RU2551396C1 - Method of contactless measurements of geometric parameters of object in space and device for its realisation - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: invention relates to the method of contactless measurements of geometric parameters of an object in space. During realisation of the method on the surface of the object they identify one and/or more separate areas, for which one may in advance make several different simplified mathematical parametric models on the basis of previously known geometric laws of the investigated object, which characterise shape, position, movement, deformation. Markers are applied onto the object surface, grouping by separate areas into separate groups. Then they register images of central projection of the specified markers. And on their basis with account of previously known geometric laws of the investigated object and using methods of multidimensional minimisation of differences they determine sought for geometric parameters of the object.

EFFECT: increased accuracy and validity of measurements of geometric parameters of an object when using one chamber, especially under conditions of restricted surrounding space and limited optical access.

4 cl, 14 dwg

Description

The invention relates to the field of optical non-contact measurements of geometric parameters of the shape, position, movement and deformation of objects in space, in particular, to close photogrammetry and video grammetry, and can be used in scientific research, in mechanical engineering, construction, medicine, and in other fields for geometric measurements parameters of objects in a cramped environment and limited optical access.

Numerous optical methods and devices for non-contact measurements of the geometric parameters of objects are known. The most widely known are photogrammetry methods [A. Lobanov Photogrammetry. - M .: Nedra, 1984]. The main purpose of photogrammetry is to measure the geometric parameters of sections of the surface of the earth from aerial photographs and images from space, i.e. from a great distance. This is the so-called far-field photogrammetry. Also, these methods are also used for non-contact measurements of the geometric parameters of objects at short distances of units and tens of meters - this is near-field photogrammetry or near photogrammetry. Recently, photogrammetry methods have been implemented using digital image registration tools and are called digital photogrammetry or video grammetry. Near-field photogrammetry is widely used in scientific research, industrial production, construction, medicine and other fields.

The essence of photogrammetry is to determine the three coordinates x, y, z of a point on the surface of an object under study from two coordinates u, v of its central projection onto a flat image. In the general formulation, such a problem is incorrect: for each point there are three unknowns and only two equations. In near photogrammetry, three ways of resolving the uncertainty of the problem of reconstructing coordinates can be formulated:

The first way is stereo shooting. In this case, two images of an object are recorded from different angles (observation points) and three coordinates are restored by combining the coordinates of the points of two images [RF Patent No. 2173445 C1, IPC G01C 11/00, 2000]. In more complex cases, you may need three or more images from different angles. To implement the stereo method, at least two

recording camera images or obtaining two frames using one camera sequentially from different points if the object under study is static.

The second way is the use of structured illumination of the object under study, in particular, a secant plane of light or a collimated beam of light rays [RF Patent No. 2105265 C1, IPC G01B 11/24, 1994]. In this case, the system of equations is supplemented by an equation describing the known trajectories of the propagation of light rays. To implement the methods of structured lighting, one camera is enough, but an additional projector is needed to ensure the formation of a beam of structured lighting.

The third way is using a priori information, i.e. data obtained from other sources. This can be, in particular, pre-known information about the limited degrees of freedom of the object, the relative position of a number of characteristic points, the nature of the movement or deformation of the object, etc. The implementation of this direction most often comes down to the method of marker points, in which the surface of the object under study is applied special markers that are clearly distinguishable in the resulting images [RF Patent No. 2316726 C1, IPC G01B 11/16, 2006]. Markers can be circles, crosses, lines, and more complex coded marks and targets [Tyuflin Yu.S., Stepanyants DG, Knyaz VA, Zheltov S.Yu. Precision calculation of the coordinates of the points of an object in near photogrammetry // Geodesy and Cartography. - 2004. No. 11. - S. 29-32]. Information on the initial coordinates of these markers on the surface of the object is usually sufficient to solve the uncertainty of the task of reconstructing the three coordinates of the points on the surface of the object in space from the two coordinates of the response of these points on the images.

Numerous methods and devices are known for non-contact measurements of the geometric parameters of objects. Most of them are based on the stereo survey method and are designed to measure the geometric parameters of the contours and terrain through aerial surveys or satellite imagery of the earth’s surface [PN Bruevich Photogrammetry. Textbook for high schools. - M .: Nedra, 1990, S.285].

There are a large number of commercial digital photogrammetry devices for measuring the geometric parameters of objects in the near zone (1-5 m), constructed according to the scheme with one, as well as with two or more cameras for recording the central projection in the form of images containing a means of measuring the coordinates of the projections of markers on the image, informationally connected via USB-, GigE-, or another interface with a central projection recording device and means for determining the parameters of exterior orientation (high-performance laptop and software) [Prospectus for SmartSCAN and StereoScan systems from Cybercom Ltd. // <http://www.cybercom.ru>].

