Internally, based on the Sobol sampling method, uniform representative points θ with low differences are generated. r = [ , ,…, ,…, ] represents the number of points N.

[0012] The weighting factor calculation process is as follows: In the Cartesian coordinate system, the sample space B... s The space is uniformly divided to generate a subspace, and the coordinates of the representative point are transformed from the spherical coordinate system to the Cartesian coordinate system using the Jacobi matrix.

[0013] The subspace containing the representative point is determined as the representative region, and the one-dimensional subspace weight factor is calculated according to the following formula:

[0014]

[0015] In the formula, D and D s Let be the volumes of the total sample space and the sample subspace, respectively; x be a random variable following a normal distribution; u be a random variable following a uniform distribution; n q Let be the number of random variables u in the q-th subspace;

[0016] Calculate the weighting factors in the s-dimensional subspace of the Cartesian coordinate system to serve as weighting factors for the representative regions of the points in the spherical coordinate sample space:

[0017] .

[0018] The weighting factor correction specifically involves: adjusting the weighting factor based on the GF-bias assessment error, where the GF-bias... When this happens, the weighting factor is corrected using the following formula:

[0019]

[0020] in, θ m w is the representative point with the largest GF deviation. m These are the corresponding weighting factors.

[0021] The pruning strategy is implemented by: adaptively reducing the sample space range using a pruning strategy, while ensuring the probability of assigning representative points within the range. , where P m Setting it to 1e-4 yields the sample space range, allowing us to obtain representative points in the high-dimensional probability space without increasing the number of representative points.

[0022] The probability normalization process involves defining the subspace without representative points as a redundant region, and multiplying the weight factor of the representative region by a scaling factor γ. m γ m = 1e+20, and calculate the representative point θ based on the weight factor of the representative region. q The probability of being assigned:

[0023]

[0024] The probabilities assigned to representative points are normalized to ensure that the total probability is 1.

[0025] Specifically, S2 is based on the probability conservation equation of infinitesimal elements: Introduce the Dirac function and perform coordinate transformation on the infinitesimal element:

[0026]

[0027] In the formula, y is the output vector in the Cartesian coordinate system, and r is the output vector in the spherical coordinate system; by introducing the Dirac function, we obtain the probability density integral equation in the spherical coordinate system for a high-dimensional random factor θ:

[0028]

[0029] in, , r1= ρ, r2= φ1, …, r n = φ n₋1 ;

[0030] By reducing the dimension of the above equation, we obtain the probability density integral equation for the structure of offshore wind turbines:

[0031] .

[0032] The probability density function in S3 is:

[0033]

[0034] in, Let be the probability density function of the wind turbine structure. These are the smoothing parameters.

[0035] The fatigue reliability calculation formula in S4 is as follows:

[0036] .

[0037] A stochastic dynamics analysis system for offshore wind turbines capable of handling high-dimensional stochastic factors includes:

[0038] Partitioning module: Used to implement adaptive uniform partitioning of high-dimensional probability space, outputting high-dimensional random input variables and the probability assigned to representative points;

[0039] Equation derivation module: Used to derive high-dimensional probability density integral equations;

[0040] Solver module: Used to solve the probability density integral equation using the direct probability integration method, and output the probability density function of the structural response;

[0041] Reliability assessment module: Used to combine equivalent extreme value mapping and Miner's criterion to output the fatigue reliability of wind turbine units.

[0042] Beneficial effects: The adaptive uniform partitioning technique based on weight factors in this invention decouples the weight factor solution from the representative point selection process, adaptively generating representative points in a high-dimensional probability space. The assigned probability of these representative points is calculated based on the weight factors, effectively handling high-dimensional probability spaces and obtaining the stochastic factors of structures in complex environments. It can be widely applied to the efficient and accurate solution of the stochastic response and reliability of offshore wind turbines under multiple stochastic excitations. Furthermore, the method in this invention is non-intrusive, easily combined with other deterministic models, suitable for software development, and convenient for engineering applications. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention;

[0044] Figure 2 A schematic diagram of the IEA 15MW semi-submersible wind turbine model;

[0045] Figure 3 A structural schematic diagram of the tower, a key component of a wind turbine.

