CN117745096A - Evaluation method and system for control screen cloth measurement scheme - Google Patents
Evaluation method and system for control screen cloth measurement scheme Download PDFInfo
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Abstract
The invention discloses a control screen cloth measurement scheme evaluation method and a control screen cloth measurement scheme evaluation system, which relate to the field of engineering measurement and comprise the following steps: acquiring a plurality of control screen cloth measurement schemes, and acquiring evaluation indexes by using five precision indexes, three reliability indexes and three expense indexes to construct an evaluation matrix; carrying out normalized treatment of eliminating dimension and magnitude order to obtain a normalized matrix; selecting an optimal evaluation value from all evaluation values of each evaluation index to construct a reference number sequence, and acquiring a correlation coefficient between a normalized matrix and the reference number sequence; and analyzing the weight of each evaluation index by using an analytic hierarchy process to construct a weight vector, acquiring absolute association degrees of various large-scale industrial control mesh measurement schemes by using association coefficients and the weight vector, sequencing and comprehensively evaluating the absolute association degrees according to the sizes of the absolute association degrees, and selecting a control mesh measurement scheme with high association degrees and high comprehensive evaluation. The invention can solve the comprehensive evaluation problem of engineering control screen cloth testing scheme under the condition of insufficient information in the design stage.
Description
Technical Field
The invention relates to the field of engineering measurement, in particular to a control screen cloth measurement scheme evaluation method and system.
Background
In recent years, large projects such as sea crossing channels, high-speed railways, large scientific devices and the like are vigorously developed in China, the complex structure and high-precision measurement requirements of the large projects are higher in requirements on precision engineering measurement in the links of construction, installation, detection, monitoring and the like, the rapid development of the precision engineering measurement is driven, and the precision engineering measurement becomes the most active research and practice direction in engineering measurement disciplines. In the field of precision engineering measurement, control network design is an extremely important problem. The design of the control network scheme involves the selection of the network shape and observation value type and weight of the control network, in order to make the control network meet certain precision, reliability and cost indexes. Different control screen cloth measurement schemes are always good and bad in quality indexes such as precision, reliability, cost and the like.
In the prior art, in the aspect of theory and method of control network design, a new method of control network type design is proposed by a researcher Postek based on computer simulation, so that the cost is reduced as much as possible while the necessary precision and reliability of a control network are maintained, the Singh perfects the objective function of the control network type design, the GPS network type design is carried out by utilizing a particle swarm algorithm, matsuoka and the like are used for determining the optimal position of a known point, the influence of measured abnormal values on the coordinates of the control network is reduced, and a method for autonomously determining the position of the known point of the control network is proposed; klein analyzes the relation between the quality indexes of the control network, and considers that the quality indexes are related, but not independent.
However, the existing control mesh measurement scheme can only acquire partial control mesh information through estimation in the design stage, namely, the design of the control mesh measurement scheme belongs to a gray system with incomplete information, so that the large-scale industrial control mesh measurement scheme cannot be accurately evaluated.
Disclosure of Invention
The embodiment of the invention provides a control screen cloth testing scheme evaluation method and a control screen cloth testing scheme evaluation system, which can solve the problem that in the prior art, accurate evaluation of a large-scale industrial control screen cloth testing scheme cannot be made by utilizing part of control screen information.
The embodiment of the invention provides a control screen cloth testing scheme evaluation method, which comprises the following steps of: acquiring a plurality of control screen cloth measurement schemes; obtaining an evaluation index by using five precision indexes, three reliability indexes and three expense indexes; selecting an optimal evaluation value from all evaluation values of each evaluation index, and acquiring relevance according to the optimal evaluation value and the evaluation index; analyzing the weight of each evaluation index by using an analytic hierarchy process, constructing a weight vector, and acquiring absolute association degree by using the association and the weight vector; and (3) carrying out comprehensive evaluation sequencing according to the absolute association degree, and selecting a control screen cloth testing scheme with high association degree, namely high comprehensive evaluation.
Further, the five precision indexes include: maximum parameter error, ratio of parameter error less than threshold value, weakest edge length relative error, ratio of edge length relative error less than threshold value and maximum value of direction error; the three reliability indexes comprise: overall reliability, a minimum reliability component, and a number of reliability components greater than a threshold; the three cost indexes comprise: maximum observer weight, sum of all observer weights, and observer type.
