CN106682245A - Method for optimizing lumped loaded antenna by ACA accelerated method of moment combined with manifold mapping - Google Patents

Abstract

The invention discloses a method for optimizing lumped loaded antenna by ACA accelerated method of moment in combination with manifold mapping. The method comprises following steps: buiding a coarse model and a fine model of the manifold mapping algorithm through setting the accuracy of the adaptive crossover approximation algorithm; firstly, optimizing the coarse model to obtain an optimal solution to further carry out fine model verification; if a designed index is satisfied, the algorithm is over; if the designed index is not satisfied, a substituted model covers the information of the coarse model and the fine model, wherein the solution of the substituted model is the approximate solution of an original optimization problem; continuously updating the substituted model until the response of the fine model satisfies the designed index and then the algorithm is over. The method of the invention adopts the method of moment adaptive crossover approximation algorithm, the coarse model and the fine model of the manifold mapping algorithm are established through setting the accuracy of the adaptive crossover approximation algorithm; designed parameters are integrally optimized; on the premise that accuracy is guaranteed, time is saved.

Description

ACA accelerates moment method to combine the method that manifold mapping optimizes lump loaded antenna

One technical field

The invention belongs to the technical field of antenna optimization design, particularly a kind of self adaptation intersect approximate data (ACA) plus Fast moment method combines the method that manifold mapping optimizes lump loaded antenna.

Two background technologies

Traditional passive circuit optimization technology directly using Electromagnetic Simulation response or its growth, is made using mathematical method optimizing Response approaches requirement.Although the method is accurately but time cost is huge, big for parameter amount and complicated problem can hardly be real It is existing.Say on ordinary meaning, carrying out simulation calculation from accurate thin model can often obtain gratifying precision, but because The time that calculating is consumed is caused to greatly increase by excessive amount of calculation；And carry out calculating past from the roughcast type of relative coarseness It is fast toward calculating speed, but the precision of eligible result cannot be guaranteed.And in complicated engineering problem, directly from accurate It is unpractical that thin model is optimized, and is also impracticable；Carried out using roughcast type, incredible result may be caused.

Three content of the invention

It is an object of the invention to provide a kind of ACA accelerates moment method to combine the side that manifold mapping optimizes lump loaded antenna Method, the method is simple to operate, and greatlys save the time of optimization design.

The technical solution for realizing the object of the invention is：A kind of ACA accelerates moment method to combine manifold mapping and optimizes lump The method of loaded antenna, step is as follows：

1st step, determines the roughcast type and thin model in manifold mapping：Using moment method, intersected closely by arranging self adaptation Roughcast type is obtained like the precision of algorithm ACA, is the far-field characteristic of voltage standing wave ratio or antenna structure according to design objective, optimization is thick Model, obtains starting point x of space reflection⁽⁰⁾；The precision for intersecting approximate data ACA by arranging self adaptation obtains thin model；

2nd step, arranges iterative steps i=1, and makes For the value of consult volume of the thin model of ith iteration；

3rd step is rightCarry out thin model emulation, if the response of thin model reaches design objective, lump loaded antenna it is excellent Change terminates；If not reaching design objective, the 4th step is carried out；

4th step, constructs alternative modelX represents variable, R to be optimized_sIt is the function with regard to x；

5th step, optimizes alternative modelObtain the value of consult volume of the i+1 time thin model of iterationJudge whether full Sufficient end conditionη≤10^-3, R_fThe response of thin model is represented, if being unsatisfactory for return to step 4, the optimization of lump loaded antenna is completed if meeting.

Compared with prior art, its remarkable advantage is the present invention：(1) the parameter global optimization to designing：Reflect for manifold Algorithm is penetrated, only alternative model need to be constructed；(2) the optimization time is saved：Complete due to many Optimization Works are put in roughcast type, Satisfied effect of optimization is obtained with the thin model emulation number of times of minimum high cost, so on the premise of result accuracy is ensured Greatly save the time；(3) it is simple to operate：Alternative model to being set up is constantly updated, and optimizes roughcast type, while constantly The predictive designs parameter new to thin model is verified, required until obtaining optimization design value satisfaction.

