CN116305534B - Efficient coaxial rigid rotor wing type multi-target robust design method - Google Patents
Efficient coaxial rigid rotor wing type multi-target robust design method Download PDFInfo
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Abstract
The invention provides a high-efficiency coaxial rigid rotor wing type multi-target steady design method. The advanced wing profile design method capable of simultaneously optimizing a plurality of rotor wing aerodynamic performance indexes under the complex constraint of the coaxial rigid rotor wing profile design and maintaining the large-scale robustness is constructed, the application of the wing profile multi-target design method to important engineering fields such as coaxial rigid helicopter wing profile design is promoted, and the important engineering application value is achieved. Compared with the classical OA series wing profile, the wing profile designed by the design method has the advantages that under the condition that the medium and low speed characteristics are improved, the high speed characteristics are improved obviously and are more stable, the moment characteristics are also better in all states, and the performance index requirements of the wing profile of the new generation coaxial rigid helicopter rotor wing can be met.
Description
Technical Field
The invention relates to the technical field of airfoil design and the technical field of computer simulation and numerical optimization, in particular to a high-efficiency coaxial rigid rotor wing type multi-target robust design method.
Background
The helicopter with the conventional configuration is limited by the large separation flow phenomenon of the backward blades of the rotor under the condition of about 300km/h (large forward ratio) high-speed forward flight, and even the radial area of the blades reaches 85% when the separation is serious, so that the aerodynamic characteristics of the backward blades are poor, the lift force and forward thrust cannot be generated, the forward blades and the backward blades are matched with each other to meet the aerodynamic characteristics of the rotor, and the profile (airfoil) of the forward blades cannot work in the attack angle range corresponding to the high lift-drag ratio, thereby seriously affecting the aerodynamic efficiency of the helicopter during the high-speed large forward ratio flight. For a long time, in order to overcome the limitation of the flying speed, the flight speed envelope of the helicopter is effectively expanded, and foreign helicopter engineers develop various high-speed helicopters with the flying speed exceeding 400km/h, and the helicopter mainly comprises a thrust conversion type, a tilting rotor type and ducted fan combined type coaxial rigid rotor high-speed helicopters based on the forward blade concept. Of these, most representative are coaxial rigid rotor high speed helicopters based on the forward blade concept, which are represented by XH-59A and X2 technical validators from Sicosky, USA, S-97 "invader" high speed armed helicopters, and the like.
The coaxial double-rotor helicopter has the opposite movement of two rotors during flight, the forward blades are simultaneously arranged on two sides of the paddle disc, the resultant force naturally acts on the rotating shaft, the high dynamic pressure of the forward blades ensures enough tension, and the backward blades can not provide tension; when the helicopter flies forward at a high speed, the backward paddles can be unloaded to avoid the problems of resistance, noise surge and the like caused by a large-scale reverse flow area, so that the forward flying speed of the helicopter can be greatly improved. The coaxial rigid rotor wing type series design is a complex multi-target multi-constraint comprehensive balance design problem, compared with the pneumatic layout of a rotor wing with a conventional configuration, the radial profile is in a non-uniform inflow condition due to the strong interference effect of the upper blade and the lower blade of the coaxial rigid rotor wing, so that the coaxial rigid rotor wing type pneumatic rotor wing is conventionally suitable for a rotor wing type with a single rotor wing complex flow field environment and excellent performance, and the performance requirement of the coaxial rigid rotor wing can be difficult to meet. When the helicopter flies forwards, the Mach number of the blade tip of the forward propeller is close to 0.9, shock waves and compressibility are very strong, the required airfoil profile has significantly higher resistance divergence Mach number than that of a conventional helicopter airfoil profile, and a lower zero-liter resistance coefficient is maintained. The shock wave intensity and shock wave position of the outer section of the blade are very sensitive to the Mach number, the aerodynamic coefficient is changed severely, and the design airfoil must maintain the robustness of the drag coefficient within a certain range. The trailing blade has a higher lift coefficient at low speed to balance the high dynamic pressure of the leading blade with the large stall angle of attack and slow stall characteristics. At the same time, the performance under the conditions of hovering, maneuvering and the like is considered, namely, the high lift-drag ratio and the maximum lift coefficient are required under the conditions of low speed to high subsonic speed. In addition, to reduce torque and handling loads, each profile airfoil has a small lift moment at all Mach number conditions. The design requirements are more stringent than for single rotor airfoils.
