CN105740635A - Cloud ideal solution evaluation method for transformer electromagnetic design scheme - Google Patents
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Abstract
The invention relates to the field of transformer electromagnetic design scheme evaluation, in particular to a cloud ideal solution evaluation method for a transformer electromagnetic design scheme. The method comprises the steps of screening evaluation indexes, collecting and arranging data, and constructing a cloud model decision matrix; according to the cloud model decision matrix, generating a deterministic decision matrix; determining a weight of a cloud model; according to the weight of the cloud model, generating a deterministic weight; determining positive ideal cloud and negative ideal cloud; calculating a comprehensive determination degree of each scheme for the positive and negative ideal cloud; calculating a close degree of each scheme; and according to the close degrees, sorting to-be-evaluated schemes. According to the method, a technique for order preference by similarity to ideal solution (TOPSIS) is improved by utilizing the randomness and fuzziness of a cloud theory, the shortcomings of a conventional TOPSIS for calculating the close degree by utilizing a Euclidean distance and determining an evaluation model are overcome, the indeterminacy in realistic evaluation is reflected, and the flexibility, effectiveness and objectivity of transformer electromagnetic design scheme evaluation are improved.
Description
Technical field
The present invention relates to transformator Electromagnetic Design schemes evaluation method, concretely relate to the cloud ideal solution evaluation methodology of a kind of transformator Electromagnetic Design scheme.
Background technology
The size of transformator and structural parameters, can affect performance and the cost of transformator, and for target, transformator Electromagnetic Design scheme being optimized design with the index such as efficiency or cost is the focus that people once paid close attention to.Personalization and variation in the face of the fierce market competition and customer demand, determine that oneself warp of transformator final design scheme can not meet demand with single goal, multi-objective optimization design of power can obtain multiple Pareto forward position and solve, but how evaluating each quality solving (scheme) is the problem needing to solve.
Research currently, with respect to transformator Electromagnetic Design scheme superior and inferior evaluating is also fewer.Document " research of transformator Electromagnetic Design schemes synthesis appraisal procedure " (Hebei University of Technology's journal, 5 phases in 2015, p1-6) assessment indicator system of a kind of transformator Electromagnetic Design scheme is established, propose a kind of fuzzy evaluation method based on grey incidence coefficient, though considering ambiguity and the grey majorized model of evaluation procedure, but determine that model evaluation, it is impossible to embodying the limitation of the uncertainty in real world and human cognitive, the information of implication is abundant not.
Cloud models theory is that the firm academician of Li De proposed in the nineties in 20th century, is the uncertain transformation model between qualitativing concept and its quantificational expression, in order to reflect the uncertainty of concept in objective things or human knowledge.Fuzzy membership distribution on common domain is called membership clouds, and what have general applicability is Normal Cloud, and the normal distribution law in the degree of membership distribution coincidence statistics meaning of each point on its domain, the point on cloud is called water dust.
The numerical characteristic of cloud can reflect the globality of concept and the quantitative performance of Qualitative Knowledge.Normal Cloud is by expecting that Ex, entropy En and super entropy He these three numerical characteristic describe.Normal Cloud expression formula is shown below:
(1)
In formula, Ex is expectation, En’It is that He is the random number of standard deviation with En for expectation.Due to En’It is the random number of Normal Distribution, so cloud has uncertainty.
TOPSIS (also known as TOPSIS method, this patent is referred to as TOPSIS) is a kind of multi-index evaluation being ranked up according to the degree of closeness of evaluation object Yu ideal goal.The method is on given data basis, constructs positive ideal solution and minus ideal result, calculates each scheme to be evaluated distance to positive ideal solution and minus ideal result, then calculates approach degree and carrys out the quality of evaluation of programme.Traditional TOPSIS numerical value used in evaluation procedure is exact numerical, but due to the limitation of the uncertainty of external environment and human cognitive in reality, the uncertain factor such as ambiguity and randomness is difficult to avoid that.In traditional TOPSIS, scheme to be evaluated adopts euclidean distance metric with the relation of ideal solution, there is also certain defect.
In the fusion of cloud models theory and TOPSIS, some scholar has done a little research.
