CN102778842A - Method for preparing product based on parameter optimization - Google Patents

Abstract

The invention provides a method for preparing a product based on parameter optimization, wherein a lagrangian function which takes a parameter to be optimized as an independent variable based on the optimization goal of the parameter to be optimized and constraint conditions at first; next, a self-adaptive annealing algorithm is adopted for the lagrangian function to optimize the parameters in order that an optimal solution of the parameter to be optimized is obtained; and at last, a corresponding product is prepared based on the obtained optimal solution of the parameter to be optimized. With the adoption of the method provided by the invention, the problem about overall optimization containing any nonlinear constrain can be treated.

Description

Come the method for preparing product based on parameter optimization

Technical field

The present invention relates to a kind of product preparation method and system, particularly a kind of method and system of coming preparing product based on parameter optimization.

Background technology

Along with the development of technology, all kinds of high in technological content products also arise at the historic moment.For most of high-tech products, it all need pass through accurate design, with practical requirement before preparation.For example, be applied to the ultra magnetic conductor of nuclear resounce imaging system,, how design magnet and make the utilization factor maximization of these superconducting lines just become particularly important because the cost of superconducting line is very high.Usually, superconducting magnet is divided into several coils, and the physical dimension of these coils and position all are difficult to confirm, and their numerical value change is very sensitive to the magnet effect.In addition; Simultaneously must guarantee also that again magnet uniformity coefficient, 5 gaussian lines, critical field etc. satisfy particular requirement minimizing cost. so; The global optimization that how obtains correlation parameter based on these non-linear constrain conditions is separated; So that it is can separate according to this global optimization and prepare corresponding superconducting magnet, especially crucial for superconducting magnet prepares enterprise.

In existing SUPERCONDUCTING MAGNET DESIGN, parameter optimization mainly contains following several kinds of modes:

1, be in the patent documentation of WO 2006/065027 at application number; Proposed to carry out in two steps magnet design; The first step utilizes in the past that experience is optimized the related parameter that has that relates to magnet structure, and second step was that condition is optimized the related parameter that has that relates to magnet stability with coil stress.The drawback of the method is need be by magnet design experience in the past, and the optimization solution that is obtained locally optimal solution just often, and efficient is lower.

2, adopt genetic algorithm to carry out parameter optimization, though the Optimization result that the method obtains is overall, this Optimization result is very sensitive to initial value, and the method operate in the parallel system just more efficient because the time that needs to spend is longer.

3, people such as L.Ingber has proposed a kind of employing adaptive modeling annealing method (ASA) and has carried out parameters optimization method; Though this method efficient is high and optimal speed is fast; But can not handle the optimization problem that comprises any non-linear constrain, thereby cause its application very limited.

Therefore, press for existing parameter optimization method is improved,, and then prepare corresponding superconducting magnet so that can the parameter under any non-linear constrain condition be optimized.

Summary of the invention

The object of the present invention is to provide a kind of method of coming preparing product, so that can handle the global optimization problem that comprises any non-linear constrain based on parameter optimization.

Reach other purposes in order to achieve the above object; Method of coming preparing product based on parameter optimization provided by the invention comprises step: 1) based on Parameter Optimization target to be optimized, and constraint condition to form with parameter to be optimized be the Lagrangian function of independent variable; 2) to said Lagrangian function, adopt the self-adaptation annealing algorithm to carry out Parameter Optimization, separate to obtain Parameter Optimization to be optimized; And 3) separate based on the Parameter Optimization to be optimized that is obtained and prepare corresponding product.

In sum; Method of coming preparing product based on parameter optimization of the present invention is based on generation Lagrangian functions such as optimization aim, constraint conditions; Carry out parameter optimization on this basis; Can handle the global optimization problem that comprises any non-linear constrain thus, it is greatly convenient that each production enterprise is obtained.

Description of drawings

Fig. 1 is the process flow diagram that comes the method for preparing product based on parameter optimization of the present invention.

Embodiment

See also Fig. 1, of the present inventionly come ten thousand methods of preparing product may further comprise the steps based on parameter optimization:

At first, based on Parameter Optimization target to be optimized, and constraint condition to form with parameter to be optimized be the Lagrangian function of independent variable.

For example, for parameter to be optimized: x=(x ₁, x ₂... x _n), wherein, U _i≤x _i≤V _i, i=1,2......n, optimization aim is: minimize f (x ₁, x ₂... x _n), constraint condition comprises: h (x)=[h ₁(x), h ₂(x) ... h _n=0 and g (x)=[g (x)] ₁(x), g ₂(x) ... g _l(x)]≤0, then can form Lagrangian function and be: L (x, λ)=f (x)+H (x, λ)+G (x, λ), wherein,

λ and r is the Lagrange multiplier.

