A method for multi-axial fatigue and reliability analysis of a semi-submersible wind turbine support structure

Abstract

The application discloses a kind of semi-submersible wind turbine support structure multi-axle fatigue and reliability analysis method, first in combination with offshore semi-submersible wind turbine motion theory, wind speed spectrum theory, wave spectrum theory, determine offshore semi-submersible wind turbine each part input load power spectral density function, then carry out finite element analysis to offshore wind turbine in frequency domain to load power spectral density function, determine dangerous point by frequency domain method, then using W-B critical plane method calculates damage, predict the fatigue life of dangerous point in time domain, and verify that wind-induced damage is much larger than wave-induced damage, finally solve wind turbine support structure failure probability curve, complete semi-submersible wind turbine support structure multi-axle fatigue and reliability analysis.The method of the application can better unify the randomness of marine environment and the calculation interval of wind turbine load, improve the accuracy of wind turbine support structure fatigue life prediction, has the universality to any type wind turbine support structure, and simple operation, wide application.

Description

Technical Field

[0001] This invention belongs to the technical field of marine equipment structural mechanical life prediction and reliability analysis, specifically relating to a multi-axis fatigue and reliability analysis method for a semi-submersible wind turbine support structure. Technical Background

[0002] As the operating environment of offshore wind turbines becomes increasingly complex, the safety of their support structures becomes more prominent. Therefore, the reliability analysis and evaluation of support structures has become a crucial technical issue in this field. In the past, much effort was devoted to the design and optimization of wind turbine support structures, while little attention was paid to their safety and reliability assessment. Wind turbines are complex in structure and operate under harsh conditions, making fatigue failure one of the main factors affecting their safety and economic efficiency. During operation, wind turbine support structures are subjected to repeated alternating loads, including wind loads, wave forces, and electromagnetic forces. These periodic changes cause significant fatigue stress to critical components such as blades, towers, and foundations. Considering the complexity of the marine environment, in-depth research has been conducted on the theory of fatigue life prediction for support structures under multiaxial loads. A practical method for estimating the multiaxial fatigue life of support structures and a reliability analysis process have been proposed, which has significant theoretical and engineering implications.

[0003] The key to predicting the multiaxial fatigue life of support structures in marine environments is finding a suitable method to combine the relationship between input-output and model parameters in the time-frequency domain to calculate cumulative fatigue damage, and then link the calculated damage parameters to the life equation. To date, there has been considerable research on support structures, with a series of analytical models established, and fatigue research is relatively mature. The main methods used include frequency domain methods, combined damage methods, or combined fatigue load methods. However, combined damage or combined fatigue load methods calculate fatigue damage or dynamic response caused by a single load, and then use a combination method to calculate damage under multiple loads acting simultaneously. These methods do not consider the interaction between input wind and wave loads and the differences in the degree of wind and wave influence. Therefore, multiaxial fatigue analysis of wind turbine support structures under wind and wave action, clarifying the influence of wind-induced and wave-induced damage, and accurately calculating the failure probability are crucial. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a multiaxial fatigue and reliability analysis method for a semi-submersible wind turbine support structure. Based on the advantages of various multiaxial fatigue methods and considering the requirements for fatigue strength design of mechanical structures under multiaxial loading, a novel time-frequency domain hybrid method for wind turbines is proposed. Furthermore, a fatigue life prediction model for the support structure is established based on the wind speed probability distribution. This method has the advantages of simplified calculation process, strong applicability, and high accuracy in fatigue life prediction results.

[0005] The technical solution adopted in this invention is: a multi-axis fatigue and reliability analysis method for a semi-submersible wind turbine support structure, the specific steps of which are as follows:

[0006] S1. Combining the motion theory, wind speed spectrum theory, and wave spectrum theory of offshore semi-submersible wind turbines, determine the power spectral density function (PSD) of the input load of each part of the offshore semi-submersible wind turbine.

[0007] S2. Based on the load power spectral density function obtained in step S1, simplify the finite element model, conduct finite element spectral analysis on the semi-submersible wind turbine in the frequency domain, and determine the danger points through the frequency domain method.

[0008] S3. After determining the critical point based on step S2, the power spectral density function PSD of the stress / strain at the critical point is transformed by inverse Fourier transform to obtain the stress / strain output time history curve in the time domain. Then, it is substituted into the WB critical plane method to calculate the damage and predict the fatigue life of the critical point in the time domain.

[0009] S4. Change the variables in the input wind and wave data, repeat steps S1-S3, verify that wind-induced damage is much greater than wave-induced damage, and then use this as a basis to obtain the improved wind turbine damage superposition equation.

[0010] The variables in the input wind and wave data include: wind and wave input angle, wind speed range, wave period, and wave height.

[0011] The expression for the improved wind turbine damage superposition equation is as follows:

[0012]

[0013] Where D represents total damage, D W Indicates wind-induced injury, D S Indicates wave-induced damage, M represents the top mass of the wind turbine, E represents the elastic modulus, gpf represents the shear fatigue ductility coefficient of the supporting structure, and υ eff It represents Poisson's ratio.

