CN103697863B

CN103697863B - A kind of model in wind tunnel anamorphic video measuring vibrations modification method of multiple constraint

Info

Publication number: CN103697863B
Application number: CN201310697880.8A
Authority: CN
Inventors: 陈德华; 杨振华; 易凡; 唐立新; 何岭松; 唐亮; 陈海峰; 陈俊明; 毛代勇; 高川; 杜宁
Original assignee: High Speed Aerodynamics Research Institute of China Aerodynamics Research and Development Center
Current assignee: High Speed Aerodynamics Research Institute of China Aerodynamics Research and Development Center
Priority date: 2013-12-18
Filing date: 2013-12-18
Publication date: 2015-10-28
Anticipated expiration: 2033-12-18
Also published as: CN103697863A

Abstract

The invention discloses a kind of model in wind tunnel anamorphic video measuring vibrations modification method of multiple constraint, comprise the steps: to arrange video observation camera; Set up picture point projection observation equation; Set up rigid body and epipolar-line constraint equation; Build iterative equation; Iteration asks for system of equations optimum solution; Reconstruct Current camera attitude and model attitude.Good effect of the present invention is: not only make use of the Rigid Constraints condition of test model fuselage features point, but also make use of the Rigid Constraints condition of test chamber wallboard unique point, further increase test model wing unique point and look the conllinear constraint condition in measure geometry more, creatively all constraint condition is become the iterative equation of Unified Form, have and solve that iteration convergence is fast, solving precision is high, the advantage such as position and attitude obtaining test model can be solved simultaneously.

Description

Multi-constraint wind tunnel test model deformation video measurement vibration correction method

Technical Field

The invention relates to the field of computer vision and photogrammetry, in particular to a multi-constraint wind tunnel test model deformation video measurement vibration correction method, which is an engineering application of a machine vision measurement technology in a high-speed wind tunnel test.

Background

In the wind tunnel test process, the test model wing is elastically deformed under the action of aerodynamic load. For a wing with a large aspect ratio, the deformation seriously affects the aerodynamic characteristics of the aircraft, deviates from the design requirement, and must be corrected, so that the deformation of a test model needs to be accurately measured in the wind tunnel test process. The non-contact optical measurement method has the advantages of small interference on a wind tunnel flow field, high measurement precision and no change of the geometric shape of a test model, and is the most widely applied wind tunnel test model deformation measurement method internationally at present.

The method is characterized in that an optical measurement technology is applied to a wind tunnel, particularly a video measurement technology is applied to a high-speed wind tunnel, and a key technical problem which needs to be solved is how to deal with the problem that the measurement precision is seriously reduced due to the change of the attitude of a camera caused by the field vibration of the wind tunnel. In order to ensure the accuracy and reliability of the measured data in the whole wind tunnel test process, vibration correction must be carried out on each frame of image in the test process. In The document "monitoring of Optical Wing formation Measurements at The imaging Development Center" (WimRuyten, Marvin transmitters.47th AIAA interference science measuring and calculating The Deformation of The wind tunnel test model, in order to correct The attitude change of The wind tunnel caused by The vibration of The test section, The method uses The stereoscopic vision measurement technique to measure The Deformation of The wind tunnel test model, and The method regards The fuselage of The test model as an ideal rigid body during The blowing process, so that when The attitude of The test model changes, The relative position of The feature mark points on The fuselage of The model should be kept constant, and The attitude change deviation between cameras caused by The vibration can be calculated by using The constant constraint relationship and The initial value of The relative position of The index points of The model in The static state. However, only by using the rigid body constraint condition of the model body, only the relative position posture between the two cameras can be corrected, and the overall offset of the camera coordinate system in the world coordinate system of the test segment cannot be corrected, so that the current posture and position of the test model cannot be obtained. Meanwhile, as the body of the test model only occupies a small part of the effective measurement area, the method does not fully utilize all measurement characteristics, and the method is very sensitive to the internal parameters of the camera, and any small deviation of the internal parameters of the camera can cause a correction result to generate a large difference. The literature, "determination of camera position coordinates and attitude angles by model deformation video measurement" (rocha, zhangxue, sunstone, etc.. experimental hydrodynamics 2010, (6): 88-91) states that the offset of a single camera relative to the world coordinate system of a wind tunnel test segment is corrected by using a pyramid method, the method independently corrects the vibration deviation of each camera by using the image coordinates of characteristic mark points on a wall plate of the test segment, but the method does not effectively use the implicit constraint relationship between each camera and the test model, so that an additional step is needed to reconstruct the position and the attitude of the test model after correcting the vibration deviation of the camera attitude.

