Embodiment
The present invention relates to a kind of layout strategy of combined sample library so that character designs per sample, synthesize, screen also measure sample storehouse.
One aspect of the present invention provides the method for design of sample library, comprises a plurality of components of sampling.Here said " combined sample storehouse " is meant the set that comprises a plurality of samples, and " sample " is meant the material that comprises various ingredients." component " is meant a kind of material, comprise as element, molecule, compound, material, thing piece etc., or the combination of these materials.
In an embodiment of the present invention, certain sample comprises the component that the n kind is different, C
1, C
2, C
3... C
i... C
n, wherein n is an integer, refers to the quantity of different components in the sample.Each component C
iThe quality representation that is had is MW
i, wherein i ∈ 0,1,2...n}, composing quantity is expressed as X in the sample
i, corresponding composition ratiometer is shown R
iMass M W
iThe molecular weight or the nucleidic mass that refer to this component.So-called composing quantity X
iBe meant the quantity of i component in the sample, so this sample can be expressed as (C
1)
X1(C
2)
X2... (C
i)
Xi... (C
n)
Xn, wherein i ∈ 0,1,2...n}, composition ratio can be characterized by the relative weight quantity of a kind of component in the sample, its available formula 1 expression:
Formula 1
Composing quantity X
iThe molar ratio that also can refer to i component in the sample.In this case, composition ratio also can be expressed as the molar fraction of a certain component in the sample, and its value can be defined by following formula 2 between 0 to 1:
Formula 2
Composition ratio also can further be expressed as a certain percentages of ingredients in the sample, and its value is between 0% to 100%.
In any sample in storehouse, whole composition ratio sums of all components are 1.As shown in Equation 3:
Formula 3
For example, glucose molecule C
6H
12O
6Can regard the sample that comprises three components as: carbon (C), protium (H) and oxygen element (O), each component has composing quantity, as C be 6, H's is 12, O's is 6.The material mass of each component (MW) can be drawn by each atomic mass, and C is 12, and H is 1, and O is 16.Therefore, (weight) composition ratio of C is 0.4 or 40%, (12*6/ (12*6+1*12+16*6)); H is 0.067 or 6.7%; O be 0.533 or the summation of the composition ratio of three components of 53.3%. be 1.
Another feature of combined sample library is, each sample all is made up of the component of same type in the sample library, but these components have different composition ratios.
Each component that the method for design of the combined sample library that the present invention provides on the other hand is included as multicomponent sample provides a variable.In other words, component is corresponding one by one in variable and the sample.Suppose that variable V is at interval [V
Min, V
Max] in a random value, V wherein
MinBe not less than 0, V
MaxBe not more than 1, and V
Min≤ V
MaxIn one embodiment, this interval is [0,1].If supposing variable V is { V between discrete regions
1, V
2... V
xIn value, then V can disperse, wherein this discrete value drops on interval [V
Min, V
Max] in (as [0,1]).If set V is interval [V
Min, V
Max] random value, then it can be a successive value.When variable is relevant with component and do not have any constraint condition or all irrelevant with other variable, then the setting of the first variable random value is not subjected to the constraint of second variable supposition.If variable is a successive,, depend on the distribution probability or the probability density of this variable possibility value then from the interval interior process of setting random value of same variable.If this variable disperses, then the particular probability of discrete value is separately depended in the interval in the setting of random value.
For example, V
iBe the first component C
iVariable, V
jBe component the 2nd C
jVariable.V
iCan be set at [V
I, min, V
I, max] interval random value, V
jCan be set at [V
J, min, V
J, max] interval random value, V
iValue and V
jIrrelevant.Work as C
i, C
jBe by C
1, C
2... C
i... C
j... C
nComponent in the sample of forming, I wherein, j ∈ 0,1,2...n}, this compositional variable V
iBecome component C
iComposition ratio R
i, compositional variable V
jBecome composition ratio R
j, and the variable summation of all components satisfies following formula 4 in the sample:
Formula 4
Another aspect of the present invention is: provide or set at least one constraint condition at least one variable in the sample in the method for design of the combined sample library that is provided." constraint condition " speech refers to the condition of at least one variable or the relation between the variable.Particularly, constraint condition is the restricted condition that a variable or a plurality of variable must satisfy in the sample.In other words, one group of value { V in effective or qualified sample
iVariable must satisfy at least one constraint condition or one group of specific constraint condition.For example, suppose that sample comprises component C
1, C
2... C
n, and each component C
iHas variable V
i, wherein i ∈ 0,1,2...n}, so, in effective sample, the summation of component variable must satisfy following constraint condition, formula 5:
Formula 5
Wherein Δ is error (as constraint tolerance or a constraint deviation), and Δ is the value that changes between 0 to 0.2.In preferred embodiment, Δ is 0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09, or 0.10.When Δ approaches 0, this constraint approaches equation as shown in formula 5.