The present invention is described in further detail below in conjunction with the accompanying drawings.

Four description of the drawings

Fig. 1 is that the present invention adopts ACA to accelerate moment method to combine the lump loading dipole antenna of manifold mapping optimization Structure chart.

Fig. 2 is to accelerate moment method to combine manifold mapping optimization lump loading dipole day using ACA in the embodiment of the present invention The voltage standing wave ratio result figure of line.

Fig. 3 is to accelerate moment method to combine manifold mapping optimization lump loading dipole day using ACA in the embodiment of the present invention The radiation efficiency figure of line.

Five specific embodiments

The present invention is described in further detail below in conjunction with the accompanying drawings.

With reference to Fig. 1, ACA of the present invention accelerates moment method to combine the method that manifold mapping optimizes lump loaded antenna, and step is such as Under：

1st step, determines the roughcast type and thin model in manifold mapping：Using moment method, intersected closely by arranging self adaptation Roughcast type is obtained like the precision of algorithm ACA, is the far-field characteristic of voltage standing wave ratio or antenna structure according to design objective, optimization is thick Model, obtains starting point x of space reflection⁽⁰⁾；The precision for intersecting approximate data ACA by arranging self adaptation obtains thin model；

The precision for intersecting approximate data ACA by arranging self adaptation obtains roughcast type and thin model, and concrete steps are such as Under：

Approximate data is intersected using self adaptation, the non-singular matrix Z that far field acts on is would indicate that^m×nApproximate representation is two matrix Us It is multiplied with V,RepresentApproximate matrix, be expressed as with expression formula：

Wherein, m, n represent respectively the line number and columns of impedance matrix Z, and r is matrix Z^m×nEffective order, r be much smaller than m and n, U^m×rAnd V^r×nFor two non-singular matrixs,Represent i-th m dimensional vector,I-th n dimension row vector is represented, self adaptation is handed over Error R that fork approximate data is decomposed^m×nIt is defined as：

Wherein, R is error matrix, | | | | what is asked is the Frobenius norms of matrix, ε₀For allowable error thresholding, lead to Cross control ε₀Size obtaining roughcast type and thin model, take ε₀=10^-1Roughcast type is represented, ε is taken₀=10^-4Represent thin model.

2nd step, arranges iterative steps i=1, and makes For the value of consult volume of the thin model of ith iteration.

3rd step is rightCarry out thin model emulation, if the response of thin model reaches design objective, lump loaded antenna it is excellent Change terminates；If not reaching design objective, the 4th step is carried out.

4th step, constructs alternative modelX represents variable, R to be optimized_sIt is the function with regard to x；Concrete steps are such as Under：

In manifold mapping, alternative model is defined as：

Wherein, R_f(x⁽ⁱ⁾) be the thin model of ith iteration response, R_c(x⁽ⁱ⁾) be ith iteration roughcast type response, R_c X () is that roughcast type to be optimized is responded, S⁽i⁾For the correction matrix of M × M, M represents that model to be optimized responds corresponding data point Number, is defined as：

S⁽i⁾=Δ F Δ C⁺ (4)

ΔC⁺Expression is asked Δ C and violates matrix, and Δ F and Δ C are expressed as：

Δ F=[R_f(x⁽ⁱ⁾)-R_f(x^(i-1))…R_f(x⁽ⁱ⁾)-R_f(x^max(i-n,0))] (5)

Δ C=[R_c(x⁽ⁱ⁾)-R_c(x^(i-1))_…R_c(x⁽ⁱ⁾)-R_c(x^max(i-n,0))] (6)

Wherein, (0) i-n represents and takes a big number in (i-n) and 0 liang of number max.

5th step, optimizes alternative modelObtain the value of consult volume of the i+1 time thin model of iterationJudge whether full Sufficient end conditionη≤10^-3, R_fThe response of thin model is represented, if being unsatisfactory for return to step 4, the optimization of lump loaded antenna is completed if meeting.