Disclosure of Invention

In order to overcome the defects in the prior art, the invention provides a multi-constraint wind tunnel test model deformation video measurement vibration correction method, which utilizes rigid constraint conditions of the fuselage characteristic points of the test model and rigid constraint conditions of the wall plate characteristic points of the wind tunnel test section, further increases collinear constraint conditions of wing characteristic points of the test model in multi-view measurement geometry, creatively changes all constraint conditions into an iterative equation in a unified form, and has the advantages of fast iterative convergence of solution, high solution precision, capability of simultaneously solving and obtaining the position and the posture of the test model and the like.

The technical scheme adopted by the invention for solving the technical problems is as follows: a multi-constraint wind tunnel test model deformation video measurement vibration correction method comprises the following steps:

step one, arranging a video observation camera:

the method comprises the following steps that two observation cameras are used for carrying out intersection imaging on measurement components of a test model, the two cameras synchronously trigger acquisition during testing, and the two cameras can simultaneously observe all characteristic mark points which are pre-arranged on a wind tunnel test section wallboard and on the test model;

establishing an image point projection observation equation;

step three, establishing a rigid body and polar line constraint equation:

step four, constructing an iterative equation;

step five, iteratively solving the optimal solution of the equation set;

and step six, reconstructing the current camera posture and the model posture.

Compared with the prior art, the invention has the following positive effects:

(1) and simultaneously, three constraint conditions of rigid body constraint of a machine body point of the test model, polar line constraint of a wing point of the test model and rigid body constraint of a wallboard point of the test section are utilized and are creatively transformed into a multivariable equation in a unified form, so that the subsequent iterative optimization solution calculation process is facilitated. Various implicit constraint conditions of a wind tunnel test section and a test model can be fully utilized, and a constraint equation and solution parameters can be flexibly selected according to the field condition; in the practical engineering application process, constraint conditions can be flexibly selected according to the wind tunnel field condition and the geometric shape of the test model, and an iterative equation and a calculation process are simplified.

(2) The method can be used for correcting the vibration deviation of the camera coordinate system in the wind tunnel test section coordinate system and the vibration deviation of the two cameras, and can calculate the real-time posture and position of the test model in the test section coordinate system at the same time.

Drawings

The invention will now be described, by way of example, with reference to the accompanying drawings, in which:

FIG. 1 is a schematic diagram of the pose arrangement of an observation camera on a test segment;

fig. 2 is a schematic diagram of the vibration situation of the observation camera in the test section when the wind tunnel blows, and the symbol in fig. 2: c1 and C2 are observation camera coordinate systems, C1 is defined to be coincident with the camera coordinate system, W is a test section coordinate system, and M is a test model coordinate system.

Detailed Description

The technical scheme of the invention is as follows:

firstly, carrying out intersection imaging on a wind tunnel test model according to a stereoscopic vision measurement principle; calibrating the system before testing; in the test process, the focal length, distortion, image principal point and other internal parameters of the camera are assumed to be kept fixed; meanwhile, the postures of the observation camera and the test model are assumed to be influenced by field airflow and vibration and have offset changes relative to a test section coordinate system.

Secondly, taking the three-dimensional initial coordinates of all the characteristic mark points in the zero state of the test model in a static state as reference, regarding a test model body and a test section wall plate as two independent rigid bodies, and keeping the three-dimensional relative position coordinates of the characteristic mark points in the test process fixed and unchanged; the wing of the test model is regarded as an elastic body, and the image coordinates of the characteristic points of the wing meet the epipolar constraint condition all the time in the test process according to the stereoscopic vision measurement principle.

And thirdly, solving the optimal solution of the equation by using a beam adjustment method by taking a photogrammetric collinear equation as an observation equation, taking rigid body constraint of a model fuselage, rigid body constraint of a test section wallboard and polar line constraint of a model wing as constraint conditions, taking the real-time attitude of the camera and the real-time attitude of the model as unknown variables, taking three-dimensional coordinates of all mark points in a zero state and the initial attitude of the camera as initial values for each frame of image in the test process.