In addition, in the sample library design, can be presented as about the experimental knowledge of the component of sample relation between a plurality of variablees also to can be understood as constraint.In other words, we can be by setting the relation that retrains between several components that realize in the experimental knowledge.For example, according to experience before, by C
1, C
2... C
nIn the sample of forming, C perhaps
iWith C
jThe ratio of composition ratio should be 2: 1, wherein i ∈ 0,1,2...n}, j ∈ 0,1,2...n}, and i ≠ j.At this moment, except that the constraint of the inherent shown in the formula 4, the variable of the component of an effective sample must satisfy the second constraint V
i: V
j=2: 1.Again for example, reach C
iAnd C
jThe composition ratio sum be x, wherein x is the value between 0 to 1.Herein, the variable of the component of an effective sample must satisfy the second constraint V
i+ V
j=x, i wherein, j ∈ 0,1,2...n} and i ≠ j.
The method of design of combined sample library provided by the invention comprises the pseudo-sample of generation." pseudo-sample " is meant a multi-component supposition sample, its each component all have one independently variable make that any assignment of some variablees is all the be under no restraint restriction of condition of entire variable with respect to the independent events of any assignment of another variable and pseudo-sample.In other words, its variable can satisfy or not satisfy constraint condition.For example, a pseudo-sample comprises C
1, C
2... C
i... C
j... C
n, i wherein, j ∈ 0,1,2...n} and i ≠ j, V
iAnd V
jBe the random value in [0,1] interval, V
iSome values between desirable [0,1], V
jAnother value between desirable [0,1].Requirement these variate-values and that need not coincidence formula 4 and 5.
Pseudo-sample can correspondence also can not corresponding real physical sample, pseudo-sample is the sample spot of independently supposing variable-value without any constraint.Therefore a large amount of pseudo-samples are formed a sample space.
Pseudo-sample can adopt random sampling to produce.Random sampling methods is a kind of by being the method that each component random assignment of a sample spot produces sample spot.At interval [V
Min, V
Max] in produce random number method be clear and definite, V wherein
MinBe not less than 0, and V
MaxBe not more than 1.Please refer to Carter " generation of random digit and application (fourth dimension) " (
" The Generation and Application of Random Numbers(Fourth Dimensions) ", Vol.XVI, 1994).The algorithm of random number generator and computation program are that computer science is known, please refer to " art-seminumerical algorithm of computer program " (the 2nd volume, A Disen-Wei Sili second edition published in 1981) of D.E.Knuth
(" The Art of Computer Programming-Seminumerical Algorithms" Vol.2,2
NdEd.Addison-Wesley, 1981); " art that numerical method prescription-science is calculated " of work such as Press ("
Numerical Recipes:The Art of Scientific Computing "Cambridge University Press, 1986; And "
Numerical Recipes (FORTRAN) ", 191-225 page or leaf, 1988); And S.L.Anderson show " random number generator on vectorial supercomputer and other advanced system " ("
Random Number Generators on Vector Supercomputers and Other Advanced Architectures ", SIAM Rev,, 32:221-225, nineteen ninety).
At random the numerical value of Chan Shenging be the generation of incident or between given zone [V
Min, V
Max] in the variable (V) of possible assignment, wherein the probability that takes place of this incident depends on the probability density or the probability distribution of this variable.Therefore, variable is further defined by the assignment of probability function to the value that the range of variables comprised.For example, discrete variable can specify dependent probability to define by giving each discrete value in the interval.Continuous variable can specify probability distribution to define by giving the interval that comprises all variablees possibility values.
Here the probability distribution that is adopted refers to reflect the arrangement of the variable-value of its observation or the theoretical frequency of occurrences.The probability distribution of knowing in this technical field comprises that equiblibrium mass distribution and lack of balance distribute.Lack of balance distributes and comprises that Bernoulli distribution, beta distribution, X square distribution, exponential distribution, F-distribution, gamma distribution, Gaussian distribution, normal distribution (for example, lognormality, multivariate normal distribution and single argument normal distribution), non-central X square distribution, noncentral f distribution, binomial distribution, negative binomial distribution, polynomial expression distribution, Pareto distribution, Bai Song distribution, Xue Shengshi t-distribution, Sa Lisi distribute and any associating of above distribution.
In one embodiment, stochastic variable for example, comprises that normal distribution, Bai Song distribute and Gaussian distribution by lack of balance probability distribution assignment.In another embodiment, the generation value at random of variable is by equiblibrium mass distribution assignment or relevant with it, and therefore, the stochastic variable of equiblibrium mass distribution can be at interval [V
Min, V
Max] (V
Min〉=0, V
Max≤ 1) supposes any random value with equal probabilities.
Persons skilled in the art as can be known, lack of balance distribution random value (or number) can produce (as the superimposed producer of linearity) by random number generator.The general formula of the superimposed producer of this linearity is V
i=(aV
I-1+ c) mod m, wherein a, c and m are predefined constants, and a is a multiplier value, and c is an increment, and m is a coefficient.Please refer to Park and Miller " random number generator: good difficulty is looked for " ("
Random Number Generators:Good Ones are Hard to Find ", Comm.ACM 31:1192-1201,1988).Random number generator comprise " the transferring the register series random number generator fast " that Kirkpatrick and Stoll show ("
A Very Fast Shift-Register Sequence Random Number Generator ", Journal ofComputational Physics 40:517-526,1981) described in the transfer register series.In addition, random number generator also comprises accurate number generator at random, please refer to Press and Teukolsky " quasi random number " ("
Quasi Random Numbers ", Computers in Physics 3:76-79,1989).
