Reliability-based Load Reduction Design and Safety Factor Verification Method for Wind Turbines

Abstract

The present invention discloses a reliability-based load reduction design and safety factor verification method for wind turbines, which takes into account multi-source uncertainties such as wind condition parameters, material properties, and aerodynamic characteristics throughout the life cycle of wind turbines, converts them into uncertainties of loads and structural resistances, and conducts reliability verification on the optimal design under different safety factors to find the optimal design that meets the reliability requirements. The present invention innovatively introduces partial safety factors into the reliability optimization design process of wind turbine components. By adjusting the partial safety factors and combining with the deterministic design process, the optimization of design variables is carried out, significantly reducing the number of reliability analyses in the optimization design process and improving the calculation efficiency. While providing the optimal design considering reliability, the present invention also provides the verified partial safety factors. Using the verified safety factors, wind turbine designers can use lower load design values, thereby achieving load reduction design of wind turbines.

Description

Technical Field

[0001] The present invention belongs to the field of uncertainty optimization design of wind turbine components, and particularly relates to a load reduction design and safety factor checking method for wind turbines based on reliability. Background Art

[0002] Most of the existing wind turbine design theories adopt a deterministic design process, that is, for the physical mechanism of failure modes, by calculating the characteristic values of loads and structural resistances, and combining partial safety factors to form deterministic design constraints. Because of its simplicity and feasibility, this method has been widely used in the wind power design industry. However, at present, the values of partial safety factors are mostly directly determined based on engineering experience. Due to the lack of guidance of reliability analysis theory and the randomness analysis of loads and structural resistances caused by multi-source uncertainties such as wind condition parameters, material properties, and aerodynamic characteristics of wind turbines, it is difficult to establish a mapping between the existing values of partial safety factors and the reliability of wind turbines, usually resulting in over-redundant designs. Therefore, the theory of reliability-based design optimization (RBDO) has been widely studied in recent years and has been applied to a certain extent in the industrial community.

[0003] RBDO makes full use of the multi-source uncertainty statistical model of wind turbines, checks the design through reliability analysis, and replaces the deterministic design equation based on partial safety factors, so as to achieve low-cost design on the premise of ensuring the design reliability. However, reliability analysis itself requires a large amount of computing resources, and in the traditional RBDO process, once the design changes, a reliability analysis needs to be carried out, so the amount of calculation is greatly increased compared with the current deterministic design process. In addition, the wind turbine structure is complex, the design variable dimension is high, and the failure modes are numerous. Directly applying the traditional RBDO process to the design of wind turbine components will result in problems that are difficult to iterate and converge. Summary of the Invention

[0004] In order to solve the deficiencies of the prior art, achieve the load reduction design of wind turbines, reduce the redundancy of safety factors, and reduce the load design value in the deterministic design process, the present invention adopts the following technical solutions:

[0005] A load reduction design and safety factor checking method for wind turbines based on reliability, comprising the following steps:

[0006] Step S1: Determine the components of the wind turbine for load reduction design, and determine the design variables, objective function, and failure modes;

[0007] Step S2: Establish a multi-source uncertainty characterization model of the wind turbine, including but not limited to wind condition parameter uncertainty and other uncertainties such as aerodynamic properties and material properties;

[0008] Step S3: Select the design load conditions of the wind turbine, determine the wind condition parameters within a certain time range and the corresponding probabilities of the wind condition parameters within a certain return period; under the wind condition parameters within a certain time range, conduct a simulation of the wind turbine performance model and fit the conditional probability distribution of the maximum value within the return period of the random load under the wind condition parameters.

[0009] Step S4: For the remaining uncertainties other than the wind condition parameters, establish a corresponding statistical model of the load uncertainty factor to characterize the influence of the remaining uncertainty sources on the random load alone.

[0010] Step S5: Based on the mechanism of the failure mode, construct a design equation containing the safety factor and the load and the characteristic value of the structural resistance, and a limit state equation containing the random load and the structural resistance respectively; determine a set of safety factors, taking the design equation as a constraint, construct and solve a deterministic optimization problem of minimizing the prime objective function to obtain the optimal design variables; for the optimal design variables, conduct a reliability check in combination with the limit state equation. If the reliability check passes, slightly lower the safety factor, otherwise, slightly increase the safety factor; re-determine a set of safety factors for the above check. When the algorithm meets the convergence requirements, select the design variables with the minimum objective function and meeting the reliability requirements and their corresponding safety factors as the results of the load reduction design and safety factor check of the wind turbine.

