CN107392248A - Gear parameter Contribution Analysis method based on PCA reconstruction errors - Google Patents

Gear parameter Contribution Analysis method based on PCA reconstruction errors Download PDF

Info

Publication number
CN107392248A
CN107392248A CN201710599975.4A CN201710599975A CN107392248A CN 107392248 A CN107392248 A CN 107392248A CN 201710599975 A CN201710599975 A CN 201710599975A CN 107392248 A CN107392248 A CN 107392248A
Authority
CN
China
Prior art keywords
value
matrix
characteristic vector
gear
sample
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201710599975.4A
Other languages
Chinese (zh)
Other versions
CN107392248B (en
Inventor
利节
龚为伦
刘松
姜艳军
孙宇
陈瑶
陈国荣
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chongqing University of Science and Technology
Chongqing Qingshan Industry Co Ltd
Chongqing Tsingshan Industrial Co Ltd
Original Assignee
Chongqing University of Science and Technology
Chongqing Qingshan Industry Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chongqing University of Science and Technology, Chongqing Qingshan Industry Co Ltd filed Critical Chongqing University of Science and Technology
Priority to CN201710599975.4A priority Critical patent/CN107392248B/en
Publication of CN107392248A publication Critical patent/CN107392248A/en
Application granted granted Critical
Publication of CN107392248B publication Critical patent/CN107392248B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G06F18/2135—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on approximation criteria, e.g. principal component analysis

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Artificial Intelligence (AREA)
  • Evolutionary Biology (AREA)
  • Evolutionary Computation (AREA)
  • Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The present invention provides a kind of gear parameter Contribution Analysis method based on PCA reconstruction errors, it is characterised in that follows the steps below：S1：N group data are inputted, each group of packet contains m characteristic value, so as to form the sample matrix X of n × m dimensions；S2：Its characteristic vector U initial value is obtained according to sample matrix X covariance matrix；S3：Establish " error and minimum " target function model；S4：According to characteristic vector U during its object function minimum value, according to its character pair value size from top to bottom by rows into matrix, h rows before taking, corresponding parameter is the maximum parameter of contribution degree, h ＜ m.Its effect is：By being improved to traditional PCA algorithms, introduce error and minimum target function model, by the characteristic vector that traditional PCA algorithms obtain as just initial value, pass through the optimization that iterates, finally give the characteristic vector of error and minimum target Function Optimization state, found by contrasting, for the algorithm after improvement for traditional PCA algorithms, its precision is higher.