Lack of balance distribution random value as normal distribution or Gaussian distribution random value, also can produce by the method that association area is known.Please refer to Robinstein " simulation and Monte Carlo method " (Rubinstein, "
Simulation and the Monte Carlo Method "By John Wiley ﹠amp; Sons published 1981).One of method comprises the conversion function, as famous Bock Shi Mole conversion, in order to the equiblibrium mass distribution stochastic variable is converted to the stochastic variable (for example, Gauss or normal distribution) that new one group of lack of balance distributes, please refer to " note that departs from generation at random " (Box of Bock Shi Mole; Muller, "
A Note on the Generation of Random Deviates ", Annals Math.Stat.29:610-611,1958).
In one embodiment, random sampling methods comprises Monte Carlo method or simulation.Here " Monte Carlo method " or " Monte Carlo simulation " speech refer to a kind of of stochastic technique or the random sampling methods of the problem probability approximation that is used for studying a question and achieve a solution.Especially, used here " Monte Carlo method " or " Monte Carlo simulation " speech is meant the process (as the occurrence value at random of any given variable) that produces random occurrence especially.This process is reached by computer algorithm usually, and this process repeats repeatedly, and analyzes and calculate all test-results in order to approximate answer to be provided.Monte Carlo simulation please refer to Mi Teluo pool rein in " Monte Carlo method " (the periodical 44:335-341 of U.S. statistical association, 1949) of this and Wu Lamu (Metropolis and Ulam, "
The Monte Carlo Method ", Journal of American StatisticalAssociation 44:335-341 1949); " Monte Carlo method " of longevity Charles Bell (Sobol, "
The Monte Carlo Method ",The University of Chicago Press, 1974); Solemn Buddhist nun's " Monte Carlo simulation " (Mooney, "
Monte Carlo Simulation ",Sage University Paper, 1997).
Monte Carlo method is constantly developed in this area.For example, this method is applied to dart on the numerical value of estimating π by going up to throw at standard coordinate (by the circumscribed circumference of square) at first.By a large amount of tests, find that dartlike weapon hits circumference and foursquare quantity is proportional with circumferential area and area respectively, and have suitable tolerance range.Correspondingly, the ratio that dartlike weapon hits circumference and square number of times is similar to the mark of π value, please refer to Luo Si " probability Lesson One " (Ross, "
AFirst Course in Probability" 2
NdEdition, Macmillan, 1976).
Another example, Monte Carlo simulation can be applicable to estimate following integral formula 6:
Formula 6
In this embodiment, function V (x) has a scope frame on every side, and the integration of V (x) can be regarded as in the scope frame part at V (x).If choosing at random and non-homogeneous of scope frame mid point, the probability that is arranged in V (x) is so then determined in the shared area portions of frame by V (x).So Monte Carlo simulation produces a large amount of random points (occurrence value at random) and calculates V (x) mid point in frame quantity is to obtain area.As a result of, the integration of formula 6 can be expressed as following formula 7:
Formula 7
Wherein A is the quantity of V (x) mid point, and B is the quantity of being had a few that produces in the frame, and C is the area of scope frame.In addition, ratio A/B is relevant with V (x) relative area occupied ratio in the scope frame.
Another example of Monte Carlo simulation comprises the random variable values that generation is stressed by experimental knowledge.For example, about the experimental knowledge of component (or component ratio) require to give variable between different given zone with different probability density (continuous variable), or require to give variable in different values with different value probability (discrete variable).The example of another Monte Carlo simulation comprises the Markov chain computing.The markov computing is a random value sequence, and the probability that its each incident takes place depends on the value that results from previous moment.Please refer to " understand molecular simulation: from algorithm to using " (Frenkel ﹠amp of Frank and Smith; Smith, "
Understanding Molecular Simulation:From Algorithm to Applications "Academic Press, 1996).
The present invention is about select the method for qualified samples from pseudo-sample on the other hand." qualified samples " speech here refers to that variable satisfies the pseudo-sample of one or more particular constraints by what method produced described in the present invention, and the pseudo-sample of non-qualified samples is called as failed test sample.In the one embodiment of the invention, pseudo-sample produces (as Monte Carlo simulation) by random sampling methods, promptly in a large amount of tests, at interval [V
Min, V
Max] (V
Min〉=0 and V
Max≤ 1) value that produces at random by uniform distribution in is given to the fractions variable, the pseudo-sample that is under no restraint with generation.Each pseudo-sample, is determined it and whether satisfies specific one or more constraints for example with a computerized algorithm by checking (investigation).Selecting the pseudo-sample that satisfies constraint stores as qualified samples.Simultaneously, all the value relevant with each qualified samples is recorded into a vector, and is mapped with the component ratio, so that synthesize in sample library and the design qualified samples, because in qualified samples, those are worth all just component ratios.
