Uncertainty evaluation method, system, equipment and medium for large-scale polygonal coordinate measurement system

Abstract

The present invention belongs to the field of dimension measurement technology, and specifically relates to a method, system, device, and medium for evaluating the uncertainty of a large-scale multilateral coordinate measurement system. The method inputs the acquired target point coordinates into an error transfer model to obtain three coordinate uncertainty components corresponding to the coordinate values. This uncertainty coefficient is then calculated based on the uncertainty introduced by the offset of the reflector's optical center, and the uncertainty evaluation is performed. The present invention, based on the fundamental principles of the multilateral coordinate measurement system, simplifies the system coordinate system to reduce parameters, thereby reducing the amount of calculations. The method also provides a specific mathematical formula, which facilitates rapid evaluation at the measurement site and is easy for metrologists to learn and apply.

Description

Technical Field

[0001] The present invention belongs to the technical field of external dimension measurement, and in particular relates to an uncertainty evaluation method, system, equipment and medium for a large-scale polygonal coordinate measurement system. Background Art

[0002] The production quality of large-scale equipment manufacturing, ranging from several meters to hundreds of meters, in aerospace, rail transportation, shipbuilding, and wind power, requires high-precision large-scale measurement technology to ensure quality. To meet the measurement accuracy requirements of various large-scale structural components, a variety of large-scale coordinate measurement systems have been developed, including 3D coordinate machines, multilateral coordinate measurement systems, laser tracking absolute rangefinders, close-range photogrammetry systems, indoor global positioning systems (iGPS), and indoor space measurement and positioning systems (wMPS). Among them, multilateral coordinate measurement systems have the highest theoretical accuracy and are flexible and have the advantages of a large range.

[0003] The measurement uncertainty of a multilateral coordinate measurement system refers to the degree of dispersion in the system's measurements of a specific measured position. There are two main methods for evaluating the uncertainty of nonlinear, multi-input systems: the uncertainty propagation law method and the Monte Carlo method. The uncertainty propagation law method evaluates the impact of various input variables on the result by solving for the measurement uncertainty coefficient, offering the advantage of speed and convenience. In existing technology, as Sun Wei et al. ("Study on the Influence of Solution Method on Measurement Accuracy in Multilateral Coordinate Measurement Systems") discloses that, compared with synchronous solution methods, accurately calibrating system parameters beforehand can effectively improve measurement accuracy. However, the method described in their technical literature only considers the system parameter calibration process as a single variable and does not propose a method for evaluating the uncertainty of the entire measurement system. The output of large-scale multilateral coordinate measurement systems is multidimensional, so their measurement uncertainty is often evaluated using the time-consuming Monte Carlo method. However, while the Monte Carlo method can effectively evaluate measurement methods with different error models, it requires a very large amount of data, is time-consuming, and expensive. Summary of the Invention

[0004] In view of the problems of long time and high cost in the prior art when using the Monte Carlo method to evaluate the uncertainty of large-scale polygonal coordinate measurement systems, the purpose of the present invention is to provide a method, system, equipment and medium for evaluating the uncertainty of large-scale polygonal coordinate measurement systems. Starting from the basic principles of polygonal coordinate measurement systems, the system coordinate system is simplified to reduce parameters and the amount of calculation, which is conducive to rapid evaluation of measurement sites and is convenient for metrologists to learn and use.

[0005] The present invention is mainly achieved through the following technical solutions: a method for evaluating the uncertainty of a large-scale multilateral coordinate measurement system, which performs uncertainty evaluation on a large-scale multilateral coordinate measurement system composed of four laser tracking interferometers and a reflector, wherein one laser tracking interferometer serves as a measuring station for constructing a three-dimensional coordinate system; the method inputs the acquired target point coordinates into an error transfer model to obtain three coordinate uncertainty components corresponding to the coordinate values, and then combines the uncertainty introduced by the optical center offset of the reflector to calculate the uncertainty coefficient of the multilateral coordinate measurement system to perform uncertainty evaluation.