Document " the Diagnostic Examination And Repair of Electric Power Facilities control strategy based on cloud model and improved TOPSIS method " (east china electric power, 42 volume 2 phases in 2014, p355-359) a kind of Diagnostic Examination And Repair of Electric Power Facilities Scheme Optimum Seeking Methods based on cloud model and improved TOPSIS method is provided, adopt cloud model to generate the initial decision matrix of traditional TOPSIS, adopt Euclidean distance and grey relational grade Weighted Fusion to calculate approach degree and improve TOPSIS.
Document " the TOPSIS Research of Decision based on cloud model " (value engineering, 29 phases in 2013, p8-10) the cloud TOPSIS method of a kind of solution interval type decision information is proposed, adopt cloud models theory that interval type numerical value is converted into the initial decision matrix of cloud model form, adopt fuzzy number method for measuring similarity to calculate the approach degree in TOPSIS, but consistent with the polar orientation of super entropy to build positive and negative desirable cloud somewhat dogmatic by the expectation of same decision attribute, entropy.
Document " the SaaS decision method based on cloud model " (electronic letters, vol, 43 volume 5 phases in 2015, p987-992) propose a kind of software based on cloud model and namely service optimal service decision method, distance measure in its TOPSIS method have employed COS distance and Euclidean distance, but when adopting weighting method to build cloud model decision matrix, institute's weighting weight of the expectation of same decision attribute, entropy and super entropy is the same not necessarily reasonable.
(commander controls and emulation document " cloud model application in radar chaff resource multiple-objection optimization configures ", 36 volume 5 phases in 2014, p39-44) cloud model is adopted to build radar chaff beneficial matrix with TOPSIS, Hungary Algorithm is used to carry out jamming resource optimized distribution, its positive and negative desirable cloud is also build by the expectation of same decision attribute, entropy are consistent with the polar orientation of super entropy, this article have employed the weight of cloud model form, but do not provide and how to ask for.
The application case that Chinese patent application publication No. is CN102156710 provides a kind of plant discrimination method based on cloud model and TOPSIS method, the situation of dividing builds trapezium cloud and the normal cloud model of plant external appearance characteristic specimen, by calculate by measuring plants about specimen cloud degree of membership build traditional TOPSIS initial decision matrix, this application case has used cloud degree of membership (degree of certainty) concept.
The application case that Chinese patent application publication No. is CN104679988 provides a kind of multiple attributive decision making method based on cloud TOPSIS, but it is the same with super entropy institute weighting weight to there is also the expectation of same decision attribute when initial cloud decision matrix builds, entropy, the problem that during positive and negative desirable cloud structure, the expectation of same decision attribute, entropy are consistent with the polar orientation of super entropy.
In above-mentioned document, cloud models theory is mainly used in generating the initial decision matrix of TOPSIS, cloud model could not be made full use of and process the characteristic of randomness and ambiguity, majority is data " cloud " to be changed, namely expression data is carried out with the three of cloud model numerical characteristics, then adopt some defining method to measure the relation of scheme to be evaluated and ideal solution, use all little of degree of certainty concept.
Document " the customer co-operation innovation work based on Clouds theory and TOPSIS is evaluated " (Creative Science and Technology Co. Ltd, 8 phases in 2015, p25-28) propose to adopt the distance in weighted comprehensive degree of certainty replacement traditional TOPSIS to improve and approach desirable method, introduce uncertainty, provide a kind of positive and negative desirable cloud building method, but weight and decision matrix or conventionally form, embody still abundant not to real world uncertain.
Summary of the invention
In view of the deficiency of above-mentioned technology, the present invention proposes the cloud ideal solution evaluation methodology of a kind of transformator Electromagnetic Design scheme.The positive and negative desirable cloud having incorporated ambiguity and randomness is adopted to replace plus-minus ideal solutions, scheme to be evaluated is adopted to replace the Euclidean distance in tradition TOPSIS to calculate nearness about the cloud degree of certainty of positive and negative desirable cloud, embody the uncertainty in human intelligence decision-making, thus providing new method for transformator Electromagnetic Design schemes synthesis evaluation.
