CN109885877A - A kind of constrained domain optimization Latin hypercube design method based on clustering algorithm - Google Patents
A kind of constrained domain optimization Latin hypercube design method based on clustering algorithm Download PDFInfo
- Publication number
- CN109885877A CN109885877A CN201910036303.1A CN201910036303A CN109885877A CN 109885877 A CN109885877 A CN 109885877A CN 201910036303 A CN201910036303 A CN 201910036303A CN 109885877 A CN109885877 A CN 109885877A
- Authority
- CN
- China
- Prior art keywords
- sample point
- denoted
- point
- domain
- clustering algorithm
- 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
Links
Abstract
The invention discloses a kind of, and the constrained domain based on clustering algorithm optimizes Latin hypercube design method, comprising the following steps: 1, the number (n according to variable number, constraint number and specified sample points), it determines the number of initial sample point, is denoted as NS；2, according to initial samples point number (N in design domainS) optimal Latin hypercube sampling is carried out, and obtained initial sample point is denoted as set A；3, the sample point in set A is screened, the sample point for meeting institute's Prescribed Properties is found, is denoted as set B, feasible point quantity is denoted as nv；4, judge whether feasible point quantity meets convergence, if not satisfied, then return step 2；Satisfaction then goes to step 5；5, n is generated in set B using clustering algorithmsA cluster centre, is denoted as set C, and set C is the set of the specified quantity sample point generated in constrained domain experimental design domain.The present invention can effectively solve the problems, such as the experimental design of high-dimensional non-interconnected constrained domain, improve design efficiency.
Description
Technical field
The invention belongs to experimental design techniques fields, and in particular to a kind of constrained domain optimization Latin based on clustering algorithm is super
Cube design method.
Background technique
With the fast development of computer technology and CAE technology, people's method that appliance computer emulates more and more
Many engineering problems are simulated and study, especially in automotive field, the design based on computer virtual simulation analysis and optimization
Leading position is already taken up.In order to shorten the R&D cycle, improving product quality and reduce research and development cost, people require computer
The precision of virtual emulation wants higher and higher, and the time of analysis and optimization wants shorter and shorter.In the experimental design stage, the choosing of sample point
The precision for determining agent model to a certain extent is taken, thus precision for simulation analysis of computer and efficiency have very big shadow
It rings.Latin hypercube is configured as a kind of common test design method, due to preferable low dimension projective property and high efficiency by
To being widely used.However, in actual Optimum design of engineering structure, the design variable being related to is more and design object and design about
Beam Relationship Comparison is complicated, and the test sample point that traditional experimental design method is chosen is easy to cause the inaccurate even structure of approximate model
It can not make response surface.Therefore, domestic and foreign scholars are directed to the experimental design problem of constrained domain, expand extensive work, but at present also
There is not preferable solution.
Summary of the invention
To solve the above problems, the present invention proposes a kind of constrained domain optimization Latin hypercube design side based on clustering algorithm
Method,
Constrained domain provided by the invention based on clustering algorithm optimizes Latin hypercube design method, comprising the following steps:
Step 1, the number (n according to variable number, constraint number and specified sample points), determine initial sample point
Number is denoted as NS；
Step 2, according to initial samples point number (N in design domainS) optimal Latin hypercube sampling is carried out, and it is first by what is obtained
Beginning sample point is denoted as set A；
Step 3, the sample point in set A is screened, finds the sample point for meeting institute's Prescribed Properties, be denoted as set
B, feasible point quantity are denoted as nv；
Step 4, judge whether feasible point quantity meets convergence, if not satisfied, then return step 2；Satisfaction then goes to step
5；
Step 5, n is generated in set B using clustering algorithmsA cluster centre, is denoted as set C, and set C is to constrain
The set of the specified quantity sample point generated in the experimental design domain of domain.
The invention has the benefit that
The Latin hypercube design method based on clustering algorithm that the present invention uses, can effectively solve it is high-dimensional it is non-interconnected about
The experimental design problem in beam domain；By traversing initial sample point, the method for screening feasible sample point, when can substantially reduce sampling
Between, improve the efficiency of computer approximate analysis；The feasible sample point condition of convergence proposed, realizes the automation of experimental design,
Avoid the process for only by virtue of experience carrying out manually adjusting parameter of designer.