[0046] Figure 4The subspace [θ] obtained by the direct probability integral method based on uniform partitioning technique is (a) 100 , θ 500 (a) The representative point of ]; (b) Subspace [θ 1001 , θ 1003 The representative point of ]; the (c) subspace [θ] obtained based on the Monte Carlo simulation method. 100 ,θ 500 [ ] sample points; (d) subspace [θ 1001 , θ 1003 [Sample points];

[0047] Figure 5 The fatigue damage probability density functions at different nodes of the wind turbine tower are obtained by the direct probability integral method based on uniform partitioning (representative points are 1000) and the Monte Carlo simulation method (sample points are 10000): (a) Node 1; (b) Node 6;

[0048] Figure 6 The three-dimensional joint probability density function of fatigue damage at the bottom of the tower is obtained by the direct probability integral method based on uniform partitioning technique.

[0049] Figure 7 The fatigue reliability of the tower of a 15MW semi-submersible wind turbine under combined wind and wave excitation. Detailed Implementation

[0050] The invention will now be further described with reference to the accompanying drawings.

[0051] Example 1

[0052] like Figure 1 As shown in the figure, this embodiment presents a stochastic dynamics analysis method for offshore wind turbines with high-dimensional random factors. Through an adaptive uniform partitioning technique based on weighting factors, it achieves the partitioning of the high-dimensional probability space. Then, based on the direct probability integral method, it develops a stochastic dynamics analysis method for offshore wind turbines with high-dimensional random factors, comprehensively analyzing the stochastic response and structural fatigue reliability of wind turbines in complex marine environments. Specifically, it includes the following steps:

[0053] S1: Establish an adaptive uniform partitioning technique based on weighting factors to partition the high-dimensional probability space and obtain high-dimensional random input variables with structure. Specifically, this includes:

[0054] S11, based on the actual requirements of the wind turbine project, determine the dimension s and spatial range R of the structural probability space, and generate the basic random variables, i.e., the random source, required for the structural stochastic dynamics analysis. At this point, the sample space can be represented as B. s ={(r, η1, η2, …, η s−1| 0 ≤ r ≤ R, 0 ≤ η1 ≤ 2π, 0 ≤ η2 ≤ 2π, …, 0 ≤ η s−1 ≤ 2π). The random variable R follows a chi-square distribution.

[0055] S12, in the s-dimensional spherical coordinate sample space B s Internally, based on the Sobol sampling method, uniform representative points θ with low differences are generated. r = [ , ,…, ,…, ] represents the number of points N.

[0056] S13, calculate the weighting factors in the Cartesian coordinate system. In the Cartesian coordinate system, calculate the sample space B. s The system is divided into uniform subspaces, and the coordinates of representative points are transformed from spherical coordinates to Cartesian coordinates using a Jacobi matrix. The subspace containing the representative points is then defined as the representative region. The one-dimensional subspace weighting factor is calculated using the following formula:

[0057]

[0058] In the formula, D and D s Let be the volumes of the total sample space and the sample subspace, respectively; x be a random variable following a normal distribution; u be a random variable following a uniform distribution; n q Let be the number of random variables u in the q-th subspace. Then, further calculate the weighting factors of the s-dimensional subspace in the Cartesian coordinate system, which serve as the weighting factors for the representative regions of the points in the spherical coordinate sample space:

[0059]

[0060] S14, based on the GF-bias, assess the error and correct the weighting factors. The smaller the GF-bias, the smaller the calculation error of the weighting factors. When the GF-bias... When this happens, the weighting factor can be corrected using the following formula:

[0061]

[0062] in, θ m w is the representative point with the largest GF deviation. m These are the corresponding weighting factors.

[0063] S15, execute the pruning strategy to adaptively obtain an appropriate sample space range to generate representative points in the high-dimensional probability space. Since the distribution of points becomes more dispersed with increasing spatial dimension, more points are needed, while the probability of representative points in edge regions is very low, having little impact on the result. Therefore, this invention uses a pruning strategy to adaptively reduce the range of the sample space, ensuring the probability of representative points within the range is maintained. (P) m It can be set to 1e-4) to obtain an appropriate sample space range, and obtain representative points in the high-dimensional probability space without increasing the number of representative points.