Description

Gear parameter Contribution Analysis method based on PCA reconstruction errors
Technical field
The present invention relates to the information processing technology in mechanical manufacturing field, and in particular to a kind of based on PCA reconstruction errors Gear parameter Contribution Analysis method.
Background technology
The influence of gear performance audient's multi-parameter, and tooth bending safety coefficient and touch-safe coefficient are to judge gear The Main Basiss of energy, in order to reduce the amount of calculation of tooth factor, people are directed to finding always maximum to index impacts degree Parameter, therefore, the Contribution Analysis of gear parameter become a study hotspot of current mechanical manufacturing field.
In the prior art, people's generally use principal component analysis (Principal Component Analysis, abbreviation PCA) algorithm carries out the searching of principal component.Principal component analytical method is a kind of Linear Mapping method commonly used in pattern-recognition, is Analysis method based on data-signal second-order statisticses.Multiple correlated variables are reduced to several uncorrelated variables lines by this method Property combination, in the case where ensureing that data message loses minimum principle, linear conversion and give up a part of information, with a small number of new changes Measure for original multidimensional variable, so as to realize the mapping to high dimensional variable space to lower dimensional space.From PCA in terms of algebra viewpoint Basic thought be exactly try original numerous indexs with certain correlation, be reassembled into one group of being independent of each other newly Overall target replaces original index.PCA is exactly to find an optimal subspace in other words, when multidimensional data is in the subspace After being projected, gained component has maximum variance, meanwhile, when initial data is reconstructed with pivot, in lowest mean square Approximation effect is optimal under error sense.
But pass through research and find, traditional PCA algorithms still have necessarily when carrying out gear parameter Contribution Analysis Limitation, determine characteristic vector only by covariance, although having approached optimum efficiency, its precision is not high, multidimensional The dimension-reduction treatment of data and not up to actual optimum.
The content of the invention
In order to improve the limitation of traditional PCA algorithms, day of the present invention proposes a kind of gear parameter based on PCA reconstruction errors Contribution Analysis method, by being improved to traditional PCA algorithms, making it, precision is more in gear parameter Contribution Analysis Height, in the case where meeting identical accumulative contribution degree, required parameter dimensions are less, so as to further reduce subsequent algorithm computing Complexity.
To achieve the above object, concrete technical scheme of the present invention is as follows：
A kind of gear parameter Contribution Analysis method based on PCA reconstruction errors, its key are to enter according to following steps OK：
S1：N group data are inputted, each group of packet contains m characteristic value, so as to form the sample matrix X of n × m dimensions；
S2：Its characteristic vector U initial value is obtained according to sample matrix X covariance matrix；
S3：Establish " error and minimum " target function model：
And seek its object function minimum value, wherein xi For i-th of sample vector in sample matrix X, γiRepresent the weight of i-th of sample andUUT=Ik, IkFor k dimensions Unit matrix, k≤m, α are regularization parameter, SFFor the bending safety coefficient of gear, SHFor the touch-safe coefficient of gear；
S4：According to characteristic vector U during its object function minimum value, according to its character pair value size from top to bottom by row Matrix is arranged in, h rows before taking, corresponding parameter is the maximum parameter of contribution degree, h ＜ m.
Further, after error and minimum target function model being established in the step S3, first with obtained by step S2 Characteristic vector U initial value is substituted into target function model, the weight γ of sample when solving object function minimum valuei；
Then γ is recycledi, i=1~n, composition diagonal matrix W=diag (γ1,γ2,…,γn), and utilize XWXTCarry out Eigenvalues Decomposition represents diagonal matrix so as to update characteristic vector U, diag ()；
The weight γ of sample when recycling the characteristic vector U after renewal to solve object function minimum value againi, so hand over Optimization is iterated for two variables, until the adjacent difference of reconstruction error twice is less than the threshold values of setting.
Further, the data inputted in step S1 have 55 groups, and each group of packet contains 81 characteristic values.
Further, the characteristic value in each group of data of step S1 inputs includes operating mode, affiliated axle, gear pair name, tooth Number, normal module, normal pressure angle, helical angle, centre-to-centre spacing, the modification coefficient method of salary distribution, modification coefficient, the work facewidth, tooth top High coefficient, bottom gap, transverse tooth thickness be thinned coefficient, the facewidth, rotation direction, pitch circle normal pressure angle, pitch circle transverse pressure angle, pitch circle helical angle, Pitch diameter, cutter radius at tooth tip, tip diameter, root diameter, maximum distance over bar, Pins diameter, height of teeth root system Number, the starting point of meshing, engagement terminating point, transverse contact ratio, Face contact ratio and engagement starting circular diameter.
Further, h specific value is determined according to whether contribution rate of accumulative total reaches 85% in step S5.
Beneficial effects of the present invention：
The present invention introduces error and minimum target function model, by traditional PCA by being improved to traditional PCA algorithms The characteristic vector that algorithm obtains, by the optimization that iterates, finally gives error and minimum target function as just initial value The characteristic vector of optimum state, found by contrasting, for the algorithm after improvement for traditional PCA algorithms, its precision is higher.
Embodiment
The embodiment of technical solution of the present invention will be described in detail below.Following examples are only used for clearer Ground illustrates technical scheme, therefore be only used as example, and can not be limited the scope of the invention with this.
It should be noted that unless otherwise indicated, technical term or scientific terminology used in this application should be this hair The ordinary meaning that bright one of ordinary skill in the art are understood.
The present embodiment discloses a kind of gear parameter Contribution Analysis method based on PCA reconstruction errors, essentially according to following Step is carried out：
S1：N group data are inputted, each group of packet of n=55 contains m characteristic value, m=81, so as to form 55 × 81 dimensions Sample matrix X；These characteristic values include operating mode, affiliated axle, gear pair name, the number of teeth, normal module, normal pressure angle, helical angle, Centre-to-centre spacing, the modification coefficient method of salary distribution, modification coefficient, work the facewidth, addendum coefficient, bottom gap, transverse tooth thickness be thinned coefficient, the facewidth, Rotation direction, pitch circle normal pressure angle, pitch circle transverse pressure angle, pitch circle helical angle, pitch diameter, cutter radius at tooth tip, tooth top Circular diameter, root diameter, maximum distance over bar, Pins diameter, height of teeth root coefficient, the starting point of meshing, engagement terminating point, end face weight Right, Face contact ratio and engagement starting circular diameter.
S2：Its characteristic vector U initial value is obtained according to sample matrix X covariance matrix；
S3：Establish " error and minimum " target function model：
And seek its object function minimum value, wherein xi For i-th of sample vector in sample matrix X, γiRepresent the weight of i-th of sample andUUT=Ik, IkFor k dimensions Unit matrix, k≤m, α are regularization parameter, take 0.2, S during specific implementationFFor the bending safety coefficient of gear, SHFor gear Touch-safe coefficient；
S4：According to characteristic vector U during its object function minimum value, according to its character pair value size from top to bottom by row Matrix is arranged in, h rows before taking, corresponding parameter is the maximum parameter of contribution degree, h ＜ m.
After error and minimum target function model are established in the step S3, first with characteristic vector U obtained by step S2 Initial value substitute into target function model in, solve object function minimum value when sample weight γi；
Then γ is recycledi, i=1~n, composition diagonal matrix W=diag (γ 1, γ2,…,γn), and utilize XWXTCarry out Eigenvalues Decomposition represents diagonal matrix so as to update characteristic vector U, diag ()；
The weight γ of sample when recycling the characteristic vector U after renewal to solve object function minimum value againi, so hand over Optimization is iterated for two variables, until the adjacent difference of reconstruction error twice is less than the threshold values of setting.
When it is implemented, determine h specific value according to whether contribution rate of accumulative total reaches 85% in step S5.In order to enter One step demonstrate,proves the validity of algorithm after improvement, also carries out PCA algorithms after traditional PCA algorithms and improvement to score in this example Analysis, concrete outcome are as shown in table 1：
It can be seen from Table 1 that compared with traditional PCA, the principal component number that the PCA based on reconstruction error retains is less, Traditional PCA preceding 6 principal components accumulation contribution rate is 88.015%, and preceding 4 principal components accumulation contribution rate of the PCA after improvement is Up to 88.591%, 6 principal components before selection, contribution rate is up to 94.915%.When choosing full detail 85%, PCA after improvement Dimensionality reduction amplitude is that 95.29%, PCA dimensionality reduction amplitudes are 92.94%.It can be seen that the gear proposed by the present invention based on PCA reconstruction errors Parameter Contribution Analysis method, the contribution degree of each gear parameter is more accurately reflected, when carrying out data analysis, effectively The processing dimension of multidimensional data is reduced, lifts the treatment effeciency of subsequent algorithm.
Table 1：Relativity before and after improvement
Method Traditional PCA Improve PCA
Principal component Accumulative variance contribution ratio/% Accumulative variance contribution ratio/%
1 45.434 63.667
2 64.077 73.757
3 73.2 82.327
4 79.889 88.591
5 84.298 92.439
6 88.015 94.915
7 90.492 96.554
8 92.383 97.871
Finally it should be noted that various embodiments above is merely illustrative of the technical solution of the present invention, rather than its limitations； Although the present invention is described in detail with reference to foregoing embodiments, it will be understood by those within the art that：Its The technical scheme described in foregoing embodiments can still be modified, either to which part or all technical characteristic Carry out equivalent substitution；And these modifications or replacement, the essence of appropriate technical solution is departed from various embodiments of the present invention skill The scope of art scheme, it all should cover among the claim of the present invention and the scope of specification.