[0014] S5. Considering the probability distribution of wind speed in my country's coastal waters, couple the fatigue life calculation framework of the wind turbine support structure described in steps S1-S4 with the calculation framework based on the cumulative damage interference model to solve the failure probability curve of the wind turbine support structure and complete the multi-axis fatigue and reliability analysis of the semi-submersible wind turbine support structure.

[0015] The life of the multi-axis fatigue calculation is corrected by combining the superposition equation improved in step S4. A common wind speed range in my country's coastal waters is selected. Within this range, considering the Weibull distribution of wind speed, the fatigue life probability distribution of the wind turbine support structure is calculated. That is, the relationship between wind speed distribution and life is established. Based on the cumulative damage interference model, the failure probability of the wind turbine support structure is calculated.

[0016] Furthermore, step S1 is specifically as follows:

[0017] Using the wind and wave load time-domain data published by the National Meteorological Administration as input, the discrete time-time wind speed, wave height, and wave period data are reasonably interpolated to obtain the wind and wave load time history curves. Then, the wind and wave load time-domain data are substituted into the wave spectrum and wind speed spectrum, that is, appropriate wind speed spectrum and wave spectrum are selected to calculate the input in the frequency domain.

[0018] The wind and wave load time-domain data refers to the measured wind and wave data. Based on the actual marine environment in my country's coastal waters, the wind speed spectrum uses the Davenport spectrum, and the wave spectrum uses the improved JONSWAP spectrum.

[0019] The PSD expression for the wind speed fluctuation process in the wind speed spectrum is as follows:

[0020]

[0021] Among them, S v The one-sided power spectrum represents wind speed fluctuations; K0 represents the dimensionless surface roughness coefficient; v h Let h represent the average wind speed at height h; ω represent the frequency in radians per second; and x represent the integer length scale of the turbulence, expressed as follows:

[0022]

[0023] Wherein, coefficient c = 600m.

[0024] The wave spectrum uses a modified JONSWAP spectrum, expressed as follows:

[0025]

[0026] Among them, S η (ω) represents the wave energy density per unit frequency, ω m H represents the peak frequency, σ represents the peak shape parameter, and H represents the peak frequency. s γ represents the effective wave height, and γ represents the calculated parameter.

[0027] Ocean waves under steady-state conditions can be viewed as a stationary random process undergoing various ergodic states. Wave motion can be considered as a superposition of an infinite number of simple harmonic cosine waves with different frequencies, amplitudes, and random initial phases, as expressed below:

[0028]

[0029] Where t represents time, a n ω represents the amplitude of the wave. n ε represents the frequency of the wave. n This represents the initial phase that is uniformly distributed in the interval [0, 2π].

[0030] The improved JONSWAP spectrum is used to describe the energy distribution of the wave, with the energy distribution at ω. L ~ω H Within the range, the frequency is decomposed into N intervals, then the amplitude a of the i-th component wave is... i The expression is as follows:

[0031]

[0032] Among them, S η ω represents wave energy density. H ω represents the upper limit of frequency. L Indicates the lower limit of frequency.

[0033] Then, the N cosine waves from all N intervals are superimposed to obtain the wavefront time history curve, as shown in the following expression:

[0034]

[0035] in, This represents the frequency of the i-th component wave.

[0036] The frequency range of energy distribution ω L ~ω H The selection process begins with determining the effective wave height H. s The calculation of the effective wave height is based on the cumulative probability of excess values, and the expression is as follows:

[0037]

[0038] in, This represents the average wave height of the first third of the waves in a wave sequence, arranged from largest to smallest; for the upper frequency ω... H and lower limit ω L The calculation expression is as follows:

[0039]

[0040] Where μ represents the percentage of total energy neglected in the spectrum. And ω is taken as the upper limit of the spectrum frequency, which is 3 to 4 times the peak frequency. H .

[0041] Furthermore, step S2 is specifically as follows:

[0042] S21. Based on the load power spectral density function obtained in step S1, the finite element model is simplified, and finite element spectral analysis is carried out on the semi-submersible wind turbine in the frequency domain. The mooring system tension, the wind turbine's own weight, and the water surface buoyancy are used as boundary conditions, and the wind and wave load power spectral density functions are used as inputs. The von Mises equivalent stress / strain cloud map of the wind turbine support structure is obtained through the modal analysis and spectral analysis modules of ANSYS software, and the von Mises equivalent stress / strain data at each tubular interface are extracted.

[0043] S22. Based on step S21, the critical points are determined by the frequency domain method. First, the spectral moments of each order of the power spectral density function of the von Mises equivalent stress / strain are calculated. Then, the Dirlik life prediction model is constructed to determine the fatigue life of each point and the critical points are identified.

[0044] The stress power spectral density at critical locations needs to be processed into a uniaxial stress power spectral density before calculating the corresponding spectral moments and fatigue damage based on the Dirlik lifetime prediction model. The Dirlik lifetime prediction model expression is as follows:

[0045]

[0046] in:

[0047]

[0048] D3 = 1 - D1 - D2

[0049]

[0050] Where C and b represent material parameters, and m0, m1, m2, and m4 represent spectral moments.

