CN101339580A - Discrete optimizing method for magnetic resonance image-forming superconducting magnet design - Google Patents

Abstract

The invention relates to an optimization design method for the discretization of magnetic resonance imaging (MRI) superconducting magnets, which belongs to a superconducting magnet design technology and is characterized in that an objective function is set by a weighting method and indexes of magnetic field intensity, uniformity of magnetic field, stray field range, thread consumption, fabrication error, and the like are taken into comprehensive consideration. The use of discrete variables as optimization variables can avoid rounding and discretization errors occurring in common methods. By considering the robustness of errors in design objectives, the optimization design of the robustness is realized. The use of the design method for designing the superconducting magnets can take a plurality of design indexes into consideration in a synthesized manner, thus having the advantages of convenient processing and manufacturing and strong error robustness.

Description

A kind of discrete optimizing method that is used for the magnetic resonance image-forming superconducting magnet design

Technical field

The invention belongs to and use the superconductor technology field, relate in particular to magnetic resonance imaging (MRI) SUPERCONDUCTING MAGNET DESIGN.

Background technology

Magnetic resonance imaging (MRI) is a kind of technology of utilizing nmr phenomena to carry out imaging.Main magnet is the vitals of MRI system, and its effect is to produce a background magnetic field with certain strength and certain uniformity coefficient in imaging region.Its Electromagnetic Design index has:

(1) magnetic field intensity B ₀, refer to imaging region (DSV) central point magnetic field value.

(2) uniformity of magnetic field, its a kind of define method is

$H_0=\frac{B_{\mathrm{dx}}-B_{\mathrm{di}}}{B_0},$

Wherein, H ₀The expression uniformity of magnetic field, B _DxAnd B _DiBe expressed as the maximal value and the minimum value of the regional internal magnetic field of picture.

(3) stray magnetic field scope is often referred to the shared spatial dimension of 0.5mT (bold and unconstrained tesla) magnetic field isoline.

Main magnet in the middle high-field MRI systems adopts superconducting magnet usually.Superconducting magnet is to use superconducting wire (for example NbTi multiple core superconductive wire) to realize at the one or more superconducting coils of magnet skeleton coiling.After superconducting magnet magnetizes, under cryogenic conditions, carry out work with constant current mode.Because the superconducting line cost is higher, thus also with superconducting line with the line amount as design objective.

A kind of common method for designing of superconducting magnet is, chosen in advance working current and coil basic structure, magnetic field in the imaging region is launched with humorous wave method, with coil dimension and position as independent variable, offset relation by main field strength and low order harmonics component and set up Nonlinear System of Equations, find the solution this equation and finish design.Another kind of conventional design method is, under specific loop construction, sets up the optimization problem model, as optimization variable, is objective function with aforementioned design objective with coil dimension and position, adopts certain optimized Algorithm to find the solution.In the final stage of these two kinds of methods, because the needs of actual processing need to consider the superconducting line sectional dimension, coil dimension is carried out discretize handle, position and radius are rounded.After rounding and dispersing, indexs such as the uniformity coefficient of magnet can descend with certain amplitude usually, make design result depart from optimum solution.In addition, owing to may there be error in actual adding man-hour, need at last to analyze the influence of possible error to the magnetic field index in design, promptly carry out robust analysis, what still can meet design requirement under the selection worst condition separates.But such consequence is to be difficult to realize that magnetic field index and robustness reach optimum simultaneously.

By adopting discrete Variable Optimum Design, avoided rounding and discretization error among the present invention, realized optimal design.By in optimization problem, considering error robustness, realized the optimal design of strong robustness.

Summary of the invention

The object of the present invention is to provide a kind of system magnetic resonance imaging (MRI) SUPERCONDUCTING MAGNET DESIGN method, its step is as follows:

Step (1) is set as follows optimization variable, and the input computing machine:

The coil number of plies and every layer of number of turn are treated to discrete variable;

Coil radius and position:

When not considering machining precision, be treated to continuous variable;

When considering machining precision, also coil radius and location variable are treated to discrete variable.