Further, the maximum error in the parameter, the proportion of the error in the parameter being smaller than a threshold value, the weakest edge length relative center error, the proportion of the edge length relative center error being smaller than a threshold value, and the maximum value of the error in the direction are obtained by the following formulas:
after the control screen cloth testing scheme is determined, obtaining a co-factor array Q of unknown parameters according to the known information of the control screen cloth testing X The formula is:
Q X ＝(B T PB) -1
wherein B is a design matrix, P is a weight matrix of observed values, and the prior error of a certain observed value is sigma i Its weight p i The method comprises the following steps:
in sigma 0 Is the error in the prior unit weight, and the covariance matrix of the parameters is:
in the design stage of the control screen cloth testing scheme, letThe error in the parameter with the largest index is:
maximum error in parameter=max (m X )
Wherein,
m X ＝sqrt(diag(D X ))
in the formula, the symbol max is calculated by maximum value, m X A medium error vector (absolute value) representing a parameter, sqrt is a square root calculation, diag is a matrix-taking main diagonal element calculation; recording tau 1 For the error threshold value in the parameter, the ratio of the error in the index parameter smaller than the threshold value is as follows:
in the formula, sum is the number operation of elements meeting the condition in the vector, and t is the number of unknown parameters;
observed value vector co-factor matrix Q L The method comprises the following steps:
Q L ＝B(B T PB) -1 B T
correspondingly, the covariance matrix of the observed value vector is:
intermediate error vector of observed value, i.e. absolute value m L The method comprises the following steps:
m L ＝sqrt(diag(D L ))
the side length and direction observation value vectors are respectively L 1 、L 2 The representation is made of a combination of a first and a second color,is viewed in side length and directionThe middle error vectors of the measured values are m L Obtaining the side length observation value L from the outline coordinates of the control net point 1 ，And L 1 The ratio of the corresponding elements is the relative middle error vector m of the side length observation value r . The relative middle error of the weakest edge length of the index is as follows:
the weakest edge length relative medium error=max (m r )
The threshold value of the edge length relative centering error is tau 2 The ratio of the index side length relative middle error is smaller than the threshold value is:
wherein n is 1 For the number of side length observations, the maximum value of the error in the index direction is:
further, the overall reliability, the minimum reliability component, and the number of reliability components greater than a threshold are obtained by the following formulas, respectively:
the overall reliability is represented by the average redundant observed component of the control screen measurement scheme, and the overall reliability of the index is:
wherein n is the total number of observed values;
obtaining a reliability matrix R according to the design matrix and the weight matrix, wherein the formula is as follows:
R＝I-B(B T PB) -1 B T P
in the formula, I is an identity matrix, main diagonal elements of a reliability matrix R are called redundant observation components of observation values, redundant observation components of all the observation values form a vector R, and the reliability component with the smallest index is:
minimum reliability component = min (r)
Wherein the symbol min is the minimum value calculation, and the threshold value of the reliability index is tau 3 The number of reliability components with an index greater than the threshold is:
number of reliability components greater than threshold = sum (r > τ) 3 )。
Further, the maximum observation weight, the sum of all the observation weights, and the observation type are obtained by the following formulas, respectively:
the observed value weight with the maximum index is expressed by an infinite norm of P, and the formula is as follows:
maximum observation weight= |p|. .
The sum of all the observation weights of the index is:
sum of all observations weights = tr (P)
Wherein tr is the operation of obtaining the matrix trace;
in the control measurement of the large engineering ground, the direction and the side length belong to basic observation values, and azimuth angles, coordinates and the like are regarded as auxiliary observation values; the cost required for auxiliary observations will also be different compared to the primary observations, and observations type factor f and a number factor ω are designed herein, the values of which are determined according to the structure, environment and construction process of the project; the index observation types are:
where u is the number of observation types.
Further, the obtaining the relevance according to the optimal evaluation value and the evaluation index is specifically explained as follows: constructing an evaluation matrix according to the evaluation index, and performing dimension elimination and magnitude order processing on the evaluation matrix to obtain a normalized matrix; constructing a reference number sequence according to the optimal evaluation value, and acquiring an association coefficient between the normalized matrix and the reference number sequence;
the method for eliminating the dimension and magnitude order of the evaluation matrix to obtain the normalized matrix comprises the following steps:
the difference of the dimension and magnitude exists among different evaluation values, and in order to eliminate the influence of the dimension and magnitude on the subsequent steps, the evaluation matrix is subjected to standardization processing, and the standardization method is as follows:
in the method, in the process of the invention,is the average value of the kth index of all the evaluated objects, S (k) is the standard deviation of the kth index of all the evaluated objects, j i (k) The evaluation value of the ith evaluated object on the kth index is represented, and the normalized evaluation matrix is:
wherein i=1, 2, …, m, k=1, 2, …, n.