[0006] In order to better implement the present invention, the method further comprises the following steps:

[0007] Step S1, establishing a coordinate system;

[0008] Specifically, a three-dimensional coordinate system is first established through four measuring stations, and the coordinates of each measuring station in the coordinate system are recorded;

[0009] Step S2, obtaining the target point coordinates;

[0010] Specifically, the laser tracking interferometer corresponding to each measuring station is used to track the reflector, and the reflector is moved to the target position. The spatial coordinates output by the multilateral coordinate measurement system are the coordinates of the target point.

[0011] Step S3, obtaining three coordinate uncertainty components corresponding to the three coordinate values;

[0012] Specifically, the target point coordinates are input into the error transfer model to calculate the three coordinate uncertainty components corresponding to the three coordinate values;

[0013] Step S4: Calculate the uncertainty coefficient of the polygonal coordinate measurement system according to the three coordinate uncertainty components corresponding to the three coordinate values ​​and the uncertainty introduced by the optical center offset of the reflector.

[0014] In order to better implement the present invention, further, the error transfer model in step S3 calculates three coordinate uncertainty components corresponding to the three coordinate values ​​according to the coordinates of each measuring station, the actual distance between each measuring station and the target point, and the distance measurement uncertainty of each measuring station.

[0015] In order to better implement the present invention, further, the actual distance between each measuring station and the target point in step S3 is obtained by the following method: first, the distance between each measuring station and the initial point when the reflector is at the initial point is obtained; then, the reflector is moved to N Each measuring station tracks the reflector from the initial point to the measuring point, and measures the difference in length between each measuring station and the initial point and the measuring point, which is recorded as the length increment. dl pk; Finally, the distance and length increment of each measuring station from the initial point dl pk The sum of the actual distances between each measuring station and the target point is N Greater than 10.

[0016] In order to better implement the present invention, further, the ranging uncertainty of each measuring station in step S3 is calculated based on the measurement uncertainty of the laser tracking interferometer itself and the uncertainty introduced by incomplete environmental compensation.

[0017] In order to better implement the present invention, further, the uncertainty coefficient of the multilateral coordinate measurement system in step S4 is obtained by the three uncertainty components corresponding to the X, Y, and Z axes in the coordinate system. u x 、 u y 、 u z and the uncertainty introduced by the offset of the optical center of the reflector u b Square the four parameters separately, sum them up, and then take the square root.

[0018] In order to better implement the present invention, further, the reflector is a cat's eye retroreflector.

[0019] The present invention provides a method for evaluating the uncertainty of large-scale polygonal coordinate measurement system, which is composed of four measuring stations and a reflector. The method first establishes a coordinate system through the four measuring stations and records the coordinates of each measuring station in the coordinate system. Then, the optical center of the reflector is used as the measured point, and the reflector is moved from the initial point to the second point. N The control points at different positions are obtained by the laser tracking interferometer corresponding to each measuring station, and the measuring stations are respectively moved to the initial point, N The relative length of each control point is calculated; then, the ranging uncertainty of each measuring station and the uncertainty introduced by the offset of the optical center of the reflector are calculated based on the measurement uncertainty of the laser tracking interferometer itself and the uncertainty introduced by the incomplete environmental compensation; finally, the reflector is placed at the position to be measured, and the coordinates of the measured point at this time are obtained. The uncertainty of the multilateral coordinate measurement system is calculated from the coordinates of the measured point, the coordinates of each measuring station in the coordinate system, the ranging uncertainty of each measuring station and the uncertainty introduced by the offset of the optical center of the reflector.

[0020] The present invention also provides an uncertainty evaluation system for a large-scale polygonal coordinate measurement system, including an error transfer model for realizing the function of obtaining three coordinate uncertainty components corresponding to the coordinate values ​​in the above method.

[0021] The present invention also provides an electronic device, comprising a memory and a processor; a computer program is stored in the memory; when the computer program is executed on the processor, the above-mentioned uncertainty evaluation method is implemented.

[0022] A computer-readable storage medium stores computer instructions; when the computer instructions are executed on the above-mentioned electronic device, the above-mentioned uncertainty evaluation method is implemented.

