CN103077315A - Method for rebuilding front and back oval edges of aerial blade based on error control - Google Patents

Abstract

The invention discloses a method for rebuilding front and back oval edges of an aerial blade based on error control, which is used for solving the technical problem of poor anti-noise performance existing in the conventional high-precision rebuilding method for a front edge of a blade. According to the technical scheme, the method comprises the following steps of: selecting region points covering the front edge or the back edge of the blade; sequencing the region points; performing spline fitting on the sequenced region points for three times; performing equal-arc-length encryption discretion on fitted spline curves, and marking beginning and end discrete points as P0i and P1i respectively; fitting discrete points at a P0iP1i section by using a least square method, and marking beginning and end discrete points on the intersection of the P0iP1i section and a fitting oval as P0(i+1) and P1(i+1) respectively; calculating an average error epsiloni ranging from the discrete points to an ith fitting oval; and setting an iteration control error as epsilon till the epsiloni is less than or equal to epsilon to finish iteration. According to the method, the front and back oval edges of the blade are rebuilt by adopting an error control-based iterative fitting method on the basis of fitting through the least square method, so that points on a non-oval circular arc in the selected region are prevented from participating in fitting, and the anti-noise performance is improved.

Description

Based on the oval front and rear edge method for reconstructing of the aerial blade of error control

Technical field

The present invention relates to the oval front and rear edge method for reconstructing of a kind of aerial blade, be specifically related to the oval front and rear edge method for reconstructing of a kind of aerial blade based on error control.

Background technology

The shape of blade front and rear edge plays key effect to the aeroperformance of whole blade.Traditional front and rear edge generally is designed to circular arc, and along with going deep into that blade is studied, numerous experiments and numerical value studies show that, adopt non-circular arc front edge, can obviously improve the aeroperformance of blade such as oval leading edge in recent years.

In the process that oval front and rear edge is rebuild based on the blade of measurement data, the selection area point for the treatment of match may comprise the point on leaf basin, the blade back, if the point on this non-elliptic arc is participated in match, can rebuild front and rear edge and have a huge impact.Document " high-precision reconstruction of blade leading edge research " aviation power journal " (2006; 21 (4): 722-726) " discloses a kind of high-precision reconstruction of blade leading edge, the method proposes based on the least square method of belt restraining data point to be carried out match, then use the result of match as initial value, determine oval center by the limit of ellipse-polar curve character, and then obtain oval characteristic parameter; Simultaneously, utilize the characteristics that lattice point increases error of fitting greatly that go out on the non-elliptic arc in the literary composition, determine lattice point: centered by leading edge point, carry out ellipse fitting after the enhancing data point, calculate the maximum relative error of oval feature parameter; Wherein, relative error can reduce along with increasing of normal point, if error of fitting increases manyfold (can set threshold values) before and after increasing certain point, and continues to increase data point, and error does not obviously reduce, and this point namely is lattice point; Point out in the literary composition that the error that random noise produces does not possess above-mentioned Variation Features; Therefore, for the measurement data of leaf packet Noise, utilize the method to carry out oval front and rear edge reconstruction and have certain difficulty.

Summary of the invention

In order to overcome the existing poor deficiency of high-precision reconstruction of blade leading edge noiseproof feature, the invention provides the oval front and rear edge method for reconstructing of a kind of aerial blade based on error control.The method is carried out in least square method on the basis of match for the measurement data of aerial blade, adopts the iterative fitting method based on error control, and the oval front and rear edge of blade is rebuild.By specification error the iterative fitting process is controlled, avoided as much as possible the participation of the point on non-elliptic arc match in the selection area; Under the prerequisite that guarantees reconstruction precision, have preferably noiseproof feature, can improve the reconstruction quality of the oval front and rear edge of blade.

The technical solution adopted for the present invention to solve the technical problems is: the oval front and rear edge method for reconstructing of a kind of aerial blade based on error control is characterized in may further comprise the steps:

(1) reads in the discrete measurement data of molded line of aerial blade, the selected region point that covers blade inlet edge or trailing edge;

(2) region point is sorted;

(3) region point after the ordering is carried out Cubic Spline Fitting;

(4) to the SPL of institute's match carry out etc. arc length encrypt discrete, and with the whole story discrete point be designated as respectively P _0i, P _1i

(5) with least square method to P _0iP _1iThe section discrete point carries out match, and with P _0iP _1iSection and fitted ellipse intersection the whole story discrete point be designated as respectively P _{0 (i+1)}, P _{1 (i+1)}Ellipse fitting method is as follows:

1. as quafric curve f (x, y)=ax ²+ 2bxy+cy ²+ 2dx+2fy+g=0 the b that satisfies condition ²-ac＜0 o'clock, quafric curve f (x, y) is expressed as ellipse.In the formula, a, b, c, d, f, g are the coefficient of quadratic polynomial equation.