More specifically say it, for example, prepare one 4 coil superconducting magnet if desired, require its PkPk＜15ppm, humorous A10=15 of ball, A30=30, independent variable to be optimized comprises: A1, B1, A2, B2 (coil 1); A1, B1, A2, B2 (coil 2), A1, B1, A2, B2 (coil 3), A1, B1, A2, B2 (coil 4), wherein, A1, A2 represent in coil is respectively, the outermost radius; B1, B2 are respectively coil minimum, maximum position in the axial direction; Thus, based on aforementioned requirement, can confirm:

1, optimization aim is: minimize

Wherein, Xi is an independent variable to be optimized, X1, and X2, X3, X4 represent the A1 of coil 1, A2, B1, B2 respectively; X5, X6, X7, X8 represent the A1 of coil 2, A2, B1, B2 respectively; X9, X10, X11, X12 represent the A1 of coil 3, A2, B1, B2 respectively; X13, X14, X15, X16 represent the A1 of coil 4 respectively, A2, B1, B2, Len (Xi) they are the superconducting line total length function of each coil;

2, constraint function is:

G (x)=[g ₁(x), g ₂(x), g ₃(x), g ₄(x)], wherein, g _j(x)=Pk _jPk _j-15≤0, j=1,2,3,4, h (x)=[h ₁(x), h ₂(x), h ₃(x), h ₄(x)], wherein, h _j(x)=(A ^j ₁₀-15) ²+ (A ^j ₃₀-15) ²=0, j=1,2,3,4,

Wherein, Pk _jPk _jBe the sign amount of the magnet uniformity coefficient of coil j, i.e. Peak-Peak can be by A1, A2, and B1, B2 calculates, A ^j ₁₀Magnetic field H armonics item for coil j

Abbreviation; A ^j ₃₀Magnetic field H armonics item for coil j

Abbreviation.Thus, based on above-mentioned optimization aim and constraint function, the Lagrangian function of formation does;

$L(x,\mathrm{\λ})=\underset{i=1}{\overset{16}{\mathrm{\Σ}}}\mathrm{Len}\left(\mathrm{Xi}\right)+\underset{j=1}{\overset{4}{\mathrm{\Σ}}}\frac{1}{2}r{[{({A^j}_{10}-15)}^2+{({A^j}_{30}-15)}^2]}^2+\stackrel{j=1}{\mathrm{\Σ}}\frac{1}{2r}[{(\max (\mathrm{\λ}+r({\mathrm{Pk}}_j{\mathrm{Pk}}_j-15),0)}^2-{\mathrm{\λ}}^2]$

Then,, adopt the self-adaptation annealing algorithm to carry out Parameter Optimization, separate to obtain Parameter Optimization to be optimized to said Lagrangian function.

As a kind of optimal way, for Lagrangian function: L (x, λ)=f (x)+H (x, λ)+(x λ), can carry out Parameter Optimization according to existing self-adaptation annealing algorithm to G.

As another kind of optimal way, for Lagrangian function: L (x, λ)=f (x)+H (x, λ)+G (x, λ), can adopt following generation function to confirm the next iteration variable:

x _i，k+1＝x _i，k+y _i(V _i-U _i)，

Wherein, y _i∈ [1,1], x _{I, k}Be current iteration variable, U _iWith V _iBe respectively variable x _iCoboundary and lower boundary, factor y _iCan select at random, also can confirm based on following probability density function:

Wherein, annealing temperature T _i(k)=T _0iExp (c _ik ^1/D), C _i=m _iExp (n _i/ D), T _0iBe initial temperature, m _i, n _iBe and preestablish, D is for optimizing degree of freedom.

And whether can be accepted as new optimization solution for determined iteration variable next time, the judgment criterion that is adopted comprises:

exp[-(L(x _k+1)-L(x _k))/T _cost]＞U，

Wherein, and U ∈ [0,1), L (x _K+1) for based on next time the Lagrangian function value that iteration variable calculated, L (x _k) be the Lagrangian function value that is calculated based on the current iteration variable, T _CostFor the predefined value assessment factor, be used to control the complexity of accepting new explanation.

Thus, as cost function, annealing temperature, the probability density function of combining adaptive simulated annealing (ASA), accept the new explanation judgment criterion, can obtain Parameter Optimization to be optimized and separate based on Lagrangian function.

At last, separate based on the Parameter Optimization to be optimized that is obtained and prepare corresponding product.