Disclosure of Invention
Aiming at the difficult problems of high-dimensional multi-objective optimization design and high-efficiency multi-objective steady design of the coaxial rigid helicopter rotor wing, the invention provides a high-efficiency coaxial rigid rotor wing multi-objective steady design method, builds an advanced wing design method capable of simultaneously optimizing a plurality of rotor aerodynamic performance indexes under the complex constraint of the coaxial rigid rotor wing design and maintaining the large-scale robustness, promotes the application of the wing multi-objective design method to important engineering fields such as the coaxial rigid helicopter wing design, and has important engineering application value.
The technical scheme of the invention is as follows:
the efficient coaxial rigid rotor wing type multi-target robust design method comprises the following steps of:
step 1: selecting an initial airfoil profile and parameterizing the initial airfoil profile;
step 2: determining the design conditions and the design requirements of the coaxial rigid rotor according to various flight states, and converting the design conditions and the design requirements into a high-dimensional multi-objective optimization problem mathematical model;
step 3: determining multi-target robustness and constraint reliability evaluation indexes in a corresponding Mach number range according to the forward speed of a blade tip airfoil when the coaxial double-rotor helicopter flies forward;
step 4: combining the multi-objective robustness and constraint reliability evaluation indexes obtained in the step 3 to establish a multi-objective robust design optimization model;
step 5: acquiring samples in a plurality of calculation states and acquiring the pneumatic characteristics of the samples; the sample comprises: random variable and design variable joint samples constructed for targets with robustness evaluation indexes and constraints with reliability evaluation indexes, and samples for deterministic design targets and constraints;
step 6: respectively constructing and training a proxy model aiming at the samples obtained in the step 5;
step 7: optimizing the multi-objective robust design optimization model established in the step 4 by adopting a MOEAs algorithm to obtain a convergence Pareto solution set, and then carrying out objective dimension reduction analysis on the obtained solution set by using a nonlinear dimension reduction method to obtain the most important set of objectives;
the Pareto solution here refers to a "bad" solution to the multi-objective optimization problem, and is therefore also called an effective solution, a non-bad solution, or an acceptable solution. And (3) in the optimization process, each iteration calls the agent model trained in the step (6) to analyze and solve the adaptation value of each target, wherein the adaptation value comprises a deterministic performance index and a robustness evaluation index. The robustness evaluation index needs to call a proxy model based on the combination of random variables and design variables, and then uncertain analysis and quantification are carried out based on Monte Carlo simulation, so that the robustness and reliability evaluation index is obtained.
Step 8: performing multi-objective optimization on the most important group of targets obtained in the step 7 by using a MOEAs algorithm, judging whether the targets are converged, if so, continuing to execute downwards, otherwise, returning to the step 7 to execute again until the multi-objective solution sets are converged;
step 9: and (3) judging the converged solution set obtained in the step (8), judging whether the design requirement is met, outputting the result and ending, otherwise, selecting a new sample point by using a multi-objective optimization point adding criterion, acquiring the pneumatic characteristics of the sample, adding the sample to a sample library, returning to the step (6), respectively constructing and training a proxy model for the samples in the sample library, and executing the model again until the convergence output result is ended.
Further, an OA407 airfoil was employed as the initial airfoil.
Further, the initial airfoil profile is parameterized using a 3-stage B-spline curve.
B-spline curves assume that a section of the space is controlled by a number of sequentially arranged points, i.e
Wherein m+1 is the number of control points, B i,k (x) Is the i-th base function of order k. Wherein B is of the 0 th order i,k (x) Is defined as
Then, it can be deduced that the k-order B-spline is
The widespread use of B-tubes is also its most important feature, in addition to its flexibility. Where i denotes the number of B-tubes and the convention 0/0=0 in the recursion procedure. By recursive definition we know that for the commonly used k times B-splines, the number of nodes to be defined is M+k+1, where M is the number of basis functions.
Further, in step 2, the flight status includes forward flight, hover and maneuver status.