[0023] The beneficial effects of the present invention are as follows:

[0024] The present invention inputs the acquired target point coordinates into the error transfer model to obtain the three coordinate uncertainty components corresponding to the coordinate values, and then combines the uncertainty introduced by the optical center offset of the reflector to calculate the uncertainty coefficient of the multilateral coordinate measurement system. Starting from the basic principle of the multilateral coordinate measurement system, the system coordinate system is simplified to reduce parameters and the amount of calculation, which is conducive to the rapid evaluation of the measurement site and is convenient for metrology personnel to learn and apply. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Station coordinate systems constructed for the four stations;

[0026] Figure 2 It is a flow chart of the main steps of the present invention. DETAILED DESCRIPTION

[0027] Example 1:

[0028] This embodiment provides an uncertainty evaluation method for a large-scale multilateral coordinate measurement system. The uncertainty evaluation is performed on a large-scale multilateral coordinate measurement system composed of four laser tracking interferometers and a reflector. One laser tracking interferometer serves as a measuring station for constructing a three-dimensional coordinate system. The method inputs the acquired target point coordinates into an error transfer model to obtain three coordinate uncertainty components corresponding to the coordinate values. Combined with the uncertainty introduced by the optical center offset of the reflector, the uncertainty coefficient of the multilateral coordinate measurement system is calculated to perform uncertainty evaluation.

[0029] This embodiment adopts an uncertainty evaluation method different from the existing technology. Starting from the basic principles of the multilateral coordinate measurement system, it simplifies the system coordinate system to reduce parameters and the amount of calculation, which is conducive to rapid evaluation of the measurement site and is easy for metrologists to learn and use.

[0030] Example 2:

[0031] Based on Example 1, this example takes a cat's eye retroreflector as an example to illustrate the details of an uncertainty evaluation method for a large-scale polygonal coordinate measurement system.

[0032] like Figure 2 As shown, the method includes the following steps:

[0033] Step S1, establishing a coordinate system;

[0034] Specifically, a three-dimensional coordinate system is first established through four measuring stations, and the coordinates of each measuring station in the coordinate system are recorded;

[0035] Step S2, obtaining the target point coordinates;

[0036] Specifically, the cat's eye retroreflector is tracked using the laser tracking interferometer corresponding to each measuring station, and the cat's eye retroreflector is moved to the target position. The spatial coordinates output by the multilateral coordinate measurement system are the coordinates of the target point.

[0037] Step S3, obtaining three coordinate uncertainty components corresponding to the three coordinate values;

[0038] Specifically, the target point coordinates are input into the error transfer model to calculate the three coordinate uncertainty components corresponding to the three coordinate values;

[0039] Step S4: Calculate the uncertainty coefficient of the multilateral coordinate measurement system based on the three coordinate uncertainty components corresponding to the three coordinate values ​​and the uncertainty introduced by the optical center offset of the cat's eye retroreflector.

[0040] Furthermore, the step S1 specifically includes:

[0041] Step S11, fixing four laser tracking interferometers at four different positions, and setting the laser tracking interferometers to measuring station A, measuring station B, measuring station C, and measuring station D in sequence;

[0042] Step S12: Establish a three-dimensional coordinate system corresponding to the measuring station. Set the measuring center of measuring station A as the origin of the coordinate system. The direction from the measuring center of measuring station A to measuring station B is the positive direction of the X axis. Set the measuring center of measuring station C on the XOY plane. The coordinates of measuring stations A, B, C, and D are: (0, 0, 0), ( x B ,0,0),( x C , y C ,0)、( x D , y D , z D ).

[0043] Furthermore, in step S3, the error transfer model calculates three coordinate uncertainty components corresponding to the three coordinate values ​​according to the coordinates of each measuring station, the actual distance between each measuring station and the target point, and the distance measurement uncertainty of each measuring station.