Embodiment 1

With reference to Fig. 1, ACA of the present invention accelerates moment method to combine the method that manifold mapping optimizes lump loaded antenna, and step is such as Under：

1st step, using moment method, the precision that approximate data is intersected by arranging self adaptation obtains roughcast type, according to design Index voltage standing wave ratio VSWR, optimizes roughcast type, obtains starting point x of space reflection⁽⁰⁾：

x⁽⁰⁾=[30.38 27.33 24.60 22.14 10.98 9.88 8.90 8.00]^T；

2nd step, arranges iterative steps i=1, and make For the value of consult volume of the 1st thin model of iteration；

3rd step is rightThin model emulation is carried out, thin model response is not reaching to design objective, carries out the 4th step；

4th step, constructs alternative modelDetailed process is as follows：

Alternative model is defined as：

Wherein, R_f(x⁽ⁱ⁾) be the thin model of ith iteration response, R_c(x⁽ⁱ⁾) be ith iteration roughcast type response, R_c X () is roughcast type response to be optimized.S⁽ⁱ⁾For the correction matrix of M × M, (M represents that model to be optimized responds corresponding data point Number), it is defined as：

S⁽ⁱ⁾=Δ F Δ C⁺

ΔC⁺Expression is asked Δ C and violates matrix, and Δ F and Δ C are expressed as：

Δ F=[R_f(x⁽ⁱ⁾)-R_f(x^(i-1))…R_f(x⁽ⁱ⁾)-R_f(x^max(i-n,0))]

Δ C=[R_c(x⁽ⁱ⁾)-R_c(x^(i-1))…R_c(x⁽ⁱ⁾)-R_c(x^max(i-n,0))]

Wherein, (0) i-n represents and takes a big number in (i-n) and 0 liang of number max.

5th step, judges whether to meet end conditionη values are 10^-3, R_fRepresent thin mould The response of type, completes the optimization of lump loaded antenna, if being unsatisfactory for return to step 4 if meeting.

In order to verify the correctness and validity of this method, the dipole antenna of lumped elements loading is optimized below as schemed Shown in 1.One brachium l=33.76m of antenna by two root radiuses is 2mm, constitute at a distance of the thin wire of 2m.In figure, 0-3 is loading Point, Z_nFor n-th loaded impedance, l_nFor the distance of n-th load(ing) point to distributing point, l is the total length of the arm of oscillator one.

Optimization aim is：VSWR≤2(2MHz≤f≤30MHz)

Variable to be optimized is：X=[l₀ l₁ l₂ l₃ Z₀ Z₁ Z₂ Z₃]

The method that moment method combines manifold mapping optimization lump loaded antenna is accelerated to optimize the idol of lump loading using ACA Pole sub-antenna, algorithm through 2 iteration, 3 thin model emulations.Fig. 2 is that the dipole antenna of lump loading meets design objective Voltage standing wave ratio VSWR figure, Fig. 3 be lump load dipole antenna radiation efficiency result figure, this also fully demonstrates ACA Moment method is accelerated to combine the validity that manifold mapping optimizes the method for lump loaded antenna.

In sum, ACA of the present invention accelerates moment method to combine the method basic flow that manifold mapping optimizes lump loaded antenna Journey is as follows：Optimize the optimal solution that roughcast type obtains roughcast type first, further thin model checking, if meeting design objective, calculates Method terminates；If being unsatisfactory for design objective, alternative model is constructed, the construction of alternative model covers the letter of roughcast type and thin model Breath, now the solution of alternative model is exactly the approximate solution of original optimization problem.Alternative model is constantly updated, until the response of thin model Meet design objective, algorithm terminates.The method intersects approximate data using moment method self adaptation, is intersected closely by arranging self adaptation The roughcast type and thin model of manifold mapping algorithm are set up like the precision of algorithm, to the parameter global optimization for designing, is ensureing essence Really save the time on the premise of property.