A common drawback of stereo imaging methods and devices and devices using structured lighting is the need to use two or more central projection recording devices or structured lighting projectors in several positions (points in space). However, in experimental aerodynamics, industrial production, and in a number of other cases, the object under investigation is usually located in a cramped environment and limited optical access, for example, in the working part of a wind tunnel, or in a test chamber having a limited number of optical windows, or on a machine, conveyor or stand. Placing two cameras to form a stereo base or a camera and a projector, as in a method using structured lighting, is often an insoluble problem. In addition, the specific features of the studied object can also impede the use of these methods. For example, in studies of fast-moving dynamic processes due to the inevitable delay of pulses in the electronic circuits of the synchronization system, it is impossible to ensure strictly simultaneous operation of two cameras or a camera and a projector, as a result of which combining data from different devices can lead to significant measurement errors.

Another disadvantage of the known methods of stereometry is that it is designed to measure the geometric parameters of undeformable static objects on the surface of the earth, characterized by a single mathematical model. Most of the tasks of scientific research are related to objects subject to significant deformations, or even to the composition of individual fragments of an object having different geometric patterns of shape, movement and deformation. Application of the method to the study of such objects leads to uncontrolled measurement errors or is completely impossible.

The most effective way of non-contact measurements of the geometric parameters of an object under such conditions is the marker method using only one camera. A known method and device for measuring small deformations of the material of structures [RF Patent No. 2316726 C1, IPC G01B 11/16, 2006], in which markers are applied to the surface of the test object, the central projection of these markers is recorded in the form of images at specified times and deformations are determined material of constructions according to the displacements of the projections of these markers in the images.

Methods and devices using a priori information are the simplest in technical implementation - they require only one digital camera and one observation point. This circumstance gives a significant advantage in the application of these methods, especially in conditions of cramped space surrounding the object or limited optical access to it, which is typical, for example, for aerodynamic, strength, flight or other experiment, industrial production control.

The closest solution is the method of non-contact measurements of the geometric parameters of an object in space using a single camera [A.W. Burner, N. Liu. "Videogrammetric Model Deformation Measurement Technique". Journal of Aircraft, vol. 38, No.3, 2001], selected as a prototype, in which markers are applied to the surface of an object at specified points, the central projection of these markers is recorded as an image, the external orientation parameters of the central projection are determined, and during processing images measure the two-dimensional coordinates of the projections of the markers on the image, from which the coordinates of the markers in space are calculated using the formulas of the central projection using certain parameters of the external orientation, and from them find the desired metric parameters of an object in space.

A device for implementing this method, also selected as a prototype [A.W. Burner, N. Liu. "Videogrammetric Model Deformation Measurement Technique". Journal of Aircraft, vol. 38, No.3, 2001], includes a means for applying markers to the surface of the object being studied, a device for recording the central projection of markers in the form of an image, a means for determining the external orientation parameters of the central projection recording device, a unit for measuring coordinates of the projections of markers in the image and a unit for computing the desired geometric parameters of the object.

The disadvantage of this method and device is that it provides for the measurement of only the coordinates of the points of the surface of an object in space, while the goal of any scientific research is to determine generalized geometric parameters that correspond to the selected hypothesis or model of the process being studied, the object. To find generalized parameters from the measured coordinates, additional data, additional procedures, and additional calculations are required, which leads to an increase in the measurement error. This is especially evident in the optimization of research results, since measuring the coordinates of points without taking into account the process model requires some optimization criteria, and binding the process to coordinates - others. And these optimization criteria often turn out to be mutually incompatible, which can often lead to conflicts in multidimensional minimization and, as a result, to uncontrolled measurement errors and a decrease in their reliability.

The technical result of the invention is to increase the accuracy and reliability of measurements of the geometric parameters of the object when using one camera, especially in conditions of cramped surrounding space and limited optical access.

The technical result is achieved by the fact that in the method of non-contact measurements of the geometric parameters of the object in space, in which markers are applied to the surface of the object at specified points, the central projection of these markers is recorded as an image, the external orientation parameters of the central projection are determined, and two-dimensional coordinates are measured during image processing projections of markers in the image, of which according to the formulas of the central projection using certain parameters of external orientation calculate the coordinates of the markers in space, and from them find the desired geometric parameters of the object in space, according to the invention, on the basis of previously known geometric laws of the studied object on its surface, separate or create additional separate zones characterized by their own geometric parameters, for each of them set their own system coordinates, form their own mathematical parametric model, whose own parameters are associated with the desired geometric these parameters of the object with known geometric laws, and they attach their own mathematical parametric model to the central projection formulas, in addition, when markers are applied to the surface, they are grouped by separate zones into separate groups, and when processing images for each of these isolated groups, two-dimensional coordinates of the projections of markers on image, determine their own parameters of the external orientation of the central projection and from them according to the formulas of the central projection and Using the intrinsic mathematical parametric model using intrinsic exterior orientation parameters, eigenparameters of the corresponding mathematical model are calculated using multidimensional minimization of differences methods, and the desired geometric parameters of the object are found using the calculated intrinsic parameters of mathematical models and previously known geometric patterns.

