WO2001007972A1

WO2001007972A1 - Method and device for designing a technical system

Info

Publication number: WO2001007972A1
Application number: PCT/DE2000/002403
Authority: WO
Inventors: Claus Hillermeier; Stefan SCHÄFFLER
Original assignee: Siemens Aktiengesellschaft
Priority date: 1999-07-23
Filing date: 2000-07-24
Publication date: 2001-02-01

Abstract

The invention concerns an operating point for designing a technical system which is defined by iteration, a present operating point being determined in the direction of a gradient whereto is superposed a random value. If the present operating point is located outside the permissible range, it is projected into said permissible range.

Description

description

Process and arrangement for the design of a technical system

The invention relates to a method and an arrangement for designing a technical system.

For the design of a complex technical system, significant sizes of this system are already in an early planning phase, e.g. Cost of manufacture or efficiency during the runtime, of great interest. The system is often implemented on the basis of empirically known parameters (design parameters).

Furthermore, operating parameters for operating the already existing technical system are often to be adapted. This adjustment (setting) is mostly based on specialist knowledge.

It is disadvantageous that both the design and the setting of the technical system are based only on empirical knowledge.

The object of the invention is to provide a method and an arrangement which avoids the disadvantages described above and thus ensures that an efficient design or adjustment takes place automatically for a complex technical system.

This object is achieved in accordance with the features of the independent claims. Further developments result from the dependent claims.

A target function is given as a function that specifies a target variable, for example the cost or efficiency of the technical system, depending on predetermined parameters of the system. Such parameters can be design parameters or drive parameters. The target function comprises a predetermined set n parameters, which are combined in a parameter vector x:

xi, * 2 '• • •' ^x n> ⁼ ≥ ^{T (1) •}

The superscript "T" indicates that the vector x has been transposed.

Dimensions of the technical system are an example of design parameters, while operating parameters preferably indicate adjustable sizes.

The target function f depends on n parameters, so the n parameters span a space R. Not all possible combinations of values for the n parameters are permissible in this space R. In many cases, the technical system would either reach a safety-critical state or not respond appropriately to an impermissible value assignment of the parameters. Accordingly, a space D ς: R ^{n is} determined, which is a (real) subset of the space R. All admissible combinations of parameter assignments are summarized in room D. In the following, these permissible combinations of value assignments are also referred to as working points (= valid design or operating parameters of the technical system).

A working point in space D should now be determined, which represents an "efficient" (working) point there. An efficient working point is characterized by the fact that no parameter of this working point can be changed without a deterioration of the associated objective function. The efficient working point thus represents at least a local optimum of a value assignment of the parameters of the parameter vector in the space of the parameter vectors (working points) predetermined as permissible. The subsequent labeling of a draft of a technical system includes both an interpretation, i.e. the draft related to a new creation, and an adaptation of an already existing system. The efficient operating point to be determined characterizes the design or setting of the technical system, which results in optimized operation of the same.

To solve the problem, a method for designing a technical system is specified, which technical system comprises a number of valid operating points. The process comprises the following steps:

a) A target function is specified for the technical system, which is influenced by a parameter vector x with n parameters.

b) A gradient of the target function overlaid with a random variable is determined with respect to the parameter vector x.

c) A new parameter vector x _n is determined, starting from the parameter vector x, by moving in the direction of the gradient overlaid with the random variable with a predetermined step size.

d) On the basis of predetermined secondary conditions, it is checked whether the new parameter vector x _{n is} a valid working point (in room D described above) or whether an abort condition is fulfilled.

e) If the new parameter vector x _{n is} not a valid working point, ie is not in space D of all permissible working points, and the termination condition is not met, the new parameter vector x _{n is} projected into space D and the projected parameter vector as new Parameter vector x _n used. The program then branches to step b).

f) If the new parameter vector x _{n is} a valid operating point and the termination condition is not met, the new parameter vector x _{n is used} as the parameter vector x and a branch is made to step b).

g) If the termination condition is met, the determined parameter vector is used as the operating point for the design of the technical system.

With the described method, it is thus possible to determine an efficient working point from a space D of permissible working points. This efficient operating point can include both operating parameters or design parameters of the technical system.

A further development consists in the fact that the projection takes into account secondary conditions. There may be several additional conditions that must be taken into account when determining the operating point. A constraint is formulated too

h _x (x) <0 (1),

where h _j _ (x) denotes a constraint i for the parameter vector x.