Further, the constructing the reference number sequence according to the optimal evaluation value specifically includes: c (C) 0 (k) The k-th evaluation index is high in all evaluation values, a large value is taken for a high-priority evaluation value, and a small value is taken for a low-priority evaluation value; constructing a reference data column, denoted as C 0 Denoted as C 0 ＝[C 0 (1)，C 0 (2)，…，C 0 (n)]N is the number of evaluation indexes.
Further, the correlation coefficient between the normalized matrix and the reference number column is obtained, and the formula is:
the correlation coefficient of the evaluation value of the ith scheme on the kth index with respect to the optimal evaluation value of the kth index is:
wherein ρ is 0.5.
Further, the obtaining the absolute relevance by using the relevance and the weight vector specifically includes:
the absolute relevance is obtained by using the relevance coefficient and the weight vector, and the formula is as follows:
wherein, xi i (j) J is the number of evaluation indexes, i is the number of schemes;
absolute degree of correlation r i The value of (2) is large, indicating that the i-th evaluated object is in line with the reference number C 0 High similarity and good comprehensive evaluation.
The embodiment of the invention provides a control screen testing scheme evaluation system, which comprises the following steps: the scheme module is used for acquiring various control screen cloth measurement schemes; the evaluation index module is used for obtaining an evaluation index by using five precision indexes, three reliability indexes and three expense indexes; the relevance module is used for selecting an optimal evaluation value from all evaluation values of each evaluation index and acquiring relevance according to the optimal evaluation value and the evaluation index; the relevance module is used for analyzing the weight of each evaluation index by using an analytic hierarchy process, constructing a weight vector and acquiring absolute relevance by using relevance and the weight vector; and the evaluation module is used for carrying out comprehensive evaluation sequencing according to the absolute association degree, and selecting a control screen cloth measurement scheme with high association degree, namely high comprehensive evaluation.
The embodiment of the invention provides a control screen cloth testing scheme evaluation method and a control screen cloth testing scheme evaluation system, which have the following beneficial effects compared with the prior art:
the evaluation indexes obtained from the five precision indexes, the three reliability indexes and the three expense indexes have correlation with the optimal evaluation value selected from the evaluation indexes; and constructing a weight vector for the evaluation index, acquiring the association degree between the association and the weight vector, sequencing the association degree, and finally determining the control screen cloth testing scheme with the highest comprehensive evaluation according to the maximum association degree. The relevance among indexes is analyzed by using the precision, reliability and cost construction indexes, and the control screen cloth measurement scheme is accurately evaluated by considering the influence on the control screen cloth measurement scheme from various factors.
Drawings
FIG. 1 shows a control mesh measurement scheme evaluation method and system for a immersed tube tunnel according to an embodiment of the present invention (a represents S) 1 All-wire net, b represents S 2 Double-line-shaped combined locking net, c represents S 3 All-wire net, d represents S 4 All-wire net, e represents S 5 All-conductor net, f represents S 6 An all-wire mesh);
FIG. 2 is a schematic diagram of a control mesh testing scheme evaluation method and a system index system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an evaluation method and system accuracy of a control mesh testing scheme according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of reliability of a control mesh testing scheme evaluation method and system according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a control mesh testing scheme evaluation method and system cost according to an embodiment of the present invention.
Detailed Description
In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The present invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit of the invention, whereby the invention is not limited to the specific embodiments disclosed below.
Referring to fig. 1 to 5, an embodiment of the present invention provides a control mesh measurement scheme evaluation method, including the steps of:
step one: and obtaining a plurality of large-scale industrial process control mesh testing schemes.
Step two: and calculating an evaluation index by using the five precision indexes, the three reliability indexes and the three cost indexes, and constructing an evaluation matrix according to the evaluation index.
Step three: and carrying out normalized treatment of eliminating dimension and magnitude order on the evaluation matrix to obtain a normalized matrix. And selecting an optimal evaluation value from all evaluation values of each evaluation index of the normalized matrix, and constructing a reference number sequence according to the optimal evaluation value.
Step four: calculating the association coefficient between the normalized matrix and the reference number row, calculating the weight of each evaluation index by using a analytic hierarchy process, constructing a weight vector according to the weight, and calculating the absolute association degree of a plurality of large-scale industrial control network measurement schemes by using the association coefficient and the weight vector.
Step five: and sorting and comprehensively evaluating according to the absolute association degree, and selecting a large industrial control screen cloth testing scheme with high association degree and high comprehensive evaluation.
