A Method and System for Fatigue Reliability Analysis of Welding Points on a Floating Platform

Abstract

The present invention discloses a method and system for fatigue reliability analysis of welding joints of a floating platform. The method includes the following steps: Step S1, based on the notch strain method, establish a fatigue damage calculation program for the welding joints of the floating platform of an offshore floating wind turbine; Step S2, construct a fatigue reliability model of the welding joints and analyze and determine its deterministic parameters and random variables; Step S3, use the first-order reliability method to iteratively solve the design point of the fatigue reliability model; Step S4, calculate the fatigue reliability of the welding joints of the floating platform of the offshore floating wind turbine and the sensitivity of each design variable according to the design point. The fatigue reliability and sensitivity analysis carried out by the present invention can also effectively identify the influence of the uncertainty of each random variable on the fatigue reliability of the welding joints of the floating platform of the offshore floating wind turbine, so as to extend it to the design of the welding joints of the floating platform of the offshore floating wind turbine to improve the fatigue reliability of the welding joints of the floating platform of the offshore floating wind turbine.

Description

Technical Field

[0001] The present invention relates to the calculation of the fatigue reliability of welded joints of a floating platform of an offshore floating wind turbine, and specifically relates to a method and system for analyzing the fatigue reliability of welded joints of a floating platform. Background Art

[0002] Fatigue caused by periodic sea winds and waves is one of the main failure modes of the welded joints of the floating platform of an offshore floating wind turbine. The floating platform of an offshore floating wind turbine is an integrated structure welded by metal columns, rods, etc. The fatigue welding opening of its welded joints directly threatens the reliability, safety and power generation efficiency of the floating platform and even the entire floating wind turbine. In the design and operation and maintenance of the floating platform of an offshore floating wind turbine, it is necessary to control or avoid the fatigue failure of its welded joints to eliminate expensive repairs and catastrophic accidents. However, due to a large number of uncertainties related to the complex fatigue process of structural components, such as fatigue loads, weld geometries, material properties, etc., it is difficult to carry out accurate and reliable fatigue reliability assessment of the welded joints of the floating platform of an offshore floating wind turbine. Although fatigue reliability analysis has become a widely accepted procedure, the fatigue analysis and fatigue reliability assessment methods specifically for the welded joints of the floating platform of an offshore floating wind turbine still do not effectively consider the influence of the uncertainties of the marine environment and the operating characteristics of the wind turbine on the fatigue strength of the welded joints of the floating platform of an offshore floating wind turbine. On the other hand, the methods for determining, describing, modeling and reasoning the uncertain factors related to the above influences have not been formed.

[0003] The weld geometry has a significant impact on the fatigue strength of the welded joints of the floating platform of an offshore floating wind turbine. Three effects of the weld geometry should be considered in fatigue analysis: the increase in the general stress level, the local notch effect and the crack-like defect. The first one is mainly caused by misalignment (dislocation). If the welded joint with dislocation is subjected to an axial load, the local stress will increase due to secondary bending. The local notch effect is related to the local discontinuity that causes stress concentration. The weld toe radius and inclination angle are the main geometric parameters used to characterize the local notch characteristics at the weld toe. Crack-like defects, such as undercut, are usually regarded as the starting positions of fatigue cracks.

[0004] Dislocations, weld toe radius, inclination angle, crack-like defects, material properties, and fatigue loads are the main influencing factors for the fatigue of welded joints on the floating platforms of offshore floating wind turbines. However, there is considerable uncertainty in the above factors under the complex and variable marine environment and the welding process that is difficult to accurately control. The variation in weld geometry is a common feature of welded joints on the floating platforms of offshore floating wind turbines. The weld geometry depends on welding conditions and manufacturing processes. Even when using the same welding technique, during the welding process, the welding current, voltage, travel speed, working angle, and welding position will change, resulting in some changes in the geometric structure. This may be one of the main reasons for the significant scatter in the fatigue life of welded joints. The uncertainty of material properties is also significant, and scattered material properties are obtained from different material tests. There is also great uncertainty in the marine environment, hydrodynamic calculation models, stress response calculation models, etc. that the offshore floating wind turbines are subjected to, resulting in great uncertainty in fatigue loads.

