CN101702183B - Method used for united optimization of iron shielding type superconducting magnet - Google Patents

Abstract

The invention discloses a method used for the united optimization of an iron shielding type superconducting magnet, taking the intensity of a magnetic field, the uniformity of the magnetic field, the range of an escape field, the use quantity of a superconducting wire material and the weight of a magnet as performance measure indexes, adopting a united optimization method of combining a finite element and a simulated annealing algorithm for design and analyzing a design result by a tolerance analysis method. The design method in the invention considers a plurality of performance indexes integrally, utilizes a global optimization algorithm, avoids running into the problem of local optimization, enables the structure of the superconducting magnet to be more reasonable, has better shielding effect and lower production cost, analyzes the design result by the tolerance analysis method and can provide a theoretical guide for engineering execution.

Description

A kind of combined optimization method that is used for iron shield formula superconducting magnet

Technical field

The present invention relates to a kind of method for designing of superconducting magnet, especially a kind of combined optimization method that is used for iron shield formula superconducting magnet.

Background technology

At present common magnet type has permanent-magnet type, often leads type, superconduct.The superconduct magnet produces magnetic field by the electric current of the superconducting coil carrying of superconducting wire coiling, adopts liquid helium as cooling medium.Superconducting magnet is compared with other magnet type, has the advantages that volume is little, in light weight, magnetic field intensity is high, demonstrates irreplaceable effect day by day in researchs such as nuclear physics, bioengineering and medical science.

Around the superconducting magnet of field intensity, can form bigger loss magnetic field usually up to several Te Lasi; its harm is that near ferromagnetic object is produced very strong attractive force; health and instrument and equipment are caused in various degree interference, infringement and destruction, and the measure that reduces magnetic field loss degree is that magnet is taked various effective shieldings.At present the shielding mode in loss magnetic field is had two kinds of initiatively shielding and passive screenings, the former mainly uses reverse superconducting coil to shield, and the latter uses iron shield to shield.Compare with the active shielding, passive screening not only need not additional superconducting coil, and iron shield can increase the intensity of main field to a certain extent, can save the superconducting wire consumption more than 30%, in addition, also can reduce coil maximum field strength on every side, it is stressed to alleviate coil, reduces the engineering construction difficulty.

In the iron shield formula SUPERCONDUCTING MAGNET DESIGN,, can't accurately find the solution Distribution of Magnetic Field with analytic method because ferromagnetic material is non-linear.It is finite element district and boundary element district that A.Ishiyama etc. will find the solution area dividing, calculate (A.Ishiyama respectively with two kinds of numerical methods, S.Kanda.Shape Optimization Of IronShield For Superconducting Solenoid Magnets.IEEE Trans On Magnetics, 1987,23:599-602), used mathematical programming approach, goal programming method and nonlinear least square method to be optimized design on this basis, but these methods can't be optimized coil and iron shield structure as optimization variable simultaneously.S.Noguchi etc. have introduced global search algorithm-simulated annealing, it is numerous electric current loop that iron shield is decomposed equivalence, considered the non-linear (S.Noguchi of ferromagnetic material, A.Ishiyama.An Optimal Design Method for High-Field Superconducting Magnets withFerromagnetic Shields.IEEE Trans on applied superconductivity, 1997,7:439-442), but also do not include the iron shield structure in optimization variable.Huawei Zhao etc. is decomposed into numerous independent magnet ring with iron shield, field expansion (the Huawei Zhao of any magnet ring under the magnetic field excitation that main coil produces derived, Stuart Crozier.Rapid field calculations for the effect offerromagnetic material in MRI magnet design.Meas.Sci.Technol, 2002,13:198-205), but the interaction after magnet ring is magnetized around not having to consider, result of calculation is not accurate enough.

Simultaneously, in the design of superconducting magnet, traditional method for designing is weighed its performance with indexs such as magnetic field intensity, uniformity of magnetic field and loss field scopes usually, and does not consider the cost problem of superconducting wire, makes production cost higher.