Described coil comprises main coil and potted coil at least.

Step (2) is calculated as follows the objective function f that uses when using described computing machine to adopt simulated annealing to carry out described discrete optimizing method,

f＝w ₁·B+w ₂·H+w ₃·S+w ₄·L+w ₅·R，

Wherein, w ₁, w ₂... w ₅Being preassigned weight coefficient, is setting value,

B is a central magnetic field intensity,

H is a uniformity of magnetic field,

S is the stray magnetic field scope,

L is a superconducting line line amount,

R is for making the error robustness coefficient.

Step (2.1) is decomposed into magnetic resonance image-forming superconducting magnet and comprises electric current in the same way or the coil combination of the column type coil of current reversal, uses the Legendre method of development of solenoid inside, is calculated as follows central magnetic field intensity B and uniformity of magnetic field H:

At first, for each column type coil, calculate preceding 10 rank even Legendre coefficients.With i coil is example, its preceding 10 rank even Legendre coefficient M _0i, M _2i..., M _10i, be shown below:

$M_{0i}={\mathrm{\β}}_i\ln \frac{{\mathrm{\α}}_i+{({\mathrm{\α}}_i^2+{\mathrm{\β}}_i^2)}^{1/2}}{1+{(1+{\mathrm{\β}}_i^2)}^{1/2}}$

$M_{2i}=\frac{1}{2{\mathrm{\β}}_i}({C_{1i}}^{3/2}-{C_{3i}}^{3/2})$

$M_{4i}=\frac{1}{24{\mathrm{\β}}_i^3}[{C_{1i}}^{3/2}(2+{3C}_{2i}+{{15C}_{2i}}^2)-{C_{3i}}^{3/2}(2+{3C}_{4i}+{{15C}_{4i}}^2)]$

$-{C_{3i}}^{3/2}(8+12C_{4i}+15{C_{4i}}^2-70{C_{4i}}^3+315{C_{4i}}^4)]$

$M_{8i}=\frac{1}{396{\mathrm{\β}}_i^7}[{C_{1i}}^{3/2}(16+24C_{2i}+30{C_{2i}}^2+35{C_{2i}}^3+315{C_{2i}}^4$

$-2079{C_{2i}}^5+3003{C_{2i}}^6)$

$-{C_{3i}}^{3/2}(16+24C_{4i}+30{C_{4i}}^2+35{C_{4i}}^3+315{C_{4i}}^4$

$-2079{C_{4i}}^5+3003{C_{4i}}^6\left)\right]$

$M_{10i}=\frac{1}{11520{\mathrm{\β}}_i^9}[{C_{1i}}^{3/2}(128+192C_{2i}+240{C_{2i}}^2+280{C_{2i}}^3+$

$315{C_{2i}}^4-2772{C_{2i}}^5+42042{C_{2i}}^6-128700{C_{2i}}^7+109395{C_{2i}}^8)$

$-{C_{3i}}^{3/2}(128+192C_{4i}+240{C_{4i}}^2+280{C_{4i}}^3+$

$315{C_{4i}}^4-2772{C_{4i}}^5+42042{C_{4i}}^6-128700{C_{4i}}^7+109395{C_{4i}}^8\left)\right]$

Wherein,

${\mathrm{\α}}_i=\frac{A_{2i}}{A_{1i}}$ ${\mathrm{\β}}_i=\frac{L_i}{A_1}$

$C_{1i}=\frac{1}{1+{\mathrm{\β}}_i^2}$ $C_{2i}=\frac{{\mathrm{\β}}_i^2}{1+{\mathrm{\β}}_i^2}$ $C_{3i}=\frac{{\mathrm{\α}}_i^2}{{\mathrm{\α}}_i^2+{\mathrm{\β}}_i^2}$ $C_{4i}=\frac{{\mathrm{\β}}_i^2}{{\mathrm{\α}}_i^2+{\mathrm{\β}}_i^2}$

A _1iBe the internal diameter of i coil, A _2iBe the external diameter of i coil, L _iBe half length of i coil.