[0011] Further, in the step S3, determine the wind condition parameter samples {(v i , c i )}, i = 1, …, N W , and the probability P(v i , c i ) of each sample, where v i represents the average wind speed sample within a certain time range, and c i represents the remaining wind condition parameters under this design load condition, including the following steps:

[0012] Step S3.1: According to the measured data or design standards, determine the probability distribution of the wind condition parameters within each certain time range i = 1, …, d c , where d c represents the dimension of the remaining wind condition parameters within a certain time range;

[0013] Step S3.2: According to the Rosenblatt transformation, transform all the wind condition parameters within a certain time range into standard normal random variables, that is:

[0014] Φ(u v ) = F V (v)

[0015]

[0016] Among them, u v represents the standard normal random variable after the average wind speed within a certain time range is transformed by the Rosenblatt transformation, represents the standard normal random variable after the wind condition parameters within a certain time range are transformed by the Rosenblatt transformation, and Φ(·) represents the cumulative distribution function of the standard normal random variable;

[0017] Step S3.3: Calculate the probability β corresponding to the wind condition parameters within a certain time range within a certain return period 1Y ;

[0018]

[0019] β 1Y =-Φ -1 (P)=4.119

[0020] Step S3.4: According to the inverse first-order reliability analysis method, it is necessary to satisfy:

[0021]

[0022] Step S3.5: According to the inverse transformation in Step S3.2, all wind condition parameters within a certain time range need to satisfy:

[0023]

[0024] Among them, Φ -1 (·) represents the inverse function of the cumulative distribution function of the standard normal random variable;

[0025] Step S3.6: According to the cut-in and cut-out wind speed ranges of the selected wind turbine type, sample the average wind speed within a certain time range at a certain interval speed ΔV (usually 2 m / s), and determine the remaining wind condition parameter samples through Step S3.5;

[0026] Step S3.7: According to the probability distribution and sampling interval of the wind condition parameters within each certain time range, determine the probability P(v i ,c i ) of each sample.

[0027] Furthermore, in Step S3, under each wind condition parameter sample {(v i ,c i )}, perform multiple simulations of the wind turbine performance model considering turbulent wind, and fit {(v i ,c i) Conditional probability distribution F of the annual maximum value of the random load L L (l|v i ,c i ), where F (·) represents the cumulative distribution function, v i represents the average wind speed samples within a certain time range, c i represents the remaining wind condition parameters under this design load condition, and l represents the load extreme value of the wind turbine within a certain time range.

[0028] Further, in the step S4, the establishment of the statistical model of the load uncertainty factor includes the following steps:

[0029] Step S4.1: According to the statistical model of the remaining uncertainties, collect N X samples;

[0030] Step S4.2: At the rated wind speed of the current wind turbine, generate N W time series of turbulent wind within a certain time range;

[0031] Step S4.3: Select a time series of turbulent wind, traverse all samples of the remaining uncertainty sources, conduct performance simulation of the wind turbine within a certain time range, obtain the load time series, and get N X load extreme value samples;

[0032] Step S4.4: Normalize the N X load extreme value samples, and calculate the standard deviation σ of the normalized load extreme values;

[0033] Step S4.5: Repeat steps S4.3 to S4.4 until all N W time series of turbulent wind are traversed, and N W load extreme value standard deviations are obtained;

[0034] Step S4.6: Establish the statistical model of the load uncertainty factor X (·) , whose distribution type is specified by the design standard, the sample mean is 1, and the sample standard deviation is the average of the N W load extreme value standard deviations obtained in step S4.5.

[0035] Further, in the step S5, the specific deterministic optimization problem for determining a set of safety factors is:

[0036] minimize Cost(d)

[0037] Subject to G i (d; L k ,R k ,γ)>0,i=1,...,n

[0038] d L d ≤ d ≤ d U , d ∈ R d

[0039] Among them, Cost(·) represents the objective function, and G i (·) represents the design equation, and L k , R k respectively represent the characteristic values of the load and the structural resistance, γ represents the safety factor, d L , d U respectively represent the upper and lower bounds of the design variables, n represents the number of design equations, and d represents the dimension of the design variables.

[0040] Furthermore, in the step S5, the passing of the reliability check is equivalent to whether the following formula holds for all i = 1, …, n:

[0041] β i = -Φ -1 (P f,i ) ≥ β t

[0042] Among them, β i represents the reliability level of the check, Φ -1 (·) represents the inverse function of the cumulative distribution function of the standard normal random variable, β t represents the required reliability level, P f,i represents the failure probability of the i-th design equation, and the calculation formula is:

[0043] P f,i = P(g i (d; l, r, X) < 0)

[0044] Among them, g i (·) represents the limit state function, L represents the random load, R represents the structural resistance, and X represents the load uncertainty factor.

