CN111368367A - Parameterization method for ice shape of icing wind tunnel icing test - Google Patents
Parameterization method for ice shape of icing wind tunnel icing test Download PDFInfo
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Abstract
The invention discloses a parameterization method for an ice shape of an icing wind tunnel icing test, which comprises the following steps of: selecting characteristic points: calculating the curvature change of the numerical ice-shaped curve, and selecting a characteristic point on the ice-shaped curve according to a curvature change rule; a curve parameterization step: and carrying out regression interpolation on the characteristic points on the numerical deicing curve by using a regression model to obtain a smooth parametric deicing curve. Aiming at irregular complex ice-shaped curves, the mechanism of filtering noise by using a regression model is utilized, and characteristic points are specified by artificially or setting a selection rule, so that the aim of quickly parameterizing the ice-shaped curves can be fulfilled under the condition of keeping the original ice-shaped characteristics.
Description
Technical Field
The invention relates to a parameterization method, in particular to a parameterization method for an icing test ice shape of an icing wind tunnel.
Background
During the flight of an airplane, water droplets in a cloud layer can be condensed at a certain height, and when the temperature is zero degrees centigrade and below, ice can be formed on the surface of the airplane and can further form accumulated ice. Icing of an aircraft is one of the main hidden dangers threatening the flight safety of the aircraft, and has received wide attention in recent years.
At present, the research means of airplane icing includes flight test, wind tunnel test and numerical simulation, wherein the wind tunnel test becomes an important means for the research of icing and deicing by virtue of the icing reproducing capability with high reliability. The icing shape is one of the important attention results of the icing wind tunnel test, and can be used for evaluating the aerodynamic characteristics of the frozen airplane. During the simulation evaluation of the pneumatic characteristic numerical value, the complexity of the ice shape directly influences the grid generation quality, thereby influencing the difficulty and precision of calculation; the complexity of the ice shape can cause great difficulty in the formation of the ice shape when the aerodynamic characteristic test is evaluated. Most of the time, the ice shape obtained by the ice wind tunnel is extremely irregular, and more burrs exist, so that the ice shape is parameterized in a later period, the parameterized ice shape can keep the characteristics of the original ice shape, and the original ice shape can be simplified to a certain extent. Therefore, a parameterization method of the ice shape obtained by an icing wind tunnel icing test needs to be developed to enhance the operability and scientificity of the later use of the ice shape.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a parameterization method for an icing wind tunnel icing test ice shape, aiming at a two-dimensional ice shape curve, a regression Kriging model is applied to filter noise on the ice shape curve to obtain a final parameterized ice shape curve, so that the aim of correcting and optimizing the ice shape is fulfilled.
The purpose of the invention is realized by the following technical scheme: a parameterization method for an icing shape of an icing wind tunnel icing test comprises the following steps:
selecting characteristic points: calculating the curvature change of the numerical ice-shaped curve, and selecting a characteristic point on the ice-shaped curve according to a curvature change rule;
a curve parameterization step: and carrying out regression interpolation on the characteristic points on the numerical deicing curve by using a regression model to obtain a smooth parametric deicing curve.
Before the step of selecting the characteristic points, a step of acquiring a numerical deicing curve is required to be completed.
The step of acquiring the numerical icing curve comprises the step of acquiring a two-dimensional numerical data point set { (x) of the test icing in the wind tunnel icing test by adopting a hot knife methodi，yi) I |, 1, 2, …, N }, and an ice-shaped curve is obtained after two-dimensional numerical representation.
The calculating the curvature change of the numerical ice curve and selecting the characteristic points on the numerical ice curve according to the curvature change rule specifically comprise:
calculating the curvatures of all data points on the numerical deicing curve and the curvature change between adjacent data points;
and m characteristic points are selected on the numerical deicing curve according to the magnitude relation of curvature change to obtain a coordinate point set { lambda } of all the characteristic pointsj(ξj，ηj)|j＝1，2，…，m}。
The method for selecting m characteristic points on the numerical deicing curve according to the size relation of curvature change comprises the following steps:
selecting a characteristic points at the positions of which the curvature change is smaller than a given threshold value;
b characteristic points are selected at all positions with curvature change larger than a given threshold value.
And the relationship between a, b and m is a + b.
The method for carrying out regression interpolation on the characteristic points on the numerical deicing curve by using the regression model to obtain the smooth parametric deicing curve comprises the following steps:
taking the numerical deicing curve as an input object, and performing regression interpolation by using a regression Kriging model to obtain an interpolation model;
and outputting interpolation results of the positions of all the characteristic points to obtain a smooth parametric deicing curve with noise points on the numerical deicing curve filtered.