Be provided with n data point P _i(x _i, y _i) participate in ellipse fitting, will be converted into based on the ellipse fitting of algebraic distance the least square problem of following belt restraining, the objective function of setting up ellipse fitting is as follows:

$\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}f{(x_i,y_i)}^{2}s.t.b^2-\mathrm{ac}=-1$

2. adopt least square method to try to achieve the coefficient a of quadratic polynomial equation, b, c, d, f behind the g, obtains fitted ellipse, and the elliptic geometry calculation of parameter is as follows:

The oval center of circle (x ₀, y ₀): $x_0=\frac{\mathrm{cd}-\mathrm{bf}}{b^2-\mathrm{ac}},$ $y_0=\frac{\mathrm{af}-\mathrm{bd}}{b^2-\mathrm{ac}}$

Transverse r _a: $r_a=\sqrt{\frac{2({\mathrm{af}}^2+{\mathrm{cd}}^2+{\mathrm{gb}}^2-2\mathrm{bdf}-\mathrm{acg})}{(b^2-\mathrm{ac})[\sqrt{{(a-c)}^2+{4b}^2}-(a+c)]}}$

Ellipse short shaft r _b: $r_b=\sqrt{\frac{2({\mathrm{af}}^2+{\mathrm{cd}}^2+{\mathrm{gb}}^2-2\mathrm{bdf}-\mathrm{acg})}{(b^2-\mathrm{ac})[-\sqrt{{(a-c)}^2+{4b}^2}-(a+c)]}}$

Rotation angle

(6) calculate discrete point to the average error ε of the i time fitted ellipse _i:

In the formula: j=1,2,3 ..., N, d _jBe the distance that j discrete point arrives gained fitted ellipse in the step (5), N is for participating in counting out of match;

(7) setting the iteration control error is ε: to ε _iCompare with ε, if ε _i≤ ε calculates and finishes; Otherwise, work as ε _iDuring ε, be positioned at P after casting out the i time iteration _{0 (i+1)}P _0iAnd P _{1 (i+1)}P _1iBetween point on the non-elliptic arc; Make i=i+1, to P _0iP _1iBetween the match of discrete point repeating step (5), until satisfy ε _iDuring≤ε, iteration finishes.

The invention has the beneficial effects as follows: because the method is carried out in least square method on the basis of match for the measurement data of aerial blade, adopt the iterative fitting method based on error control, the oval front and rear edge of blade is rebuild.By specification error the iterative fitting process is controlled, avoided as much as possible the participation of the point on non-elliptic arc match in the selection area; Under the prerequisite that guarantees reconstruction precision, have preferably noiseproof feature, improved the reconstruction quality of the oval front and rear edge of blade.

Below in conjunction with drawings and Examples the present invention is elaborated.

Description of drawings

Fig. 1 is the oval front and rear edge method for reconstructing of the aerial blade process flow diagram that the present invention is based on error control.

Fig. 2 the present invention is based on the oval front and rear edge method for reconstructing of the aerial blade embodiment of error control through the reconstruction design sketch of seven matches.

Fig. 3 is the synoptic diagram that the present invention is based on the oval front and rear edge method for reconstructing of the aerial blade first fit of error control.

Fig. 4 is the synoptic diagram that the present invention is based on the i time match of the oval front and rear edge method for reconstructing of aerial blade of error control.

Fig. 5 is the synoptic diagram that the present invention is based on the final match of the oval front and rear edge method for reconstructing of aerial blade of error control.