[0045] Furthermore, in the step S5, the calculation of the failure probability and reliability of each limit state function includes the following steps:

[0046] Step S5.1: According to the failure probability required by the design standard, determine the number of samples per round and the total number of sampling rounds under the wind condition parameter samples within each certain time range;

[0047] Step S5.2: According to the statistical distributions of the characterized random load and the structural resistance, collect the joint samples of each random load, structural resistance, and uncertainty factor to calculate the limit state equation and obtain the number of failure samples;

[0048] Step S5.3: Calculate the failure probability and the error of the failure probability estimation based on the number of failure samples and the number of samplings.

[0049] Step S5.4: If the error is less than the threshold value, or there are no failure samples, or the round ends, then take the probability that the limit state is less than 0 as the failure probability calculation result; otherwise, conduct a new round and execute Step S5.2 and Step S5.3.

[0050] Step S5.5: Repeat Step S5.1 to Step S5.3 until all the wind condition parameter samples {(v i , c i )} are traversed.

[0051] Step S5.6: Based on the obtained failure probability calculation result and the probability of each sample obtained in Step S3, calculate the total failure probability of the limit state function, and calculate the reliability index based on the total failure probability.

[0052] Further, in Step S5.1, according to the failure probability P f,t = Φ(-β t ) required by the design standard, within each certain time range T for the wind condition parameter samples {(v i , c i )}, determine the number of samplings N b = T / P f,t and the total number of sampling rounds K, set the sampling round number k = 1, v i represents the average wind speed sample within a certain time range, and c i represents the remaining wind condition parameters under this design load condition.

[0053] In Step S5.2, according to the statistical distribution model characterizing the random load and the structural resistance, collect N b groups of joint samples of the random load, the structural resistance, and the uncertainty factor, calculate the values of N b limit state equations, and record the number of samples N i where the failure occurs, that is, the limit state g f,k < 0.

[0054] In Step S5.3, calculate the failure probability P f,k and the error δ k of the failure probability estimation:

[0055]

[0056] Further, in Step S5.4, if δ k is less than the threshold value or the number of samples N f,k= 0 or the round k is the total number of rounds K, then the reliability analysis calculation terminates, and the probability P(g < 0|v i ,c i ) = P f,k is used as the failure probability calculation result under {(v i ,c i ). Otherwise, let k = k + 1 and repeat steps S5.2 and S5.3. v i represents the average wind speed sample within a certain time range, and c i represents the remaining wind condition parameters under this design load condition.

[0057] Furthermore, in the step S5.6, the failure probability of the limit state function is:

[0058]

[0059] The reliability index is calculated as:

[0060] β = -Φ -1 (P f ).

[0061] Constructing the design equation and the limit state equation into a deterministic optimization problem of minimizing the objective function, and the determination of a set of safety factors, corresponding to two different optimization problems respectively, can be solved using optimization algorithms such as the interior point method, genetic algorithm, and sequential quadratic programming.

[0062] The advantages and beneficial effects of the present invention are as follows:

[0063] Aiming at the existing deterministic design redundancy of wind turbines and the problem that the overall calculation time of the RBDO process is too long, the present invention introduces partial safety factors into the traditional RBDO process, optimizes the design variables through the deterministic design process, and greatly reduces the number of reliability analysis calculations in the optimization design process. When the dimension of the design variables is high, the method of the present invention can converge to the optimal design faster. In addition, while the method of the present invention outputs the optimal design considering reliability, it also provides the checked partial safety factors. Using the checked safety factors, wind turbine designers can use lower load design values, thereby achieving the load reduction design of wind turbines. The checked partial safety factors can be transferred to similar models, and the load reduction design can be quickly realized directly through the deterministic design process. Brief Description of the Drawings

[0064] Figure 1 is the flowchart of the method of the present invention.

[0065] Figure 2 is the schematic diagram of the wind turbine tower for the embodiment of the present invention.

[0066] Figure 3 Schematic diagram of wind condition parameter sampling for the embodiments of the present invention under DLC 1.3 condition.

[0067] Figure 4 Schematic diagram of wind condition parameter sampling for the embodiments of the present invention under DLC 1.4 condition.

[0068] Figure 5 Comparison diagram before and after the optimized design of the diameter of each section of the tower for the embodiments of the present invention.

[0069] Figure 6 Comparison diagram before and after the optimized design of the wall thickness of each section of the tower for the embodiments of the present invention. Detailed implementation manners

[0070] The following further elaborates on the detailed implementation manners of the present invention with reference to the accompanying drawings. It should be understood that the detailed implementation manners described herein are only for the purpose of illustrating and explaining the present invention, and are not intended to limit the present invention.