Additionally, the technical result in the method is achieved by the fact that on the basis of previously known geometric patterns of the object under study, one of the isolated zones is isolated or created in such a way that it is possible to consider the points of its surface as mutually fixed, take it as the base, determine the parameters of the relative position of the markers in it own coordinate system and own parameters of the external orientation of the central projection of the base zone, when forming your own mathematical parameter cal models take into account the basic zone settings mutual arrangement of markers in it, and the image processing parameters of all the other own their own mathematical models calculated using their own parameters of external orientation of the central projection of the base area and the desired geometric object options are in the system chassis region coordinates.

In many cases, increasing the accuracy of measurements is also facilitated by the fact that, on the basis of previously known geometric laws of the object under study, separate zones are isolated or created in the form of sections so that in each of them surface points can be considered mutually stationary and moving as a whole when forming their own mathematical parametric models of sections determine the parameters of the relative positions of the markers in their own coordinate systems, their own mathematical pair etricheskie model equations form a position and movement of said sections own coordinate system, and image processing determined external orientation parameters own central projection sections and the desired geometrical parameters of the object is found from the values of its own external orientation parameters for each section.

The specified technical result is achieved by the fact that in the device for non-contact measurements of the geometric parameters of the object in space, containing means for applying markers on the surface of the object being studied, a device for recording the central projection of markers in the form of an image, a means for determining the external orientation parameters of the registration device for the central projection, a unit for measuring coordinates of the projections of markers on the image and the calculation unit of the desired geometric parameters of the object, according to the invention, additionally introduced a tool for creating separate groups of markers associated with a tool for applying markers on the surface of the studied object, a tool for determining the parameters of the relative positions of markers in a separate group, a tool for generating mathematical parametric models for separate groups of markers, information related to a tool for creating separate groups of markers and a means for determining parameters relative position of markers, block for isolating isolated groups of projections of markers on the image the image, connected to the block for measuring the coordinates of the projections of markers on the image, and the block for multidimensional minimization of discrepancies for each isolated group of markers, connected by its input to the block for selecting separate groups of projections of markers and informationally connected with the tool for generating mathematical parametric models and with the tool for determining the parameters of exterior orientation output - with the unit for calculating the desired geometric parameters of the object.

The technical effect in the method and device in all cases is achieved due to the optimal use of a priori information both for solving the uncertainty of the task of restoring the coordinates of the object’s points in space, and for matching the geometric parameters of the isolated zones with the general parameters of the position, movement and deformation of objects in space. At the same time, it is proposed to formulate mathematical regression problems for multidimensional minimization in connection with the mathematical model of the process under study, which leads to a reduction in the number of integral transformations, the number of degrees of freedom in regression problems and, thereby, minimization of methodological and computational errors in determining the desired generalized geometric parameters.

The list of figures illustrating the operation of the proposed method and device.

Figure 1 shows a structural diagram of a device for non-contact measurements of the geometric parameters of an object in space for the implementation of this method.

Figure 2 shows a diagram illustrating the proposed method of non-contact measurements of the geometric parameters of the object in space with the allocation of separate zones characterized by their geometric parameters.

Figure 3 shows a diagram of the allocation of separate zones on the surface of the model wing of the aircraft.

Figure 4 shows a diagram of a device with the allocation of separate sections on the surface of the model of the wing of the aircraft and the base zone based on the mounting model.

Figure 5 shows an example of a working image of an elastic-like model of a wing in a T-103 TsAGI wind tunnel and a graph of the results of measurements of bending strain at different values of the flow velocity.

Figure 6 shows a diagram of a device for measuring deformations of the upper and lower surfaces of an airplane wing model simultaneously.

Figure 7 shows photographs of the installation for studies of the deformation of the upper and lower surfaces of the model of an airplane wing in the wind tunnel T-101 TsAGI.

On Fig shows the result of measurements of the shape of the wing slat of the aircraft in deviated and non-deviated positions in 10 sections of the wing (280 points).

Figure 9 shows an example implementation of a method and apparatus for studying the warping strain of large-scale samples and structural elements during strength studies.

Figure 10 shows the result of measuring the field of normal deformations of the structural panel of the aircraft.

Figure 11 shows a diagram of non-contact measurements of distributed tangential deformations of structural elements when they are tensile during strength studies with the addition of a base zone.

On Fig shows the result of measurements in this way the fields of two components of the tangent deformation of a structural panel of composite material with a gap on the stand for static strength tests.

On Fig shows a diagram of a device for implementing the method of non-contact measurements of geometric parameters of the position of the object in space.

On Fig shows working images of a helicopter device in two angular positions and graphs of the results of measurements of linear displacements and orientation angles of the model in different modes in the flow of the wind tunnel T-104 TsAGI.