(2.1) described method is calculated each rank Legendre coefficient in described preceding 10 rank of all column type coils then, set by step.

Then, calculate each rank Legendre coefficient M of described magnetic resonance image-forming superconducting magnet ₀, M ₂... M ₁₀During calculating, remember that each coil current density amplitude is | J _i|=J, the coil of note radius minimum is the Line 1 circle, and each rank Legendre coefficients of other each coils is carried out electric current and internal diameter by its conversion summation, and is as follows:

$M_j=\underset{i=1}{\overset{K}{\mathrm{\Σ}}}\mathrm{sign}\left(J_i\right)M_{\mathrm{ji}}{\left(\frac{A_{11}}{A_{1i}}\right)}^{j-1},$

Wherein, M _j, j=0,2 ... 10 is magnet Legendre coefficient, A ₁₁Be Line 1 circle internal diameter, A _1iBe i internal coil diameter, M _JiBe the j rank Legendre coefficient of i coil, sign (Ji) represents i the direction of the winding current symbol, and K is the coil number.

Be calculated as follows central magnetic field intensity B again,

B＝μ ₀JA ₁M ₀；

Be calculated as follows uniformity of magnetic field H again,

H＝k ₂M ₂ ²+k ₄M ₄ ²+…+k ₁₀M ₁₀ ²，

Wherein, μ ₀Be air permeability, J is the current density amplitude, A ₁Be inner coil internal diameter, weighting coefficient k ₂, k ₄..., k ₁₀Be setting value.

Step (2.2), described magnetic resonance image-forming superconducting magnet resolve into comprise electric current in the same way or the column type coil of current reversal after interior coil combination, use the Legendre method of development of described solenoid outside to calculate described stray magnetic field scope S as follows:

At first, to each column type coil, calculate preceding 6 rank odd Legendre expansion coefficients.With i coil is example, its preceding 6 rank odd Legendre coefficient N _1i, N _3i, N _5i, be shown below:

$N_{1i}=\frac{1}{3}(1-{\mathrm{\α}}_i){\mathrm{\β}}_i{D}_{1i}$

$N_{3i}=-\frac{1}{30}(1-{\mathrm{\α}}_i){\mathrm{\β}}_i({9D}_{2i}-20D_{1i}{\mathrm{\β}}_i^2)$

$N_{5i}=\frac{1}{56}(1-{\mathrm{\α}}_i){\mathrm{\β}}_i(15D_{3i}-84D_{2i}{\mathrm{\β}}_i^2+56D_{1i}{\mathrm{\β}}_i^4)$

Wherein,

${\mathrm{\α}}_i=\frac{A_{2i}}{A_{1i}}$ ${\mathrm{\β}}_i=\frac{L}{A_{1i}}$

$D_{1_i}=1+{\mathrm{\α}}_i+{\mathrm{\α}}_i^2$ D _2i＝1+α _i+α _i ²+α _i ³+α _i ⁴

D _3i＝1+α _i+α _i ²+α _i ³+α _i ⁴+α _i ⁵+α _i ⁶

A _1i, A _2iAnd L _iImplication is the same.

(2.2) described method is calculated each rank Legendre coefficient of all column type coils then, set by step.

Then, calculate the algebraic sum of each rank Legendre coefficient of all column type coils, use N ₁, N ₃, N ₅Expression.During calculating, remember that each coil current density amplitude is | J _i|=J, the coil of note radius minimum is the Line 1 circle, and each rank Legendre coefficients of other each coils is carried out electric current and internal diameter by its conversion summation, and is as follows:

$N_j=\underset{i=1}{\overset{K}{\mathrm{\Σ}}}\mathrm{sign}\left(J_i\right)N_{\mathrm{ji}}{\left(\frac{A_{1i}}{A_{11}}\right)}^{j+3},$

Wherein, N _j, j=1,3,5 is magnet Legendre coefficient, N _JiBe the j rank Legendre coefficient of i coil, other implications are the same.