[0044] Furthermore, the actual distance between each measuring station and the target point in step S3 is obtained by the following method: first, the distance between each measuring station and the initial point is obtained when the reflector is at the initial point; then, the reflector is moved to N Each measuring station tracks the reflector from the initial point to the measuring point, and measures the difference in length between each measuring station and the initial point and the measuring point, which is recorded as the length increment. dl pk ; Finally, the distance and length increment of each measuring station from the initial point dl pk The sum of the actual distances between each measuring station and the target point is N Greater than 10.

[0045] Furthermore, the ranging uncertainty of each measuring station in step S3 is calculated based on the measurement uncertainty of the laser tracking interferometer itself and the uncertainty introduced by incomplete environmental compensation.

[0046] Furthermore, the uncertainty coefficient of the multilateral coordinate measurement system in step S4 is obtained by the three uncertainty components corresponding to the X, Y, and Z axes in the coordinate system. u x 、 u y 、 u z and the uncertainty introduced by the offset of the optical center of the reflector u b Square the four parameters separately, sum them up, and then take the square root.

[0047] The uncertainty evaluation method described in this embodiment first constructs a coordinate system through the measuring stations and obtains the coordinates of each measuring station in the coordinate system; then, the optical center of the reflector is used as the measured point, and the reflector is moved from the initial point to the N The control points at different positions are obtained by the laser tracking interferometer corresponding to each measuring station to obtain the distance from the measuring station to the initial point and N The relative length of each control point is calculated; then, according to the measurement uncertainty of the laser tracking interferometer itself and the uncertainty introduced by the incomplete environmental compensation, the ranging uncertainty of each measuring station and the uncertainty introduced by the offset of the optical center of the reflector are calculated; finally, the uncertainty of the multilateral coordinate measurement system is calculated from the coordinates of each measuring station in the coordinate system, the ranging uncertainty of each measuring station and the uncertainty introduced by the offset of the optical center of the reflector.

[0048] Example 3:

[0049] This embodiment provides a specific usage scenario based on Embodiment 1 or Embodiment 2.

[0050] The multilateral coordinate measurement system used in this embodiment is composed of four laser tracking interferometers and a cat's eye retroreflector. The uncertainty evaluation method of the large-scale multilateral coordinate measurement system includes the following operations:

[0051] First, fix the four laser tracking interferometers at four different positions and set them as measurement stations A, B, C, and D in any order.

[0052] Secondly, establish the station coordinate system, set the measurement center of station A as the origin of the coordinate system, and the direction from the measurement center of station A to B as the positive direction of the X axis; set the measurement center of station C on the XOY plane, and the coordinates of A, B, C, and D are: (0, 0, 0), ( x B ,0,0),( x C , y C ,0)、( x D , y D , z D );

[0053] Then, the laser tracking interferometer of the multilateral coordinate measurement system tracks the cat's eye retroreflector, and the cat's eye retroreflector is placed at the position to be measured. The output of the multilateral coordinate measurement system is the spatial coordinate of a certain position in the measuring station coordinate system. x 、 y 、 z , evaluate according to the following error transfer formula x 、 y 、 z Standard uncertainty u x 、 u y 、 u z :

[0054] (1)

[0055] (2)

[0056] (3)

[0057] Finally, the uncertainty coefficient of the multilateral coordinate measurement system is u G The calculation method is shown in formula (4):

[0058] (4)

[0059] The parameters used in formula (1), formula (2), and formula (3) are: x B 、 x C 、 y C 、 u A 、 u B 、 u C 、 l PA 、 l PB 、 l PC There are 9 independent parameters in total.

[0060] in: x B is the X-axis coordinate value of measuring station B, x C is the X-axis coordinate value of measuring station C, y C is the Y-axis coordinate value of measuring station C; u A 、 u B 、 u C are the ranging uncertainties of station A, station B, and station C respectively; l PA 、 l PB 、 l PC are the lengths from station A, station B, and station C to the optical center of the cat's eye retroreflector, respectively; u b Uncertainty introduced for the offset of the cat's eye retroreflector's optical center.

[0061] In another specific embodiment, a derivation process of the uncertainty evaluation formula in this embodiment is provided.

[0062] There are three laser tracking interferometers: station A, station B, and station C. According to step S1 of embodiment 2, a station coordinate system is established, such as Figure 1 As shown, P is the target point, that is, the coordinate of the optical center of the cat's eye retroreflector when the cat's eye retroreflector is at the measured position.

[0063] If known x B 、 x C 、 y C According to the principle of multilateral coordinate measurement, the measured position corresponds to the coordinates of the target point P x 、y 、 z The solution formula is as follows:

[0064] (5)

[0065] (6)

[0066] (7)

[0067] The “±” sign in formula (7) can be positive or negative according to the measurement requirements.

[0068] The method of synthesizing random errors of functions is as follows: Let the estimated value of the measured value Y be y Depend on n Independent measurements x 1 , x 2 ,…, x n The function is obtained, that is: y = f ( x 1 , x 2 , …, x n ); y The random error of the function is synthesized as u G The calculation formula is:

[0069] (8)

[0070] in, d x1 , d x2 ,…, d xn The measured values x 1 , x 2 , …, x n The error, For function f For variables x i The partial differential of .

[0071] In formula (8), formula (5), and formula (7), x 、 y 、 z Separate and independent measurements l PA 、 lPB 、 l PC The following is a functional relationship based on the results of the multilateral method. x 、 y 、 z Coordinate error limit of direction d x 、 d y 、 d z To characterize uncertainty u x 、 u y 、 u z :

[0072] (9)

[0073] (10)

[0074] (11)

[0075] in: d A 、 d B 、 d C are the laser ranging errors of station A, station B, and station C respectively.

[0076] (12)

[0077] (13)

[0078] (14)

[0079] Characterizing uncertainty through limit error, we have Equations (12), (13), and (14).

[0080] In another embodiment, the x B 、 x C 、 y C 、 l PA 、 l PB 、 l PC 、 x 、 y 、 z 、 u A、 u B 、 u C The measurement and calculation methods of each independent parameter.

[0081] 1. Acquisition x B 、 x C 、 y C .

[0082] x B 、 x C 、 y C These are the X-axis coordinate value of measuring station B, the X-axis coordinate value of measuring station C, and the Y-axis coordinate value of measuring station C. They can be read directly.

[0083] 2. Acquisition l PA 、 l PB 、 l PC .

[0084] The measurement value directly obtained by the laser tracking interferometer is the relative distance, which is generally expressed in the following way: define an initial point P0, set l A0 、 l B0 、 l C0 、 l D0 The distances from station A, station B, station C, and station D to the initial point P0 are respectively. When a station k moves from the initial point P0 to the measuring point P by tracking the cat's eye retroreflector, the difference in length between the connecting lines of station k and P0 and P can be measured. dl Pk ; k=A, B, C, D. dl Pk The essence is increment, so dl Pk and l k0 The sum of is the distance from measuring station k to measuring point P.

[0085] so l PA 、 l PB 、 l PC and l PD Generally expressed as:

[0086] (15)

[0087] in, dl Pk It is the direct measurement value of the laser tracking interferometer.

[0088] 3. Get the coordinates of the target point P x 、 y 、 z .

[0089] The distance from the measuring station D to the target point needs to be introduced in the derivation process of calculating the measured position coordinates. l PD and coordinates x D 、 y D 、 z D , but in actual calculation only x B 、 x C 、 y C 、 l PA 、 l PB 、 l PC 6 parameters can be used to calculate the coordinates of the measured position. x B 、 x C 、 y C 、 l PA 、 l PB 、 l PC Substitute the six parameters into equations (5), (6), and (7) to obtain the coordinates of the target point P: x 、 y 、 z .

[0090] 4. Calculate the minimum value of the control point.

[0091] It should be noted that x B 、 x C 、 y C 、 x D 、 y D 、 z D 、 lA0 、 l B0 、 l C0 、 l D0 It is necessary to construct equations through redundant information and then solve them; the solution method is as follows.

[0092] (1) Four laser tracking interferometers track the same cat's eye retroreflector, and place the cat's eye retroreflector P 0 for measurement, and move the cat's eye reflectors to relatively dispersed N Positions, measured N The relative length of the control points relative to the initial point, where N Not less than 20, i The equations corresponding to the control points are as follows:

[0093] (16)

[0094] in, f i For the i The difference between the estimated value and the measured value of the distance from the control point to the measuring station D.

