DE102014207683A1 - Method and device for creating a data-based function model - Google Patents

Abstract

The invention relates to a method for creating a data-based function model, in particular a Gaussian process model, with the following steps: providing (S1) training data; - dividing (S2) the training data into subsets of training data; - creating (S3) a data-based local sub-model (51) based on each of the subset of the training data; and - combining (S5) the local submodels (51) to obtain the data-based functional model.

Description

Technical area

The present invention relates to control devices for engine systems, in particular control devices with a separate computing unit for evaluating data-based function models, such as Gaussian process models. The present invention further relates to algorithms for creating data-based function models based on training data.

State of the art

So far, functional models in ECUs, i. H. Track and system models, implemented by the specification of maps, characteristics or a physical system replicating functions. These are adapted by a user by adapting the model parameters to the conditions of the physical system.

An alternative is the use of non-parametric, data-based function models, with which the functions of physical systems can be simulated essentially without the specification of parameters. As a data-based functional model, for example, a Gaussian process model can be used, which is essentially defined by hyperparameters and support points. The data-based functional models are created on the basis of training data that can be determined in a test system. The support points for the Gaussian process model can correspond to the training data or can be selected from it or generated.

In particular, local effects may not be adequately mapped by the created data-based function model. If a data-based functional model has already been determined on the basis of training data of an initial training data record, then it is difficult to appropriately include training data of a subsequently determined training data record in the already created data-based functional model. However, by simply merging the training data sets with or without varying the hyperparameters of the data-based model, local effects can only be adequately considered if the training data of the subsequently added training data set has a sufficient number of measurement points. Furthermore, it is necessary that the measurement points of the subsequently added training data set are not inconsistent with already existing measurement points of the initial training data set, ie. H. have a relatively large deviation from these. Otherwise, one obtains data-based function models with high measurement noise and consequently high model error for the function values in the area of the local effect.

Control units with a microcontroller and a separate model calculation unit for calculating data-based models in a control unit are known from the prior art. For example, this is off DE 10 2010 028 259 A1 a controller with an additional logic circuit, which is designed to calculate exponential functions, in order to support the implementation of Bayes regression methods, which are needed in particular for the calculation of Gaussian process models.

Furthermore, it is off C. Plagemann, K. Kersting, W. Burgard, "Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness", ICML Proceedings, pages 204-2116, 2006 , another method for adding measurement points of another training data set to an existing Gaussian process model is known. However, this method is inefficient, especially since the parameter optimization is difficult.

Disclosure of the invention

According to the invention, the method for creating a data-based functional model based on training data according to claim 1 and the device, the computer program and the control device are provided according to the independent claims.

Further embodiments are specified in the dependent claims.

• – Bereitstellen von Trainingsdaten;
• – Unterteilen der Trainingsdaten in Untermengen von Trainingsdaten;
• – Erstellen eines datenbasierten lokalen Teilmodells basierend auf jeder der Untermengen der Trainingsdaten; und
• – Kombinieren der lokalen Teilmodelle, um das datenbasierte Funktionsmodell zu erhalten.

According to a first aspect, a method for creating a data-based function model, in particular a Gaussian process model, is provided, which comprises the following steps:

• - providing training data;
• - dividing the training data into subsets of training data;
• - creating a data-based local sub-model based on each of the subsets of the training data; and
• Combining the local submodels to obtain the data-based function model.

One idea of the above method for creating a data-based function model is to subdivide training data of a given training data set into a plurality of sub-sets and to generate data-based local submodels therefrom. The data-based function model to be created is then formed as a combination of the weighted local submodels. The creation of the local data-based submodels takes place in the same way as the known creation of non-parametric data-based models.

In particular, when modeling dynamic behavior, creating the data-based function model via local submodels is advantageous because creating a global data-based function model based on the total amount of training data is inaccurate. One reason for this, for example, is that one single record (either stationary or dynamic) can not map the overall dynamics of the system.

Usually, an input size space of dynamic systems has more complex envelopes and is larger than input size spaces with only stationary input variables. The envelopes of dynamic input size spaces also have concave shapes, making it difficult to estimate the envelope.

The use of local submodels allows incremental adaptation or expansion of data-based functional models for dynamic systems by adding and possibly removing data-based submodels that have been created based on the dynamic input space of the physical model. The above method also allows improved modeling of the local effects caused by the dynamic behavior of the physical system by taking into account the dynamics-filling input space.