Taking the numerical deicing curve as an input object, and performing regression interpolation by using a regression Kriging model to obtain an interpolation model, which specifically comprises the following steps:
the data point set of the numerical icing curve { (x)i，yi) 1, 2, …, N into a polar coordinate data point set { (r)i，θi)|i＝1，2，…，N}；
Using a set of polar data points { (r)i，θi) And (3) performing regression Kriging model on the | i ═ 1, 2, …, N to obtain an interpolation model Y (X).
Outputting interpolation results of positions of all the characteristic points to obtain a smooth parametric deicing curve with noise points on the numerical deicing curve filtered, wherein the smooth parametric deicing curve specifically comprises the following steps:
set of coordinate points of m feature points { lambdaj(ξj，ηj) 1, 2, …, m into a corresponding set of polar points kj(ρj，εj)|j＝1，2，…，m}；
Each polar coordinate ρjSubstitution into interpolation model Y (X) yields a new set of polar coordinate points { κ'j(ρj，ε′j)|j＝1，2，…，m}；
Converting the coordinate points into a coordinate point set { (x) 'in a Cartesian coordinate system'j，y′j) And j equals to 1, 2, …, m, and a parametric deicing curve for filtering noise is obtained.
The invention has the beneficial effects that: a parameterization method for an icing test ice shape of an icing wind tunnel aims at an irregular complex ice shape curve, utilizes a mechanism of noise filtering of a regression model, and can achieve the purpose of rapid parameterization of the ice shape curve under the condition of keeping original ice shape characteristics by specifying characteristic points through artificial or set selection rules.
Drawings
FIG. 1 is a schematic illustration of the ice parameterization process of the present invention;
FIG. 2 is a schematic diagram of the transformation of coordinates of an ice-shaped curve;
FIG. 3 is a graph showing the comparison between the ice-shaped curve and the parameterized curve
In the figure, 1-an ice-shaped profile curve, 1-1-an ice-shaped profile curve under a polar coordinate system, 2-icing of the leading edge of the blade, 3-icing of the leading edge of the blade, 4-characteristic points and 5-parametric icing of the ice-shaped curve.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the present invention, it should be noted that the terms "upper", "inner", "outer", etc. indicate orientations or positional relationships based on those shown in the drawings or orientations or positional relationships that the products of the present invention conventionally use, which are merely for convenience of description and simplification of description, but do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.
In the description of the present invention, it should also be noted that, unless otherwise explicitly specified or limited, the terms "disposed," "mounted," and "connected" are to be construed broadly, e.g., as meaning fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 1, a parameterization method for an icing test ice shape of an icing wind tunnel includes the following steps:
s1, acquiring a numerical deicing curve: blade leading edge icing 2 is formed on the blade leading edge 3, and a two-dimensional numerical data point set { (x) of a test ice shape in a wind tunnel icing test is obtained by adopting a hot knife methodi，yi) 1, 2, …, N }, and obtaining a two-dimensional numerical ice-shaped profile curve 1;
s2, selecting characteristic points: calculating the curvature change of the numerical ice-shaped profile curve 1, and selecting a characteristic point 4 on the ice-shaped profile curve 1 according to the curvature change rule;
s3, curve parameterization step: and (3) carrying out regression interpolation on the characteristic points on the numerical deicing contour curve 1 by using a regression model to obtain a smooth parametric deicing curve 5.
Further, the calculating the curvature change of the numerical icing shape profile curve 1 and selecting the feature point 4 on the numerical icing shape profile curve 1 according to the curvature change rule specifically include:
s21, calculating the curvatures of all data points on the numerical deicing contour curve 1 and the curvature change between adjacent data points;
s22, selecting m characteristic points on the numerical deicing contour curve 1 according to the magnitude relation of curvature change to obtain a coordinate point set { lambda } of all the characteristic pointsj(ξj，ηj)|j＝1，2，…，m}。
Further, the selection of m feature points on the numerical icing profile curve 1 according to the magnitude relation of the curvature change includes the following steps:
selecting a characteristic points at the positions of which the curvature change is smaller than a given threshold value;
b characteristic points are selected at all positions with curvature change larger than a given threshold value.
And the relationship between a, b and m is a + b.