The evaluation method is explained specifically as follows:
1. comprehensive evaluation of Gray
The gray comprehensive evaluation utilizes limited known information to determine the unknown information of the system, and the method has no requirement on sample size and distribution, has wide application range and can better process the gray system. The basic steps of gray comprehensive evaluation are as follows:
1.1 obtaining raw evaluation data and normalization processing
If a certain system to be evaluated contains n evaluation indexes and m objects to be evaluated, m.n evaluation data of m objects to be evaluated can be obtained by a certain method to form an evaluation matrix J
Wherein j is i (k) The evaluation value of the i-th object under evaluation on the k-th index is i=1, 2, …, m, k=1, 2, …, n.
The difference of the dimension and magnitude of different evaluation values is generated, in order to eliminate the influence of the dimension and magnitude on the subsequent steps, the evaluation matrix is normalized, and the normalization method is as follows
In the method, in the process of the invention,is the average value of the kth index of all the evaluated objects, and S (k) is the standard deviation of the kth index of all the evaluated objects. Normalized evaluation matrix is
1.2 calculating the correlation coefficient and the absolute correlation degree
First a reference data column is formulated. The reference number series is marked as C 0 Denoted as C 0 ＝[C 0 (1)，C 0 (2)，…，C 0 (n)]Wherein C 0 (k) The optimal value of all the evaluation values of the kth index is represented, and the maximum value is taken for the high-priority evaluation value and the minimum value is taken for the low-priority evaluation value. The correlation coefficient of the evaluation value of the ith scheme on the kth index with respect to the optimal evaluation value of the kth index is
Where ρ generally takes a value of 0.5. Thereby obtaining the association coefficient matrix
If the weight vector of the n evaluation indexes is w= [ W ] 1 ，w 2 ，…，w n ] T The absolute association degree of the i-th evaluated object is
Absolute degree of correlation r i The larger the value of (C) indicates the i-th evaluated object and the reference number series C 0 The closer the comprehensive evaluation is, the better the comprehensive evaluation is, so that the ranking of the evaluation objects is obtained, and the comprehensive evaluation and analysis are performed.
2. Control mesh cloth measurement scheme design method based on gray comprehensive evaluation
2.1 construction of an index System
The index system should be constructed in accordance with scientific, flexible and practical principles. In large-scale industrial process control measurement, different control screen measurement schemes comprise different control screen types, observation value precision, observation value number, known point number and the like, and indexes for measuring the advantages and disadvantages of the control screen measurement schemes comprise precision, reliability and cost, and the control screen measurement scheme index system is constructed from the three aspects.
According to the relevant regulations of plane control measurement by using wires and triangular networks in GB 50026-2020 engineering measurement standard, main technical requirements of different measurement grades comprise a side length relative middle error and a side angle middle error, and 5 precision indexes such as the maximum parameter middle error, the proportion of the parameter middle error smaller than a threshold value, the weakest side length relative middle error, the proportion of the side length relative middle error smaller than the threshold value, the maximum value of the direction middle error and the like are determined in combination with the aim of large engineering control measurement.
The internal reliability of the control mesh testing scheme refers to the capability of the control mesh to find the coarse difference of the observed value, the capability is reflected on the redundant observed components of the observed value, the external reliability refers to the capability of the control mesh to resist the influence of the coarse difference of the observed value on the adjustment result, the capability is described by the influence factors of the system, and the internal reliability and the external reliability have consistency. Through analysis, 3 reliability indexes such as overall reliability, minimum reliability components, number of reliability components larger than a threshold value and the like are determined.
The cost of controlling web testing generally involves a number of factors, which are more difficult to describe with an accurate function, and the literature, "track control web design based on multiple objective decisions" uses the sum of the observations weights as the cost criterionHowever, when the sum of the weights of the observed values is very small, the cost of field measurement will be quite different when the sum of the weights of the observed values is very small for the various control screen measurement schemes discussed in document "Anew alignment andbreakthrough accuracy optimization strategy in long immersed tunnel surveys", and the index c shown in the raw evaluation data of each control screen measurement scheme of table 4 is shown below 10 . Thus, in addition to the sum of the observations weights, a total of 3 cost metrics, such as maximum observations weight and observations type, are determined herein.