In addition, because the computational complexity of traditional data-based function models is n ³ (n = number of training data points), complexity can be significantly reduced by building sub-models from subsets of the dynamics-filling training data.

The weighting of the submodels can be done using the predictive variance. The predictive variance can serve as a metric indicating the distance of the query point from the shell of the respective submodel. The distance measure serves as a description of the uncertainty of the submodel.

The additive combination of several data-based submodels has the further advantage that they can be easily calculated in a control unit with an additional model calculation unit.

By providing the model calculation unit which independently calculates a plurality of data-based submodels one by one and adds up the resulting sub-results, a simple determination of a function value based on the above additive function model is enabled. By avoiding that the arithmetic unit must prepare the model calculation unit for the calculation of each individual submodel, the calculation of a corresponding function value can be significantly accelerated.

Furthermore, the training data may comprise training data points, the training data comprising training data points, each training data point having a value of at least one measurement variable of a current calculation cycle, a value of at least one output variable of a current calculation cycle, at least one value of one of the measurement variables from a preceding calculation cycle and / or a value of Output variable from a previous calculation cycle includes as input values.

According to one embodiment, the subdivision of the training data may be performed manually or automatically, in particular using a k-means algorithm or a mean-shift algorithm.

It can be provided that the subdivision of the training data is performed by forming subsets of training data points, wherein the training data points of a subset so are selected to have an Euclidean distance from each other that is less than a predetermined threshold.

In particular, the combining of the local submodels may be performed by forming a weighted average of the local submodels.

According to one embodiment, the local submodels may be weighted depending on a measure of the model uncertainty, in particular depending on a predictive variance.

Furthermore, in the created data-based function model, new training data points can be taken into account by adding them to one of the subsets of the training data.

In the created data-based function model, a new training data point may be taken into account by adding it to one of the subsets of the original training data, building the local sub-model from the corresponding subset of the original training data, and then combining the corresponding local sub-model with the remaining local sub-models.

According to a further aspect, a method for providing a data-based function model is provided, wherein training data points are selected from one or more functional areas of the data-based functional model and another data-based functional model is determined based on the selected training data points according to the above method, wherein the data-based functional model and the other data-based functional model can be combined.

Furthermore, the training data points may be selected from the training data if their variance exceeds a predetermined variance threshold.

Furthermore, the data-based function model and the further data-based function model can be combined by forming a weighted average from the function models, wherein the function models are weighted in particular on the basis of the predictive variance.

• – Trainingsdaten bereitzustellen;
• – die Trainingsdaten in Untermengen von Trainingsdaten zu unterteilen;
• – ein datenbasiertes lokales Teilmodell basierend auf jeder der Untermengen der Trainingsdaten zu erstellen; und
• – die lokalen Teilmodelle zu kombinieren, um das datenbasierte Funktionsmodell zu erhalten.

According to a further aspect, a device, in particular a computing unit, for creating a data-based function model, in particular a Gaussian process model, is provided, wherein the device is designed to

• - provide training data;
• - subdivide the training data into subsets of training data;
• To create a data-based local sub-model based on each of the subsets of the training data; and
• - Combine the local submodels to obtain the data-based functional model.

According to a further aspect, a computer program is provided, which is set up to execute all steps of the above method for creating a data-based function model.

Brief description of the drawings

Embodiments are explained below with reference to the accompanying drawings. Show it:

1 a schematic representation of a test bench for measuring a physical system to obtain an output variable y for measured variables;

2 a schematic representation of a dynamic system to be modeled with an input variable vector u and an output variable y;

3 a function model structure with an input variable vector u comprising values of measured variables and an output variable y of a current computing cycle and values of measured variables and the output of preceding computing cycles;

4 a flowchart for illustrating the method for creating a data-based function model;

5 a schematic representation of the basic structure of determining a function value for a data-based function model, which is created from local sub-models;

6 a diagram of a two-dimensional input size space with training data points in a first subset and a second subset and to be added new training data points;

7 a flowchart for illustrating a method for adding a new training data point to an existing data-based function model;

8th a diagram illustrating the addition of the new training data to the subsets; and

9 a flowchart for illustrating a method for adding a new training data point to an existing data-based function model.