Claims (5)

  1. A kind of 1. gear parameter Contribution Analysis method based on PCA reconstruction errors, it is characterised in that follow the steps below：
    S1：N group data are inputted, each group of packet contains m characteristic value, so as to form the sample matrix X of n × m dimensions；
    S2：Its characteristic vector U initial value is obtained according to sample matrix X covariance matrix；
    S3：Establish " error and minimum " target function model：
    And seek its object function minimum value, wherein xiFor sample I-th of sample vector, γ in this matrix XiRepresent the weight of i-th of sample andUUT=Ik, IkFor the unit square of k dimensions Battle array, k≤m, α are regularization parameter, SFFor the bending safety coefficient of gear, SHFor the touch-safe coefficient of gear；
    S4：According to characteristic vector U during its object function minimum value, according to its character pair value size from top to bottom by rows Into matrix, h rows before taking, corresponding parameter is the maximum parameter of contribution degree, h ＜ m.
  2. 2. the gear parameter Contribution Analysis method according to claim 1 based on PCA reconstruction errors, it is characterised in that：
    After error and minimum target function model are established in the step S3, first with the first of characteristic vector U obtained by step S2 Initial value substitute into target function model in, solve object function minimum value when sample weight γi；
    Then γ is recycledi, i=1~n, composition diagonal matrix W=diag (γ1,γ2,…,γn), and utilize XWXTCarry out feature Value is decomposed represents diagonal matrix so as to update characteristic vector U, diag ()；
    The weight γ of sample when recycling the characteristic vector U after renewal to solve object function minimum value againi, such alternating pair Two variables are iterated optimization, until the adjacent difference of reconstruction error twice is less than the threshold values of setting.
  3. 3. the gear parameter Contribution Analysis method according to claim 1 based on PCA reconstruction errors, it is characterised in that： The data inputted in step S1 have 55 groups, and each group of packet contains 81 characteristic values.
  4. 4. the gear parameter Contribution Analysis method based on PCA reconstruction errors according to claim 1 or 3, its feature exist In：Characteristic value in each group of data of step S1 inputs includes operating mode, affiliated axle, gear pair name, the number of teeth, normal module, method To pressure angle, helical angle, centre-to-centre spacing, the modification coefficient method of salary distribution, modification coefficient, the work facewidth, addendum coefficient, bottom gap, tooth The thinned coefficient of thickness, the facewidth, rotation direction, pitch circle normal pressure angle, pitch circle transverse pressure angle, pitch circle helical angle, pitch diameter, cutter teeth Tip circle angular radius, tip diameter, root diameter, maximum distance over bar, Pins diameter, height of teeth root coefficient, the starting point of meshing, nibble Close terminating point, transverse contact ratio, Face contact ratio and engagement starting circular diameter.
  5. 5. the gear parameter Contribution Analysis method according to claim 1 based on PCA reconstruction errors, it is characterised in that： In step S5 h specific value is determined according to whether contribution rate of accumulative total reaches 85%.
CN201710599975.4A 2017-07-21 2017-07-21 Gear parameter contribution degree analysis method based on PCA reconstruction error Active CN107392248B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710599975.4A CN107392248B (en) 2017-07-21 2017-07-21 Gear parameter contribution degree analysis method based on PCA reconstruction error

