CN103383705A - Metamaterial meta-modeling method and system, and metamaterial electromagnetic response curve acquisition method - Google Patents
Metamaterial meta-modeling method and system, and metamaterial electromagnetic response curve acquisition method Download PDFInfo
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- CN103383705A CN103383705A CN2012101335291A CN201210133529A CN103383705A CN 103383705 A CN103383705 A CN 103383705A CN 2012101335291 A CN2012101335291 A CN 2012101335291A CN 201210133529 A CN201210133529 A CN 201210133529A CN 103383705 A CN103383705 A CN 103383705A
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Abstract
The invention discloses a meta-modeling method and system, and a metamaterial electromagnetic response curve acquisition method. The metamaterial meta-modeling method comprises the following steps: obtaining an electromagnetic response curve corresponding to structure parameters through simulation; performing primary modeling on the electromagnetic response curve by using a first model to obtain a first model coefficient; performing secondary modeling on the structure parameters and the first model coefficient by using a second model. According to the invention, simulation is performed on the known structure parameters to obtain the electromagnetic response curve formed by a series of discrete response data, the parameter model is utilized to perform the primary modeling on the electromagnetic response curve so as to use the new model to replace the electromagnetic response curve, and then the other model is utilized to perform modeling on the new model coefficient and the structure parameters; manual design for modeling is eliminated, the optimal design can be quickly completed by using the conventional model to realize modeling, the indeterminateness and the randomness in a manual modeling process can be reduced, and the automation process of the design of the metamaterial is promoted.
Description
Technical field
The present invention relates to super Material Field, be specifically related to the acquisition methods of the electromagnetic response curve of a kind of first modeling method of super material and system and super material.
Background technology
In super material technology field, for the micro unit structure of super material, different structural parameters input x can obtain corresponding electromagnetic response curve during emulation.
At present the design setting model of super material still being rested on the manual designs stage, is generally that the dependence experience is carried out manual adjustment and design.But the development along with technology, super material is brought into use in increasing field, the micro unit structure species of super material more and more comes, the response data amount of corresponding emulation is also more and more huger, traditional method for designing manually can't satisfy the demand of large-scale production design, and the hand-designed debugging has also increased uncertainty and the randomness of modeling.
Summary of the invention
The present invention mainly solves the technical matters that traditional manual designs method can't satisfy the demand of super material large-scale production design, and the acquisition methods of the electromagnetic response curve of a kind of first modeling method of super material and system and super material is provided.
For solving the problems of the technologies described above, the technical scheme that the present invention adopts is: a kind of first modeling method of super material is provided, comprises: obtain electromagnetic response curve corresponding to structural parameters by emulation; Utilize the first model to carry out a modeling to this electromagnetic response curve, to obtain the first model coefficient; Utilize the second model to carry out the secondary modeling to these structural parameters and this first model coefficient.
Wherein, this first model is the cubic spline model, this utilizes the first model to carry out a modeling to this electromagnetic response curve, comprises with the step that obtains the first model coefficient: utilize this cubic spline model to carry out modeling to this electromagnetic response curve, to obtain the cubic spline coefficient.
Wherein, this second model is Gauss model, and this utilizes the second model that the step that these structural parameters and this first model coefficient carry out the secondary modeling is comprised: with Gauss model, these structural parameters and this cubic spline coefficient are carried out the secondary modeling.
Wherein, this utilizes this cubic spline model to carry out modeling to this electromagnetic response curve, comprises with the step that obtains the cubic spline coefficient: according to a plurality of structural parameters of this electromagnetic response curve acquisition and corresponding frequency response values thereof with the structural segmentation cubic spline function; Utilize the basic difference coefficient formula of newton and derivative condition to obtain the cubic spline coefficient expression formula of this segmentation cubic spline function; Utilize three moments euqation group and boundary condition to calculate this cubic spline coefficient expression formula to obtain this cubic spline coefficient.
For solving the problems of the technologies described above, another technical solution used in the present invention is: a kind of first modeling of super material is provided, comprises emulation module, the first MBM and the second MBM.This emulation module is used for obtaining electromagnetic response curve corresponding to structural parameters by emulation; This first MBM is used for utilizing the first model to carry out a modeling to this electromagnetic response curve, to obtain the first model coefficient; This second MBM is used for utilizing the second model to carry out the secondary modeling to these structural parameters and this first model coefficient.
Wherein, this first model is the cubic spline model, and this first MBM utilizes this cubic spline model to carry out modeling to this electromagnetic response curve, to obtain the cubic spline coefficient.
Wherein, this second model is Gauss model, and this second MBM is carried out the secondary modeling with Gauss model to these structural parameters and this cubic spline coefficient.
Wherein, this first MBM comprises constructed fuction unit, coefficient expression formula acquiring unit and coefficient calculation unit.This constructed fuction unit is used for according to a plurality of structural parameters of this electromagnetic response curve acquisition and corresponding frequency response values thereof with the structural segmentation cubic spline function; This coefficient expression formula acquiring unit is used for utilizing the basic difference coefficient formula of newton and derivative condition to obtain the cubic spline coefficient expression formula of this segmentation cubic spline function; This coefficient calculation unit is used for utilizing three moments euqation group and boundary condition to calculate this cubic spline coefficient expression formula to obtain this cubic spline coefficient.
For solving the problems of the technologies described above, another technical solution used in the present invention is: a kind of acquisition methods of electromagnetic response curve of super material is provided, comprises: obtain structural parameters; With this structural parameters input the first model, to obtain the first model coefficient corresponding to these structural parameters; These structural parameters and this first model coefficient are input to the second model, to obtain electromagnetic response curve corresponding to these structural parameters.
Wherein, this first model is Gauss model, and this second model is the cubic spline model.
The invention has the beneficial effects as follows: the situation that is different from prior art, the present invention is by carrying out emulation to obtain the formed electromagnetic response curve of series of discrete response data to known structural parameters, then utilize parameter model to carry out a modeling to utilize new model to replace this electromagnetic response curve to the electromagnetic response curve, the recycling model is with new model coefficient and structural parameters modeling, the present invention has replaced artificial design setting model, adopt existing model modeling to complete rapidly optimal design, reduced uncertainty and the randomness of manual modeling; And after completing modeling, for the arbitrary structures parameter of not passing through emulation, can oppositely derive by above-mentioned twice modeler model, to obtain the electromagnetic response curve of corresponding response.The present invention has improved the speed of super design of material modeling effectively, uncertainty and the randomness of modeling have been reduced, and for the structural parameters that do not carry out emulation, can obtain to express delivery its corresponding electromagnetic response curve, advanced the automated process of super design of material.
Description of drawings
Figure 1A is the process flow diagram of first modeling method one embodiment of the super material of the present invention;
Figure 1B is first modeling method specific works flow process and the accordingly result schematic diagram thereof of the super material of the present invention;
Fig. 2 is the process flow diagram of first another embodiment of modeling method of the super material of the present invention;
Fig. 3 is the module connection layout of first modeling of the super material of the present invention; And
Fig. 4 is the process flow diagram of acquisition methods one embodiment of the electromagnetic response curve of the super material of the present invention.
Embodiment
See also Figure 1A and Figure 1B, Figure 1A is the process flow diagram of first modeling method one embodiment of the super material of the present invention, Figure 1B is first modeling method specific works flow process and the accordingly result schematic diagram thereof of the super material of the present invention, and in the present embodiment, first modeling method of this super material comprises the steps.
Step S100 obtains electromagnetic response curve corresponding to structural parameters by emulation.Step S100 is corresponding with " emulation " in Figure 1B, in the process of emulation, with structural parameters as input, can obtain the formed electromagnetic response curve of response data of series of discrete, for example, represent that take x structural parameters, f represent its response data (can as frequency or refractive index etc.), the function expression of its electromagnetic response curve is y=F (x; F).
Step S101 utilizes the first model to carry out a modeling to this electromagnetic response curve, to obtain the first model coefficient.In step S101, can adopt parameter model to carry out modeling, such as cubic spline model, least-squares linear regression model, fitting of a polynomial model, sine function model of fit and ridge regression model etc., adopt the above-mentioned parameter model, can carry out match fast to discrete structural parameters and electromagnetic response curve thereof, in the scope that the art personnel understand, at this, above-mentioned parameter model is not given unnecessary details.In concrete application, the first model is the cubic spline model, if represent the first model coefficient (being the cubic spline parameter) with coef, after passing through step S101, the expression formula that can obtain its model is y=S (coef), in other words, the present embodiment adopts y=S (coef) to substitute this y=F (x; F), to realize " recovery " match to this electromagnetic response curve.
Step S102 utilizes the second model to carry out the secondary modeling to these structural parameters and this first model coefficient.After getting the first model parameter, can carry out the nonparametric modeling by step S102, such as MCMC (Ma Er Kraft chain Monte Carlo) model, Gauss model and neural network model etc., make the curve Fast Fitting of model return, can make model and the electromagnetic response curve similarity or the likelihood probability that obtain through emulation reach maximal value, certainly, also can adopt Lorentz model etc., be not construed as limiting at this.In concrete application, the second model is Gauss model, and the expression formula of the model that step S102 sets up is coef=GP (x).Be not difficult to find out, follow-up to each structural parameters without emulation, can by coef=GP (x) and y=S (coef) is counter push away to obtain its electromagnetic response curve, carefully do not state at this.
Wherein, after the first modeling process through step S101 and step S102, can obtain the modeling result shown in Figure 1B, its electromagnetic response curve similarity with emulation generally can reach optimum.
The present invention is by carrying out emulation to obtain the formed electromagnetic response curve of series of discrete response data to known structural parameters, then utilize parameter model to carry out a modeling to utilize new model to replace this electromagnetic response curve to the electromagnetic response curve, the recycling model is with new model coefficient and structural parameters modeling, the present invention has replaced artificial design setting model, adopt existing model modeling can complete rapidly optimal design, reduce uncertainty and the randomness of manual modeling, advanced the automated process of super design of material.
Seeing also Fig. 2, is the process flow diagram of first another embodiment of modeling method of the super material of the present invention, and in the present embodiment, first modeling method of this super material comprises the steps.
Step S200 obtains electromagnetic response curve corresponding to structural parameters by emulation.In the process of emulation, with structural parameters as input, can obtain the formed electromagnetic response curve of response data of series of discrete, for example, represent that take x structural parameters, f represent its response data (can as frequency or refractive index etc.), the function expression of its electromagnetic response curve is y=F (x; F).
Step S201, according to a plurality of structural parameters of this electromagnetic response curve acquisition and corresponding frequency response values thereof with the structural segmentation cubic spline function.In step S201, choosing a plurality of structural parameters in arbitrary section interval in this electromagnetic response curve is x
1, x
2X
n, its functional value can pass through the electromagnetic response curve acquisition, then exists the conditions such as continuous single order and second order inverse with the structural segmentation cubic spline function according to cubic polynomial, in the interval, in the scope that the art personnel understand, does not give unnecessary details.
Step S202 utilizes the basic difference coefficient formula of newton and derivative condition to obtain the cubic spline coefficient expression formula of this segmentation cubic spline function.In step S202, the condition that above-mentioned arbitrary interval domestic demand is satisfied is P
i(x
i)=y
iAnd P
i(x
i+1)=y
i+1, then according to P
i(x
i)=y
iAnd P
i(x
i+1)=y
i+1Calculate relational expression P by the basic difference coefficient formula of newton
i(x
i), then to P
i(x
i) carry out a differentiate and secondary differentiate, determining respectively the expression formula of one order polynomial, quadratic polynomial and cubic polynomial, and finally pass through P
i(x
i) series of values P
0(x), P
1(x) ... P
n(x) to obtain its cubic spline parameter expression.
Step S203 utilizes three moments euqation group and boundary condition to calculate this cubic spline coefficient expression formula to obtain this cubic spline coefficient.Step S203 also can adopt the given slope value of three moments euqation group and frontier point or sealing smooth curve condition to limit to obtain its cubic spline coefficient coef, in the scope that the art personnel understand, does not give unnecessary details.
Step S204 carries out the secondary modeling with Gauss model to these structural parameters and this cubic spline coefficient.After getting cubic spline parameter c oef, can carry out the nonparametric modeling by step S204, such as MCMC (Ma Er Kraft chain Monte Carlo) model, Gauss model and neural network model etc., make the curve Fast Fitting of model return.Adopt nonparametric model can make model and the electromagnetic response curve similarity or the likelihood probability that obtain through emulation reach maximal value, certainly, also can adopt Lorentz model etc., be not construed as limiting at this.In concrete application, the second model is Gauss model, and the expression formula of the model that step S102 sets up is coef=GP (x).Be not difficult to find out, follow-up to each structural parameters without emulation, can by coef=GP (x) and y=S (coef) is counter push away to obtain its electromagnetic response curve, carefully do not state at this.
The present invention is by carrying out emulation to obtain the formed electromagnetic response curve of series of discrete response data to known structural parameters, then utilize the cubic spline model to carry out a modeling to utilize new model to replace this electromagnetic response curve to the electromagnetic response curve, the recycling model is with cubic spline coefficient coef and structural parameters x modeling, the present invention has replaced artificial design setting model, adopt existing model modeling can complete rapidly optimal design, reduce uncertainty and the randomness of manual modeling, advanced the automated process of super design of material.
Seeing also Fig. 3, is the module connection layout of first modeling of the super material of the present invention, and in the present embodiment, this system comprises emulation module 30, the first MBM 31 and the second MBM 32.
The first MBM 31 utilizes the first model to carry out modeling to this electromagnetic response curve that is obtained by emulation module 30 emulation, to obtain the first model coefficient.Wherein, the first MBM 31 can adopt parameter model to carry out modeling, such as cubic spline model, least-squares linear regression model, fitting of a polynomial model, sine function model of fit and ridge regression model etc., adopt the above-mentioned parameter model, can carry out match fast to discrete structural parameters and electromagnetic response curve thereof, in the scope that the art personnel understand, the above-mentioned parameter model is not given unnecessary details.
In a preferred embodiment, the first model of the first MBM 31 adopts the cubic spline model, if represent the cubic spline parameter with coef, can obtain the model that expression formula is y=S (coef) after modeling, the present embodiment adopts y=S (coef) to substitute this y=F (x; F), to realize " recovery " match to this electromagnetic response curve.
And the first MBM 31 is in concrete modeling process, can be respectively carries out substep by constructed fuction unit 310, coefficient expression formula acquiring unit 311 and the coefficient calculation unit 312 of the first MBM 31 and calculates.
At first, constructed fuction unit 310 according to a plurality of structural parameters of this electromagnetic response curve acquisition and corresponding frequency response values thereof with structural segmentation cubic spline letter.For example first choosing a plurality of structural parameters in arbitrary section interval in this electromagnetic response curve is x
1, x
2X
n, its functional value can pass through the electromagnetic response curve acquisition, then has the condition structural segmentation cubic spline functions such as continuous single order and second order inverse according to cubic polynomial, in the interval;
Then, coefficient expression formula acquiring unit 311 utilizes the basic difference coefficient formula of newton and derivative condition to obtain the cubic spline coefficient expression formula of this segmentation cubic spline function.The condition that 311 pairs of above-mentioned arbitrary interval domestic demands of coefficient expression formula acquiring unit satisfy comprises P
i(x
i)=y
iAnd P
i(x
i+1)=y
i+1, to P
i(x
i)=y
iAnd P
i(x
i+1)=y
i+1Calculate relational expression P by the basic difference coefficient formula of newton
i(x
i), then to P
i(x
i) carry out a differentiate and secondary differentiate, determining respectively the expression formula of one order polynomial, quadratic polynomial and cubic polynomial, and finally pass through P
i(x
i) series of values P
0(x), P
1(x) ... P
n(x) to obtain its cubic spline parameter expression;
Then coefficient calculation unit 312 utilizes three moments euqation group and boundary condition to calculate this cubic spline coefficient expression formula to obtain this cubic spline coefficient coef, certainly, also can adopt the given slope value of three moments euqation group and frontier point or sealing smooth curve condition to limit to obtain its cubic spline coefficient coef, in the scope that the art personnel understand, do not give unnecessary details.
After completing a modeling through the first MBM 31, the second MBM 32 utilizes the second model to carry out the secondary modeling to these structural parameters x and this first model coefficient coef.Wherein, the second MBM 32 is after getting cubic spline parameter c oef, carry out the nonparametric modeling, for example adopt MCMC (Ma Er Kraft chain Monte Carlo) model, Gauss model and neural network model etc., make the curve Fast Fitting of model return.Adopt nonparametric model can make model and the electromagnetic response curve similarity or the likelihood probability that obtain through emulation reach maximal value, certainly, also can adopt Lorentz model etc., be not construed as limiting at this.
In a preferred embodiment, the second model that the second MBM 32 adopts is Gauss model, the model tormulation formula that obtains after modeling is coef=GP (x), be the cubic spline parameter c oef of higher-dimension for the response of structural parameters x arbitrarily due to Gauss model, and between different cubic spline parameter c oef, similarity is higher, thereby is conducive to carry out regression modeling.
The present invention is by carrying out emulation to obtain the electromagnetic response curve to known structural parameters x, then utilize parameter model to carry out a modeling to utilize new model to replace this electromagnetic response curve to the electromagnetic response curve, the recycling model is with new model coefficient and structural parameters modeling, the present invention has replaced artificial design setting model, adopt existing model modeling can complete rapidly optimal design, reduce uncertainty and the randomness of manual modeling, advanced the automated process of super design of material.
Seeing also Fig. 4, is the process flow diagram of acquisition methods one embodiment of the electromagnetic response curve of the super material of the present invention.
Carry out a modeling and secondary modeling based on previous embodiment, the present embodiment of the present invention provides a kind of acquisition methods of electromagnetic response curve of super material, and it comprises following following steps.
Step S400 obtains structural parameters.As previously mentioned, after completing modeling by first modeling, can be to the structural parameters of super material in the situation that do not carry out emulation, obtain its electromagnetic response curve, can obtain the structural parameters x such as two-dimensional of super material by step S400.
Step S401 is with this structural parameters input the first model, to obtain the first model coefficient corresponding to these structural parameters.In a preferred embodiment, this first model is Gauss model, can infer according to structural parameters x by Gauss model such as coef=GP (x) to obtain the first follow-up model coefficient coef, certainly, this first model also can for other models, be not construed as limiting at this.
Step S402 is input to the second model with these structural parameters and this first model coefficient, to obtain electromagnetic response curve corresponding to these structural parameters.After obtaining the first model coefficient coef from step S401, input second model is counter pushes away to obtain the electromagnetic response curve with it, preferably, this second model is cubic spline model y=S (coef), in the present embodiment, this y=S (coef) is replaced by the electromagnetic response curve that original a plurality of discrete point forms.
After completing modeling, the present invention need not through emulation, can oppositely derive by the model that first modeling obtains to the arbitrary structures parameter, to obtain the electromagnetic response curve of corresponding response.The present invention has further advanced the automated process of super design of material.
The above is only embodiments of the invention; not thereby limit the scope of the claims of the present invention; every equivalent structure or equivalent flow process conversion that utilizes instructions of the present invention and accompanying drawing content to do; or directly or indirectly be used in other relevant technical fields, all in like manner be included in scope of patent protection of the present invention.
Claims (10)
1. first modeling method of a super material, is characterized in that, comprising:
Obtain electromagnetic response curve corresponding to structural parameters by emulation;
Utilize the first model to carry out a modeling to described electromagnetic response curve, to obtain the first model coefficient;
Utilize the second model to carry out the secondary modeling to described structural parameters and described the first model coefficient.