[0051] Furthermore, step S3 is specifically as follows:

[0052] S31. Obtain the stress / strain output time history curve in the time domain by using the inverse Fourier transform of the power spectral density function of the stress / strain at the critical point.

[0053] S32. Use the WB critical plane method to calculate damage and predict the fatigue life N at the critical point in the time domain. f ;

[0054] The WB critical plane method requires rotating and projecting the stress / strain components onto all planes to find the plane with the greatest fatigue damage. Then, the stress / strain history calculated in step S31 is used to perform fatigue calculations on all planes.

[0055] First, the calculated stress / strain history is transformed using a coordinate transformation matrix to obtain the stress / strain on any plane. The expression for the transformation matrix is ​​as follows:

[0056]

[0057] Where θ represents the angle between the projection of the transformed X-axis onto the initial XY plane and the initial X-axis. This indicates the angle between the transformed X-axis and the original Z-axis.

[0058] Then θ, Increase the angle by 5° each time, changing the plane, and calculate the damage D under each plane. WB The plane with the greatest damage is taken as the critical plane.

[0059] Furthermore, in step S4, the verification that wind-induced damage is much greater than wave-induced damage is as follows:

[0060] A1. Select the wind speed range of 3m / s to 20m / s, and use OPENFAST+MATLAB software to simulate and calculate the wave conditions under the corresponding wind conditions.

[0061] A2. Time-frequency domain transformation of wind and wave loads yields the input power spectral density function;

[0062] A3. Substitute the model and input load into the finite element analysis software to obtain the power spectral density function of the equivalent stress;

[0063] A4. Calculate the fatigue life under various sea conditions based on the Dirlik model, plot the results for comparison, and summarize the differences.

[0064] Furthermore, in step S5, the failure probability curve of the wind turbine support structure is solved, as follows:

[0065] B1. Simulate the service environment of a semi-submersible wind turbine at sea, establish a long-term wind field with different wind speed distributions, and divide the wind field calculation area into a grid.

[0066] The different wind speed distribution ranges are 5m / s to 13m / s; the wind field calculation grid area is above sea level and several meters above the top of the wind turbine blades, with a width of 3 to 4 times the diameter of the blade sweep surface, and the top of the wind turbine tower as the horizontal center.

[0067] B2. Perform probability statistics on the different wind speed ranges in step B1, and generate wave height probability distribution and wave period probability distribution based on the wind speed probability distribution and the OPENFAST software.

[0068] B3. Couple the long-term wind speed probability distribution and cumulative damage interference model obtained in step B2, perform reliability analysis, and calculate the fatigue failure probability.

[0069] The fatigue reliability analysis method based on cumulative damage uses the cumulative damage of the wind turbine support structure as the reliability analysis index. If the cumulative damage value is greater than the critical damage value, the structure is considered to have failed; otherwise, it is considered to be in a safe and reliable state. The failure probability expression for the weak points of the offshore semi-submersible wind turbine support structure is as follows:

[0070]

[0071] Among them, P f Let D represent the failure probability, g represent the limit state function, and D represent the limit state function. c D represents the critical damage to the supporting structure. T This represents the total damage at the design life of T.

[0072] The formula for calculating the failure probability is as follows:

[0073]

[0074] Where μ represents the mean, It represents the standard deviation.

[0075] The beneficial effects of this invention are as follows: First, the method of this invention combines the motion theory, wind speed spectrum theory, and wave spectrum theory of semi-submersible wind turbines to determine the power spectral density function of the input loads of each part of the semi-submersible wind turbine. Then, finite element analysis is performed on the wind turbine in the frequency domain using the load power spectral density function to identify critical points. Next, the WB critical plane method is used to calculate damage, predict the fatigue life of the critical points in the time domain, and verify that wind-induced damage is much greater than wave-induced damage. Finally, the failure probability curve of the wind turbine support structure is solved, completing the multiaxial fatigue and reliability analysis of the semi-submersible wind turbine support structure. Based on wind speed spectrum, wave spectrum, and wind turbine motion theory, this invention can effectively unify the randomness of the marine environment with the calculation range of wind turbine loads. Furthermore, considering the superposition equation of wind turbine material parameters improves the accuracy of fatigue life prediction for the wind turbine support structure. The coupled fatigue life probability distribution and cumulative damage interference model of the wind turbine support structure are universal for any type of wind turbine support structure, and the method is simple to operate and widely applicable.