Another aspect of the present invention provides a kind of method for the sample that produces at sample library to determined number.This method may further comprise the steps:
(1) provides the fractions of forming sample;
(2) give each component one variable;
(3) be at least one constraint condition of specification of variables;
(4) provide needed sample size;
(5) produce pseudo-sample;
(6), determine that this puppet sample is a qualified samples if the variable of pseudo-sample satisfies this constraint condition;
(7) repeating step (5) and (6) reach desired number until qualified samples quantity.
The present invention has disclosed a kind of method of calculating the qualified samples ratio on the other hand, the " qualified samples ratio (R here
Qs) " speech is meant that in random sampling methods, variable satisfies the ratio of the pseudo-sample of one or more constraints.In one embodiment, qualified samples ratio (R
Qs) can be by qualified samples quantity (N in the random sampling methods
Qs) divided by pseudo-sample size (N
Ps) estimate (formula 8).
Formula 8
Work as N
PsIncrease, counting accuracy diminishes, and rule change is followed following formula 9:
Formula 9
Wherein N is stochastic simulation (if you would a special Caro) experiment quantity.After having carried out a large amount of Monte Carlo simulation tests, along with 1/N constantly reduces, the change of qualified samples ratio reduces and tolerance range increases.In other words, after the test of carrying out sufficient amount, the ratio of qualified samples can reach quite high tolerance range and accuracy.For example, with regard to constraint condition
Sample (the V of Monte Carlo simulation
i) many more, tolerance range is high more.
In one embodiment, produce at the random number generator (C++ compiler 7.1.3091 version, 2003) that adopts Microsoft in the Monte Carlo experiment operation of random digit function, observe and obtain a qualified samples (as N
QsThe tolerance range of calculating=1) reaches-100% to 100%; Work as N
QsReach at 10 o'clock, its tolerance range is between-30% to 30%; Work as N
QsReach 10
2, its tolerance range is between-10% to 10%; Work as N
QsReach 10
3, its tolerance range is between-3% to 3%; Work as N
QsReach 10
4, its tolerance range is between-1% to 1%.
On the other hand, the present invention has also disclosed the method for estimating the qualified samples optimal number." qualified samples optimal number " speech here refers to, satisfies specific one or more constraint and can show the sample number of the random sampling of sample space rightly.
In one embodiment of this invention, the qualified samples optimal number obtains by detecting all pseudo-samples that satisfy particular constraints by the possible pseudo-samples and the identification of discrete variable generation.For to discrete variable, by with interval [V
I, min, V
I, max] cut apart (evenly or anisotropically) and become M part or lattice to give particular variables V
iProduce one group of discrete value, thus produce one group should the interval definition value.If the interval evenly is divided into the M part, the discrete value of variable can be { V
iMiddle arbitrary value, wherein V
i-V
I, min+ l* (V
I, max-V
I, Min)/M
i, l ∈ 0,1,2 ... M}.M is positive integer and can is 1 to 1,000, any number between 000.In one embodiment, M ∈ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 17,18 ... 20..25...30...40..50..10
2.10
3..10
4..10
5.10
6.
If variable only is set at the discrete values in the interval, the sum of pseudo-sample (Z) can be produced by the quantity of the particular grid of variable.For example, comprising component C arbitrarily
1, C
2... C
nSample in, each component C
iHas variable V
i, wherein i ∈ 0,1,2...n}, each V
iBe separated into M
iPart or grid or point, so V
iBe taken at interval [V
Min, V
Max] (V
Min〉=0 and V
Max≤ 1) one group of discrete value.According to us the experience of the pairing variable of component is determined this separation, it can be uniform segmentation or segmentation heterogeneous.If do not consider or do not provide the constraint condition of variable, based on one group of { M
iPseudo-total number of samples amount (Z) represented the sample spot of n dimension sample space, Z can calculate by following formula 10:
Formula 10
When given at least one when constraint, can detect all pseudo-samples, select variable and satisfy the pseudo-sample of this constraint and store into and constitute the qualified samples collection in the vector.After whole sample spaces (whole Z pseudo-sample) were detected, the quantity of qualified samples, that is the number of above-mentioned vector were exactly the optimal number corresponding to qualified samples in the sample space of given one group of discrete value.
If relevant component (or variable) quantity increases, and the number of fragments of each component also increases, and then the search fully by sample space can become quite heavy.For example, to being separated into the sample library that 100 lattice are constituted between each given zone by five components and every component variable, sample space is a quintuple space, and the sum of all pseudo-samples (Z) is 100
5(or 10
10,10,000,000,000).When introducing one or more constraints, it is more complicated that calculating can become.Although can discern it and whether satisfy these one or more constraints by detecting each pseudo-sample, can adopt other method, promptly provide the approximate evaluation of optimal values by carrying out random sampling described here (as Monte Carlo simulation).
Therefore, in one embodiment, we produce pseudo-sample by stochastic simulation, detect this puppet sample and whether satisfy described constraint, obtain qualified samples and qualified samples ratio according to method of the present invention.In this stochastic simulation, randomized number can be based on that one group of discrete value produces, and wherein each discrete value is arranged in the interval that variable supposes and has certain probability.Randomized number also can be any value that particular probability distributes that has in corresponding a certain interval.Therefore, the optimal number of qualified samples depends on Z and R
QsProduct.Can expect that the optimal number of qualified samples has change, this depends on one group of parameter.The variable in the sample of comprising for example of this parameter is cut apart (M) number, the method that produces random digit, statistical distribution state, Monte Carlo simulation mode, Monte Carlo experiment number of times, variable bound, tolerance limits and the required accuracy or the precision of variable.