The structural diagram of the device for implementing the proposed method of non-contact measurements of the geometric parameters of the object in space is shown in figure 1. The diagram shows conventionally:

1 investigated object;

2 means of applying markers on the surface of the investigated object;

3 markers;

4 means for creating separate groups of markers associated with means 2 for applying markers to the surface of the object under study;

5 separate group of markers;

6 basic group of markers;

7 means for determining the relative positions of markers in a separate group,

8 device for recording the central projection of markers in the form of an image - camera;

9 means for determining the parameters of the external orientation of the device 8 registration of the Central projection,

10 central projection - image;

11 projections of markers in the image;

12 means for generating mathematical parametric models for separate groups of 5 and 6 markers, information related to means 4 for creating separate groups of markers and means 7 for determining the relative positions of markers,

13 unit for measuring coordinates of projections of markers in the image;

14 block allocation of separate groups of projections of markers in the image connected to the block 13 measuring the coordinates of the projections of markers;

15 block multidimensional minimization of discrepancies for each separate group of markers, connected by its input to the block 14 of the allocation of separate groups of projections of markers, and information related to the means 12 of the formation of mathematical parametric models and means 9 for determining the parameters of exterior orientation;

16 block calculating the desired geometric parameters of the object, connected by its input to block 15 multidimensional minimization of discrepancies;

17 subsystem for collecting and processing images, combining blocks 13-16;

18 base of the investigated object;

19 light source.

Functional blocks 13-16, forming a subsystem 17 for collecting and processing images, are usually implemented on the basis of a personal or mobile computer.

When registering the central projection, the functional dependence of the desired coordinates x, y, z of points in space on the projected coordinates u, v of the projections of these points measured in the image has the form

Here: x ₀ , y ₀ , z ₀ are the coordinates of the projection center in the coordinate system of the object,

u ₀ , v ₀ , w ₀ - coordinates of the origin of the coordinate system (SC) of the image in the coordinate system of the camera,

M _ij (i, j = 1, 2, 3) - matrix elements of the guide cosines of the camera coordinate system sequentially at angles α, β, γ around the coordinate axes of the SK object. The matrix of guide cosines can have several different presentation options through the angles of successive rotations in the form of a rotation matrix, in particular,

Thus, the functional dependence (1) is determined by a set of at least nine constants. Six of them x ₀ , y ₀ , z ₀ and α, β, γ determine the position and orientation of the device for recording the central projection in the coordinate system of the object. In photogrammetry, they are usually called exterior orientation parameters, and the three remaining u ₀ , v ₀ , w ₀ are called interior orientation parameters. The parameters u ₀ , v ₀ are the coordinates of the main point of the image, and w ₀ - the rear conjugate distance of the lens. When registering a distant object, the value of w ₀ is close to the focal length of the lens. When using digital cameras as the registration device for the central projection of the internal cameras, it is more convenient to express the internal orientation parameters in units of image resolution - pixels. Parameters of interior orientation also include parameters of geometric image distortions, such as distortion coefficients, different scales, etc.

The internal orientation parameters are a characteristic of the central projection recording device (camera). They are usually determined by a separate procedure when setting up the center projection recording device.

Markers on the surface of the investigated object are applied using a variety of means. It can be laser printers, spray guns with stencils, paint brushes, markers and other tools. The technique has proved itself well, in which single or groups of markers are printed using a laser printer on self-adhesive paper, and then glued to the surface of the object under study. Markers 3 can be of any shape, be flat concentrated marks, small-scale regular or irregular structures, bulk targets distributed on the surface systematically or randomly. They must be clearly distinguishable in images and identifiable, i.e. establishing a unique correspondence between their spatial coordinates and the two-dimensional coordinates of their projections on the images.

The central projection is recorded as an image using various means, conventionally called cameras. This can be, for example, photo, film, video or digital cameras recording the image of an object in the optical, infrared, ultraviolet or other spectral range, can be optical, laser, radar, acoustic scanners or other devices that form the central projection of the object as an image.

The external orientation parameters of the central projection are determined, as a rule, in the calibration procedure using additional tools called control devices or test objects containing a set of markers with known coordinates in space. The test object is placed in the measurement space, its central projection is recorded in the form of an image, and two-dimensional coordinates of the projections of markers on the image are measured. Knowing the initial coordinates of the markers of the test object and the measured coordinates of the projections of these markers on the image, numerical values of the external orientation parameters of the central projection are calculated by multidimensional minimization of differences according to the central projection formulas (1).

When processing digital images, the two-dimensional coordinates of the projections of markers on the image are measured in a computer using specialized programs that provide measurements of the two-dimensional coordinates of specified image features by group statistics analysis, correlation analysis, sequential tracking, etc. These methods allow you to measure the coordinates of image points with a subpixel error reaching 0.1-0.01 pixel shares.

Usually, the coordinates of the markers in space are calculated from these coordinates using the central projection formulas using certain external orientation parameters, and from them the desired geometric parameters of the object in space are found.

However, the functional dependence (1) is not enough to reliably find the desired coordinates x, y, because the unknown z coordinate is included in the right side of the equations. According to the method of a priori information, system (1) must be supplemented with another equation, which is a mathematical model of the shape, position, movement or deformation, for example, in the form

where P is the vector of eigenparameters characterizing the object or the process under study as a whole or its individual zone.

When processing data, dependence (3) is attached to the operating characteristic (1) and, the resulting system of equations is solved with respect to x, y and z.