[0064] S16, Calculate the probability of assigning representative points based on the weighting factor. First, define the subspace without representative points as redundant regions. Multiply the weighting factor of the representative region by a large scaling factor γ. m (It is suggested that γ be used) m = 1e+20), to eliminate the influence of redundant regions. Subsequently, the representative point θ is calculated based on the weighting factor of the representative region. q The probability of being assigned:

[0065]

[0066] The probabilities assigned to representative points are normalized to ensure that the total probability is 1.

[0067] S2: Derive the probability density integral equation for offshore wind turbines with high-dimensional random factors to characterize the propagation process of structural uncertainty.

[0068] Probability conservation equations based on infinitesimal elements:

[0069]

[0070] Introducing the Dirac function, and performing the following coordinate transformation on the infinitesimal element:

[0071]

[0072] In the formula, y is the output vector in the Cartesian coordinate system, and r is the output vector in the spherical coordinate system. Furthermore, by introducing the Dirac function, we can obtain the probability density integral equation for a high-dimensional random factor θ in the spherical coordinate system:

[0073]

[0074] in, , r1= ρ, r2= φ1, …, r n = φn-1 .

[0075] Pair After dimensionality reduction, the probability density integral equation of the response of interest to the offshore wind turbine structure is obtained:

[0076]

[0077] S3: The probability density integral equation is solved by the direct probability integral method based on uniform partitioning technology to obtain the probability density function of the wind turbine structural response with high-dimensional random factors.

[0078] The probability density integral equation with high-dimensional random factors in the spherical coordinate system established in step (2) is solved using the direct probability integral method. The key technologies include the uniform partitioning technique based on weight factors and the Dirac function smoothing technique invented in step (1), thereby obtaining the numerical solution formula for the probability density integral equation of the wind turbine structure with high-dimensional random factors:

[0079]

[0080] in, Let be the probability density function of the response of interest to the wind turbine structure. The smoothing parameters can be adaptively obtained using the following kernel-based formula:

[0081]

[0082] S4: Combining equivalent extreme value mapping, the direct probability integral method based on uniform partitioning technology is further used to solve the fatigue reliability of wind turbine units.

[0083] According to Miner's linear cumulative damage criterion, the damage generated by all stress cycles can be accumulated, and the fatigue cumulative damage can be expressed as:

[0084]

[0085] In the formula, n i S represents the i-th stress level. i The number of cycles can be determined using the rainflow counting method; N i This represents the fatigue cycle life under the corresponding stress level.

[0086] The fatigue limit state function can be expressed as:

[0087]

[0088] Introducing the Heaviside function, the equation derived in step (2) is... Integrating, we obtain the formula for calculating the fatigue reliability of structures with high-dimensional random factors without needing to smooth the Dirac function:

[0089]

[0090] Furthermore, from the formula The fatigue reliability of offshore wind turbines in complex marine environments was obtained.

[0091] Example 2

[0092] This embodiment of the stochastic dynamics analysis system for offshore wind turbines with high-dimensional stochastic factors includes:

[0093] Partitioning module: Used to implement adaptive uniform partitioning of high-dimensional probability space, outputting high-dimensional random input variables and the probability assigned to representative points;

[0094] Equation derivation module: Used to derive high-dimensional probability density integral equations;

[0095] Solver module: Used to solve the probability density integral equation using the direct probability integration method, and output the probability density function of the structural response;

[0096] Reliability assessment module: Used to combine equivalent extreme value mapping and Miner's criterion to output the fatigue reliability of wind turbine units.

[0097] Example 3

[0098] This embodiment is a reference example, based on the direct probability integral method based on uniform partitioning technology given in this invention, using an IEA 15MW semi-submersible wind turbine under combined wind and wave action, such as... Figure 2 As shown in Table 1, taking stochastic dynamics analysis as an example, the main parameters of the wind turbine are shown in Table 1.

[0099] Table 1. Main parameters of IEA 15 MW semi-submersible wind turbine

[0100]

[0101] The specific calculation steps are as follows:

[0102] (1) A semi-submersible wind turbine is a coupled dynamic system consisting of an upper turbine, a tower, a floating foundation, and a mooring system. To describe the motion characteristics of this system, the floating foundation can be assumed to be a six-degree-of-freedom rigid body, and its motion is described using multibody dynamics theory; the turbine blades and tower can be simulated as elastic bodies using the modal reduction method, retaining the key low-order modes; the mooring system is simulated based on the finite element method. Based on the above modeling method, the motion equations of the floating wind turbine can be obtained in the following form:

[0103]

[0104] Where M is the mass matrix of the structure. and Displacement, velocity, and acceleration vectors are defined respectively, θ is the input random factor, t represents time, and p is the load vector.