For achieving the above object, the present invention adopts following technical proposals and step:
Step 1: screening and assessment index, collection, disposal data, construct cloud model decision matrix.
Consider cost, life-span, benefit and on Factor Selection indexs such as the impacts of environment, collect, arrange each protocol, for quantitative target data can by inquiry, statistics, the mode such as measurement directly obtain, some needs carry out certain calculating and conversion；To quantify for qualitative index, as expert directly gives a mark, gives the numerical value that can reflect difference to each grading index.All achievement datas adopt three numerical characteristics (Ex, En, He) of cloud model to describe, and are the original decision matrix of cloud model.The cloud model building method that this patent proposes provides in step 3.
Step 2: according to cloud model decision matrix, generates determinization decision matrix.
This step produces exact value according to cloud model numerical characteristic, it is desirable to its degree of certainty more than a certain threshold value δ, 0 < δ < 1.δ is more big, and the exact value degree of certainty of generation is more high.This step has randomness, can embody the uncertainty of real world.Considering inventive feature, decision matrix need not standardization processing and weighting.
The numerical characteristic (Ex, En, He) of known cloud and degree of certainty lower limit δ, the method asking for exact value is (going cloud or determinization):
1) one is generated with En for expecting with the He normal random number En being standard deviation’, and require En’Degree of certainty more than δ.
2) one is generated with Ex for expectation with En’For the normal random number x of standard deviation, and require that the degree of certainty of x is more than δ.
A kind of simple formula that generates is:
x=Ex+rnd×En’(2)
Rnd is the random number that can just can bearing, less than certain number, | rnd | can ensure that the degree of certainty of x is more than δ.The difference degree of determining that of the method and reverse cloud algorithm is a random number in [δ, 1] interval；The technology asking for cloud model provided by step 3 is it can be seen that can have significantly high identification between this step gained x.Degree of certainty computing formula adopts formula (1)；Step 1) and 2) in δ can be different.
Step 3: determine the cloud model weight of each index.
Determine that the method for cloud model weight has method of expertise and numerical method two class.Method of expertise is the numerical characteristic determining cloud model weight according to expertise.The present invention is based on the position relationship of adjacent cloud, it is proposed to generate cloud model weight according to weight expected data.Obtain weight and be contemplated to be prerequisite, empirical method, analytic hierarchy process (AHP) or entropy assessment etc. can be adopted.
W=[w is expected with known weight1,w2,w3,…,wn] for example, the method generating cloud model weight that the present invention proposes is as follows:
1) first W is sorted from small to large, obtain Ws=[ws1,ws2,ws3,…,wsn], W and WsUnit have the corresponding relation determined.If there being the weight of repetition, then weed out.
2) WsCloud characteristic computational methods as follows:
wsEx(1)=ws1, wsEn (1)=Min (| ws1-0|,|ws2-ws1|)/3, wsHe (1)=wsEn (1)/C1(3)
wsEx(n)=wsn, wsEn (n)=| wsn-wsn-1|/3, wsHe (n)=wsEn (n)/Cn(4)
wsEx(i)=wsi, wsEn (i)=Min (| wsi+1-wsi|,|wsi-wsI-1|)/3, wsHe (i)=wsEn (i)/Ci, other (5)
WsEx (i), wsEn (i) and wsHe (i) are W respectivelysThe expectation of i-th element, entropy and super entropy, CiFor the constant much larger than 1, i=1,2 ..., n；It can be seen that between each weight, the probability of magnitude relationship backward is very low.
3) by W and WsElement corresponding relation obtain weight W cloud model, and recover 1) in reject weight.
Step 4: according to cloud model weight, generates determinization weight.
This step requires the same with step 2, cloud model numerical characteristic produce determinization weight, and its degree of certainty is greater than a certain threshold value δ；This step has uncertainty, and the determinization weight directly generated to be normalized.
Step 5: determine positive desirable cloud and negative desirable cloud.
Plus-minus ideal solutions is really optimum and the most bad two Natural language evaluation set.The corresponding positive desirable cloud of each index and negative desirable cloud, if there being n index, then have 2n cloud.More big closer to its degree of certainty of ideal solution, it is determined that degree value is in [0,1] interval.