Calculate stray magnetic field scope S again:

S＝l ₁N ₁ ²+l ₃N ₃ ²+l ₅N ₅ ²，

Wherein, l ₁, l ₃, l ₅Be weighting coefficient, be setting value.

Step (2.3) is calculated as follows superconducting coil with line amount L:

L＝V/S _cr，

Wherein, V is the coil cumulative volume, S _CrBe sectional area of wire.

Step (2.4) is calculated as follows magnet robustness coefficients R.

Step (2.4.1), (2.1) described method set by step, the calculation optimization variable does not have the uniformity of magnetic field H ' when making error.

Step (2.4.2), (2.1) described method set by step, there is the uniformity of magnetic field H when making error in the calculation optimization variable ".

Step (2.4.3) is calculated as follows and makes the error robustness coefficient,

R＝|H′-H″|。

Step (3) is optimized described objective function with simulated annealing, and its step is as follows:

Step (3.1) to computing machine input simulated annealing initial parameter, comprising: initial temperature, final temperature, temperature decline rate, maximum search number of times under the same temperature, step-size in search, variable initial value.The variable initial value is changed to current separating and optimum solution, and calculates its target function value.

Step (3.2) is searched for new explanation in the current neighborhood of separating.Neighborhood is defined as in the solution space, is the center with current separating, in its component one or several amplitude that step-size in search is set (as former variate-value 10%) in the zone of random variation.

Step (3.3), the target function value of COMPUTER CALCULATION new explanation correspondence.

Step (3.4), the constraint of COMPUTER CALCULATION new explanation correspondence is if employing adds penalty function method punishment above constraint then to objective function.Constraint condition is dimension constraint, if there is the situation that surpasses setting value in each component of new explanation, then is considered as surpassing constraint.When needs limit the particular characteristic index, also it can be treated to constraint condition, use the method identical to calculate, if surpass setting value then punish with respective items in the objective function.The method that use adds penalty function method punishment is as follows:

f ₂＝f ₁+Δ，

Wherein, f ₁Be former target function value, f ₂For punishing the back target function value, Δ is the punishment amount.

Step (3.5), judging whether to accept new explanation according to the Metropolis criterion is current separating, and the record optimum solution; The Metropolis criterion is as follows

Wherein, x ₁Be new explanation, x ₂Separate for current, T is a Current Temperatures, rand _[0,1]Be the random number between [0,1].

Step (3.6), if the maximum search number of times reaches setting value under the same temperature, then temperature descends, otherwise returns (3.2).

Step (3.7), algorithm stops if temperature reaches final temperature, the output optimum solution, otherwise return (3.2).

Method for designing among the present invention is provided with objective function by weighted method, takes all factors into consideration above-mentioned every optimization index; By adopting discrete variable, avoided rounding and discretization error in the usual method; By in design object, considering the error robustness index, realized the optimal design of strong robustness.Use the design's method to carry out SUPERCONDUCTING MAGNET DESIGN, can take all factors into consideration a plurality of design objectives, design result has the processing and fabricating of being convenient to, the advantage that error robustness is strong.

Description of drawings

Fig. 1 is a kind of active shielding superconducting magnet structure of using the present invention's design.

Fig. 2 is that the optimization variable of using a kind of active shielding superconducting magnet of the present invention's design is provided with figure.

Fig. 3 is a kind of simulated annealing heuritic approach process flow diagram of using the present invention's design.

Fig. 4 is that the imaging region uniformity of magnetic field of using a kind of active shielding superconducting magnet of the present invention's design distributes.

Fig. 5 is a 0.5mT isoline of using a kind of active shielding superconducting magnet of the present invention's design.

Table 1 is an optimization variable of using a kind of active shielding superconducting magnet of the present invention's design.

Table 2 is design results of using a kind of active shielding superconducting magnet of the present invention's design.

Embodiment

Below in conjunction with accompanying drawing principle of the present invention and concrete embodiment are described once.

Fig. 1 is a selected magnet structure in the embodiment of the invention.Coil is about the Z rotational symmetry, and about the Z=0 plane symmetry.The magnet inboard circle of serving as theme adopts outer recess form, and the outside is two pairs of potted coils, and potted coil and main coil are oppositely contacted, and pore radius is 0.15m in the magnet.Select SuperCon C54S43 type superconducting line, electric current is made as I=240A.

Fig. 2 is that the Optimization Model variable is provided with figure in the embodiment of the invention.Be illustrated as the shaft section first quartile.Variable X=[x1, x2, x3, x4, x5, x6, x7, x8, x9, x10], each component implication of variable is as shown in the table:

Table 1

Component	Implication	Component	Implication
				x1	Every layer of number of turn of main coil	x6	Two potted coil spacings
x2	Every layer of number of turn of concave circle	x7	Every layer of number of turn of inner screening coil
				x3	The main coil number of plies	x8	Inner screening coil and middle section distance
x4	Concave ring layer number	x9	The potted coil number of plies
				x5	Every layer of number of turn of external shield coil	x10	Potted coil and concave circle spacing

X1 wherein, x2, x3, x4, x5, x7, x9 are discrete variable, x6, x8, x10 are continuous variable.

In advance each variable is carried out manual analysis to the influence that magnetic field index H causes, select y1=φ x8 and y2=φ (x1-x2) as error robustness coefficient verification object, wherein φ is the superconducting line diameter, makes error and gets 0.5mm.

Constraint condition is that magnet half is long less than 0.5m, and the potted coil external diameter is less than 0.5m.

Fig. 3 is the simulated annealing process flow diagram that is used to find the solution the discrete optimization problem in the embodiment of the invention, and its basic step is as follows:

(1) optimization variable is set, comprises: each coil number of plies, every layer of number of turn, radius and position.

(2) set up aforementioned optimization aim function f.

(3) to computing machine input simulated annealing initial parameter, comprising: initial temperature, final temperature, temperature decline rate, maximum search number of times under the same temperature, step-size in search (initial value 10%), variable initial value.The variable initial value is changed to current separating and optimum solution, and calculates its target function value.

(4) computing machine is searched for new explanation in the current neighborhood of separating.Neighborhood is defined as in the solution space, is the center with current separating, the zone of its component random variation in step-size in search is set.

(5) target function value of COMPUTER CALCULATION new explanation correspondence.

(6) constraint of COMPUTER CALCULATION new explanation correspondence is if employing adds penalty function method punishment above constraint then to objective function.Constraint condition is described dimension constraint, if there is the situation that surpasses setting value in each component of new explanation, then is considered as surpassing constraint.The method that use adds penalty function method punishment is as follows:

f ₂＝f ₁+Δ

f ₁Be former target function value, f ₂For punishing the back target function value, Δ is the punishment amount.

(7) judging whether to accept new explanation according to the Metropolis criterion is current separating, and the record optimum solution; The Metropolis criterion is as follows,

Wherein, x ₁Be new explanation, x ₂Separate for current, T is a Current Temperatures.Rand _[0,1]Be the random number between [0,1]

(8) if the maximum search number of times reaches setting value under the same temperature, then temperature descends, otherwise returns (4).

(9) algorithm stops if temperature reaches final temperature, and the output optimum solution continues to carry out otherwise return (4).

(10) finish optimized Algorithm.

Optimized Algorithm is carried out following aftertreatment after finishing, and calculates final performance parameter:

Use the simple integral method magnetic field intensity B of computing center ₀If B ₀≠ 7.00T then regulates electric current I, and it is equated;

Use simple integral method calculating magnetic field uniformity coefficient H ₀

Use the simple integral method to calculate 0.5mT isoline scope;

Use the simple integral method to calculate maximum magnetic field strength B in the coil _MaxBring Bmax the Bc-Ic family curve of super electric wire material into, try to achieve Bc=B _MaxThe time quench electric current I c, obtain superconducting line utilization factor I/Ic

Check the uniformity of magnetic field H of all variablees ₀The robustness coefficient.

