Multi-objective reliability optimization design method for wind driven generator tower

Abstract

The invention relates to the field of uncertainty optimization design of wind driven generator towers, in particular to a multi-objective reliability optimization design method of a wind driven generator tower based on double-stage multi-fidelity simulation, which comprises the following steps of: in the first stage, efficiently constructing a design constraint agent model of the wind driven generator tower based on an importance sampling theory; and in the second stage, on the basis of the proxy model and the real constraint model constructed in the previous stage, a failure probability proxy model is constructed by adopting multi-fidelity simulation, and then multi-target reliability optimization design of the wind driven generator tower is carried out on the basis of a multi-target optimization design method NSGA-II algorithm. According to the method, a traditional single-target reliability optimization design problem is converted into a multi-target reliability optimization problem, the calculation cost is greatly reduced, meanwhile, the agent model construction cost is reduced in combination with a self-adaptive sampling strategy and a multi-fidelity model simulation method, the solving calculation efficiency is improved, and the calculation efficiency is improved. Meanwhile, optimization design values under different reliability degrees are obtained, and the test cost is saved.

Description

Technical Field

[0001] The present invention relates to the field of uncertainty optimization design of wind turbine towers, and particularly to a multi-objective reliability optimization design method for wind turbine towers based on two-stage multi-fidelity simulation. Background Art

[0002] Traditional reliability-based design optimization (RBDO) can often only optimize the design for a single objective reliability. This usually can obtain the optimized design value that meets the set objective reliability. However, the model obtained by the traditional surrogate model construction method in RBDO is only applicable to a single reliability. When it is applied to solve other reliabilities, it often brings large errors. Therefore, when solving for another reliability, only repeated calculations can be performed, which will bring high computational costs. And the structure of the wind turbine tower is complex, and it is difficult to obtain experimental samples. Therefore, how to efficiently construct a surrogate model applicable to multiple reliabilities and solve for the optimal design value under multi-objective reliability is the key.

[0003] To consider uncertainty, the reliability-based design optimization (RBDO) method has been widely applied to various engineering applications, including the wind power field, aerospace engineering, and vehicle engineering. In most RBDO studies, the main objective is to determine the optimal design under a specified reliability. However, high reliability is often associated with an increase in cost. Therefore, it is beneficial for designers to understand how the cost fluctuates with the reliability. Designers can make a trade-off between minimizing cost and maximizing reliability. However, finding the RBDO optimal values corresponding to different objective reliability requirements is a major challenge. Summary of the Invention

[0004] In order to solve the above technical problems existing in the prior art, the present invention proposes a multi-objective reliability optimization design method for wind turbine towers based on two-stage multi-fidelity simulation. Considering the load uncertainty during the actual service process, combining the adaptive sampling theory and multi-fidelity model simulation, a high-precision failure probability surrogate model is constructed for the constraint boundary, and the NSGA-II algorithm is used to search for the optimal design under different reliability requirements of the wind turbine tower. The specific technical solution is as follows:

[0005] A multi-objective reliability optimization design method for wind turbine towers includes the following steps:

[0006] S1: Generate initial sample points for all constraints and construct an initial surrogate model;

[0007] S2: Based on the initial surrogate model, perform deterministic optimization design and solution for the wind turbine tower, and denote the obtained design point as and set the iteration number iter = 1;

[0008] S3: With the current design point as the center, delimit a sampling window, and judge the activity of the constraint function for all constraints. Subsequent sampling and surrogate model update are only carried out for active constraints;

[0009] S4: Generate subsequent sample points within the sampling window. For active constraints, use a learning function to select the new sample point x new ;

[0010] S5: Update the surrogate model of active constraints, perform deterministic optimization design and solution for the wind turbine tower, and denote the obtained design point as and make the iteration number iter = iter + 1; Judge whether the accuracy requirement is met according to the convergence index. If the convergence condition is met, execute S6; if not, execute S3;

[0011] S6: Regard the current constraint surrogate model as a low-fidelity model Based on this low-fidelity model, construct a surrogate model of the failure probability

[0012] S7: Substitute the obtained into the current surrogate model of the failure probability to judge whether the design point falls into the target reliability interval [P L , P U , and select the design points falling into this interval as the second-stage data points

[0013] S8: For each data point Based on the high-fidelity model - the true constraint response model G(x), reconstruct the limit state function, then recalculate the failure probability, and correct the surrogate model of the failure probability

[0014] S9: According to the design objectives and constraints of the wind turbine tower, transform the multi-reliability optimization design problem into a multi-objective optimization design problem, and based on the current surrogate model of the failure probability Use the NSGA-II algorithm to solve the multi-objective optimization design problem and obtain the optimized design values of the wind turbine tower under different reliabilities.