Step 6: calculate the comprehensive degree of certainty that each scheme aligns, bears desirable cloud.
First calculate each scheme each index degree of certainty to the positive and negative desirable cloud of this index, then pass through weighted sum method and try to achieve each scheme comprehensive degree of certainty about positive and negative desirable cloud.Positive and negative desirable cloud is made up of index ideal cloud.
Step 7: calculate the approach degree of each scheme.
Step 8: the size according to approach degree, is ranked up scheme to be evaluated, and relative similarity degree is more big more excellent.Also can revalue after the approach degree normalization of each scheme during concrete evaluation, not affect result.
In step 5, the numerical characteristic of positive and negative desirable cloud is determined by following formula:
Exj +=zj +, Enj +=|zj +-zj -|/3, Hej +=Enj +/C+(6)
Exj -=zj -, Enj -=|zj +-zj -|/3, Hej -=Enj -/C-(7)
Wherein zj +For the positive ideal solution of jth index, zj -For the minus ideal result of jth index, C+And C-For the constant much larger than 1, such as 100；Exj +、Exj -、Enj +、Enj -、Hej +、Hej -It is the positive and negative desirable expectation of cloud, entropy and super entropy respectively；Positive and negative ideal solution component zj +And zj -Can according to practical situation and empirically determined, it is possible to asking for relative ideal solution according to decision matrix data, wherein profit evaluation model index is the bigger the better, and cost type index is the smaller the better.
The method asking for comprehensive degree of certainty in step 6 is: set μij +For the jth index of i-th scheme for the degree of certainty of the positive desirable cloud of jth index, this patent adopts weighted sum method to determine comprehensive degree of certainty, and scheme to be evaluated is for the comprehensive degree of certainty r of positive desirable cloudi +For:
(8)
wjWeight for jth index.The program is for the degree of certainty r of negative desirable cloudi -Calculating similar.
The relative similarity degree computing formula of described step 7 is:
Di=ri +/(ri ++ri -)(9)
ri +、ri -Respectively scheme i is for the comprehensive degree of certainty of positive and negative desirable cloud.
Considering randomness and the uncertain factor of real world, step 2, step 4 and step 6 can repeatedly take assembly average；But also certain step one of (step 2,4,6) repeatedly takes assembly average；Also all only can carry out once, but whole evaluation procedure is repeatedly, repeatedly result is compared analysis.If repeatedly evaluation result is consistent, then illustrate that the method robustness is better, reliable results, if evaluation result changes, then can deeply excavate more information.
Beneficial effects of the present invention: introduce cloud models theory in evaluation procedure, the ambiguity of real world, randomness can be embodied, make whole evaluation procedure contain uncertainty；Middle finding uncertainty from determining, from uncertain middle searching definitiveness, relatively conventional evaluation methodology cover half type really, the art of this patent is more flexible, closer to reality.
Owing to evaluation result is had impact by different data normalization methods, initial data need not be standardized by the present invention, has avoided this problem.
Adopting cloud degree of certainty to replace the distance of tradition TOPSIS, add the uncertainty of cloud model itself, overcoming distance method cannot the defect of scheme on the positive and negative ideal solution perpendicular bisector of effective evaluation.
The present invention gives the method building cloud decision matrix, cloud weight and plus-minus ideal solutions cloud numerical characteristic, under lacking expertise circumstances, remain to use, there is good universality.
Technology used by the present invention contains uncertainty, after programming realization, by repeatedly running, and relative analysis, some potential information can be excavated.
Accompanying drawing explanation
Fig. 1 is the flow chart of steps of the present invention.
Fig. 2 is cloud model weight and the determinization interval schematic diagram (for W=[0.10.150.30.250.2], δ=0.9) thereof that the cloud model that the present invention proposes generates that method generates.
Fig. 3 is the schematic diagram (certain result) of positive and negative desirable cloud in embodiment.
Fig. 4 is comprehensive degree of certainty computing block diagram.
Detailed description of the invention
Below in conjunction with embodiment, the invention will be further described.
The present invention adopts cloud TOPSIS that 6 dry-type distribution transformer Electromagnetic Design schemes are evaluated, to verify the effectiveness of the method.
