CN115494881B - Unconstrained optimization index weighting method for unmanned aerial vehicle formation collaborative track planning - Google Patents

Unconstrained optimization index weighting method for unmanned aerial vehicle formation collaborative track planning Download PDF

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CN115494881B
CN115494881B CN202211442903.6A CN202211442903A CN115494881B CN 115494881 B CN115494881 B CN 115494881B CN 202211442903 A CN202211442903 A CN 202211442903A CN 115494881 B CN115494881 B CN 115494881B
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CN115494881A (en
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张通
杨忠龙
许涛
沈昊
杨韬
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Northwestern Polytechnical University
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    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
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Abstract

The invention relates to an unconstrained optimization index weighting method for unmanned aerial vehicle formation collaborative flight path planning, which is characterized in that combination weighting is carried out in a subjective and objective combination mode, and meanwhile, a subjective weighting method is reasonably improved. The flight path generated by the unmanned aerial vehicle formation in the flying process is more scientific and reasonable by the combined empowerment mode, and the requirements of task scenes are met. Different empowerment results can be calculated according to different requirements of the task scene. However, the weighting result obtained by artificial experience is not objective enough because of being too dependent on subjective experience, and the weight coefficient is obtained by multiple experimental adjustments.

Description

Unconstrained optimization index weighting method for unmanned aerial vehicle formation collaborative track planning
Technical Field
The invention belongs to the technical field of unmanned aerial vehicles, and particularly relates to an unconstrained optimization index weighting method for unmanned aerial vehicle formation collaborative track planning.
Background
Along with the development of scientific technology, research and application of the concept of unmanned aerial vehicle formation cooperation in various fields are more and more, and due to the fact that the function of a single unmanned aerial vehicle with low cost is limited, a plurality of unmanned aerial vehicles need to be used for forming a formation cooperation execution task. Wherein formation track generation is an unconstrained optimization problem, based on an objective function
Figure 325298DEST_PATH_IMAGE001
Therein is described
Figure 570335DEST_PATH_IMAGE002
Is the weight vector of seven cost indexes of the objective function, we need to find the objective function in the next step of path pointsAnd taking the point with the minimum value as a track point of the next track. The weight vector of each cost index is specified by human experience and is obtained by lacking of scientific method calculation.
At present, research results aiming at the problems are few, the existing methods are that weight coefficients of all indexes in a cost function are manually specified, experience components are more, and scientific method calculation is lacked.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides the unconstrained optimization index empowering method for unmanned aerial vehicle formation collaborative track planning, which can scientifically and reasonably empowering indexes and solve the irrationality caused by artificial experience empowering.
Technical scheme
An unconstrained optimization index weighting method for unmanned aerial vehicle formation collaborative track planning is characterized in that: the evaluation system is constructed into seven evaluation indexes which need to be considered for generating track points during formation flight of unmanned aerial vehicles, the evaluation system needs to be subjected to combined weighting to determine the weight of each index, and the seven evaluation indexes are respectively the minimum control force cost
Figure 5864DEST_PATH_IMAGE003
Total time cost
Figure 604336DEST_PATH_IMAGE004
And avoid barrier cost
Figure 481025DEST_PATH_IMAGE005
Team similarity cost
Figure 631384DEST_PATH_IMAGE006
Collision avoidance between machines
Figure 981242DEST_PATH_IMAGE007
Collision avoidance between machines
Figure 508038DEST_PATH_IMAGE008
And the cost of uniform distribution of the restriction points
Figure 239234DEST_PATH_IMAGE009
(ii) a The method comprises the following steps:
step 1: according to
Figure 560494DEST_PATH_IMAGE010
The scaling method obtains the weight vector of each index according to the calculation steps of the AHP method;
step 2: according to
Figure 377140DEST_PATH_IMAGE011
The scaling method obtains the weight vector of each index according to the calculation steps of the AHP method;
and step 3: performing discrimination mixing on the results of the two scaling methods to obtain a subjective weighting result;
and 4, step 4: calculating five subjective weighting results to form an initial correction matrix;
and 5: and correcting the initial correction matrix according to the entropy weight method calculation step and finally correcting the weighted result of the subjective and objective combination.