Description of embodiments

1 shows a schematic representation of a test bench 1 for testing a physical system 2 , such as an internal combustion engine. The test bench 1 further comprises a test control unit 3 , the measured quantities u (input signals) for the internal combustion engine 2 provides. Corresponding output variables of the internal combustion engine 2 measured, which are assigned to the measured quantities and as test data in a test data memory 4 get saved. The test data thus obtained are then used to evaluate the behavior of the internal combustion engine 2 or for the creation of the internal combustion engine 2 descriptive models available.

Possible measured variables generated by the test control unit 3 are generated, represent an internal combustion engine 2 For example, manipulated variables for a throttle valve actuator, the speed of the internal combustion engine 2 , the load of the internal combustion engine 2 , a manipulated variable for a camshaft phaser and a manipulated variable for setting an ignition timing, an injection quantity and the like. Output variables of the internal combustion engine 2 may be a lambda value, an exhaust backpressure, an engine temperature, a rotational speed, an engine torque, and the like.

To the dynamic behavior of the internal combustion engine 2 to fully test, it is not sufficient to vary the measurands u in their value ranges, in the internal combustion engine 2 apply and the corresponding resulting behavior of the internal combustion engine 2 in the form of self-adjusting output variables. Rather, it is desirable, even the dynamic behavior of the internal combustion engine 2 in a corresponding manner in a data-based function model to be created. Therefore, the values of the applied measured quantities u, which define the input quantity space, can be varied with different dynamic behavior or different temporal gradient, respectively, to the corresponding dynamic response of the internal combustion engine 2 in the form of the corresponding output quantities.

The measuring points X defined by the combination of the values of the measured quantities u in an input variable space should as far as possible be both space-filling and dynamic-filling. The measuring points X thus generated are space-filling if the distance of each measuring point X determined by the combination of the discretized signal values of the input signals from at least one further of the measuring points X thus determined is smaller than a predetermined distance value. Analogously, the measuring points X generated in this way are dynamic filling when the distance of each measuring point X determined by the combination of the discretized signal values of the input signals and their temporal gradients from at least one further of the measuring points X thus determined is smaller than a predetermined dynamic distance value.

The with the above test bench 1 certain measurement points X are now used to create a data-based function model, which also maps the dynamic properties of the physical system 2.

The use of non-parametric, data-based function models is based on a Bayes regression method. The basics of Bayesian regression are, for example, in CE Rasmussen et al., Gaussian Processes for Machine Learning, MIT Press 2006 , described. Bayesian regression is a data-based method based on a model. To create the model, measurement points of training data and associated output data of an output variable to be modeled are required. The modeling is done by using support point data that contains the Training data completely or partially correspond or be generated from these. Furthermore, abstract hyperparameters are determined which parameterize the space of the model functions and effectively weight the influence of the individual measurement points of the training data on the later model prediction.

The abstract hyperparameters are determined by an optimization method. One possibility for such an optimization method is an optimization of a marginal likelihood p (Y | H, X). The marginal likelihood p (Y | H, X) describes the plausibility of the measured y-values of the training data, represented as vector Y, given the model parameters H and the x-values (input values) of the training data. In model training, p (Y | H, X) is maximized by searching for suitable hyperparameters that result in a course of the model function determined by the hyperparameters and the training data and map the training data as accurately as possible. To simplify the calculation, the logarithm of p (Y | H, X) is maximized because the logarithm does not change the continuity of the plausibility function.

Conventional modeling of non-parametric, data-based function models does not always yield sufficiently accurate models. One reason for this is that the large number of dynamically acquired measurement data results in 100,000 or more training data points, so the original data must be reduced and / or sparse Gaussian processes applied. Thus, the resulting data-based functional models may be inaccurate in accuracy due to information loss.

Furthermore, it is generally not possible to vary the input quantities x for mapping all the dynamic effects of the physical system 2, so that a resulting data-based function model often can not accurately map all the effects that can occur in the physical system 2. Traditional modeling for a data-based function model, such as the Gaussian process model, provides a global dynamic representation of the training data that can neglect local dynamic effects.

Furthermore, with traditional data-based function models, it is difficult to adapt already created models in the presence of new training data. So far, it is necessary to re-learn the entire data-based function model if additional training data is to be added. However, this is particularly difficult if the total amount of training data significantly increases the computational effort to create the data-based functional model.