Design result in the embodiment of the invention is as shown in the table:

Table 2

Design item	Design result
		The superconducting line model	SuperCon C54S43，Cu:SC＝1.3
Working current I	244.5A
		Magnetic field intensity B 0	7.00T
Uniformity of magnetic field H 0	10.54ppm diameter 15cm spheroid distributes as shown in Figure 4
		0.5mT isoline	As shown in Figure 5
The superconducting line consumption	41km
		Maximum magnetic induction B on the coil max	7.41T, corresponding critical current Ic=417.4A
Superconducting line utilization factor I/Ic	58.6％
		Make error uniformity coefficient robustness	41.4ppm

Claims (2)

1, a kind of discrete optimization method for designing that is used for the magnetic resonance image-forming superconducting magnet design is characterized in that, contains following steps successively:

Step (1) is set as follows optimization variable, and the input computing machine:

The coil number of plies and every layer of number of turn are treated to discrete variable;

Coil radius and position:

When not considering machining precision, be treated to continuous variable;

When considering machining precision, also coil radius and location variable are treated to discrete variable;

Described coil comprises main coil and potted coil at least;

Step (2) is calculated as follows the objective function f that uses when using described computing machine to adopt simulated annealing to carry out described discrete optimizing method,

f＝w ₁·B+w ₂·H+w ₃·S+w ₄·L+w ₅·R，

Wherein, w ₁, w ₂... w ₅Being preassigned weight coefficient, is setting value,

B is a central magnetic field intensity,

H is a uniformity of magnetic field,

S is the stray magnetic field scope,

L is a superconducting line line amount,

R is for making the error robustness coefficient;

Step (2.1) is decomposed into magnetic resonance image-forming superconducting magnet and comprises electric current in the same way or the coil combination of the column type coil of current reversal, uses the Legendre method of development of solenoid inside, is calculated as follows central magnetic field intensity B and uniformity of magnetic field H:

At first, for each column type coil, calculate preceding 10 rank even Legendre coefficients; With i coil is example, its preceding 10 rank even Legendre coefficient M _0i, M _2i..., M _10i, be shown below:

$M_{0i}={\mathrm{\β}}_i\ln \frac{{\mathrm{\α}}_i+{({{\mathrm{\α}}_i}^2+{{\mathrm{\β}}_i}^2)}^{1/2}}{1+{(1+{{\mathrm{\β}}_i}^2)}^{1/2}}$

$M_{2i}=\frac{1}{2{\mathrm{\β}}_i}({C_{1i}}^{3/2}-{C_{3i}}^{3/2})$

$M_{4i}=\frac{1}{24{{\mathrm{\β}}_i}^3}[{C_{1i}}^{3/2}(2+3C_{2i}+15{C_{2i}}^2)-{C_{3i}}^{3/2}(2+3C_{4i}+15{C_{4i}}^2)]$

$M_{6i}=\frac{1}{240{{\mathrm{\β}}_i}^5}[{C_{1i}}^{3/2}(8+12C_{2i}+15{C_{2i}}^2-70{C_{2i}}^3+315{C_{2i}}^4)$

$-{C_{3i}}^{3/2}(8+12C_{4i}+15{C_{4i}}^2-70{C_{4i}}^3+315{C_{4i}}^4)]$

$M_{8i}=\frac{1}{396{{\mathrm{\β}}_i}^7}[{C_{1i}}^{3/2}(16+24C_{2i}+30{C_{2i}}^2+35{C_{2i}}^3+315{C_{2i}}^4$

$-2079{C_{2i}}^5+3003{C_{2i}}^6)$

$-{C_{3i}}^{3/2}(16+24C_{4i}+30{C_{4i}}^2+35{C_{4i}}^3+315{C_{4i}}^4$

$-2079{C_{4i}}^5+3003{C_{4i}}^6\left)\right]$

$M_{10i}=\frac{1}{11520{{\mathrm{\β}}_i}^9}[{C_{1i}}^{3/2}(128+192C_{2i}+240{C_{2i}}^2+280{C_{2i}}^3+$

$315{C_{2i}}^4-2772{C_{2i}}^5+42042{C_{2i}}^6-128700{C_{2i}}^7+109395{C_{2i}}^8)$