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710599975.4A CN107392248B (en) 2017-07-21 2017-07-21 Gear parameter contribution degree analysis method based on PCA reconstruction error

Publications (2)

Publication Number Publication Date
CN107392248A true CN107392248A (en) 2017-11-24
CN107392248B CN107392248B (en) 2020-04-24

Family

ID=60336702

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710599975.4A Active CN107392248B (en) 2017-07-21 2017-07-21 Gear parameter contribution degree analysis method based on PCA reconstruction error

Country Status (1)

Country Link
CN (1) CN107392248B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
IN2015MU01447A (en) * 2015-04-07 2015-04-24 Vasant Dudul Sanjay
CN106599448A (en) * 2016-12-12 2017-04-26 北京航空航天大学 Dynamic reliability-based gear system tolerance optimization calculation method
CN106777606A (en) * 2016-12-02 2017-05-31 上海电机学院 A kind of gearbox of wind turbine failure predication diagnosis algorithm

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
IN2015MU01447A (en) * 2015-04-07 2015-04-24 Vasant Dudul Sanjay
CN106777606A (en) * 2016-12-02 2017-05-31 上海电机学院 A kind of gearbox of wind turbine failure predication diagnosis algorithm
CN106599448A (en) * 2016-12-12 2017-04-26 北京航空航天大学 Dynamic reliability-based gear system tolerance optimization calculation method

Also Published As

Publication number Publication date
CN107392248B (en) 2020-04-24

Similar Documents

Publication Publication Date Title
CN104750979B (en) The synthesization risk priority number calculating method of Architecture-oriented
CN110245783B (en) Short-term load prediction method based on C-means clustering fuzzy rough set
CN110110434B (en) Initialization method for probability load flow deep neural network calculation
CN110874381B (en) Spatial density clustering-based user side load data abnormal value identification method
CN104462459A (en) Neural network based big data analysis and processing system and method
CN107169511A (en) Clustering ensemble method based on mixing clustering ensemble selection strategy
CN111159638A (en) Power distribution network load missing data recovery method based on approximate low-rank matrix completion
CN107528322A (en) A kind of Probabilistic Load Flow analysis method of the NATAF conversion based on the Gauss Hermite method of quadratures
CN105160196A (en) Dynamic mutation policy based group global optimization method
CN107507078A (en) A kind of distributed energy distribution of income strategy based on bargaining game
CN113240263A (en) Comprehensive energy system planning combination evaluation method based on entropy weight fuzzy
CN104077769A (en) Error matching point pair removing algorithm in image registration
Ho Income thresholds and growth convergence: A panel data approach
CN107392248A (en) Gear parameter Contribution Analysis method based on PCA reconstruction errors
Zhao et al. A novel short‐term load forecasting approach based on kernel extreme learning machine: A provincial case in China
CN113627753A (en) Comprehensive evaluation method for market power of electric power market
CN107145732A (en) A kind of method based on the rapid solving target list station Electromagnetic Scattering Characteristics for improving CBFM
CN108694475B (en) Short-time-scale photovoltaic cell power generation capacity prediction method based on hybrid model
CN115841280A (en) Photovoltaic monthly scene generation method and system
CN111178699A (en) Method for constructing intelligent checking system of scheduling operation tickets
Peng et al. Stochastic scenario generation for wind power and photovoltaic system based on CGAN
CN113437749A (en) Reactive power optimization method, device and equipment for power system
CN111159882A (en) Method for describing wind speed frequency distribution characteristics of wind power plant
CN113469566B (en) Method and system for determining initial distribution scheme of generator
CN107330442A (en) In a kind of combination class between compactness and class separation property increment fuzzy clustering method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant