CN109871664B - Station transfer precision optimization method for large-size multi-station measuring field assembled on airplane - Google Patents
Station transfer precision optimization method for large-size multi-station measuring field assembled on airplane Download PDFInfo
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Abstract
A method for optimizing the accuracy of the transfer station of large-size multi-station measuring field for airplane assembly features that on the basis of the reference points of transfer station such as TB/ERS point, a temporary reinforcing point without theoretical value is introduced, and two or more measuring stations measure the reinforcing points of transfer station simultaneously to increase the balance constraint between different measuring stations, decrease the parameter variance-covariance matrix of transfer station from measuring station to global station, and increase the accuracy of transfer station. The invention is characterized in that: 1) Compared with the method that the layout number of the transfer station reference points such as TB/ERS points is increased to realize the optimization of the transfer station precision, the transfer station enhancement points do not have theoretical values, so that the layout and later maintenance cost is greatly reduced. 2) The station transfer enhancement points can be temporarily flexibly arranged according to the measurement precision requirement difference of different areas of the component to be measured and the on-site measurement openness condition, and the use is convenient.
Description
Technical Field
The invention relates to the technical field of airplane assembly measurement, in particular to a method for improving the accuracy of a transfer station parameter during large-size multi-station measurement, and specifically relates to a transfer station accuracy optimization method for an airplane assembly large-size multi-station measurement field.
Background
Due to the large structural size of products such as airplanes and ships, when the products are detected and measured on line in the assembly process, a plurality of stations are usually required to be arranged for complete measurement of the products, and firstly, the measurement coordinate system of each station needs to be converted into the global coordinate system. The conventional station transfer method mainly depends on pre-arranged reference points such as TB/ERS points and the like, the arrangement and maintenance cost is high, and the conditions of reference point shielding, abrasion and the like often exist, so that the error of the station transfer is greatly increased, and the assembly measurement precision is directly influenced.
Therefore, there is a need to improve the prior art to overcome the deficiencies of the prior art.
Disclosure of Invention
The invention aims to solve the problems that the existing station transfer measuring method using TB/ERS points as reference points is high in layout and maintenance cost, and the assembly measuring precision is directly influenced due to the fact that the reference points are often shielded and abraded, so that the station transfer error is greatly increased.
The technical scheme of the invention is as follows:
a method for optimizing the accuracy of a transfer station for assembling a large-size multi-station measuring field on an airplane comprises a component to be measured, a large-size measuring system, reference points such as TB/ERS points and station transfer enhancement points, and is characterized in that: on the basis of a common station transferring method based on reference points such as TB/ERS points and the like for airplane assembly, temporary station transferring enhancement points without theoretical values are introduced, station transferring parameter adjustment constraints are increased by simultaneously measuring the station transferring enhancement points during multi-station measurement, and a station transferring parameter variance-covariance matrix of a measuring station to an assembly global station is reduced, so that station transferring errors are reduced or station transferring precision is improved.