$-{C_{3i}}^{3/2}(128+192C_{4i}+240{C_{4i}}^2+280{C_{4i}}^3+$

$315{C_{4i}}^4-2772{C_{4i}}^5+42042{C_{4i}}^6-128700{C_{4i}}^7+109395{C_{4i}}^8\left)\right]$

Wherein,

${\mathrm{\α}}_i=\frac{A_{2i}}{A_{1i}}$ ${\mathrm{\β}}_i=\frac{L_i}{A_1}$

$C_{1i}=\frac{1}{1+{{\mathrm{\β}}_i}^2}$ $C_{2i}=\frac{{{\mathrm{\β}}_i}^2}{1+{{\mathrm{\β}}_i}^2}$ $C_{3i}=\frac{{{\mathrm{\α}}_i}^2}{{{\mathrm{\α}}_i}^2+{{\mathrm{\β}}_i}^2}$ $C_{4i}=\frac{{{\mathrm{\β}}_i}^2}{{{\mathrm{\α}}_i}^2+{{\mathrm{\β}}_i}^2}$

A _1iBe the internal diameter of i coil, A _2iBe the external diameter of i coil, L _iBe half length of i coil;

(2.1) described method is calculated each rank Legendre coefficient in described preceding 10 rank of all column type coils then, set by step;

Then, calculate each rank Legendre coefficient M of described magnetic resonance image-forming superconducting magnet ₀, M ₂... M ₁₀During calculating, remember that each coil current density amplitude is | J _i|=J, the coil of note radius minimum is the Line 1 circle, and each rank Legendre coefficients of other each coils is carried out electric current and internal diameter by its conversion summation, and is as follows:

$M_j=\underset{i=1}{\overset{K}{\mathrm{\Σ}}}\mathrm{sign}\left(J_i\right)M_{\mathrm{ji}}{\left(\frac{A_{11}}{A_{1i}}\right)}^{j-1},$

Wherein, M _j, j=0,2 ... 10 is magnet Legendre coefficient, A ₁₁Be Line 1 circle internal diameter, A _1iBe i internal coil diameter, M _JiBe the j rank Legendre coefficient of i coil, sign (J _i) i the direction of the winding current symbol of expression, K is the coil number;

Be calculated as follows central magnetic field intensity B again,

B＝μ ₀JA ₁M ₀；

Be calculated as follows uniformity of magnetic field H again,

H＝k ₂M ₂ ²+k ₄M ₄ ²+…+k ₁₀M ₁₀ ²，

Wherein, μ ₀Be air permeability, J is the current density amplitude, A ₁Be inner coil internal diameter, weighting coefficient k ₂, k ₄..., k ₁₀Be setting value;

Step (2.2), described magnetic resonance image-forming superconducting magnet resolve into comprise electric current in the same way or the column type coil of current reversal after interior coil combination, use the Legendre method of development of described solenoid outside to calculate described stray magnetic field scope S as follows:

At first, to each column type coil, calculate preceding 6 rank odd Legendre expansion coefficients; With i coil is example, its preceding 6 rank odd Legendre coefficient N _1i, N _3i, N _5i, be shown below:

$N_{1i}=\frac{1}{3}(1-{\mathrm{\α}}_i){\mathrm{\β}}_i{D}_{1i}$

$N_{3i}=-\frac{1}{30}(1-{\mathrm{\α}}_i){\mathrm{\β}}_i({9D}_{2i}-20D_{1i}{{\mathrm{\β}}_i}^2)$

$N_{5i}=\frac{1}{56}(1-{\mathrm{\α}}_i){\mathrm{\β}}_i({15D}_{3i}-{84D}_{2i}{{\mathrm{\β}}_i}^2+56D_{1i}{{\mathrm{\β}}_i}^4)$

Wherein,

${\mathrm{\α}}_i=\frac{A_{2i}}{A_{1i}}$ ${\mathrm{\β}}_i=\frac{L}{A_{1i}}$

$D_{1_i}=1+{\mathrm{\α}}_i+{{\mathrm{\α}}_i}^2$ D _2i＝1+α _i+α _i ²+α _i ³+α _i ⁴