2 schematically shows a dynamic system to be modeled with a measured variable vector u and an output variable y. The elements of the measurand vector u are u ₁ (k), u ₂ (k), ..., u _n (k). A training data set resulting from a measurement of the dynamic system can be given as follows:

To model dynamic processes, an input structure known as Nonlinear Autoregression With Exogenous Inputs (NARX) may be used. A typical NARX structure is in 3 shown, for at least one of the measured variables u historical values, ie values of previous calculation cycles and historical values of the output variable y, as input variables x in the data-based function model to be created. Mathematically, this NARX structure is described as follows: y (k) = f _NL ((u ₁ (k), ..., u ₁ (k - τ ₁ ), ..., u _n (k), ..., u _n (k - τ _n ) , y (k - 1), ..., y (k - τ _y)) = f _NL ((x (k)) where u is the measured variable vector, d is the input dimension, k is the sampling time, and x and y are the input quantities and output quantities at the specified time. f _NL corresponds to a nonlinear function that can be described using the data-based function model, such as the Gaussian process regression described above.

A Gaussian process corresponds to a multivariate Gaussian with random variable points. A Gaussian process is fully described by the mean value function μ (x) and the covariance k (X, X) function. y ~N (μ (X), k (X, X))

wobei σ_n ² dem Ausgangsrauschen und f_* dem zu schätzenden Ausgangswert entsprechen. Für den obige Gauß-Prozess entspricht die posterior Verteilung für X_* ebenfalls einem Gauß-Prozess und kann angegeben werden als: f_*|X, Y, X_* ~ N(f(X_*), cov(X_*)), mit einer Mittelwertfunktion, die bestimmt ist als: f_* ≙ E[f_*|X, Y, X_*] = K(X_*, X)[K(X, X) + σ_n ²I]^–1Y und der entsprechenden prädiktiven Varianz cov(X_*) = K(X_*, X_*) – K(X_*, X)[K(X, X) + σ_n ²I]^–1K(X, X_*). The covariance function can be described with a positive definite nucleus, for example a quadratic exponential nucleus: k (x _i, x _i) = σ 2 / Fexp (1 / 2Σ D / d = 1 (x _i - x _i) ² / l _d ^2), where σ _f and I _d correspond to the hyperparameters. These parameters can be optimized using training data. Thus the Gaussian process can be written as

where σ _n ² corresponds to the output noise and f _{* to} the initial value to be estimated. For the above Gaussian process, the posterior distribution for X _* also corresponds to a Gaussian process and can be given as: f _* | X, Y, X _* N (f (X _* ), cov (X _* )), with an average function determined as: f _* ≙ E [f _* | X, Y, X _* ] = K (X _* , X) [K (X, X) + σ _n ² I] ^-1 Y and the corresponding predictive variance cov (X _*) = K (X _*, X _*) - K (X _* X) [K (X, X) + σ _n ² I] ^-1 K (X, X _*).

The predictive variance can be interpreted as a measure of model uncertainty. The larger the value of the variance, the more uncertain the data-based function model is in terms of prediction of the query point. This variance can be used for the prediction in the method described below for creating a data-based function model. The method described is based on the separate creation of local submodels 51 ie local data-based function models. The submodels 51 are created with subsets of the original measurement data as training data. The subsets of the measurement data correspond to smaller local subspaces of the measurement data.

In 4 FIG. 4 is a flow chart illustrating a method of creating a data-based function model from sub-models.

In step S1, an input variable vector x is provided for each computing cycle, which measures the measured values of the measured quantities u u by the test system 1 and at least one of the measured quantities u comprises one or more historical or past measured variable values. The historical measured values relate to values of a measured variable u from previous calculation cycles. Furthermore, the input variable vector x may also include historical values of the considered output variable y. The input variable vector x determined in this way and the value of the output variable y obtained for the relevant measurement time for a plurality of measurement times represent the training data for the Gauss process model to be created.

In step S2, the training data is divided into clusters. The splitting of the training data may be performed either manually by expert knowledge or by conventional automated clustering techniques to obtain subsets of the training data. The division by expert knowledge can be done manually based on physical findings. For example, in the presence of various system modes, an expert may identify the particular modes of operation based on ranges of values of one, more, or all inputs x, thus subdividing the provided training data into appropriate subsets. In many applications, the expert can manually select the training data points and thereby improve the functional model to be learned.

If no expert knowledge is available, conventional automatic clustering or classification methods can be used, such as a k-means algorithm, a mean-shift algorithm and the like. In doing so, suitable metrics for the classification of the training data must be examined and selected.