[0015] Furthermore, in S1, the Latin hypercube sampling method is used to generate the initial sample points.

[0016] Furthermore, in S2, the deterministic optimization design of the wind turbine tower is specifically:

[0017] minimize Cost(d)

[0018] Subject to H i(d) = 0, i = 1, ..., na

[0019] G j (X) > 0, j = 1, ..., nc

[0020] d L ≤ d ≤ d U , d ∈ R nd and X ∈ R nr ,

[0021] where d, i = 1, ..., nd are design variables; X = {X v , X p} T , X v and X p represent random design variables and random parameters respectively; d U and d L are the upper and lower bounds of the design variables; Cost(d) is the objective function; H i (d) is the equality constraint, and na is the number of equality constraints; G j (X) is the inequality constraint, and nc is the number of inequality constraints.

[0022] Furthermore, the specific content of S3 is as follows:

[0023] Calculate the sampling region radius R using the following formula:

[0024] R = c R σ,

[0025] where c R is the adaptive coefficient; σ is the maximum standard deviation of all uncertainty variables;

[0026] Then, determine whether each constraint function is an active constraint based on its failure contribution degree; the failure contribution degree CPF(i) of each constraint function is calculated by the following formula:

[0027]

[0028] where represents the number of failure samples for this constraint function; N f represents the total number of failure samples for all constraint functions; when CPF(i) is greater than the set threshold η, it is regarded as an active constraint.

[0029] Furthermore, in S4, the learning function is specifically:

[0030]

[0031] where Φ is the standard normal cumulative distribution function and φ is the standard normal distribution density function, For the constructed surrogate model, ε is the allowable deviation; denote the variance at the sample x, σ G (x) represents the variance of the tower constraint performance at the sample x.

[0032] Furthermore, in S5, the specific expression of the convergence index is:

[0033]

[0034] Furthermore, S6 is specifically: Randomly generate sampling points in the design domain, and calculate the failure probability at each sampling point using the Monte Carlo simulation method, where each Monte Carlo point is substituted into the low-fidelity model to obtain the response; then, based on the sampling points and the corresponding failure probabilities, fit the failure probability surrogate model

[0035] Furthermore, S8 is specifically: For the data point Find the point closest to the failure boundary according to the Monte Carlo simulation method, and substitute it into the true constraint response model G(x) to reconstruct the data point of the limit state function, and the expression is as follows:

[0036]

[0037] Then recalculate its failure probability; use the data point and the corresponding recalculated failure probability to correct the failure probability surrogate model

[0038] Furthermore, in S9, it is transformed into a multi-objective optimization design problem, and its expression is as follows:

[0039] minimize{Cost(d),P[G j (X)]},j = 1,...,nc

[0040] Subject to H i (d) = 0,i = 1,...,na

[0041] G j (d)>0

[0042] P j L <P[G j (X)]<P j U

[0043] d L ≤d≤d U ,d∈Rnd and X∈R nr ,

[0044] where P[G j (X)] is the failure probability for the inequality constraint G j (X); P j L and P j U are the upper and lower bounds of the target failure probability.

[0045] Advantageous effects: Aiming at the design requirements of different reliabilities of wind turbines and the problems of high test costs and difficulty in obtaining sample data, the method of the present invention transforms the traditional single-objective reliability optimization design problem into a multi-objective reliability optimization problem, greatly reducing the calculation cost. At the same time, combined with an adaptive sampling strategy and a multi-fidelity model simulation method, the cost of constructing a surrogate model is reduced, the solving calculation efficiency is improved, and the optimized design values under different reliabilities are obtained, saving the test cost. Brief description of the drawings

[0046] Figure 1 is a schematic flow chart of a multi-objective reliability optimization design method for a wind turbine tower of the present invention;

[0047] Figure 2 is a load action diagram of a wind turbine tower in an embodiment of the present invention;

[0048] Figure 3 is an optimized result diagram of the method of the present invention for the embodiment. Detailed implementation manners

[0049] In order to make the objectives, technical solutions and technical effects of the present invention clearer and more understandable, the following further elaborates on the present invention in detail with reference to the accompanying drawings of the specification and embodiments.

