CN104077485B - Model correctness evaluation method based on goodness of fit - Google Patents

Abstract

The invention discloses a model correctness evaluation method based on goodness of fit. The model correctness evaluation method is characterized by comprising the following steps of 1, establishing the hierarchical structure of a model, 2, calculating the individual goodness of fit of each parameter of a child node of the bottommost layer of the hierarchical structure, 3, calculating the weight of each parameter of each child node relative to the child node, 4, calculating the goodness of fit of each child node, 5, calculating the weight of each parameter of each child node relative to a target node, and 6, calculating the goodness of fit of the target node. The model correctness evaluation method based on goodness of fit is capable of evaluating the correctness degree of the model as long as the input and output parameters of the model are known and in case that the output parameters are measureable; the method does not need to find out complex principle and the inherent working mode of the model, and therefore, the method has remarkable advantages.

Description

Evaluation method based on the Correctness of model of the goodness of fit

Technical field

The present invention relates to a kind of evaluation method of Correctness of model, and in particular to a kind of Correctness of model based on the goodness of fit Evaluation method, belong to model evaluation method and technology field.

Background technology

The correctness of model directly affects the performance quality of Related product, so carry out evaluation to the correctness of model having Great meaning.

By taking skin antenna stress-electric coupling model as an example：

Skin antenna refer to the radio-frequency enabled part of integrated micro-strip antenna array is embedded in Weapons platform construction, by profit The Active Arrays of the Highgrade integration manufactured with advanced composite moulding process, it both can be used as the power of Weapons platform construction Learn bearing function part, it is also possible to as the function solenoid part of transmitting/receiving wireless electromagnetic wave.

With traditional antenna contrast, the characteristics of there is skin antenna the height of structure/circuit to merge, make antenna become weapon and put down Part or all of platform structure, reduces antenna weights and space occupancy rate.Skin antenna can be widely applied to a new generation In the fields such as opportunity of combat, unmanned plane, early warning dirigible, intelligent battlebus, stealthy battleship.

Affecting the unit for electrical property parameters of skin antenna performance mainly has gain, beam angle, standing-wave ratio and secondary lobe, mechanical property Parameter mainly has stress, strain and displacement.

Skin antenna stress-electric coupling model represent skin antenna under different load antenna electric performance and mechanical property with The situation of change of time.The correctness of the model directly affects the performance quality of skin antenna, so to skin antenna power thermocouple The correctness of matched moulds type carries out evaluation and is significant.

However, the method for existing evaluation model correctness is both for specific model using specific method, and It must be appreciated that the complicated operation principle of model and its inherent working method, evaluation method is numerous, understanding is difficult, without a kind of unified The adoptable correctness of the model to meeting certain condition evaluation method.

The content of the invention

For solve the deficiencies in the prior art, it is an object of the invention to provide a kind of application it is wide, practical, based on kiss It is right to evaluate that input/output argument is known and method of the correctness of the measurable model of output parameter.

In order to realize above-mentioned target, the present invention is adopted the following technical scheme that：

A kind of evaluation method of the Correctness of model based on the goodness of fit, it is characterised in that comprise the following steps：

(1) recursive hierarchy structure of model, is set up：

Degree of membership relation according to each factor sets up recursive hierarchy structure, is divided into top level goal node, middle straton section Point, bottom three levels of sub- child node, upper layer node has dominating role to lower level node, and same layer factor is separate；

(2) the individual event goodness of fit of each parameter of the sub- child node of the recursive hierarchy structure bottom, is calculated：

(1), in the case of known to the size and |input paramete in model, calculate or emulation obtains the output parameter of model Calculated value；

(2) the actual test value of the corresponding output parameter of the model under identical input, is measured by experiment；

(3) relative error between the calculated value and actual test value of output parameter, is calculated；

(4), relative error is mapped as into the goodness of fit by type gauss of distribution function less than normal；

(3) weight of each parameter of sub- child node relative to child node, is calculated；

(4) goodness of fit of each child node, is calculated：

Each sub- section is obtained according to the weight calculation of the relative child node of the goodness of fit and each parameter of each parameter of sub- child node The goodness of fit of point；

(5) weight of each parameter of child node relative to destination node, is calculated；

(6) goodness of fit of destination node, is calculated：

Target section is obtained according to the weight calculation of the relative target node of the goodness of fit and each parameter of each parameter of child node The goodness of fit of point.

