WO2001040883A1 - Method for a data-based modeling of technical processes - Google Patents

Abstract

The invention relates to a method for modeling the behavior of technical processes, for example industrial processes using block diagrams (3, 4), the model of the industrial process or processes being encoded in a tree structure (7, 10). Said tree structure (10) comprises structure-defining branches (11) and input-specifying branches (12). The structure-defining branches (11) consist of structure-defining instructions (for example 13.2, 14.2, 14.3, 16.1 and 16.2), the input-specifying branches consist of input-specifying instructions (for example 13.1, 14.1). Both structure-defining and input-specifying branches (11 or 12) may issue forth from the structure-defining instructions. The tree structure (10) comprises a root (15) from which both a structure-defining branch (11) and an input-specifying branch (12) may issue forth.

Description

 Process for data-driven modeling of technical processes

The invention relates to a method for modeling technical processes such as e.g. Process engineering processes in which, for example, chemical synthesis processes or biotechnological processes take place, in which metabolic processes are used.

To optimize technical processes, the method of modeling is often used in order to plan experiments, to reduce time-consuming laboratory and pilot plant experiments, and to identify and correct measurement problems in advance. Model-based methods are also used to develop new processes or improve the cost-effectiveness of old processes and to identify potential weak points. When generating models, a distinction is made between methods of data-driven modeling and those of analytical modeling. In the case of data-driven methods, one proceeds empirically and looks for a model that describes the observed process behavior, whereas the theoretical knowledge, for example about physical laws, is the starting point for analytical model formation.

When it comes to data-driven modeling, it is advisable to use the existing expert knowledge as far as possible to complete and expand it. The model building tool should therefore not only limit data-based knowledge acquisition to the setting of numerical parameters, but also continuously improve and adapt the model structure. The data-based model structure generation considered here represents an iterative optimization. In order to bring about a match between model and real process behavior. The optimization strategy that is followed is of crucial importance. Unlike parameter optimization, structures can be optimized variable length do not define gradients or directions. Therefore, iterative progress in the form of random or heuristic steps is necessary. With the iterative progress, the use of evolutionary algorithms (Kursawe Frank and Hans Paul Schwefel 1997, Optimization of Evolutionary Algorithms. ATP Automation Practice 39 (9), pages 10 to 17). proven. These have in common that they use mechanisms of natural evolution to solve technical optimization problems. The distinguishing feature of the evolutionary optimization concepts is, in particular, their form of representation, i.e. the coding with which the solution space can be represented internally. Genetic programming is used as an approach to the data-driven generation of model structures (Koza John 1990, Genetic Programming: a Paradigm for Genetically Breeding Populations of Computer Programs to Solve Problems, technical report STAN-CS-90-1314 Computer Since Department Stanford University California) , Koza John R. (1992): Genetic Programming: On the Programming of Computer by Means of Natural Selection, The MIT Press. Cambridge, Massachusetts, USA), in which the solution is encoded in a tree structure of variable size. Within this tree structure, a distinction is made between inner nodes, of which at least one branch branches off, and terminating nodes, which have no further branches. The said tree structure is based on a syntax on the basis of which it can be converted into an interpretable solution structure, the syntax also being contained in variation operations.

When using genetic programming to generate a model, there are degrees of freedom such that the form of representation in which the structure to be optimized is encoded as a tree can be freely selected. The iterative procedure when using evolutionary algorithms implies that a new solution only results from variation operations of a previous solution. Coding of the structure to be optimized should therefore be aimed for, in which a possible solution can be converted into any other solution in as few variation steps as possible.

A representation of a process model consists in an equation-oriented coding. Internal nodes and connection nodes correspond directly to mathematical equations because the structure of the tree structure on recursive Calculation steps with a digital computer is oriented. A weakness of the equation-oriented coding is that only comparatively simple tasks can be considered. Necessary constants are put together from a set of randomly chosen constants, which leads to very extensive and elongated expressions.

Another disadvantage of an equation-oriented coding is that presumed dependencies and interrelationships and their dynamics can only be mapped inadequately. The automatically generated models are difficult to interpret for the user and therefore not transparent.