Embodiment

With reference to Fig. 1～5.The oval front and rear edge method for reconstructing of the aerial blade concrete steps that the present invention is based on error control are as follows:

(1) reads in the discrete measurement data of molded line of blade, the selected region point that covers blade inlet edge or trailing edge;

(2) region point is sorted;

(3) region point after the ordering is carried out Cubic Spline Fitting;

(4) to the SPL of institute's match carry out etc. arc length encrypt discrete, and with the whole story discrete point be designated as respectively P _0i, P _1i

(5) with least square method to P _0iP _1iThe section discrete point carries out match, and with P _0iP _1iSection and fitted ellipse intersection the whole story discrete point be designated as respectively P _{0 (i+1)}, P _{1 (i+1)}Ellipse fitting method is as follows:

1. set up the objective function of ellipse fitting:

In the plane, by the quadratic polynomial equation

F (x, y)=ax ²+ 2bxy+cy ²The curve that+2dx+2fy+g=0 is represented is called quafric curve.

In the formula, a,, c, d, f, g are the coefficient of quadratic polynomial equation.In above-mentioned equation, satisfy condition: b ²-ac＜0 o'clock, quafric curve f (x, y) is expressed as ellipse.

Be provided with n data point P _i(x _i, y _i) participate in ellipse fitting, will be converted into based on the ellipse fitting of algebraic distance the least square problem of following belt restraining, the objective function of setting up ellipse fitting is as follows:

$\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}f{(x_i,y_i)}^{2}s.t.b^2-\mathrm{ac}=-1$

2. adopt least square method to try to achieve the coefficient a of quadratic polynomial equation,, c, d, f behind the g, obtains fitted ellipse, and the elliptic geometry calculation of parameter is as follows:

The oval center of circle (x ₀, y ₀): $x_0=\frac{\mathrm{cd}-\mathrm{bf}}{b^2-\mathrm{ac}},$ $y_0=\frac{\mathrm{af}-\mathrm{bd}}{b^2-\mathrm{ac}}$

Transverse r _a: $r_a=\sqrt{\frac{2({\mathrm{af}}^2+{\mathrm{cd}}^2+{\mathrm{gb}}^2-2\mathrm{bdf}-\mathrm{acg})}{(b^2-\mathrm{ac})[\sqrt{{(a-c)}^2+{4b}^2}-(a+c)]}}$

Ellipse short shaft r _b: $r_b=\sqrt{\frac{2({\mathrm{af}}^2+{\mathrm{cd}}^2+{\mathrm{gb}}^2-2\mathrm{bdf}-\mathrm{acg})}{(b^2-\mathrm{ac})[-\sqrt{{(a-c)}^2+{4b}^2}-(a+c)]}}$

Rotation angle

(6) calculate discrete point to the average error ε of the i time fitted ellipse _i:

In the formula: j=1,2,3 ..., N, d _jBe the distance that j discrete point arrives gained fitted ellipse in (5), N is for participating in counting out of match;

(7) setting the iteration control error is ε: to ε _iCompare with ε, if ε _i≤ ε calculates and finishes; Otherwise, work as ε _iDuring ε, be positioned at P after casting out the i time iteration _{0 (i+1)}P _0iAnd P _{1 (i+1)}P _1iBetween point on the non-elliptic arc; Make i=i+1, to P _0iP _1iBetween the match of discrete point repeating step (5), until satisfy ε _iDuring≤ε, iteration finishes.

Preferred embodiment.Oval O ₇For satisfying the fitted ellipse of specification error requirement, i.e. O ₇Be its center, R _a, R _bBe respectively its long and short axle radius.Arbitrarily selected certain blade measurement data, concrete steps are as follows:

(1) reads in the discrete measurement data of molded line of blade, choose the region point that covers leading edge;

(2) region point is sorted, data point is from 0,1,2 ..., N;

(3) adopt cubic spline to carry out curve fitting, get curve L ₀

(4) to the SPL L of institute's match ₀The arc-length methods such as employing are encrypted discrete, get 1000 points, i=1, and the whole story, discrete point was designated as respectively P _0i, P _1iThe arc length such as the uniform sampling method of curved surface has, etc. parameter, etc. the action method, in same sampling precision situation, the image data amount is little by arc length sampling methods such as simulating, verifyings, it is discrete that the sample mode of the arc length such as present embodiment employing carries out the encryption of data.

(5) to comprising P _0i, P _1iAt interior P _0iP _1iBetween discrete point adopt least square method to carry out ellipse fitting; And with P _0iP _1iSection is designated as respectively P with the discrete point at the whole story of fitted ellipse intersection _{0 (i+1)}, P _{1 (i+1)}

The average error of (6) establishing the i time match is ε _i, and

D in the formula _jBe the distance of a j discrete point to the (5) step gained fitted ellipse, N is for participating in counting out of match;

(7) preset error ε=0.005, to error ε _iCompare with predefined error ε; If ε _i≤ ε calculates and finishes.Otherwise, work as ε _iDuring ε, be positioned at P after casting out the i time iteration _{0 (i+1)}P _0iAnd P _{1 (i+1)}P _1iBetween point on the non-elliptic arc; Make i=i+1, to P _0iP _1iBetween the match of discrete point repeating step (5), until satisfy ε _iDuring≤ε, iteration finishes.