Summary of the invention

The present invention seeks to: a kind of combined optimization method that is used for iron shield formula superconducting magnet is provided, and performance index consider that optimizing process is reasonable comprehensively, and global optimum as a result makes the more reasonable structure of superconducting magnet, and shield effectiveness is better, and production cost is lower.

Technical scheme of the present invention is: a kind of combined optimization method that is used for iron shield formula superconducting magnet, with magnetic field intensity, uniformity of magnetic field, loss field scope, superconducting wire consumption, magnet weight is the performance measurement index, the combined optimization method that adopts finite element to combine with simulated annealing designs, with the TOLERANCE ANALYSIS method design result is analyzed, idiographic flow is as follows:

1) starting condition is set, comprises main coil number, magnetic field of the goal intensity, homogeneity range diameter, superconducting wire type and sectional dimension, working current intensity, iron shield material type and TOLERANCE ANALYSIS target.

2) constraint condition is set, comprises magnet length, magnet weight, magnet internal diameter.

3) optimization variable of discretize is set, comprises main coil variable and iron shield variable, wherein the main coil variable comprises the individual layer number of turn, the coiling number of plies, internal diameter and the locus of each coil; The iron shield variable comprises thickness and length, the thickness of side iron shield and the locus of the two of end face iron shield.

4) objective definition function

f＝k ₁·(B ₀-B _obj)+k ₂·P _pm+k ₃·D+k ₄·L+k ₅·T

B wherein ₀Be homogeneity range internal magnetic field average strength, can obtain by finite element method and data interpolating method;

B _ObjBe homogeneity range internal object magnetic field intensity;

P _PmBe the uniformity of magnetic field in the homogeneity range;

D is a loss field scope, D=D ₁D ₂, D wherein ₁, D ₂Be respectively five Gauss's isoline axially and radially with the distance of magnet geometric center point;

L is the superconducting wire consumption, $L=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\π}\·d_i\·M_i\·N_i,$ D wherein _i, M _i, N _iBe respectively i internal coil diameter, the individual layer number of turn and the coiling number of plies;

T is the magnet general assembly (TW), T=ρ _cLS _c+ ρ _FeV _Fe, ρ wherein _c, S _cBe superconducting wire density and sectional area, ρ _Fe, V _FeBe iron shield density of material and iron shield volume, S _c, V _FeCan be by 3) optimization variable of input calculates;

k ₁, k ₂, k ₃, k ₄, k ₅Be weight coefficient, can suitably regulate size to obtain best optimization result.

5) combined optimization method that utilizes finite element to combine with simulated annealing is optimized objective function, and concrete steps are:

A) the initial controlled variable of simulated annealing is set, comprises 3) in the initial value, corresponding search volume and step-size in search, isothermal frequency in sampling, lower the temperature number of times, initial temperature acceptance probability, final temperature acceptable conditions of each optimization variable; Initial value with optimization variable is that current separating is saved in destination file.

B) utilize finite element algorithm to read in current separating, try to achieve the axial flux density value B at N some place of the first-class radian of homogeneity range sphere _Z1, B _Z2, B _Z3..., B _Zn, and five Gauss's isoline axially and radially with the distance D of magnet geometric center point ₁, D ₂

C) utilize simulated annealing to read in B _Z1, B _Z2, B _Z3..., B _Zn, D ₁, D ₂, the calculating target function value.

D) in the search volume of each optimization variable correspondence, produce one group of new explanation at random.

E) according to step b), c) calculate the target function value of new explanation correspondence.

F) judging whether to accept new explanation according to the Metropolis criterion is current separating, and the record optimum solution.

G) if the isothermal frequency in sampling reaches setting value, then temperature descends, otherwise returns d).

H) if reach the cooling number of times or satisfy the final temperature acceptable conditions, then finish computing, the output optimum solution, otherwise return d).

