METHOD AND DEVICE FOR SETTING OPERATING PARAMETERS OF A PHYSICAL SYSTEM

Abstract

A method for setting operating parameters of a system, in particular, a manufacturing machine, with the aid of Bayesian optimization of a data-based model, which (in the Bayesian optimization) is trained to output a model output variable, which characterizes an operating mode of the system, as a function of the operating parameters. The training of the data-based model takes place as a function of at least one experimentally ascertained measured variable of the system and the training also taking place as a function of at least one simulatively ascertained simulation variable. The measured variable and the simulation variable each characterize the operating mode of the system. The measured variable and/or the simulation variable is transformed during training with the aid of an affine transformation.

Claims

1-15. (canceled)

16. A method for setting operating parameters of a system, using Bayesian optimization of a data-based model, the method comprising the following steps: training the data-based model, in the Bayesian optimization, to output a model output variable which characterizes an operating mode of the system, as a function of the operating parameters, the training of the data-based model taking place as a function of at least one experimentally ascertained measured variable of the system, and the training also taking place as a function of at least one simulatively ascertained simulation variable, the measured variable and the simulation variable each characterizing the operating mode of the system, the measured variable and/or the simulation variable being transformed during the training using an affine transformation.

17. The method as recited in claim 16, wherein the system is a manufacturing machine.

18. The method as recited in claim 16, wherein the measured variable and/or the simulation variable is multiplied during the affine transformation by a factor, and the factor is selected as a function of a simulative model uncertainty and as a function of an experimental model uncertainty.

19. The method as recited in claim 18, wherein the factor is selected as a function of ae quotient of the simulative model uncertainty and of the experimental model uncertainty.

20. The method as recited in claim 18, wherein the data-based model includes a simulatively trained first submodel which is a first Gaussian process model, and an experimentally trained second submodel which is a second Gaussian process model, the simulative model uncertainty being ascertained using the first submodel and the experimental model uncertainty being ascertained using the second submodel.

21. The method as recited in claim 20, wherein the data-based model includes an experimentally trained third submodel which is a third Gaussian process model, and which is trained to output a difference between the experimentally ascertained measured variable and an output variable of the first submodel.

22. The method as recited in claim 20, wherein the second submodel is not trained using the transformed measured variable, but is trained using the measured variable.

23. The method as recited in claim 22, wherein the third submodel is trained using the transformed measured variable.

24. The method as recited in claim 21, wherein when ascertaining the transformed measured variable, the measured variable is transformed using the affine transformation, the difference being multiplied by the factor.

25. The method as recited in claim 21, wherein to ascertain the model output variable of the data-based model, an output variable of the first submodel and an output variable of the third submodel are added up and are transformed with an inverse of the affine transformation.

26. The method as recited in claim 21, wherein to ascertain an uncertainty of the model output variable of the data-based model, the uncertainty is ascertained using the second submodel.

27. The method as recited in claim 16, wherein the measured variable and the variable simulated by the simulation variable are different physical variables and include different physical units.

28. The method as recited in claim 16, wherein subsequent to the setting of the operating parameters, the system is operated with the operating parameters thus set.

29. A test stand for a laser material processing machine, the test stand configured to set operating parameters of a system, using Bayesian optimization of a data-based model, the test stand configured to; train the data-based model, in the Bayesian optimization, to output a model output variable which characterizes an operating mode of the system, as a function of the operating parameters, the training of the data-based model taking place as a function of at least one experimentally ascertained measured variable of the system, and the training also taking place as a function of at least one simulatively ascertained simulation variable, the measured variable and the simulation variable each characterizing the operating mode of the system, the measured variable and/or the simulation variable being transformed during the training using an affine transformation.

