WO2000072096A1

WO2000072096A1 - Method, arrangement and computer program for designing a technical system

Info

Publication number: WO2000072096A1
Application number: PCT/DE2000/001530
Authority: WO
Inventors: Reinhart Schultz
Original assignee: Siemens Aktiengesellschaft
Priority date: 1999-05-25
Filing date: 2000-05-15
Publication date: 2000-11-30
Also published as: EP1183575A1; JP2003500717A

Abstract

Disclosed is a method for the design of a technical system whereby a statistical model is determined by means of at least one measuring value. At least one model parameter of the statistical model is determined. The technical system is optimized in a predetermined area by means of said statistical model and at least one parameter vector is determined. The at least one parameter vector is used to design a technical system.

Description

description

Process, arrangement and computer program for the design of a technical system

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

Optimizing a technical system or an operating process requires quantitative knowledge

Impact relationships between predefined target values (e.g. system and quality indicators) and controllable or non-controllable influencing factors. In the case of a complex operating process, for example in the area of process engineering, validated computing models are usually not explicitly available. Nevertheless, the technical system or the operating process should be designed and adjusted as optimally as possible. The setting or the design lies in particular in a determination of a parameter vector, that is to say an assignment of influencing factors for the technical system. The quality of the settings depends on the experience of an expert and is therefore highly error-prone in complex applications.

Conventional methods work as follows: First, a data-driven system model is developed based on measurement data. For example, polynomials, spline approaches or neural networks are used. An optimization calculation is then carried out on the basis of the data-driven system model. Classic mathematical methods of non-linear optimization, such as gradient-based methods, Quadratic Programming (QP) or Sequential Quadratic Programming (SQP) are used. An overview is given, for example, in [1]. Depending on the module classes used, the techniques of experimental design are also used for the subtask of data-driven modeling. For the definition of new Measuring points with the aim of increasing the significance of the data-driven system model become

Optimality criteria such as D-optimality, A-optimality or E-optimality are used (see [2]).

The object of the invention is to create a possibility for the design of a technical system, in particular an optimized setting of the technical system is guaranteed without a validated global computing model of the system being available.

It is a great advantage that the presented methodology can be used for initial setup, design, design, adaptation, redesign, control and operation of a technical system.

To solve the problem, a method for designing a technical system is specified in which a statistical model is determined on the basis of at least one measured value of the technical system. At least one model parameter of the statistical model is determined. The technical system is optimized in a predetermined range on the basis of the statistical model and at least one parameter vector is determined in the process. The at least one parameter vector is used to design the technical system.

An advantage of the method is to automatically ensure a suitable parameter vector, that is to say an assignment of possible adjustable parameters (which are expediently summarized and referred to as a parameter vector). These individual parameters for the respective technical system ensure optimized operation, in particular with regard to energy consumption, environmental compatibility, costs, and the technical system. A further development is that a further measured value is determined for the value of the at least one parameter vector, or the target variable is measured at the location of the parameter vector, and the statistical model is determined taking this further measured value into account.

The process then branches to the step at which at least one model parameter of the statistical model is determined. The method can advantageously be carried out iteratively until an abort condition is met. Such a termination condition can consist, for example, that in a further iteration step, compared to the previous step or several previous steps, an insignificant improvement is achieved, that is to say that the improvement lies below a predetermined threshold value.

To solve the problem, a method for designing a technical system is also specified, in which a statistical model is determined on the basis of at least one measured value of the technical system. The scatter component of the statistical model is taken into account by determining several model parameters that lie in a confidence range. Optimizations are carried out for the models determined by the several model parameters, a parameter vector being determined for each optimization. Using an opti ality criterion, a suitable parameter vector is determined with regard to significance and process behavior. This suitable parameter vector is used to design the technical system.

The Opti ality criterion ensures that an improvement is achieved both in terms of the significance of the statistical model and in terms of process behavior, that is, in terms of optimizing the process size. It is advantageous to focus on an improvement in significance, because the Meaningfulness with regard to an improved process behavior is only made possible.

One embodiment consists in that a further measured value is determined for the value of the suitable parameter vector and the statistical model is determined on the basis of the further measured value. It is then preferably branched to the step of the method in which a dispersion of the statistical model is taken into account (step b).