[0050] This embodiment discloses a multi-objective reliability optimization design method for a wind turbine tower based on two-stage multi-fidelity simulation, which constructs a high-precision surrogate model for the constraint model by using an advanced sampling strategy, constructs a multi-objective reliability optimization design problem, and uses the NSGA-II algorithm to perform the optimization design. The specific process is as Figure 1 shown, including the following steps:

[0051] S1: For all constraints, use the Latin hypercube sampling method to generate initial sample points and construct a surrogate model.

[0052] S2: Based on the initial surrogate model, perform deterministic optimization design and solution for the wind turbine tower, and denote the obtained design point as and set the iteration number iter = 1.

[0053] Among them, the deterministic optimization design of the wind turbine tower specifically is as follows:

[0054]

[0055] where d, i = 1, ..., nd are design variables; X = {X v , X p}, T , X v and X p represent random design variables and random parameters respectively; d U and d L are the upper and lower bounds of the design variables; Cost(d) is the objective function; H i (d) is the equality constraint, and na is the number of equality constraints; G j (X) is the inequality constraint, and nc is the number of inequality constraints.

[0056] S3: Taking the current design point as the center, use the following formula to calculate the sampling region radius R:

[0057] R = c R σ,

[0058] where c R is the adaptive coefficient; σ is the maximum standard deviation of all uncertainty variables;

[0059] Then, judge whether each constraint function is an active constraint according to the failure contribution degree of each constraint function; the failure contribution degree CPF(i) of each constraint function is calculated by the following formula:

[0060]

[0061] where represents the number of failure samples for this constraint function; N f represents the total sum of the number of failure samples for all constraint functions. When CPF(i) is greater than the set threshold η, it is regarded as an active constraint, and subsequent sampling and surrogate model update are only carried out for active constraints.

[0062] S4: Generate subsequent sample points within the sampling window. For active constraints, use a learning function to select the new sample point x new . The learning function is specifically as follows:

[0063]

[0064] where Φ is the standard normal cumulative distribution function, φ is the standard normal distribution density function, is the constructed surrogate model, and ε is the allowable deviation; denotes The variance at sample x, σ G (x) represents the variance of the tower constraint performance at sample x.

[0065] S5: Update the surrogate model of the active constraints. For the deterministic optimization design solution of the wind turbine tower, the obtained design point is denoted as and let the iteration number iter = iter + 1; judge whether the accuracy requirement is met according to the convergence index. The convergence condition is as follows. If the convergence condition is met, execute S6; if not, execute S3. The specific expression of the convergence index is:

[0066]

[0067] S6: Regard the current constraint surrogate model as a low-fidelity model Randomly generate sampling points in the design domain. Calculate the failure probability at each sampling point using the Monte Carlo simulation method, where each Monte Carlo point is substituted into the low-fidelity model to obtain the response; then, based on the sampling points and the corresponding failure probabilities, fit the failure probability surrogate model

[0068] S7: Substitute the obtained into the current failure probability surrogate model to judge whether the design point falls into the target reliability interval [P L , P U . Select the design points falling into this interval as the second-stage data points

[0069] S8: For each data point Find the point closest to the failure boundary according to the Monte Carlo simulation method and substitute it into the true constraint response model G(x) to reconstruct the limit state function of the data point as shown in the following formula:

[0070]

[0071] Then recalculate its failure probability; use the data point and the corresponding recalculated failure probability to correct the failure probability surrogate model

[0072] S9: According to the design objectives and constraints of the wind turbine tower, transform the multi-reliability optimization design problem into a multi-objective optimization design problem as follows:

[0073]

[0074] where P[G j (X)] is for the inequality constraint G j(X) failure probability; P j L and P j U are the upper and lower bounds of the target failure probability;

[0075] and based on the current failure probability surrogate model The NSGA-II algorithm is used to solve the multi-objective optimization design problem, and the optimized design values of the wind turbine tower under different reliabilities are obtained.