It has been found that block diagrams for a data-driven model structure search represent a more suitable approach than the equation-oriented representation. When coding this form of representation into a structure to be optimized by genetic programming, the nodes used each represent a model block. Necessary constants, which can also be contained in the model blocks, are determined by classic optimization strategies, such as the Rosenbrock, Hoke-Jeeves or Gauss-Newton method.

In the direct block-oriented coding, the block diagram itself is formulated in a tree structure. The signal flow in the block diagram corresponds to the direction from the branches to the trunk in the tree structure. The root of a tree structure represents the initial size of the model, from which the model is developed to the input sizes, which are coded by the end points (= leaves) of the tree structure.

It follows from this that in direct block-oriented coding, due to the strict tree structure, branches can only be made against the signal flow, ie from the output to the input variables. Branches in which a size or intermediate size affects several paths of the overall model are not possible. Another disadvantage is that with this procedure, the input variable is only selected as the last step in the sense of selecting a final node.

Finally, with the method of direct block-oriented coding, it is disadvantageous that when the above-mentioned evolutionary optimization strategy is used, blocks are cascaded in series, whereas different influences due to parallel paths of an additive or multiplicative nature cannot be represented.

Based on the outlined attempts to solve the prior art, the object of the invention is to optimize process engineering processes using a model. This requires a process that is able to independently improve the model structure, whereby existing models can also be assumed.

According to the invention, this object is achieved by a method for modeling the behavior of technical processes, for example process engineering processes, using models, the model of the technical process or processes being represented as a block diagram and using genetic programming for finding model structure with an indirect block-oriented coding in one Tree structure is coded, following the following process steps:

a tree structure contains structure-defining branches and input-specifying branches,

structure-defined branches consist of structure-defined instructions, input-specifying branches consist of input-specifying instructions whereby structure-defining instructions themselves can originate both structure-defining and input-specifying branches,

the tree structure contains a root from which both a structure-defining branch and an input-specifying branch extend. According to the proposed method, the model which depicts the process or processes to be optimized can essentially be composed of structure-defining instructions which, for example, represent model blocks with an input variable.

In addition, structure-defining statements can also define link operators.

In contrast, input-specifying instructions preferably represent model input variables; references to output variables of other tree structures or constants can also be represented in this form. In addition to the root of a tree structure, the input-specific branches only assume instructions that branch in the block diagram.

In the process models coded as tree structures in this way, feedback loops can be represented.

To do this, a structure-defining statement is followed by several structure-defining branches, each of which describes a parallel path. Each of these parallel paths is connected to the same input variable, which in turn is represented by an input-specifying instruction.

The advantages associated with this solution are, inter alia, that a model design which is carried out in accordance with the proposed procedure provides a model structure which is constantly improving. A step-by-step, iterative approach to model determination is possible, in which the result obtained from previous iteration steps is taken into account step by step and developed further and can be influenced interactively.

With the method proposed according to the invention for forming a model depicting a technical process, for example, a model for describing a biotechnological process are provided, in which an educt is taken up by microorganisms, modified and excreted as a product.

The codes required for data-driven modeling are explained in more detail using a drawing.

It shows:

La is a block diagram with a delay element of the second order and a dead time element,

Lb its associated tree structure in direct coding,

2 a tree structure of the indirect coding with structure-defining and input-specifying branches describing the block diagram from FIG.

3 shows the block diagram after interpretation of the elements of the first level of the tree structure according to FIG. 2,

Fig. 4 shows the block diagram after interpreting the elements of the second level

2 with input-specifying instructions of this level,

5 shows the block diagram after interpretation of the elements of the third level of the tree structure according to FIG. 2,

6 shows the block diagram after interpretation of the entire tree structure according to FIG. 2, 7 shows the realization of a feedback loop with a second order delay element and

8 shows a tree structure for describing a block diagram with multiplicative coupling of two parallel paths, and

Fig. 9 represents the first of the listed examples

Tree structure.