The evaluation method of the aforesaid Correctness of model based on the goodness of fit, it is characterised in that in step (three), calculates son The each parameter of child node includes following sub-step relative to the weight of child node：

(1), Judgement Matricies：

In the recursive hierarchy structure of model, each element of child node is under the jurisdiction of as first element of judgment matrix The element of its each sub- child node is arranged in order the first row behind and the 1st row, for the criterion of judgment matrix, to each yuan The importance degree of element presses 1-9 assignment；

(2), Consistency Check in Judgement Matrix；

(3), weight vectors are calculated：

To meeting conforming judgment matrix, rank of advanced units vector normalization, then seek row and normalize, obtain each index Relative weighting.

The evaluation method of the aforesaid Correctness of model based on the goodness of fit, it is characterised in that Consistency Check in Judgement Matrix The step of be：

A, the Maximum characteristic root λ that judgment matrix R is calculated by | λ I-R |=0_max, wherein I is unit matrix；

B, byObtain coincident indicator C.I.；

C, table look-up the corresponding Aver-age Random Consistency Index R.I. of determination；

D, calculating consistency ration C.R. are simultaneously judged：

Work as C.R.<When 0.1, the uniformity of judgment matrix can be received；

Work as C.R.>When=0.1, judgment matrix does not meet coherence request, and needs are corrected again to the judgment matrix.

The evaluation method of the aforesaid Correctness of model based on the goodness of fit, it is characterised in that in step (five), calculates son The each parameter of node includes following sub-step relative to the weight of destination node：

(1), Judgement Matricies：

In the recursive hierarchy structure of model, destination node element is under the jurisdiction of it as first element of judgment matrix The element of each child node be arranged in order the first row behind and the 1st row, for the criterion of judgment matrix, to each element Importance degree presses 1-9 assignment；

(2), Consistency Check in Judgement Matrix：

A, the Maximum characteristic root λ that judgment matrix R is calculated by | λ I-R |=0_max, wherein I is unit matrix；

B, byObtain coincident indicator C.I.；

C, table look-up the corresponding Aver-age Random Consistency Index R.I. of determination；

D, calculating consistency ration C.R. are simultaneously judged：

Work as C.R.<When 0.1, the uniformity of judgment matrix can be received；

Work as C.R.>When=0.1, judgment matrix does not meet coherence request, and needs are corrected again to the judgment matrix；

(3), weight vectors are calculated：

To meeting conforming judgment matrix, rank of advanced units vector normalization, then seek row and normalize, obtain each index Relative weighting.

The evaluation method of the aforesaid Correctness of model based on the goodness of fit, it is characterised in that in step (), with known The goodness of fit of each output parameter of model as the sub- child node of bottom, with the kiss of all kinds of integrated performance indexs belonging to output parameter Right conduct centre level of child nodes, use can embody total goodness of fit of the model of Correctness of model as top level goal node.

The invention has benefit that：The input/output argument of model need to only be known, and it is detectable in output parameter In the case of, the correctness degree of model can be entered using the Correctness of model evaluation method based on the goodness of fit proposed by the present invention Row is evaluated, and the method is not required to will be clear that the principle of model complexity and its working method of inherence, therefore the method for the present invention has Significant advantage.

Description of the drawings

Fig. 1 is the flow chart for calculating the goodness of fit；

Fig. 2 is the flow chart of the correctness for evaluating skin antenna electromechanical Coupling Model；

Fig. 3 is the appraisement system figure of skin antenna electromechanical Coupling Model；

Fig. 4 is the evaluation model figure of skin antenna electromechanical Coupling Model；

Fig. 5 is the curve map of the type gauss of distribution function less than normal for calculating the single index goodness of fit；

Fig. 6 is the hierarchy structure chart of weight calculation.

Specific embodiment

Make specific introduction to the present invention below in conjunction with the drawings and specific embodiments.

With reference to Fig. 2, the evaluation method of the present invention is applied to known to input/output argument and the measurable model of output parameter, its Principle is as follows：

The thinking of the present invention is in the case of the input of known models, to calculate or emulation obtains corresponding output parameter Calculated value, experiment measures the actual test value of the corresponding output parameter of the model under identical input, by calculating output ginseng Relative error between several calculated value and actual test value, and the relative error by type gauss of distribution function less than normal Be mapped as certain score, the score number just embody the size of the goodness of fit, i.e. the size of the goodness of fit is embodying model just True property degree, so can be verified to the correctness of model by the goodness of fit.