In summary, the complete control net testing scheme evaluation index system consists of 11 indexes of 3 types, and the last column of different control net evaluation index systems in table 1 is shown. The different control network evaluation index systems of table 1 are compared with the index systems established in the literature "Multicriteria decision making in geodetic network design", "track control network shape design based on multi-objective decision", and the main differences are that: in terms of precision, the method considers the middle error of parameters and the relative middle error and the middle error of the weakest edge length and the direction, and is more consistent with the technical requirements of control measurement in related specifications; in the aspect of reliability, the overall reliability of the control network layout scheme and the reliability component of the observed value are considered; in terms of cost, since the type of observed value is related to the method of instrument and data acquisition employed, the cost of different instruments and data acquisition methods are also different, and a new cost indicator of the type of observed value is designed.
Table 1 different control network evaluation index systems
2.2 acquiring evaluation data
The step of obtaining evaluation data is to obtain all quality evaluation data of different schemes by means of theoretical evaluation, expert consultation and the like in the design stage of the control screen cloth testing scheme.
(1) Precision index
After the control net testing scheme is determined, according to the control net outline coordinate, the nominal precision of the instrument to be selected and the control net grade, estimating to obtain the co-factor array Q of unknown parameters X The scheme precision is estimated. Q (Q) X The calculation formula of (2) is as follows:
Q X ＝(B T PB) -1
wherein B is a design matrix, and P is a weight matrix of observed values. If the prior error of a certain observed value is sigma i Its weight p i The method comprises the following steps:
in sigma 0 Is the error in the a priori unit weights. The covariance matrix of the parameters is:
in the design stage of the control screen cloth testing scheme, the control screen cloth testing scheme can be made toIndex c 1 The method comprises the following steps:
c 1 ＝max(m X )
wherein,
m X ＝sqrt(diag(D X ))
in the formula, the symbol max is calculated by maximum value, m X The medium error vector (absolute value) representing the parameter, sqrt is the square root operation, diag is the matrix main diagonal element operation. Recording tau 1 For the error threshold in the parameter, index c 2 Is that
In the formula, sum is the number operation of elements satisfying the condition in the vector, and t is the number of unknown parameters.
Observed value vector co-factor matrix Q L Is that
Q L ＝B(B T PB) -1 B T
Correspondingly, the covariance matrix of the observed value vector is
Medium error vector (absolute value) m of observed value L Is that
m L ＝sqrt(diag(D L ))
If the observed value includes different types such as side length, direction, azimuth angle, and coordinates, the observed value vector is respectively represented by L 1 、L 2 、L 3 、L 4 And then m is represented by L Can be expressed as
The middle error vectors of the side length and the direction observation values are m L From the rough coordinates of the control net point, the side length observation value L can be calculated 1 ，And L 1 The ratio of the corresponding elements is the relative middle error vector m of the side length observation value r 。And respectively representing the azimuth angle and the middle error vector of the coordinate observation value. Index c 3 Is that
c 3 ＝max(m r )
If the threshold value of the error in the side length is tau 2 Index c 4 Is that
Wherein n is 2 The number of the side length observations. Index c 5 Is that
(2) Reliability index
The overall reliability is represented by the average redundant observed component of the control web measurement scheme, index c 6 The method comprises the following steps:
where n is the total number of observations.
Calculating a reliability matrix R according to the design matrix and the weight matrix, wherein the formula is that
R＝I-B(B T PB) -1 B T P
Wherein I is an identity matrix. The main diagonal element of the reliability matrix R is called the redundant observation component of the observation value, and the redundant observation components of all the observation values form a vector R, then the index c 7 The method comprises the following steps:
c 7 ＝min(r)
in the formula, the symbol min is the minimum value calculation. If the threshold value of the reliability index is tau 3 Index c 8 The method comprises the following steps:
c 8 ＝sum(r＞τ 3 )
the more reliability indexes that are greater than the threshold, the higher the reliability of the control mesh design scheme.
(3) Cost index
And (3) determining a weight formula according to the observed value:
it can be seen that the higher the accuracy of the observed value, the greater the weight thereof, meaning that a greater number of returns, more complex measurement rules or more accurate measuring instruments are required, and the higher the cost is, therefore the index c 9 Expressed by an infinite norm of P, the formula is:
c 9 ＝||P||∞
the smaller the total weight of the observations, the smaller the number of observations, and the lower the total cost, thus the index c 10 The method comprises the following steps:
c 10 ＝tr(P)
where tr is the operation for taking the matrix trace.
In the large-scale engineering ground control measurement, the direction and the side length belong to basic observation values, and azimuth angles, coordinates and the like can be regarded as auxiliary observation values. The cost required for auxiliary observations will also be different compared to the primary observations, so that the observations type factor f and the number factor ω are designed herein, the values of which are determined according to the structure, environment and construction process of the project. Index c 11 The method comprises the following steps:
where u is the number of observation types.