La shows a block diagram with a delay element of the second order and a dead time element.

The block diagram has two input variables 1 and 2, namely ui and u. The input signal passes through two model blocks 3 and 4 before it is passed together with the first input signal 1 to a summation point 5, at which the output signal 6 is formed. The associated tree structure 7 is shown in FIG. 1b, which is shown in a direct block-oriented representation form. In this case, branches against the signal flow are not possible due to the strict tree structure. Branches in which, for example, an intermediate variable influences several paths of the overall model are not provided.

2 shows a tree structure for describing a block diagram in indirect coding with structure-defining and input-specifying instructions.

Starting from a root shown at the head of the tree structure 10, the tree structure 10 shown can be divided into three levels 13, 14 and 16. The input-specifying instruction 13.1 represents the first influencing variable on the output Y represented by the root 15, which runs in an input-specifying branch 12 of the tree structure 10. In contrast, the structure-defining branch 11 contains an addition node 13.2, that is to say a structure-defining instruction, from which the structure-defining part branches to levels 14, 16 below. The underlying second level 14 contains an input-specifying branch 12, via which the input-specifying instruction 14.1 is connected to the branching point 13.2 of the first level 13 lying above it. In addition, in the second level 14 there are a termination instruction 14.2 which closes a gap in the block diagram and a branch instruction 14.3 with which it is possible to selectively connect several model blocks in series. The nodes 14.2 and 14.3 mentioned lie in the structure-defining branch 11 of the tree structure 10; Since the addition instruction 13.2 in the first level 13 results in a branching in the block diagram, the tree structure 10 according to FIG. 2 contains not only two structure-defining branches 11 starting from the instruction 13.2, but also the input-specifying branch 12.

In the third level 16 of the tree structure 10 according to FIG. 2, the structure-specifying instruction 14.2 can be used to produce a conclusion of the tree structure 10 at this well-defined point. In this sense, instruction 14.2 represents a termination instruction. In contrast, structure-specifying instruction 14.3 can be used to selectively connect several blocks in series.

Starting from the structure-defining instruction 14.3 provided in the second level 14, the instructions 16.1 and 16.2 of the third level 16 form the

Final instruction of the structure-defining part 11 of the tree structure 10 according to FIG.

Second

3 to 6 show how a block diagram can be developed successively, in accordance with the levels 13, 14 and 16 of the tree structure 10 according to FIG. 2 described.

3 shows the result of the input-specifying instruction 13.1, which influences the output variable y via an addition instruction 13.2. Since the addition instruction 13.2 branches further, its outlines are only shown in dashed lines. As can be seen, the output signal y is initially only dependent on the input-specifying instruction 13.1. FIG. 4 shows the effect of the elements of the second level 14. The input-specifying instruction shown in the tree structure 10 according to FIG. 2 in the second level 14

14.1 serves as the input variable for the new path; this is described by the left of the two structure-defining branches 11 from 13.2 to 14.2 and 14.3 lying in the second plane 14.

5 shows the changes after interpreting the two structure-defining instructions 14.2 and 14.3. While out of the instruction

14.2 no further addition results in the block diagram, the instruction 14.3 effects a series connection. The elements connected in series are defined by structure-defining instructions 16.1 and 16.2. 6 finally shows the effect of the interpretation of the closing instructions 16.1 and 16.2 in the structure-defining branch 11 of the third level 16. Model blocks 17 and 18 were inserted into the two gaps.

Compared to direct coding, the indirect coding described here results in improved search behavior when using the evolutionary optimization strategy of the shape, that more compact models are created which are limited to the dominant effects and are easier for the user to interpret.

FIGS. 7 and 8 show design variants of feedback loops and multiplicative coupling of two parallel branches.

FIG. 7 shows how a block diagram with inhibitory feedback is encoded in the tree structure. The structure-defining instruction 19 is interpreted as a branch point in the block diagram. At the same time, instruction 19 contains the information that the left structure-defining branch originating from the node describes the forward path of the loop and the right describes the feedback path in the block diagram. In the case of inhibitory feedback, both paths are linked on the input side to a subtraction point. 8 shows a multiplicative coupling of two parallel branches as a tree structure and as a block diagram.

The input-specifying instruction 25 can accordingly be taken into account as an input variable in two different branches of the block diagram, which is not possible with the direct coding according to FIG. 1b.

The present invention is illustrated by the following examples, which, however, are not limiting:

The fermentation of recombinant Escherichia coli bacteria may be mentioned as exemplary processes whose behavior could be optimized by means of the method described above. Fermentation is a sub-step of a complex synthesis process for the artificial production of a protein suitable for cancer therapy. This active ingredient has so far been obtained from a plant extract. In order to ensure high purity and in particular a defined concentration of the active ingredient, a high level of technological effort is necessary. A number of biological and chemical reactions are required to synthesize the active substance. An essential process here is the fermentative production of the protein in a stirred tank reactor. Genetically modified, recombinant Escherichia Koli bacteria serve as the production strain. They start production in the presence of an activating substance (inductor). Glycose is added during the fermentation in order to keep its concentration neither in the limiting nor in the inhibiting range between 10 and 25 g / l. The addition of oxygen beyond the usual gassing of the reactor is dispensed with. It is characteristic of this process that the growth behavior of the cells changes completely upon induction, ie when the inductor (isopropyl-β-D-thiogalactopyranoside) is added. The microorganisms stop growing and are devoted almost exclusively to product formation. Since after a while even the proteins necessary for the survival of the cells are no longer available in sufficient quantities, the process passes into the death phase after a comparatively short production phase, regardless of the oxygen and glycose availability. Important process parameters of this process can be optimized based on models. In which The process under consideration is of particular interest when it comes to choosing the best time for induction. Since the product is formed and accumulated intracellularly, the amount that can be achieved is limited. In order to achieve high productivity, as much biomass as possible must be produced in the shortest possible time. If the induction is too early, the cell density is low, and induction too late means a waste of time and resources.

This point in time could be optimized with the method according to the invention.

A tree structure according to the invention, which describes the process outlined here, is shown in FIG. 9.

The represented tree structure according to FIG. 9 finds its counterpart in the differential equations given further below.

Another example is an enzymatic conversion in which a biotechnologically obtained enzyme is used. In this process, the reactor is filled with water and a varying concentration of an enzyme at the start of the reaction. During the reaction, a reactant E _A is zugefuttert continuously. A product is created as well as two intermediate products and a by-product. Product formation takes place in two different ways. The chemical reaction results in a chemical equilibrium between the two enantiomers of the feed educt E _A and the corresponding enantiomer of the product. During the enzymatic conversion, only an R-form of the product is generated, which is why one speaks of an enzyme-catalyzed synthesis. In the example considered here, the kinetics of the chemical conversion were known, while there was great uncertainty for the enzyme kinetics. The effects of varying enzyme kinetics can be run through using the method described above and the resulting consequences can be estimated.

An example of a chemical process is ethoxylation, which is a highly complex process. A reactor is at the beginning of the reaction the educts EQ, the solvent E _L and the catalyst Co. The ethoxylation process is also operated as a semi-batch process, with the educt E _N being added. In the course of the reaction, the products P _G and Pi as well as a number of by-products (BB, B, BE, B _K , BM) and intermediates (Iß, IR, I _S , I _D , I _H ) exist - in the reaction balances of the 17th In addition to the change in concentration through dilution D, the substances involved also deal with the chemical back and forth reactions taking place in the reactor. The behavior of this highly complex process could be described using the process described above.

B = B _B - D + r! 2h

B = Bc D + r9h - r9r + rl3h

X = I _D 'D + r6h - r9h + r9r

B _L = B _E ^' D + r7h = P _G ' D - r 11 h + r5h - r5r - r2h

In addition to data-driven model generation, the method according to the invention can also be used for computer-aided controller design.