For example, based on the parameter to be optimized that is obtained: A1, B1, A2, B2 (coil 1), A1, B1, A2, B2 (necklace 2), A1, B1, A2, B2 (coil 3), A1, B1, A2, B2 (necklace 4), optimization solution, can prepare corresponding 4 coil superconducting magnets.

In addition, in order to raise the efficiency, when adopting the self-adaptation annealing algorithm to be optimized, after iteration is carried out preset times, also can adjust annealing temperature, that is: based on following mode

Each variable to be optimized is obtained the differential s of Lagrangian function earlier _i:

$s_i=\frac{\∂L}{\∂x_i}$

Then, again based on the maximal value s of differential _Max=max (S ₁, S ₂..S _n) calculate annealing temperature, that is:

With k=s _Max/ s _iSubstitution T _i(k)=T _0iExp (c _ik ^1/D) calculate and obtain T _i(k).

In sum; The adaptive modeling annealing algorithm that comes the method for preparing product based on the band non-linear constrain based on parameter optimization of the present invention; Can handle the global optimization problem that comprises any non-linear constrain; For the parameter optimization of superconducting magnet provides a kind of efficient optimization method, and then can satisfy various demands.

The foregoing description is just listed expressivity principle of the present invention and effect is described, but not is used to limit the present invention.Any personnel that are familiar with this technology all can make amendment to the foregoing description under spirit of the present invention and scope.Therefore, rights protection scope of the present invention should be listed like claims.

Claims (7)

1. method of coming preparing product based on parameter optimization is characterized in that comprising step:

1) based on Parameter Optimization target to be optimized, and constraint condition to form with parameter to be optimized be the Lagrangian function of independent variable;

2) to said Lagrangian function, adopt the self-adaptation annealing algorithm to carry out Parameter Optimization, separate to obtain Parameter Optimization to be optimized;

3) separate based on the Parameter Optimization to be optimized that is obtained and prepare corresponding product.

2. method of coming preparing product based on parameter optimization as claimed in claim 1 is characterized in that: for parameter to be optimized: x=(x ₁, x ₂... x _n), wherein, A _i≤x _i≤B _i, i=1,2......n, optimization aim is: minimize f (x ₁, x ₂... x _n), constraint condition comprises: h (x)=[h ₁(x), h ₂(x) ... h _m=0 and g (x)=[g (x)] ₁(x), g ₂(x) ... g _l(x)]≤0, the Lagrangian function that then forms is: and L (x, λ)=f (x)+H (x, λ)+G (x, λ), wherein,

λ and r is the Lagrange multiplier.

3. method of coming preparing product based on parameter optimization as claimed in claim 1 is characterized in that: for parameter to be optimized: x=(x ₁, x ₂... x _n), wherein, A _i≤x _i≤B _i, i=1,2......n, said step 2) comprising: confirm next iteration variable: x in such a way _{I, k+1}=x _{I, k}+ y _i(B _i-A _i), wherein, y _i∈ [1,1], x _{I, k}Be the current iteration variable.

4. method of coming preparing product based on parameter optimization as claimed in claim 3 is characterized in that: based on probability density function be:

Confirm the factor y in the next iteration variable _i, wherein, annealing temperature T _i(k)=T _0iExp (c _ik ^1/D), C _i=m _iExp (n _i/ D), T _0iBe initial temperature, m _i, n _iAll preestablish, D is for optimizing degree of freedom.

5. method of coming preparing product based on parameter optimization as claimed in claim 4 is characterized in that: said step 2) also comprise: after iteration is carried out preset times, adjust annealing temperature based on following mode:

Each variable to be optimized is obtained the differential s of Lagrangian function _i:

$s_i=\frac{\∂L}{\∂x_i}$

Maximal value s based on differential _Max=max (S ₁, S ₂..S _n) calculate annealing temperature, that is:

With k=s _Max/ s _iSubstitution T _i(k)=T _0iExp (c _ik ^1/D) calculate and obtain T _i(k).

6. method of coming preparing product based on parameter optimization as claimed in claim 1 is characterized in that: said step 2) also comprise: confirm based on following judgment criterion whether iteration variable next time can be accepted as new optimization solution:

exp[-(L(x _k+1)-L(x _k))/T _cost]＞U，

Wherein, and U ∈ [0,1), L (x _K+1) for based on next time the Lagrangian function value that iteration variable calculated, L (x _k) be the Lagrangian function value that is calculated based on the current iteration variable, T _CostBe the predefined value assessment factor.

7. method of coming preparing product based on parameter optimization as claimed in claim 1 is characterized in that: said product comprises ultra magnetic conductor.

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