30. A non-transitory machine-readable memory medium on which is stored a computer program for setting operating parameters of a system, using Bayesian optimization of a data-based model, the computer program, when executed by a computer, causing the computer to perform the following steps: training the data-based model, in the Bayesian optimization, to output a model output variable which characterizes an operating mode of the system, as a function of the operating parameters, the training of the data-based model taking place as a function of at least one experimentally ascertained measured variable of the system, and the training also taking place as a function of at least one simulatively ascertained simulation variable, the measured variable and the simulation variable each characterizing the operating mode of the system, the measured variable and/or the simulation variable being transformed during the training using an affine transformation.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Specific embodiments of the present invention are explained in greater detail below with reference to the figures.

[0048] FIG. 1 schematically shows a structure of a laser drilling machine.

[0049] FIG. 2 schematically shows a structure of a laser welding machine.

[0050] FIG. 3 schematically shows a structure of a test stand, in accordance with an example embodiment of the present invention.

[0051] FIG. 4 shows in a flowchart one specific embodiment for operating the test stand, in accordance with the present invention.

[0052] FIG. 5 shows by way of example a profile of simulated and measured and trained output variables over an operating variable, in accordance with the present invention.

[0053] FIG. 6 shows by way of example a profile of further simulated and measured and trained output variables over an operating variable, in accordance with the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0054] FIG. 1 schematically shows a structure of a laser drilling machine 1. An activation signal A is provided by an activation logic 40 in order to activate laser 10a. The laser beam strikes a material piece 12, where it generates a drill hole 11.

[0055] FIG. 2 schematically shows a structure of a laser welding machine 2. An activation signal A is provided here as well by an activation logic 40 in order to activate a laser 10b. The laser beam strikes two material pieces 13, 14 where it generates a weld seam 15.

[0056] A laser cutting machine (not represented) is also similarly possible.

[0057] FIG. 3 schematically shows a structure of a test stand 3 for ascertaining optimal process parameters x. Instantaneous process parameters x are provided by a parameter memory P via an output interface 4 of the laser material processing machine such as, for example, of laser drilling machine 1 or of laser welding machine 2. This carries out the laser material processing as a function of these provided process parameters x. Sensors 30 ascertain sensor variables S, which characterize the result of the laser material processing. These sensor variables S are provided via an input interface 50 as quality characteristics y.sub.exp to a machine learning block 60.

[0058] Machine learning block 60 in the exemplary embodiment includes a data-based model which, as illustrated in FIG. 4 and FIG. 5, is trained as a function of provided quality characteristics y.sub.exp. Varied process parameters x′, which are stored in parameter memory P, may be provided as a function of the data-based model.

[0059] Process parameters x may be alternatively or additionally provided for also providing an estimation model 5 via output interface 4, which provides estimated quality characteristics y.sub.sim instead of actual quality characteristics y.sub.exp to machine learning block 60.

[0060] The test stand in the exemplary embodiment includes a processor 45, which is configured to play back a computer program, which is stored on a computer-readable memory medium 46. This computer program includes instructions, which prompt processor 45 to carry out the method illustrated in FIG. 4 and FIG. 5 when the computer program is played back. This computer program may be implemented in software, or in hardware, or in a mixed form of hardware and software.

[0061] FIG. 4 shows in a flowchart a method for setting process parameters x of test stand 3. The method starts 200 by providing a respectively initialized first Gaussian process model GP.sub.0, second Gaussian process model GP.sub.V and third Gaussian process model GP.sub.1. The sets of the previously recorded test data belonging to the respective Gaussian process models are each initialized as an empty set.

[0062] First Gaussian process model GP.sub.0 is then 210 simulatively trained. For this purpose, initial process parameters x.sub.init are provided as process parameters x and process parameters x are optionally predefined with a design-of-experiment method and, as explained in greater detail below, ascertained with simulation data y.sub.sim associated with these process parameters x, and first Gaussian process model GP.sub.0 is trained with the test data thus ascertained.

[0063] A simulation model of laser material processing machine 1, 2 is then carried out using instantaneous process parameters x and simulative variables y.sub.sim are ascertained 220, which characterize the result of the laser material processing.