Further, the design conditions and design requirements of the coaxial rigid rotor wing profile in different flight states are as follows:
wherein Ma dd The high-dimensional multi-objective optimization problem mathematical model obtained by resistance divergence Mach number and conversion is as follows:
Min:(f 1 ,f 2 ,f 3 ,f 4 ,f 5 ,f 6 ,f 7 ,f 8 ,f 9 ,f 10 ,f 11 ,f 12 ,f 13 )
S.t.t≥7％
wherein X is the parameterized airfoil design variable obtained in step 1; t is the airfoil thickness.
Further, the multi-objective robustness and constraint reliability evaluation indexes determined in the step 3 are the mean and variance of the lift drag and moment characteristics in the Mach number range of 0.84-0.87:
further, in step 4, the multi-objective robust design optimization model is built as follows:
S.t.t≥7％
further, in step 5, the random variable and design variable joint samples constructed for the constraint of the target with the robustness evaluation index and the reliability evaluation index are: extracting Mach number and design variable combination samples in the range of the corresponding airfoil design variables from Ma epsilon [0.85,0.87 ]; the samples for deterministic design goals and constraints are: samples are extracted over a range of corresponding airfoil design variables at the determined Mach number and lift coefficient.
Further, a Kriging proxy model is used to construct a proxy model for the samples obtained in the step 5.
Further, the multi-objective dotting method in step 9 uses a desired improved dotting method based on euclidean distance.
Advantageous effects
The invention breaks through the difficult problems of high-dimensional multi-objective optimization design and the challenges of high-dimensional multi-objective steady design faced by the traditional airfoil design method, provides a high-efficiency coaxial rigid rotor airfoil multi-objective steady design method aiming at the severe aerodynamic performance requirement of a new generation coaxial rigid helicopter on rotor airfoils, and constructs a high-efficiency reliable coaxial rigid rotor airfoil design new method by combining an uncertainty modeling technology, a nonlinear objective dimension reduction technology, a multi-objective optimization technology, an uncertainty-based steady design method and the like. Compared with the classical OA series wing profile, the wing profile designed by the design method has the advantages that under the condition that the medium and low speed characteristics are improved, the high speed characteristics are improved obviously and are more stable, the moment characteristics are also better in all states, and the performance index requirements of the wing profile of the new generation coaxial rigid helicopter rotor wing can be met.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1B spline basis function
FIG. 2B spline curve fitting airfoil
FIG. 3 robustness evaluation index illustration
FIG. 4 constraint reliability evaluation index diagram
FIG. 5 is a nonlinear dimension reduction flow diagram based on maximum variance expansion
FIG. 6 real Pareto front after pneumatic performance verification
FIG. 7 optimized airfoil and classical airfoil profile comparison
FIG. 8 zero rise airfoil pressure profile comparison
FIG. 9 wing section zero rise resistance divergence curve contrast
FIG. 10 airfoil zero lift torque characteristic comparison
Fig. 11 ma=0.3 airfoil lift coefficient variation curve comparison
Fig. 12 ma=0.3 airfoil lift-to-drag ratio variation curve comparison
Fig. 13 ma=0.4 airfoil lift coefficient variation curve comparison
Fig. 14 ma=0.4 airfoil lift-to-drag ratio variation curve comparison
Fig. 15 ma=0.5 curve comparison of airfoil lift coefficient versus angle of attack
Fig. 16 ma=0.5 airfoil lift-to-drag ratio variation curve comparison
Fig. 17 ma=0.6 airfoil lift coefficient vs. angle of attack curve comparison
Fig. 18 ma=0.6 airfoil lift-to-drag ratio variation curve comparison
FIG. 19 is a flow chart of a method
Detailed Description
Aiming at the problems of high-dimensional multi-objective and complex constraint design brought by ten design indexes such as lift resistance characteristics, moment characteristics and the like in a plurality of states such as forward flight, hovering, maneuvering and the like in a wide Mach number range (Ma=0.2-0.9) of the rigid coaxial rotor wing profile, and the challenges of a rotor wing profile design method caused by the design requirements of multiple objective robustness, the invention provides a high-efficiency coaxial rigid rotor wing profile multi-objective robust design method. The rotor wing profile is subjected to fine design by the method, so that the aerodynamic characteristics of the optimized wing profile under medium and low speed Mach numbers are improved, the high-speed aerodynamic characteristics are improved remarkably, the robustness is maintained in a large range, and the design requirement of the rotor wing profile of the new generation coaxial rigid helicopter can be met.