The position where the curvature change is smaller than the given threshold value represents that the curve is relatively smooth and has fewer burrs, and the position where the curvature change is larger than the given threshold value represents that the curve has larger curvature or is more prominent and has more burrs; more characteristic points are selected at positions with larger curvature change, so that the geometric characteristics of the icing curve can be retained to the greatest extent; in fig. 1, a total of 15 feature points are selected on the ice-shaped profile curve 1, 8 feature points are selected on the middle projection portion (the position where the curvature change is large) of the ice-shaped profile curve 1, and the remaining feature points are selected on both sides (the position where the curvature change is small).
Further, the obtaining of the smooth parametric icing curve by performing regression interpolation on the characteristic points on the numerical icing curve by using the regression model includes the following steps:
s31, taking the numerical deicing curve as an input object, and performing regression interpolation by using a regression Kriging model to obtain an interpolation model;
and S32, outputting interpolation results of all the feature point positions to obtain a smooth parametric deicing curve with noise points on the numerical deicing curve filtered.
Further, taking the numerical deicing curve as an input object, and performing regression interpolation by using a regression Kriging model to obtain an interpolation model specifically as follows:
the data point set of the numerical icing curve { (x)i，yi) 1, 2, …, N into a polar coordinate data point set { (r)i，θi)|i＝1，2，…，N}；
Using a set of polar data points { (r)i，θi) Carrying out regression Kriging model interpolation on | i ═ 1, 2, …, N } to obtainInterpolation model y (x).
Specifically, the model function y (x) is:
wherein f isj(X) is a basis function, here chosen as constant 1, βjIs the coefficient corresponding to the basis function,
a mathematical expectation value representing y (x); z (X) is mean zero and variance
The static random process of (a); for any two positions X and X' in the design space, the covariance of the random quantity is:
wherein, the correlation function R (X, X') is only related to the space distance and represents the correlation between random variables at different positions, when the distance between two positions in the correlation function is infinite, R is 0, and when the distance between two positions is zero, R is 1; r decreases with increasing distance. Wherein, the correlation matrix and the correlation vector are defined as:
R(R(X(i),X(j))i，j
rx＝[R(X(1)，X)，R(X(2)，X)，…，R(X(n)，X)]T
the correlation model satisfies the following conditions: 1. when the sample point X(i)And X(j)When the distance tends to 0, the corresponding correlation function value tends to 1; 2. when the sample point distance tends to infinity, the correlation function value tends to 0; 3. as the sample point distance increases, the correlation function value decreases smoothly; 4. at least one order of conductability is satisfied. Selecting a gaussian function as a correlation model:
wherein theta is a Kriging hyper-parameter and can be obtained by utilizing a maximum likelihood estimation method; for the regression Kriging model needing to filter noise, a constant needs to be added to the diagonal line of the correlation matrix to improve the positive nature of the matrix:
R′＝R+γI
wherein, I is a unit diagonal matrix, γ is a constant, the larger the value thereof is, the stronger the noise filtering effect is, further, the value range is 0-10, preferably, the value is 10, and can be adjusted according to the characteristics of the ice-shaped contour curve 1.
Outputting interpolation results of positions of all the characteristic points to obtain a smooth parametric deicing curve with noise points on the numerical deicing curve filtered, wherein the smooth parametric deicing curve specifically comprises the following steps:
set of coordinate points of m feature points { lambdaj(ξj，ηj) 1, 2, …, m into a corresponding set of polar points { κ |j(ρj，εj)|j＝1，2，…，m}；
Each polar coordinate ρjSubstitution into interpolation model Y (X) yields a new set of polar points, { kappa', in the interpolation modelj(ρj，ε＇j)|j＝1，2，…，m}；
Converting the coordinate points into a coordinate point set { (x) 'in a Cartesian coordinate system'j，y′j) And j equals to 1, 2, …, m, and a parametric deicing curve for filtering noise is obtained.
Further, as shown in fig. 1 and fig. 2, the two-dimensional ice-shaped profile curve 1 obtained by one test is described by 123 discrete data points, and one x coordinate of the data point set in the rectangular coordinate system of the two-dimensional ice-shaped profile curve 1 corresponds to at least two y coordinates, which is inconvenient for performing regression interpolation, so that the data point set is converted into the polar coordinate system to ensure the one-to-one correspondence of the coordinates, and the ice-shaped profile curve 1-1 in the polar coordinate system is obtained.
The ice-shaped profile curve 1-1 under the polar coordinate is also described by 123 discrete data points, regression Kriging model interpolation is carried out by using the 123 discrete data points, a positive fixed parameter gamma is adjusted, and the best effect is obtained when the gamma is 10 through test verification, so that the parameterized ice-shaped curve 5 which can reflect the characteristics of the ice-shaped profile curve 1 and has smooth curvature is obtained.