The further technical scheme of the invention is as follows: the step 1 is as follows:
step 11: by using
Figure 582993DEST_PATH_IMAGE012
Scaling, judging matrices based on different constructions of the index importance
Figure 699854DEST_PATH_IMAGE013
；
Step 12: calculating a decision matrix
Figure 332960DEST_PATH_IMAGE014
Product of elements in each column
Figure 168061DEST_PATH_IMAGE015
；
Step 13: to pair
Figure 912026DEST_PATH_IMAGE016
Root of Japanese Kai 7 times
Figure 883393DEST_PATH_IMAGE017
；
Step 14: for vector
Figure 814965DEST_PATH_IMAGE018
Carrying out normalization treatment, wherein the normalization formula of each component is
Figure 12728DEST_PATH_IMAGE019
To obtain a vector
Figure 419439DEST_PATH_IMAGE020
Immediate decision matrix
Figure 386258DEST_PATH_IMAGE021
The feature vector of (2);
step 15: evaluating a decision matrix
Figure 220221DEST_PATH_IMAGE022
Maximum eigenvalue of
Figure 498756DEST_PATH_IMAGE023
；
Step 16: calculating a decision matrix
Figure 974737DEST_PATH_IMAGE024
The consistency index of (2):
Figure 796062DEST_PATH_IMAGE025
whereinn=7；
And step 17: calculating a decision matrix
Figure 332086DEST_PATH_IMAGE026
Uniformity ratio of (a):
Figure 973283DEST_PATH_IMAGE027
whereinRIIs an average random consistency index; when in use
Figure 721796DEST_PATH_IMAGE028
When the judgment matrix is in the allowable range, the judgment matrix is consistent; then
Figure 787841DEST_PATH_IMAGE029
Is correspondingly composed of
Figure 370132DEST_PATH_IMAGE030
The weighting factor of each index is scaled.
The further technical scheme of the invention is as follows: the step 2 is as follows:
step 21: by using
Figure 620329DEST_PATH_IMAGE031
Scaling, judging matrices based on different constructions of importance of the indicators
Figure 313478DEST_PATH_IMAGE032
；
Step 22: calculating a decision matrix
Figure 437292DEST_PATH_IMAGE033
Product of elements in each column
Figure 315118DEST_PATH_IMAGE034
；
Step 23: to pair
Figure 196487DEST_PATH_IMAGE035
Root of Japanese Kai 7 times
Figure 552382DEST_PATH_IMAGE036
；
Step 24: for vector
Figure 327440DEST_PATH_IMAGE037
Carrying out normalization treatment, wherein the normalization formula of each component is
Figure 720375DEST_PATH_IMAGE038
To obtain a vector
Figure 213673DEST_PATH_IMAGE039
Immediate decision matrix
Figure 107680DEST_PATH_IMAGE040
The feature vector of (2);
step 25: evaluating a decision matrix
Figure 878190DEST_PATH_IMAGE041
Maximum eigenvalue of
Figure 832239DEST_PATH_IMAGE042
；
Step 26: calculating a decision matrix
Figure 422621DEST_PATH_IMAGE043
The consistency index of (2):
Figure 388827DEST_PATH_IMAGE044
whereinn=7；
Step 27: calculating a decision matrix
Figure 341740DEST_PATH_IMAGE045
Uniformity ratio of (a):
Figure 466690DEST_PATH_IMAGE046
whereinRIIs an average random consistency index; when in use
Figure 544368DEST_PATH_IMAGE047
When the judgment matrix is in the allowable range, the judgment matrix is consistent; then
Figure 45756DEST_PATH_IMAGE048
Is correspondingly composed of
Figure 384334DEST_PATH_IMAGE049
The weighting factor of each index is scaled.