The specific steps are as follows:
1) Coarse estimation of transfer station parameters
When the assembly measurement is finished, m stations are required to be arranged, namely, the stations are required to be transferred for m-1 times. k p i ＝[ k x i k y i k z i ] T (i＝1,2,…,N k ) Represents the coordinates of the ith TB/ERS point measured at site k (k =1,2, \8230;, m), with the number of all TB/ERS measured at that site being N k 。 k q j ＝[ 0 x j 0 y j 0 z j ] T (j =1,2, \8230;, N) is the nominal coordinate of the corresponding TB/ERS point in the assembly coordinate system, N (N ≧ N) k ) The total number of all TB/ERS points. Making a great deal through a point set matching algorithm such as a standard SVD algorithm and a quaternion algorithm k p i }、{ k q j Matching to obtain coarse transformation parameters
The transformed coordinates k p′ i Will be very close to the nominal value k q j Which is calculated as
Wherein
By the RPY angle->
To represent
In the formula (2)
2) Transit modeling without transit enhancement points
a) Bursa-Wolf model representation
After the coarse conversion is carried out, the conversion is carried out, k q j 、 k p′ i will be in close proximity. Order to k Mu is a scaling factor and is a function of the scaling factor, k ε x 、 k ε y 、 k ε z in the case of a minute rotation angle, k t x 、 k t y 、 k t z for small translation amount, then k q j 、 k p′ i Can be expressed by an approximate burst-Wolf model:
k q j ＝ k p′ i + k M k p′ i + k T (3)
wherein
k T＝[ k t x k t y k t z ] T 。
The equation (3) is not completely equal between the left and right sides due to measurement errors in the measurement coordinates. Order to k Δp′ i Representing the measurement error vector, the correct conversion relationship is:
k q j -( k p′ i - k Δp′ i )＝ k M( k p′ i - k Δp′ i )+ k T (4)
due to the fact that k Δp′ i 、 k ε x 、 k ε y 、 k ε z Are all of a small value, and k μ is very close to zero, so equation (4) can be approximated as:
k L i ＝ k A i k ξ- k Δp′ i (5)
wherein k L i ＝ k q j - k p′ i ， k ξ＝[ k t x k t y k t z k ε x k ε y k ε z k μ] T In order to be a parameter vector of the transfer station, k A i as a variable matrix:
b) Transit parameter indirection adjustment calculation
Order to
And the measured error vector of the TB/ERS point of the station k, all the TB/ERS points of the station k are converted into a global coordinate system:
k L＝ k A k ξ- k Δp′ (7)
all the station positions 1,2, \8230, the conversion of m to the global coordinate system can be expressed as an indirect adjustment model, let L = [, ] 1 L T 2 L T … m L T ] T 、V＝[ 1 Δp ′T 2 Δp′ T … m Δp′ T ] T 、A＝Diag( 1 A, 2 A,…, m A) The model is
V＝Aξ-L (8)
Wherein xi is k ξ vector combinations. The adjustment objective function is:
in the formula (9), Q VV A variance-covariance matrix for the measurement error is constructed from the block diagonal matrix according to the accuracy parameters of the measurement system. Then the least squares adjustment solution of the transfer station parameters is:
the variance-covariance matrix of the transfer station parameters is:
3) Coordinate transformation modeling including transstation enhancement points
a) Single site, single to station enhanced point transition representation
For any two station positions k1 and k2, the two stations are arranged to measure N together k1,k2 A common trans-station enhancement point, the coordinates of which after the coarse transformation are,
make->
Is->
Is selected, is selected>
For the error vector, the transformation of the two into the global coordinate system should be equal, as shown in FIG. 2, with
Wherein k1 ξ、 k2 ξ are the trans-station parameters of k1 and k 2.
Order to
Formula (12) is represented by
b) Transit adjustment model with transit enhancement points
For all N of k1, k2 k1,k2 The public transfer station enhancement point is
H (k1,k2) -S (k1,k2) ＝[0 k1 A (k1,k2) 0- k2 A (k1,k2) 0]ξ (14)
Considering that there may be a common transfer enhancement point for any two stations, the station combinations may be (1, 2), (1, 3) \8230; (1, m), (2, 3), (2, 4) \8230; (2, m); (m-1, m). The station transfer enhancement points of all station position combinations form the following equation
H-S-Bξ＝0 (15)
Wherein
Combining with the formulas (8) and (15), an extended Gauss-Markov model can be constructed
c) Transit parameters and variance-covariance matrix thereof
The adjustment objective function of the formula (17) is
To minimize the function Ψ, it is necessary to satisfy
Then there is
Substituting (17) into (19) and transferring to obtain
The final station-switching parameter xi is
Due to Q VV 、Q SS Is a symmetric matrix, such that
It is also a symmetric matrix having
By comparing the variance-covariance matrix of the station transfer parameter errors of the respective equations (11) and (22)
It is directly seen that after the station transfer enhancement points are introduced, the variance covariance matrix of the station transfer parameters is reduced, namely, the station transfer precision is improved.
The invention has the following beneficial effects:
1) Compared with the method that the layout number of the transfer station reference points such as TB/ERS points is increased to realize the optimization of the transfer station precision, the transfer station enhancement points do not have theoretical values, so that the layout and later maintenance cost is greatly reduced.