For a continuously operating stirred tank reactor (Klart, KO and Engel, p. 1992 "Test example for the design of non-linear controllers", second version of a technical report, chair for plant control technology, Department of Chemistry, Technology, University of Dortmund) with side and follow-up reactions is the controlled variable Product concentration C _ß . The economy of the process depends on the temperature of the reactor contents teta, which must also be kept at a constant operating point. Control variables are the inlet V. N _R based on the reactor volume and the cooling capacity Q. _κ . Fluctuations in the educt concentration in Intake C _AO appear as interference. the Prozeßt has an unstable zero dynamics, whose influence occurs more strongly in appearance depending economically more favorable the operating point is selected. by means of the inventively proposed method, the design of a control task solved controller be made.

P = π-X _r

ϊ = (η-μ)-X_a S = S ₀ F-X -mX

ϊ = (η-μ) -X _a

π =

π =

4.99 + p

Y _PIS = \ 0

Bezugszeichenliste erste Eingangsgröße zweite Eingangsgröße erstes Blockschaltbild zweites Blockschaltbild

Reference character list first input variable second input variable first block diagram second block diagram

Summation point

output

Threaded

Second order delay element dead time element

Tree structure structure-defining branch input-specifying branch first level 13.1 input-specifying instruction

13.2 Second level addition node

14.1 instruction specifying the input

14.2 conclusion 14.3 branch node root third level

16.1 Final node

16.2 Termination node first model block second model block feedback loop loop end multiplicative coupling block diagram K 24. second parallel circuit first parallel circuit 25. first input variable for 21

Claims

claims 1.Procedure for modeling the behavior of technical processes, e.g. process engineering processes using block diagrams (3, 4), whereby the model of the technical process or processes for internal computer processing and in particular for the automatic generation and improvement of the model structures in a tree structure (7, 10 ) is coded, characterized in that - The tree structure (10) contains structure-defining branches (11) and input-specifying branches (12). - Structure-defining branches (11) from structure-defining instructions (13.2, 14.2, 14.3, 16.1, 16.2) and input-specifying branches (12) consist of input-specifying instructions (e.g. 13.1, 14.1), whereby structure-defining instructions themselves start with both structure-defining and input-specifying branches (11 and 12), the tree structure (10) contains a root (15) from which both a structure-defining branch (11) and an input-specifying branch (12) extend. 2. The method according to claim 1, characterized in that the tree structure to be optimized (10) contains essentially structure-defining instructions (for example 13.2, 14.2, 14.3, 16.1, 16.2). 3. The method according to claim 1, characterized in that the model blocks by structure-defining instructions e.g. (17, 18) are encoded. 4. The method according to claim 3, characterized in that the structure-defining instructions for model blocks (17, 18) with an input variable (13.1, 14.1) Represent termination nodes. 5. The method according to claim 1, characterized in that the structure-defining branches (11) contain only structure-defining instructions (13.2, 14.2, 14.3, 16.1, 16.2). 6. The method according to claim 1, characterized in that the input-specific branches (12) of the tree structure (10) contain only input-specifying instructions (13.1, 14.1). 7. The method according to claim 1, characterized in that linking operators are coded by structure-defining instructions (13.2, 14.2, 14.3, 16.1, 16.2). 8. The method according to claim 1, characterized in that the beginning of loops or parallel paths in the block diagram by structure-defining instructions (19, 20) are encoded. 9. The method according to claim 1, characterized in that model input variables are encoded by the input-specifying instructions (13.1, 14.1). 10. The method according to claim 1, characterized in that references to output variables of another tree structure (7) or constants (22) are coded by input-specifying instructions (13.1, 14.1). 11. The method according to claim 1, characterized in that the input-specifying branches (12) except from the root (15) only start from structure-defining instructions (13.2) which cause branching within the tree structure (10). 12. The method according to claim 1, characterized in that the series connections are coded by a structure-defining instruction (14.3). 13. The method according to claim 1, characterized in that a model for describing a biotechnological process is formed, wherein an educt of Microorganisms are absorbed, modified and excreted as a product. 14. The method according to claims 1 and 2, characterized in that classically created models are automatically modified and / or optimized and supplemented by the user.