The further technical scheme of the invention is as follows: the step 3 is specifically as follows:
will be provided with
Figure 821131DEST_PATH_IMAGE050
Scaling method and
Figure 245159DEST_PATH_IMAGE031
the weighted results of the scaling method are mixed with the degree of distinction to establish a function of the degree of distinction
Figure 425605DEST_PATH_IMAGE051
Through reaction with
Figure 618689DEST_PATH_IMAGE052
And
Figure 85442DEST_PATH_IMAGE053
performing simultaneous calculation to obtain the three formulas
Figure 728258DEST_PATH_IMAGE054
And
Figure 305870DEST_PATH_IMAGE055
the final subjective weighted result is
Figure 494405DEST_PATH_IMAGE056
。
The further technical scheme of the invention is as follows: the step 4 is specifically as follows:
respectively carrying out discrimination mixing on five groups of indexes with different importance sequences according to two scaling methods to obtain corresponding weight vectors
Figure 132060DEST_PATH_IMAGE057
And the five results constitute the repairPositive matrix
Figure 530680DEST_PATH_IMAGE058
：
Figure 115246DEST_PATH_IMAGE059
。
The further technical scheme of the invention is as follows: the step 5 is as follows:
step 51: calculating an indexjEntropy of (d):
Figure 282922DEST_PATH_IMAGE060
whereinmIs composed of
Figure 91478DEST_PATH_IMAGE061
The number of the rows,jthe number of indexes to be entitled is
Figure 711815DEST_PATH_IMAGE062
The number of columns;
step 52: calculating the entropy weight of the index:
Figure 37754DEST_PATH_IMAGE063
；
step 53: calculating the average weight of the index:
Figure 62866DEST_PATH_IMAGE064
；
step 54: calculating the correction weight of the index:
Figure 183269DEST_PATH_IMAGE065
；
step 55: the final combination weight is obtained by calculation
Figure 822061DEST_PATH_IMAGE066
。
A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the above-described method.
A computer-readable storage medium having stored thereon computer-executable instructions for performing the above-described method when executed.
Advantageous effects
Compared with the artificial designated weight vector, the calculation process of the unconstrained optimization index weighting method for collaborative flight path planning of unmanned aerial vehicle formation provided by the invention adopts a combined weighting method of subjective and objective combination, improves the subjective weighting method, scientifically calculates the weight coefficient of each index by combining the subjective and objective combination, replaces the coefficient which is considered to be designated by people, has more scientific and reasonable calculation result, and is beneficial to generating more reasonable flight path when the unmanned aerial vehicle formation flies.
Drawings
The drawings, in which like reference numerals refer to like parts throughout, are for the purpose of illustrating particular embodiments only and are not to be considered limiting of the invention.
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a non-constrained optimization index weighting method for unmanned aerial vehicle formation collaborative track planning. And then, the subjective weighting result is corrected by adopting an objective weighting method of an entropy weighting method, and finally, a combined weighting result of the subjective and objective combination is obtained. The method can scientifically calculate the weight vector required by the formation of the unmanned aerial vehicle to generate the flight path, and is used for replacing the artificially-specified weight vector obtained through experience.
The solving method comprises the following five steps:
1. according to
Figure 545166DEST_PATH_IMAGE067
The scaling method obtains a weight vector according to the calculation steps of the AHP method;
2. according to
Figure 562801DEST_PATH_IMAGE068
The scaling method obtains a weight vector according to the calculation steps of the AHP method;
3. performing discriminative degree mixing on the results of the two scaling methods to obtain a subjective weighting result;
4. calculating five subjective weighting results to form an initial correction matrix;
5. and correcting the final weighting result of the subjective and objective combination according to the entropy weight method calculation step.