The invention is described below in connection with specific embodiments:
1. the OA407 airfoil was chosen as the initial airfoil.
2. And selecting a 3-order B-spline curve as an airfoil parameterization method. B-spline curves assume that a section of the space is controlled by a number of sequentially arranged points, i.e
Wherein m+1 is the number of control points, B i,3 (x) Is the i-th base function of order 3. Wherein B is of the 0 th order i,0 (x) Is defined as
Then, it can be deduced that 3-order B-splines are
Details on B-splines can be found in the reference: zhu Xinxiong free curve surface modeling technique Beijing: scientific press, 2000.
3. A mathematical model of the optimization problem is defined. According to the coaxial rigid rotor wing profile, more than ten design index requirements such as lift resistance characteristics, moment characteristics and the like under a plurality of states such as forward flight, hovering, maneuvering and the like are considered; at the same time, as the flying speed increases, the range of conditions to be considered is wider (ma=0.2-0.9) to design the performance. The detailed aerodynamic performance requirements of the rigid coaxial tip airfoil are shown in the following table
Wherein Ma dd A mach number for drag divergence; converting the physical model described by the table into a high-dimensional multi-objective optimization problem mathematical model, specifically
Min:(f 1 ,f 2 ,f 3 ,f 4 ,f 5 ,f 6 ,f 7 ,f 8 ,f 9 ,f 10 ,f 11 ,f 12 ,f 13 )
S.t.t≥7％
4. Multi-objective robustness and constraint reliability evaluation indexes are defined. Since the forward speed of coaxial twin-rotor helicopters is particularly high, the forward speed of the tip airfoil exceeds 0.85Ma, the shock wave position and strength changes very severely, and the high-speed aerodynamic characteristics of the rotor airfoil are very sensitive, a robust design is required. The method defines the mean value and the variance of the high-speed rise resistance characteristic within a certain Mach number range based on the probability theory as a robustness evaluation index. Taking the mean value and variance of the lift drag and moment characteristics in the Mach number range of 0.84-0.87 as the robustness and feasible robustness evaluation index, namely
Definition of the robustness evaluation index can be referred to in the literature: zhao H, gao Z, xu F, et al review of Robust Aerodynamic Design Optimization for Air Vehicles [ J ]. Archives of Computational Methods in Engineering,2019,26 (3): 685-732.
5. A multi-objective robust design optimization model is defined. And (3) defining a multi-target robust design optimization model by combining the target robustness and constraint reliability evaluation indexes defined in the step 4. The optimization model should consider the performance and target robustness, constraint reliability and target robustness of each target in the optimization process, and the influence of mutual restriction or mutual promotion between the target performance and constraint reliability, and a reasonable multi-target robust optimization model is formulated. Accordingly, the coaxial rigid rotor wing tip wing type multi-target steady design mathematical model is established as
S.t.t≥7％
6. High confidence samples (of the same and different computational states) were obtained using the latin hypercube sampling method and evaluated. And selecting a proper initial sample number according to sample requirements of the proxy modeling method on each target and constraint. Wherein for the constraint (such as mean and variance of resistance coefficient and probability density function of pitching moment coefficient) of the target with robustness evaluation index and reliability evaluation index, a sample of random variable and design variable combination should be constructed, and for the deterministic design target and constraint (such as resistance coefficient and pitching moment coefficient), the sample is extracted in corresponding state. A total of 6 samples were taken, the first group at Ma ε [0.85,0.87]],x i ∈[-0.02,0.02]Samples of the combination of mach number and design variable are extracted within the range of i=1, 2,3, …,16, and the second group to the sixth group are in the states (1 ma=0.5, c, respectively) l ＝0.6,②Ma＝0.6,C l ＝0.6,③Ma＝0.3,C l ＝1.0,④Ma＝0.4,C l ＝0.9,⑤Ma＝0.5,C l =0.8, a suitable number of samples is drawn down, the design variable range is x i ∈[-0.02,0.02]I=1, 2,3, …,16. And then respectively using a high-reliability CFD model for analysis and evaluation to obtain aerodynamic characteristics.
Specific use of the Latin hypercube sampling method can be referred to as: stocki R.A method to improve design reliability using optimal Latin hypercube sampling [ J ]. Computer Assisted Mechanics and Engineering Sciences,2005,12 (4): 393.