Detailed description of the invention
Fig. 1 is a kind of constrained domain optimization Latin hypercube design method flow diagram based on clustering algorithm of the present invention；
Fig. 2 is the flow chart illustration of example 1 of the present invention；
Wherein (a) indicates sample point set after initial samples；(b) feasible sample point set is indicated；(c) cluster centre is indicated
Point set；(d) optimum results set is indicated.
Fig. 3 is the result schematic diagram of example 2 of the present invention.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings.
As shown in Figure 1, the present invention provides a kind of, the constrained domain based on clustering algorithm optimizes Latin hypercube design method,
The following steps are included:
Step 1: according to variable number (n), constraint number (na) and specified sample point number (ns), determine initial sample
The number of this point, is denoted as NS.Comprehensively consider variable number (n), constraint number (na) and specified sample point number (ns) to first
The influence of beginning sample point number determines initial sample point number N according to formula (1)S；
NS=na·ns·10n (1)
Step 2: according to initial sample point number (N in design domainS) optimal Latin hypercube sampling is carried out, and it is first by what is obtained
Beginning sample point is denoted as set A；
Further, the detailed process of the step 2 are as follows:
S2.1 determines experimental design domain:
According to each input variable and the value range of each variable, experimental design domain is determined；
According to the number of input variable and its domain of variable, variable number (n) and experimental design domain are determined.
S2.2 obtains initial sample point:
The initial sample point number (N obtained according to step 1S), optimal Latin hypercube sampling, tool are carried out in experimental design domain
Sampler body process is as follows:
It is first depending on variable number (n) and constructs n dimension unit cube [0,1]n, then according to initial sample point number
(NS), each one-dimensional coordinate section [0,1] is divided into NSEach minizone is denoted as by equal partNote
u1k,…uNSkThe N of coordinate is tieed up for kthSOne random alignment of a section number, and assume that this n random alignment is mutually indepedent,
N finally can be obtainedSRandom matrix U=(the u of × m dimensionij), wherein
The N obtained by the above processSA sample point is as initial sample point xij, it is denoted as set A.
Step 3: obtaining feasible point in set A, and feasible sample point is denoted as set B；
All sample points in set A are traversed, find the constrained feasible point of satisfaction institute, and feasible point is denoted as set B, it can
Row point quantity is denoted as nv；
Step 4: judging feasible point quantity (nv) whether meet the condition of convergence, if not satisfied, then return step 2；Meet then
Go to step 5；
Further, the detailed process of the step 4 are as follows:
S4.1 determines the condition of convergence:
Since the size of initial data set has a certain impact to clustering algorithm effect, it is contemplated that specified sample point quantity
(ns) and constraint number (na), the condition of convergence is defined as following formula；
nv> na·ns (2)
S4.2 judges whether to restrain:
Feasible point quantity (the n that will be obtainedv) substitute into formula (2) in judged, if being unsatisfactory for restraining, increase initial samples
Point number (NS), then return step 2.2；If meeting the condition of convergence, step 5 is turned to.
S4.3 optimizes initial samples point number (NS):
To accelerate convergence rate, initial samples point number (N is reconfiguredS), process is as follows:
Due to feasible point number (nv) it is unsatisfactory for the condition of convergence, i.e. nv< na·ns, it is known thatIt will be in formula (1)
NSExpandTimes, obtain the initial samples point number (N such as formula (3)S) expression formula；
Step 5: generating n in set B using Fuzzy C-Means Cluster AlgorithmsA cluster centre is denoted as set C, set C
The set of the specified quantity sample point as generated in constrained domain experimental design domain.
Further, the detailed process of the step 5 are as follows:
S5.1, Initialize installation:
Since the process is to generate n in set B using FCM algorithmsA cluster centre, therefore FCM algorithm parameter is carried out
Initialize installation, using the sample point number ns of specified quantity as the class number of FCM algorithm, i.e. the number c of cluster centre.It will
Data set of the set B as FCM algorithm, and by the quantity n of feasible point in set BvSample size as FCM algorithm data collection
N is denoted as X=(x1,…xk,…xN), i=1,2 ... c.
Cluster loss function J based on subordinating degree functionfAre as follows:
In formula: μj(xi) it is k-th of sample xkThe degree of membership of corresponding i-th class；M is Fuzzy Exponential, indicates the journey of fuzzy clustering
It spends, m value is 2 in the present invention.
S5.2, the weighted average v of the data item of computing clusteriAre as follows:
In formula: μikIt is the cluster centre point relative to data point.
S5.3 calculates the distance between sample point and cluster centre point Dik:
In formula: A is positive definite symmetric matrices.