According to one embodiment, a step size can be halved in addition to the projection into the space of permissible working points. The iterative determination of a respective next parameter vector x _n results in a path that leads from a start parameter vector to an efficient point. The path is continued from one parameter vector to the next with a specified length. This predetermined length (= step size) can be shortened, in particular halved, if the next parameter vector outside of space D lies. If by then the next parameter vector still au ^¬ ßerhalb the space D so again shortening and / or the projection can take place.

If, as part of a further development, the new parameter vector x _{n has} less than a predetermined minimum distance from the edge of space D, the following steps are carried out:

a) If a subsequent parameter vector leads out of space D, a plumb line is dropped from this subsequent (outside of space D) vector vector onto a tangential plane of the edge of the permissible space D and the subsequent parameter vector is defined there.

b) Otherwise, the following parameter vector is not changed if it is not outside of space D.

An additional development consists in the fact that the termination condition is fulfilled when a predetermined number of iterations has been carried out.

Another development is that the termination condition is met when the gradient falls below a predetermined threshold. If a negligibly small improvement is achieved (repeatedly) with a new parameter vector along the path, the method is ended automatically.

It is also a further development of the invention that the working point from a set of working points is determined as the efficient working point which concludes the method and which leads quantitatively, used in the respective objective function, to the best result. For this purpose, the working points determined step by step in the method are temporarily stored, so that the best of all stored working points can be determined in a final comparison. In particular, it is useful to sort the working points determined in this way according to their quality, in order to be able to switch to a next best working point if a design or adjustment of a technical system is not desired or cannot be implemented.

Finally, it is also a further development that the technical system is implemented on the basis of the efficient working point found. For example, a power plant is built according to the design parameters that are the result of one of the described methods, or an existing power plant is set according to the operating parameters determined by the parameters.

In the context of an additional embodiment, the gradient of the target function overlaid with a random variable is given by

dx = -Vf (x) dt + ε • dB (2),

where x is the parameter vector,

-Vf (x) the negative gradient of the objective function f, depending on the parameter vector x, ε a scaling constant of the random variable B and

B denote the random size.

To solve the problem, an arrangement for designing a technical system is also specified, which technical system comprises a number of valid operating points. The arrangement has a processor unit which is set up in such a way that

a) the technical system comprises a target function, which target function is derived from a parameter vector x with n parameters ter values can be influenced;

b) a gradient of the target function with respect to the parameter vector x superimposed with a stochastic variable can be determined;

c) a new parameter vector x _{n can be determined} starting from the parameter vector x with a predetermined step size in the direction of the gradient superimposed with a random variable;

d) it can be checked on the basis of predetermined auxiliary conditions whether the new parameter vector x _{n is} a valid operating point or whether an abort condition is fulfilled;

e) if the new parameter vector x _{n is} not a valid working point and the termination condition is not met, a projection of the new parameter vector x _n into the space of valid working points is carried out and branching to step b);

f) if the new parameter vector x _{n is} a valid working point and the termination condition is not met, this new parameter vector x _{n is set} as parameter vector x and a branch is made to step b);

This arrangement is particularly suitable for performing the method according to the invention or one of its developments explained above.

Further developments of the invention also result from the dependent claims. _A execution examples of the invention are illustrated and explained below with reference to the drawing.

Show it

Fig.l is a sketch representing a space D c R ⁿ ;

Fig.2 is a sketch that shows a section of Fig.l and shows what each an invalid parameter vector

(outside of room D) and is a valid working point;

3 shows a sketch which shows how an area D is determined by several secondary conditions;

4 shows a first possibility for a projection of the next parameter vector into the area D;

5 shows a second possibility for a projection of the next parameter vector into the area D;

Fig. 6 is a flowchart illustrating a first method of designing a technical system;

7 shows a processor unit.

Figure 1 shows a sketch representing a space D c R ⁿ . For reasons of clarity, a dimension n = 2 is selected, the "space" thus corresponds to one level. In real systems and systems, a high-dimensional space is generally used; the influences of the parameters on the target function f are highly complex in this space and can often only be determined using a computer simulation. In this way, a function value f (x) is checks whether it is in the permissible area D of the operating points or not.

In the present case of FIG. 1, the clarity of the two-dimensional representation clearly explains the relationship. The transfer into an n-dimensional space (n> 2) takes place analogously.