[0076] In an embodiment of the present invention, in order to verify the effectiveness of the method of the present invention, a 47-section wind turbine tower is used, and the bottommost section of the tower is selected for multi-objective reliability optimization design. The design variables are the top diameter, bottom diameter, and thickness of the tower. The optimization objective of this embodiment is the tower volume, and the constraint is that the maximum stress cannot exceed the allowable stress. As the external wind load fluctuates, the forces and torques acting on the tower also change. Through a large number of Bladed simulation fitting results, the forces and torques acting on the tower are as Figure 2 shown. The optimization problem is defined as:

[0077] minimize{V(t,D base ,D top ),β}

[0078] Subject to 1.5≤β≤3

[0079] σ allow -σ max (D top ,D base ,t,F xy ,F z ,M xy ,M z )>0

[0080] 2≤D top ≤7

[0081] 2≤D base ≤7

[0082] 10≤t≤70

[0083] where the allowable stress is σ allow = 230 Mpa. The variable distribution of this embodiment is shown in Table 1.

[0084]

[0085]

[0086] Table 1 Design variable and its distribution parameter table of the embodiment.

[0087] In this embodiment, the surrogate model is selected as the Kriging model, and the target reliability interval is [1.5, 3].

[0088] The optimal design reliability distribution results are obtained by using the method of the present invention, as Figure 3 shown. And it is compared with the optimization results corresponding to the LUOC method proposed by domestic scholars Zhang et al. (Zhang J, Xiao M, Gao L. A new local update-based method for reliability-based design optimization[J]. Engineering with Computers, 2020, 37(4): 3591-3603.). As shown in Table 2 below, under the same initial conditions and the same test case, the method proposed by the present invention requires fewer total function evaluation times. The efficiency of the present method is greatly improved in the case of multiple reliabilities, because the present method only needs to construct a failure probability surrogate model and apply it to the optimization design of the wind turbine tower under different reliabilities, without performing RBDO optimization design for each reliability. This is mainly because the present method adopts the adaptive importance sampling method and the two-stage multi-fidelity model simulation method, which not only avoids the phenomenon of sample point aggregation during the sampling process, but also can further perform model calibration in the target failure probability interval, thus accelerating the convergence of the surrogate model.

[0089]

[0090]

[0091] Table 2 Comparison table of calculation results of the embodiment.

[0092] In summary, a multi-objective reliability optimization design method for a wind turbine tower based on two-stage multi-fidelity simulation of the present invention adopts a two-stage surrogate model construction method. In the first stage, a design constraint surrogate model of the wind turbine tower is efficiently constructed based on the importance sampling theory. In the second stage, based on the surrogate model constructed in the previous stage and the true constraint model, a failure probability surrogate model is constructed by using multi-fidelity simulation. Subsequently, the multi-objective reliability optimization design of the wind turbine tower is carried out based on the multi-objective optimization design method NSGA-II algorithm.

[0093] The present invention innovatively proposes a method for constructing a surrogate model of the failure probability of a wind turbine tower, and applies it to multi-objective reliability optimization design. It integrates the importance sampling method, multi-fidelity simulation technology, and multi-objective optimization design algorithm. Samples are taken for the design constraints to construct a surrogate model, and the obtained surrogate model is combined with the NSGA-II algorithm for solution to obtain the optimal design under different reliabilities. This method can be used for constructing a surrogate model of the failure probability of a wind turbine tower and searching for the optimal design under different reliability requirements.