S5.4 calculates subordinating degree function value:
S5.5 updates step 5.3 and 5.4, until terminating tolerance ε < 0.001, meets convergence, exports the seat of cluster centre
Mark, is denoted as set C.
Embodiment
Example is sampled with several low-dimensionals and higher-dimension constrained domain below, the validity of this algorithm is verified.It does not lose general
Property, all variable initial ranges are all set to [0,1].
Two-dimentional example: specified sample point number 50, experiment domain are the region being overlapped between circle and parabola that radius is 0.4
And the center of circle is located at the quadrant of origin.Shown in constraint expression formula such as formula (8):
In formula: x1,x2Independent variable, g (x) are variable x1,x2The constraint that need to meet.
Firstly, determining the initial samples point number of the example, and Latin square sampling is optimized in design space and is obtained
Set A, as shown in Fig. 2 (a)；Then sample point in set A is traversed, all sample points for meeting constraint condition is found, is denoted as collection
B is closed, as shown in Fig. 2 (b)；Secondly, generating 50 cluster centres in set B using Fuzzy C-Means Cluster Algorithm, it is denoted as set
C, as shown in Fig. 2 (c)；Finally, the coordinate in output set C, obtains the result as shown in Fig. 2 (d).It can be seen that side of the present invention
Method can realize that Latin square samples in non-interconnected irregular experiment domain, and can guarantee uniformity and orthogonality.
Three-dimensional example: specified sample point number 50, test field are in two non-interconnected eighth balls.Constraint expression formula
As shown in formula (9):
In formula: x1,x2,x3For independent variable, g (x) is variable x1,x2, x3The constraint that need to meet.
Sampled result is as shown in figure 3, it can be seen that this method can realize the Latin of the non-interconnected irregular constrained domain of higher-dimension
The sampling of side side.
The series of detailed descriptions listed above only for feasible embodiment of the invention specifically
Protection scope bright, that they are not intended to limit the invention, it is all without departing from equivalent implementations made by technical spirit of the present invention
Or change should all be included in the protection scope of the present invention.
Claims (9)
1. a kind of constrained domain based on clustering algorithm optimizes Latin hypercube design method, which comprises the steps of:
Step 1, according to variable number n, constraint number naAnd the number n of specified sample points, determine the number of initial sample point,
It is denoted as NS；
Step 2, according to initial samples point number N in design domainSCarry out optimal Latin hypercube sampling, and the initial sample that will be obtained
Point is denoted as set A；
Step 3, the sample point in set A is screened, finds the sample point for meeting institute's Prescribed Properties, be denoted as set B, it can
Row point quantity is denoted as nv；
Step 4, judge feasible point quantity nvWhether satisfaction restrains, if not satisfied, then return step 2；Satisfaction then goes to step 5；
Step 5, n is generated in set B using clustering algorithmsA cluster centre, is denoted as set C, and set C is in constrained domain reality
Test the set of the specified quantity sample point generated in design domain.
2. a kind of constrained domain based on clustering algorithm according to claim 1 optimizes Latin hypercube design method, special
Sign is, the N of the step 1SDetermination method are as follows: NS=na·ns·10n。
3. a kind of constrained domain based on clustering algorithm according to claim 1 optimizes Latin hypercube design method, special
Sign is that the specific implementation of the step 2 includes:
S2.1 determines experimental design domain:
According to each input variable and the value range of each variable, experimental design domain is determined；
S2.2 obtains initial sample point:
The initial sample point number N obtained according to step 1S, optimal Latin hypercube sampling is carried out in experimental design domain, by what is obtained
Sample point is denoted as set A.
4. a kind of constrained domain based on clustering algorithm according to claim 1 optimizes Latin hypercube design method, special
Sign is, in the step 2.2, the specific method of sampling are as follows:
It is first depending on variable number (n) and constructs n dimension unit cube [0,1]n, then according to initial sample point number (NS),
Each one-dimensional coordinate section [0,1] is divided into NSEach minizone is denoted as by equal partNote
u1k,…uNSkThe N of coordinate is tieed up for kthSOne random alignment of a section number, and assume that this n random alignment is mutually indepedent,
N finally can be obtainedSRandom matrix U=(the u of × m dimensionij), wherein
The N obtained by the above processSA sample point is denoted as set A as initial sample point.
