CN103136396B - A kind of metamaterial structure unit parameter simulation selection method and device - Google Patents
A kind of metamaterial structure unit parameter simulation selection method and device Download PDFInfo
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- CN103136396B CN103136396B CN201110390831.0A CN201110390831A CN103136396B CN 103136396 B CN103136396 B CN 103136396B CN 201110390831 A CN201110390831 A CN 201110390831A CN 103136396 B CN103136396 B CN 103136396B
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Abstract
The invention provides a kind of metamaterial structure unit parameter simulation selection method and device.This metamaterial structure unit parameter simulation selection method includes step: obtain geometric parameter and the span of geometric parameter of construction unit；Span according to geometric parameter divides first area and second area；Geometric parameter in first area is carried out orthogonal design, obtains the first experiment set；Geometric parameter in second area is carried out uniform Design, obtains the second experiment set.The metamaterial structure unit parameter simulation selection method of the present invention and device, while ensureing the space " representative " that experimental point is chosen, can comparatively fast, accurately find the parameter of the construction unit corresponding to electromagnetic property meeting the Meta Materials that initial experiment is assumed, reduce experiment number, improve work efficiency and saved experimental cost.
Description
Technical field
The present invention relates to Meta Materials field, particularly to a kind of metamaterial structure unit parameter simulation selection method and device.
Background technology
Meta Materials (Metamaterials) is that the sub-wavelength macrostructure unit with geometry in particular is periodically or aperiodically arranged constituted artificial material, and its medium characteristic depends on structure and the spatial distribution of its construction unit.
Measure the electromagnetic property of metamaterial structure unit, be an important step in Meta Materials design process.And the metamaterial structure unit how choosing certain size is the problem that have to solve in whole design process for Electromagnetic Simulation measurement.The geometry information of single microstructure unit is described by one group of parameter, and the value of parameter represents the size of its shape.In the range of rational parameter value, the most corresponding multiple value levels of each parameter.In order to obtain the electromagnetic response characteristic rule of particular type microstructure unit, need to carry out metamaterial structure unit electromagnetic property emulation experiment, the geometric parameter corresponding due to the complex topology structure of some construction unit is more, the most mutually retrain between parameter, it is intended to verify its electromagnetic property, often needs to do extremely large number experiment.
As each for each parameter horizontal one_to_one corresponding is measured the electromagnetic property of derived material, the topological structure template that needs are made will in the millions, and the biggest experimental quantities brings the biggest difficulty to concrete enforcement.For optimization experiment step, the most conventional method is only the experiment experience accumulated before relying on and to the cognition substantially in terms of electromagnetic principle, in the range of parameter each to construction unit is allowed, it is finely adjusted, the method is complete by rule of thumb, and unpredictable whole heuristic process required time, it is difficult to be directly realized by the optimization of experimental procedure；Conventional Orthogonal Experiment and Design requires that each level of each factor does the experiment of equal number, so thus derivative experimental procedure is many and loaded down with trivial details, arranges the so many l-G simulation test undoubtedly can too time-consuming, effort, cost source；And as according to uniform test design, although experimental procedure can be reduced, but the information representation ability of uniform test design edge region is the best, if requiring again, the while that the information of marginal portion being than mid portion important, the scheme that uses experimental quantities less, then this method cannot meet experiment demand.
Therefore, needs verify a kind of metamaterial structure unit parameter simulation selection method and device, the electromagnetic response rule to particular type construction unit is obtained by the fewest experiment number, to learning how that expanding the application to this micro structure has highly important meaning, the most also has the most positive effect to the industrialization process promoting Meta Materials.
Summary of the invention
The technical problem that present invention mainly solves is to provide a kind of metamaterial structure unit parameter simulation selection method and device, the method and device can comparatively fast, accurately find the parameter of the construction unit corresponding to electromagnetic property meeting the Meta Materials that initial experiment is assumed.
The invention provides a kind of metamaterial structure unit parameter simulation selection method, this metamaterial structure unit parameter simulation selection method includes step: obtain geometric parameter and the span of geometric parameter of construction unit；Span according to geometric parameter divides first area and second area；Geometric parameter in first area is carried out orthogonal design, obtains the first experiment set；Geometric parameter in second area is carried out uniform Design, obtains the second experiment set.
According to a preferred embodiment of the invention, span division first area and the step of second area according to geometric parameter comprise the steps: to set the first step-length of the number of levels for obtaining geometric parameter, and set geometric parameter bandwidth number in first area, wherein the first step-length is that the method adopting by reference the number of levels that orthogonal design obtains multiple factors obtains；Span, the first step-length and the geometric parameter according to geometric parameter bandwidth number in first area determines bandwidth, and the region in span bandwidth covered is set to first area；Region in unlapped for bandwidth span is set to second area.
According to a preferred embodiment of the invention, geometric parameter in first area is carried out orthogonal design, the step obtaining the first experiment set includes step: according to geometric parameter value region, the first step-length and the geometric parameter in first area bandwidth number in first area, obtain the first experiment set according to orthogonal design.
According to a preferred embodiment of the invention, geometric parameter in second area is carried out uniform Design, the step obtaining the second experiment set includes: set the second step-length being used for obtaining the number of levels of geometric parameter, and the method for the number of levels that the second step-length obtains multiple factors with reference to uniform Design obtains；According to geometric parameter value region in second area and the second step-length, obtain the second experiment set according to uniform design.
According to a preferred embodiment of the invention, geometric parameter in second area is carried out uniform Design, obtain in the step of the second experiment set, uniform Design has used grid point method, for n experiment, good grid point method comprises the steps: the jth row using congruence method to generate uniform designs table, and its formula is expressed as:
uij=ihj[modn]
Wherein, i is the line number of uniform designs table, and n is the least common multiple of the sample point number that each geometric parameter is corresponding, and h is the vector of the positive integer composition less and relatively prime with n than n, i.e. h=(h1, h2..., hm), m is determined by Euler's function φ (n), works as ihjDuring more than n, by ihjThe multiple deducting n makes difference fall among [1, n], and other row of uniform designs table can be generated by equation below recursion:
u1j=hj
Wherein, i=1 ..., n-1；Use the uniformity of centralization L2 deflection measure uniform designs table, take the minimum uniform designs table of deviation and gather as the second experiment, be denoted as Un(ns)。
Present invention also offers a kind of metamaterial structure unit parameter emulation selecting device, this metamaterial structure unit parameter emulation selecting device includes: geometric parameter acquiring unit, obtains geometric parameter and the span of geometric parameter of construction unit；Analytic unit, divides first area and second area according to the span of geometric parameter；First experiment set acquiring unit, carries out orthogonal design to the geometric parameter in first area, obtains the first experiment set；Second experiment set acquiring unit, carries out uniform Design to the geometric parameter in second area, obtains the second experiment set.
According to a preferred embodiment of the invention, analytic unit includes: setup unit, set the first step-length being used for obtaining the number of levels of geometric parameter, and set geometric parameter bandwidth number in first area, wherein the first step-length is that the method adopting by reference the number of levels that orthogonal design obtains multiple factors obtains；First area acquiring unit, determines bandwidth according to span, the first step-length and the geometric parameter of the geometric parameter bandwidth number in first area, and the region in span bandwidth covered is set to first area；Second area acquiring unit, is set to second area by the region in unlapped for bandwidth span.
According to a preferred embodiment of the invention, the first experiment set acquiring unit is used for: according to geometric parameter value region, the first step-length and the geometric parameter in first area bandwidth number in first area, obtain the first experiment set according to orthogonal design.
According to a preferred embodiment of the invention, the second experiment set acquiring unit is used for: setting the second step-length being used for obtaining the number of levels of geometric parameter, the method for the number of levels that the second step-length obtains multiple factors with reference to uniform Design obtains；According to geometric parameter value region in second area and the second step-length, obtain the second experiment set according to uniform design.
According to a preferred embodiment of the invention, uniform Design has used grid point method, and for n experiment, good grid point method comprises the steps: the jth row using congruence method to generate uniform designs table, and its formula is expressed as:
uij=ihj[modn]
Wherein, i is the line number of uniform designs table, and n is the least common multiple of the sample point number that each geometric parameter is corresponding, and h is the vector of the positive integer composition less and relatively prime with n than n, i.e. h=(h1, h2..., hm), m is determined by Euler's function φ (n), works as ihjDuring more than n, by ihjThe multiple deducting n makes difference fall among [1, n], and other row of uniform designs table can be generated by equation below recursion:
u1j=hj
Wherein, i=1 ..., n-1；Use the uniformity of centralization L2 deflection measure uniform designs table, take the minimum uniform designs table of deviation and gather as the second experiment, be denoted as Un(ns)。
The invention has the beneficial effects as follows: be different from the situation of prior art, the metamaterial structure unit parameter simulation selection method of the present invention and device, while ensureing the space " representative " that experimental point is chosen, can comparatively fast, accurately find the parameter of the construction unit corresponding to electromagnetic property meeting the Meta Materials that initial experiment is assumed, reduce experiment number, improve work efficiency and saved experimental cost.
Accompanying drawing explanation
Fig. 1 is the perspective view of the metamaterial structure unit with " snowflake " type topological structure；
Fig. 2 is that prior art orthogonal experiment method is to " snowflake " type topological structure parameters simulation reconnaissance result figure；
Fig. 3 is that prior art uniform experiments method is to " snowflake " type topological structure parameters simulation reconnaissance result figure；
Fig. 4 is the schematic flow sheet of the metamaterial structure unit parameter simulation selection method of the embodiment of the present invention；
Fig. 5 is that metamaterial structure unit parameter simulation selection method of the present invention is to " snowflake " type shown in Fig. 1 topological structure parameters simulation reconnaissance result figure；And
Fig. 6 is the structural representation of the metamaterial structure unit parameter emulation selecting device of the embodiment of the present invention.
Detailed description of the invention
The present invention is described in detail with embodiment below in conjunction with the accompanying drawings.
The geometry information of the single microstructure unit of Meta Materials is described by one group of parameter, and geometric parameter corresponding to complex topology structure is more, the most mutually retrains between parameter.As a example by the metamaterial structure unit with " snowflake " type topological structure illustrated in fig. 1.As it is shown in figure 1, the topological structure of this construction unit has 4 corresponding geometric parameter { a1, a2, b1, b2}.Definition { s1=a1+b1, s2=a2+b2, G is geometric parameter vector, i.e. G=[s1, s2]。
For this structure, it is assumed that ignore live width, parameter s1, s2Span be respectively [1.60,3.00], [1.60,3.00].According to Orthogonal Experiment and Design principle experiment arrangement, each factor is with 0.1 as step-length, then generate reconnaissance figure as shown in Figure 2, as in figure 2 it is shown, according to orthogonal experimental method, one like this has 2 geometric parameters, level corresponding to each parameter is 15, the topological structure of 15, the electromagnetic property of derived material to be measured, need to make 225 topological structure templates.As according to uniform experiments method, each factor with 0.01 as step-length, then generates reconnaissance figure as shown in Figure 3, although the most only need to make 140 topological structure templates and be achieved with at s1, s2The space expression in regulation region, but this kind of method edge region information representation ability is the best.
Fig. 4 is the schematic flow sheet of the metamaterial structure unit parameter simulation selection method of the embodiment of the present invention.As shown in Figure 4, the metamaterial structure unit parameter simulation selection method of one embodiment of the present invention includes step S10, step S20, step S30 and step S40, specific as follows:
Step S10: obtain geometric parameter and the span of geometric parameter of construction unit.
Such as, for topological structure shown in Fig. 1, ignoring its live width, get parms s respectively1, s2Span be [1.60,3.00] and [1.60,3.00].
Step S20: divide first area and second area according to the span of geometric parameter.In the present embodiment, step S20 specifically includes following steps:
Setting the first step-length being used for obtaining the number of levels of geometric parameter, and set geometric parameter bandwidth number in first area, wherein the first step-length is that the method adopting by reference the number of levels that orthogonal design obtains multiple factors obtains；
Span, the first step-length and the geometric parameter according to geometric parameter bandwidth number in first area determines bandwidth, and the region in span bandwidth covered is set to first area；
Region in unlapped for bandwidth span is set to second area.
Step S30: the geometric parameter in first area carries out orthogonal design, obtains the first experiment set.In the present embodiment, step S30 includes, according to geometric parameter value region, the first step-length and the geometric parameter in first area bandwidth number in first area, obtaining the first experiment set according to orthogonal design.
Step S40: the geometric parameter in second area carries out uniform Design, obtains the second experiment set.In the present embodiment, step S40 specifically includes following steps:
Setting the second step-length being used for obtaining the number of levels of geometric parameter, the method for the number of levels that the second step-length obtains multiple factors with reference to uniform Design obtains；
According to geometric parameter value region in second area and the second step-length, obtain the second experiment set according to uniform design.
In the present embodiment, uniform Design has used grid point method, and for n experiment, good grid point method comprises the steps:
Using congruence method to generate the jth row of uniform designs table, its formula is expressed as:
uij=ihj[modn]
Wherein, i is the line number of uniform designs table, and n is the least common multiple of the sample point number that each geometric parameter is corresponding, and h is the vector of the positive integer composition less and relatively prime with n than n, i.e. h=(h1, h2..., hm), m is determined by Euler's function φ (n),
Work as ihjDuring more than n, by ihjThe multiple deducting n makes difference fall among [1, n], and other row of uniform designs table can be generated by equation below recursion:
u1j=hj
Wherein, i=1 ..., n-1；
Use the uniformity of centralization L2 deflection measure uniform designs table, take the minimum uniform designs table of deviation and gather as the second experiment, be denoted as Un(ns)。
Employing of the present invention metamaterial structure unit parameter simulation selection method is presented herein below the metamaterial structure unit with " snowflake " type topological structure shown in Fig. 1 is carried out the detailed description of the invention that parameters simulation is chosen.
In the present embodiment, parameter s of topological structure shown in Fig. 11, s2Span be respectively [1.60,3.00], [1.60,3.00], and ignore live width.
Fig. 5 is that metamaterial structure unit parameter simulation selection method of the present invention is to " snowflake " type shown in Fig. 1 topological structure parameters simulation reconnaissance result figure.As it is shown in figure 5, the first step-length that definition orthogonal part uses, by two factors s1, s2The first step-length be all defined as dotho=0.1, in the present embodiment, first area i.e. marginal area, the bandwidth number of definition marginal area part is front n2Individual, define n2=2, the then a width of 2*0.1=0.2 of band that marginal area part is paid close attention to emphatically.Then first area relates to region and includes (s1, s2)=([1.6,1.8], [1.6,3]) U ([1.6,3], [1.6,1.8]) U ([2.8,3], [1.6,3]) U ([1.6,3], [2.8,3]).Region in unlapped for bandwidth span is set to second area, and second area part relates to region and includes (s1, s2)=([1.8,2.8], [1.8,2.8]).
Geometric parameter in first area carries out orthogonal experiment, then the number of levels of orthogonal test part isTotal experiment number of orthogonal test part is (15*2*4-2*2*4=104).In Fig. 5, the intersection point of Box Section that is first tests set, the experimental point that i.e. orthogonal experiment method is generated.
The second step-length that the uniform experiments of definition second area part uses, by two factors s1, s2Observation step-length be all defined as duni=0.01, then the number of levels of uniform experiments part is ((3-0.2)-(1.6+0.2))/0.01=100, and uniform experiments number of levels is the experiment sum of uniform experiments.And used grid point method to generate uniform experiments scheme.And using the uniformity of centralization L2-deflection measure uniform test design table commonly used in uniform experiments, degree surveys the representational quality of this lab space according to this.As little in spent measured value, then corresponding uniform experiments scheme may be utilized.The technical characteristic of this part refer to the description of step S40 of metamaterial structure unit parameter simulation selection method of the present invention.
To sum up, present embodiment will select 104+100=204 different size of " snowflake " type construction unit for electromagnetic property simulated measurement, can clearly sum up its electromagnetic property.
Fig. 6 is the structural representation of the metamaterial structure unit parameter emulation selecting device of the embodiment of the present invention.As shown in Figure 6, metamaterial structure unit parameter emulation selecting device 100 includes that geometric parameter acquiring unit 110, analytic unit 120, first test set acquiring unit 130 and the second experiment set acquiring unit 140.
Wherein, geometric parameter acquiring unit 110 is for obtaining the geometric parameter of construction unit and the span of geometric parameter.
Analytic unit 120 divides first area and second area for the span according to geometric parameter.In the present embodiment, analytic unit 120 also includes setup unit, first area acquiring unit and second area acquiring unit.Wherein, setup unit is for setting the first step-length of the number of levels for obtaining geometric parameter, and sets geometric parameter bandwidth number in first area, and wherein the first step-length is that the method adopting by reference the number of levels that orthogonal design obtains multiple factors obtains.First area acquiring unit is used for the bandwidth number in first area of span, the first step-length and the geometric parameter according to geometric parameter and determines bandwidth, and the region in span bandwidth covered is set to first area.Second area acquiring unit is for being set to second area by the region in unlapped for bandwidth span.
First experiment set acquiring unit 130, for the geometric parameter in first area carries out orthogonal design, obtains the first experiment set.In the present embodiment, the first experiment set acquiring unit 130 is for according to geometric parameter value region, the first step-length and the geometric parameter in first area bandwidth number in first area, obtaining the first experiment set according to orthogonal design.
Second experiment set acquiring unit 140, for the geometric parameter in second area carries out uniform Design, obtains the second experiment set.In the present embodiment, the second experiment set acquiring unit 140 is for setting the second step-length of the number of levels for obtaining geometric parameter, and the method for the number of levels that the second step-length obtains multiple factors with reference to uniform Design obtains；According to geometric parameter value region in second area and the second step-length, obtain the second experiment set according to uniform design.Uniform Design has used grid point method, and the concrete technical characteristic of good grid point method refer to described in step S40, and here is omitted.
The metamaterial structure unit parameter simulation selection method of the present invention and device, while ensureing the space " representative " that experimental point is chosen, can comparatively fast, accurately find the parameter of the construction unit corresponding to electromagnetic property meeting the Meta Materials that initial experiment is assumed, reduce experiment number, improve work efficiency and saved experimental cost.
The foregoing is only embodiments of the invention; not thereby the scope of the claims of the present invention is limited; every equivalent structure utilizing description of the invention and accompanying drawing content to be made or equivalence flow process conversion; or directly or indirectly it is used in other relevant technical fields, the most in like manner it is included in the scope of patent protection of the present invention.
Claims (4)
1. a metamaterial structure unit parameter simulation selection method, it is characterised in that described metamaterial structure unit parameter simulation selection method includes step:
Obtain geometric parameter and the span of described geometric parameter of described construction unit；
Span according to described geometric parameter divides first area and second area；Comprise the steps: to set the first step-length of the number of levels for obtaining described geometric parameter, and setting described geometric parameter bandwidth number in first area, wherein said first step-length is that the method adopting by reference the number of levels that orthogonal design obtains multiple factors obtains；Span according to described geometric parameter, described first step-length and described geometric parameter bandwidth number in first area determine bandwidth, region in the described span described bandwidth covered is set to first area, and the region in unlapped for described bandwidth described span is set to second area；
Geometric parameter in described first area is carried out orthogonal design, obtains the first experiment set；Including step: according to described geometric parameter value region, described first step-length and described geometric parameter bandwidth number in first area in described first area, obtain described first experiment set according to orthogonal design；
Geometric parameter in described second area is carried out uniform Design, obtains the second experiment set；Including: setting the second step-length being used for obtaining the number of levels of described geometric parameter, the method for the number of levels that described second step-length obtains multiple factors with reference to uniform Design obtains；According to described geometric parameter value region in described second area and described second step-length, obtain described second experiment set according to uniform design.