6) after combined optimization method finishes, carry out aftertreatment, design result is carried out TOLERANCE ANALYSIS.

Last handling process mainly carries out TOLERANCE ANALYSIS to uniformity of magnetic field.

Advantage of the present invention is:

The method for designing of iron shield formula superconducting magnet is used weighted method establishing target function and by weights Control and Optimization result is set among the present invention, except that traditional performance index such as magnetic field intensity, uniformity of magnetic field, loss field scope, factors such as superconducting wire consumption and magnet weight have also been taken all factors into consideration, make the more reasonable structure of superconducting magnet, shield effectiveness is better, and production cost is lower; Utilize finite element and simulated annealing to carry out combined optimization, can obtain globally optimal solution, avoid being absorbed in local optimum; Use the TOLERANCE ANALYSIS method that design result is analyzed, can be engineering construction theoretical direction is provided.

Description of drawings

Below in conjunction with drawings and Examples the present invention is further described:

Fig. 1 is a kind of combined optimization method process flow diagram that is used for iron shield formula superconducting magnet;

Fig. 2 is a kind of Magnetic resonance imaging/wave spectrum of using the present invention's design iron shield formula superconducting magnet structure synoptic diagram;

Fig. 3 is provided with figure for a kind of Magnetic resonance imaging/wave spectrum of using the present invention's design with the optimization variable of iron shield formula superconducting magnet.

Wherein: 1 is coil; 2 is the end face iron shield; 3 is the side iron shield.

Embodiment

Embodiment: a kind of combined optimization method that is used for iron shield formula superconducting magnet, as shown in Figure 1, utilize Magnetic resonance imaging/wave spectrum iron shield formula superconducting magnet of this method design, structure is as shown in Figure 2.Superconducting magnet comprises main coil and iron shield two parts, and main coil is made up of three pairs of solenoid type coils 1, and iron shield is made up of end face iron shield 2 and side iron shield 3.The axis direction of definition coil 1 is the Z axle, and the radial direction of coil 1 is the R axle, and superconducting magnet integral body is about the Z rotational symmetry.

A kind of combined optimization method that is used for iron shield formula superconducting magnet, it is the performance measurement index with magnetic field intensity, uniformity of magnetic field, loss field scope, superconducting wire consumption, magnet weight, the combined optimization method that adopts finite element to combine with simulated annealing designs, with the TOLERANCE ANALYSIS method design result is analyzed, idiographic flow is as follows:

1) starting condition is set, as shown in table 1, comprise main coil number, magnetic field of the goal intensity, homogeneity range diameter, superconducting wire type and sectional dimension, working current intensity, iron shield material type and TOLERANCE ANALYSIS target.

Table 1

Starting condition	Preset value
		The main coil number	6
Magnetic field of the goal intensity	1.5T
		The homogeneity range diameter	400mm
The superconducting wire type	Square line

The superconducting wire sectional dimension	1.2mm×0.8mm
		Working current intensity	260A
The iron shield material type	Electrical pure iron
		The TOLERANCE ANALYSIS target	Uniformity of magnetic field

2) constraint condition is set, as shown in table 2, comprise magnet length, magnet weight, magnet internal diameter.

Table 2

Constraint condition	Binding occurrence
		Magnet length	?＜1.6mm
Magnet weight	?＜15t
		The magnet internal diameter	?＞0.9mm

3) optimization variable of discretize is set, as table 3, shown in Figure 3, comprises main coil variable and iron shield variable, wherein the main coil variable comprises the individual layer number of turn, the coiling number of plies, internal diameter and the locus of each coil 1; The iron shield variable comprises thickness and length, the thickness of side iron shield 3 and the locus of the two of end face iron shield 2.