The specific steps comprise the following steps 1-16, wherein the steps 1 to 11 are an improved mixed AHP calculation flow of a subjective weighting part, and the steps 12 to 16 are an entropy weight method correction calculation flow of an objective weighting part:
step 1: the evaluation system is constructed into seven evaluation indexes which need to be considered when the track point is generated during the formation flight of the unmanned aerial vehicle, the evaluation system needs to be subjected to combined weighting to determine the weight of each index, and each index is the minimum control force cost
Figure 978739DEST_PATH_IMAGE069
Total time cost
Figure 573668DEST_PATH_IMAGE070
And obstacle avoidance cost
Figure 241410DEST_PATH_IMAGE071
Team similarity cost
Figure 707026DEST_PATH_IMAGE072
Collision avoidance between machines
Figure 559445DEST_PATH_IMAGE073
Collision avoidance between machines
Figure 782615DEST_PATH_IMAGE074
And the cost of uniform distribution of the restriction points
Figure 847523DEST_PATH_IMAGE075
。
Step 2: subjective weighting segment selection
Figure 839750DEST_PATH_IMAGE012
Scaling method and
Figure 594561DEST_PATH_IMAGE076
the idea of mixing the results of the scaling calculations, the description of both scaling methods is shown in table 1;
TABLE 1 description of the two scales
Degree of importance
Figure 164083DEST_PATH_IMAGE077
Method of scaling
Figure 908048DEST_PATH_IMAGE078
Method of scaling
A i AndA j of equal importance 1 1
A i Ratio ofA j Of slight importance 3 1.492
A i Ratio ofA j Of obvious importance 5 2.226
A i Ratio ofA j Of strong importance 7 3.320
A i Ratio ofA j Of utmost importance 9 4.953
Intermediate between the above two determinations 2、4、6、8 1.221、1.822、2.718、4.055
And step 3: respectively according to two scaling methods (table 1) according to different structures of index importance degree
Figure 144994DEST_PATH_IMAGE079
And
Figure 542477DEST_PATH_IMAGE080
；
and 4, step 4: respectively calculating two judgment matrixes
Figure 333716DEST_PATH_IMAGE081
And
Figure 881372DEST_PATH_IMAGE082
product of each column element of
Figure 707245DEST_PATH_IMAGE083
And
Figure 806788DEST_PATH_IMAGE084
；
and 5: are respectively paired
Figure 226268DEST_PATH_IMAGE085
And
Figure 436670DEST_PATH_IMAGE086
root of Japanese Kai 7 times
Figure 119980DEST_PATH_IMAGE087
And
Figure 531369DEST_PATH_IMAGE088
；
step 6: respectively to vector
Figure 562779DEST_PATH_IMAGE089
And
Figure 311292DEST_PATH_IMAGE090
performing normalization processing to
Figure 252704DEST_PATH_IMAGE091
For example, the normalization formula of each component is
Figure 162891DEST_PATH_IMAGE092
The resulting vector
Figure 681597DEST_PATH_IMAGE093
Is the decision matrix
Figure 374746DEST_PATH_IMAGE094
The feature vector of (2);
and 7: respectively solving the maximum eigenvalues of two judgment matrixes
Figure 29719DEST_PATH_IMAGE095
And
Figure 782911DEST_PATH_IMAGE096
wherein
Figure 523334DEST_PATH_IMAGE097
Is that
Figure 613650DEST_PATH_IMAGE098
To (1) aiThe number of the components is such that,
Figure 264074DEST_PATH_IMAGE099
；
and step 8: respectively calculating consistency indexes of the two judgment matrixes:
Figure 67730DEST_PATH_IMAGE100
whereinn=7；
And step 9: the consistency ratio of the two decision matrices is calculated:
Figure 561028DEST_PATH_IMAGE101
whereinRIThe average random consistency index is obtained by taking the following table as followsCRThe smaller the matrix is, the better the consistency of the judgment matrix is, when
Figure 330401DEST_PATH_IMAGE102
When the difference of the judgment matrix is within the allowable range, the judgment matrix is consistent becausen=7 soRIIs 1.32 corresponding to dimension 7;
TABLE 2 table for taking values of average random consistency index
Dimension number 2 3 4 5 6 7 8 9
RI 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45
Step 10: if two decision matrices are present
Figure 428807DEST_PATH_IMAGE103
And
Figure 382856DEST_PATH_IMAGE104
all pass the consistency check, then
Figure 363451DEST_PATH_IMAGE105
And
Figure 670935DEST_PATH_IMAGE106
are respectively corresponding
Figure 155006DEST_PATH_IMAGE107
Scaling method and
Figure 279957DEST_PATH_IMAGE108
the weighting coefficient of each index obtained by the scaling method is calculated.