[0005] The widely used fatigue analysis methods: the S-N curve method and the crack propagation method are difficult to explicitly consider all the uncertainties of the welded joints on the floating platforms of offshore floating wind turbines. In the S-N curve method, the nominal stress, hot spot stress, and effective notch stress methods can only consider the influence of dislocations. Due to the limitation of the stress intensity factor solution, the crack propagation method cannot properly consider the local notch effect. Summary of the Invention

[0006] The object of the present invention is to overcome the deficiencies in the prior art and provide a fatigue reliability analysis method and system for welded joints on floating platforms. The present invention well integrates the uncertainty of weld geometry into the fatigue reliability assessment of welded joints on the floating platforms of offshore floating wind turbines.

[0007] To achieve the above object, the present invention is realized through the following technical solutions:

[0008] A fatigue reliability analysis method for welded joints on a floating platform, comprising the following steps:

[0009] Step S1, based on the notch strain method, establish a fatigue damage calculation program for welded joints on the floating platforms of offshore floating wind turbines;

[0010] Step S2, construct a fatigue reliability model for welded joints on the floating platforms of offshore floating wind turbines and analyze and determine its deterministic parameters and random variables;

[0011] Step S3, use the first-order reliability method to iteratively solve the design point of the fatigue reliability model;

[0012] Step S4, calculate the fatigue reliability of welded joints on the floating platforms of offshore floating wind turbines and the sensitivity of each design variable according to the design point.

[0013] Preferably, the procedure for calculating the fatigue damage of the welding points of the floating platform of the offshore floating wind turbine established based on the notch strain method in step S1 includes the following steps:

[0014] S11. Considering that the floating platform of the floating wind turbine is subjected to cyclic loads in the marine environment, the long-term cyclic nominal stress range suffered by the welding points of the floating platform of the floating wind turbine is fitted with the Weibull distribution as:

[0015]

[0016] where Δσn is the nominal stress range, q and h are the scale parameter and shape parameter of the Weibull distribution, and the total number of cycles is 108;

[0017] S12. Based on the geometric shape of the weld of the floating platform of the floating wind turbine, calculate the notch elastic stress:

[0018] Δσ e =K t Δσ n

[0019] where Δσe is the notch elastic stress range, Kt is the stress concentration factor, considering the influence of the geometric shape of the weld of the floating platform of the floating wind turbine such as dislocations, weld toe radius, and inclination angle;

[0020] S13. Combining the cyclic stress-strain relationship of the material and the equivalent strain energy density method, calculate the notch elastoplastic strain. The cyclic stress-strain relationship of the material under uniaxial loading is expressed as:

[0021]

[0022] where E is Young's modulus, ε a and σ a are the amplitudes of the uniaxial cyclic strain and stress respectively, and K′ and n′ are the cyclic strain hardening coefficient and exponent respectively;

[0023] When the stress concentration at the weld of the floating platform of the floating wind turbine is in a plane strain state, the relationship between the first principal stress and strain in the plane strain state and the uniaxial stress and strain is:

[0024]

[0025] where ε 1a and σ 1a are the amplitudes of the first principal strain and stress in the plane strain state respectively, ν is Poisson's ratio, and μ is the generalized Poisson's ratio;

[0026] The equivalent strain energy density method is expressed as:

[0027]

[0028] S14. Considering the influence of crack-like defects, the strain-life curve of the welding points on the floating platform of the offshore floating wind turbine is modeled as follows:

[0029]

[0030] where k is the depth of the crack-like defect, and ε f ′(k) and σ f ′(k) are respectively

[0031]

[0032] where ε f ′ is the fatigue ductility coefficient of the material; σ f ′ is the fatigue strength coefficient of the material. In the formula, a i and a f are respectively the average grain size of the material and the radius of the smooth cylindrical specimen. a0 is defined as:

[0033]

[0034] where ΔK th,LC is the critical value of long crack propagation, Δσ w is the fatigue limit (stress range). To ensure consistency, the value of the stress ratio R = -1 is used. The critical value of crack propagation at any stress ratio can be calculated by ΔK th =(1 - 0.73R)ΔK th0 and ΔK th0 is the critical value of crack propagation when R = 0.