7. A plurality of proxy models are constructed that combine design variables and uncertainty (random) variables for different targets and constraints. The Kriging proxy model was used to construct a proxy model for each of the 6 sets of samples. Wherein the Kriging proxy model is used as an interpolation model and consists of a mean part and a Gaussian random process, namely
Wherein beta is i Is the regression coefficient, f i (x) Is x= (X) 1 ,x 2 ,…,x n ) As a global trend model or a mean part, there are 0-order, first-order or second-order regression polynomials in common; z (X) represents a mean value of 0 and a variance of sigma 2 (σ 2 (X)≡σ 2 ) Is a static gaussian random process with covariance Cov (z (X (i) ),z(X (j) ))＝σ 2 R(X (i) ,X (j) The method comprises the steps of carrying out a first treatment on the surface of the θ). Wherein X is (i) And X (j) Is any two points in design space, R (X (i) ,X (j) The method comprises the steps of carrying out a first treatment on the surface of the θ) is a Gaussian exponential correlation function defined as
R k (Δ k ,θ k )＝exp(-θ k |Δ k | q )，q＞0
Training the Kriging model super-parameters by using maximum likelihood estimation based on the sample obtained in the step 5, and then performing Gaussian process fitting to obtain a Kriging regression prediction model of the given training sample set, wherein the prediction response value of any point in space is as follows:
the use of a specific Kriging proxy model can be referred to in the literature: J.Toal D, BRESSLOFF N W, KEANE A J.Kriging hyperparameter tuning strategies [ J ]. AIAA Journal,2008,46 (5): 1240-1252.
8. The MOEAs algorithm is used for directly optimizing a multi-target robust design model to obtain a convergence Pareto solution set, then a nonlinear dimension reduction method is used for carrying out target dimension reduction analysis on the obtained solution set to obtain the most important group of dimension reduced targets, and the method specifically comprises the following steps:
(1) first by classical MOEAs algorithms such as MOThe EA/D performs optimized search on the high-dimensional problem for some algebra to obtain an approximate Pareto solution set. Let the population quantity of each generation be N p The target number is M, and the obtained searching multi-target result set isWherein column vector->Indicating the fitness of each target of the ith particle of this generation.
(2) Centering F to obtainWherein the method comprises the steps ofAnd +.>Finding high dimensional data by maximum variance expansion (MVU) algorithm +.>The corresponding low-dimensional manifold, y= { Y 1 ,y 2 ,…,y M }, wherein->
(3) The resulting kernel matrix K or R is subjected to a feature decomposition, i.e., k=vΛv. Wherein V is a feature vector matrix v= [ V ] 1 ,v 2 ,…,v M ]，v i ＝[v i1 ,v i2 ,…,v iM ] T And the corresponding eigenvalue Λ=diag (λ 1 ,λ 2 ,…,λ M )(λ 1 ≥λ 2 ≥…≥λ M ≥0)。
(4) Calculating the contribution of each feature directionWherein->Definition v ij For the ith target f i For v j Contribution of direction, f i For the most important main direction { v 1 ,v 2 ,…,v m The total contribution of } (M < M) isAnd->Wherein m is obtained by selecting an energy threshold value of theta not less than 0.95, namelyThe first m main directions are required to possess almost all the energy.
(5) Defining an initial target set after dimension reductionFor the first significant direction v j (j＝1,2,…,m)：
a) If f i (i=1, 2, …, M) target pair v 1 If there are some contributions with opposite signs, selecting two targets corresponding to the most positive and most negative contributions to enter the set
b) If f i (i=1, 2, …, M) target pair v j Some of the contributions in the (j.gtoreq.2) direction are of opposite sign, and the most positive contribution is denoted v pj The most negative contribution is v nj If |v nj |≥v pj ≥θ t |v nj I then select v pj And v nj Corresponding to both directions enterIf v pj <θ t |v nj I then select v nj Corresponding direction entry->If v pj ≥|v nj |≥
θ t v pj Then select v pj And v nj Corresponding to both directions enterIf |v nj |<θ t v pj Then select v pj Corresponding direction entry->The method takes theta t ＝0.8。
c) If all f i (i=1, 2, …, M) vs v j The contribution symbols of the directions are the same, then the two targets with the largest contribution are selected to enter the collection Should satisfy->Record->
(6) At this step we use correlation analysis pairsFurther identification and reduction of related objects (contributing equivalently). Will opt in->The targets in (a) are placed in the matrix in column order +.>In, then calculate the correlation matrix +.>For->And +.>If sign (R) ik )＝sign(R jk ) (k=1, 2, …, M) and R ij ≥R θ Description f i And f j If the contribution directions of (c) are the same, then the one of them contributing more to the dominant direction is selected, i.e. if c i ≥c j Then select f i From->Middle rejection f j And vice versa. R is R θ Is related to redundancy between targets, the more redundant the target is R θ The larger the smaller the opposite.