Step 11: will be provided with
Figure 357635DEST_PATH_IMAGE109
Scaling method and
Figure 124602DEST_PATH_IMAGE110
the weighted results of the scaling method are mixed with the degree of distinction to establish a function of the degree of distinction
Figure 466109DEST_PATH_IMAGE111
Through reaction with
Figure 902907DEST_PATH_IMAGE112
And
Figure 795777DEST_PATH_IMAGE113
performing simultaneous calculation to obtain the three formulas
Figure 569698DEST_PATH_IMAGE114
And
Figure 28361DEST_PATH_IMAGE115
the final subjective weighted result is
Figure 636060DEST_PATH_IMAGE116
；
Step 12: respectively carrying out discriminative degree mixing on five groups of indexes with different importance ranks according to two scaling methods, namely respectively obtaining weight vectors corresponding to the five groups of indexes with different importance ranks according to the calculation processes from step 1 to step 11
Figure 547384DEST_PATH_IMAGE117
And forming a correction matrix from the five results
Figure 390575DEST_PATH_IMAGE118
：
Figure 579111DEST_PATH_IMAGE119
Step 13: calculating an indexjEntropy of (d):
Figure 216766DEST_PATH_IMAGE120
whereinmIs composed of
Figure 880965DEST_PATH_IMAGE121
The number of the rows,jthe number of indexes to be entitled is
Figure 137634DEST_PATH_IMAGE122
The number of columns;
step 14: calculating the indexjEntropy weight of (2):
Figure 36801DEST_PATH_IMAGE123
；
step 15: calculating an indexjAverage weight of (d):
Figure 110937DEST_PATH_IMAGE124
；
step 16: calculating an indexjCorrection weight of (2):
Figure 731274DEST_PATH_IMAGE125
；
and step 17: the final combining weight obtained from the above calculations of step 12 to step 16 is
Figure 791634DEST_PATH_IMAGE126
。
In order that those skilled in the art will better understand the present invention, the following detailed description is given with reference to specific examples.
Example 1:
the evaluation system is calculated and a judgment matrix is constructed according to two scaling methods in table 1, and the importance degree judgment of the first group of indexes with different importance ranks is as follows:
Figure 813816DEST_PATH_IMAGE127
by
Figure 58853DEST_PATH_IMAGE128
Scaling method and
Figure 307432DEST_PATH_IMAGE129
the judgment matrixes constructed by the scale method are respectively as follows:
Figure 30537DEST_PATH_IMAGE130
Figure 907226DEST_PATH_IMAGE131
according to the calculation flow from step 4 to step 11, the weight calculation results of the two scaling methods are respectively:
Figure 57585DEST_PATH_IMAGE132
it corresponds to
Figure 655444DEST_PATH_IMAGE133
，
Figure 792027DEST_PATH_IMAGE134
All pass consistency check, so simultaneous solution can be obtained according to the mixed calculation formula of the degrees of distinction in the step 11
Figure 54381DEST_PATH_IMAGE135
，
Figure 641220DEST_PATH_IMAGE136
And finally, mixing the results of the two scaling methods, wherein the subjective mixing weight result is as follows:
Figure 333233DEST_PATH_IMAGE137
similarly, the importance degree of the second group of indexes with different importance ranks is judged as follows:
Figure 663720DEST_PATH_IMAGE138
by
Figure 780580DEST_PATH_IMAGE128
Scaling method and
Figure 148108DEST_PATH_IMAGE129
the judgment matrixes constructed by the scale method are respectively as follows:
Figure 983209DEST_PATH_IMAGE139
Figure 851808DEST_PATH_IMAGE140
according to the calculation flow from step 4 to step 11, the weight calculation results of the two scaling methods are respectively:
Figure 292016DEST_PATH_IMAGE141
corresponding thereto
Figure 361603DEST_PATH_IMAGE142
，
Figure 149912DEST_PATH_IMAGE143
All pass consistency check, so simultaneous solution can be obtained according to the mixed calculation formula of the degrees of distinction in the step 11
Figure 822202DEST_PATH_IMAGE144
，
Figure 789021DEST_PATH_IMAGE145
And finally, mixing the weights of the two scaling methods, wherein the subjective mixed weight result is as follows:
Figure 888564DEST_PATH_IMAGE146
at this time, the two groups of subjective mixed weights are adjusted to the same index weight sequence and combined into a correction matrix
Figure 308044DEST_PATH_IMAGE147
：
Figure 784025DEST_PATH_IMAGE148
The final combining weight obtained by performing the above calculation from step 13 to step 16 on the matrix is:
Figure 464405DEST_PATH_IMAGE149
this weight is used as the final weight of the index system described above in place of the individual weights specified empirically, i.e. manually
Figure 938111DEST_PATH_IMAGE150
。
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.