[0035] S15. Based on the linear cumulative damage theory, calculate the cumulative damage caused by fatigue loads to the welding points on the floating platform of the offshore floating wind turbine during its service life:

[0036]

[0037] where N i is the number of cycles to failure under the action of the i-th stress cycle, obtained from the strain-life curve, and n is the total number of all stress cycles within the life cycle.

[0038] Preferably, the fatigue reliability model of the welding point in step S2 is

[0039] g(X, d)=Δ-D;

[0040] where X=(X1, X2, ···, X n ) T is a vector of random variables, d is a deterministic parameter, Δ is the damage value at failure, and D is the cumulative damage caused by fatigue loads to the welding points on the floating platform of the offshore floating wind turbine during its service life.

[0041] Preferably, in step S3, the first-order reliability method is used to iteratively solve the design point of the fatigue reliability model, including the following steps:

[0042] S31. Assume the initial design point X k (k = 0);

[0043] S32. Calculate the sensitivity coefficient

[0044]

[0045] where k is the number of iterations; is the variance of the random variable X i ;

[0046] S33. Calculate the reliability index β:

[0047]

[0048] where, is the mean value of the random variable X i ;

[0049] S34. Calculate the new design point X k+1 :

[0050]

[0051] S35. When ||X k+1 - X k || ≤ ε and |g(X k+1 , d)| ≤ ε (ε > 0 is the specified convergence accuracy), output the design point X * = ||X k+1 ||; otherwise, let k = k + 1 and return to step S32.

[0052] Preferably, in step S4, the fatigue reliability p f of the welding points of the floating platform of the offshore floating wind turbine and the sensitivity of each design variable are calculated by the following formulas respectively:

[0053]

[0054] System for fatigue reliability analysis method of welding points on a floating platform, the system includes an establishment module, a construction module, a determination module, a solution module, and a calculation module. The establishment module is used to establish a fatigue damage calculation program for welding points. The construction module is used to construct a fatigue reliability model for welding points. The determination module is used to determine its deterministic parameters and random variables. The solution module is used to solve the design point of the fatigue reliability model. The calculation module is used to calculate the fatigue reliability of the welding points on the floating platform of an offshore floating wind turbine and the sensitivity of each design variable.

[0055] The beneficial effects of the present invention are as follows: In view of the large number of uncertainty problems existing in the current fatigue analysis of welding points on the floating platform of offshore floating wind turbines, starting from the influence of the uncertainty of weld geometry on the fatigue reliability of welding points on the floating platform of offshore floating wind turbines, the notch strain method is used to conduct fatigue analysis on the welding points on the floating platform of offshore floating wind turbines. On this basis, the first-order reliability method is used to carry out the fatigue reliability analysis of the welding points. In addition, the fatigue reliability and sensitivity analysis carried out by the present invention can also effectively identify the influence of the uncertainty of each random variable on the fatigue reliability of the welding points on the floating platform of offshore floating wind turbines, so as to extend it to the design of the welding points on the floating platform of offshore floating wind turbines to improve the fatigue reliability of the welding points on the floating platform of offshore floating wind turbines. Brief Description of the Drawings

[0056] Figure 1 is the flow chart of the present invention;

[0057] Figure 2 is the welding point for fatigue reliability analysis of the floating platform of an offshore floating wind turbine. Detailed Description of the Invention

[0058] The technical solutions of the present invention will be further described below in conjunction with the drawings in the specification:

[0059] As Figure 1 shown, taking a welding point on the floating platform of a certain offshore floating wind turbine as an example, the present invention of a fatigue reliability analysis method for welding points on a floating platform includes the following steps:

[0060] Step S1: Based on the notch strain method, establish a fatigue damage calculation program for the welding points on the floating platform of an offshore floating wind turbine;

[0061] Step S2: Construct a fatigue reliability model for the welding points on the floating platform of an offshore floating wind turbine and analyze and determine its deterministic parameters and random variables;

[0062] Step S3: Use the first-order reliability method to iteratively solve the design point of the fatigue reliability model;

[0063] Step S4. Calculate the fatigue reliability of the welding points of the floating platform of the offshore floating wind turbine and the sensitivity of each design variable according to the design points.