[0076] This invention's method starts with monitoring data from my country's coastal waters, determining sea state, quantifying input, and simplifying the model. Similarly, it can be extended to the temperature field to consider fatigue life calculations for wind turbines in ice-covered areas. It is simple to operate and highly versatile. This invention combines offshore wind turbines with a hybrid time-frequency domain analysis method for predicting the multi-axis stochastic fatigue life of structures. It uses the equivalent stress method in the frequency domain to determine the location of structural critical points and employs the critical plane method to predict the fatigue life of these critical points in the time domain, effectively improving the accuracy of the prediction results and appropriately reducing the computational load. The superposition equation proposed in this invention considers the relationship between material parameters and wave-induced and wind-induced damage. Compared with the existing three types of superposition equations, the calculation results are more accurate and have a wider range of applications. This invention predicts the probability-load-life (PSN) relationship of wind speed distribution through a large-scale data model, revealing the correlation between sea state randomness and fatigue life. Based on national meteorological data and measured data from offshore wind power, it calculates the failure probability, providing new ideas for designing support structures with high reliability requirements and promoting the development of disciplines related to structural strength, damage, fracture, and fatigue. Attached Figure Description

[0077] Figure 1 This is a flowchart of a multi-axis fatigue and reliability analysis method for a semi-submersible wind turbine support structure according to the present invention.

[0078] Figure 2 This is a schematic diagram of the dimensions of the OC4-DeepCwind semi-submersible wind turbine provided in an embodiment of the present invention.

[0079] Figure 3 This is a schematic diagram of wind and wave input data provided in an embodiment of the present invention.

[0080] Figure 4 This is a flowchart of the WB critical plane method calculation in an embodiment of the present invention.

[0081] Figure 5 This is a schematic diagram showing the results of fatigue reliability analysis of a semi-submersible wind turbine under wind and wave loads in an embodiment of the present invention. Detailed Implementation

[0082] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0083] like Figure 1 The flowchart shown is a method for multiaxial fatigue and reliability analysis of a semi-submersible wind turbine support structure according to the present invention. The specific steps are as follows:

[0084] S1. Combining the motion theory, wind speed spectrum theory, and wave spectrum theory of offshore semi-submersible wind turbines, determine the power spectral density function (PSD) of the input load of each part of the offshore semi-submersible wind turbine (wave spectrum, wind speed spectrum).

[0085] S2. Based on the load power spectral density function obtained in step S1, simplify the finite element model, conduct finite element spectral analysis on the semi-submersible wind turbine in the frequency domain, and determine the danger points through the frequency domain method.

[0086] S3. After determining the critical point based on step S2, the power spectral density function PSD of the stress / strain at the critical point is transformed by inverse Fourier transform to obtain the stress / strain output time history curve in the time domain. Then, it is substituted into the WB critical plane method to calculate the damage and predict the fatigue life of the critical point in the time domain.

[0087] S4. Change the variables in the input wind and wave data, repeat steps S1-S3, verify that wind-induced damage is much greater than wave-induced damage, and then use this as a basis to obtain the improved wind turbine damage superposition equation.

[0088] The variables in the input wind and wave data include: wind and wave input angle, wind speed range, wave period, and wave height.

[0089] The expression for the improved wind turbine damage superposition equation is as follows:

[0090]

[0091] Where D represents total damage, D W Indicates wind-induced injury, D S Indicates wave-induced damage, M represents the mass of the wind turbine top, E represents the elastic modulus, gpf represents the shear fatigue ductility coefficient of the supporting structure, and v eff It represents Poisson's ratio.

[0092] S5. Considering the probability distribution of wind speed in my country's coastal waters, couple the fatigue life calculation framework of the wind turbine support structure described in steps S1-S4 with the calculation framework based on the cumulative damage interference model to solve the failure probability curve of the wind turbine support structure and complete the multi-axis fatigue and reliability analysis of the semi-submersible wind turbine support structure.

[0093] The life of the multi-axis fatigue calculation is corrected by combining the superposition equation improved in step S4. A common wind speed range in my country's coastal waters is selected. Within this range, considering the Weibull distribution of wind speed, the fatigue life probability distribution of the wind turbine support structure is calculated. That is, the relationship between wind speed distribution and life is established. Based on the cumulative damage interference model, the failure probability of the wind turbine support structure is calculated.

[0094] In this embodiment, step S1 is specifically as follows:

[0095] This embodiment uses the OC4-DeepCwind semi-submersible wind turbine to verify the hybrid time-frequency domain multi-axis fatigue calculation process. A schematic diagram of the OC4-DeepCwind semi-submersible wind turbine is shown below. Figure 2As shown, in order to reduce the amount of calculation while ensuring accuracy requirements, the wind turbine model is simplified to a certain extent, specifically including:

[0096] 1. Simplify the blades and nacelle, considering them as a mass unit at the top of the tower, and set the mass as 2 × 10⁻⁶. 5 Kg;

[0097] 2. The mooring system is simplified. The tension time history curves of the mooring chain under the action of waves and ocean currents are obtained by simulation software ORCAFLEX and OPENFAST and used as boundary conditions. Therefore, the mooring system is not reflected in the model.

[0098] 3. The total height of the tower is 120m, including the parts above and below the water surface, and the flange connection effect of the tower is not considered.