D _3i＝1+α _i+α _i ²+α _i ³+α _i ⁴+α _i ⁵+α _i ⁶

A _1i, A _2iAnd L _iImplication is the same;

(2.2) described method is calculated each rank Legendre coefficient of all column type coils then, set by step;

Then, calculate the algebraic sum of each rank Legendre coefficient of all column type coils, use N ₁, N ₃, N ₅Expression; During calculating, remember that each coil current density amplitude is | J _i|=J, the coil of note radius minimum is the Line 1 circle, and each rank Legendre coefficients of other each coils is carried out electric current and internal diameter by its conversion summation, and is as follows:

$N_j=\underset{i=1}{\overset{K}{\mathrm{\Σ}}}\mathrm{sign}\left(J_i\right)N_{\mathrm{ji}}{\left(\frac{A_{1i}}{A_{11}}\right)}^{j+3},$

Wherein, N _j, j=1,3,5 is magnet Legendre coefficient, N _JiBe the j rank Legendre coefficient of i coil, other implications are the same;

Calculate stray magnetic field scope S again:

S＝l ₁N ₁ ²+l ₃N ₃ ²+l ₅N ₅ ²，

Wherein, l ₁, l ₃, l ₅Be weighting coefficient, be setting value;

Step (2.3) is calculated as follows superconducting coil with line amount L:

L＝V/S _cr，

Wherein, V is the coil cumulative volume, S _CrBe sectional area of wire;

Step (2.4) is calculated as follows magnet robustness coefficients R;

Step (2.4.1), (2.1) described method set by step, the calculation optimization variable does not have the uniformity of magnetic field H ' when making error;

Step (2.4.2), (2.1) described method set by step, there is the uniformity of magnetic field H when making error in the calculation optimization variable ";

Step (2.4.3) is calculated as follows and makes the error robustness coefficients R,

R＝|H′-H″|；

Step (3) is optimized described objective function with simulated annealing, and its step is as follows:

Step (3.1) to computing machine input simulated annealing initial parameter, comprising: initial temperature, final temperature, temperature decline rate, maximum search number of times under the same temperature, step-size in search, variable initial value; The variable initial value is changed to current separating and optimum solution, and calculates its target function value;

Step (3.2) is searched for new explanation in the current neighborhood of separating; Neighborhood is defined as in the solution space, is the center with current separating, in its component one or several amplitude that step-size in search is set (as former variate-value 10%) in the zone of random variation;

Step (3.3), the target function value of COMPUTER CALCULATION new explanation correspondence;

Step (3.4), the constraint of COMPUTER CALCULATION new explanation correspondence is if employing adds penalty function method punishment above constraint then to objective function; Constraint condition is dimension constraint, if there is the situation that surpasses setting value in each component of new explanation, then is considered as surpassing constraint; When needs limit the particular characteristic index, also it can be treated to constraint condition, use the method identical to calculate, if surpass setting value then punish with respective items in the objective function; The method that use adds penalty function method punishment is as follows:

f ₂＝f ₁+Δ，

Wherein, f ₁Be former target function value, f ₂For punishing the back target function value, Δ is the punishment amount;

Step (3.5), judging whether to accept new explanation according to the Metropolis criterion is current separating, and the record optimum solution; The Metropolis criterion is as follows:

Wherein, x ₁Be new explanation, x ₂Separate for current, T is a Current Temperatures, rand _[0,1]Be the random number between [0,1];

Step (3.6), if the maximum search number of times reaches setting value under the same temperature, then temperature descends, otherwise returns (3.2);

Step (3.7), algorithm stops if temperature reaches final temperature, the output optimum solution, otherwise return (3.2).

2, the discretize optimization method of a kind of magnetic resonance image-forming superconducting magnet design according to claim 1 is characterized in that when the robustness coefficient of calculating magnetic field uniformity coefficient, the variable quantity of optimization variable is 0.5mm or 1mm.

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