Be appreciated that the generation of the randomized number that random sampling (as Monte Carlo simulation) is relevant with probability distribution, the selection and the calculating of the qualified samples of doing according to method provided by the present invention are all carried out by computer system or server system usually.
Computer system among the present invention (as server system) is meant design and is disposed for carrying out the computer or the computer-readable media of part or all of method described in the invention.Here the computer of Cai Yonging (as server) can be the computer of any broad variety general applications, as PC, the webserver, workstation or other computer platform of development now or in the future.Known in the art, computer include especially as treater, operating system, computer memory, input unit and these parts of output equipment partly or entirely.Computer can further comprise as cache memory, data backup unit and some miscellaneous equipments.Persons skilled in the art are appreciated that these machine elements can have many other possible structures.
But the treater that is adopted can comprise one or more microprocessors territory programmed logic array (PLA) here, or one or more special unicircuit corresponding to the special type application.For example, but treater includes but not limited to the Pentium series processors of Intel company, the microprocessor of Sun Microsystems, the workstation system treater of Sun Microsystems, the personal desktop machine treater of Motorola Inc., the MIPs treater of MIPS Science and Technology Ltd., the highest series territory programmed logic array (PLA) and some other treater of Xilinx company.
Here the operating system that is adopted comprises machine code, by the execution of treater, can coordinate and object computer in the function of other parts, and help treater to carry out the function of the various computing machine program that may write with multiple programming language.The data stream of other parts, operating system also provides scheduling arrangement, input and output control, file data management, memory management and Communication Control and related service in supervisory computer, and all these is a prior art.Unix that typical operating system comprises Windows as Microsoft, provided by all multi-providers or (SuSE) Linux OS, other or the operating system of development in the future, and the combination of these operating systems.
Here the computer memory that is adopted dissimilar memory storage arbitrarily.For example comprise optical mediums such as magneticmedium storages such as the random access memory that is seen everywhere, permanent hard disk or tape, read-write compact disc, or other accessing storage devices.Memory storage can be any one device existing or that develop in the future, comprises compact disc driving mechanism, tape drive, removable hard disk drive or disc driver.The memory storage of these types generally is to be read or written to from computer program memory medium in this medium, as CD, tape, removable hard disk or floppy disk.All these computer program memory mediums can be considered to the product of computer program.The product of these computer programs is stored computer software programs and/or data usually.Computer software programs generally are stored in system memory and/or the memory storage.
Persons skilled in the art readily understand, thereby the computer software programs among the present invention can be by coming execution in loading system storer and/or the memory storage with certain input unit.On the other hand, this software program of all or part also can be present in read-only storage or the similar memory storage, and such device does not need this software program at first to be written into by input unit.Those possessing an ordinary skill in the pertinent arts are appreciated that this software program or its some part can be loaded into system memory or cache memory or the combination of the two by treater by existing manner, are beneficial to carry out and carry out random sampling.
In one embodiment of this invention, software is stored in the computer server, and this computer server is connected with use terminal, input unit or output equipment by data line, radiolink or network system.The present technique field is generally known, and network system is included in the hardware and software that is electrically connected in computer or the device.For example network system can comprise the equipment on the medium basis of internet, 10/1000 Ethernet, the 802.11x of electric electronic engineering association, electric electronic engineering association 1394, xDSL, bluetooth, local area network, WLAN (wireless local area network), GSP, CDMA, 3G, PACS or any other ANSI Recognized Standards.
General description is carried out to the present invention in the front, next exemplifies some certain embodiments and further describes, to help understanding the present invention.
Embodiment 1
How present embodiment shows from the pseudo-sample of being made up of two components (cerium and iron) that the Monte Carlo simulation mode produces selects qualified samples.The variable V of cerium
CeValue between 0 to 1, the variable V of iron
FeIt equally also is value between 0 to 1.Monte Carlo simulation adopt equally distributed produce at random 0 to 1 between V
CeAnd V
FeValue is carried out, V in this simulation
CeGeneration value at random and V
FeGeneration at random value separate.And in this simulation, V
CeAnd V
FeThe pressure that there is no any relation or constraint limits.The result of Monte Carlo simulation has produced pseudo-sample group.The pseudo-samples set of whole formations of point (comprising hollow, grey and dark color) as shown in fig. 1.
We can utilize experimental knowledge to reduce the number of qualified samples, and this realizes by introducing constraint condition.First constraint condition is defined as 0.2<V
Ce<0.8 and 0.2<V
Fe<0.8.After the selection process had been considered first constraint, one group of pseudo-sample selecting was shown as stain or grey point as shown in Figure 1.Second constraint definition is 1-Δ<V
Ce+ V
Fe<1+ Δ when further contemplate this second constraint condition on the basis of first constraint condition, is selected simultaneously the one group of pseudo-sample that satisfies two constraint conditions and is shown as shown in Figure 1 stain.