[0099] Because the materials used in the submersible wind turbine have different requirements for seawater corrosion resistance compared to those used above water, and because the material properties of the tubular nodes and annular welds in the hazardous area are also different, it is necessary to take the average value of the SN curves of each part of the material and substitute it into the fatigue life prediction calculation process. The SN curve parameters of the steel structure are shown in Table 1, which is taken from "DESIGN OF OFFSHORE WIND TURBINE STRUCTURES". In engineering applications, these parameters can also be obtained through experiments. Those skilled in the art can refer to material data sheets for the physical meaning of the parameters involved, and this invention will not elaborate on them in detail here.

[0100] Table 1

[0101]

[0102] For marine steel structures, the SN curve expression is as follows:

[0103]

[0104] Where N represents the lifespan, i.e., the number of stress cycles within the stress range Δσ; Δσ represents the stress range (MPa); ρ represents the slope of the negative tangent line of the SN curve; lgA represents the intersection point with the lgN axis; t ref The reference wall thickness is 32 mm for tubular nodes and 25 mm for edge areas; th represents the thickness at which the crack may develop, when th ≤ th ref When, take th = th ref k represents the thickness index, also known as the proportional index.

[0105] This embodiment uses publicly available wind and wave load time-domain data from a coastal site in my country as input. Discrete time-series data of wind speed, wave height, and wave period are interpolated appropriately to obtain wind and wave load time-history curves. The wind and wave load time-domain data are then substituted into the wave spectrum and wind speed spectrum, i.e., appropriate wind speed and wave spectra are selected to calculate the input in the frequency domain. The wind and wave input data provided in this embodiment are as follows: Figure 3 As shown.

[0106] The wind and wave load time-domain data refers to the measured wind and wave data. Based on the actual marine environment in my country's coastal waters, the wind speed spectrum uses the Davenport spectrum, and the wave spectrum uses the improved JONSWAP spectrum.

[0107] The PSD expression for the wind speed fluctuation process in the wind speed spectrum is as follows:

[0108]

[0109] Among them, S v One-sided power spectrum representing wind speed fluctuations (m 2 / s); K0 represents the dimensionless surface roughness coefficient; v h Let represent the average wind speed at a height of h = 10 m; ω represent the frequency in radians per second; and x represent the integer length scale of the turbulence, expressed as follows:

[0110]

[0111] Wherein, coefficient c = 600m.

[0112] The JONSWAP spectrum calculation expression is as follows:

[0113]

[0114] For ease of application, this embodiment uses a modified JONSWAP spectrum, expressed as follows:

[0115]

[0116] Among them, S η (ω) represents the wave energy density per unit frequency, g represents the gravitational acceleration, and a represents the energy scale parameter. m H represents the peak frequency, σ represents the peak shape parameter, and H represents the peak frequency. s This represents the significant wave height, and γ = 3.3 represents the calculated parameter.

[0117] Ocean waves under steady-state conditions can be viewed as a stationary random process undergoing various ergodic states. Wave motion can be considered as a superposition of an infinite number of simple harmonic cosine waves with different frequencies, amplitudes, and random initial phases, as expressed below:

[0118]

[0119] Where t represents time, a n ω represents the amplitude (m) of the constituent waves. n ε represents the frequency (rad / s) of the wave. n This represents the initial phase that is uniformly distributed in the interval [0, 2π].

[0120] The improved JONSWAP spectrum is used to describe the energy distribution of the wave, with the energy distribution at ω. L ~ω H Within the range, the frequency is decomposed into N intervals, then the amplitude a of the i-th component wave is... i The expression is as follows:

[0121]

[0122] Among them, S σ ω represents wave energy density. H ω represents the upper limit of frequency. L Indicates the lower limit of frequency.

[0123] Then, the N cosine waves from all N intervals are superimposed to obtain the wavefront time history curve, as shown in the following expression:

[0124]

[0125] in, This represents the representative frequency (rad / s) of the i-th component wave.

[0126] By describing the energy distribution of ocean waves and optimizing computational efficiency, the problem that needs to be solved is the energy distribution frequency range ω. L ~ω H The selection of effective wave height H is the first step. s The calculation of significant wave height. The meaning of significant wave height refers to the average wave height of the first third of the waves in a wave sequence, arranged from largest to smallest. Research indicates that at greater water depths, wave heights follow a sharp distribution. Therefore, the significant wave height can be calculated using the excess cumulative probability, as shown in the following expression:

[0127]

[0128] The calculated value is 1.598, so the effective wave height can be calculated as 1.598 times the average wave height from the observed data. Regarding the upper frequency limit ω... H and lower limit ω L The calculation expression is as follows:

[0129]

[0130] Where μ represents the percentage of total energy omitted from the spectrum, and in this embodiment, μ = 0.2%. Furthermore, 3 to 4 times the peak frequency is taken as the upper limit of the spectrum frequency ω. H .

[0131] In this embodiment, step S2 is specifically as follows:

[0132] S21. Based on the load power spectral density function obtained in step S1, the finite element model is simplified, and finite element spectral analysis is carried out on the semi-submersible wind turbine in the frequency domain. The mooring system tension, the wind turbine's own weight, and the water surface buoyancy are used as boundary conditions, and the wind and wave load power spectral density functions are used as inputs. The von Mises equivalent stress / strain cloud map of the wind turbine support structure is obtained through the modal analysis and spectral analysis modules of ANSYS software, and the von Mises equivalent stress / strain data at each tubular interface are extracted.