[0105] (2) Simulation of random wind and wave loads on semi-submersible wind turbines. The example follows the relevant standards set by the International Electrotechnical Commission (IEC). The normal turbulence model (NTM) is used to simulate turbulent wind, and the power spectrum of the wind speed is the Kaimal spectrum. The number of random variables is set to 501 to ensure sufficient wind spectrum sampling points in the time domain, thereby ensuring the simulation accuracy of wind loads. The harmonic superposition method is used to simulate the sea surface, and the wave spectrum is the Jonswap spectrum. The number of random variables is set to 502 to ensure simulation accuracy. Subsequently, the random wave loads are calculated using the Morison formula.

[0106] (3) A model of the wind turbine was built using the OpenFAST open-source software, and numerical simulation of its structural response was performed. This example mainly studies the following: Figure 3 The stochastic dynamic characteristics of the tower, a key component of the wind turbine, are shown. Therefore, the stress at the tower nodes is extracted as the structural response of interest. The stress amplitude and mean stress are obtained. The number of cycles is calculated by combining the rainflow counting method and the SN curve. Finally, the Miner linear cumulative damage criterion is introduced to estimate the fatigue damage of the tower.

[0107] (4) Treat fatigue damage as a response and substitute it into the probability density integral equation (equation). By utilizing the direct probability integral method based on uniform partitioning technology, the probability density integral equation of wind turbine with high-dimensional random factors is numerically solved, and the probability density function curve of fatigue damage of key components of semi-submersible wind turbine is obtained. Figure 4 The representative points obtained by the direct probability integral method based on uniform partitioning technology are compared with the sample points of the Monte Carlo simulation method to verify the effectiveness of the uniform partitioning technology based on weight factors proposed in this invention. Figure 5The probability density functions of fatigue damage at different nodes of the tower are presented and compared with the results of Monte Carlo simulation to verify the effectiveness of the method. The joint probability density function of different nodes, obtained through the surface integral form of the probability density integral equation, is shown below. Figure 6 As shown.

[0108] (5) Solve for the fatigue reliability of key components of the IEA 15MW semi-submersible wind turbine. Substitute the functional functions of the structure under different thresholds into the dynamic reliability calculation formula of the direct probability integral method based on uniform partitioning technology (Equation 1). The fatigue reliability curves of the wind turbine tower under the combined action of wind and waves at different service years were obtained, as shown below. Figure 7 As shown, the results were compared with those calculated using the Monte Carlo simulation method to verify the computational accuracy of the method.

[0109] This invention achieves efficient partitioning of the high-dimensional probability space, obtaining the high-dimensional stochastic factors required for the stochastic dynamics analysis of wind turbines in complex marine environments. Furthermore, based on the principle of probability conservation, starting from the spherical coordinate system, the structural probability density integral equation with high-dimensional stochastic factors is derived. A direct probability integration method based on uniform partitioning technology is developed, achieving efficient solution of the probability density integral equation and obtaining the stochastic response of the offshore wind turbine structure. Combined with equivalent extremum mapping, a structural fatigue reliability assessment technique with high-dimensional stochastic factors is proposed.

Claims

1. A method of handling offshore wind turbine generator unit stochastic dynamics analysis with high dimensional random factors, characterized in that, The method comprises the following steps: S1: high-dimensional probability space adaptive uniform subdivision: an adaptive weight factor-based uniform subdivision technique is established, high-dimensional random input variables of the structure in a complex environment are obtained through representative point generation, weight factor calculation and correction, cutting strategy execution and probability normalization; S2: construction of high-dimensional probability density integral equation: the probability density integral equation of the offshore wind turbine with high-dimensional random factors is derived to depict the propagation process of structural uncertainty; S3: efficient solution of the probability density integral equation: the direct probability integral method based on the uniform subdivision technique is adopted to solve the probability density integral equation, and the probability density function of the structural response of the wind turbine is obtained; S4: high-dimensional random fatigue reliability evaluation: the direct probability integral method is used to solve the fatigue reliability of the wind turbine by combining the equivalent extreme value mapping and the Miner linear cumulative damage criterion.

