WO2001007973A1

WO2001007973A1 - Method and device for developing a technical system

Info

Publication number: WO2001007973A1
Application number: PCT/DE2000/002406
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 present invention relates to a method that involves determining in an iterative manner an efficient working point for developing a technical system, wherein a path is determined towards a gradient to which a random value has been added. When leaving a valid area, the path is progressively shortened or is diverted into the valid area.

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 a major disadvantage 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 of the invention also 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 of n parameters, which are combined in a parameter vector x:

X] _, X2, ..-, x _n ) ⁼ 2 ^{T (} 1 ⁾ •

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

The target function is a function n f: R → R x i → f (x).

Each optimization task can be understood as "find an x so that f (x) is minimal".

An example of design parameters are dimensions or parameters of the technical system, while operating parameters preferably indicate adjustable sizes.

The target function f depends on n parameters, and the n parameters therefore span a space R. Not all possible combinations of values for the n parameters are generally 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. As a result, a space D c 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 effective 3 cient working point is characterized by the fact that no parameter of this working point can be changed without causing 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, ie the draft relating 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 (predetermined) set of valid working points, which contains 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 with respect to the parameter vector x overlaid with a random variable is determined.

c) A new parameter vector x _n is started from the

Parameter vector x, determined with a predetermined step size in the direction of the gradient superimposed on the random variable.

d) It is checked whether the new parameter vector x _{n is} a valid working point and whether an abort condition is satisfied .

e) If the new parameter vector x _{n is} not a valid operating point and the termination condition is not met, the new parameter vector x _{n is} rejected and branched to step b).

f) If, on the other hand, 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} considered

Parameter vector x set and branched to step b).

g) If the termination condition is met, the determined operating point is used to design the technical system.

In particular, it is possible to use a simulation program to determine whether a certain working point is valid or not.

It should be noted here that a negative gradient is determined in the case of minimization tasks.

It is particularly advantageous that the room D is not left with valid working points when searching for an efficient point and that a suitable method at the (multidimensional) edge of the room D prevents the room D from being left. This is done by repeated determination of a new direction: the random size results in a random portion of the direction with each direction determination (= gradient + random size), so that a direction that no longer results after a manageable number of new direction determinations also at the edge of space D. points outside of room D and can therefore be used as a value assignment for the new parameter vector. Another solution to the problem is a method for designing a technical system, which technical system comprises a (predetermined) set of valid working points. This procedure includes the following steps:

b) A gradient of the superimposed with a random variable

Target function with regard to the parameter vector x is determined.

c) 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 on the random variable.

d) It is checked whether the new parameter vector x _{n is} a valid operating point and whether an abort condition is met.

e) If the new parameter vector x _{n is} not a valid operating point and the termination condition is not met, the step size that led to the new parameter vector x _n is shortened by a predetermined value and branched to step d).

f) If, on the other hand, 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 branched to step b).

g) If the termination condition is met, the determined operating point is used to design the technical system. Here, the direction in each iteration step is advantageously shortened (by a predetermined length) until there is no parameter vector outside the set of working points (= space D) along this direction with the shortened length. In particular, the predetermined length, which is moved along the direction, can be halved in each iteration step, so that after a manageable number of iteration steps, a parameter vector results that lies within the space D. If this shortened step only goes a very short distance and the parameter vector obtained in this way is close to the edge of space D, the proportion of the random variable results in a new direction when the direction is determined again, which with a sufficient probability is in a different direction than to the edge of room D.

The termination criterion mentioned several times above is intended to end the above-mentioned processes. If there is no termination criterion, this is equivalent to an termination criterion that cannot be met. In this case, the procedure does not terminate easily.

One embodiment of the invention is that the termination criterion is met when a predetermined number of iteration steps has taken place.

In this case, depending on the computing power of a computer on which the method is running, the predetermined number of iteration steps can be determined in such a way that, after a reasonable period of time, an operating point last determined by the method for the design or setting of the technical system is used.

Another development is that the termination criterion is met when the gradient falls below a predetermined threshold value, that is, an additional improvement on the way to the efficient working point is an insignificant assumes the extent. The importance of this extent depends on the specific application, which is why the threshold value can preferably be specified individually.

It is also a further development of the invention that that working point from a set of working points is determined as the efficient working point that concludes the method and that, quantitatively, used in the respective objective function, leads to the best result. For this purpose, the working points determined step by step in the method are preferably 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 feasible.

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 denotes a scaling constant of the random size B and B the random size.

Furthermore, there are two arrangements for solving the above-mentioned task, each of which has a processor unit, which is each set up in such a way that one of the methods described above can be executed on this processor unit.

The respective arrangement is particularly suitable for carrying out the individual methods according to the invention or one of its explained further developments.

Embodiments 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 ;

2 shows a sketch that shows a section of FIG. 1 and shows how a valid operating point is determined from an invalid parameter vector (outside of space D);

3 shows a sketch that shows a section of FIG. 1 and shows another possibility than FIG. 3 of how a valid operating point is determined from an invalid parameter vector (outside of space D);

Fig. 4 is a flowchart illustrating a first method of designing a technical system;

5 is a flowchart illustrating a second method of designing a technical system; 6 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. A working point x is thus checked in the high-dimensional space to determine whether it lies in the permissible area D of the working points or not.

In the present case of FIG. 1, the relationship can be clearly explained by the clarity of the two-dimensional representation. 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 x] _ and X2 are combined in a parameter vector x. The area D (here an area since n = 2; with n> 2 D is a space) is drawn in, which is part of the total x] _, X2 area (

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

A parameter vector xo ^with the parameters (coordinates) x] _o and X20 represents a starting point. A path Pf which shows a possible course to an efficient working point ends at a point xi. Starting from this point X_ points a next direction with a given length to one Point outside of area D. How to proceed in such a case 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 that (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. In particular, it cannot be stated analytically whether the working point x is a valid or an invalid working point.

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

Now a new direction 204 is determined from point xi 201, which points to a point 202 with a predetermined length. The point 202 lies outside the area D of the permissible operating points. Accordingly, point 202 does not become part of the path Pf. In order to obtain a valid point via the the path Pf can be continued, the point 202 is discarded and another component of the path is determined again. Another direction 205 results, which ends with the predetermined length in a point 203 which lies within the area D and is therefore a next valid parameter vector xi ₊ i. If no point had been found in area D even if the direction had been determined again, the direction determination would have been repeated until an abort condition would have ended the method or a next valid parameter vector would have been found. The exact sequence of the method is explained in more detail in the explanation of FIG. 4.

Another possibility of determining a valid parameter vector when a current parameter vector lies outside of region D is shown in FIG. 3.

As in FIG. 2, the detail 101 and the point xi from FIG. 1 are also shown in FIG. Along a new direction with a predetermined length, the point x ^ 301 results in a point 302 which lies outside the region D. Now the step size from point 301 to point 302 is iteratively shortened by a predetermined factor until a point 305 results which lies within the area D and thus represents a valid parameter vector xι ₊ ι. In FIG. 3, the step size is halved iteratively, a point 303 results from point 302, then a point 304 and finally point 305. From the valid parameter vector x_i + ι 305, a next point x_i ₊ 2 follows on the basis of a next direction determination 306 in path Pf. This point 306 is again a point in area D, the iterative step size halving is omitted.

FIG. 4 shows steps of a flow chart for the design of a technical system, in particular for determining the operating point of the same. In step 401 there is a target function, which target function is influenced by a parameter vector x with a number n parameters. In a subsequent step 402, preferably starting from a start parameter vector xo, a gradient of the target function overlaid with a random variable is determined (direction determination, in particular using equation (2)). In a step 403, a predetermined step size is used in the direction of the negative gradient, that is to say multiplied by “-1”, overlaid with the random variable, and a new parameter vector x _n results. If an abort condition is met (cf. step 404), ie if a predetermined limit for a number of iteration steps has already been exceeded, the method is ended in a step 408 and the best operating point from a set of valid operating points determined using the method becomes certainly. If, on the other hand, the termination condition in step 404 has not (yet) been fulfilled, a query is made in step 405 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 and a jump is made to step 402. If this is not the case, however, the new parameter vector x _{n is} discarded and branched to step 402.

An alternative method for determining an efficient operating point, which is used to design a technical system, is shown in FIG. 5. 5 is largely to be understood analogously to FIG. 4. Blocks 501, 502, 503, 504, 505, 507 and 508 correspond to blocks 401-405, 407 and 408, which have already been discussed in detail. The only difference is block 506. Thus, if the new parameter vector x _n in step 505 is invalid Parameter vector is recognized, in step 506 the part of the path Pf which leads to the parameter vector x _n is shortened by a predetermined part, and then to step 504 or 505 Jump. Further explanations for FIG. 5 result analogously from FIG. 4.

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 is visible on a monitor MON and / or on a printer via a graphic interface PRT issued. 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 overlaid with a random variable is determined;

c) in which a new parameter vector x _n , starting from the parameter vector x, is determined with a predetermined step size in the direction of the gradient superimposed on the random variable;

d) it is checked 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 operating point and the termination condition is not met, the current new parameter vector is discarded and branched to step b);

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

g) at which, if the termination condition is met, the determined operating point for the design of the technical

Systems is used. Process for designing a technical system, which technical system comprises a set of valid operating points

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

c) in which a new parameter vector x _n , starting from the parameter vector x, is determined with a predetermined step width in the direction of the gradient superimposed on the random variable;

e) in which, if the new parameter vector x _{n is} not a valid operating point and the termination condition is not met, the step size which has led to the new parameter vector x _n is shortened by a predetermined value and branched to step d);

g) in which, if the termination condition is met, the determined operating point is used to design the technical system.

3. The method according to any one of the preceding claims, in which in step d) an abort criterion is that a predetermined number of iterations has been carried out.

4. The method according to claim 1 or 2, in which in step d) an abort criterion is that the gradient falls below a predetermined threshold.

5. The method according to any one of the preceding claims, wherein the working point for the design of the technical system is that of several determined working points that has the best functional value quantitatively.

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

7. The method as claimed in one of the preceding claims, in which 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,

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

8. The method according to any one of claims 2 to 7, wherein the predetermined value by which the step size is shortened is 2.

9. 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.

10. Arrangement for the design of a technical system, which technical system comprises a set 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;

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

c) a new parameter vector x _n , starting from the parameter vector x, with a predetermined step size in

Direction of the gradient superimposed on the random variable can be determined;

d) it can be checked whether the new parameter vector x _{n is} a valid working point or whether an abort condition is fulfilled;

e) if the new parameter vector x _{n is} not a valid operating point and the termination condition is not met, the current new parameter vector is discarded and branched to step b);

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

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

c) a new parameter vector x _n , starting from the parameter vector x, can be determined with a predetermined step size in the direction of the gradient superimposed on the random variable;

d) it can be checked 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 operating point and the termination condition is not met, the step size that led to the new parameter vector x _n is shortened by a predetermined value and a branch is made to step d);

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