[0094] As described above, the above is only the preferred embodiment of the present invention and does not impose any formal limitations on the present invention. Although the implementation process of the present invention has been described in detail above, those familiar with the art can still modify the technical solutions recorded in the foregoing examples or make equivalent replacements for some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A multi-objective reliability optimization design method for a wind turbine tower, characterized in that: The steps include: S1: Generate initial sample points and build an initial proxy model for all constraints; S2: Based on the initial proxy model, the deterministic optimization design of the wind turbine tower is solved and the obtained design point is recorded as And set the number of iterations iter = 1; S3: At the current design point The sampling window is defined as the center, and the activity of constraint functions is judged for all constraints. Subsequent sampling and proxy model updates are only performed for active constraints. S4: Generate subsequent sample points within the sampling window, and use the learning function to generate new sample points x for active constraints. new Selection of S5: Update the proxy model of active constraints and solve the deterministic optimization design of the wind turbine tower. The obtained design point is recorded as And the number of iterations iter=iter+1; judge whether the accuracy requirement is met according to the convergence index, if the convergence condition is met, execute S6, if not, execute S3; S6: Treat the current constraint surrogate model as a low-fidelity model Build a failure probability proxy model based on this low-fidelity model S7: The obtained Bring in the current failure probability proxy model Determine whether the design point falls within the target reliability interval [P L ,P U ], and the design points falling within this interval are selected as the second stage data points S8: For each data point Reconstruct the limit state function based on the high-fidelity model-true constraint response model G(x), then recalculate the failure probability and correct the failure probability proxy model S9: According to the design objectives and constraints of wind turbine tower, the multi-reliability optimization design problem is transformed into a multi-objective optimization design problem, and based on the current failure probability proxy model The NSGA-Ⅱ algorithm is used to solve the multi-objective optimization design problem and the optimal design values ​​of wind turbine towers under different reliabilities are obtained.

2. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1 is characterized in that: In S1, the Latin hypercube sampling method is used to generate initial sample points.

3. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1 is characterized in that: In S2, the deterministic optimization design of the wind turbine tower is specifically as follows: minimize Cost(d) Subject to H i (d)=0,i=1,...,na G j (X)>0,j=1,...,nc d L ≤d≤d U ,d∈R nd and X∈R nr , where d,i=1,...,nd are design variables; X={X v ,X p } T , X v and X p represent random design variables and random parameters respectively; d U and d L are the upper and lower bounds of the design variables; Cost(d) is the objective function; H i (d) is the equality constraint, na is the number of equality constraints; G j (X) is the inequality constraint and nc is the number of inequality constraints.

4. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1, characterized in that: The S3 is specifically: The sampling area radius R is calculated using the following formula: R=c R s, Among them, c R is the adaptive coefficient; σ is the maximum standard deviation of all uncertainty variables; Then, the failure contribution of each constraint function is used to determine whether it is an active constraint. The failure contribution CPF(i) of each constraint function is calculated by the following formula: in Represents the number of failure samples for this constraint function; N f Represents the sum of the number of failed samples for all constraint functions; when CPF(i) is greater than the set threshold η, it is considered an active constraint.

5. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1, characterized in that: In S4, the learning function is specifically: Among them, Φ is the standard normal cumulative distribution function, φ is the standard normal distribution density function, is the constructed proxy model, ε is the permissible deviation; express Variance at sample x, σ G (x) represents the variance of the tower restraint performance at sample x.

6. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1, characterized in that: In S5, the specific expression of the convergence index is:

7. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1, characterized in that: S6 specifically includes: randomly generating sampling points in the design domain, calculating the failure probability at each sampling point using the Monte Carlo simulation method, wherein each Monte Carlo point is brought into the low-fidelity model Get the response; then fit the failure probability proxy model based on the sampling points and the corresponding failure probabilities 8. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1, characterized in that: The S8 is specifically as follows: for the data point According to the Monte Carlo simulation method, the point closest to the failure boundary is found and brought into the true constraint response model G(x) to reconstruct the data point The limit state function is expressed as follows: Then recalculate its failure probability; Put the data point and the corresponding recalculated failure probability are used to modify the failure probability proxy model 9. The multi-objective reliability optimization design method for a wind turbine tower according to claim 1, characterized in that: In S9, it is converted into a multi-objective optimization design problem, and its expression is as follows: minimize{Cost(d),P[G j (X)]},j=1,...,nc Subject to H i (d)=0,i=1,...,na G j (d)>0 d L ≤d≤d U ,d∈R nd and X∈R nr , Where P[G j (X)] is for the inequality constraint G j (X) failure probability; P j L and P j U are the upper and lower bounds of the target failure probability.

Images