Therefore, designing by C
eAnd F
eDuring the sample library formed, this Monte Carlo simulation has been introduced design by these two constraints with experience, and has obtained definite information in design sample storehouse.As, since satisfy relevant digital known of the pseudo-sample size of two constraints, the quantity of qualified samples can be known so.As shown in Table I, our component ratio of each qualified samples as can be known.Table I shows the pseudo-sample value that produces by Monte Carlo simulation, is the pseudo-sample value that satisfies first constraint with the italics display digit, and the numeral in the square frame is to satisfy the pseudo-sample value of first and second constraints.
If variable is cut apart by specific lattice point, the optimal number of sample can obtain according to method provided by the present invention.
V in the Table I Monte Carlo simulation
CeAnd V
FeValue
Fe Ce
0.040000 0.160000
0.120000 0.340000
0.440000 0.120000
0.160000 0.040000
0.460000 0.020000
0.460000 0.040000
0.460000 1.000000
0.560000 0.060000
0.860000 0.040000
0.960000 0.020000
0.000000 0.180000
0.000000 0.500000
0.000000 0.720000
0.320000 0.560000
0.520000 0.580000
0.540000 0.380000
0.600000 0.000000
0.720000 0.520000
0.760000 0.140000
1.000000 0.260000
1.000000 0.760000
0.180000 0.020000
0.280000 0.080000
0.360000 0.240000
0.660000 0.240000
0.740000 0.480000
0.820000 0.620000
0.820000 0.660000
0.840000 0.440000
0.960000 0.220000
0.560000 0.340000
0.820000 0.740000
0.820000 0.780000
0.860000 0.320000
0.040000 0.620000
0.060000 0.460000
0.120000 0.880000
0.180000 0.280000
0.320000 0.880000
0.420000 0.880000
0.480000 0.220000
0.680000 0.240000
0.940000 0.680000
0.020000 0.960000
0.020000 0.980000
0.520000 0.940000
0.720000 0.980000
0.740000 0.740000
0.760000 0.580000
0.820000 0.940000
0.840000 0.740000
0.880000 0.320000
0.880000 0.360000
0.980000 0.320000
0.980000 0.340000
0.540000 0.840000
0.180000 0.580000
0.240000 0.980000
0.340000 0.920000
0.380000 0.520000
0.760000 0.760000
0.880000 0.580000
0.980000 0.520000
0.280000 0.620000
0.360000 0.820000
0.560000 0.840000
0.860000 0.880000
0.560000 0.960000
0.780000 0.780000
0.860000 0.920000
0.880000 0.760000
0.580000 0.860000
0.680000 0.960000
0.720000 0.500000
0.240000 0.200000
0.240000 0.400000
0.240000 0.600000
0.340000 0.400000
0.440000 0.200000
0.540000 1.000000
0.740000 0.060000
0.740000 0.600000
0.100000 0.560000
0.100000 0.640000
0.200000 0.160000
0.400000 0.220000
0.400000 0.520000
0.400000 0.760000
0.500000 0.320000
0.500000 0.700000
0.500000 0.740000
0.500000 0.980000
0.600000 0.420000 |
0.600000 0.440000 |
0.600000 0.780000
0.700000 0.120000
0.700000 0.840000
0.800000 0.140000
0.800000 0.280000
0.900000 0.800000
0.060000 0.200000
0.360000 0.100000
0.360000 0.200000
0.460000 0.700000
0.560000 0.500000
0.860000 0.100000
0.860000 0.600000
0.960000 0.700000
0.380000 0.100000
0.380000 0.700000
0.480000 0.800000
0.580000 0.600000
0.120000 0.080000
0.520000 1.000000
0.720000 1.000000
0.920000 0.020000
0.020000 0.180000
0.620000 0.160000
Embodiment 2
How present embodiment shows from the pseudo-sample of being made up of four components (cerium, iron, tungsten and nickel) that the Monte Carlo simulation mode produces selects qualified samples.The variable V of cerium, iron, tungsten and nickel
Ce, V
Fe, V
W, V
NiValues between 0 to 1 all.We adopt equally distributed 0 to 1 the numerical value that produces at random, the separate and qualification that is under no restraint of the generation value at random in this simulation to each variable in the Monte Carlo simulation.The result of Monte Carlo simulation is the sample spot (pseudo-sample) of four-dimentional space, and this four-dimension sample spot projection in three-dimensional space as shown in Figure 2.
For selecting to have proposed first constraint condition here corresponding to real sample physically, it is defined as V
Ce+ V
Fe+ V
W+ V
Ni=1.When considering first constraint in the selection process, the one group of pseudo-sample of selecting (the first pseudo-sample) that satisfies this first constraint condition is presented among Fig. 3.
Certain experience of imagination makes us conclude that the component sum of cerium and iron always equals the component sum of tungsten and nickel, and we can introduce second constraint so, and it is defined as V
Ce+ V
Fe=V
W+ V
NiWhen further contemplate this second constraint condition on the basis of first constraint condition, the one group of pseudo-sample (the second pseudo-sample) that satisfies these two constraint conditions when selecting is shown as on the two dimensional surface that is dispersed in three confining spaces (as shown in Figure 4).This shown qualified samples point is to observe from a side of two dimensional surface among Fig. 4.