[0064] In the case of laser drilling, this may take place, for example, as follows: for a radius r of drill hole 11 along a deep coordinate z, r(z) is numerically ascertained as the solution of the equation

[1−R(r,z,α,θ)].Math.cos θ.Math.F.sub.0(r,z)−{tilde over (F)}.sub.th=0  (8)

where

[00001]$\begin{array}{cc}1-R=\frac{1}{2}.Math.\left(\frac{4n\cos \theta }{\left(n^2+k^2\right)+2n\cos \theta +{\cos }^2\theta }+\frac{4n\cos \theta }{\left(n^2+k^2\right){\cos }^2\theta +2n\cos \theta +1}\right)& \left(9\right)\\ F_0\left(r,z\right)=\frac{2Q}{\pi w^2\left(z\right)}.Math.\exp \left(-\frac{2r^2}{w^2\left(z\right)}\right)& (10\\ w\left(z\right)=\frac{d_{Fok}}{2}\sqrt{1+{\left(\frac{z}{l_{\mathrm{Rayleigh}}}\right)}^2}& \left(11\right)\\ \tan \alpha =\frac{r}{w\left(z\right)}\frac{dw\left(z\right)}{dz}& \left(12\right)\end{array}$

[0065] In this case: [0066] n=n+ik is a predefinable complex refractive index of material piece 12, with refractive index n and extinction coefficient k, [0067] {tilde over (F)}.sub.th is a predefinable ablation threshold fluence of material piece 12, [0068] Q is a predefinable pulse energy of laser 10a, [0069] d.sub.Fok is a predefinable focus diameter of laser 10a, [0070] l.sub.Rayleigh is a predefinable Rayleigh length of laser 10a, [0071] R is an ascertained reflectivity of material piece 12, [0072] α is an ascertained angle of the local beam propagation direction, [0073] θ is a predefinable relative angle between incident laser beam and surface normal of material piece 12, [0074] F.sub.0 is an ascertained radiated fluence of laser 10a, [0075] w(z) is an ascertained local beam radius.

[0076] In the case of laser welding, the ascertainment of estimated variables y.sub.sim may take place, for example, as follows:

[00002]$\begin{array}{cc}T\left(x,y,z\right)-T_0=\frac{1}{2\pi \lambda h}\exp \left(-\frac{v\left(x-x_0\right)}{2a}\right)\left(q_{net}{K}_0\left(\frac{\mathrm{vr}}{2a}\right)+2{.Math.}_{m=1}\cos \left(\frac{m\pi z}{h}\right)K_0\left(\frac{\mathrm{vr}}{2a}\sqrt{1+{\left(\frac{2\mathrm{ma}}{\mathrm{vh}}\right)}^2}\right)I_m\right)& \left(13\right)\\ \mathrm{with}& \\ r=\sqrt{{\left(x-x_0\right)}^2+y^2}& \left(14\right)\\ I_m={\int }_0^h{q}_{1\mathrm{net}}\left(z\right)\cos \left(\frac{m\pi z}{h}\right)\mathrm{dz}& \left(15\right)\end{array}$

and the parameters
T.sub.0—a predefinable ambient temperature;
x.sub.0—a predefinable offset of the beam of laser 10b relative to the origin of a coordinate system movable with laser 10b;
λ—a predefinable heat conductivity of material pieces 13, 14;
a—a predefinable temperature conductivity of material pieces 13, 14;
q.sub.net—a predefinable power of laser 10b;
q.sub.1net—a predefinable power distribution of laser 10b along a depth coordinate of material pieces 13, 14;
v—a predefinable speed of laser 10b;
h—a predefinable thickness of material pieces 13, 14;
and with Bessel function

[00003]$K_0\left(\omega \right)=\frac{1}{2}{\int }_{-\infty }^{\infty }\frac{e^{i\omega t}}{\sqrt{t^2+1}}dt$

as well with an ascertained temperature distribution T(x,y,z). From the temperature distribution, it is possible to ascertain a width and a depth of the weld seam (for example, via the ascertainment of isotherms at a melting temperature of one material of material pieces 13, 14). From the temperature distribution, it is possible, for example, to also directly ascertain an entire power input.