Referring to the flow chart of steps of Fig. 1, the cloud ideal solution evaluation methodology embodiment of the transformator Electromagnetic Design scheme of the present invention, comprise the following steps:
Step 1: screening and assessment index, collection, disposal data, construct cloud model decision matrix.
This example chooses manufacturing cost, operating cost, temperature rise and 4 indexs of noise to characterize transformator Electromagnetic Design scheme performance, and these 4 indexs constitute transformator Electromagnetic Design scheme appraisement system.
Table 1 is 6 transformator Electromagnetic Design protocol.
Table 1 dry-type distribution transformer design scheme evaluation achievement data
This example is totally 6 schemes, 4 evaluation indexes, can be made up of the decision matrix that 6 row 4 arrange table 1 data.
According to formula (3-5), cloud model decision matrix can be obtained:
。
Step 2: according to cloud model decision matrix, generates determinization decision matrix.
Determinization decision matrix can be obtained according to formula (2), owing to numerical value is the random value meeting rated condition, the uncertainty of real world evaluation and measurement can be embodied.Certain result is:
。
Step 3: determine the cloud model weight of each index.
This embodiment adopts analytic hierarchy process (AHP) to determine initial weight, then adopts formula (3-5) to generate cloud weight.Adopting 1～9 scaling law to be compared between two by evaluation index, it is believed that manufacturing cost important, ratio noise somewhat the more important the same as temperature rise, operating cost is more important than manufacturing cost, ratio noise much more significant, then judgment matrix is:
。
This matrix Maximum characteristic root is λmax=4.0375, characteristic of correspondence vector is v1=[0.2251,0.9434,0.2251,0.0927]；Normalization can obtain weight:
W=[0.1514,0.6348,0.1514,0.0624].
According to formula (3-5), cloud model weight can be obtained:
Wc=[(0.1514,0.0297,0.0003)、(0.6348,0.1611,0.0016)、(0.1514,0.0297,0.0003)、(0.0624,0.0208,0.0002)]。
Step 4: according to cloud model weight, generates determinization weight.
Being calculated by formula (2), then normalization obtains determinization weight.This step has uncertainty, because rnd is random number.
Certain result is W0=[0.1515,0.6342,0.1520,0.0622].
Step 5: determine positive desirable cloud and negative desirable cloud.4 indexs are cost type index, calculate positive and negative desirable cloud characteristic according to formula (6-7), take C+=C-=100。
Positive and negative ideal solution can be tried to achieve by step 2 gained decision matrix:
z+=[3.1606,205379.9556,93.3884,66.1274]
z-=[3.2904,219549.0974,99.2306,66.9810].
Positive desirable cloud numerical characteristic be respectively as follows: [(3.1606,0.0433,0.0004), (205379.9556,4723.0473,47.2305), (93.3884,1.9472,0.0195), (66.1274,0.2845,0.0028)].
Negative desirable cloud numerical characteristic be respectively as follows: [(3.2904,0.0433,0.0004), (219549.0974,4723.0473,47.2305), (99.2301,1.9472,0.0195), (66.9810,0.2845,0.0028)].
Step 6: calculate each scheme comprehensive degree of certainty for positive and negative desirable cloud.
First calculating each index of each scheme degree of certainty about the positive and negative desirable cloud of corresponding index, calculate comprehensive degree of certainty referring next to formula (8), certain evaluation result is:
r+=[0.0102,1,0.01533,1]
r-=[1,0.0116,0.9939,0.0119].
Step 7: calculate the relative similarity degree D of each scheme.
D=[0.2085,0.3788,0.2518,0.6357,0.5327,0.6927].
Step 8: the size according to relative similarity degree, is ranked up scheme to be evaluated.Relative similarity degree is more big more excellent, the sequence of 6 schemes by excellent to bad: 6 > 4 > 5 > 2 > 3 > 1, scheme 6 is optimum.No. 1 scheme is worst, and No. 6 schemes are best, coincide with practical situation.This approach degree difference evaluating each scheme is more apparent, and identification is higher.