If the statistical model does not completely match the values of the technical system that have already been measured, this results in a scatter which is taken into account in the context of the different model parameters. For example, a confidence interval of 95% determined by the scatter can expediently be specified. Iterations of the described method or the described methods increasingly determine measured values which make it possible to model the underlying technical system ever better. This results in an increasingly better confidence interval for several model parameters. The iteration, that is to say the determination of the further measured value, preferably places the predetermined range around this newly ascertained measured value and thus, if necessary, a different range is taken into account in the modeling than in the previous iteration step. As a result of this, with increasing iteration number, more and more measured values result, which cause a drift towards a (local) optimum by shifting the range. There, the local optimum (in relation to the target size, for example the energy consumption) is determined within the area in the course of the iterations.

An advantageous embodiment consists in that, as stated above, taking into account the further measured value, the predetermined range around this measured value, preferably symmetrically around this measured value, is created. As a result, in the space created via the target variable (or target variables), which is determined by the parameter vector, a possibly multidimensional area shifted in the direction of the local optimum. If the local optimum is within the range, the suitable parameter vector is determined in the course of the iterations.

An advantageous embodiment also consists in that not only the position but also the size of the area is adapted for statistical modeling. This can e.g. about statistical tests of the residuals of the statistical model. Tests of the variance or the normal distribution assumption of the residuals can be considered.

A further development consists in particular in that the optimality criterion for selection from a plurality of parameter vectors is a D optimality criterion.

It is also a further development that the statistical model is a method of statistical compensation calculation. In particular, an approximative can be created using a

Polynomial approach, preferably using quadratic polynomials. Alternatively, the statistical compensation calculation can use a function that takes into account the specified properties of the underlying technical system (for example an e-function).

The optimization itself can be carried out using one of the following methods:

• Is the set of all quadratic for the statistical model as a class of modeling functions

If polynomials are used, special quadratic optimization (QP) methods can be used for the optimization calculation.

• If complicated model classes are used for statistical modeling or if complex non-linear restrictions have to be taken into account, universal methods for nonlinear optimization, e.g. Sequential Quadratic Programming (SQP) can be used.

Furthermore, an arrangement for designing a technical system is specified to solve the problem, the one

Processor unit which is set up in such a way that a) a statistical model can be determined on the basis of at least one measured value of the technical system; b) at least one model parameter of the statistical model can be determined; c) an optimization in a predetermined area of the technical system can be carried out on the basis of the statistical model and at least one parameter vector can be determined; d) the at least one parameter vector can be used to design the technical system.

In addition, to achieve the object, an arrangement for designing a technical system is provided, which has a processor unit which is set up in such a way that a) a statistical model can be determined on the basis of at least one measured value of the technical system; b) a dispersion of the statistical model is taken into account in that several model parameters which lie in a confidence range can be determined; c) optimizations can be carried out for the models determined by the several model parameters, a parameter vector being determined for each optimization; d) a parameter vector suitable in terms of significance and process behavior can be determined on the basis of an optimality criterion; e) the suitable parameter vector can be used to design the technical system. To solve the problem, a computer program is also specified which is set up in such a way that it executes the following steps when it runs on a processor unit: a) a statistical model is determined on the basis of at least one measured value of the technical system; b) at least one model parameter of the statistical model is determined; c) an optimization in a predetermined area of the technical system is carried out on the basis of the statistical model, and at least one parameter vector is determined; d) the at least one parameter vector is used to design the technical system.

Furthermore, to solve the problem, a computer program is specified which is set up in such a way that it executes the following steps when running on a processor unit: a) a statistical model is determined on the basis of at least one measured value of the technical system; b) a dispersion of the statistical model is taken into account by determining several model parameters that lie within a confidence range; c) optimizations are carried out in each case for the models determined by the multiple model parameters, a parameter vector being determined for each optimization; d) on the basis of an optimality criterion, a parameter vector that is suitable with regard to significance and process behavior is determined; e) the appropriate parameter vector is used to design the technical system.

The arrangement or the computer program are each particularly suitable for carrying out the method according to the invention or one of its developments explained above. Exemplary embodiments of the inventions are illustrated and explained below with reference to the drawing.

Show it

Fig.l is a block diagram with steps of a method for designing a technical system;

2 shows a block diagram with steps of an alternative method for designing a technical system;

3 shows a sketch of a function course as a function of a parameter vector;

4 shows a processor unit.

In Fig.l is a block diagram showing steps of a method for designing a technical system. According to the above, the draft can be a redesign, an adaptation, a validation, a simulation, a realization or a control of the technical system.

A measured value is determined in a block 101, on the basis of which a statistical model is calculated in a block 102, preferably using a statistical compensation calculation, in particular using a polynomial approach. The adjustment of the measured value (or the measured values, as soon as there are several) to the model can serve as a default according to the following relationship (for the quadratic approach):

T MW = a + bx + x ex + ε,

where MW denotes the measured value or the already existing measured values, x a parameter vector, a to c model parameters and ε a statistical scatter. It should be noted that the parameter vector x preferably includes influencing factors, that is to say influenceable variables of the technical system. In addition, the parameter vector x can also have variables of the technical system that cannot be influenced. For the design of the technical system, a value assignment of the parameter vector x is preferably to be determined, on the basis of which the system is optimally set or designed. The model parameters a, b and c are intended to adapt the quadratic model to the real specification. For this purpose, common methods of

Compensation calculation used. The model parameters a, b and c are subject to variation if they do not model the technical system exactly (which is rarely the case); this variation gives a possibility of variation in the selection of the model parameters within a confidence interval.

This means that each value assignment of the model parameters a, b and c leads to a modeling. Within the scope of the confidence interval, several value assignments of model parameters are preferably determined.

In FIG. 1, a value assignment for the model parameters is determined in step 103. A modeling results which is optimized in a step 104. The optimization is expediently carried out with regard to a target function; For example, an objective function "energy consumption" should be minimized from an economic point of view. For the modeling, the assignment that is optimal for the current model is determined from the space of the possible parameter vectors (design variants of the technical system) (see block 105). For this, e.g. a method of quadratic optimization.

At the location of the determined parameter vector, ie for the design or setting of the real system, a measurement is carried out - simulated or actually - and a value for the target function is determined in step 106. This value is used for an area that contains a section of the indicates the entire course of the target function in the space of the parameter vector (step 107). When the range for the new value of the parameter vector is shifted, it follows that there is a gradual development towards the locally optimal value of the parameter vector. The method can thus terminate as soon as a further iteration step no longer results in a sufficient improvement, ie that the improvement achieved is below a predetermined limit.

Fig.2 is partially analogous to Fig.l (especially the

Steps 201 and 202) with the additional requirement that several assignments of the model parameters a, b and c are determined which are in the range of the confidence interval (cf. step 203). There is then an optimization for each modeling, that is to say each assignment of the model parameters results in its own optimization, which as a result provides an assignment of the parameter vector (step 204). From a multiplicity of value assignments of the parameter vectors determined in this way, using a D-optimality criterion, the value assignment of the

Parameter vector (cf. step 206) is determined, which is optimal in terms of significance and the size of the target function. The D optimality criterion is primarily based on the significance. Thus, by increasing the significance, a confidence interval with higher reliability ("confidence") can be achieved, the meaningfulness of the value of the objective function increases with increasing confidence interval and thus with reduced scatter. By adding a further measured value (step 207) at the location of the parameter vector determined by means of the D-optimality criterion, on average, a statement of higher quality with regard to the significance results in the following iteration steps. By shifting the range (for an explanation, see Fig. 1 above), a drift to the local optimum is achieved on average. It should be noted here that the optimization is preferably limited to the area and is therefore usually only moved in the medium term towards the local optimum by the drift movement of the area (the shift is caused by new parameter vectors which lie outside the center). When looking at the area in the course of the optimization, a parameter vector can also result that lies on the limitation of the area. This leads to a shift in the direction of this parameter vector, the parameter vector preferably indicating the center of the shifted area.

It should also be noted that the illustrative representation of the displacement is not limited to an imaginable space (e.g. dimension three). The parameter vector usually comprises a large number of components, each of which adds a dimension to the space of the parameter vector. There is also the value of the objective function. In these high-dimensional rooms, too, the design mechanisms are as described, only for reasons of clarity, a low-dimensional example is taken up.

1 and 2 each contain an iteration loop from step 107 to step 102 and from step 208 to step 202. As mentioned, an abort condition can ensure that this is not an endless loop.

3 shows a sketch of a function curve 301 as a function of a parameter vector xl. An example is the parameter vector x of dimension one, indicated by the only component xl.

It will take advantage of the area

A <xl <B considered, where the limits A, B may or may not be included (as here). Several measured values 302, 303, 304, 305 and 306 are contained in this area. The curve course 301 shows the actual but unknown course of the target function. The objective function is the

Energy consumption that should be minimized. Modeling on the basis of the measured values known in the area results, for example, in a curve 307, the minimum of which lies at point B (or shortly before if B itself is not contained in the area).

In the next iteration step, the parameter value xl = B is used to determine a new measured value. The area wanders and is thus determined by

C <xl <D.

Now modeling is determined for this area (by varying the model parameters within a confidence interval). Each modeling gives an optimized value xl. The set of all values xl for the respective area are taken into account in a D optimality criterion, from which the value xl follows that is the best choice in terms of significance and improvement of the target function "energy consumption".