2.3 design method based on gray comprehensive evaluation
According to the control screen cloth measurement scheme and the method for acquiring the evaluation data, acquiring the evaluation indexes of different schemes to form an evaluation matrix J; in order to eliminate the influence of different evaluation index dimensions and magnitude orders such as precision, reliability and cost on subsequent steps, the matrix J is normalized to obtain a normalized matrix C; selecting an optimal value from all evaluation values of each index, taking a maximum value for a high-optimal evaluation value and a minimum value for a low-optimal evaluation value, and forming a reference sequence c 0 And calculating the association coefficient according to the following formula:
obtaining an association coefficient matrix (Xi); calculating the weight of each index by using an analytic hierarchy process to obtain a weight vector W of the index; finally, the absolute relevance of each scheme is calculated according to the following formula:
and sequencing the absolute association degree, and making comprehensive evaluation.
The invention also has the following beneficial effects: the method comprises the steps of calculating the weight of each evaluation index by using an analytic hierarchy process, calculating the absolute association degree of a plurality of large-scale industrial control network measurement schemes by combining the association coefficient, and sorting and comprehensively evaluating the absolute association degree to ensure that the obtained information has strong association and accurate evaluation, so that the association between each evaluation index and the large-scale industrial control network measurement scheme can be comprehensively considered, and the large-scale industrial control network measurement scheme with optimal comprehensive quality is selected.
The embodiment of the invention provides a control screen testing scheme evaluation system, which comprises the following steps:
the scheme module is used for acquiring various control screen measurement schemes.
And the evaluation index module is used for obtaining an evaluation index by using the five precision indexes, the three reliability indexes and the three expense indexes.
And the relevance module is used for selecting an optimal evaluation value from all the evaluation values of each evaluation index and acquiring relevance according to the optimal evaluation value and the evaluation index.
And the relevance module is used for analyzing the weight of each evaluation index by using an analytic hierarchy process, constructing a weight vector and acquiring absolute relevance by using relevance and the weight vector.
And the evaluation module is used for carrying out comprehensive evaluation sequencing according to the absolute association degree, and selecting a control screen cloth measurement scheme with high association degree, namely high comprehensive evaluation.
One specific example is as follows:
and carrying out unidirectional control measurement with the length of about 5.8km, and determining 6 control screen cloth measurement schemes in total by changing the number and the positions of azimuth angles and coordinate observation values. For convenience of expression, the scheme names are denoted by the symbol S, and the basic information of each scheme is shown in table 2 and fig. 1. In all control screen cloth measurement schemes, the side length of the wire screen is about 700m, and the tunnel portal is controlled to be at a point J 1 About 5.8km to the end of the control network, scheme S 2 About 25m on the short side of (c). The a priori errors in the direction, side length and azimuth observations are 1', (0.6+10 respectively -6 D) mm and 3.5 ".
Table 2 basic information of simulation experiment control mesh design scheme
According to the method for acquiring the evaluation data, index data of each testing scheme are calculated respectively.
Threshold τ of error in parameter 1 Set to 3.5cm, the side length is relative to the threshold τ of the middle error 2 Set to 1/150000, threshold τ of reliability index 3 Set to 0.5. The design conditions of the observation value type factors and the quantity factors are shown as the observation value type factors and the quantity factors in table 3, and because the azimuth angle measurement needs to adopt a high-precision gyro total station, the measurement is charged according to the number of azimuth angles, and the measurement rule is far more complex than the measurement of the side length and the direction, the quantity factors of the azimuth angles are equal to the number of azimuth angles.
TABLE 3 Observation value type factor and quantity factor
According to the basic information of the 6 schemes, the length of the side length and the prior error of the observed value, according to the method for acquiring the evaluation data, the evaluation index data of each of the 6 schemes are shown as the original evaluation data of each control screen testing scheme in table 4.
Table 4 raw evaluation data for each control web measurement protocol
In order to eliminate the influence of the dimension and the magnitude on the subsequent steps, the original evaluation indexes are normalized, and the normalized results are shown as normalized values of the evaluation indexes of the control network layout schemes in table 5. According to the normalized value of the evaluation index, the correlation coefficient matrix xi is calculated, and the result is shown as the correlation coefficient of each control network layout scheme in table 6.