5. a kind of constrained domain based on clustering algorithm according to claim 1 optimizes Latin hypercube design method, special
Sign is that the specific implementation of the step 4 includes:
S4.1 determines the condition of convergence, and the condition of convergence is defined as following formula；
nv> na·ns
S4.2 judges whether to restrain:
Feasible point quantity (the n that will be obtainedv) substitute into above-mentioned convergence expression formula and judged, if meeting the condition of convergence, turn to step
5；If being unsatisfactory for restraining, increase initial samples point number (NS), return step 2.2；
S4.3 optimizes initial samples point number NS:
To accelerate convergence rate, initial samples point number (N is reconfiguredS), process is as follows:
For feasible point number (nv) it is unsatisfactory for the condition of convergence, i.e. nv< na·ns, it is known thatTherefore by formula NS=na·
ns·10nIn NSExpandTimes, obtain the initial samples point number (N of following formulaS) expression formula:
6. a kind of constrained domain based on clustering algorithm according to claim 1 optimizes Latin hypercube design method, special
Sign is that the clustering algorithm in the step 5 uses Fuzzy C-Means Cluster Algorithm.
7. a kind of constrained domain based on clustering algorithm according to claim 6 optimizes Latin hypercube design method, special
Sign is, the concrete methods of realizing of the step 5:
S5.1, Initialize installation:
Using the sample point number ns of specified quantity as the class number of FCM algorithm, i.e. the number c of cluster centre, set B is made
For the data set of FCM algorithm, and by the quantity n of feasible point in set BvAs the sample size N of FCM algorithm data collection, it is denoted as X
=(x1,…xk,…xN), i=1,2 ... c, then the cluster loss function J based on subordinating degree functionfAre as follows:
In formula: μj(xi) it is k-th of sample xkThe degree of membership of corresponding i-th class；M is Fuzzy Exponential, indicates the degree of fuzzy clustering；
S5.2, the weighted average of the data item of computing cluster:
S5.3 calculates the distance between sample point and cluster centre point:
S5.4 calculates subordinating degree function value:
S5.5 updates step 5.3 and 5.4, until meeting convergence, exports cluster centre mjCoordinate, be denoted as set C, obtain about
The set of the specified quantity sample point generated in the experimental design domain of beam domain.
8. a kind of constrained domain based on clustering algorithm according to claim 1-7 optimizes Latin hypercube design side
Method, which is characterized in that the design method is applied in two-dimentional example, specifies sample point number 50, it is 0.4 that experiment domain, which is radius,
Circle and parabola between the region that is overlapped and the center of circle be located at the quadrant of origin, constraint expression formula are as follows:
g1(x)=x2-4(x1-0.5)2≥0；
g2(x)=x2-4(x1-0.5)2≥0；
g3(x)=(x2-0.5)2+(x1-0.5)2-0.16≥0；
g4(x)=x2 2+x1 2-0.04≥0；
Wherein: x1,x2Independent variable, g (x) are variable x1,x2The constraint that need to meet.
9. a kind of constrained domain based on clustering algorithm according to claim 1-7 optimizes Latin hypercube design side
Method, which is characterized in that the design method is applied in three-dimensional example, and sample point number 50 is specified, and test field is two non-companies
In logical eighth ball, constraint expression formula are as follows:
g1(x)=x1 2+x2 2+x3 2-0.16≤0；
g2(x)=(x1-1)2+(x2-1)2+(x3-1)2-0.16≤0；
Wherein: x1,x2,x3For independent variable, g (x) is variable x1,x2, x3The constraint that need to meet.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910036303.1A CN109885877B (en) | 2019-01-15 | 2019-01-15 | Constraint domain optimization Latin hypercube design method based on clustering algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910036303.1A CN109885877B (en) | 2019-01-15 | 2019-01-15 | Constraint domain optimization Latin hypercube design method based on clustering algorithm |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109885877A true CN109885877A (en) | 2019-06-14 |
| CN109885877B CN109885877B (en) | 2023-04-18 |
Family
ID=66926021
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910036303.1A Active CN109885877B (en) | 2019-01-15 | 2019-01-15 | Constraint domain optimization Latin hypercube design method based on clustering algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109885877B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110674373A (en) * | 2019-09-17 | 2020-01-10 | 上海森亿医疗科技有限公司 | Big data processing method, device, equipment and storage medium based on sensitive data |