2. method according to claim 1, is characterized in that, described the first model is the cubic spline model, and described first model that utilizes carries out a modeling to described electromagnetic response curve, comprises with the step that obtains the first model coefficient:
Utilize described cubic spline model to carry out modeling to described electromagnetic response curve, to obtain the cubic spline coefficient.
3. method according to claim 2, is characterized in that, described the second model is Gauss model, and described second model that utilizes comprises the step that described structural parameters and described the first model coefficient carry out the secondary modeling:
With Gauss model, described structural parameters and described cubic spline coefficient are carried out the secondary modeling.
4. method according to claim 2, is characterized in that, describedly utilizes described cubic spline model to carry out modeling to described electromagnetic response curve, comprises with the step that obtains the cubic spline coefficient:
According to a plurality of structural parameters of described electromagnetic response curve acquisition and corresponding frequency response values thereof with the structural segmentation cubic spline function;
Utilize the basic difference coefficient formula of newton and derivative condition to obtain the cubic spline coefficient expression formula of described segmentation cubic spline function;
Utilize three moments euqation group and boundary condition to calculate described cubic spline coefficient expression formula to obtain described cubic spline coefficient.
5. first modeling of a super material, is characterized in that, comprising:
Emulation module is used for obtaining electromagnetic response curve corresponding to structural parameters by emulation;
The first MBM is used for utilizing the first model to carry out a modeling to described electromagnetic response curve, to obtain the first model coefficient;
The second MBM is used for utilizing the second model to carry out the secondary modeling to described structural parameters and described the first model coefficient.
6. system according to claim 5, is characterized in that, described the first model is the cubic spline model, and described the first MBM utilizes described cubic spline model to carry out modeling to described electromagnetic response curve, to obtain the cubic spline coefficient.
7. system according to claim 6, is characterized in that, described the second model is Gauss model, and described the second MBM is carried out the secondary modeling with Gauss model to described structural parameters and described cubic spline coefficient.
8. system according to claim 6, is characterized in that, described the first MBM comprises:
The constructed fuction unit is used for according to a plurality of structural parameters of described electromagnetic response curve acquisition and corresponding frequency response values thereof with the structural segmentation cubic spline function;
Coefficient expression formula acquiring unit is used for utilizing the basic difference coefficient formula of newton and derivative condition to obtain the cubic spline coefficient expression formula of described segmentation cubic spline function;
Coefficient calculation unit is used for utilizing three moments euqation group and boundary condition to calculate described cubic spline coefficient expression formula to obtain described cubic spline coefficient.
9. the acquisition methods of the electromagnetic response curve of a super material, is characterized in that, comprising:
Obtain structural parameters;
With described structural parameters input the first model, to obtain the first model coefficient corresponding to described structural parameters;
Described structural parameters and described the first model coefficient are input to the second model, to obtain electromagnetic response curve corresponding to described structural parameters.
10. method according to claim 9, is characterized in that, described the first model is Gauss model, and described the second model is the cubic spline model.
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| CN105095065A (en) * | 2014-05-16 | 2015-11-25 | 中国航空工业第六一八研究所 | Optimization method for formalized modeling |
| CN111581826A (en) * | 2020-05-09 | 2020-08-25 | 清华大学 | Metamaterial design method and device, computer equipment and storage medium |
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2012
- 2012-05-02 CN CN201210133529.1A patent/CN103383705B/en active Active
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| CN105095065A (en) * | 2014-05-16 | 2015-11-25 | 中国航空工业第六一八研究所 | Optimization method for formalized modeling |
| CN111581826A (en) * | 2020-05-09 | 2020-08-25 | 清华大学 | Metamaterial design method and device, computer equipment and storage medium |
| CN111581826B (en) * | 2020-05-09 | 2022-03-25 | 清华大学 | Metamaterial design method and device based on Bayes combined modeling optimization algorithm |
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