Table 3

Optimization variable	The variable implication
		M 1、M 2、M 3	The individual layer number of turn of each coil
N 1、N 2、N 3	The coiling number of plies of each coil
		r 1、r 2、r 3	The internal diameter of each coil
d 1、d 2、d 3	Each coil is with respect to the distance of R axle
		d 4	The end face iron shield is with respect to the distance of R axle
d 5	The side iron shield is with respect to the distance of Z axle
		t 1	The thickness of end face iron shield
t 2	The thickness of side iron shield
		l 1	The length of end face iron shield

4) objective definition function

f＝k ₁·(B ₀-B _obj)+k ₂·P _pm+k ₃·D+k ₄·L+k ₅·T

B wherein ₀Be homogeneity range internal magnetic field average strength, B _ObjBe homogeneity range internal object magnetic field intensity, P _PmBe the uniformity of magnetic field in the homogeneity range, D is a loss field scope, and L is the superconducting wire consumption, and T is the magnet general assembly (TW), k ₁, k ₂, k ₃, k ₄, k ₅Be weight coefficient, can suitably regulate size to obtain best optimization result.

Calculate B ₀, P _Pm, D, L, T method:

Superconducting magnet is an axially symmetric structure, and working current is constant, therefore can be reduced to two-dimentional static magnetic field problem and find the solution.Because the nonlinear characteristic of iron shield material adopts finite element method to calculate.

The Maxwell system of equations differential form of two dimension static magnetic field is:

$\left\{\begin{array}{c}\▿\×\stackrel{\→}{H}=J_S\\ \▿\·\stackrel{\→}{B}=0\end{array}\right.$

Constitutive relation is:

$\stackrel{\→}{B}=\mathrm{\μ}\stackrel{\→}{H}$

Wherein,

Be the magnetic field intensity vector,

Be the magnetic flux density vector, μ is a magnetic permeability, J _SThe loop current density of serving as theme.

Magnetic flux density

Be not have to loose, adopt the vector potential method to find the solution the top differential equation, introduce vector magnetic potential

Can be expressed as

Curl, promptly have:

$\stackrel{\→}{B}=\▿\×\stackrel{\→}{A}$

Derive the governing equation of two-dimentional static magnetic field:

$\▿\×\frac{1}{\mathrm{\μ}}\▿\×\stackrel{\→}{A}=J_s$

Choose vector virtual displacement function

Further derive the weak form of the differential equation:

$\frac{1}{\mathrm{\μ}}(\▿\×\stackrel{\→}{A};\▿\×\stackrel{\→}{V})=(J_s;\stackrel{\→}{V})$

Write finite element program according to this equation and find the solution, obtain the vector magnetic potential at each point place, space

Take out n point (n 〉=100), foundation at the first-class radian of homogeneity range sphere $\stackrel{\→}{B}=\▿\×\stackrel{\→}{A}$ Obtain the axial flux density value B of these points _Z1, B _Z2, B _Z3..., B _Zn

Definition one-dimensional vector x _n:

$x_n=[\cos \mathrm{\π},\cos \left(\frac{(n-2)\mathrm{\π}}{n-1}\right),\cos \left(\frac{(n-3)\mathrm{\π}}{n-1}\right),\cos \left(\frac{(n-4)\mathrm{\π}}{n-1}\right),...,\cos 0]$

Definition one-dimensional vector B _Zn:

B _zn＝[B _z1，B _z2，B _z3，...，B _zn]

Definition interpolating function B _z=f (x), x _nAnd B _ZnSatisfy B _Zn=f (x _n).

Adopt method of interpolation that data point is carried out interpolation; Interior to interpolating function B after the interpolation in the field of definition [1,1] of x _zAsk definite integral, can obtain B ₀, that is:

$B_0=\frac{1}{2}{\∫}_{-1}^1{B}_z{d}_x$

Axial flux density B on the homogeneity range sphere _zExpand into by Legendre function:

$B_z=B_0+\underset{n}{\mathrm{\Σ}}{A}_n\·r^n\·P_n\left(\cos \mathrm{\θ}\right)$

Make B _z=B _Zn, r is the homogeneity range radius, θ is B _ZnAn expansion coefficient A can be obtained according to following formula in middle each point and z axle clamp angle _n