| CN117113732A (en) * | 2023-10-24 | 2023-11-24 | 南方电网调峰调频发电有限公司 | Latin hypercube design method suitable for non-hypercube constraint space |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101944141A (en) * | 2010-08-18 | 2011-01-12 | 北京理工大学 | High-efficiency global optimization method using adaptive radial basis function based on fuzzy clustering |
| CN106202667A (en) * | 2016-07-01 | 2016-12-07 | 中国人民解放军国防科学技术大学 | Constrained domain optimizes Latin hypercube method for designing |
| CN108649605A (en) * | 2018-05-22 | 2018-10-12 | 国网内蒙古东部电力有限公司通辽供电公司 | A kind of grid-connected allowed capacity planing methods of DER based on the double-deck scene interval trend |
-
2019
- 2019-01-15 CN CN201910036303.1A patent/CN109885877B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101944141A (en) * | 2010-08-18 | 2011-01-12 | 北京理工大学 | High-efficiency global optimization method using adaptive radial basis function based on fuzzy clustering |
| CN106202667A (en) * | 2016-07-01 | 2016-12-07 | 中国人民解放军国防科学技术大学 | Constrained domain optimizes Latin hypercube method for designing |
| CN108649605A (en) * | 2018-05-22 | 2018-10-12 | 国网内蒙古东部电力有限公司通辽供电公司 | A kind of grid-connected allowed capacity planing methods of DER based on the double-deck scene interval trend |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110674373A (en) * | 2019-09-17 | 2020-01-10 | 上海森亿医疗科技有限公司 | Big data processing method, device, equipment and storage medium based on sensitive data |
| CN110674373B (en) * | 2019-09-17 | 2020-08-07 | 上海森亿医疗科技有限公司 | Big data processing method, device, equipment and storage medium based on sensitive data |
| CN117113732A (en) * | 2023-10-24 | 2023-11-24 | 南方电网调峰调频发电有限公司 | Latin hypercube design method suitable for non-hypercube constraint space |
| CN117113732B (en) * | 2023-10-24 | 2024-02-06 | 南方电网调峰调频发电有限公司 | Latin hypercube design method suitable for non-hypercube constraint space |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109885877B (en) | 2023-04-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109086700B (en) | Radar one-dimensional range profile target identification method based on deep convolutional neural network | |
| CN106940439B (en) | K mean cluster based on wireless acoustic sensor network weights sound localization method | |
| CN103902826B (en) | Method for tracking multiple moving targets under impact noise environment | |
| CN106897511A (en) | Annulus tie Microstrip Antenna Forecasting Methodology | |
| CN104239901B (en) | Classification of Polarimetric SAR Image method based on Fuzzy particle swarm artificial and goal decomposition | |
| CN106156067B (en) | For creating the method and system of data model for relation data | |
| CN109885877A (en) | A kind of constrained domain optimization Latin hypercube design method based on clustering algorithm | |
| Lu et al. | Clustering by Sorting Potential Values (CSPV): A novel potential-based clustering method | |
| CN105930859B (en) | Radar Signal Sorting Method based on linear manifold cluster | |
| CN103440275A (en) | Prim-based K-means clustering method | |
| CN106908774B (en) | One-dimensional range profile identification method based on multi-scale nuclear sparse preserving projection | |
| CN109801208B (en) | SAR image change detection method based on multi-GPU task optimization | |
| Mooers et al. | Generative modeling of atmospheric convection | |
| CN109146055A (en) | Modified particle swarm optimization method based on orthogonalizing experiments and artificial neural network | |
| CN104899440B (en) | A kind of pipeline magnetic flux leakage defect reconstructing method based on gravitation searching algorithm | |
| Du et al. | CAPTCHA recognition based on faster R-CNN | |
| CN109447158A (en) | A kind of Adaboost Favorable Reservoir development area prediction technique based on unbalanced data | |
| CN106203520B (en) | SAR image classification method based on depth Method Using Relevance Vector Machine | |
| Liu et al. | Multi-objective recognition based on deep learning | |
| CN105044698B (en) | Method suitable for micro-Doppler analysis of space target in short-time observation | |
| CN104463227A (en) | Polarimetric SAR image classification method based on FQPSO and target decomposition | |
| Dalton | Optimal ROC-based classification and performance analysis under Bayesian uncertainty models | |
| Liu et al. | Nuno: A general framework for learning parametric pdes with non-uniform data | |
| Fischer et al. | Cosmological and idealized simulations of dark matter haloes with velocity-dependent, rare and frequent self-interactions | |
| Challenor | Using emulators to estimate uncertainty in complex models |
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 |