[0071] For the reliability-based load reduction design and safety factor verification method of a wind turbine of the present invention, an uncertainty model of load and structural resistance is established considering the multi-source uncertainty of the wind turbine. The present invention iteratively adjusts the partial safety factors, quickly obtains the design variables through a deterministic design process, and then conducts a verification based on reliability analysis, so as to search for the optimal design of the wind turbine components that meet the reliability requirements of the design standards, and at the same time obtain the results of the verified partial safety factors. As Figure 1 shown, it specifically includes the following steps:

[0072] Step S1: Determine the components of the wind turbine for load reduction design, and determine the design variables, objective function, and failure mode;

[0073] Step S2: Establish a multi-source uncertainty characterization model of the wind turbine, including but not limited to uncertainties such as wind condition parameters, aerodynamic properties, and material properties;

[0074] Step S3: Select the design load conditions of the wind turbine, and determine the 10-minute wind condition parameter samples {(v i , c i )}, i = 1,..., N W , and the probability P(v i , c i ) of each sample. Wherein, v i represents the 10-minute average wind speed sample, and c i is the remaining wind condition parameters under this design load condition; under each 10-minute wind condition parameter sample {(v i , c i )}, conduct multiple simulations of the wind turbine performance model considering turbulent wind, and fit {(vi , c i ) conditional probability distribution F of the annual maximum value of the random load L L (l | v i , c i ), where F (·) represents the cumulative distribution function;

[0075] Specifically, the determination of the 10-minute wind condition parameter samples includes the following steps:

[0076] Step S3.1: Determine the probability distribution of each 10-minute wind condition parameter according to the measured data or design standards i = 1, …, d c , d c is the dimension of the remaining 10-minute wind condition parameters;

[0077] Step S3.2: According to the Rosenblatt transformation, transform all 10-minute wind condition parameters into standard normal random variables, that is:

[0078] Φ(u v ) = F V (v)

[0079]

[0080] Step S3.3: Calculate the probability corresponding to the 10-minute wind condition parameters with a return period of 1 year:

[0081]

[0082] β 1Y = -Φ -1 (P) = 4.119

[0083] Step S3.4: According to the inverse first-order reliability analysis method, it is necessary to satisfy:

[0084]

[0085] Step S3.5: According to the inverse transformation of Step S3.2, all 10-minute wind condition parameters need to satisfy:

[0086]

[0087] Step S3.6: Sample the 10-minute average wind speed at intervals of ΔV (usually 2 m / s) between the cut-in and cut-out wind speed ranges of the selected wind turbine type, and determine the remaining wind condition parameter samples through Step S3.5.

[0088] Step S3.7: Determine the probability P(v i ,c i ) for each sample according to the probability distribution and sampling interval of the 10-minute wind condition parameters.

[0089] Step S4: For the remaining uncertainties other than the wind condition parameters, establish a corresponding load uncertainty factor X (·) statistical model to characterize the influence of this uncertainty source alone on the random load;

[0090] Specifically, the calculation of the load uncertainty factor X (·) statistical model includes the following steps:

[0091] Step S4.1: Collect N X samples according to the statistical model of this uncertainty;

[0092] Step S4.2: Generate N W 10-minute turbulent wind time series at the rated wind speed of this model;

[0093] Step S4.3: Select a turbulent wind time series, traverse all the uncertainty source samples, perform 10-minute wind turbine performance simulations, obtain the load time series, and get N X load extreme value samples;

[0094] Step S4.4: Normalize the N X load extreme value samples and calculate the standard deviation σ of the normalized load extreme values;

[0095] Step S4.5: Repeat Steps S4.3 to S4.4 until all N W turbulent wind time series are traversed to obtain N W load extreme value standard deviations;

[0096] Step S4.6: The load uncertainty factor X (·) statistical model, whose distribution type is specified by the design standard, with a sample mean of 1 and a sample standard deviation equal to the average of the N W load extreme value standard deviations obtained in Step S4.5.

[0097] Step S5: Based on the mechanism of failure modes, design equations containing safety factors, loads, and structural resistance characteristic values are constructed respectively, and limit state equations containing random loads and structural resistance are determined; a set of safety factors is determined, and a deterministic optimization problem of minimizing the objective function is constructed and solved with the design equation as a constraint to obtain the optimal design variables; for the optimal design variables, reliability verification is carried out in combination with the limit state equation. If the reliability verification passes, the safety factor is slightly reduced; otherwise, the safety factor is slightly increased, a new set of safety factors is determined, and subsequent verification is carried out; when the algorithm meets the convergence requirements, the design variables with the minimum objective function and meeting the reliability requirements and their corresponding safety factors are selected as the results of the load reduction design and safety factor verification of the wind turbine.

