WO2022117424A2

WO2022117424A2 - Method and device for operating a technical system

Info

Publication number: WO2022117424A2
Application number: PCT/EP2021/082949
Authority: WO
Inventors: Andreas Michalowski; Martin Lustfeld
Original assignee: Robert Bosch Gmbh
Priority date: 2020-12-01
Filing date: 2021-11-25
Publication date: 2022-06-09
Also published as: DE102020215138A1

Description

description

title

Method and device for operating a technical system

The invention relates to a method for creating a mathematical equation, a test stand, a computer program, a machine-readable one

Storage medium, a measuring device and a control device.

State of the art

Buckinghan's n-theorem is known, which makes it possible to determine dimensionless quantities, so-called n-factors, for a system that is characterized by an (unknown) relationship between physical dimensional quantities. In this case, these n-factors are multiplication products of the physically dimensional variables raised to respective predeterminable powers.

Methods of machine learning are known from https://de.wikipedia.org/wiki/Maschinelles Lern, with which statistical models can be determined using suitable training algorithms, which can use the relationships between input and output variables of a system contained in the training data to represent.

Advantages of the Invention

If the input and output variables are not arbitrary data, but physically dimensioned variables, the invention with the features of independent claim 1 allows a particularly simple system description of a technical system, i.e. a model, by exploiting the physical dimensions, that output variables of the technical system depends on input variables of the technical system, which can be extrapolated particularly well and also has a particularly simple structure, so that it is possible to determine a controller for the technical system that can also be secured for safety-critical applications.

Disclosure of Invention

In a first aspect, the invention therefore relates to a method for creating a mathematical equation that describes a dependency of at least one output variable of a technical system on at least one input variable of the technical system, each of the input variables and each of the output variables being assigned its respective physical dimension, where by means of physically dimensionless fl factors, which are assigned to the input variable(s) and output variable(s), candidate functions for the mathematical equation are provided and depending on how well the candidate functions can be adapted to a provided sequence of measured values, the mathematical equation depends on one of these candidate functions is determined. The candidate functions thus each characterize a possible dependency of one of the fl factors on the other fl factors.

This method can be given in particular by a method with the steps: a) determining the input variable(s) and output variable(s) associated with physically dimensionless fl factors, b) providing candidate functions, the candidate functions having a complexity no greater than a specifiable one have maximum complexity, c) providing the sequence of measured values comprising data points from input variables and output variables assigned to each other, d) determining a respective accuracy of fit of the candidate functions to the sequence of measured values provided (ie converting the measured values into sequences of fl factors, and determining the accuracy of fit to the converted sequences of fl factors), e) selection of a candidate function depending on the determined accuracy of fit, and f) providing the selected candidate function (through the associated expression of input and output variables).

In this case, a candidate function is preferably a mathematical function defined by a combination of predeterminable function blocks, which are preferably provided from a predeterminable set of possible function blocks. In this case, the combination can be a successive concatenation using mathematical operations that are provided from a predeterminable set of possible mathematical operations, for example “+” (addition),

(subtraction) or "°" (concatenation). The complexity of the candidate function can preferably be characterized by a number of possible mathematical operations in the candidate function. A candidate function that only consists of a single function block that can be specified is conceivable.

Provision can then be made for a measuring device to be controlled as a function of the candidate functions in order to set prescribable input variables on the technical system in order to determine associated output variables.

This is particularly useful if, in the step of selecting a candidate function, depending on the determined accuracy of fit, several of the candidate functions have a similar determined accuracy of fit, so that it is not possible to differentiate sufficiently well which of the candidate functions is to be selected. By controlling the measuring device and adding the specifiable input variables and associated determined output variables to the sequence of measured values, the accuracy of fit of the candidate functions can be better determined and a particularly well-fitting candidate function can be selected with improved differentiation between the candidate functions.

In an advantageous development, it can be provided that the predeterminable input variable is determined as a function of which value at least one of the candidate functions assumes for the predeterminable input variable. With that it is particularly good to find a value at which the candidate functions can be well differentiated with regard to their accuracy of fit.

For example, the predefinable input variable can be determined as a function of the size of the difference between the associated output variables that the candidate functions of at least one pair of candidate functions assume for the predefinable input variable. This enables a particularly good pairwise differentiation of the candidate functions of the at least one pair from one another.

Alternatively or additionally, the definable input variable can be determined depending on how great the expected accuracy of fit is when the accuracy of fit is determined again using the measuring point determined for this input variable (comprising the definable input variable and associated output variable).