As shown in fig. 3, a lot of burrs exist on the icing test ice-shaped profile curve 1, that is, "noise" exists in the curve data, and through regression Kriging interpolation, the outputted parameterized ice-shaped curve 5 well retains the main characteristics of the icing test ice-shaped profile curve 1, successfully filters the noise of the curve data, and obtains the parameterized ice-shaped curve 5 with smooth curvature.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (8)
1. A parameterization method for an icing shape of an icing wind tunnel icing test is characterized by comprising the following steps: the method comprises the following steps:
selecting characteristic points: calculating the curvature change of the numerical ice-shaped curve, and selecting a characteristic point on the ice-shaped curve according to a curvature change rule;
a curve parameterization step: and carrying out regression interpolation on the characteristic points on the numerical deicing curve by using a regression model to obtain a smooth parametric deicing curve.
2. The parameterization method for the ice shape of the icing wind tunnel icing test according to claim 1, characterized by comprising the following steps of: before the step of selecting the characteristic points, a step of acquiring a numerical deicing curve is required to be completed.
3. The parameterization method for the ice shape of the icing wind tunnel icing test according to claim 2, characterized by comprising the following steps of: the step of obtaining the numerical icing curve comprises the step of obtaining a two-dimensional numerical data point set { (x) of test icing in a wind tunnel icing test by adopting a hot knife methodi，yi) I |, 1, 2, …, N }, and an ice-shaped curve is obtained after two-dimensional numerical representation.
4. The parameterization method for the ice shape of the icing wind tunnel icing test according to claim 1, characterized by comprising the following steps of: the calculating the curvature change of the numerical ice curve and selecting the characteristic points on the numerical ice curve according to the curvature change rule specifically comprise:
calculating the curvatures of all data points on the numerical deicing curve and the curvature change between adjacent data points;
and m characteristic points are selected on the numerical deicing curve according to the magnitude relation of curvature change to obtain a coordinate point set { lambda } of all the characteristic pointsj(ξj，ηj)|j＝1，2，…，m}。
5. The parameterization method for the ice shape of the icing wind tunnel icing test according to claim 4, characterized by comprising the following steps of: the method for selecting m characteristic points on the numerical deicing curve according to the size relation of curvature change comprises the following steps:
selecting a characteristic points at the positions of which the curvature change is smaller than a given threshold value;
b characteristic points are selected at all positions with curvature change larger than a given threshold value.
6. The parameterization method for the ice shape of the icing wind tunnel icing test according to claim 1, characterized by comprising the following steps of: the method for carrying out regression interpolation on the characteristic points on the numerical deicing curve by using the regression model to obtain the smooth parametric deicing curve comprises the following steps:
taking the numerical deicing curve as an input object, and performing regression interpolation by using a regression Kriging model to obtain an interpolation model;
and outputting interpolation results of the positions of all the characteristic points to obtain a smooth parametric deicing curve with noise points on the numerical deicing curve filtered.
7. The parameterization method for the ice shape of the icing wind tunnel icing test according to claim 6, characterized by comprising the following steps of: taking the numerical deicing curve as an input object, and performing regression interpolation by using a regression Kriging model to obtain an interpolation model, wherein the interpolation model specifically comprises the following steps:
the data point set of the numerical icing curve { (x)i，yi) 1, 2, …, N into a polar coordinate data point set { (r)i，θi)|i＝1，2，…，N}；
Using a set of polar data points { (r)i，θi) And (3) performing regression Kriging model on the | i ═ 1, 2, …, N to obtain an interpolation model Y (X).
8. The parameterization method for the ice shape of the icing wind tunnel icing test according to claim 7, characterized by comprising the following steps of: outputting interpolation results of positions of all the characteristic points to obtain a smooth parametric deicing curve with noise points on the numerical deicing curve filtered, wherein the smooth parametric deicing curve specifically comprises the following steps:
set of coordinate points of m feature points { lambdaj(ξj，ηj) 1, 2, …, m into a corresponding set of polar points { κ |j(ρj，εj)|j＝1，2，…，m}；
Each polar coordinate ρjSubstitution into interpolation model Y (X) yields a new set of polar coordinate points { κ'j(ρj，ε′j)|j＝1，2，…，m}；
Converting the coordinate points into a coordinate point set { (x) 'in a Cartesian coordinate system'j，y′j) And j equals to 1, 2, …, m, and a parametric deicing curve for filtering noise is obtained.
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| CN118351336B (en) * | 2024-06-17 | 2024-08-20 | 上海交通大学四川研究院 | Icing wind tunnel test similarity conversion method based on ice complexity |
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