According to following formula calculating magnetic field uniformity coefficient P _Pm:

$P_{\mathrm{pm}}=\underset{n}{\mathrm{\Σ}}{w}_n\·A_n$

Generally get n＜12 in the actual computation, more the coefficient of high-order is very little, can ignore.Get over the A of high-order _nTherefore the difficult more elimination of magnetic field unevenness that produces is optimizing P _PmThe time, weight coefficient w _nIncrease progressively setting by exponent number, force down the A of high-order as far as possible _n

Calculate loss field scope D according to following formula:

D＝D ₁·D ₂

D wherein ₁, D ₂Be respectively five Gauss's isoline axially and radially with the distance of magnet geometric center point.

According to following formula approximate treatment superconducting wire consumption L:

$L=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\π}\·d_i\·M_i\·N_i$

D wherein _i, M _i, N _iBe respectively i internal coil diameter, the individual layer number of turn and the coiling number of plies.

According to following formula approximate treatment magnet general assembly (TW) T:

T＝ρ _c·L·S _c+ρ _fe·V _fe

ρ wherein _c, S _cBe superconducting wire density and sectional area, ρ _Fe, V _FeBe iron shield density of material and iron shield volume.S _c, V _FeCan calculate by the optimization variable of step 3) input.

5) combined optimization method that utilizes finite element to combine with simulated annealing is optimized objective function, and concrete steps are:

A) the initial controlled variable of simulated annealing is set, comprises 3) in the initial value, corresponding search volume and step-size in search, isothermal frequency in sampling, lower the temperature number of times, initial temperature acceptance probability, final temperature acceptable conditions of each optimization variable; Initial value with optimization variable is that current separating is saved in destination file.

B) utilize finite element algorithm to read in current separating, try to achieve the axial flux density value B at N some place of the first-class radian of homogeneity range sphere _Z1, B _Z2, B _Z3..., B _Zn, and five Gauss's isoline axially and radially with the distance D of magnet geometric center point ₁, D ₂

C) utilize simulated annealing to read in B _Z1, B _Z2, B _Z3..., B _Zn, D ₁, D ₂, the calculating target function value.

D) in the search volume of each optimization variable correspondence, produce one group of new explanation at random.

E) according to step b), c) calculate the target function value of new explanation correspondence.

F) according to the Metropolis criterion:

Judging whether to accept new explanation is current separating, and the record optimum solution.

G) if the isothermal frequency in sampling reaches setting value, then temperature descends, otherwise returns d).

H) if reach the cooling number of times or satisfy the final temperature acceptable conditions, then finish computing, the output optimum solution, otherwise return d).

6) to finish to obtain net result as shown in table 4 for optimized Algorithm, and the operation post processor is carried out TOLERANCE ANALYSIS to the optimum solution of design, the one or more tolerances of stack on the optimum solution basis, set by step 4) described method calculated tolerances evaluating objects, analysis result is as shown in table 5, A ₁～A ₈Be the expansion item coefficient of uniformity of magnetic field, more the coefficient of high-order is very little with the variable quantity of tolerance, can ignore.

Table 4

Design object	Design result
		Main field strength B 0	1.5002T
Uniformity of magnetic field P pm	2.245ppm
		Loss field scope D 1×D 2	7.1m×5.3m
Superconducting wire consumption L	15.4km
		Magnet general assembly (TW) T	12.5t

Table 5

The method for designing of iron shield formula superconducting magnet is used weighted method establishing target function and by weights Control and Optimization result is set among the present invention, remove the traditional design index of magnet, outside magnetic field intensity, uniformity of magnetic field, loss field scope, also superconducting wire consumption and magnet weight are included in and be the complex optimum target, make the more reasonable structure of superconducting magnet, shield effectiveness is better, and production cost is lower; Utilize finite element and simulated annealing to carry out combined optimization, can obtain globally optimal solution, avoid being absorbed in local optimum; Use the TOLERANCE ANALYSIS method that design result is analyzed, can be engineering construction theoretical direction is provided.