[0098] Specifically, the deterministic optimization problem of determining a set of safety factors is as follows:

[0099] minimize Cost(d)

[0100] Subject to G i (d; L k , R k , γ) > 0, i = 1,..., n

[0101] d L ≤ d ≤ d U , d ∈ R d

[0102] Where G i (·) represents the design equation, L k , R k represent the characteristic values of the load and structural resistance respectively, γ represents the safety factor, d L , d U represent the upper and lower bounds of the design variables respectively, n represents the number of design equations, and d represents the dimension of the design variables.

[0103] Specifically, passing the reliability verification is equivalent to whether the following formula holds for all i = 1,…, n

[0104] β i = -Φ -1 (P f,i ) ≥ β t

[0105] Where P f,i is the failure probability, and the calculation formula is:

[0106] P f,i = P(g i (d; L, R, X) < 0)

[0107] Where g i(·) represents the limit state function, L represents the random load, R represents the structural resistance, and X is the load uncertainty factor.

[0108] Specifically, the calculation of the failure probability and reliability of each limit state function includes the following steps:

[0109] Step S5.1: According to the failure probability P f,t = Φ(-β t ), under each 10-minute wind condition parameter sample {(v i , c i ), determine the number of samples N b = 20 / P f,t for each round of sampling and the total number of sampling rounds K, and set the sampling round number k = 1;

[0110] Step S5.2: According to the statistical distribution models of the random load and the structural resistance characterized in Steps S3 and S4, collect

[0111] N b groups of joint samples of the random load, the structural resistance, and the uncertainty factor, calculate the values of N b limit state equations, and record the number of failed (i.e., g i < 0) samples N f,k ;

[0112] Step S5.3: Calculate the failure probability P f,k and the error δ k in the failure probability estimation:

[0113]

[0114] Step S5.4: If any of the following three convergence conditions is satisfied, the reliability analysis calculation terminates, and take

[0115] P(g < 0|v i , c i ) = P f,k as the calculation result of the failure probability under {(v i , c i ). Otherwise, let k = k + 1 and repeat Steps

[0116] S5.2 and Step S5.3: (1) δ k is less than a certain threshold (usually 0.1 or 0.05); (2) N f,k = 0; (3) k = K;

[0117] Step S5.5: Repeat Steps S5.1 to S5.3 until all {(v i , c i )} are traversed;

[0118] Step S5.6: The failure probability of the limit state function is calculated as follows:

[0119]

[0120] The reliability index is calculated as:

[0121] β = -Φ -1 (P f ).

[0122] Furthermore, constructing the design equation and the limit state equation into a deterministic optimization problem of minimizing the objective function, and the determination of a set of safety factors, corresponding to two different optimization problems respectively, can be solved using optimization algorithms such as the interior point method, genetic algorithm, sequential quadratic programming, etc.

[0123] Embodiment

[0124] To verify the effectiveness of the present invention, an optimization design is carried out on a certain type of tower of Dongfang Wind Power Co., Ltd. As Figure 2 shown, the tower has 7 sections and a total of 47 joints, including five conical sections and two cylindrical sections. The wall thickness (denoted as t 1 , t 2 , …, t 47 ) and diameter (denoted as d 1 , d 2 , …, d 47 ) of each joint are design variables. Since the topmost joint is connected to the nacelle flange, its diameter d 47 and wall thickness t 47 are fixed. In addition, only the diameters at the bottoms of the conical sections of the tower (in this example, d 1 , d 2 , d 15 , d 23 , d 39 ) need to be known, and the diameters of the remaining joints can be obtained by linear interpolation based on the height of the joint. Therefore, the design variables in this example are d = [d 1 , d 2 , d 15 , d 23 , d 39 , t 1 , t 2 , …, t 46 , a total of 51.