Claims (3)

1. An unconstrained optimization index weighting method for unmanned aerial vehicle formation collaborative track planning is characterized in that: the evaluation system is constructed into seven evaluation indexes which need to be considered for generating track points during formation flight of unmanned aerial vehicles, the evaluation system needs to be subjected to combined weighting to determine the weight of each index, and the seven evaluation indexes are respectively the minimum control force cost
Figure DEST_PATH_IMAGE001
Total time cost
Figure DEST_PATH_IMAGE002
And avoid barrier cost
Figure DEST_PATH_IMAGE003
Team similarity cost
Figure DEST_PATH_IMAGE004
Collision avoidance between machines
Figure DEST_PATH_IMAGE005
Collision avoidance between machines
Figure DEST_PATH_IMAGE006
And the cost of uniform distribution of the restriction points
Figure DEST_PATH_IMAGE007
(ii) a The method comprises the following steps:
step 1: according to
Figure DEST_PATH_IMAGE008
The scaling method obtains the weight vector of each index according to the calculation steps of the AHP method;
step 11: by using
Figure DEST_PATH_IMAGE009
Scaling, judging matrices based on different constructions of importance of the indicators
Figure DEST_PATH_IMAGE010
；
Step 12: calculating a decision matrix
Figure DEST_PATH_IMAGE011
Product of elements in each column
Figure DEST_PATH_IMAGE012
；
Step 13: to pair
Figure DEST_PATH_IMAGE013
Root of Japanese Kai 7 times
Figure DEST_PATH_IMAGE014
；
Step 14: for vector
Figure DEST_PATH_IMAGE015
Carrying out normalization treatment, wherein the normalization formula of each component is
Figure DEST_PATH_IMAGE016
To obtain(Vector)
Figure DEST_PATH_IMAGE017
Immediate decision matrix
Figure DEST_PATH_IMAGE018
The feature vector of (2);
step 15: evaluating and judging matrix
Figure 840512DEST_PATH_IMAGE018
Maximum eigenvalue of
Figure DEST_PATH_IMAGE019
；
Step 16: calculating a decision matrix
Figure 554390DEST_PATH_IMAGE018
The consistency index of (2):
Figure DEST_PATH_IMAGE020
whereinn=7；
And step 17: calculating a decision matrix
Figure 927602DEST_PATH_IMAGE018
Uniformity ratio of (a):
Figure DEST_PATH_IMAGE021
whereinRIIs an average random consistency index; when in use
Figure DEST_PATH_IMAGE022
When the judgment matrix is in the allowable range, the judgment matrix is consistent; then
Figure DEST_PATH_IMAGE023
Is correspondingly composed of
Figure DEST_PATH_IMAGE024
Weight coefficient of each index of scale method；
Step 2: according to
Figure DEST_PATH_IMAGE025
The scaling method obtains the weight vector of each index according to the calculation steps of the AHP method;
step 21: by using
Figure DEST_PATH_IMAGE026
Scaling, judging matrices based on different constructions of the index importance
Figure DEST_PATH_IMAGE027
；
Step 22: calculating a decision matrix
Figure DEST_PATH_IMAGE028
Product of elements in each column
Figure DEST_PATH_IMAGE029
；
Step 23: for is to
Figure DEST_PATH_IMAGE030
Root of Japanese Kai 7 times
Figure DEST_PATH_IMAGE031
；
Step 24: for vector
Figure DEST_PATH_IMAGE032
Carrying out normalization treatment, wherein the normalization formula of each component is
Figure DEST_PATH_IMAGE033
To obtain a vector
Figure DEST_PATH_IMAGE034
Immediate decision matrix
Figure DEST_PATH_IMAGE035
The feature vector of (2);
step 25: evaluating a decision matrix
Figure DEST_PATH_IMAGE036
Maximum eigenvalue of
Figure DEST_PATH_IMAGE037
；
Step 26: calculating a decision matrix
Figure DEST_PATH_IMAGE038
The consistency index of (2):
Figure DEST_PATH_IMAGE039
whereinn=7；
Step 27: calculating a decision matrix
Figure DEST_PATH_IMAGE040
Uniformity ratio of (a):
Figure DEST_PATH_IMAGE041
in whichRIIs an average random consistency index; when in use
Figure DEST_PATH_IMAGE042
When the judgment matrix is in the allowable range, the judgment matrix is consistent; then
Figure DEST_PATH_IMAGE043
Is correspondingly composed of
Figure DEST_PATH_IMAGE044
Weighting coefficients of each index by a scaling method;
and step 3: performing discrimination mixing on the results of the two scaling methods to obtain a subjective weighting result;
will be provided with
Figure DEST_PATH_IMAGE045
Scaling method and