[0064] The fatigue damage calculation procedure for the welding points of the floating platform of the offshore floating wind turbine established based on the notch strain method in Step S1 includes the following steps

[0065] S11. Considering that the floating platform of the floating wind turbine is subjected to cyclic loads in the marine environment, the long-term cyclic nominal stress range suffered at the welding points of the floating platform of the floating wind turbine is fitted with the Weibull distribution as:

[0066]

[0067] where Δσn is the nominal stress range, q and h are the scale parameter and shape parameter of the Weibull distribution, and the total number of cycles is 108;

[0068] S12. Calculate the notch elastic stress based on the weld geometry:

[0069] Δσ e =K t Δσ n ;

[0070] where Δσe is the notch elastic stress range, Kt is the stress concentration factor, considering the influence of weld geometry such as dislocations, weld toe radius, and inclination angle;

[0071] S13. Combine the material cyclic stress-strain relationship and the equivalent strain energy density method to calculate the notch elastic-plastic strain. The material cyclic stress-strain relationship under uniaxial loading is expressed as:

[0072]

[0073] where E is the Young's modulus, ε a and σ a are the amplitudes of the uniaxial cyclic strain and stress respectively, and K′ and n′ are the cyclic strain hardening coefficient and exponent respectively.

[0074] The weld stress concentration is generally in a plane strain state. The relationship between the first principal stress and strain in the plane strain state and the uniaxial stress and strain is:

[0075]

[0076] where ε 1a and σ 1a are the amplitudes of the first principal strain and stress in the plane strain state respectively, ν is the Poisson's ratio, and μ is the generalized Poisson's ratio.

[0077] The equivalent strain energy density method is expressed as:

[0078]

[0079] S14. Considering the influence of crack-like defects, the strain-life curve of the welding points of the floating platform of the offshore floating wind turbine is modeled as:

[0080]

[0081] where k is the depth of the crack-like defect, ε f ′(k), σ f ′(k) are respectively

[0082]

[0083] where ε f ′ is the fatigue ductility coefficient of the material; σ f ′ is the fatigue strength coefficient of the material. In the formula, a i and a f are respectively the average grain size of the material and the radius of the smooth cylindrical specimen, and a0 is defined as:

[0084]

[0085] where ΔK th,LC is the critical value of long crack propagation, and Δσ w is the fatigue limit (stress range). To ensure consistency, the value of the stress ratio R = -1 is used. The critical value of crack propagation at any stress ratio can be estimated by ΔK th =(1 - 0.73R)ΔK th0 , and ΔK th0 is the critical value of crack propagation when R = 0.

[0086] S15. Based on the linear cumulative damage theory, calculate the cumulative damage caused by fatigue load on the welding points of the floating platform of the offshore floating wind turbine during its service life:

[0087]

[0088] where Ni is the number of cycles to failure under the action of the i-th stress cycle, obtained from the strain-life curve, and n is the total number of stress cycles within the life cycle.

[0089] The fatigue reliability model of the welding points of the floating platform of the offshore floating wind turbine established in step S2 is

[0090] g(X,d)=Δ - D

[0091] where X=(X1,X2,···,X n ) Tis a random variable vector; d is a deterministic parameter; Δ is the damage value at failure, and D is the cumulative damage caused by fatigue loads at the welded joints of the floating platform of an offshore floating wind turbine during its service life.

[0092] In the embodiment of the present invention, the welded joints for fatigue reliability analysis of the floating platform of an offshore floating wind turbine are as Figure 2 shown, and the random variables and deterministic parameters are shown in Tables 1 and 2.

[0093] Table 1 Statistical parameters of random variables

[0094]

[0095] * Mean and standard deviation corresponding to the normal distribution, t is the thickness of the welded joint

[0096] Table 2 Values of deterministic parameters

[0097]

[0098] In step S3, the first-order reliability method is used to iteratively solve the design point of the fatigue reliability model, including the following steps:

[0099] S31. Assume the initial design point X k (k = 0);

[0100] S32. Calculate the sensitivity coefficient

[0101]

[0102] where k is the iteration number; is the variance of the random variable X i .