As shown in fig. 1 and fig. 2, a multi-constraint wind tunnel test model deformation video measurement vibration correction method specifically includes the following steps:

step one, arranging a video observation camera:

the method comprises the following steps that two observation cameras (marked as a 1# camera and a 2# camera) are used for carrying out intersection imaging on measurement parts of a test model, the two cameras synchronously trigger acquisition during testing, and all characteristic mark points which are arranged on a wind tunnel test section wallboard and the test model in advance can be observed by the two cameras simultaneously. The arrangement method of the characteristic mark points comprises the following steps:

using the circular characteristic mark points, regarding the body of the test model as a rigid body, arranging more than 3 characteristic mark points on the rigid body, wherein the position distribution of the mark points can not be all on the same straight line; regarding the wing of the test model as an elastic body, and arranging more than 2 characteristic mark points on each measuring section in a straight line; the bottom of the wall plate of the test section is also regarded as a rigid body, more than 3 characteristic mark points are arranged on the rigid body, and the position distribution positions of the mark points cannot be all on the same straight line.

Step two, establishing an image point projection observation equation:

in the zero state of the wind tunnel test model, the initial value image coordinates and three-dimensional coordinates of all characteristic points are collected and calculated, and the initial value of the three-dimensional coordinates of the characteristic points corresponding to the test section coordinate system is set asThe relative pose relationship matrix between the two cameras isDefining a camera coordinate system as a No. 1 camera coordinate system, and defining the initial value of the three-dimensional coordinate of the feature point in the camera coordinate system asIn the wind tunnel test process, due to the influence of field vibration, the position of the camera in the test section deviates from the initial value, and a new pose relationship between the n frame image cameras is set asThe three-dimensional coordinates of the feature points in the camera coordinate system areCorresponding to the three-dimensional coordinates under the coordinate system of the test section as

Setting the three-dimensional coordinates of any feature point P in the coordinate systems of the 1# camera and the 2# camera as P₁=[X₁ Y₁ Z₁]^TAnd P₂=[X₂ Y₂ Z₂]^TWhich satisfy the relationshipThe normalized image point coordinates after corresponding distortion correction are(normalized formula isWherein x and y are characteristic point image coordinates, u and v are image principal points, and f_x、f_yEquivalent focal length).

From the above definitions and the camera aperture imaging principle, the collinearity equation for the feature points P is simplified as follows:

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rewriting is in matrix form:

\{\begin{matrix} M_{1} P_{1} = 0 \\ M_{2} (R_{c}^{n} P_{1} + T_{c}^{n}) = 0 \end{matrix} - - - (0.1)

in the formula

<math><mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mn>1</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow></math>

<math><mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow></math>

The above equation holds for all feature points at all times:

in the zero state, the voltage of the power supply is zero,

\{\begin{matrix} M_{1}^{i} P_{1}^{0} = 0 \\ M_{2}^{i} (R_{c}^{0} P_{1}^{0} + T_{c}^{0}) = 0 \end{matrix}

the image of the n-th frame is processed,

\{\begin{matrix} M_{1}^{i} P_{1}^{n} = 0 \\ M_{2}^{i} (R_{c}^{n} P_{1}^{n} + T_{c}^{n}) = 0 \end{matrix} - - - (0.2)

wherein,

<math><mrow> <msubsup> <mi>M</mi> <mn>1</mn> <mi>i</mi> </msubsup> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>-</mo> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mn>1</mn> <mi>i</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mn>1</mn> <mi>i</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow></math>

<math><mrow> <msubsup> <mi>M</mi> <mn>2</mn> <mi>i</mi> </msubsup> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>-</mo> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mn>2</mn> <mi>i</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mn>2</mn> <mi>i</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow></math>

step three, establishing a rigid body and polar line constraint equation:

(1) for the three-dimensional coordinates of the feature mark points on the test model body, the three-dimensional coordinates meet rigid body constraint conditions, and for a rigid body, the rotation and translation are only 6 degrees of freedom in total. When the wind tunnel blows, the observed position and posture of the model body under the camera coordinate system change intoThe following rigid body can be obtainedConstraint equation:

P_{ic}^{n} = R_{mc}^{n} P_{ic}^{0} + T_{mc}^{n} - - - (0.3)

wherein i represents the characteristic points of the model fuselage,and representing the three-dimensional coordinate values of all the feature points in the camera coordinate system in the zero state of the model.

The position and attitude change of the lower camera coordinate system of the test segment coordinate system is represented as Rⁿ、TⁿThe position and posture change of the test model is expressed asThe following relationship holds:

\{\begin{matrix} R_{m}^{n} = R^{n} R_{mc}^{n} \\ T_{m}^{n} = R^{n} T_{mc}^{n} + T^{n} \end{matrix} - - - (0.4)

(2) for the characteristic mark points of the wall plate of the test section, the three-dimensional coordinates under the coordinate system of the test section are kept fixed, and the three-dimensional coordinates under the corresponding camera coordinate system also meet the rigid body constraint condition:

R^{n} P_{jc}^{0} + T^{n} = P_{jc}^{n} - - - (0.5)

where j represents a wallboard feature point.