Embodiments of the invention are explained in more detail below with reference to the accompanying drawings. In the drawings show:

FIG. 1 shows a preferred embodiment of the method according to the invention in a flow chart;

FIG. 2 shows an illustration of how a next value to be set for the input variables of the technical system is determined;

FIG. 3 shows an embodiment of a construction of the measuring device.

FIG. 4 illustrates an exemplary embodiment of a control device for controlling the technical system.

Description of the exemplary embodiments

FIG. 1 shows a preferred embodiment of the method according to the invention in a flow chart. The method starts with step (100).

Predeterminable function blocks and predeterminable mathematical operations for Concatenation of the function blocks are provided. The physical dimensions of the input variables and output variables of the technical system are also provided, preferably as products of powers of physical dimensions or as products of base units of a specifiable physical base unit system, for example the SI base unit system or the cgs base unit system. This is followed by step (HO).

In step (110) sets of n-factors associated with the inputs and outputs are provided. This is done, for example, by identifying the physical dimensions or physical base units, each with one dimension of a vector space, and identifying the respective exponents of the physical dimensions of the input variables and output variables with entries in the vectors of this vector space. Finding n-factors then corresponds to searching for linear combinations resulting in zero vectors in this vector space.

Subsequently, candidate functions are provided which characterize the dependency of one of the provided n-factors on the remaining n-factors. These candidate functions are those, preferably all, candidate functions in the provided function blocks of the provided n-factors and the predefinable mathematical operations for concatenation between the provided function blocks. A candidate function is therefore an alternating sequence of function blocks and operations.

Function Block — Operation — Function Block — Operation — ... — Function Block

In the exemplary embodiment, the candidate functions provided are all such combinations up to a specifiable maximum complexity, ie the number of operations is not greater than the specifiable maximum complexity. These candidate functions can be determined using a backtracking algorithm, for example. This is followed by step (120). In step (120), sequences of measured values are provided, which include input variables and output variables of the technical system for each of the measuring points. These sequences of measured values are converted into sequences of the corresponding n-factors and made available. This is followed by step (130).

In step (130), the candidate functions are fitted to the sequence of measured values, ie free parameters that parameterize the function blocks are each adapted in such a way that the respective candidate function best fits the sequence of measured values. A respective accuracy of fit of the candidate function to the sequence of measured values is determined for each of the candidate functions, for example a ² -fit quality.

In the exemplary embodiment, the worst-fitting candidate functions are then eliminated, for example all those whose determined ² -fit quality exceeds a predeterminable threshold value (the higher the value of the 2-fit quality, the poorer the fitting accuracy). Step (140) follows.

In step (140) it is checked whether the number of remaining candidate functions is less than or equal to one. If this is the case, step (150) follows, otherwise step (160).

In step (150), the remaining candidate function is provided as a determined candidate function, if a candidate function is left. If no candidate function remains, the method terminates with an error message and can be restarted, for example, with an increased maximum complexity that can be specified or an increased threshold value that can be specified. This ends the procedure.

In step (160), as illustrated in FIG. 2, a next value to be set for the input variables of the technical system is determined. Step (170) follows.

In step (170), the measuring device is used to control the technical system with the determined next value to be set for the input variable and the associated output variables are determined. This measurement point is added to the sequence of measurement values. A branch is then made back to step (130).

FIG. 2 illustrates, by way of example, the selection of the next value (E _o ) to be set for the input variables of the technical system from step (160). An output variable ( ) over an input variable (E) is shown one-dimensionally. Measured values (200) show pairs of input variable (E) and output variable ( ) that have already been determined. Input variable (E) can be set in a range (B), given here by way of example through the range between a lower limit (B _o ) and an upper limit

A first candidate function j (210) (shown as a dashed line), a second candidate function f ₂ (220) (shown as a dashed line) and a third candidate function f ₃ (230) (shown as a solid line) are attached to the course of the measurement points (200) fitted. The first candidate function j has an associated first uncertainty <j (not shown), the second candidate function f ₂ has an associated second uncertainty <J ₂ (not shown), and the third candidate function f ₃ has an associated third uncertainty <J ₃ (not shown). The next value to be set (E _o ) is now determined in the exemplary embodiment in such a way that as many of the candidate functions f 1 , f ₂ , f ₃ as possible can be ruled out as not matching the measurement data as reliably as possible.

This can be done, for example, in that the sum of the pairwise distances of the candidate functions, ie eg

- /s(E)|,

| f ₃ (E) - f ₂ (E) | are to be maximized, for example normalized by the associated inaccuracies, i.e. ö ö ö ö >

In the exemplary embodiment, the next value E _o to be set is selected in such a way that it maximizes the sum of these three terms.