Therefore, this Monte Carlo simulation of considering two constraints provides about the definite information of design by four components sample library that form, that possess these two constraints.For example, the qualified samples ratio can calculate by removing the pseudo-sample size that satisfies two constraints with pseudo-sample all amts.Since it is digital known that the pseudo-sample size of satisfied two constraints is correlated with, the quantity of qualified samples can be known so.Write down the component ratio of variable in each qualified samples, as can be known the component ratio of this qualified samples.If variable is cut apart by specific lattice point, the optimal number of sample can obtain according to method provided by the present invention equally.
In above-mentioned Monte Carlo simulation, obtain whole 28561 pseudo-samples, wherein 460 are satisfied first constraint, and 47 are satisfied two constraints simultaneously, and the qualified samples ratio that therefore should the puppet sample satisfies two constraints is 0.0016456.
Embodiment 3
Present embodiment has illustrated that the permission user calculates and simulate (comprising Monte Carlo simulation) computer program with design qualified samples storehouse by graphic user interface input information and execution.
As shown in Figure 5, graphic user interface allows the user to select the required component of design sample.For example, a sample of being made up of component A, B and C, component A can be any one from the element set of being made up of vanadium (V), niobium (Nb) and molybdenum (Mo), the variable (V of component A
a) variation range (please refer to the scope of 0.00 shown in Fig. 5 to 1.00) between 0 to 1, this variable change scope is divided into 10 parts (as shown in Figure 5 10 sections).Consequently, component A is endowed the variable (V of value between 0 to 1
a) (please refer to Fig. 6), similarly, B component and C also are endowed variables corresponding (V
bAnd V
c) (please refer to Fig. 6).
As a kind of mode of experimental knowledge being included in the sampling design, graphic user interface allows the user that the constraint condition of specifying between a variable or a plurality of variable is provided.Variable V
a, V
bAnd V
cGive tacit consent to or the first hiding constraint is V
a+ V
b+ V
c=1 ± Δ.Δ is error (or constraint tolerance), and is given as 0.01 (please refer to Fig. 6) in this example.The second required constraint is V
a: V
b=2: 1, and by graphic user interface input (please refer to Fig. 7).
Graphic user interface further allows the user to determine how to estimate the optimal number of qualified samples.As shown in Figure 8, graphic user interface provides six other calculating of different class of accuracies.In the accurate calculation therein, pseudo-sample produces according to the formula 10 of no any constraint shown in the present, should also only select to satisfy the part that retrains by the puppet sample by COMPUTER DETECTION then.In this example, 198 samples satisfy constraint.In addition, also obtained the component ratio of all 198 qualified samples.
When counting accuracy is considered to very low-100% between 100% the time, when it thinks low between-30% to 30%, tolerance range-10% to 10% is medium, and is high between-3% to 3%, then is very high tolerance range between-1.0% to 1.0%.
Embodiment 4
Present embodiment has shown the computer program that obtains the qualified samples point of specified quantity.This computer program allows the user to calculate and simulation (comprising Monte Carlo simulation) by graphic user interface input information and execution, draws all component ratios of each sample spot in these sample spot with this.
Fig. 9 display graphics user interface allows the user to import specified gross sample point 125, and wherein each sample spot all has 4 components.The component (please refer to Figure 10) that graphic user interface also allows the user to specify to want, and the constraint condition of defined variable (please refer to Figure 11).After definition constraint tolerance (please refer to Figure 12), begin to carry out simulation test, each pseudo-sample all checks whether satisfy set constraint therebetween.When the quantity of qualified samples reaches 125, stop simulation, obtain the component ratio (as shown in Table II) of four components (element Pd, Pt, Ce and V) in 125 sample spot with this.