(7) With newly-obtained collectionsReplacing old set F, repeating steps (2) - (6) until the set obtained twice in succession +.>If the same, stopping iteration and outputting a dimension reduction target set +.>
(8) Using MOEAs algorithm on new target setSearching the selected target to obtain a Pareto optimal solution set, and selecting the most appropriate design in a compromise mode to evaluate and analyze. The process may refer to the flowchart of fig. 5.
Where Pareto solution refers to a "bad" solution to the multi-objective problem, so it is also called an effective solution, a non-bad solution, or an acceptable solution. In the optimization process, each iteration needs to call the proxy model to analyze the adaptation value of each target, including deterministic performance indexes and robustness evaluation indexes. The robustness evaluation index needs to call a proxy model based on the combination of random variables and design variables, and then uncertain analysis and quantification are carried out based on Monte Carlo Simulation (MCS), so that the robustness and reliability evaluation index is obtained.
MVU algorithm can be referred to in: saxena D K, deb K.non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: employing correntropy and a novel maximum variance unfolding [ C ]. International Conference on Evolutionary Multi-Criterion Optimization,2007:772-787.
MCS method can be referred to as: shahbaz M, han Z-H, song W, et al Surrogate-based robust design optimization of airfoil using inexpensive Monte Carlo method [ C ].2016 13th International Bhurban Conference on Applied Sciences and Technology (IBCAST), 2016:497-504.
9. And (3) performing multi-objective optimization on the most important group of targets by using a MOEAs algorithm, judging whether the targets are converged, if so, continuing to execute downwards, otherwise, returning to the step 7, and executing backwards again until the multi-objective solution set is converged. The double-target and complex constraint optimization model after the dimension reduction is obtained by executing the step 7 is as follows
Min:(f 1 ′,f 2 ′)
S.t.
10. Judging whether the converged solution set meets the design requirement or not, outputting the result and ending if the converged solution set meets the design requirement, otherwise, selecting a new sample point by using a multi-objective optimization and point adding criterion, evaluating the sample point, adding the sample point into a sample library, returning to the step 6, and executing again and afterwards until the converged output result is ended. The multi-objective dotting method uses a Euclidean distance-based expected improved dotting method, and the evaluation of each objective and constraint value is the same as the step 7.
And analyzing the obtained rotor wing profile by using a high-reliability CFD value transition program in a large range of Ma=0.3-0.5 and Ma=0.85-0.87, updating a real Pareto front edge, selecting a rotor wing profile corresponding to the coaxial double-rotor helicopter engineering requirement, and outputting for use.
In the embodiment, three representative wing profiles OPT0701, OPT0702 and OPT0703 are selected from the Pareto front edge obtained according to the multi-objective optimization result; the implementation result shows that compared with the traditional OA407 airfoil, the designed OPT0701 airfoil has overall improved high, medium and low speed aerodynamic performance indexes compared with the OA407 airfoil, but the improvement of high speed performance is very limited; and under the condition that the low-speed characteristic loss is not large, the high-speed characteristic is remarkably improved and is more stable by the OPT0702 and OPT0703 wing profiles. The torque characteristics of the three design airfoils are also better than those of the OA407 airfoil in all states. The design airfoil exhibits significant advantages over the classical OA-series airfoil in view of the special design requirements of coaxial rigid dual rotor helicopter rotor airfoils.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations may be made in the above embodiments by those skilled in the art without departing from the spirit and principles of the invention.