TABLE 5 normalized values of evaluation index for control network layout scheme
Establishing judgment matrixes of different layers by using a analytic hierarchy process, calculating weights of all indexes through the judgment matrixes, and indicating the calibration weight results as shown in the index weights and types of table 7, c 2 Is the greatest in weight. And calculating the absolute relevance of each scheme by using a relevance coefficient, an index weight and a relevance calculation formula, wherein the result is shown in the last row of the relevance coefficient of each control network layout scheme in table 6.
The comprehensive scheme ordering result is shown as a multi-scheme comprehensive ordering result in table 8. S is S 6 And S is 2 Is a control screen cloth measurement scheme with better comprehensive quality. Schemes with errors less than the threshold in the parameters and ratios less than 1 are ranked later, due to the error threshold τ in the parameters 1 The value is 3.5cm, if the error in the parameters does not meet the threshold condition, the accuracy of the scheme cannot meet the engineering requirement.
TABLE 6 correlation coefficient for control network layout schemes
TABLE 7 index weight and type
TABLE 8 Multi-scheme comprehensive ranking results
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (10)
1. A control web testing scheme evaluation method, comprising the steps of:
acquiring a plurality of control screen cloth measurement schemes;
obtaining an evaluation index by using five precision indexes, three reliability indexes and three expense indexes;
selecting an optimal evaluation value from all evaluation values of each evaluation index, and acquiring relevance according to the optimal evaluation value and the evaluation index;
analyzing the weight of each evaluation index by using an analytic hierarchy process, constructing a weight vector, and acquiring absolute association degree by using the association and the weight vector;
and (3) carrying out comprehensive evaluation sequencing according to the absolute association degree, and selecting a control screen cloth testing scheme with high association degree, namely high comprehensive evaluation.
2. A control web testing regimen evaluation method according to claim 1, wherein,
the five precision indexes comprise: maximum parameter error, ratio of parameter error less than threshold value, weakest edge length relative error, ratio of edge length relative error less than threshold value and maximum value of direction error;
the three reliability indexes comprise: overall reliability, a minimum reliability component, and a number of reliability components greater than a threshold;
the three cost indexes comprise: maximum observer weight, sum of all observer weights, and observer type.
3. A control web testing scheme evaluation method according to claim 2 wherein the maximum error in the parameter, the ratio of the error in the parameter to the threshold value, the weakest edge length to the center error, the ratio of the edge length to the center error to the threshold value, and the maximum value of the error in the direction are obtained by the following formulas, respectively:
after the control screen cloth testing scheme is determined, obtaining a co-factor array Q of unknown parameters according to the known information of the control screen cloth testing X The formula is:
Q X ＝(B T PB) -1
wherein B is a design matrix, P is a weight matrix of observed values, and the prior error of a certain observed value is sigma i Its weight p i The method comprises the following steps:
in sigma 0 Is the error in the prior unit weight, and the covariance matrix of the parameters is:
in the design stage of the control screen cloth testing scheme, letThe error in the parameter with the largest index is:
maximum error in parameter=max (m X )
Wherein,
m X ＝sqrt(diag(D X ))
in the formula, the symbol max is calculated by maximum value, m X A medium error vector (absolute value) representing a parameter, sqrt is a square root calculation, diag is a matrix-taking main diagonal element calculation; recording tau 1 For the error threshold value in the parameter, the ratio of the error in the index parameter smaller than the threshold value is as follows:
in the formula, sum is the number operation of elements meeting the condition in the vector, and t is the number of unknown parameters;
observed value vector co-factor matrix Q L The method comprises the following steps:
Q L ＝B(B T PB) -1 B T
correspondingly, the covariance matrix of the observed value vector is:
intermediate error vector of observed value, i.e. absolute value m L The method comprises the following steps:
m L ＝sqrt(diag(D L ))
the side length and direction observation value vectors are respectively L 1 、L 2 The representation is made of a combination of a first and a second color,the median error vectors, i.e. absolute values, of the side and direction observations are m L Obtaining the side length observation value L from the outline coordinates of the control net point 1 ，And L 1 The ratio of the corresponding elements is the relative middle error vector m of the side length observation value r . The relative middle error of the weakest edge length of the index is as follows:
the weakest edge length relative medium error=max (m r )
The threshold value of the edge length relative centering error is tau 2 The ratio of the index side length relative middle error is smaller than the threshold value is:
wherein n is 1 For the number of side length observations, the maximum value of the error in the index direction is:
4. a control web testing scheme evaluation method according to claim 2 wherein said overall reliability, said minimum reliability component and said number of reliability components greater than a threshold value are obtained by the following formulas, respectively:
the overall reliability is represented by the average redundant observed component of the control screen measurement scheme, and the overall reliability of the index is:
wherein n is the total number of observed values;
obtaining a reliability matrix R according to the design matrix and the weight matrix, wherein the formula is as follows:
R＝I-B(B T PB) -1 B T P
in the formula, I is an identity matrix, main diagonal elements of a reliability matrix R are called redundant observation components of observation values, redundant observation components of all the observation values form a vector R, and the reliability component with the smallest index is:
minimum reliability component = min (r)
Wherein the symbol min is the minimum value calculation, and the threshold value of the reliability index is tau 3 The number of reliability components with an index greater than the threshold is:
number of reliability components greater than threshold = sum (r>τ 3 )。
5. A control mesh testing scheme evaluation method according to claim 2 wherein the maximum observed value weight, the sum of all observed value weights and the observed value type are obtained by the following formulas, respectively:
the observed value weight with the maximum index is expressed by an infinite norm of P, and the formula is as follows:
maximum observation weight= |p|| ∞
The sum of all the observation weights of the index is:
sum of all observations weights = tr (P)
Wherein tr is the operation of obtaining the matrix trace;
in the control measurement of the large engineering ground, the direction and the side length belong to basic observation values, and azimuth angles, coordinates and the like are regarded as auxiliary observation values; the cost required for auxiliary observations will also be different compared to the primary observations, and observations type factor f and a number factor ω are designed herein, the values of which are determined according to the structure, environment and construction process of the project; the index observation types are:
where u is the number of observation types.
6. A control mesh testing scheme evaluation method according to claim 1, wherein the obtaining of the association according to the optimal evaluation value and the evaluation index is specifically explained as follows:
constructing an evaluation matrix according to the evaluation index, and performing dimension elimination and magnitude order processing on the evaluation matrix to obtain a normalized matrix; constructing a reference number sequence according to the optimal evaluation value, and acquiring an association coefficient between the normalized matrix and the reference number sequence;
the method for eliminating the dimension and magnitude order of the evaluation matrix to obtain the normalized matrix comprises the following steps:
the difference of the dimension and magnitude exists among different evaluation values, and in order to eliminate the influence of the dimension and magnitude on the subsequent steps, the evaluation matrix is subjected to standardization processing, and the standardization method is as follows:
in the method, in the process of the invention,is the average value of the kth index of all the evaluated objects, S (k) is the standard deviation of the kth index of all the evaluated objects, j i (k) The evaluation value of the ith evaluated object on the kth index is represented, and the normalized evaluation matrix is:
where i=1, 2, …, m, k=1, 2, …, n.
7. A control mesh testing scheme evaluation method according to claim 6, wherein the constructing a reference sequence according to the optimal evaluation value specifically comprises:
C 0 (k) The k-th evaluation index is high in all evaluation values, a large value is taken for a high-priority evaluation value, and a small value is taken for a low-priority evaluation value;
constructing a reference data column, denoted as C 0 Denoted as C 0 ＝[C 0 (1),C 0 (2),…,C 0 (n)]N is the number of evaluation indexes.
8. A control web testing scheme evaluation method according to claim 6 wherein the obtaining of the correlation coefficient between the normalized matrix and the reference sequence has the formula:
the correlation coefficient of the evaluation value of the ith scheme on the kth index with respect to the optimal evaluation value of the kth index is:
wherein ρ is 0.5.
9. A control mesh testing scheme evaluation method according to claim 1 or 8, wherein the absolute relevance is obtained by using relevance and weight vector, specifically:
the absolute relevance is obtained by using the relevance coefficient and the weight vector, and the formula is as follows:
wherein, xi i (j) J is the number of evaluation indexes, i is the number of schemes;
absolute degree of correlation r i The value of (2) is large, indicating that the i-th evaluated object is in line with the reference number C 0 High similarity and good comprehensive evaluation.
10. A control web testing scheme evaluation system, comprising:
the scheme module is used for acquiring various control screen cloth measurement schemes;
the evaluation index module is used for obtaining an evaluation index by using five precision indexes, three reliability indexes and three expense indexes;
the relevance module is used for selecting an optimal evaluation value from all evaluation values of each evaluation index and acquiring relevance according to the optimal evaluation value and the evaluation index;
the relevance module is used for analyzing the weight of each evaluation index by using an analytic hierarchy process, constructing a weight vector and acquiring absolute relevance by using relevance and the weight vector;
and the evaluation module is used for carrying out comprehensive evaluation sequencing according to the absolute association degree, and selecting a control screen cloth measurement scheme with high association degree, namely high comprehensive evaluation.
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