Definition to the goodness of fit：In the case of each index key factor is considered, calculated value and actual test value are close to The tolerance of degree.

The calculation process of the goodness of fit as shown in figure 1, first, is measured by exemplar/model machine to relevant parameter, is joined Several actual test values；Then, the calculated value of correspondence parameter is measured by known models (under identical input)；Finally, count Calculation obtains the relative error between parameter theory calculated value and actual test value, and the relative error is passed through certain mapping function Corresponding scoring is obtained, the overall merit of calculated value and actual test value degree of agreement is obtained after synthesis.

For convenience of skilled artisan understands that the evaluation method of the present invention, now known to input/output argument and exporting ginseng Describe in detail as a example by the measurable skin antenna stress-electric coupling model of number.

First, the recursive hierarchy structure of model is set up

Degree of membership relation according to each factor sets up recursive hierarchy structure, is divided into top level goal node, middle straton section Point, bottom three levels of sub- child node.It is simple to understand to be exactly that the factors of same layer are subordinated to the factor of last layer or to upper strata Factor has an impact, while and arranging next layer of factor or being acted on by lower layer factors.

Specifically, with the goodness of fit of each output parameter of skin antenna electromechanical Coupling Model as the sub- child node of bottom, example Such as affecting the mechanical performance index of antenna stress-electric coupling performance includes stress, strain, displacement, then coincide with stress in sub- child node Degree x₁₁, strain goodness of fit x₁₂, displacement goodness of fit x₁₃To represent the individual event goodness of fit of stress, strain and displacement respectively, antenna is affected The electrical characteristics index of stress-electric coupling performance includes gain, beam angle, standing-wave ratio, secondary lobe, then coincide with gain in sub- child node Degree x₂₁, beam angle goodness of fit x₂₂, standing-wave ratio goodness of fit x₂₃With secondary lobe goodness of fit x₂₄To represent gain, beam angle respectively, stay Bob, the individual event goodness of fit of secondary lobe；With the goodness of fit of all kinds of integrated performance indexs belonging to output parameter as middle straton section Point, such as affecting the integrated performance index of destination layer skin antenna stress-electric coupling performance includes mechanical property and electrical performance indexes, Therefore in goodness of fit X of child node mechanical characteristic₁With goodness of fit X of electrical characteristics₂To represent the goodness of fit of child node respectively；With Total goodness of fit D of model of Correctness of model can be embodied as top level goal node.

The recursive hierarchy structure of skin antenna stress-electric coupling model is thus established, in the recursive hierarchy structure, on Node layer has dominating role to lower level node, and same layer factor is separate.As shown in Figure 4.Wherein：

W_iWeight of child node i relative to top mode is represented,

w_1iWeight of sub- child node i relative to child node 1 is represented,

w_2jRepresent weight of sub- child node j relative to child node 2.

So when the goodness of fit for learning each sub- child node of bottom and per individual sub- child node relative to middle straton section After the weight (importance degree) of point, by the computing formula coincideing, the goodness of fit of each child node of intermediate layer just can be obtained, After knowing the weight of the goodness of fit and each of which child node of each child node of intermediate layer relative to target node layer, target just can be obtained The total goodness of fit of node layer, by the stool and urine of total goodness of fit the correctness journey of known skin antenna stress-electric coupling model is can verify that Degree.

Appraisement system such as Fig. 3, evaluation model of skin antenna stress-electric coupling model is as shown in Figure 4.

2nd, the individual event goodness of fit of each parameter of the sub- child node of the recursive hierarchy structure bottom is calculated

1st, in the case of known to the size and |input paramete in model, calculate or emulate the reason of the output parameter for obtaining model By calculated value.

For 3 parameters (stress, strain and displacement) of the sub- child node that child node 1 includes, son that child node 2 includes 4 parameters (gain, beam angle, standing-wave ratio and secondary lobe) of node, by calculating or emulating the output parameter for obtaining model Calculated value y₁₁、y₁₂、y₁₃、y₂₁、y₂₂、y₂₃、y₂₄。

2nd, the actual test value of the corresponding output parameter of the model under identical input is measured by experiment.The reality of output parameter Border test value z₁₁、z₁₂、z₁₃、z₂₁、z₂₂、z₂₃、z₂₄Represent.