Claims (7)
1. A high-efficiency coaxial rigid rotor wing type multi-target robust design method is characterized in that: the method comprises the following steps:
step 1: selecting an initial airfoil, and parameterizing the initial airfoil to obtain parameterized airfoil design variables;
step 2: determining the design conditions and the design requirements of the coaxial rigid rotor wings according to various flight states of the coaxial double-rotor wing helicopter, and converting the design conditions and the design requirements into a high-dimensional multi-objective optimization problem mathematical model;
the flight conditions include forward flight, hover, and maneuver conditions; the design conditions and design requirements of the coaxial rigid rotor wing type under different flight states are as follows:
Ma dd the high-dimensional multi-objective optimization problem mathematical model obtained by resistance divergence Mach number and conversion is as follows:
Min:(f 1 ,f 2 ,f 3 ,f 4 ,f 5 ,f 6 ,f 7 ,f 8 ,f 9 ,f 10 ,f 11 ,f 12 ,f 13 )
S.t.t≥7％
wherein X is the parameterized airfoil design variable obtained in step 1; t is the airfoil thickness;
step 3: determining multi-target robustness and constraint reliability evaluation indexes in a corresponding Mach number range according to the forward speed of a blade tip airfoil when the coaxial double-rotor helicopter flies forward;
step 4: combining the multi-objective robustness and constraint reliability evaluation indexes obtained in the step 3 to establish a multi-objective robust design optimization model;
step 5: acquiring samples in a plurality of calculation states and acquiring the pneumatic characteristics of the samples; the sample comprises: random variable and design variable joint samples constructed for targets with robustness evaluation indexes and constraints with reliability evaluation indexes, and samples for deterministic design targets and constraints;
step 6: respectively constructing and training a proxy model aiming at the samples obtained in the step 5;
step 7: optimizing the multi-objective robust design optimization model established in the step 4 by adopting a MOEAs algorithm to obtain a convergence Pareto solution set, and then carrying out objective dimension reduction analysis on the obtained solution set by using a nonlinear dimension reduction method to obtain the most important set of objectives; in the optimization process, calculating the adaptation value of each target by adopting the agent model obtained in the step 6;
step 8: performing multi-objective optimization on the most important group of targets obtained in the step 7 by using a MOEAs algorithm, judging whether the targets are converged, if so, continuing to execute downwards, otherwise, returning to the step 7 to execute again until the multi-objective solution sets are converged;
step 9: and (3) judging the converged solution set obtained in the step (8), judging whether the design requirement is met, outputting the result and ending, otherwise, selecting a new sample point by using a multi-objective optimization point adding criterion, acquiring the pneumatic characteristics of the sample, adding the sample to a sample library, returning to the step (6), respectively constructing and training a proxy model for the samples in the sample library, and executing the model again until the convergence output result is ended.
2. An efficient coaxial rigid rotor airfoil multi-target robust design method according to claim 1, characterized by: in step 1, the initial airfoil profile is parameterized using a 3-order B-spline curve.
3. An efficient coaxial rigid rotor airfoil multi-target robust design method according to claim 1, characterized by: the multi-objective robustness and constraint reliability evaluation indexes determined in the step 3 are the mean value and the variance of the lift drag and moment characteristics in the Mach number range of 0.84-0.87:
4. a method of efficient coaxial rigid rotor airfoil multi-target robust design according to claim 3, characterized by: in step 4, a multi-objective robust design optimization model is established as follows:
S.t.t≥7％
5. an efficient coaxial rigid rotor airfoil multi-target robust design method according to claim 1, characterized by: in step 5, the random variable and design variable joint samples constructed for the target with the robustness evaluation index and the constraint of the reliability evaluation index are: extracting Mach number and design variable combination samples in the range of the corresponding airfoil design variables from Ma epsilon [0.85,0.87 ]; the samples for deterministic design goals and constraints are: samples are extracted over a range of corresponding airfoil design variables at the determined Mach number and lift coefficient.
6. An efficient coaxial rigid rotor airfoil multi-target robust design method according to claim 1 or 5, characterized by: and (5) respectively constructing a proxy model for the samples obtained in the step (5) by using a Kriging proxy model.
7. An efficient coaxial rigid rotor airfoil multi-target robust design method according to claim 1, characterized by: the multi-objective dotting method in step 9 uses a desired improved dotting method based on euclidean distance.
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