[0095] x i 、 y i Respectively i The X-axis and Y-axis coordinates of the control points, and x i = , y i = ; d for( x B , x C , y C , x D , y D , z D , l A0 , l B0 , l C0 , l D0 ).

[0096] (2) Use a tape measure or other length measuring instrument to measure the position spacing of the four laser tracking interferometers and the distance from the four laser tracking interferometers to the initial point P0 to obtain the iterative initial value of the parameter to be determined.

[0097] (3) Using Matlab software, N The sum of squares of the equations of the control points is minimized to solve, let:

[0098] (17)

[0099] function The minimum point That's right The solution is:

[0100] (18)

[0101] To seek By multivariate function The necessary condition for taking the extreme value is The gradient function ,Right now:

[0102] (19)

[0103] in, , recorded as J ( d ).

[0104] d When there is a solution, N At least greater than 10, that is, the number of control points must be greater than 10.

[0105] 5. Acquisition u A 、 u B 、 u C .

[0106] Uncertainty of length measurement corresponding to measuring station A u A , the length measurement uncertainty corresponding to measuring station B u B And the length measurement uncertainty corresponding to measuring station C u C The evaluation can be performed as follows: Station k represents any station among stations A, B, and C.

[0107] (1) The present invention uses Etalon's laser tracking interferometer, with a normal distribution 95% confidence interval and a ranging uncertainty of U = 0.2 μm + 0.3 μm / m. The standard uncertainty of the laser tracking interferometer ranging is:

[0108] (20)

[0109] (2) The refractive index of air changes due to random environmental factors such as temperature, humidity and air pressure, which causes the ranging error of the laser tracking interferometer. Assuming the air temperature gradient is 0.5℃ / m, the standard uncertainty introduced by incomplete environmental compensation is:

[0110] (twenty one)

[0111] (3) Synthesis of standard uncertainty of distance measurement:

[0112] (twenty two)

[0113] in, l The distance from the measuring station to the measured point, unit: m.

[0114] 6. Acquisition u b .

[0115] In this embodiment, the optical center error of the cat's eye retroreflector is ±4 μm. Assuming that it obeys uniform distribution, the standard uncertainty introduced by the optical center offset of the cat's eye retroreflector is calculated as follows:

[0116] (twenty three)

[0117] When the optical center error of the cat's eye retroreflector is known, u b Can be solved directly.

[0118] The uncertainty of the length measurement of each measuring station will be obtained u A 、 u B 、 u C And the standard uncertainty introduced by the cat's eye retroreflector optical center offset u b , the uncertainty coefficient of the multilateral coordinate measurement system can be obtained u G .

[0119] Example 4:

[0120] This embodiment provides a verification method based on embodiment 3.

[0121] This embodiment uses the estimation of the coordinate error limit as the verification method of the present invention, and the specific method is described and explained below.

[0122] Assume that the theoretical distances between the target point P and the measuring stations A, B, and C are l PA 、 l PB 、 l PC , and the distance measurement values ​​are l PA + δl PAi 、 l PB + δl PBi 、 l PC + δl PCi ,in δl PAi 、 δl PBi 、 δl PCi is the error of laser ranging of point P at each measuring station; i =1, 2, ..., n .

[0123] Assume that the theoretical coordinates of the target point P in the station coordinate system are x 0 、 y 0 、 z 0 The actual measured value is x i 、 y i 、 z i .

[0124] Assume that the theoretical value of space coordinates x 0 、 y 0 、 z 0 The functional relationships of the laser ranging theoretical values ​​are:

[0125] (twenty four)

[0126] in l =( l PA , l PB , l PC ) T .

[0127] Let the spatial coordinate measurement value x i 、y i 、 z i The functional relationships of the laser ranging theoretical values ​​are:

[0128] (25)

[0129] in δl =( δl PAi , δl PBi , δl Pci ) T .