In the general case, for the entire surface of the investigated object, a unified mathematical model (3) cannot be compiled in advance, since often this is the ultimate goal of research and measurement. However, one can always distinguish one, two or more separate zones based on previously known geometric laws of the object under study, characterized by their separate geometric parameters, for which several different simplified mathematical parametric models can be prepared in advance. Therefore, to increase the accuracy and reliability of the results of measurements of the geometric parameters of an object in space, based on previously known geometric laws of the object under study, additionally isolated zones are identified or created on its surface, characterized by their own geometric parameters of shape, position, movement and deformation. For each of them, they set their own coordinate system, form their own mathematical parametric model (3), whose own parameters P are related to the desired geometric parameters of the object by known geometric patterns, and attach their own mathematical parametric model to the central projection formulas (1). When markers are applied to the surface, they are grouped in separate zones into separate groups, and when processing images for each of these separate groups, two-dimensional coordinates of the projections of markers in the image are distinguished, their own parameters for the external orientation of the central projection are determined, and from them using the central projection formulas (1) and attached own mathematical parametric model (3) using the own parameters of external orientation is calculated by multidimensional minimization methods expectations own parameters of the corresponding mathematical model.

The desired geometric parameters of the object are found using the calculated proper parameters of mathematical models and previously known geometric patterns.

The diagram in figure 2 illustrates the essence of the method. The diagram shows the studied object 1, markers 3, marker groups 5, a device (camera) 8 for recording the central projection in the form of an image, and the central projection (image) 10. Let the studied surface 1 perform some complex movements and deformations. The diagram shows two states of this surface. It is not possible to formalize these movements with a single equation. However, zones I-VII are distinguished on the surface of the object under study so that, for example, zone / can be considered immovable, zone II as performing parallel movements, zone III as performing angular slopes, zones IV and V - performing linear movements and bending, and zones VI and VII - linear displacements, inclinations and bends. Each zone has its own simplified mathematical parametric model (3).

When markers are applied to the surface, they are grouped according to the selected zones, and during image processing, the corresponding groups of marker projections in the image are distinguished and their two-dimensional coordinates are measured. After that, for each group of markers, a mathematical nonlinear regression is compiled that relates the measured coordinates of the markers in the image with the desired coordinates of the markers in space using the system of equations (1) and (3) using the previously defined exterior orientation parameters. Having solved the regression using multidimensional minimization of discrepancies (usually the least squares method), they find the desired coordinates of the markers in space, as well as the values of the isolated parameters of the corresponding mathematical models. In some cases, the found coordinates of the markers in space are the final result of measurements. In other cases, generalized geometric parameters, which are found using well-known patterns from the isolated parameters P of the corresponding mathematical models, are of great interest. Regression can be built, in particular, so that the result of its solution will be its own parameters of external orientation in the coordinate system of the corresponding zone.

The most urgent task of experimental aerodynamics is associated with measurements of the deformation of load-bearing structural elements with aerodynamic profiling: wings, tail elements, controls, propeller blades and rotors, etc. All of them are characterized by high elongation and rigidity along the longitudinal axis, many times exceeding the rigidity in two other axes. Figure 3 shows a diagram of the implementation of the method of non-contact measurements of the geometric parameters of the deformation of the model of the wing of an aircraft in the flow of a wind tunnel. The diagram shows the studied object 1, markers 3, groups of markers 5, a device (camera) 8 for recording the central projection in the form of an image and the selected surface areas of the object I-III. Let us direct the Oz axis along the wing stiffness axis. We can assume that along this axis, the deformation is negligible, and the cross sections as a whole acquire linear Δx, Δy and angular Δα displacements in the plane perpendicular to the Oz axis. The coordinate z of the sections in the general case cannot be considered constant, but due to the smallness of its changes, mathematical models can be specified as a series expansion in powers of small deviations along the axes Ox and Oy

where the coefficients a _x , a _y , b _x , b _y , ... are set according to the known stiffness matrix of the object. At the same time, on the Oz axis, a number of zones can be distinguished in which mathematical models have a simple form:

- in the zone z = z ₀₁ = const

- in the zone z = z ₀₂ + a _x · Δx ₂ + a _y · Δy ₂

, и т.д.- in zone III

, etc.

In the tasks of near photogrammetry and videogrammetry, a digital camera or video camera usually serves as a registration device for the central projection in the form of an image. A means of creating and marking groups of markers can be means of applying markers directly to the surface of the object under study with paint (black on a light background or white on a dark) in the form of round, oval or other shapes of spots, crosses, lines or marks of a more complex shape. A laser marker was a convenient means of applying markers, which prints markers of a given shape on self-adhesive paper and then sticks them on. Often used means of applying markers in the form of a self-adhesive retroreflective film, also glued to the surface of the object. In this case, high luminous efficiency is achieved. This method of applying markers has advantages in studies of large objects, when its illumination is of technical complexity, or in fast-moving processes when a very short exposure is required. In some cases, markers can be independent structures (targets) that have the property of retroreflection, and are attached mechanically to the surface of the object.