2) The station transfer enhancement points can be temporarily and flexibly arranged according to the measurement precision requirement difference of different areas of the component to be measured and the situation of the open property of field measurement, so that the use is convenient;
drawings
FIG. 1 is a schematic diagram of the assembly measuring field transfer station accuracy optimization of the present invention.
Fig. 2 is a schematic diagram of the transfer station enhancement point principle of the present invention.
1-a component to be tested; 2-large size measurement system; 3-TB/ERS point; 4-station transfer enhancement point; 5-measuring station positions; 6-assembling the global site.
Detailed Description
Referring to fig. 1, the station transferring precision optimization method for the large-size multi-station measuring field for aircraft assembly according to the present invention includes a component to be measured 1, a large-size measuring system 2, a TB/ERS point 3, a station transferring enhancement point 4, a measuring station 5, and an assembly global station 6 (see fig. 2). The large-size measuring system 2 is used for measuring key characteristics of the component 1 to be measured, the TB/ERS point 3 is a common transfer station reference point for airplane assembly, and the transfer station enhancing point 4 is a temporary multi-station measuring reference point without theoretical values, and plays roles in increasing the adjustment constraint of the multi-station transfer station and improving the transfer station precision.
Please refer to fig. 1 and 2. A station transfer precision optimization method for an airplane assembled large-size multi-station measuring field specifically comprises the following steps:
1) Coarse estimation of transfer station parameters
When the assembly measurement is finished, m measurement stations 5 (hereinafter referred to as stations) are required to be arranged, namely, the stations are required to be switched for m-1 times, and each station has a Measurement Coordinate System (MCS). k p i ＝[ k x i k y i k z i ] T (i＝1,2,…,N k ) Denotes the coordinates of the ith TB/ERS point 3 of a station k (k =1,2, \8230;, m) measurement, the number of all TB/ERS points 3 of which station measurement is N k 。 k q j ＝[ 0 x j 0 y j 0 z j ] T (j =1,2, \8230;, N) is the nominal coordinate in the rigged global site 6 corresponding to TB/ERS point 3, N (N ≧ N) k ) The total number of all TB/ERS points 3. Making a great deal through a point set matching algorithm such as a standard SVD algorithm and a quaternion algorithm k p i }、{ k q j Matching to obtain coarse transformation parameters
The transformed coordinates k p′ i Will be very close to the nominal value k q j Which is calculated as
Wherein
By the RPY angle->
To represent
In the formula (2)
2) Transit modeling without transit enhancement points
a) Bursa-Wolf model representation
After the coarse conversion has been carried out, the conversion is carried out, k q j 、 k p′ i will be in close proximity. Order to k Mu is a scaling factor and is a function of the scaling factor, k ε x 、 k ε y 、 k ε z in the case of a minute rotation angle, k t x 、 k t y 、 k t z for small translation amount, then k q j 、 k p′ i Can be expressed by an approximate burst-Wolf model:
k q j ＝ k p′ i + k M k p′ i + k T (3)
wherein
k T＝[ k t x k t y k t z ] T 。
The equation (3) is not completely equal to the left and right sides due to measurement errors in the measurement coordinates. Order to k Δp′ i Representing the measurement error vector, the correct conversion relationship is:
k q j -( k p′ i - k Δp′ i )＝ k M( k p′ i - k Δp′ i )+ k T (4)
due to the fact that k Δp′ i 、 k ε x 、 k ε y 、 k ε z Are all of a small value, and k μ is very close to zero, so equation (4) can be approximated as:
k L i ＝ k A i k ξ- k Δp′ i (5)
wherein k L i ＝ k q j - k p′ i ， k ξ＝[ k t x k t y k t z k ε x k ε y k ε z k μ] T In order to be a vector of the parameters of the transfer station, k A i as a variable matrix:
b) Transit parameter indirection adjustment calculation
Order to
For the measured error vector of TB/ERS point 3 of site k, then all TB/ERS points 3 of site k are converted to the assembled global site 6 as:
k L＝ k A k ξ- k Δp′ (7)
the station 1,2, \ 8230;, the transition of m to the assembly global site 6 can be represented as an indirect adjustment model, let L = [ 2 ] 1 L T 2 L T … m L T ] T 、V＝[ 1 Δp′ T 2 Δp′ T … m Δp′ T ] T 、A＝Diag( 1 A, 2 A,…, m A) The model is
V＝Aξ-L (8)
The adjustment objective function is:
in the formula (9), Q VV A variance-covariance matrix for the measurement error is constructed from the block diagonal matrix according to the accuracy parameters of the measurement system. Then the least squares adjustment solution of the transfer station parameters is:
the variance-covariance matrix of the transfer station parameters is:
3) Coordinate transformation modeling including transstation enhancement points
a) Single site 5, single transfer enhancement point 4 conversion representation
For any two stations 5k1 and k2, the two stations are arranged to measure N together k1,k2 A common trans-station enhancement point 4, whose coordinates after coarse conversion are,
make->
Is->
Is selected, is selected>
For the error vector, the two should be equal when switched to the global site 6, as shown in FIG. 2, with
Wherein k1 ξ、 k2 ξ are the trans-station parameters of k1 and k 2.