The force characteristic parameter of table 1 with load changing value

The unit for electrical property parameters of table 2 with load changing value

3rd, the relative error between the calculated value and actual test value of output parameter is calculated.

M=1,2,3；

N=1,2,3,4.

The each relative error of parameter of table 3

4th, relative error is mapped as into the goodness of fit by type gauss of distribution function less than normal.

In view of the calculated value of each parameter and the difference value of actual measured value, the smaller the better (error is getting over mini Mod just Really property degree is higher), so we are mapped as the relative error that step 3 is obtained to coincide using type gauss of distribution function less than normal Degree, calculates the inclined of the single index goodness of fit

Small-sized Gaussian distribution curve figure is as shown in Figure 5.

Computing formula is as follows：

M=1,2,3；

N=1,2,3,4,

x_1mRepresent and pass through relative error △ E_1mThe goodness of fit of sub- child node m that mapping is obtained；

x_2nRepresent and pass through relative error △ E_2nThe goodness of fit of sub- child node n that mapping is obtained；

Represent relative error error value bound.

Typically take in above-mentioned calculating formulaThus obtain 3 of the sub- child node included by child node 1 Goodness of fit x of individual parameter₁₁、x₁₂、x₁₃, goodness of fit x of 4 parameters of the sub- child node included by child node 2₂₁、x₂₂、x₂₃、x₂₄。

The each parameter individual event goodness of fit of table 4

The individual event goodness of fit of each parameter of i.e. sub- child node is：

x₁₁=90, x₁₂=88, x₁₃=89,

x₂₁=93, x₂₂=92, x₂₃=87, x₂₄=91.

3rd, weight of each parameter of sub- child node relative to child node is calculated

Weight of the sub- child node relative to each child node is calculated using analytic hierarchy process (AHP), in recursive hierarchy structure, in order to Convenient quantificational expression below, typically with A, B, C... represents different levels from top to bottom, same level from left to right with 1,2, 3rd, 4 ... represent different factors, as shown in Figure 6.

The weight that sub- child node is calculated relative to each child node specifically includes following steps：

1st, Judgement Matricies

In the recursive hierarchy structure of model, each has the element of downward membership as the first of judgment matrix Individual element (is located at the upper left corner), is under the jurisdiction of its each element and is arranged in order the first row behind and first row, i.e. child node Each element as first element of judgment matrix, be under the jurisdiction of its each sub- child node element be arranged in order behind A line and the 1st row.For the criterion of judgment matrix, it is important which two elements compare two-by-two, how much important, to each element Importance degree presses 1-9 assignment, and importance scale value see the table below 5.

The importance scale implication table of table 5

Importance scale implication table according to table 5 filling in judgment matrix, the judgment matrix for filling such as table 6, table 7 It is shown：

The judgment matrix B of table 6₁

B1	C1	C2	C3
				C1	1	1/5	1/3
C2	5	1	3
				C3	3	1/3	1

The judgment matrix B of table 7₂

B2	C4	C5	C6	C7
					C4	1	1/7	1/3	1/5
C5	7	1	5	3
					C6	3	1/5	1	1/3
C7	5	1/3	3	1

2nd, Consistency Check in Judgement Matrix

A, the Maximum characteristic root λ that judgment matrix R is calculated by | λ I-R |=0_max, wherein I is unit matrix.

B, byObtain coincident indicator C.I..

C, table look-up the corresponding Aver-age Random Consistency Index R.I. of determination.

The Aver-age Random Consistency Index R.I. tables of table 8

D, calculating consistency ration C.R. are simultaneously judged

Work as C.R.<When 0.1, the uniformity of judgment matrix can be received；

Work as C.R.>When=0.1, judgment matrix does not meet coherence request, and needs are corrected again to the judgment matrix.

Table 9 is to judgment matrix B₁Consistency check result

Table 10 is to judgment matrix B₂Consistency check result

Can be seen that each judgment matrix is satisfied by coherence request, i.e. CR by the result of calculation of table 9, table 10<0.1.

3rd, weight vectors are calculated

To meeting conforming judgment matrix, rank of advanced units vector normalization, then seek row and normalize, you can obtain each The relative weighting of index.

Each sub- child node is respectively relative to child node weighted value：

w₁₁=0.105, w₁₂=0.637, w₁₃=0.258,

w₂₁=0.550, w₂₂=0.064, w₂₃=0.118, w₂₄=0.268.

4th, the goodness of fit of each child node is calculated

Goodness of fit x of each parameter of sub- child node obtained according to step 2₁₁、x₁₂、x₁₃、x₂₁、x₂₂、x₂₃、x₂₄, and according to The each sub- child node that step 3 is obtained is relative to child node weight w₁₁、w₁₂、w₁₃、w₂₁、w₂₂、w₂₃、w₂₄, each sub- section can be calculated Goodness of fit X1 and X2 of point：

5th, weight of each parameter of child node relative to destination node is calculated

Computational methods are identical with step 3, specific as follows：

1st, Judgement Matricies

In the recursive hierarchy structure of model, each has the element of downward membership as the first of judgment matrix Individual element, is under the jurisdiction of its each element and is arranged in order the first row behind and first row, i.e. destination node element as sentencing First element of disconnected matrix, the element for being under the jurisdiction of its each child node is arranged in order the first row behind and the 1st row, for The criterion of judgment matrix, to the importance degree of each element 1-9 assignment is pressed.Judgement square of each child node relative to destination node A is as shown in table 11 below for battle array：

The judgment matrix A of table 11

A	B1	B2
			B1	1	3
B2	1/3	1

2nd, Consistency Check in Judgement Matrix

A, the Maximum characteristic root λ that judgment matrix R is calculated by | λ I-R |=0_max, wherein I is unit matrix；

B, byObtain coincident indicator C.I.；

C, table look-up the corresponding Aver-age Random Consistency Index R.I. of determination；

D, calculating consistency ration C.R. are simultaneously judged：

Work as C.R.<When 0.1, the uniformity of judgment matrix can be received；

Work as C.R.>When=0.1, judgment matrix does not meet coherence request, and needs are corrected again to the judgment matrix.

Child node is as shown in table 12 below relative to each index relative weighting of destination node and its consistency check result.

Consistency check result of the table 12 to judgment matrix A

3rd, weight vectors are calculated

To meeting conforming judgment matrix, rank of advanced units vector normalization, then seek row and normalize, obtain each index Relative weighting W₁And W₂。

Each child node is respectively relative to destination node weighted value：

W₁=0.492, W₂=0.508.

6th, the goodness of fit of destination node is calculated

Goodness of fit X of each parameter of child node obtained according to step 4₁And X₂, and the relative target node of each parameter Weight W₁And W₂, it is calculated goodness of fit D of destination node：

The correctness of skin antenna stress-electric coupling model can be evaluated by total goodness of fit D：If total goodness of fit D Value is bigger, then the correctness degree of the model is higher；Conversely, the correctness degree of the model is lower.

Evaluate：Because specific technology and manufacturability difficulty determine and Correctness of model evaluation are determined in engineering Position, if technology and manufacturability difficulty are all higher, then can be with the corresponding index for model being met actual requirement Reduce a bit, such as thinking that in this case the model just meets indices requirement when total goodness of fit reaches 85, Can practical operation application in the middle of engineering；If technology and manufacturability difficulty are related to the important ring in project all than relatively low Section, then can be the stricter of the index regulation of model satisfaction requirement, such as in this case when total goodness of fit of model reaches Indices requirement could be met when 95.So set forth herein skin antenna electromechanical Coupling Model based on the goodness of fit Evaluation method, sets up evaluation model, calculates final result, and the result is a quantitative criterion, concrete to rely on item Related request in the middle of mesh carrys out rational evaluation.

As can be seen here, evaluation method of the invention has the advantage that：

Only the input/output argument of model need to be known and in the case of output parameter is detectable, it is not necessary to understand that model is answered Miscellaneous principle and its working method of inherence, just can be evaluated the correctness of model, no using method proposed by the present invention It is only practical, and application is wide.

It should be noted that above-described embodiment the invention is not limited in any way, all employing equivalents or equivalent change The technical scheme that the mode changed is obtained, all falls within protection scope of the present invention.