Table 1 is the oval leading edge process of reconstruction that this example is specifically controlled based on error, and iteration seven times satisfies the error requirements of setting, the average error of match this moment: ε ₇=0.005mm, oval long and short semiaxis is respectively: R _a=1.011mm, R _b=0.604mm.

Table 1

According to embodiment as can be known, the present invention carries out iterative fitting by adopting the method for error control to discrete point, and casts out one by one the point on the non-elliptic arc in the selection area.In actual applications, the user only needs by setup control error ε process of reconstruction to be controlled, and can obtain required reconstructed results.

Claims (2)

1. oval front and rear edge method for reconstructing of the aerial blade based on error control is characterized in that may further comprise the steps:

(1) reads in the discrete measurement data of molded line of aerial blade, the selected region point that covers blade inlet edge or trailing edge;

(2) region point is sorted;

(3) region point after the ordering is carried out Cubic Spline Fitting;

(4) to the SPL of institute's match carry out etc. arc length encrypt discrete, and with the whole story discrete point be designated as respectively P _0i, P _1i

(5) with least square method to P _0iP _1iThe section discrete point carries out match, and with P _0iP _1iSection and fitted ellipse intersection the whole story discrete point be designated as respectively P _{0 (i+1)}, P _{1 (i+1)}Ellipse fitting method is as follows:

1. as quafric curve f (x, y)=ax ²+ 2bxy+cy ²+ 2dx+2fy+g=0 the b that satisfies condition ²-ac＜0 o'clock, quafric curve f (x, y) is expressed as ellipse; In the formula, a, b, c, d, f, g are the coefficient of quadratic polynomial equation;

Be provided with n data point P _i(x _i, y _i) participate in ellipse fitting, will be converted into based on the ellipse fitting of algebraic distance the least square problem of following belt restraining, the objective function of setting up ellipse fitting is as follows:

$\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}f{(x_i,y_i)}^{2}s.t.b^2-\mathrm{ac}=-1$

2. adopt least square method to try to achieve the coefficient a of quadratic polynomial equation, b, c, d, f behind the g, obtains fitted ellipse, and the elliptic geometry calculation of parameter is as follows:

The oval center of circle (x0, y0): $x_0=\frac{\mathrm{cd}-\mathrm{bf}}{b^2-\mathrm{ac}},$ $y_0=\frac{\mathrm{af}-\mathrm{bd}}{b^2-\mathrm{ac}}$

Transverse ra: $r_a=\sqrt{\frac{2({\mathrm{af}}^2+{\mathrm{cd}}^2+{\mathrm{gb}}^2-2\mathrm{bdf}-\mathrm{acg})}{(b^2-\mathrm{ac})[\sqrt{{(a-c)}^2+{4b}^2}-(a+c)]}}$

Ellipse short shaft r _b: $r_b=\sqrt{\frac{2({\mathrm{af}}^2+{\mathrm{cd}}^2+{\mathrm{gb}}^2-2\mathrm{bdf}-\mathrm{acg})}{(b^2-\mathrm{ac})[-\sqrt{{(a-c)}^2+{4b}^2}-(a+c)]}}$

Rotation angle

(6) calculate discrete point to the average error ε of the i time fitted ellipse _i:

In the formula: j=1,2,3 ..., N, d _jBe the distance that j discrete point arrives gained fitted ellipse in the step (5), N is for participating in counting out of match;

(7) setting the iteration control error is ε: to ε _iCompare with ε, if ε _i≤ ε calculates and finishes; Otherwise, work as ε _iDuring ε, be positioned at P after casting out the i time iteration _{0 (i+1)}P _0iAnd P _{1 (i+1)}P _1iBetween point on the non-elliptic arc; Make i=i+1, to P _0iP _1iBetween the match of discrete point repeating step (5), until satisfy ε _iDuring≤ε, iteration finishes.

2. the oval front and rear edge method for reconstructing of the aerial blade based on error control according to claim 1 is characterized in that: described setting iteration control error ε=0.005.

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