As mentioned, a level is spanned by parameters xi and X2. The parameters are accepted as positive without restriction. The parameters xi and X2 are combined in a parameter vector x. Furthermore, the area D (here an area since n = 2; if n> 2 D is a space) is drawn in which part of the total x, X2 ~ area (

2 characterized by R). A parameter vector x lying within the area D is a valid operating point, outside the area D the parameter vector x contains an invalid value assignment of its parameters x and X2 for the technical system.

A parameter vector xo ^with the parameters (coordinates) xio and X20 represents a starting point. A path Pf, which shows a possible course to an efficient working point, ends at a point x_. Starting from this point xi, a next direction with a predetermined length points to a point outside the area D. How to proceed in such a case is shown in FIGS. 2 and 3 and is explained below.

It should be noted here that the course of the path Pf is shown in FIG. 1 as a continuous course, but in fact it is discrete in sections, that is to say in each section in a determined direction with a predetermined step size. If the sections are chosen to be sufficiently small, the path Pf appears as a continuous curve. As already mentioned, it is not always possible to determine the functional value of the objective function analytically. In many cases, this function value is calculated for any given value assignment of the parameter vector using a simulator with any effort. The result provides a value for the parameter vector, which (generally) represents a point in space R. This point is checked to see whether it is in the range of the valid working points D. The further steps are described in detail below. It is only important in this context that it does not matter how the function values are obtained. Most of them cannot be determined analytically.

Figure 2 shows the detail 101 from Figure 1 enlarged. Again, the space D (here a surface) and the point xi can be seen. A part of the path Pf that led to the point x ^ is also shown. The path Pf here comprises several discrete sections.

Starting from point i 201, a new direction 204 is now determined, which points to a point 202 with a predetermined length. The point 202 lies outside the area D of the permissible operating points. Accordingly, the point 202 does not become part of the path Pf. In order to obtain a valid point via which the path Pf can be continued, the point 202 is discarded and a point (eg point 203) along which the path within the Area D can continue. How an admissible point 203 is determined from an impermissible point 202 is explained below.

A region D is shown by way of example in FIG. 3, which is determined by a plurality of secondary conditions hi, h2 and I13. The parameter vector x lies in this area D and is therefore a permissible assignment, since all secondary conditions for this parameter vector x are fulfilled. Figure 4 shows a projection of a lying outside the area D parameter vector Xi ₊ 1 ^'to the parameter vector x 401 is a new parameter vector X ₊ ι 402 is determined, the outside of the area D indicated by the limiting secondary condition HJ_ lies. The point 402 (parameter vector x_i ₊ ι) is projected onto the edge of the area D, so the point 403 results as a valid new parameter vector i ₊ i. This ensures that the path Pf does not leave the area D. The projection is carried out by dropping the solder onto a tangent (in the case n> 2: tangential plane) through the point xi, the intersection of the solder with the edge of D determining the point 403.

An alternative projection is shown in FIG. 5. Starting from a point 501, the subsequent point 502 is projected into the area D, in that at 502 the solder is dropped onto the route from point 501 to point 502. The intersection with the area boundary hi defines point 503 as the new, permissible parameter vector following point 501.

Furthermore, an edge R is determined for the area D at a predetermined distance from the area boundary, which is given by the respective secondary condition hi. If a next parameter vector lies in the area between the edge R and the area boundary hi, a projection is already taking place in order to deflect a next point from area D with a high degree of certainty.

FIG. 6 shows steps of a flow chart for designing a technical system, in particular for determining the operating point of the same.

In step 601 there is a target function, which target function is influenced by a parameter vector x with a number n parameters. In a subsequent step 602, preferably starting from a start Parameter vector xrj determined a gradient of the target function superimposed with a random variable. In a step 603, a predetermined step size is used in the direction of the gradient superimposed on the random variable, and a new parameter vector x _n results. If an abort condition is fulfilled (cf. step 604), ie if a predetermined limit for a number of iteration steps has already been exceeded, the method is ended in a step 608 and the best working point from a set of valid working points determined using the method becomes certainly. If, on the other hand, the termination condition in step 604 has not (yet) been fulfilled, a query is made in step 605 as to whether the newly determined parameter vector x _{n is} a valid working point, that is to say whether the parameter vector x _{n is} in space D. If this is the case, then the new parameter vector x _{n is set} as parameter vector x (cf. step 607) and a jump is made to step 602. If, on the other hand, this is not the case, a projection takes place in a step 606 (as described above), the projected parameter editor is set as the new parameter vector (cf. step 607) and a branch is made to step 602.