Claims (3)

1. a kind of ACA accelerates moment method to combine the method that manifold mapping optimizes lump loaded antenna, it is characterised in that step is such as Under：

1st step, determines the roughcast type and thin model in manifold mapping：Using moment method, by arranging self adaptation approximate calculation is intersected The precision of method ACA obtains roughcast type, is the far-field characteristic of voltage standing wave ratio or antenna structure according to design objective, optimizes roughcast Type, obtains starting point x of space reflection⁽⁰⁾；The precision for intersecting approximate data ACA by arranging self adaptation obtains thin model；

2nd step, arranges iterative steps i=1, and makes For the value of consult volume of the thin model of ith iteration；

3rd step is rightThin model emulation is carried out, if thin model response reaches design objective, the optimization knot of lump loaded antenna Beam；If not reaching design objective, the 4th step is carried out；

4th step, constructs alternative modelX represents variable, R to be optimized_sIt is the function with regard to x；

5th step, optimizes alternative modelObtain the value of consult volume of the i+1 time thin model of iterationJudge whether to meet eventually Only conditionη≤10^-3, R_fThe response of thin model is represented, if being unsatisfactory for return to step 4, such as Fruit meets the optimization for then completing lump loaded antenna.

2. according to claim 1 ACA accelerates moment method to combine the method that manifold mapping optimizes lump loaded antenna, its feature It is that the precision for intersecting approximate data ACA described in the 1st step by arranging self adaptation obtains roughcast type and thin model, concrete step It is rapid as follows：

Approximate data is intersected using self adaptation, the non-singular matrix Z that far field acts on is would indicate that^m×nApproximate representation is two matrix Us and V It is multiplied,Represent Z^m×nApproximate matrix, be expressed as with expression formula：

$Z^{m\×n}\≈{\tilde{Z}}^{m\×n}=U^{m\×r}{V}^{r\×n}=\underset{i=1}{\overset{r}{\Σ}}{u}_i^{m\×1}{v}_i^{1\×n}---\left(1\right)$

Wherein, m, n represent respectively the line number and columns of impedance matrix Z, and r is matrix Z^m×nEffective order, r is much smaller than m and n, U^m×r And V^r×nFor two non-singular matrixs,Represent i-th m dimensional vector,I-th n dimension row vector is represented, self adaptation is intersected near Like error R that algorithm decomposes^m×nIt is defined as：

$\left|\right|R^{m\×n}\left|\right|=\left|\right|Z^{m\×n}-{\tilde{Z}}^{m\×n}\left|\right|\≤{\mathrm{\ϵ}}_0\left|\right|Z^{m\×n}\left|\right|---\left(2\right)$

Wherein, R is error matrix, | | | | what is asked is the Frobenius norms of matrix, ε₀For allowable error thresholding, by control ε₀Size obtaining roughcast type and thin model, take ε₀=10^-1Roughcast type is represented, ε is taken₀=10^-4Represent thin model.

3. according to claim 1 ACA accelerates moment method to combine the method that manifold mapping optimizes lump loaded antenna, its feature It is to construct alternative model described in the 4th stepComprise the following steps that：

In manifold mapping, alternative model is defined as：

$R_s^{\left(i\right)}\left(x\right)=R_f\left(x^{\left(i\right)}\right)+S^{\left(i\right)}\left(R_c\right(x)-R_c(x^{\left(i\right)}\left)\right)---\left(3\right)$

Wherein, R_f(x⁽ⁱ⁾) be the thin model of ith iteration response, R_c(x⁽ⁱ⁾) be ith iteration roughcast type response, R_cX () is Roughcast type response to be optimized, S⁽ⁱ⁾For the correction matrix of M × M, M represents that model to be optimized responds the number of corresponding data point, It is defined as：

S⁽ⁱ⁾=Δ F Δ C⁺ (4)

ΔC⁺Expression is asked Δ C and violates matrix, and Δ F and Δ C are expressed as：

Δ F=[R_f(x⁽ⁱ⁾)-R_f(x^(i-1))…R_f(x⁽ⁱ⁾)-R_f(x^max(i-n,0))] (5)

Δ C=[R_c(x⁽ⁱ⁾)-R_c(x^(i-1))…R_c(x⁽ⁱ⁾)-R_c(x^max(i-n,0))] (6)

Wherein, (0) i-n represents and takes a big number in (i-n) and 0 liang of number max.