[0125] In this example, the multiple-source uncertainties of the wind turbine mainly include the uncertainties of wind condition parameters, site conditions, aerodynamic properties, simulation model errors, dynamic properties, and material properties. For the selection of sample points of wind condition parameters, this example selects the design load conditions of "DLC 1.3 Extreme Turbulent Wind (ETM)" and "DLC 1.4 Extreme Gust with Wind Direction Change (ECD)" required by the IEC61400-1 standard. The wind condition parameter samples under DLC 1.3 and DLC 1.4 obtained through step S3 of the present invention are respectively as Figure 3 , Figure 4 shown. For the uncertainty of aerodynamic properties, the wind tunnel test data of the National Renewable Energy Laboratory (NREL) in the United States are used; for material properties, in this embodiment, based on the recommendation of the Joint Committee on Structural Safety (JCSS), it is assumed that the Young's modulus of the material follows a lognormal distribution, with a sample mean of 2.1×10 5 MPa and a coefficient of variation of 0.03. Through step S5 of the present invention, the load uncertainty factor X aero corresponding to aerodynamic properties and the load uncertainty factor X mat corresponding to material property uncertainties are respectively obtained. For the load uncertainty factors corresponding to site conditions, simulation model errors, and dynamic properties, the statistical distribution models required by the IEC 61400-9 standard are used, as shown in Table 1;

[0126] Table 1 Statistical distribution models of load uncertainty factors

[0127] Source of uncertainty Load uncertainty factor Type of statistical distribution Sample mean Coefficient of variation Site conditions <![CDATA[X site > Log-normal distribution 1 0.10 Simulation model error <![CDATA[X sim > Log-normal distribution 1 0.05 Dynamic properties <![CDATA[X dyn > Log-normal distribution 1 0.05

[0128] In this example, the objective function cost(d) is the structural steel consumption of the tower, that is,

[0129]

[0130] where h i represents the tower height of the i-th section.

[0131] In this example, the failure modes considered for the tower include axial buckling failure, tangential buckling failure, and maximum stress failure. For these failure modes, each section of the tower needs to be checked. The failure of any one section of the tower is regarded as the failure of the entire tower. The limit state function of axial buckling failure is:

[0132]

[0133] where χ xis the axial buckling reduction factor, calculated according to the diameter, thickness, Young's modulus of the steel, yield strength, etc. of each section of the tower through Section 8.5.2 of EN 1993-1-6:2007; f y is the yield strength of the structural steel; F z represents the axial structural response force generated at the cross-section of this section of the tower; A represents the cross-sectional area of this section of the tower; M xy represents the resultant in-plane structural response moment generated at the cross-section of this section of the tower; W b represents the flexural stiffness of the cross-section of this section of the tower. Accordingly, the design equation for axial buckling failure is:

[0134]

[0135] where, γ M represents the partial safety factor for materials, γ G represents the partial safety factor for the dead load (since F z is mainly generated by the dead loads of the nacelle and the wind turbine acting on the tower), γ W represents the partial safety factor for the wind load, f yk , F z,k , M xy,k respectively represent the characteristic values of the yield strength of the structural steel, the axial structural response force, and the resultant in-plane structural response moment.

[0136] The limit state function for tangential buckling failure is:

[0137]

[0138] where, χ τ is the axial buckling reduction factor, calculated according to the diameter, thickness, Young's modulus of the steel, yield strength, etc. of each section of the tower through Section 8.5.2 of EN 1993-1-6:2007; F xy represents the resultant tangential structural response force generated at the cross-section of this section of the tower; M z represents the structural response torque generated at the cross-section of this section of the tower. Accordingly, the design equation for tangential buckling failure is:

[0139]

[0140] where, F xy,k , M z,k respectively represent the characteristic values of the resultant tangential structural response force and the structural response torque.

[0141] The limit state function for maximum stress failure is:

[0142]

[0143] where, σx , τ are respectively the maximum axial and tangential stresses on the cross-section of this section of the tower:

[0144]

[0145] Correspondingly, the design equation for maximum stress failure is:

[0146]

[0147] In this example, the reliability level required in step S5 is β t = 3.3, corresponding to a failure probability of P f,t = 5×10 -4 . In this example, the fixed material partial safety factor γ M is 1.10, and the partial safety factors γ W , γ G are checked.

[0148] The results obtained by using the method of the present invention are shown in Table 2 (where " / " for reliability means that the failure probability calculated by the method of step S9 of the present invention is extremely low). As a comparison, for the traditional RBDO method (for example: Oza, K, & Gea, HC. "Two-Level Approximation Method for Reliability-Based Design Optimization." Proceedings of the ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 30th Design Automation Conference. Salt Lake City, Utah, USA. September 28–October 2, 2004. pp. 885-891. ASME. https: / / doi.org / 10.1115 / DETC2004-57463) facing this high-dimensional design problem, due to the need for a large number of reliability analyses when optimizing the design variables in each iteration, there is a phenomenon that the computational load is too large and the design result cannot be given within an acceptable time. As a comparison, the method proposed by the present invention successfully gives the result of the optimal design within an acceptable computational time (the optimized tower diameter and wall thickness are as Figure 5 , Figure 6 shown). From the comparison of the design results given in Table 2, it is found that the safety factor (γW = 1.35, γ G = 1.10), the designs under various failure modes in different working conditions all have a certain degree of reliability margin. For the optimized design obtained in the present invention, the steel consumption is reduced by about 3.19%, and the reliability of axial buckling failure under the DLC 1.4 condition is 3.31, approaching the boundary of the design requirements and reducing the design redundancy. The load factor of safety after checking is: γ W = 1.281, γ G = 1.082, the wind load (F xy , M xy , M z ) and the gravity load (M z ) design values are reduced by 5.11% and 1.64% respectively, achieving the load reduction design of the wind turbine. This result fully demonstrates that the method of the present invention, by establishing a design equation by combining the safety factor and the characteristic value, avoids the reliability analysis in the process of optimizing the design variables, and only performs a reliability check on the design after iteration, thereby greatly reducing the calculation amount in the high-dimensional design problem. At the same time, the method of the present invention fully combines the characteristics of RBDO, reducing the design redundancy while ensuring the reliability.

[0149] Table 2 Comparison table of calculation results of examples

[0150]

[0151] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reliability-based wind turbine load reduction design and safety factor verification method, characterized by: The steps include: Step S1: determining the components of the wind turbine for load reduction design, and determining the design variables, objective functions and failure modes; Step S2: Establishing a multi-source uncertainty characterization model for wind turbines, including wind condition parameter uncertainty and other uncertainties; Step S3: Select the design load condition of the wind turbine generator, determine the wind condition parameters within a certain time range and the corresponding probability of the wind condition parameters within a certain regression period; simulate the performance model of the wind turbine generator under the wind condition parameters within a certain time range, and fit the maximum conditional probability distribution of the random load under the wind condition parameters within the regression period; Step S4: For the remaining uncertainties, a corresponding load uncertainty factor statistical model is established to characterize the influence of the remaining uncertainty sources on the random load alone; Step S5: Based on the failure mode mechanism, constructing a design equation containing a safety factor and the load, a characteristic value of structural resistance, and a limit state equation containing the random load and structural resistance; A set of safety factors is determined, and a deterministic optimization problem of minimizing the prime objective function is constructed and solved with the design equation as a constraint to obtain the optimal design variables; reliability verification is performed on the optimal design variables in combination with the limit state equation, and if the reliability verification passes, the safety factor is lowered, otherwise, the safety factor is increased; a set of safety factors is re-determined for the above verification, and when the convergence requirements are met, the design variables with the smallest objective function and meeting the reliability requirements and their corresponding safety factors are selected as the results of the wind turbine load reduction design and safety factor verification.

2. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 1 is characterized in that: In step S3, the wind condition parameter samples {(v i ,c i )},i=1,…,N W , and the probability P(v i ,c i ), v i represents the average wind speed sample within a certain time range, c i Representing the remaining wind parameters under the design load condition includes the following steps: Step S3.1: Determine the probability distribution F of wind parameters within a certain time range according to measured data or design standards V (v), d c The dimension representing the wind condition parameters within a certain time range; Step S3.2: According to the Rosenblatt transformation, all wind parameters within a certain time range are converted into standard normal random variables, that is: Φ(u v )=F V (v) Among them, u v It represents the standard normal random variable of the average wind speed within a certain time range after Rosenblatt transformation. represents the standard normal random variable after Rosenblatt transformation of wind parameters within a certain time range, Φ(·) represents the cumulative distribution function of the standard normal random variable; Step S3.3: Calculate the wind condition parameters within a certain time range, and the corresponding probability within a certain regression period is β 1Y ; Step S3.4: According to the inverse first-order reliability analysis method, u v , Need to meet: Step S3.5: According to the inverse transformation of step S3.2, all wind parameters within a certain time range need to satisfy: Among them, Φ -1 (·) represents the inverse function of the cumulative distribution function of the standard normal random variable; Step S3.6: based on the cut-in and cut-out wind speed ranges of the selected wind turbine type, the average wind speed within a certain time range is sampled at a certain interval speed ΔV, and the remaining wind condition parameter samples are determined through step S3.5; Step S3.7: Determine the probability P(v i ,c i ).

3. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 1 is characterized in that: In step S3, the wind condition parameter samples {(v i ,c i )}, multiple simulations of wind turbine performance models considering turbulent wind were performed to fit {(v i ,c i The conditional probability distribution F of the annual maximum value of the random load L under L (l|v i ,c i ), where F (·) represents the cumulative distribution function, v i represents the average wind speed sample within a certain time range, c i represents the other wind parameters under the design load condition, and l represents the load extreme value of the wind turbine within a certain time range.

4. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 1 is characterized in that: In step S4, the establishment of the load uncertainty factor statistical model includes the following steps: Step S4.1: Based on the statistical model of the remaining uncertainties, collect N X samples; Step S4.2: At the rated wind speed of the current wind turbine, generate N W A time series of turbulent wind within a certain time range; Step S4.3: Select a turbulent wind time series, traverse all other uncertainty source samples, simulate the performance of wind turbines within a certain time range, obtain the load time series, and obtain N X load extreme value samples; Step S4.4: For N X The load extreme value samples are normalized and the normalized load extreme value standard deviation σ is calculated; Step S4.5: Repeat steps S4.3 to S4.4 until all N W Turbulent wind time series, get N W The standard deviation of the load extremes; Step S4.6: Establish the load uncertainty factor X (·) The statistical model has a distribution type specified by the design criteria, a sample mean of 1, and a sample standard deviation of N obtained in step S4.

5. W The standard deviations of the load extremes are averaged.

5. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 1 is characterized in that: In step S5, the deterministic optimization problem of determining a set of safety factors is specifically: minimize Cost(d) Subject to G i (d;L k ,R k ,γ)>0,i=1,...,n d L ≤d≤d U ,d∈R d Among them, Cost(·) represents the objective function, G i (·) represents the design equation, L k ,R k denote the characteristic values ​​of load and structural resistance, γ denotes the safety factor, and d L ,d U They represent the upper and lower bounds of the design variables, n represents the number of design equations, and d represents the dimension of the design variables.

6. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 1 is characterized in that: In step S5, the reliability check is performed by determining whether the following equations are all valid for i=1, ..., n: b i =-Φ -1 (P f,i )≥β t Among them, β i Indicates the reliability level of the calibration, Φ -1 (·) represents the inverse function of the cumulative distribution function of the standard normal random variable, β t Indicates the required reliability level, P f,i represents the failure probability of the i-th design equation, and the calculation formula is: P f,i =P(g i (d;L,R,X)<0) Among them, g i (·) represents the limit state function, L represents the random load, R represents the structural resistance, and X represents the load uncertainty factor.

7. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 1 is characterized in that: In step S5, the failure probability and reliability calculation of each limit state function includes the following steps: Step S5.1: According to the failure probability required by the design standard, under each wind parameter sample within a certain time range, determine the number of samples in each round and the total number of sampling rounds; Step S5.2: According to the statistical distribution of the characterized random loads and structural resistance, collect joint samples of each random load, structural resistance and uncertainty factor to calculate the limit state equation and obtain the number of failure samples; Step S5.3: Calculate the failure probability and the error of the failure probability estimation by the number of failure samples and the number of samples; Step S5.4: If the error is less than the threshold or there is no failed sample or the round ends, the probability of the limit state being less than 0 is taken as the failure probability calculation result. Otherwise, a new round is performed and steps S5.2 and S5.3 are executed; Step S5.5: Repeat steps S5.1 to S5.3 until all wind condition parameter samples are traversed; Step S5.6: Based on the obtained failure probability calculation result and the probability of each sample obtained in step S3, calculate the total failure probability of the limit state function, and calculate the reliability index based on the total failure probability.

8. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 7 is characterized in that: In step S5.1, according to the failure probability P required by the design standard f,t , in each certain time range T, the wind condition parameter sample {(v i ,c i )}, determine the number of samples N in each round b =T / P f,t And the total number of sampling rounds K, v i represents the average wind speed sample within a certain time range, c i Represents the remaining wind parameters under the design load condition; In step S5.2, according to the statistical distribution model of the random load and structural resistance, N b The combined sample of random load, structural resistance and uncertainty factor is calculated to obtain N b The value of the limit state equation is recorded, and the failure, i.e., the limit state g i The number of samples N < 0 f,k ; In step S5.3, the failure probability P is calculated. f,k The error δ with the failure probability estimate k :

9. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 8 is characterized in that: In step S5.4, if δ k The number of samples N that are less than the threshold or limit state f,k = 0 or round k is the total number of rounds K, the reliability analysis calculation is terminated, and the probability P(g<0|v i ,c i )=P f,k As {(v i ,c i )}, otherwise, let k = k + 1 and repeat steps S5.2 and S5.3, v i represents the average wind speed sample within a certain time range, c i Represents the remaining wind parameters under this design load condition.

10. The reliability-based wind turbine load reduction design and safety factor verification method according to claim 9 is characterized in that: In step S5.6, the failure probability of the limit state function is: The calculated reliability index is: β=-Φ -1 (P f ) Among them, Φ -1 (·) represents the inverse function of the cumulative distribution function of the standard normal random variable.

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