The means 7 for determining the parameters of the relative positions of the markers in the group can be instrumental measuring tools, contact or optical, special test objects installed on the site of the studied group of markers with the combination of coordinate systems.

The subsystem 17 for collecting and processing images is usually a computer or laptop with the appropriate software package, but it is also possible to use autonomous means for registering and storing images, for example, in the memory of the camera itself, which is typical for high-speed cameras.

The tool for determining the parameters of exterior orientation (calibration tool) is a special test object containing a group of markers, the coordinates of which are pre-measured with accuracy that exceeds the planned accuracy of the measuring system. These test objects can have a linear shape with the location of the markers in one coordinate, a flat shape with the location of the markers in two coordinates, or a three-dimensional structure with markers located in space. Means for determining the parameters of exterior orientation should usually be supplemented by means of orientation of the test object and the binding of coordinate systems.

The light sources 19 can be continuous, pulsed or stroboscopic depending on the nature of the task. They can differ in the principle of operation (incandescent, gas-discharge, semiconductor, spark, luminescent, etc.) with power or energy and radiation spectrum.

The proposed measurement method in various versions has been tested in experimental aerodynamics in the study of aeroelasticity and strength of aerodynamic models and structural elements of aircraft in the following current tasks:

- studies of the deformation of "rigid", elastic-like and dynamically-like models of an aircraft in the flow of a wind tunnel;

- measuring the position parameters of the fixed models of the aircraft in the flow of the wind tunnel;

- measurement of motion parameters in the space of free-flying models;

- studies of the motion and deformation of rotating structural elements: blades, blades, etc .;

- studies of the fields of tangential deformations of samples of new structural materials and structural elements from them;

- studies of warping and buckling of shells, skins and structural elements of aircraft.

Consider the most characteristic examples of the implementation of the method and device.

a) The measuring system (camera) and the base (attachment point) of the object under study are mutually immobile, and the object under study has limited degrees of freedom. In this case, choose the direction in which the displacements of the object’s points are minimal and orient the OZ axis of the working coordinate system along this direction. When markers are applied to the surface of a sample, they are grouped according to sections perpendicular to the OZ axis. When compiling a mathematical parametric model, the z coordinate of these sections is measured by tools, equations (3) are set for possible changes of this coordinate during object movements, and they supplement the system of equations (1). Due to the small displacements along the Oz axis, such a mathematical model can be very simple.

b) If it is impossible to assume for the same objects of research that the camera and the base of the object are mutually motionless, then according to claim 2, an object is allocated or additionally created on the object or its base to create a base zone in which surface points can be considered mutually motionless (for example , zone I in figure 2 and figure 3). The three-dimensional coordinates of the markers on it are measured in advance by tools in its own coordinate system, which is associated with the base of the object. A basic parametric model is created for the basic group of markers, a mathematical regression is created and solved, and the parameters found from the regression determine the new external orientation parameters for the functional dependence (1), which are then used to solve the regressions for the remaining zones. As a result, the coordinates of the markers in space and the geometric parameters of the corresponding zones will be found in the coordinate system of the base zone or associated with the base of the object.

Figure 4 shows a diagram of non-contact strain measurements of a model of an airplane wing in the air flow of a wind tunnel. The diagram shows: the studied object 1, markers 3, separate groups of markers 5, applied to the measuring zones of the surface of the object in the form of sections, the basic group of markers 6, a device (camera) 8 for recording the central projection in the form of an image, means 9 for determining external orientation parameters , subsystem 17 for collecting and processing images, base 18 of the investigated object. The model is cantilevered on a flat base 18. In the air flow under the action of aerodynamic loads, the model undergoes displacements and deformations, and the base only displaces as a whole. Therefore, the basic group of markers 6 is selected on the basis of 18, and the results of measurements of the linear and angular displacements of the wing sections 5 will be presented in the coordinate system associated with the base. An example of a working image (central projection) of an elastic-like model of a wing in a T-103 TsAGI wind tunnel and a graph of the results of measurements of bending strain at different values of the speed of the incoming air flow are shown in Fig. 5. The round black markers were printed by a laser printer on white self-adhesive paper, the paper was cut into squares and the squares were glued in predetermined sections to the lower surface of the model. The bottom row of markers is glued to the base and serves as the basis for measurements.

c) When researching large-scale objects or objects of complex shape, when the research area cannot be covered by one central projection (one camera), it is recommended to register two or more central projections of different parts of the object’s surface as separate images, and apply several measuring groups of markers on its surface the number of cameras and one or more additional, basic, so that the measuring groups of markers each fall into the field of view of their camera, and the basic ones, at least partially, in the field of rhenium of two or more cameras at the same time. When processing camera images covered by one group of basic markers, it is advisable to determine additional functional dependences of the coordinate system of points in space on the SK points of each image, and set the coordinate system of points in space and the mathematical parametric model common for all central projections, and make mathematical regressions separately for each central projection. Solving the regression, it is possible to determine the parameters of mathematical models, from which to find the desired parameters of the shape, movement and deformation of the entire object under study.