Metamaterial structure unit parameter simulation selection method the most according to claim 1, it is characterized in that, described geometric parameter in second area is carried out uniform Design, obtain in the step of the second experiment set, described uniform Design has used grid point method, for n experiment, described good grid point method comprises the steps:
Using congruence method to generate the jth row of uniform designs table, its formula is expressed as:
uij=ihj[modn]
Wherein, i is the line number of uniform designs table, and n is the least common multiple of the sample point number that each geometric parameter is corresponding, and h is the vector of the positive integer composition less and relatively prime with n than n, i.e. h=(h1, h2..., hm), m is determined by Euler's function φ (n),
Work as ihjDuring more than n, by ihjThe multiple deducting n makes difference fall among [1, n], and other row of uniform designs table can be generated by equation below recursion:
uij=hj
Wherein, i=1 ..., n-1；
Wherein, i=1 ..., n-1；
Use the uniformity of centralization L2 deflection measure uniform designs table, take the minimum uniform designs table of deviation and gather as described second experiment, be denoted as Un(ns)。
3. according to a kind of metamaterial structure unit parameter emulation selecting device, it is characterised in that described metamaterial structure unit parameter emulation selecting device includes:
Geometric parameter acquiring unit, obtains geometric parameter and the span of described geometric parameter of described construction unit；
Analytic unit, divides first area and second area according to the span of described geometric parameter；Described analytic unit includes: setup unit, set the first step-length being used for obtaining the number of levels of described geometric parameter, and setting described geometric parameter bandwidth number in first area, wherein said first step-length is that the method adopting by reference the number of levels that orthogonal design obtains multiple factors obtains；First area acquiring unit, determines bandwidth according to the span of described geometric parameter, described first step-length and described geometric parameter bandwidth number in first area, and the region in the described span described bandwidth covered is set to first area；Second area acquiring unit, is set to second area by the region in unlapped for described bandwidth described span；
First experiment set acquiring unit, carries out orthogonal design to the geometric parameter in described first area, obtains the first experiment set；Described first experiment set acquiring unit is used for: according to described geometric parameter value region, described first step-length and described geometric parameter bandwidth number in first area in described first area, obtain described first experiment set according to orthogonal design；
Second experiment set acquiring unit, carries out uniform Design to the geometric parameter in described second area, obtains the second experiment set；Described second experiment set acquiring unit is used for: setting the second step-length being used for obtaining the number of levels of described geometric parameter, the method for the number of levels that described second step-length obtains multiple factors with reference to uniform Design obtains；According to described geometric parameter value region in described second area and described second step-length, obtain described second experiment set according to uniform design.
Metamaterial structure unit parameter the most according to claim 3 emulation selecting device, it is characterised in that described uniform Design has used grid point method, for n experiment, described good grid point method comprises the steps:
Using congruence method to generate the jth row of uniform designs table, its formula is expressed as:
uij=ihj[modn]
Wherein, i is the line number of uniform designs table, and n is the least common multiple of the sample point number that each geometric parameter is corresponding, and h is the vector of the positive integer composition less and relatively prime with n than n, i.e. h=(h1, h2..., hm), m is determined by Euler's function φ (n),
Work as ihjDuring more than n, by ihjThe multiple deducting n makes difference fall among [1, n], and other row of uniform designs table can be generated by equation below recursion:
uij=hj
Wherein, i=1 ..., n-1；
Wherein, i=1 ..., n-1；
Use the uniformity of centralization L2 deflection measure uniform designs table, take the minimum uniform designs table of deviation and gather as described second experiment, be denoted as Un(ns)。
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