(3) For a test model wing, the rigidity is relatively weak, elastic deformation occurs due to the action of aerodynamic load, and the image point coordinates meet the epipolar constraint condition:

{(P_{k 2}^{n})}^{T} {EP}_{k 1}^{n} = 0 - - - (0.6)

in the formula, k represents the characteristic point of the model wing,homogeneous coordinates of normalized image points for 1# camera and 2# cameraAnd

order to

T_{c}^{n} = [\begin{matrix} t_{1} \\ t_{2} \\ t_{3} \end{matrix}],

Then

E = R_{c}^{n} [\begin{matrix} 0 & {- t}_{3} & t_{2} \\ t_{3} & 0 & {- t}_{1} \\ {- t}_{2} & t_{1} & 0 \end{matrix}]

Step four, constructing an iterative equation:

substituting the constraint (0.3) into the observation equation (0.2) yields:

\{\begin{matrix} M_{1}^{i} (R_{mc}^{n} P_{ic}^{0} + T_{mc}^{n}) = 0 \\ M_{2}^{i} (R_{c}^{n} (R_{mc}^{n} P_{ic}^{0} + T_{mc}^{n}) + T_{c}^{n}) = 0 \end{matrix}

setting function

\{\begin{matrix} F_{1} = M_{1}^{i} (R_{mc}^{n} P_{ic}^{0} + T_{mc}^{n}) = 0 \\ F_{2} = M_{2}^{i} (R_{c}^{n} (R_{mc}^{n} P_{ic}^{0} + T_{mc}^{n}) + T_{c}^{n}) = 0 \end{matrix}

Definition vector w = [ a b c =]^TOperator of

Using the formula of Rodrigues transformation R = (I + | w_×)(I-|w|_×)^-1Representing a rotation matrix, definingCorresponding parameters are

w_{mc} = [\begin{matrix} a_{mc} \\ b_{mc} \\ c_{mc} \end{matrix}],

Corresponding parameters are

w_{c} = [\begin{matrix} a_{c} \\ b_{c} \\ c_{c} \end{matrix}] .

Will function F₁And F₂To perform a first order TaylorAnd expanding to obtain an error formula:

let the objective function L₁And L₂The mode of (2) is minimum, a normal equation set can be obtained, and the method is rewritten into a matrix form:

the above formula holds for all fuselage points i, where

Similarly, the coordinates of the characteristic points of the wallboard satisfy the formula:

\{\begin{matrix} F_{3} = M_{1}^{j} (R^{n} P_{jc}^{0} + T^{n}) = 0 \\ F_{4} = M_{2}^{j} (R_{c}^{n} (R^{n} P_{jc}^{0} + T^{n}) + T_{c}^{n}) = 0 \end{matrix} .

definition of RⁿHas a mean difference parameter of

w_{n} = [\begin{matrix} a_{3} \\ b_{3} \\ c_{3} \end{matrix}],

ΔTⁿ=ΔT_nAnd performing first-order Taylor expansion on the above formula to obtain an error formula:

to make the objective function L₃And L₄Is minimized, can be obtainedThe system of normal equations:

the above formula holds true for all the feature points j of the wall plate, wherein

Defining function for model wing feature pointsWhereinDefinition of

P_{k 1}^{n} = {[\begin{matrix} x_{1} & y_{1} & 1 \end{matrix}]}^{T},

Function f₅Is deformed into

f_{5} = {(P_{k 2}^{n})}^{T} [x_{1} R_{c}^{n} t_{1} + y_{1} R_{c}^{n} t_{2} + R_{c}^{n} t_{3}] = 0

For function f₅To carry outFirst order taylor expansion, resulting in an error equation:

in the formula,

rewriting is in matrix form:

the above equation holds for all the wing feature points k, so that the objective function is

The norm is the minimum, and a system of normal equations can be obtained:

assuming that the system has i model fuselage feature points, j test segment wall plate points and k model wing feature points, combining the formulas (0.7), (0.8) and (0.10), and assuming that all the formulas have the same weight, an iterative equation containing 18 adjustment variables can be obtained:

in the above formula

In the process of actual engineering application, the equation can be simplified according to the actual test conditions of the wind tunnel site. For example, for missile-type test models without elastomeric components, all of the equations above may be eliminatedAndthe iterative equation can also hold; for another example, without considering the constraints of the panel points of the test segment, the coefficient matrix of the above iterative equation removes the last 4j rows and modifies the adjustment parameter to

The vibration deviation of the camera can be solved, but the current posture of the model cannot be solved at the moment.