We will consider in more detail the operation of this method in the most typical application using the example of measurements of the deformation of an elastic slat of a large-scale model of an airplane wing in the flow of a large wind tunnel T-101 TsAGI. Based on the requirements of the test task, a measuring system was developed that contains two identical channels for measuring the deformation of the upper and lower surfaces of the toe of the model at the same time. Fig. 6 is a diagram, and Fig. 7 is a photograph showing the implementation of the method for measuring deformation of both the upper and lower surfaces of the wing model in the flow of a wind tunnel. Two cameras 8 with receiving lenses are located in the left cutter above and below the symmetrical wing chords. It was not possible to see both surfaces with one camera, so two cameras were used, and the SCs are connected by a group of markers deposited on the base and falling into the field of view of both cameras simultaneously (see Fig. 7, c).

An important element of the measuring system is a system of markers applied to the surface of the model. Here, concentrated markers are used in the form of white oval spots on a black background applied to the surface of the model. The sizes and orientation of the spots were chosen so that their central projections in the image had a round shape and the same predetermined diameter of about 5-7 pixels. The purpose of the base marker system is to provide the possibility of combining the coordinate systems of two cameras with the coordinate system of the model. In addition, in conditions where the cameras are not stationary due to the general deformation of the model and cut-offs, the system of basic markers must fulfill an additional role - compensation of camera displacements.

On Fig shows a graph with the results of measurements of the shape of the elastic toe of the slat in the deflected and non-deflected positions.

g) Another example demonstrates the implementation of the proposed method for non-contact measurements of the distributed normal deformation of the structural panel in the study of its strength (Fig.9). A panel subjected to compression loading undergoes warping in a local area of the surface at the center of which the origin of the coordinate system is placed. The perimeter of this area, supported by stiffeners, does not experience warping. Therefore, two zones are distinguished on the studied surface region, one along the perimeter is taken as the base, and the other in the middle is the measurement region. Applying the considered version of the measurement method, we obtain the distribution of the normal warpage in the second zone in the coordinate system specified by the first zone. An example of the result of such measurements is shown in FIG. 10.

e) There are frequent cases when on the surface of the object there is no undeformable zone, which can be taken as the base. Then it is advisable to introduce an additional object in the field of view of the camera that is not subject to deformation, and apply a basic group of markers with previously measured three-dimensional coordinates on its surface. Figure 11 shows a diagram of non-contact measurements of distributed tangential deformations of structural elements when they are tensile during strength studies with the addition of a base zone. Under load, the entire sample is deformed, therefore, an additional element 20 is introduced as a base zone, on which a basic group of markers 6 is placed. Additional element 20 is semi-rigidly connected to sample 1 so that, remaining undeformed, it does not introduce distortions into the deformation picture. On Fig shows the result of measurements in this way the fields of two components of the tangent deformation of a structural panel of composite material with a gap when testing for strength.

, М₁. Затем в ходе испытаний в заданные моменты времени производят отсчеты текущих значений параметров внешнего ориентирования $${\overrightarrow{X}}_2=\left(x_2,y_2,z_2\right)$$

, М₂. Искомые параметры положения объекта в исходной СК можно найти с помощью преобразований видаf) In the particular case when all points of the object’s surface can be considered mutually motionless and moving as a whole, according to claim 2 of the formula, one zone is distinguished, it is taken as the base, when creating its mathematical parametric model, three-dimensional parameters of the relative positions of the markers in their own system are measured coordinates, and when processing images using multidimensional minimization of discrepancies, determine the values of the external orientation parameters, which are the geometric parameters of the position of the system oordinat camera in its own UK facility. If the parameters obtained are reversed according to the rules of coordinate transformation, then we obtain six parameters of the position of the object in the camera coordinate system. To determine the parameters of the position of the object in a given coordinate system that is not associated with the camera SK, for example, laboratory, the following procedure is recommended. First, the object is set to its original position so that its coordinate system coincides with the specified one. A count is made, according to the method according to claim 2, and the initial values of the parameters of the exterior orientation are fixed, vector in the form $${\overrightarrow{X}}_{\mathrm{one}}=\left(x_{\mathrm{one}},y_{\mathrm{one}},z_{\mathrm{one}}\right)$$

, M ₁ . Then, during the tests at specified times, the current values of the parameters of the external orientation are counted $${\overrightarrow{X}}_2=\left(x_2,{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000011.png,00000019.png"\; state="\{\{state\}\}">y</figure-callout>}}_2,z_2\right)$$

, M ₂ . The desired parameters of the position of the object in the original SK can be found using transformations of the form

- текущее положение начала СК, т.е положение объекта в исходной системе координат, M₂₁ - матрица направляющих косинусов СК объекта в текущем положении в исходной СК. Углы ориентации объекта в исходной СК можно определить из матрицы M₂₁, воспользовавшись формулой матрицы вращения (2).Where $${\overrightarrow{X}}_{21}=\left(x_{21},y_{21},z_{21}\right)$$

- the current position of the beginning of the SK, that is, the position of the object in the original coordinate system, M ₂₁ is the matrix of directional cosines of the SK of the object in the current position in the original SK. The orientation angles of the object in the initial SC can be determined from the matrix M ₂₁ using the formula of the rotation matrix (2).