[0077] A cost function K is evaluated as a function of these variables, as it may be provided, for example by equation 1, variables y.sub.sim being provided as features q.sub.i and corresponding target values of these variables q.sub.i,target.

[0078] A cost function K is also possible, which punishes deviations of the features from the target values, in particular if they exceed a predefinable tolerance distance, and rewards a high productivity. The “punishment” may be implemented, for example by a high value of cost function K, the “reward” correspondingly by a low value.

[0079] It is then ascertained whether cost function K indicates that instantaneous process parameters x are good enough; in the event that a punishment means by a high value and a reward means by a low value it is checked whether cost function K drops below a predefinable maximum cost value. If this is the case, the simulative training ends with instantaneous process parameters x.

[0080] If this is not the case, data point x,y.sub.sim thus obtained from process parameters x and associated variables y.sub.sim characterizing the result is added to the ascertained test data and first Gaussian process model GP.sub.0 is retrained, i.e., hyperparameters Θ.sub.0,Θ.sub.1 of first Gaussian process model GP.sub.0 are adapted in such a way that a probability that the test data result from the first Gaussian process model GP.sub.0 is maximized.

[0081] An acquisition function is then evaluated, as is illustrated, for example, in formula 7, and a new process parameter x′ hereby ascertained. The step of evaluating the simulation model is then returned to, new process parameters x′ being used as instantaneous process parameters x and the method runs through a further iteration.

[0082] After simulative training of first Gaussian process model GP.sub.0 has occurred, process parameters x are subsequently evaluated using an acquisition function, as is illustrated, for example, in formula 7 and new process parameters referred to below as x.sub.exp, are ascertained 230 in order to experimentally train second Gaussian process model GP.sub.V and third Gaussian process model GP.sub.2. With these process parameters x.sub.exp, laser material processing machine 1, 2 is activated and measured variables y.sub.exp are ascertained, which characterize the actual result of the laser material processing, and the data-based model is trained with the test data thus ascertained as described below.

[0083] In the case of laser drilling, these process parameters x include, for example, a pulse duration and/or a focus position time-dependently resolved via a characteristic diagram and/or a focal length and/or a pulse repetition frequency and/or a circular path diameter time-dependently resolved via a characteristic diagram (time-dependent) and/or a circular path frequency and/or a setting angle time-dependently resolved via a characteristic diagram and/or a drilling duration and/or a pulse energy time-dependently resolved via a characteristic diagram and/or a wavelength and/or parameters, which characterize a process inert gas such as, for example, a process gas type or a process gas pressure. The aforementioned circular path in this case is a known feature in many drilling methods, for example, in spiral drilling or in trepanning. Measured variables y.sub.exp include, variables, for example, which characterize the size of drill hole 11 and/or the circularity of drill hole 11 and/or the shape of a wall of drill hole 11 and/or the presence of melt deposits and/or a quantity of droplet ejection during the drilling process and/or a rounding of the edges of drill hole 11 and/or the productivity.

[0084] In the case of laser welding, process parameters x include, for example, laser power time-dependently or position-dependently resolved via characteristic diagrams and/or a focus diameter and/or a focus position and/or a welding speed and/or a laser beam inclination and/or a circular path frequency of a laser wobbling and/or parameters that characterize a process inert gas. Measured variables y.sub.exp include, for example, variables which characterize a minimal weld seam depth and/or a minimal weld seam width along weld seam 15 and/or the productivity and/or a number of weld spatters and/or a number of pores and/or a welding distortion and/or internal welding stresses and or welding cracks.

[0085] To train the data-based model using the ascertained pair of process parameters x.sub.exp and measured variables y.sub.exp, the following variables are initially ascertained 230: [0086] a simulative model uncertainty σ.sub.P as the square root of variance σ.sup.2 of first Gaussian process model GP.sub.0 at position x.sub.exp, [0087] a simulative model prediction μ.sub.P as the most probable value of first Gaussian process model GP.sub.0 at position x.sub.exp, [0088] an experimental model uncertainty σ.sub.exp as the square root of variance σ.sup.2 of second Gaussian process model GP.sub.V at position x.sub.exp, [0089] an experimental model prediction μ.sub.exp as the most probable value μ.sub.exp of third Gaussian process model GP.sub.1 at position x.sub.exp.