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: 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 connects a memory

MEM, the processor CPU and the input / output interface IOS guaranteed. There are also additional data buses Components can be connected, e.g. additional memory, data storage (hard disk) or scanner. A database interface is provided in particular for access to stored measurement data.

Bibliography :

[1] P. Spelluci: "Numerical methods of non-linear optimization", Birkhäuser, Basel 1993.

[2] Box et al .: "Empirical Model Building and Response Surfaces", Wiley, New York 1987.

Claims

claims

1. Method for designing a technical system, a) in which a statistical model is determined on the basis of at least one measured value of the technical system; b) in which at least one model parameter of the statistical model is determined; c) in which an optimization in a predetermined area of the technical system based on the statistical

Model and at least one parameter vector is determined; d) in which the at least one parameter vector is used to design the technical system.

2. The method of claim 1, e) in which a further measured value is determined for the value of the at least one parameter vector and the statistical model is determined taking into account the further measured value; f) branching to step b).

3. Method for designing a technical system, a) in which a statistical model is determined on the basis of at least one measured value of the technical system; b) in which a dispersion of the statistical model is taken into account by determining several model parameters which lie in a confidence range; c) in which optimizations are carried out in each case for the models determined by the multiple model parameters, a parameter vector being determined for each optimization; d) in which a parameter vector that is suitable in terms of significance and process behavior is determined on the basis of an optimality criterion; e) in which the appropriate parameter vector is used to design the technical system.

4. The method according to claim 3, f) in which a further measured value is determined for the value of the suitable parameter vector and the statistical model is determined on the basis of the further measured value; g) branching to step b).

5. The method according to claim 3 or 4, wherein the optimality criterion is a D-optimality criterion.

6. The method according to claim 2, 4 or 5, in which the method is applied iteratively.

7. The method according to claim 6, in which the method is applied iteratively until a drift of the newly determined measured value compared to the last determined measured value lies within the predetermined range below a predetermined threshold value.

8. The method according to any one of the preceding claims, wherein the predetermined area under a section of the space spanned by the parameter vector

Consideration of at least one target.

9. The method according to any one of the preceding claims, wherein the statistical model is a method of statistical compensation calculation.

10. The method of claim 9, wherein the method of statistical compensation calculation an approximation is carried out by means of a polynomial approach.

11. The method according to claim 10, in which the approximation is carried out by means of quadratic polynomials.

12. The method of claim 10, wherein the method of statistical compensation calculation uses a function that takes into account the specified properties of the technical system.

13. The method according to any one of the preceding claims, wherein the optimization is carried out according to one of the following methods: a) QP method; b) SQP procedure.

14. The method according to any one of the preceding claims, wherein the design comprises an adaptation, a redesign, an operation or a control of the technical system.

15. Arrangement for designing a technical system, with a processor unit, which is set up in such a way that a) a statistical model can be determined on the basis of at least one measured value of the technical system; b) at least one model parameter of the statistical model can be determined; c) an optimization in a predetermined area of the technical system can be carried out on the basis of the statistical model and at least one parameter vector can be determined; d) the at least one parameter vector can be used to design the technical system.

16. Arrangement for designing a technical system, with a processor unit, which is set up in such a way that a) a statistical model can be determined on the basis of at least one measured value of the technical system; b) a dispersion of the statistical model is taken into account in that several model parameters which lie in a confidence range can be determined; c) optimizations can be carried out for the models determined by the several model parameters, a parameter vector being determined for each optimization; d) a parameter vector suitable in terms of significance and process behavior can be determined on the basis of an optimality criterion; e) the suitable parameter vector can be used to design the technical system.

17. Computer program for the design of a technical system, which computer program when executed on a

Processor unit carries out the following steps: a) a statistical model is determined on the basis of at least one measured value of the technical system; b) at least one model parameter of the statistical model is determined; c) an optimization in a predetermined area of the technical system is carried out on the basis of the statistical model, and at least one parameter vector is determined; d) the at least one parameter vector is used to design the technical system.

18. Computer program for designing a technical system, which computer program executes the following steps when executed on a processor unit: a) a statistical model is determined on the basis of at least one measured value of the technical system; b) a dispersion of the statistical model is taken into account by determining several model parameters that lie in a confidence range; c) optimizations are carried out in each case for the models determined by the multiple model parameters, a parameter vector being determined for each optimization; d) on the basis of an optimality criterion, a parameter vector which is suitable with regard to significance and process behavior is determined; e) the appropriate parameter vector is used to design the technical system.