[0130] make( δl PAi , δl PBi , δl Pci ) Take the values ​​in Table 1 respectively, and then calculate the verification value M 核验 .

[0131] M 核验 =(( x 0 - x i ) 2 +( y 0 - y i ) 2 +( z 0 - z i ) 2 ) 0.5 , not considered u b Under the premise of u G .because u G is calculated based on the error limit, so u G Greater than M 核验 But it does not exceed 1μm, that is 0.001mm.

[0132] Table 1 Ranging error values

[0133]

[0134] Specific parameters are given with examples.

[0135] Step a. First, estimate the uncertainty of the coordinates of a certain point according to the method of the present invention.

[0136] The coordinate values ​​of measuring stations A, B, C and measured point P are shown in Table 2.

[0137] Table 2 Coordinate values ​​of A, B, C and measured point P (mm)

[0138]

[0139] Then the theoretical distances from the target point P to the measuring stations A, B, and C can be obtained: l PA 、 l PB 、 l PC See Table 3.

[0140] Table 3 Theoretical distance values ​​from P to A, B, and C (mm)

[0141]

[0142] According to the uncertainty of laser interferometry U =0.1μm + 0.15μm / m, u A 、 u B 、 u C , see Table 4.

[0143] Table 4 Uncertainty of distance measurement from three measuring stations to point P (mm)

[0144]

[0145] According to formula (1), formula (2), and formula (3) in Example 3, it is estimated that u x 、 u y 、 u z , see Table 5.

[0146] Table 5 x 、 y 、 z Uncertainty of direction

[0147]

[0148] Not included u b Time coordinate uncertainty u G The estimate is: .

[0149] Step b. Then perform verification according to the verification method mentioned above.

[0150] First calculate x 0 、 y 0 、 z 0 as well as x i 、 y i 、 z i .

[0151] (26)

[0152] Calculated ( x 0 , y 0 , z 0 )=(2000mm, 4000mm, 2000mm).

[0153] The ranging error set according to Table 1 is shown in Table 6:

[0154] Table 6 Combination of simulated ranging error values ​​(mm)

[0155]

[0156] Then calculate x i 、 y i 、 z i .

[0157] make:

[0158] (27)

[0159] (28)

[0160] Finally, the verification value M is calculated according to the ranging error combination in Table 7. 核验 =(( x 0 - x i ) 2 + ( y 0 - y i ) 2 +( z 0 - z i )2 ) 0.5 .

[0161] Table 7 Calculation and verification values ​​of distance measurement error combination (mm)

[0162]

[0163] M 核验 The maximum value of 0.0059 mm is equal to the uncertainty estimate calculated in step a. u G =0.0061mm, which is only 0.0002mm less than 0.001mm, or 1μm.

[0164] The reasons for the verification method described in this embodiment are as follows:

[0165] because x 0 - x i , y 0 - y i , z 0 - z i There are the following relationships:

[0166] (29)

[0167] make δx = x 0 - x i ,δy = y 0 - y i , δz = z 0 - z i , and let d ( x )=( δx , dy , δz ), then:

[0168] (30)

[0169] According to the first-order Taylor expansion formula, we have:

[0170] (31)

[0171] (32)

[0172] in, .

[0173] Taking the 2-norm of formula (32), we have:

[0174] (33)

[0175] According to the compatibility of the 2-norm, there is an inequality:

[0176] (34)

[0177] That is:

[0178] (35)

[0179] That is, the maximum error represented by the distance between the theoretical coordinates of P and the measured coordinate points does not exceed The position of the measuring station M and the position of the measuring point relative to the measuring station are determined; Take the maximum value (i.e. the value of the distance uncertainty u A 、 u B 、 u C ) can estimate the maximum value of the coordinate error and approach the limit error.

[0180] Example 5:

[0181] Based on any one of the above-mentioned embodiments 1 to 3, this embodiment proposes an uncertainty evaluation system for a large-scale polygonal coordinate measurement system, including an error transfer model, which is used to realize the function of obtaining three coordinate uncertainty components corresponding to the coordinate values ​​in the above-mentioned method.