Claims (1)

1. the evaluation method of the correctness of the skin antenna stress-electric coupling model of the goodness of fit is based on, it is characterised in that including following Step：

(1) recursive hierarchy structure of model, is set up：

Degree of membership relation according to each factor sets up recursive hierarchy structure, is divided into top level goal node, middle level of child nodes, bottom Three levels of straton child node, wherein, the goodness of fit with each output parameter of skin antenna stress-electric coupling model is sub as bottom Child node, including：Stress goodness of fit x₁₁, strain goodness of fit x₁₂, displacement goodness of fit x₁₃, gain goodness of fit x₂₁, beam angle coincide Degree x₂₂, standing-wave ratio goodness of fit x₂₃With secondary lobe goodness of fit x₂₄；Made with the goodness of fit of all kinds of integrated performance indexs belonging to output parameter For middle level of child nodes, including：Goodness of fit X of mechanical characteristic₁With goodness of fit X of electrical characteristics₂；With Correctness of model can be embodied Model total goodness of fit D as top level goal node；

The recursive hierarchy structure of skin antenna stress-electric coupling model is thus established, in the recursive hierarchy structure, upper strata section Point has dominating role to lower level node, and same layer factor is separate, wherein：

$D=\underset{i=1}{\overset{2}{\&Sigma;}}{W}_i{X}_i,X_1=\underset{i=1}{\overset{3}{\&Sigma;}}{w}_{1i}{x}_{1i},X_2=\underset{j=1}{\overset{4}{\&Sigma;}}{w}_{2j}{x}_{2j}$

W_iWeight of child node i relative to top mode is represented,

w_1iWeight of sub- child node i relative to child node 1 is represented,

w_2jRepresent weight of sub- child node j relative to child node 2；

(2) the individual event goodness of fit of each parameter of the sub- child node of the recursive hierarchy structure bottom, is calculated：

(1), in the case of known to the size and |input paramete in model, calculate or emulate the theory of the output parameter for obtaining model Calculated value, wherein, the calculated value of stress, strain and displacement is designated as respectively y₁₁、y₁₂、y₁₃, gain, beam angle, standing-wave ratio Y is designated as respectively with the calculated value of secondary lobe₂₁、y₂₂、y₂₃、y₂₄；

(2) the actual test value of the corresponding output parameter of the model under identical input, is measured by experiment, wherein, stress, strain Z is designated as respectively with the actual test value of displacement₁₁、z₁₂、z₁₃, the actual test value point of gain, beam angle, standing-wave ratio and secondary lobe Z is not designated as it₂₁、z₂₂、z₂₃、z₂₄；

(3) relative error between the calculated value and actual test value of output parameter, is calculated, wherein：

${\mathrm{\&Delta;E}}_{1m}=\frac{\left|y_{1m}-z_{1m}\right|}{y_{1m}}\&times;100\%,m=1,2,3;$

${\mathrm{\&Delta;E}}_{2n}=\frac{\left|y_{2n}-z_{2n}\right|}{y_{2n}}\&times;100\%,n=1,2,3,4;$

(4), relative error is mapped as into the goodness of fit by type gauss of distribution function less than normal, calculates the less than normal of the single index goodness of fit Type Gaussian distribution curve, computing formula is as follows：

$x_{1m}=\left\{\begin{array}{c}100,{\mathrm{\&Delta;E}}_{1m}\&le;\underset{\&OverBar;}{x}\\ 100e^{-{\left(\frac{{\mathrm{\&Delta;E}}_{1m}-\underset{\&OverBar;}{x}}{\mathrm{\&delta;}}\right)}^2},\underset{\&OverBar;}{x}<{\mathrm{\&Delta;E}}_{1m}<\stackrel{\&OverBar;}{x}\\ 0,{\mathrm{\&Delta;E}}_{1m}\&GreaterEqual;\stackrel{\&OverBar;}{x}\end{array}\right.,m=1,2,3;$