Table II
Pd Pt Ce V
0.039474 0.105263 0.039474 0.815789
0.065789 0.118421 0.144737 0.671053
0.078947 0.171053 0.684211 0.065789
0.052632 0.144737 0.776316 0.026316
0.078947 0.184211 0.684211 0.052632
0.013158 0.118421 0.723684 0.144737
0.026316 0.157895 0.697368 0.118421
0.039474 0.105263 0.723684 0.131579
0.052632 0.105263 0.407895 0.434211
0.052632 0.131579 0.697368 0.118421
0.065789 0.105263 0.552632 0.276316
0.065789 0.118421 0.381579 0.434211
0.065789 0.144737 0.381579 0.407895
0.013158 0.184211 0.407895 0.394737
0.026316 0.144737 0.552632 0.276316
0.039474 0.184211 0.381579 0.394737
0.052632 0.105263 0.355263 0.486842
0.065789 0.144737 0.210526 0.578947
0.013158 0.157895 0.815789 0.013158
0.039474 0.157895 0.644737 0.157895
0.078947 0.105263 0.671053 0.144737
0.105263 0 0.644737 0.25
0.184211 0 0.065789 0.75
0.065789 0.131579 0.421053 0.381579
0.078947 0.157895 0.302632 0.460526
0.078947 0.184211 0.447368 0.289474
0.105263 0 0.75 0.144737
0.184211 0 0.315789 0.5
0.026316 0.144737 0.539474 0.289474
0 0 0.302632 0.697368
0.039474 0.157895 0.407895 0.394737
0.078947 0.144737 0.026316 0.75
0.078947 0.144737 0.276316 0.5
0.052632 0.144737 0.552632 0.25
0.013158 0.026316 0.776316 0.184211
0.013158 0.092105 0.618421 0.276316
0.013158 0.092105 0.710526 0.184211
0.092105 0.092105 0.447368 0.368421
0 0.171053 0.526316 0.302632
0.039474 0.118421 0.75 0.092105
0.039474 0.013158 0.513158 0.434211
0.065789 0 0.092105 0.842 105
0.171053 0.013158 0.210526 0.605263
0.171053 0.039474 0.184211 0.605263
0.026316 0.013158 0.342105 0.618421
0.171053 0.026316 0.144737 0.657895
0.171053 0.092105 0.394737 0.342105
0.184211 0.013158 0.184211 0.618421
0.184211 0.092105 0.592105 0.131579
0.013158 0.052632 0.605263 0.328947
0.013158 0.078947 0 0.907895
0.039474 0 0.052632 0.907895
0.026316 0.092105 0.736842 0.144737
0.184211 0.052632 0.434211 0.328947
0.184211 0.092105 0.684211 0.039474
0.026316 0.013158 0.105263 0.855263
0.065789 0.026316 0.776316 0.131579
0.105263 0.039474 0.342105 0.513158
0.118421 0.131579 0.039474 0.710526
0.184211 0.013158 0.592105 0.210526
0.013158 0.013158 0.407895 0.565789
0.013158 0.039474 0.565789 0.381579
0.052632 0.026316 0.342105 0.578947
0.065789 0.092105 0.815789 0.026316
0.078947 0.013158 0.881579 0.026316
0.105263 0.052632 0.131579 0.710526
0.144737 0.026316 0.184211 0.644737
0.144737 0.092105 0.118421 0.644737
0.157895 0.184211 0.026316 0.631579
0.171053 0.092105 0.578947 0.157895
0.184211 0.026316 0.052632 0.736842
0.026316 0.039474 0.552632 0.381579
0.026316 0.092105 0.315789 0.565789
0.052632 0.026316 0.723684 0.197368
0.052632 0.052632 0.592105 0.302632
0.078947 0.092105 0.618421 0.210526
0.092105 0.052632 0.552632 0.302632
0.105263 0.026316 0.276316 0.592105
0.105263 0.052632 0.394737 0.447368
0.184211 0.078947 0.302632 0.434211
0.013158 0.078947 0.723684 0.184211
0.026316 0.065789 0.723684 0.184211
0.039474 0.039474 0.736842 0.184211
0.052632 0.065789 0.789474 0.092105
0.065789 0.039474 0.802632 0.092105
0.105263 0.026316 0.394737 0.473684
0.144737 0.092105 0.026316 0.736842
0.171053 0.039474 0.026316 0.763158
0 0.118421 0.355263 0.526316
0.092105 0.026316 0.236842 0.644737
0.184211 0.026316 0.302632 0.486842
0 0.105263 0.447368 0.447368
0.026316 0.065789 0.552632 0.355263
0.078947 0.026316 0.815789 0.078947
0.131579 0.052632 0.684211 0.131579
0.157895 0.039474 0.184211 0.618421
0.157895 0.052632 0.684211 0.105263
0 0.171053 0.789474 0.039474
0.013158 0.039474 0.144737 0.802632
0.052632 0.039474 0.473684 0.434211
0.052632 0.065789 0.723684 0.157895
0.065789 0.078947 0.789474 0.065789
0.092105 0.171053 0.736842 0
0.105263 0.065789 0.105263 0.723684
0.118421 0.013158 0.842105 0.026316
0.131579 0.078947 0.434211 0.355263
0.157895 0.026316 0.513158 0.302632
0.026316 0.078947 0.736842 0.157895
0.039474 0.052632 0.210526 0.697368
0.065789 0.013158 0.315789 0.605263
0.092105 0.078947 0.118421 0.710526
0.092105 0.078947 0.210526 0.618421
0.105263 0.039474 0.592105 0.263158
0.184211 0.013158 0.210526 0.592105
0 0.157895 0.223684 0.618421
0 0.184211 0.618421 0.197368
0.013158 0.078947 0.315789 0.592105
0.065789 0.078947 0.802632 0.052632
0.078947 0.026316 0.381579 0.513158
0.105263 0.065789 0.684211 0.144737
0.131579 0.013158 0.618421 0.236842
0.157895 0.092105 0.539474 0.210526
0.157895 0.144737 0.078947 0.618421
0.013158 0.118421 0.868421 0
0.105263 0.013158 0.223684 0.657895
Listed paper and patent all are to quote as a reference in the present patent application.Related description in the above-mentioned embodiment that exemplifies, for example and data only as demonstrating and the usefulness of illustration, and non-limiting scope of the present invention.Any insubstantial modifications processing of being done according to the present invention all falls in the claim scope of the present invention.Therefore, the spirit and scope of annex claims are not limited to the explanation version of the application to this invention.