Claims (2)

1. combined optimization method that is used for iron shield formula superconducting magnet, it is characterized in that: it is the performance measurement index with magnetic field intensity, uniformity of magnetic field, loss field scope, superconducting wire consumption, magnet weight, the combined optimization method that adopts finite element to combine with simulated annealing designs, with the TOLERANCE ANALYSIS method design result is analyzed, idiographic flow is as follows:

1) starting condition is set, comprises main coil number, magnetic field of the goal intensity, homogeneity range diameter, superconducting wire type and sectional dimension, working current intensity, iron shield material type and TOLERANCE ANALYSIS target;

2) constraint condition is set, comprises magnet length, magnet weight, magnet internal diameter;

3) optimization variable of discretize is set, comprises main coil variable and iron shield variable, wherein the main coil variable comprises the individual layer number of turn, the coiling number of plies, internal diameter and the locus of each coil (1); The iron shield variable comprises thickness and length, the thickness of side iron shield (3) and the locus of the two of end face iron shield (2);

4) objective definition function

f＝k ₁·(B ₀-B _obj)+k ₂·P _pm+k ₃·D+k ₄·L+k ₅·T

B wherein ₀Be homogeneity range internal magnetic field average strength, can obtain by finite element method and data interpolating method;

B _ObjBe homogeneity range internal object magnetic field intensity;

P _PmBe the uniformity of magnetic field in the homogeneity range;

D is a loss field scope, D=D ₁D ₂, D wherein ₁, D ₂Be respectively five Gauss's isoline axially and radially with the distance of magnet geometric center point;

L is the superconducting wire consumption,

D wherein _i, M _i, N _iBe respectively i internal coil diameter, the individual layer number of turn and the coiling number of plies;

T is the magnet general assembly (TW), T=ρ _cLS _c+ ρ _FeV _Fe, ρ wherein _c, S _cBe superconducting wire density and sectional area, ρ _Fe, V _FeBe iron shield density of material and iron shield volume, S _c, V _FeCan be by 3) optimization variable of input calculates;

k ₁, k ₂, k ₃, k ₄, k ₅Be weight coefficient, can suitably regulate size to obtain best optimization result;

5) combined optimization method that utilizes finite element to combine with simulated annealing is optimized objective function, and concrete steps are:

A) the initial controlled variable of simulated annealing is set, comprises 3) in the initial value, corresponding search volume and step-size in search, isothermal frequency in sampling, lower the temperature number of times, initial temperature acceptance probability, final temperature acceptable conditions of each optimization variable; Initial value with optimization variable is that current separating is saved in destination file;

B) utilize finite element algorithm to read in current separating, try to achieve the axial flux density value B at N some place of the first-class radian of homogeneity range sphere _Z1, B _Z2, B _Z3..., B _Zn, and five Gauss's isoline axially and radially with the distance D of magnet geometric center point ₁, D ₂

C) utilize simulated annealing to read in B _Z1, B _Z2, B _Z3..., B _Zn, D ₁, D ₂, the calculating target function value;

D) in the search volume of each optimization variable correspondence, produce one group of new explanation at random;

E) according to step b), c) calculate the target function value of new explanation correspondence;

F) judging whether to accept new explanation according to the Metropolis criterion is current separating, and the record optimum solution;

G) if the isothermal frequency in sampling reaches setting value, then temperature descends, otherwise returns d);

H) if reach the cooling number of times or satisfy the final temperature acceptable conditions, then finish computing, the output optimum solution, otherwise return d);

6) after combined optimization method finishes, carry out aftertreatment, design result is carried out TOLERANCE ANALYSIS.

2. a kind of combined optimization method that is used for iron shield formula superconducting magnet according to claim 1, it is characterized in that: described last handling process mainly carries out TOLERANCE ANALYSIS to uniformity of magnetic field.

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