Order to
Formula (12) is represented by
b) Transit adjustment model with transit enhancement points 4
For all N of k1, k2 k1,k2 A common transfer station enhancement point 4 has
H (k1,k2) -S (k1,k2) ＝[0 k1 A (k1,k2) 0- k2 A (k1,k2) 0]ξ (14)
Considering that there may be a common transfer station reinforcement point 4 for any two station sites, the station site combinations may be (1, 2), (1, 3) \ 8230: (1, m), (2, 3), (2, 4) \ 8230; (2, m); (m-1, m). The station transfer enhancement points 4 of all station position combinations form the following equation
H-S-Bξ＝0 (15)
Wherein
Combining the formulas (8) and (15), an extended Gauss-Markov model can be constructed
c) Transit parameter and variance-covariance matrix thereof
The adjustment objective function of the formula (17) is
To minimize the function Ψ, one must satisfy
Then there is
Substituting (17) into (19) and inverting to obtain
The final station-switching parameter xi is
Due to Q VV 、Q SS Is a symmetric matrix, such that
It is also a symmetric matrix having
By comparing the variance-covariance matrix of the error of the transfer station parameter in each of the equations (11) and (22)
It is intuitive to see that after the station transfer enhancement point 4 is introduced, the variance covariance matrix of the station transfer parameters is reduced, i.e. the station transfer precision is improved.
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.
The present invention is not concerned with parts which are the same as or can be implemented using prior art techniques.
Claims (1)
1. A station transfer precision optimization method for an airplane assembly large-size multi-station measuring field is characterized by comprising the following steps: on the basis of a common TB/ERS point (3) station transfer reference point for airplane assembly, a temporary station transfer enhancement point (4) without a theoretical value is introduced, and two or more than two measuring station positions (5) are used for simultaneously measuring the station transfer enhancement point (4), so that station transfer adjustment constraints among different measuring station positions (5) are increased, station transfer parameter errors from the measuring station positions (5) to an assembly global station position (6) are reduced, and station transfer precision is improved; the method comprises the following steps:
1) Roughly estimating transfer station parameters;
setting that m measuring stations (5) are required to be arranged in total after the assembly measurement is finished, namely, the stations are required to be transferred for m-1 times; k p i ＝[ k x i k y i k z i ] T i＝1,2,L,N k denotes the measurement station (5), k =1,2, L, m, coordinates of the measured ith TB/ERS point (3), the measurement station (5) measuring all TB/ERS points (3) with the number N k ； k q j ＝[ 0 x j 0 y j 0 z j ] T j =1,2,L, N is the nominal coordinate of the corresponding TB/ERS point (3) in the assembly global site (6), N ≧ N k The total number of all TB/ERS points (3); point set matching algorithm for a great data volume by means of standard SVD algorithm and quaternion algorithm k p i }、{ k q j Matching to obtain coarse transformation parameters
The transformed coordinates k p′ i Will be very close to the nominal value k q j Which is calculated as
Wherein
Is based on the Euler angle->
And &>
To represent
In the formula (2)
2) Modeling the transfer station without the transfer station enhancement point;
a) Bursa-Wolf model representation
After the coarse conversion is carried out, the conversion is carried out, k q j 、 k p′ i will be in close proximity; order to k Mu is a scaling factor of the image data, k ε x 、 k ε y 、 k ε z in the case of a minute rotation angle, k t x 、 k t y 、 k t z for small translation amount, then k q j 、 k p′ i Can be expressed by an approximate burst-Wolf model:
k q j ＝ k p′ i + k M k p′ i + k T (3)
wherein
k T＝[ k t x k t y k t z ] T ；
Because the measurement coordinate has measurement error, the left and right of the formula (3) are not completely equal; order to k Δp i ' denotes the measurement error vector, the correct conversion relationship is:
k q j -( k p′ i - k Δp′ i )＝ k M( k p′ i - k Δp′ i )+ k T (4)
due to the fact that k Δp′ i 、 k ε x 、 k ε y 、 k ε z Are all of a small value, and k μ is very close to zero, so equation (4) can be approximated as:
k L i ＝ k A i k ξ- k Δp′ i (5)
wherein k L i ＝ k q j - k p′ i ， k ξ＝[ k t x k t y k t z k ε x k ε y k ε z k μ] T In order to be a vector of the parameters of the transfer station, k A i as a variable matrix:
b) Transfer parameter indirect adjustment resolving
Order to
For the measurement error vector of the TB/ERS point (3) of the measurement station (5) k, the conversion of all the TB/ERS points (3) of the measurement station (5) k to the assembly global station (6) is as follows:
k L＝ k A k ξ- k Δp′ (7)
the conversion of all measuring stations (5) 1,2, L, m to the assembly global station (6) can be expressed as an indirect adjustment model, with L = [ [ solution ] ] 1 L T2 L T L m L T ] T 、V＝[ 1 Δp′ T2 Δp′ T L m Δp′ T ] T 、A＝Diag( 1 A, 2 A,L, m A) The model is
V＝Aξ-L (8)
Wherein xi is k Xi vector combinations; the adjustment objective function of the above equation is:
in the formula (9), Q VV For measuring the variance-covariance matrix of the error, according to the block according to the precision parameters of the measuring systemConstructing a diagonal matrix; then the least squares adjustment solution of the transfer station parameters is:
the variance-covariance matrix of the transfer station parameters is:
3) Coordinate transformation modeling of the station transfer enhancement points is included;
a) Single survey station (5), single transstation enhancement point (4) conversion representation
For any two measuring stations (5) k1 and k2, the two stations are arranged to measure N together k1,k2 A common trans-station enhancement point (4) having coordinates after a coarse transformation of, k1 p i ′ (k1,k2) 、 k2 p i ′ (k1,k2) (i＝1,2,L,N k1,k2 ) (ii) a Order to
Is composed of k1 p i ′ (k1,k2) 、 k2 p i ′ (k1,k2) The matrix of the variables of (a), k1 Δp i ′ (k1,k2) 、 k2 Δp i ′ (k1,k2) for error vectors, the two should be equal when switched to the assembled global position, have
Wherein k1 ξ、 k2 Xi is the transtation parameters of k1 and k 2;
order to
Formula (12) is represented by
b) Transit adjustment model with transit enhancement points (4)
For all N of k1, k2 k1,k2 The public transfer station enhancement point is
H (k1,k2) -S (k1,k2) ＝[0 k1 A (k1,k2) 0- k2 A (k1,k2) 0]ξ (14)
Considering that a common transfer station enhancing point (4) may exist in any two measuring stations (5), the combination of the measuring stations (5) can be (1, 2), (1, 3) L (1, m), (2, 3), (2, 4) L (2, m); (m-1, m); the station transfer enhancement points (4) of all the measurement station positions (5) form the following equation
H-S-Bξ＝0 (15)
Wherein
Combining the formulas (8) and (15), an extended Gauss-Markov model can be constructed
c) The station transfer parameters and their variance-covariance matrix:
the adjustment objective function of the formula (17) is
To minimize the function Ψ, it is necessary to satisfy
Then there is
Substituting (17) into (19) and transferring to obtain
The final station transfer parameter xi is
Due to Q VV 、Q SS Is a symmetric matrix, such that
It is also a symmetric matrix having
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