[0103] S33. Calculate the reliability index β:

[0104]

[0105] where, is the mean value of the random variable X i .

[0106] S34. Calculate the new design point X k+1 :

[0107]

[0108] S35. When ||X k+1 - X k || ≤ ε and |g(X k+1 , d)| ≤ ε (ε > 0 is the specified convergence accuracy), output the design point X * = ||Xk+1 ||; Otherwise, let k = k + 1, and return to step S32. In step S4, calculate the fatigue reliability p of the welding points of the floating platform of the offshore floating wind turbine f and each design variable The calculation formulas for the sensitivity are as follows:

[0109] p f = Pr[g(X, d) ≤ 0] = Φ(-||X * ||)

[0110]

[0111] In the embodiments of the present invention, the calculated results are shown in Tables 3 and 4 below.

[0112] Table 3 Sensitivity Results

[0113]

[0114]

[0115] Table 4 Reliability Results

[0116]

[0117] A system for the fatigue reliability analysis method of the welding points of the floating platform, the system includes an establishment module, a construction module, a determination module, a solution module, and a calculation module. The establishment module is used to establish a calculation program for the fatigue damage of the welding points. The construction module is used to construct a fatigue reliability model of the welding points. The determination module is used to determine its deterministic parameters and random variables. The solution module is used to solve the design points of the fatigue reliability model. The calculation module is used to calculate the fatigue reliability of the welding points of the floating platform of the offshore floating wind turbine and the sensitivity of each design variable.

[0118] In view of the large number of uncertainty problems existing in the current fatigue analysis of the welding points of the floating platform of the offshore floating wind turbine, starting from the influence of the uncertainty of the weld geometry on the fatigue reliability of the welding points of the floating platform of the offshore floating wind turbine, the notch strain method is used to conduct fatigue analysis on the welding points of the floating platform of the offshore floating wind turbine. On this basis, the first-order reliability method is used to carry out the fatigue reliability analysis of the welding points. In addition, the fatigue reliability and sensitivity analysis carried out by the present invention can also effectively identify the influence of the uncertainty of each random variable on the fatigue reliability of the welding points of the floating platform of the offshore floating wind turbine, so as to extend it to the design of the welding points of the floating platform of the offshore floating wind turbine to improve the fatigue reliability of the welding points of the floating platform of the offshore floating wind turbine.

[0119] It should be noted that the above-listed is only a specific embodiment of the present invention. Obviously, the present invention is not limited to the above embodiments and there can be many variations. In short, all variations that can be directly derived or associated by those of ordinary skill in the art from the disclosed content of the present invention should be considered within the protection scope of the present invention.