A processor unit PRZE is shown in FIG. The processor unit PRZE comprises a processor CPU, a memory SPE and an input / output interface IOS, which is used in different ways via an interface IFC: an output on a monitor MON becomes visible and / or on via a graphic interface output to a printer PRT. An entry is made using a mouse MAS or a keyboard TAST. The processor unit PRZE also has a data bus BUS, which ensures the connection of a memory MEM, the processor CPU and the input / output interface IOS. Furthermore, additional components can be connected to the data bus BUS, e.g. additional memory, data storage (hard disk) or scanner.

Claims

claims

1. Procedure for designing a technical system, which technical system comprises a set of valid working points,

a) in which the technical system comprises a target function, which target function is influenced by a parameter vector x with n parameter values;

b) in which a gradient of the target function with respect to the parameter vector x is overlaid with a stochastic variable;

c) in which a new parameter vector x _{n is determined} starting from the parameter vector x with a predetermined step size in the direction of the gradient superimposed with a random variable;

d) in the case of which it is checked on the basis of predetermined secondary conditions whether the new parameter vector x _{n is} a valid operating point or whether an abort condition is fulfilled;

e) in which, if the new parameter vector x _{n is} not a valid working point and the termination condition is not met, a projection of the new parameter vector x _n into the space of valid working points is carried out and branching to step b);

in which, if the new parameter vector x _{n is} a valid operating point and the termination condition is not met, this new parameter vector x _{n is set} as parameter vector x and branched to step b); g) in which, if the termination condition is met, the determined parameter vector is used as the operating point for the design of the technical system.

2. The method according to claim 1, wherein the projection is carried out by determining one of the secondary conditions that the new parameter vector x _n does not meet and the new parameter vector x _{n is} modified such that

hi (x) <0

applies, where hi (x) denotes a secondary condition i for the parameter vector x.

3. Method according to one of the preceding claims, in which, in addition to the projection, a step size is halved by modifying the new parameter vector x _{n in} such a way that the step size is shortened to a predetermined part.

4. The method of claim 3, wherein the predetermined part is half.

5. The method according to claim 3 or 4, in which the step size halving is applied iteratively, so that there is a gradual approach to an area marked by the secondary conditions as a permissible space.

6. The method as claimed in claim 5, in which the following steps are carried out when the new parameter vector x _n falls below a predetermined distance from the edge of the permissible space: Parameter _vector x _nn plumb a tangential plane of the edge of the permissible space is dropped and the new parameter vector x _{n is} defined there; b) if the next step does not lead outside the permissible space, new parameter vector x _n is thereby determined.

7. The method according to any one of the preceding claims, wherein the termination condition is met if a predetermined number of iterations has been carried out.

8. The method according to any one of the preceding claims, wherein the termination condition is met when the gradient falls below a predetermined threshold.

9. The method as claimed in one of the preceding claims, in which the working point for the design of the technical system is that of a plurality of determined working points which has the best quantitative functional value.

10. The method according to any one of the preceding claims, in which the technical system is implemented on the basis of the operating point.

11. The method according to any one of the preceding claims, wherein the gradient of the objective function with respect to the parameter vector x, superimposed with a random variable, is determined by

dx = -Vf (x) dt + ε ^• dB,

where x is the parameter vector,

B the random size describe.

12. The method according to any one of the preceding claims, wherein the parameter vector contains operating points and / or design points of the technical system.

13. Arrangement for the design of a technical system, which technical system comprises a number of valid operating points, with a processor unit which is set up in such a way that

a) the technical system comprises a target function, which target function can be influenced by a parameter vector x with n parameter values;

c) a new parameter vector x _{n can be determined} starting from the parameter vector x with a predetermined step size in the direction of the gradient overlaid with a random variable;

e) if the new parameter vector x _{n is} not a valid working point and the termination condition is not met, a projection of the new parameter vector x _n into the space of valid working points is carried out and branching to step b); f) if the new parameter vector x _{n is} a valid operating point and the termination condition is not met, this new parameter vector x _{n is set} as parameter vector x and a branch is made to step b);