$x_{2n}=\left\{\begin{array}{c}100,{\mathrm{\&Delta;E}}_{2n}\&le;\underset{\&OverBar;}{x}\\ 100e^{-{\left(\frac{{\mathrm{\&Delta;E}}_{2n}-\underset{\&OverBar;}{x}}{\mathrm{\&delta;}}\right)}^2},\underset{\&OverBar;}{x}<{\mathrm{\&Delta;E}}_{2n}<\stackrel{\&OverBar;}{x}\\ 0,{\mathrm{\&Delta;E}}_{2n}\&GreaterEqual;\stackrel{\&OverBar;}{x}\end{array}\right.,n=1,2,3,4;$

x_1mRepresent and pass through relative error △ E_1mThe goodness of fit of sub- child node m that mapping is obtained,

x_2nRepresent and pass through relative error △ E_2nThe goodness of fit of sub- child node n that mapping is obtained,

xRelative error error value bound is represented,

Typically take

(3) weight of each parameter of sub- child node relative to child node, is calculated：

Weight of the sub- child node relative to each child node is calculated using analytic hierarchy process (AHP), in recursive hierarchy structure, for convenience Quantificational expression below, typically with A, B, C... represents different levels from top to bottom, and same level is from left to right with 1,2,3,4 ... Different factors are represented, the weight for calculating sub- child node relative to each child node specifically includes following steps：

(1), Judgement Matricies：

In the recursive hierarchy structure of model, each element of child node is under the jurisdiction of its as first element of judgment matrix The element of each sub- child node is arranged in order the first row behind and the 1st row, for the criterion of judgment matrix, to each element Importance degree presses 1-9 assignment；

(2), Consistency Check in Judgement Matrix：

A, the Maximum characteristic root λ that judgment matrix R is calculated by | λ I-R |=0_max, wherein I is unit matrix；

B, byObtain coincident indicator C.I.；

C, table look-up the corresponding Aver-age Random Consistency Index R.I. of determination；

D, calculating consistency ration C.R. are simultaneously judged：

$C.R.=\frac{C.I.}{R.I.}$

Work as C.R.<When 0.1, the uniformity of judgment matrix can be received；

When C.R. >=0.1, judgment matrix does not meet coherence request, and needs are corrected again to the judgment matrix；

(3), weight vectors are calculated：

To meeting conforming judgment matrix, rank of advanced units vector normalization, then seek row and normalize, obtain the phase of each index To weight；

(4) goodness of fit of each child node, is calculated：

Goodness of fit x of each parameter of sub- child node obtained according to step (two)₁₁、x₁₂、x₁₃、x₂₁、x₂₂、x₂₃、x₂₄, and according to step Weight w of the relative child node of each parameter of sub- child node that suddenly (three) obtain₁₁、w₁₂、w₁₃、w₂₁、w₂₂、w₂₃、w₂₄, it is calculated each Goodness of fit X of child node₁And X₂；

(5) each parameter of child node, is calculated relative to the weight of destination node, specifically include following sub-step：

(1), Judgement Matricies：

In the recursive hierarchy structure of model, destination node element is under the jurisdiction of each of it as first element of judgment matrix The element of child node is arranged in order the first row behind and the 1st row, for the criterion of judgment matrix, to the important of each element Property degree presses 1-9 assignment；

(2), Consistency Check in Judgement Matrix：

A, the Maximum characteristic root λ that judgment matrix R is calculated by | λ I-R |=0_max, wherein I is unit matrix；

B, byObtain coincident indicator C.I.；

C, table look-up the corresponding Aver-age Random Consistency Index R.I. of determination；

D, calculating consistency ration C.R. are simultaneously judged：

$C.R.=\frac{C.I.}{R.I.}$

Work as C.R.<When 0.1, the uniformity of judgment matrix can be received；

When C.R. >=0.1, judgment matrix does not meet coherence request, and needs are corrected again to the judgment matrix；

(3), weight vectors are calculated：

To meeting conforming judgment matrix, rank of advanced units vector normalization, then seek row and normalize, obtain the phase of each index To weight W₁And W₂；

(6) goodness of fit of destination node, is calculated：

Goodness of fit X of each parameter of child node obtained according to step (four)₁And X₂, and the phase of each parameter of step (five) acquisition Weight W to destination node₁And W₂, it is calculated goodness of fit D of destination node；

(7) correctness of skin antenna stress-electric coupling model, is evaluated by goodness of fit D：

Goodness of fit D value is bigger, and the correctness degree of the model is higher, and the performance of skin antenna is better；Conversely, the model is correct Property degree is lower, and the performance of skin antenna is poorer.