On Fig shows a diagram of a device for implementing the method of non-contact measurements of geometric parameters of the position of the object in space. When testing the rotors of a helicopter in a wind tunnel, the model is mounted on shock absorbers. Under the influence of main rotor thrust and aerodynamic forces from the incoming flow, the position of the model changes, in particular, the angle of attack of the model changes, which leads to significant errors in determining the aerodynamic characteristics. To correct the results of determining the aerodynamic characteristics, it is necessary to measure the current values of the model position parameters in the wind tunnel flow. Experience has shown that such measurements should be non-contact. To perform such measurements by the proposed method, a basic group of markers is created on the model, the relative position of which cannot be changed, three-dimensional parameters of the relative position of these markers are measured, a reference is made in the initial position of the model, and then at each current set position. Fig. 14 shows two working images of a model with basic markers in positions with angles of attack α of model 0 (a) and -10 ° (b), as well as graphs of linear (c) and angular (d) parameters obtained by the considered method in a series testing measurements of orientation angles and linear displacements of the model of a helicopter device in different modes in the flow of a wind tunnel T-104 TsAGI. The measurement results showed that under the influence of forces the angle of attack changes by 1-2 °.

Claims (4)

1. The method of non-contact measurements of the geometric parameters of the object in space, in which markers are applied to the surface of the object at specified points, the central projection of these markers is recorded in the form of an image, the external orientation parameters of the central projection are determined, and when processing images, two-dimensional coordinates of the projections of the markers on the image are measured, of which, according to the formulas of the central projection using certain parameters of the external orientation, the desired geometric parameters are found about object in space, characterized in that on the basis of previously known geometric laws of the object under study, additionally isolated zones are identified or created on its surface, characterized by their own geometric parameters, for each of them they set their own coordinate system, form their own mathematical parametric model, whose own parameters are connected with the desired geometric parameters of the object with known geometric patterns, and attach their own mathematical parametric model to the central projection formulas, in addition, when markers are applied to the surface, they are grouped by separate zones into separate groups, and when processing images for each of these isolated groups, two-dimensional coordinates of the marker projections on the image are distinguished, their own parameters for the external orientation of the central projection are determined and from them according to the formulas of the central projection and the attached own mathematical parametric model using eigenpairs ters exterior orientation are computed by minimizing the differences multidimensional own parameters appropriate mathematical model and the desired geometric parameters of the object found using the calculated own parameters of mathematical models and geometric patterns known in advance. 2. The method according to claim 1, characterized in that on the basis of previously known geometric laws of the object under study, one of the isolated zones is isolated or created in such a way that it is possible to consider the points of its surface as mutually fixed, take it as the base, and determine the parameters of the mutual the location of the markers in their own coordinate system and their own parameters of the external orientation of the central projection of the base zone, when forming your own mathematical parametric model of the base zone yvayut parameters mutual arrangement of markers in it, and image processing parameters of all other own own mathematical models calculated using the exterior orientation parameters own central projection base zone and the desired geometric object parameters are in the coordinate system of the base zone. 3. The method according to claim 1 or 2, characterized in that on the basis of previously known geometric patterns of the object under study, separate zones are isolated or created in additional sections in such a way that in each of them surface points can be considered mutually fixed and moving as a whole, when forming their own mathematical parametric models of cross sections, they determine the parameters of the relative positions of the markers in their own coordinate systems, their own mathematical parametric models are formed in de equations of position and motion of the indicated own coordinate systems of the sections, and when processing images, they determine their own parameters of the external orientation of the central projection of the sections and the desired geometric parameters of the object are found from the values of the own parameters of the external orientation of each section. 4. A device for non-contact measurements of the geometric parameters of an object in space, containing means for applying markers to the surface of the object under study, a device for recording the central projection of markers in the form of an image, a means for determining the parameters of the external orientation of the registration device for the central projection, a unit for measuring coordinates of the projections of markers in the image, and a unit for calculating the desired geometric parameters of an object, characterized in that a means of creating groups of markers associated with the means of applying markers on the surface of the studied object, a means of determining the parameters of the relative positions of the markers in a separate group, a means of generating mathematical parametric models for separate groups of markers, information related to the means of creating separate groups of markers and a means of determining the parameters of the relative position of markers, block allocation of separate groups of projections of markers in the image connected to the coordinate measurement unit t projections of markers in the image, and a multidimensional minimization discrepancy unit for each isolated group of markers, connected by its input to the block for separating isolated groups of marker projections and information related to the tool for generating mathematical parametric models and the tool for determining the parameters of exterior orientation, and the output to the unit for calculating the desired geometric parameters of the object.

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