Repeat above evaluation procedure, be analyzed comparing to the intermediate data in evaluation procedure and evaluation result, utilize the uncertainty that the art of this patent self has, more information can be excavated.
The present invention is on forefathers' Research foundation, consider the ambiguity in the evaluation of transformator Electromagnetic Design scheme and randomness, positive and negative desirable cloud is adopted to replace the plus-minus ideal solutions in traditional TOPSIS, cloud degree of certainty is adopted to replace Euclidean distance, a kind of cloud ideal solution assessment method is proposed, overcome based on a determination that some shortcomings of traditional evaluation methodology of model, embody the uncertainty in Realistic Evaluation, provide new thought for transformator Electromagnetic Design scheme evaluation.Above-described embodiment is it is shown that the present invention is feasible and effective.
Method of the present invention is not limited to the embodiment described in detailed description of the invention, any one of skill in the art of being familiar with is in the technical scope that the present invention discloses, the change that can readily occur in or replacement, or it is applied to other professional field, all should be encompassed within scope of the presently claimed invention.
Some concrete formula and content that this specification is used when setting forth the present invention, in order to express needs and consider that integrity provides (concrete steps of such as analytic hierarchy process (AHP) and formula), also some is Conventional wisdom, and these are not in the middle of the right of patent of the present invention.But the entire content of this patent and the combined innovation some prior art being merged and producing, then within scope of the presently claimed invention.
Claims (10)
1. a cloud ideal solution evaluation methodology for transformator Electromagnetic Design scheme, is characterized in that comprising the following steps:
Step 1: screening and assessment index, collection, disposal data, construct cloud model decision matrix；
Step 2: according to cloud model decision matrix, generates determinization decision matrix；
Step 3: determine the cloud model weight of each index；
Step 4: according to cloud model weight, generates determinization weight；
Step 5: determine positive desirable cloud and negative desirable cloud；
Step 6: calculate the comprehensive degree of certainty that each scheme aligns, bears desirable cloud；
Step 7: calculate the approach degree of each scheme；
Step 8: the size according to approach degree, is ranked up scheme to be evaluated, and relative similarity degree is more big more excellent.
2. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, it is characterized in that: the determinization initial decision matrix generated by cloud model decision matrix, there is ambiguity and randomness, compare closing to reality, and do not need standardization processing, it is not necessary to weighting；The determinization weight generated by cloud model weight, it may have ambiguity and randomness.
3. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, it is characterized in that: when adopting cloud model decision matrix generate determinization initial evaluation matrix and adopt cloud model weight to generate determinization weight, the exact value generated, the degree of certainty of its correspondence should be greater than certain degree of certainty threshold value δ, and 0 < δ < 1；δ is more big, and the exact value degree of certainty of generation is more high, and evaluation result concordance is more high；The determinization weight directly generated to be normalized.
4. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, is characterized in that: when structure cloud model decision matrix and cloud model weight, it is possible to adopt method of expertise and numerical method according to the priori grasped；For numerical method, having two kinds: one is reverse Membership Cloud Generators, each index for each scheme is required for substantial amounts of data (including expert estimation data)；Generally, first obtain expected value more real, such as directly measure or marking；This patent is according to the relative position relation between adjacent cloud, it is proposed to entropy and the method for super entropy are asked in a kind of known expectation, expects W=[w with known weight1,w2,w3,…,wn] for example, step is as follows:
1) first W is sorted from small to large, obtain Ws=[ws1,ws2,ws3,…,wsn], W and WsUnit have the corresponding relation determined, if there being the weight of repetition, then weed out；
2) WsCloud numerical characteristic computational methods as follows:
wsEx(1)=ws1, wsEn (1)=Min (| ws1-0 |, | ws2-ws1|)/3, wsHe (1)=wsEn (1)/C1
wsEx(n)=wsn, wsEn (n)=| wsn-wsn-1|/3, wsHe (n)=wsEn (n)/Cn
wsEx(i)=wsi, wsEn (i)=Min (| wsi+1-wsi|,|wsi-wsI-1|)/3, wsHe (i)=wsEn (i)/CiOther
WsEx (i), wsEn (i) and wsHe (i) are W respectivelysThe expectation of i-th element, entropy and super entropy;CiFor the constant much larger than 1, i=1,2 ..., n；It can be seen that between each weight component, the probability of magnitude relationship backward is very low；
3) by W and WsElement corresponding relation obtain weight W cloud model, and recover 1) in reject weight.
5. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, is characterized in that: the numerical characteristic (Ex, En, He) of known cloud and degree of certainty lower limit δ, and the method asking for exact value is (going cloud or determinization):
1) one is generated with En for expecting with the He normal random number En being standard deviation’, and require En’Degree of certainty more than δ；
2) one is generated with Ex for expectation with En’For the normal random number x of standard deviation, and require that the degree of certainty of x is more than δ；
A kind of straightforward procedure asking for exact value is x=Ex+rnd × En’, rnd is the random number that can just can bearing, less than certain number, | rnd | can ensure that the degree of certainty of x is more than δ；The difference degree of determining that of the method and reverse cloud algorithm is a random number in [δ, 1] interval；According to claim 4 being asked for the technology of cloud model it can be seen that can have significantly high identification between this step gained x；Step 1) and 2) in δ can be different.
6. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, is characterized in that: in step 5, the numerical characteristic of positive and negative desirable cloud is determined by following formula:
Exj +=zj +, Enj +=|zj +-zj -|/3, Hej +=Enj +/C+
Exj -=zj -, Enj -=|zj +-zj -|/3, Hej -=Enj -/C-
Wherein zj +For the positive ideal solution of jth index, zj -For the minus ideal result of jth index, C+And C-For the constant much larger than 1, such as 100；Exj +、Exj -、Enj +、Enj -、Hej +、Hej -It is the positive and negative desirable expectation of cloud, entropy and super entropy respectively；Positive and negative ideal solution component zj +And zj -Can according to practical situation and empirically determined, it is possible to asking for relative ideal solution according to decision matrix data, wherein profit evaluation model index is the bigger the better, and cost type index is the smaller the better.
7. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, it is characterized in that: the method calculating comprehensive degree of certainty in step 6 is: first calculate each scheme each index degree of certainty to the positive and negative desirable cloud of this index, then pass through weighted sum method and ask for each scheme comprehensive degree of certainty about positive and negative desirable cloud；Positive and negative desirable cloud is made up of index ideal cloud.
8. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, is characterized in that: calculating each scheme each index degree of certainty formula to the positive and negative desirable cloud of this index is:
Ex is expectation, En’It is with En for the expectation He random number being standard deviation.
9. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, is characterized in that: the relative similarity degree computing formula of described step 7 is:
Di=ri +/(ri ++ri -)
ri +、ri -Respectively scheme i is for the comprehensive degree of certainty of positive and negative desirable cloud.
10. the cloud ideal solution evaluation methodology of transformator Electromagnetic Design scheme according to claim 1, is characterized in that: considering randomness and the uncertain factor of real world, step 2, step 4 and step 6 can repeatedly take assembly average；But also certain step one of (step 2,4,6) repeatedly takes assembly average；Also all only can carry out once, but whole evaluation procedure is repeatedly, repeatedly result is compared analysis；If repeatedly evaluation result is consistent, then illustrate that the method robustness is better, reliable results, if evaluation result changes, then can deeply excavate more information.
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| CN107203842A (en) * | 2017-05-18 | 2017-09-26 | 西南交通大学 | Harmonic pollution level evaluation method based on extension cloud similarity and similarity to ideal solution |
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| CN107292090B (en) * | 2017-05-31 | 2020-07-03 | 浙江大学 | Comprehensive evaluation method for structural scheme of high-speed press |
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| CN113567785A (en) * | 2021-07-24 | 2021-10-29 | 福州大学 | Intelligent electromagnetic appliance performance evaluation method and system |
| CN114996897A (en) * | 2022-04-06 | 2022-09-02 | 武昌首义学院 | Multi-attribute group decision method based on cloud model joint coefficient |
| CN114996897B (en) * | 2022-04-06 | 2023-03-07 | 武昌首义学院 | Multi-attribute group ship anti-settling capacity evaluation decision method based on cloud model joint coefficient |
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