2. A method of handling offshore wind turbine generator unit stochastic dynamics analysis with high dimensional random factors according to claim 1, characterized in that, The representative points are generated, specifically: according to actual requirements of the wind turbine engineering, dimensions s and a space range R of a structure probability space are determined, and basic random variables required for structure random dynamics analysis are generated; in a s-dimensional spherical coordinate sample space B s , based on a Sobol sampling method, low-difference uniform representative points θ r = [ , , , ] are generated, and the number of representative points is N.

3. A method of handling offshore wind turbine unit stochastic dynamic analysis with high dimensional random factors according to claim 2, characterized in that, The sample space is represented as B when the basic random variable is generated s = {(r, η1, η2, …,η s−1 | 0 ≤ r ≤ R, 0 ≤ η1 ≤ 2π, 0 ≤ η2 ≤ 2π, …, 0 ≤ η s−1 ≤ 2π)}; the random variable R is subject to chi-square distribution.

4. A method of handling offshore wind turbine unit stochastic dynamic analysis with high dimensional random factors according to claim 3, characterized in that, The weight factor calculation process is: uniformly dividing the sample space B s in the Cartesian coordinate system to generate a subspace, converting the representative point coordinates from the spherical coordinate system to the Cartesian coordinate system through the Jacobi matrix; determining the subspace where the representative point is located as a representative region, and calculating the one-dimensional subspace weight factor according to the following formula: where D and D s are the volume of the total sample space and the sample subspace, respectively; x is a random variable following a normal distribution; u is a random variable following a uniform distribution; n q is the number of random variables u in the qth subspace. The weight factor of the s-dimensional subspace in the Cartesian coordinate system is calculated as the weight factor of the representative region of the representative point in the spherical coordinate sample space: 。 5. A method of handling offshore wind turbine unit stochastic dynamic analysis with high dimensional random factors according to claim 1, characterized in that, The weight factor is corrected, specifically: based on the GF-bias evaluation error, the weight factor is corrected when the GF-bias is greater than the preset threshold, the weight factor is corrected by the following formula: wherein , θ m is the most representative point of the GF bias, w m is the corresponding weight factor.

6. A method of handling offshore wind turbine unit stochastic dynamic analysis with high dimensional random factors according to claim 1, characterized in that, The cutting strategy is executed, specifically: the cutting strategy is adopted to adaptively reduce the sample space range, and the probability of representative points in the range is ensured wherein P m =1e-4, the sample space range is obtained.

7. A method of handling offshore wind turbine unit stochastic dynamic analysis with high dimensional random factors according to claim 6, characterized in that, The assigned probability is normalized, specifically, a subspace not containing a representative point is defined as a redundant region, and a weight factor of a representative region is multiplied by a proportional factor γ m , γ m = 1e+20, and the assigned probability of a representative point θ q is calculated according to the weight factor of the representative region: .

8. A method of handling offshore wind turbine unit stochastic dynamic analysis with high dimensional random factors according to claim 1, characterized in that, The probability density function in S3 is: wherein, is the probability density function of the wind turbine structure, is a smoothing parameter.

9. A method of handling offshore wind turbine unit stochastic dynamic analysis with high dimensional random factors according to claim 7, characterized in that, The fatigue reliability calculation formula in S4 is: 。 10. A system for handling offshore wind turbine stochastic dynamics analysis with high dimensional random factors, the system being configured to implement the offshore wind turbine stochastic dynamics analysis method of any one of claims 1 to 9, wherein the system comprises: a computer system configured to implement the offshore wind turbine stochastic dynamics analysis method of any one of claims 1 to 9. It comprises: a subdivision module: used for realizing adaptive uniform subdivision of the high-dimensional probability space, and outputting high-dimensional random input variables and representative point assigned probabilities; an equation derivation module: used for deriving the high-dimensional probability density integral equation; a solution module: used for solving the probability density integral equation by the direct probability integral method, and outputting the probability density function of the structural response; a reliability evaluation module: used for outputting the fatigue reliability of the wind turbine by combining the equivalent extreme value mapping and the Miner criterion.

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