[0133] S22. Based on step S21, the critical points are determined by the frequency domain method. First, the spectral moments of each order of the power spectral density function of the von Mises equivalent stress / strain are calculated. Then, the Dirlik life prediction model is constructed to determine the fatigue life of each point and the critical points are identified.

[0134] The stress power spectral density at critical locations needs to be processed into a uniaxial stress power spectral density before calculating the corresponding spectral moments and fatigue damage based on the Dirlik lifetime prediction model. The Dirlik lifetime prediction model expression is as follows:

[0135]

[0136] in:

[0137]

[0138] D3 = 1 - D1 - D2

[0139]

[0140] Where C and b represent material parameters, and m0, m1, m2, and m4 represent spectral moments.

[0141] In this embodiment, step S3 is specifically as follows:

[0142] S31. Obtain the stress / strain output time history curve in the time domain by using the inverse Fourier transform of the power spectral density function of the stress / strain at the critical point.

[0143] S32. Use the WB critical plane method to calculate damage and predict the fatigue life N at the critical point in the time domain. f ;

[0144] The calculation process of the WB critical plane method is as follows: Figure 4 As shown, the calculation process requires rotating and projecting the stress / strain components onto all planes to find the plane with the greatest fatigue damage. Therefore, the stress / strain history calculated in step S31 needs to be used for fatigue calculation on all planes.

[0145] In the figure, θ, ξ represents the angle between the normal vector of any plane and the three-dimensional coordinate axis, α represents the angle increment, and i, j, and k represent the cycle count value.

[0146] First, the calculated stress / strain history is transformed using a coordinate transformation matrix to obtain the stress / strain on any plane. The expression for the transformation matrix is ​​as follows:

[0147]

[0148] Then θ, Increase the angle by 5° each time, changing the plane, and calculate the damage D under each plane. WB The plane with the greatest damage is taken as the critical plane.

[0149] In this embodiment, in step S4, the verification of wind-induced damage is much greater than wave-induced damage, as detailed below:

[0150] A1. Select the wind speed range of 3m / s to 20m / s, and use OPENFAST+MATLAB software to simulate and calculate the wave conditions under the corresponding wind conditions.

[0151] A2. Time-frequency domain transformation of wind and wave loads yields the input power spectral density function;

[0152] A3. Substitute the model and input load into the finite element analysis software to obtain the power spectral density function of the equivalent stress;

[0153] A4. Calculate the fatigue life under various sea conditions based on the Dirlik model, plot the results for comparison, and summarize the differences.

[0154] In this embodiment, step S5 involves solving for the failure probability curve of the wind turbine support structure, as detailed below:

[0155] B1. Simulate the service environment of a semi-submersible wind turbine at sea, establish a long-term wind field with different wind speed distributions, and divide the wind field calculation area into a grid.

[0156] The different wind speed distribution ranges are 5m / s to 13m / s; the wind field calculation grid area is above sea level and several meters above the top of the wind turbine blades, with a width of 3 to 4 times the diameter of the blade sweep surface, and the top of the wind turbine tower as the horizontal center.

[0157] B2. Perform probability statistics on the different wind speed ranges in step B1, and generate wave height probability distribution and wave period probability distribution based on the wind speed probability distribution and the OPENFAST software.

[0158] B3. Couple the long-term wind speed probability distribution and cumulative damage interference model obtained in step B2, perform reliability analysis, and calculate the fatigue failure probability.

[0159] The fatigue reliability analysis method based on cumulative damage uses the cumulative damage of the wind turbine support structure as the reliability analysis index. If the cumulative damage value is greater than the critical damage value, the structure is considered to have failed; otherwise, it is considered to be in a safe and reliable state. The critical damage value of the material is usually considered to be a fixed value of 1.

[0160] The failure probability expression for the weak points of the support structure of a semi-submersible wind turbine is as follows:

[0161]

[0162] Among them, P f Let D represent the failure probability, g represent the limit state function, and D represent the limit state function. c D represents the critical damage to the supporting structure. T This represents the total damage at the design life of T.

[0163] The formula for calculating the failure probability is as follows:

[0164]

[0165] Where μ represents the mean, It represents the standard deviation.

[0166] This embodiment, through the fatigue analysis of the entire process described above, finally yields the following result: Figure 5 The lifetime curve and probabilistic failure curve shown are as follows. Figure 5 (a) Comparison of fatigue life predictions before and after correction using the superposition equation. Figure 5 (b) is the failure probability curve based on the cumulative damage interference model.

[0167] in, Figure 5 (a) This shows that the lifetime calculated using the modified superposition equation is more conservative, and the relationship between wind speed and lifetime is non-linear, which is consistent with reality; Figure 5 (b) It demonstrates the relationship between the service life of a wind turbine and the probability of failure, which is of great engineering significance; the two figures fully illustrate that the maximum service life of the wind turbine in this embodiment is about 26 years.