Figure 775341DEST_PATH_IMAGE044
the weighted results of the scaling method are mixed with the degree of distinction to establish a function of the degree of distinction
Figure DEST_PATH_IMAGE046
By reacting with
Figure DEST_PATH_IMAGE047
And
Figure DEST_PATH_IMAGE048
performing simultaneous calculation to obtain the three formulas
Figure DEST_PATH_IMAGE049
And with
Figure DEST_PATH_IMAGE050
The final subjective weighted result is
Figure DEST_PATH_IMAGE051
；
And 4, step 4: calculating five subjective weighting results to form an initial correction matrix;
respectively carrying out discrimination mixing on five groups of indexes with different importance sequences according to two scaling methods to obtain corresponding weight vectors
Figure DEST_PATH_IMAGE052
And forming a correction matrix from the five results
Figure DEST_PATH_IMAGE053
：
Figure DEST_PATH_IMAGE054
；
And 5: correcting the initial correction matrix according to the entropy weight method calculation step and finally correcting the weighted result of the subjective and objective combination;
step 51: calculating an indexjEntropy of (d):
Figure DEST_PATH_IMAGE055
whereinmIs composed of
Figure DEST_PATH_IMAGE056
The number of the rows,jthe number of indexes to be entitled is
Figure DEST_PATH_IMAGE057
The number of columns;
step 52: calculating the entropy weight of the index:
Figure DEST_PATH_IMAGE058
；
step 53: calculating the average weight of the index:
Figure DEST_PATH_IMAGE059
；
step 54: calculating the correction weight of the index:
Figure DEST_PATH_IMAGE060
；
step 55: the final combination weight is obtained by calculation
Figure DEST_PATH_IMAGE061
。
2. A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of claim 1.
3. A computer-readable storage medium having stored thereon computer-executable instructions for, when executed, implementing the method of claim 1.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105469196A (en) * 2015-11-18 2016-04-06 山东科技大学 Comprehensive evaluation method and comprehensive evaluation system for evaluating mine construction project process
CN106202267A (en) * 2016-06-30 2016-12-07 四川农业大学 The Citrus chachiensis Hort. integrated quality evaluation methodology of a kind of yellow fruit
CN110599011A (en) * 2019-08-29 2019-12-20 广东省水利水电科学研究院 Aqueduct safety evaluation method, system and storage medium based on improved AHP-FCE method
CN112950008A (en) * 2021-02-08 2021-06-11 北京理工大学 Flight path planning evaluation method of aircraft
CN114548725A (en) * 2022-02-15 2022-05-27 大连理工大学 Deep foundation pit stability evaluation method based on entropy weight-level analysis fuzzy comprehensive evaluation method
CN115168870A (en) * 2022-07-29 2022-10-11 江苏大学 Block chain safety assessment method based on comprehensive evaluation

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11727812B2 (en) * 2017-07-27 2023-08-15 Beihang University Airplane flight path planning method and device based on the pigeon-inspired optimization
CN113537663A (en) * 2020-04-15 2021-10-22 海鹰航空通用装备有限责任公司 Unmanned aerial vehicle track evaluation method based on TOPSIS algorithm

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105469196A (en) * 2015-11-18 2016-04-06 山东科技大学 Comprehensive evaluation method and comprehensive evaluation system for evaluating mine construction project process
CN106202267A (en) * 2016-06-30 2016-12-07 四川农业大学 The Citrus chachiensis Hort. integrated quality evaluation methodology of a kind of yellow fruit
CN110599011A (en) * 2019-08-29 2019-12-20 广东省水利水电科学研究院 Aqueduct safety evaluation method, system and storage medium based on improved AHP-FCE method
CN112950008A (en) * 2021-02-08 2021-06-11 北京理工大学 Flight path planning evaluation method of aircraft
CN114548725A (en) * 2022-02-15 2022-05-27 大连理工大学 Deep foundation pit stability evaluation method based on entropy weight-level analysis fuzzy comprehensive evaluation method
CN115168870A (en) * 2022-07-29 2022-10-11 江苏大学 Block chain safety assessment method based on comprehensive evaluation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
基于改进AHP-熵权法的雷达装备可靠性评估指标赋权方法;翟芸 等;《现代防御技术》;20220831;第50卷(第4期);第2.1节，第3.1节，及表3-表8 *

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