The above iterative equation is abbreviated below as:

JΔD=ΔF (0.11)

step five, iteratively solving the optimal solution of the equation set:

relative attitude between cameras at system zero state(derived from system calibration) decomposition constitutes the initial value of the iteration

D_{0} = [\begin{matrix} 0 \\ 0 \\ w_{c} \\ T_{c} \\ 0 \\ 0 \end{matrix}],

Taking the three-dimensional coordinates and image coordinates of all characteristic points in the zero state of the model asAnd the normalized coordinates of the image points of the wing feature points at the moment of the image frame nA deviation matrix deltaf is constructed. The correction Δ D = (J) of the current adjustment parameter D is obtained by using equation (0.11)^T J)^-1J^TΔ F, update iteration parameter D = D₀+ΔD。

Recalculating matrices J and delta F by using the new iteration parameter as an initial value, calculating the correction delta D of the new adjustment parameter D, and repeating the iteration calculation until delta F^TAnd when the delta F is smaller than a given threshold value, the iterative calculation process is ended, and the obtained iterative parameter D is the optimal solution meeting all constraint conditions of the system.

And step six, reconstructing the current camera posture and the model posture. Including new pose relationships for the camera at the current timeCamera coordinate system vibration correction Rⁿ、TⁿAnd model pose

And expressing the optimal solution D obtained by the calculation in the steps as follows: d = [ a ]₁ b₁ c₁ t₁₁ t₁₂ t₁₃ a₂ b₂ c₂ t₂₁ t₂₂ t₂₃ a₃ b₃ c₃ t₃₁ t₃₂ t₃₃]^TAnd if so, the pose relationship between the 1# camera and the 2# camera at the current moment of the system is as follows:

\{\begin{matrix} R_{c}^{n} = (I + S_{2}) {(I - S_{2})}^{- 1} \\ T_{c}^{n} = {[\begin{matrix} t_{21} & t_{22} & t_{23} \end{matrix}]}^{T} \end{matrix},

wherein

S_{2} = [\begin{matrix} 0 & {- c}_{2} & b_{2} \\ c_{2} & 0 & {- a}_{2} \\ {- b}_{2} & a_{2} & 0 \end{matrix}]

The vibration correction quantity of the camera coordinate system is as follows:

\{\begin{matrix} R^{n} = (I + S_{3}) {(I - S_{3})}^{- 1} \\ T^{n} = {[\begin{matrix} t_{31} & t_{32} & t_{33} \end{matrix}]}^{T} \end{matrix},

wherein

S_{3} = [\begin{matrix} 0 & - c_{3} & b_{3} \\ c_{3} & 0 & {- a}_{3} \\ - b_{3} & a_{3} & 0 \end{matrix}]

The attitude of the test model in the test section coordinate system is as follows:

\{\begin{matrix} R_{m}^{n} = R^{n} (I + S_{1}) {(I - S_{1})}^{- 1} \\ T_{m}^{n} = R^{n} [\begin{matrix} t_{11} \\ t_{12} \\ t_{13} \end{matrix}] + T^{n} \end{matrix},

wherein

S_{1} = [\begin{matrix} 0 & - c_{1} & b_{1} \\ c_{1} & 0 & - a_{1} \\ {- b}_{1} & a_{1} & 0 \end{matrix}]

。

Claims

1. A multi-constraint wind tunnel test model deformation video measurement vibration correction method is characterized by comprising the following steps: the method comprises the following steps:

step one, arranging a video observation camera:

establishing an image point projection observation equation;

step three, establishing rigid body and polar line constraint equations;

step four, constructing an iterative equation;

step five, iteratively solving the optimal solution of the equation set;

and step six, reconstructing the current camera posture and the model posture.

2. The multi-constraint wind tunnel test model deformation video measurement vibration correction method according to claim 1, characterized in that: the arrangement method of the characteristic mark points comprises the following steps: using circular characteristic mark points, arranging more than 3 characteristic mark points on a machine body of the test model, wherein the position distribution of the mark points can not be all on the same straight line; more than 2 characteristic mark points are arranged on each measuring section of the wing of the test model in a straight line; more than 3 characteristic mark points are arranged at the bottom of the wallboard of the test section, and the distribution positions of the mark points cannot be all on the same straight line.

3. The multi-constraint wind tunnel test model deformation video measurement vibration correction method according to claim 1, characterized in that: and step three, the constraint equations comprise a test model fuselage rigid constraint equation, a test section wallboard rigid constraint equation and a test model wing polar line constraint equation.