[0090] Measured variables y.sub.exp, are now each affinely transformed 240 according to the following formula:

[00004]$\begin{array}{cc}{y}_{exp}.fwdarw.y_{exp}^{aff}=\frac{{\sigma }_P}{{\sigma }_{exp}}.Math.\left(y_{exp}-{\mu }_{exp}\right)+{\mu }_P& \left(16\right)\end{array}$

[0091] Second Gaussian process model GP.sub.V and third Gaussian process model GP.sub.1 are subsequently trained 250.

[0092] Second Gaussian process model GP.sub.V in this case is trained with the aid of non-transformed measured variables y.sub.exp, in that data point x,y.sub.exp from process parameters x and associated measured variables y.sub.exp are added to the ascertained test data for second Gaussian process model GP.sub.V and second Gaussian process model GP.sub.V is retrained, i.e., associated hyperparameters Θ.sub.0,Θ.sub.1 of second Gaussian process model GP.sub.V are adapted in such a way that a probability that the test data result from second Gaussian process model GP.sub.V is maximized.

[0093] Third Gaussian process model GP.sub.1 in this case is trained with the aid of affinely transformed measured variables y.sub.exp.sup.aff, in that data point x,y.sub.exp.sup.aff from process parameters x and associated affinely transformed measured variables y.sub.exp are added to the ascertained test data for third Gaussian process model GP.sub.1 and third Gaussian process model GP.sub.1 is retrained, i.e., associated hyperparameters Θ.sub.0,Θ.sub.1 of third Gaussian process model GP.sub.1 are adapted in such a way that a probability that the test data result from third Gaussian process model GP.sub.1 is maximized.

[0094] A further cost function K′ is evaluated 160, similar to the evaluation of cost function K in step 210, as it may be provided for example, by equation 1, measured variables y.sub.exp being provided as features q.sub.i and as corresponding target values of these variables q.sub.i,target.

[0095] It is then ascertained whether cost function K indicates that instantaneous process parameters x are good enough. (260) If this is the case (“yes”), the method ends 270 with instantaneous process parameters x.

[0096] If this is not the case, (“no”), a return is made to step 220.

[0097] FIGS. 5 and 6 show, by way of example, for a laser welding machine, a successfully trained data-based model including the first, second and third Gaussian process model. FIG. 5 shows a depth ST of a weld seam as a function of speed v of laser 10b;

[0098] FIG. 6 shows a number N of spatters that form during the welding process as a function of speed v.

[0099] The output of the simulation model (dotted) used for the simulative training of first Gaussian process model GP.sub.0, experimentally ascertained measured points x,y.sub.exp (black circles), model prediction μ as the most probable value of the data-based model (center black line) and a prediction inaccuracy (95% confidence interval) of the data-based model (gray hatched area) are each represented. FIG. 6 shows the successful training of the data-based model, even though the experimentally ascertained measured variable of spatter number N is not able to be simulatively ascertained. It was discovered, however, that the number of the spatters strongly correlates with the simulatively ascertainable power input, so that this simulatively ascertainable variable is used as simulation data.

[0100] To ascertain model prediction μ as the most probable value of the data-based model with predefined process parameters x, the sum of the model prediction of first Gaussian process model GP.sub.0 and of third Gaussian process model GP.sub.1 is used and subsequently transformed with the inverse of formula 16, the parameters being ascertained similarly to step 230.

[0101] The described method of the present invention is not limited to laser material processing, but may be applied similarly to arbitrary manufacturing methods and to arbitrary (technical or physical) systems such as, for example, mechatronic systems, in which an operating variable is optimally set in such a way that a model output variable of the system that characterizes the operating mode of the system is optimized.