Claims

1. A method for analyzing the fatigue reliability of welding joints of a floating platform, characterized in that, It includes the following steps: Step S1: Based on the notch strain method, establish a fatigue damage calculation program for the welding points of the floating platform of an offshore floating wind turbine; Step S2: Construct a fatigue reliability model for the welding points of the floating platform of an offshore floating wind turbine and analyze and determine its deterministic parameters and random variables; Step S3: Use the first-order reliability method to iteratively solve the design point of the fatigue reliability model; Step S4: Calculate the fatigue reliability of the welding points of the floating platform of an offshore floating wind turbine and the sensitivity of each design variable according to the design point; The step of establishing a fatigue damage calculation program for the welding points of the floating platform of an offshore floating wind turbine based on the notch strain method in Step S1 includes the following steps: S11: Considering that the floating platform of the floating wind turbine is subjected to cyclic loads in the marine environment, use the Weibull distribution to fit the long-term cyclic nominal stress range suffered by the welding points of the floating platform of the floating wind turbine as: where Δσ n is the nominal stress range, q and h are the scale parameter and shape parameter of the Weibull distribution, and the total number of cycles is 10 8 ; S12: Calculate the notch elastic stress based on the geometric shape of the weld of the floating platform of the floating wind turbine; Δσ e = K t Δσ n where Δσ e is the elastic stress range of the notch, and K t is the stress concentration factor, which takes into account the effects of the weld geometry of the floating platform of the floating wind turbine, such as dislocations, weld toe radius, and inclination angle; S13: Combine the material cyclic stress-strain relationship and the equivalent strain energy density method to calculate the notch elastic-plastic strain. The material cyclic stress-strain relationship under uniaxial loading is expressed as: where E is Young's modulus, ε a and σ a are the amplitudes of uniaxial cyclic strain and stress, respectively, and K′ and n′ are the cyclic strain hardening coefficient and exponent, respectively; When the stress concentration area of the weld of the floating platform of the floating wind turbine is in a plane strain state, the relationship between the first principal stress and strain in the plane strain state and the uniaxial stress and strain is: where ε 1a and σ 1a are respectively the amplitudes of the first principal strain and stress in the plane strain state, ν is the Poisson's ratio, and μ is the generalized Poisson's ratio; The equivalent strain energy density method is expressed as: S14: Considering the influence of crack-like defects, model the strain-life curve of the welding points of the floating platform of the offshore floating wind turbine as: where k′ is the depth of the crack-like defect, ε′ f (k′), σ′ f (k′) are respectively where ε f ′ is the fatigue ductility coefficient of the material; σ f ′ is the fatigue strength coefficient of the material. In the formula, a i and a f are the average grain size of the material and the radius of the smooth cylindrical specimen respectively. a0 is defined as: Among them, ΔK th,LC is the critical value for long crack propagation, and Δσ w is the fatigue limit. To ensure consistency, the value of the stress ratio R = -1 is used. The critical value of crack propagation under any stress ratio can be calculated from ΔK th =(1 - 0.73R)ΔK th0 , where ΔK th0 is the critical value of crack propagation when R = 0; S15: Based on the linear cumulative damage theory, calculate the cumulative damage caused by fatigue loads to the welding points of the floating platform of the offshore floating wind turbine during its service life; where N i is the number of cycles to failure under the action of the i-th stress cycle, obtained from the strain-life curve, and n is the total number of all stress cycles within the life cycle.

2. The fatigue reliability analysis method for the welding points of the floating platform according to claim 1, wherein The fatigue reliability model of the welding points in Step S2 is g(X,d) = Δ - D; where X = (X1, X2, ···, X n ) T is a random variable vector, d is a deterministic parameter, Δ is the damage value at failure, and D is the cumulative damage caused by fatigue loads to the welding points of the floating platform of the offshore floating wind turbine during its service life.

3. The fatigue reliability analysis method for the welding points of the floating platform according to claim 2, characterized in that The step of using the first-order reliability method to iteratively solve the design point of the fatigue reliability model in Step S3 includes the following steps: S31. Assume the initial design point X k , k = 0; S32. Calculate the sensitivity coefficient where k is the number of iterations; is the random variable X i variance; S33: Calculate the reliability index β; where, μ Xi is the mean of the random variable X i ; S34. Calculate the new design point X k+1 : S35. When ||X k+1 -X k || ≤ ε and |g(X k+1 , d)| ≤ ε, where ε > 0 is the specified convergence precision, output the design point X * = ||X k+1 ||; otherwise, let k = k + 1 and return to step S32.

4. According to the fatigue reliability analysis method for the welding points of the floating platform described in claim 3, characterized in that Calculate the fatigue reliability p of the welding points of the floating platform of the offshore floating wind turbine in step S4 f and the sensitivity of each design variable The calculation formulas are as follows:

5. A system for fatigue reliability analysis method of welding points of a floating platform according to claim 1, characterized in that, The system includes an establishment module, a construction module, a determination module, a solution module, and a calculation module. The establishment module is used to establish a fatigue damage calculation program for the welding points. The construction module is used to construct a fatigue reliability model for the welding points. The determination module is used to determine its deterministic parameters and random variables. The solution module is used to solve the design point of the fatigue reliability model. The calculation module is used to calculate the fatigue reliability of the welding points of the floating platform of the offshore floating wind turbine and the sensitivity of each design variable.

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