FIG. 3 shows an exemplary embodiment of a structure of a measuring device (3) for carrying out the method illustrated in FIG. The measuring device (3) includes a machine-readable storage medium (45) on which a computer program is stored that is set up to carry out the method illustrated in FIG. It also includes a processor (46) that executes the computer program.

A sensor (30) detects a sensor variable (S) that characterizes a state of the technical system (1). An input interface (50) converts the sensor variable (50) into the output variable (A) and feeds it to a control block (60), which determines the next input variable (E _o ) to be set and transmits it as an input variable (E) to an output interface (40 ) transmitted, which from this provides a control signal (x) with which the technical system (1) is controlled. Previously set input variables (E) and output variables (A) are stored in a memory (P) and are made available from there to the control block (60).

The technical system (1) can be, for example, a manufacturing machine, such as a laser material processing machine (e.g. a laser drilling machine or a laser cutting machine or a laser welding machine) or a machine for the mechanical (e.g. machining) processing of components, or a machine for the mechanical joining of components, e.g. screwing.

Alternatively, the technical system (1) can be a robot, for example a mobile robot or a gripping robot.

Alternatively, the technical system (1) can be a subsystem, e.g. e.g. a fuel cell

FIG. 4 illustrates an exemplary embodiment of a control device (10) for controlling the technical system (1), which includes a representation of the mathematical equation that is generated using the method illustrated in FIG was determined, wherein the control device (10) is set up to provide a control signal (x) for controlling the technical system (1) by means of the mathematical equation determined in this way. For example, the control device (10) includes a model-predictive regulation for determining the control signal (x), the mathematical equation being used as a forward model of the technical system (1). Alternatively, the control device (10) includes a specification of a target value that is provided by means of the determined mathematical equation, with the control signal (x) being provided by regulation to this target value.

Claims

Expectations

1. Method for creating a mathematical equation that describes a dependency of at least one output variable of a technical system (1) on at least one input variable (E) of the technical system (x), each of the input variables (E) and each of the output variables (A) their respective physical dimension is assigned, using physically dimensionless n-factors assigned to the input variable(s) and output variable(s), candidate functions (f .f2.f3) are provided for the mathematical equation and depending on how well the Candidate functions ( ^f1.f2.f3 can be ^{adapted to} a sequence of measured values provided, the mathematical equation is determined as a function of one of these candidate functions (/n/2,/3).

2. The method according to claim 1, with the steps: a) determining the input variable (s) and output variable (s) associated with physically dimensionless n-factors, b) providing candidate functions (f1.f2.f3) that depend on one of the Characterize n factors from the remaining n factors, with the candidate functions (f , f ₂ , f ₃ ) having a complexity no greater than a specifiable maximum complexity, c) providing the sequence of measured values each comprising data points from input variables (E ) and output variables (A), d) determining a respective accuracy of fit of the candidate functions (f1.f2.f3) ^to the sequence of measured values provided, e) selection of ^a candidate function ( ₁ , ₂ ,/3) depending on the accuracy of fit determined, and f) Providing the selected candidate function (f1.f2.f3)- Method according to Claim 1 or 2, in which, depending on the candidate functions (fi, f ₂ , /sJ), a measuring device (3) is controlled to set predeterminable input variables (E) on the technical system (1) in order to determine associated output variables (A). Method according to Claim 3, in which the predeterminable input variable (E) is determined as a function of which value at least one of the candidate functions (/x^/2^/3) assumes for the predeterminable input variable (E). Input variable (E) is determined depending on how large a distance between the associated output variables (A) is, which the candidate functions of at least one pair of candidate functions (/x^/2^/3) assume for the predeterminable input variable (E). Claim 4 or 5, wherein the predeterminable input variable (E) is determined depending on how large the expected accuracy of fit is if the accuracy of fit is determined by means of the measuring point determined for this input variable (E). n be determined again. Method according to one of the preceding claims, in which, after the mathematical equation has been created, the technical system (1) is operated using the determined mathematical equation. Method according to claim 7, wherein an input variable (E) characterizing a control of the technical system (1) is supplied to the determined mathematical equation and an associated output variable (A) characterizing a state of the technical system (1) is determined, and wherein the technical system (1) is operated depending on this associated output variable (A). Computer program set up to carry out the method according to one of Claims 1 to 7. Machine-readable storage medium (45) on which the computer program according to claim 9 is stored. Measuring device which is set up to carry out the method according to any one of claims 3 to 7. Control device (10) for controlling the technical system (1), which comprises a representation of the mathematical equation that is determined using the method according to one of Claims 3 to 7, wherein the control device (10) is set up to transmit a control signal (x) for Provide control of the technical system (1) by means of the mathematical equation determined in this way.