[0168] In summary, the method of this invention establishes a novel method for predicting the lifespan of offshore wind turbines based on a hybrid time-frequency domain multiaxial fatigue analysis model. The improved superposition equation and cumulative damage interference model are coupled to calculate the failure probability and compared with data from existing methods. This verification shows that the method of this invention can comprehensively characterize the combined effect of multiaxial loads and input quantization, resulting in high accuracy in lifespan prediction. By considering the material parameters of the wind turbine, the calculation accuracy is improved while enhancing the practicality of the method.

[0169] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A multi-axis fatigue and reliability analysis method for a semi-submersible wind turbine support structure, the specific steps of which are as follows: S1. Combining the motion theory, wind speed spectrum theory, and wave spectrum theory of offshore semi-submersible wind turbines, determine the power spectral density function (PSD) of the input load of each part of the offshore semi-submersible wind turbine. S2. Based on the load power spectral density function obtained in step S1, simplify the finite element model, conduct finite element spectral analysis on the semi-submersible wind turbine in the frequency domain, and determine the danger points through the frequency domain method. S3. After determining the critical point based on step S2, the power spectral density function PSD of the stress / strain at the critical point is transformed by inverse Fourier transform to obtain the stress / strain output time history curve in the time domain. Then, it is substituted into the WB critical plane method to calculate the damage and predict the fatigue life of the critical point in the time domain. S4. Change the variables in the input wind and wave data, repeat steps S1-S3, verify that wind-induced damage is much greater than wave-induced damage, and then use this as a basis to obtain the improved wind turbine damage superposition equation. The variables in the input wind and wave data include: Wind and wave input angle, wind speed range, wave period, and wave height; The expression for the improved wind turbine damage superposition equation is as follows: where D represents total damage, D W represents wind-induced damage, D S represents wave-induced damage, M represents the mass of the top of the wind turbine, E represents the modulus of elasticity, gpf represents the support structure shear fatigue ductility factor, v eff represents the Poisson's ratio; S5. Considering the probability distribution of wind speed in my country's coastal waters, couple the fatigue life calculation framework of the wind turbine support structure described in steps S1-S4 with the calculation framework based on the cumulative damage interference model to solve the failure probability curve of the wind turbine support structure and complete the multi-axis fatigue and reliability analysis of the semi-submersible wind turbine support structure. The life of the multi-axis fatigue calculation is corrected by combining the superposition equation improved in step S4. A common wind speed range in my country's coastal waters is selected. Within this range, considering the Weibull distribution of wind speed, the fatigue life probability distribution of the wind turbine support structure is calculated. That is, the relationship between wind speed distribution and life is established. Based on the cumulative damage interference model, the failure probability of the wind turbine support structure is calculated.

2. The multiaxial fatigue and reliability analysis method for a semi-submersible wind turbine support structure according to claim 1, characterized in that, The specific steps of S1 are as follows: Using the wind and wave load time-domain data published by the National Meteorological Administration as input, the discrete time-time wind speed, wave height, and wave period data are reasonably interpolated to obtain the wind and wave load time history curves. Then, the wind and wave load time-domain data are substituted into the wave spectrum and wind speed spectrum, that is, appropriate wind speed spectrum and wave spectrum are selected to calculate the input in the frequency domain. Among them, the wind and wave load time domain data are the measured wind and wave data. Combined with the actual marine environment in my country's coastal waters, the wind speed spectrum is selected from the Davenport spectrum, and the wave spectrum is selected from the improved JONSWAP spectrum. The PSD expression for the wind speed fluctuation process in the wind speed spectrum is as follows: where S v represents the one-sided power spectrum of wind speed fluctuations; K0represents the dimensionless surface roughness coefficient; v h represents the average wind speed at height h; ω represents the frequency in radians per second; x represents the integral length scale of turbulence, expressed as follows: Wherein, coefficient c = 600m; The wave spectrum uses a modified JONSWAP spectrum, expressed as follows: where S η (ω) represents the wave energy density at unit frequency, ω m represents the spectral peak frequency, σ represents the peak shape parameter, H s represents the significant wave height, and γ represents a calculation parameter; Ocean waves under steady-state conditions can be viewed as a stationary random process undergoing various ergodic states. Wave motion can be considered as a superposition of an infinite number of simple harmonic cosine waves with different frequencies, amplitudes, and random initial phases, as expressed below: where t denotes time, a n denotes the amplitude of the constituent wave, ω n denotes the frequency of the constituent wave, ε n denotes the initial phase uniformly distributed in the interval [0, 2π]; The improved JONSWAP spectrum is chosen to describe the energy distribution of the wave, and the energy distribution is in the range of ω L ~ ω H The frequency is divided into N intervals, and the amplitude a i of the ith component wave is expressed as follows: where S η represents the wave energy density, ω H represents the upper frequency limit, ω L represents the lower frequency limit; Then, the N cosine waves from all N intervals are superimposed to obtain the wave surface time history curve, as shown in the following expression: in, This represents the frequency of the i-th component wave; The frequency range of energy distribution ω L ~ω H The selection process begins with determining the effective wave height H. s The calculation of the effective wave height is based on the cumulative probability of excess values, and the expression is as follows: in, This represents the average wave height of the first third of the waves in a wave sequence, arranged from largest to smallest; for the upper frequency limit ω... H and lower limit ω L The calculation expression is as follows: Wherein, μ indicates the percentage of total energy omitted from the spectrum high and low; and 3-4 times the peak frequency is taken as the upper limit of the spectrum frequency ω H .