[0182] Example 6:

[0183] The present invention also provides an electronic device, comprising a memory and a processor; a computer program is stored in the memory; when the computer program is executed on the processor, the above-mentioned uncertainty evaluation method is implemented.

[0184] Example 7:

[0185] A computer-readable storage medium stores computer instructions; when the computer instructions are executed on the above-mentioned electronic device, the above-mentioned uncertainty evaluation method is implemented.

[0186] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technical essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for uncertainty evaluation of a large-scale multilateral coordinate measurement system, comprising four laser tracking interferometers and a reflector, is provided. Each laser tracking interferometer serves as a measuring station for constructing a three-dimensional coordinate system. The method is characterized by: The method inputs the acquired target point coordinates into the error transfer model to obtain three coordinate uncertainty components corresponding to the coordinate values, and then combines the uncertainty introduced by the optical center offset of the reflector to calculate the uncertainty coefficient of the multilateral coordinate measurement system to perform uncertainty evaluation; The method comprises the following steps: Step S1, establishing a coordinate system; Specifically, a three-dimensional coordinate system is first established through four measuring stations, and the coordinates of each measuring station in the coordinate system are recorded; Step S2, obtaining the target point coordinates; Specifically, the laser tracking interferometer corresponding to each measuring station is used to track the reflector, and the reflector is moved to the target position. The spatial coordinates output by the multilateral coordinate measurement system are the coordinates of the target point. Step S3, obtaining three coordinate uncertainty components corresponding to the three coordinate values; Specifically, the target point coordinates are input into the error transfer model to calculate the three coordinate uncertainty components corresponding to the three coordinate values; Step S4, calculating the uncertainty coefficient of the multilateral coordinate measurement system according to the three coordinate uncertainty components corresponding to the three coordinate values ​​and the uncertainty introduced by the optical center offset of the reflector; In step S3, the error transfer model calculates three coordinate uncertainty components corresponding to the three coordinate values ​​according to the coordinates of each measuring station, the actual distance between each measuring station and the target point, and the distance measurement uncertainty of each measuring station; The actual distance between each measuring station and the target point in step S3 is obtained by the following method: first, the distance between each measuring station and the initial point is obtained when the reflector is at the initial point; then, the reflector is moved to N Each measuring station tracks the reflector from the initial point to the measuring point, and measures the difference in length between each measuring station and the initial point and the measuring point, which is recorded as the length increment. dl pk ; Finally, the distance and length increment of each measuring station from the initial point dl pk The sum of the actual distances between each measuring station and the target point is N Greater than 10.

2. The uncertainty evaluation method for a large-scale multilateral coordinate measurement system according to claim 1, characterized in that: In step S3, the distance measurement uncertainty of each measuring station is calculated based on the measurement uncertainty of the laser tracking interferometer itself and the uncertainty introduced by incomplete environmental compensation.

3. The uncertainty evaluation method for a large-scale multilateral coordinate measurement system according to claim 1, characterized in that: The uncertainty coefficient of the multilateral coordinate measurement system in step S4 is obtained by the three uncertainty components corresponding to the X, Y, and Z axes in the coordinate system. u x 、 u y 、 u z and the uncertainty introduced by the offset of the optical center of the reflector u b Square the four parameters separately, sum them up, and then take the square root.

4. The uncertainty evaluation method for a large-scale multilateral coordinate measurement system according to any one of claims 1 to 3, characterized in that: The reflector is a cat's eye retroreflector.

5. An uncertainty evaluation system for a large-scale multilateral coordinate measurement system, characterized in that: An error transfer model is included, which is used to achieve the function of obtaining three coordinate uncertainty components corresponding to the coordinate values ​​in the method according to any one of claims 1 to 4.

6. An electronic device, characterized in that: The method comprises a memory and a processor; a computer program is stored in the memory; when the computer program is executed on the processor, the uncertainty evaluation method according to any one of claims 1 to 4 is implemented.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions; when the computer instructions are executed on the electronic device according to claim 6, the uncertainty evaluation method according to any one of claims 1 to 4 is implemented.

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