3. The multiaxial fatigue and reliability analysis method for a semi-submersible wind turbine support structure according to claim 1, characterized in that, Step S2 is as follows: S21. Based on the load power spectral density function obtained in step S1, the finite element model is simplified, and finite element spectral analysis is carried out on the semi-submersible wind turbine in the frequency domain. The mooring system tension, the wind turbine's own weight, and the water surface buoyancy are used as boundary conditions, and the wind and wave load power spectral density functions are used as inputs. The von Mises equivalent stress / strain cloud map of the wind turbine support structure is obtained through the modal analysis and spectral analysis modules of ANSYS software, and the von Mises equivalent stress / strain data at each tubular interface are extracted. S22. Based on step S21, the critical points are determined by the frequency domain method. First, the spectral moments of each order of the power spectral density function of the von Mises equivalent stress / strain are calculated. Then, the Dirlik life prediction model is constructed to determine the fatigue life of each point and the critical points are identified. The stress power spectral density at critical locations needs to be processed into a uniaxial stress power spectral density before calculating the corresponding spectral moments and fatigue damage based on the Dirlik lifetime prediction model. The Dirlik lifetime prediction model expression is as follows: in: Where C and b represent material parameters, and m0, m1, m2, and m4 represent spectral moments.

4. The multiaxial fatigue and reliability analysis method for a semi-submersible wind turbine support structure according to claim 1, characterized in that, Step S3 is as follows: S31. Obtain the stress / strain output time history curve in the time domain by inverse Fourier transforming the power spectral density function of the stress / strain at the critical point. S32. Use the WB critical plane method to calculate damage and predict the fatigue life N at the critical point in the time domain. f ; The WB critical plane method requires rotating and projecting the stress / strain components onto all planes to find the plane with the greatest fatigue damage. Then, the stress / strain history calculated in step S31 is used to perform fatigue calculations on all planes. First, the calculated stress / strain history is transformed using a coordinate transformation matrix to obtain the stress / strain on any plane. The expression for the transformation matrix is ​​as follows: Where θ represents the angle between the projection of the transformed X-axis onto the initial XY plane and the initial X-axis. This indicates the angle between the transformed X-axis and the original Z-axis; Then θ, Increase the angle by 5° each time, changing the plane, and calculate the damage D under each plane. WB The plane with the greatest damage is taken as the critical plane.

5. The multiaxial fatigue and reliability analysis method for a semi-submersible wind turbine support structure according to claim 1, characterized in that, In step S4, the verification that wind-induced damage is much greater than wave-induced damage is as follows: A1. Select the wind speed range of 3m / s to 20m / s, and use OPENFAST+MATLAB software to simulate and calculate the wave conditions under the corresponding wind conditions. A2. Time-frequency domain transformation of wind and wave loads yields the input power spectral density function; A3. Substitute the model and input load into the finite element analysis software to obtain the power spectral density function of the equivalent stress; A4. Calculate the fatigue life under various sea conditions based on the Dirlik model, plot the results for comparison, and summarize the differences.

6. The multiaxial fatigue and reliability analysis method for a semi-submersible wind turbine support structure according to claim 1, characterized in that, In step S5, the failure probability curve of the wind turbine support structure is calculated, as follows: B1. Simulate the service environment of a semi-submersible wind turbine at sea, establish a long-term wind field with different wind speed distributions, and divide the wind field calculation area into a grid. The different wind speed distribution ranges are 5m / s to 13m / s; the wind field calculation grid area is: above sea level and several meters above the top of the wind turbine blades, with a width of 3 to 4 times the diameter of the blade sweep surface, and the top of the wind turbine tower as the horizontal center. B2. Perform probability statistics on the different wind speed ranges in step B1, and generate wave height probability distribution and wave period probability distribution based on the wind speed probability distribution and the OPENFAST software. B3. Couple the long-term wind speed probability distribution and cumulative damage interference model obtained in step B2, perform reliability analysis, and calculate the fatigue failure probability. The fatigue reliability analysis method based on cumulative damage uses the cumulative damage of the wind turbine support structure as the reliability analysis index. If the cumulative damage value is greater than the critical damage value, the structure is considered to have failed; otherwise, it is considered to be in a safe and reliable state. The failure probability expression for the weak point of the offshore semi-submersible wind turbine support structure is as follows: Among them, P f Let D represent the failure probability, g represent the limit state function, and D represent the limit state function. c D represents the critical damage to the supporting structure. T This represents the total damage over a design life of T. The formula for calculating the failure probability is as follows: Where μ represents the mean and θ represents the standard deviation.

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