In step S3, a local submodel is now determined for each of the subset of training data obtained in the manner described above 51 created. Each data-based function model is determined by its nodes, which can correspond to the subset of training data, the vector Q _y and the hyperparameters.

In step S4, for all local submodels 51 additionally determines the predictive variances cov (X _* ). The training process for the local submodels 51 may correspond to a conventional process for creating a Gaussian process model. Other training processes known per se can also be used. Here are the local submodels 51 learned independently, ie the hyperparameters of the local submodels 51 are optimized separately from each other using previously determined subsets of training data.

In step S5, a weighted average of the local submodels now becomes 51 determines the weighting of each of the local submodels 51 depends on its predictive variance cov (X _* ).

After the weighting of the individual partial models, these are summed up in step S6 in order to obtain the data-based functional model. For a number m of local submodels 51 For example, a weighted average y can be calculated from a query point x _* , for example:

Here, the predictive variance cov ⁱ (x _* ) becomes the weighting of the corresponding mean prediction values f ⁱ (x _* ) for each local submodel (i: index of the local submodel) used.

The basic structure of weighted prediction is in 5 shown. One recognizes that the functional values f ¹ (x _* ), f ² (x _* ), ..., f ⁿ (x _* ) from m local submodels 51 with the corresponding predictive variance cov ¹ (x _* ), cov ² (x _* ), ..., cov ⁿ (x _* ) for a query point x _* together in respective multiplication blocks 52 multiplied and then in an addition block 53 be added. The sum thus obtained is in a divider 54 through the in a summator 55 obtained sum of the predictive variances cov ¹ (x _* ), cov ² (x _* ), ..., cov ⁿ (x _* ) of all local submodels 51 divided by the weighted average ŷ for all local submodels 51 to obtain.

The corresponding variance of the local submodels 51 can be determined as

Using these equations, the mean prediction and variance of the local submodels 51 for a query point x _* .

The above method can significantly improve the accuracy of function value calculations using data-based function models. This is due in particular to the fact that the complex envelope of the input variable space of a dynamic system can be mapped better in the resulting data-based functional model than in the case of the combination of the dynamic consideration of the measured quantities u and / or the output variable y in conjunction with the subdivision of the resulting input variable space a mere stationary consideration would be the case.

With regard to the above classification step, the metrics for classifying the training data may also be used to retrofit new training data to a local submodel 51 add. For example, if the new training data is similar to the existing training data, then that training data may be added to a subset or portions of several already defined subsets. In order to adapt the data-based function model, only the one or more changed subsets need to be re-trained and, as described above, the weighted sum over all submodels has to be trained 51 ie the existing submodels 51 based on the unchanged subsets and the changed submodels 51 based on the changed subsets.

If new training data points NTP are added after the creation of a data-based function model based on original training data, these can also be added to the existing subsets of the original training data. 6 For a two-dimensional input size space, it is possible to add new training data points NTP to a first subset GPR1 or to a second subset GPR2. Conventional methods based on the distance to the midpoint of the respective subset may include: U. but not lead to the optimal solution.

In 7 FIG. 3 is a flowchart for illustrating a method for adding a new training data point NTP.

In step S11, the respective new training data point NTP is added to each of the previously determined subsets of the original training data points and the respective predictive variance is determined. The new training data point NTP is added in step S12 to the subset at which the least variance has been found. Since the predictive variance is part of the approach of the local submodels 51 is calculated, and can be used directly to solve the selection problem. Subsequently, as described above, in step S13, the partial models determined with respect to the remaining subsets and the subset with the new training data point NTP added are obtained 51 weighted and added to obtain the data-based function model.

In the diagram of 8th it can be seen that the new training data points NTP lying outside the shells of the subgroups GPR1, GPR2 are added by the above method to those subgroups GPR1, GPR2 whose sheath is closest to the respective new training data point NTP.

In order to take into account a measurement noise in the classification of the training data, which leads to deviations of the value of the output variable y at a position in the input size space, the division of the training data into subsets can be performed using the Euclidean distance of the training data points in the input size space. That is, training data points are subdivided into subsets using their Euclidean distance so that differences in their variances can be detected.

The splitting of the training data taking into account the Euclidean distance can serve to optimize the variance in the input size space. The division into subsets can be carried out, for example, by a threshold value comparison of the Euclidean distance with a predetermined threshold value. That is, training data points whose Euclidean distances are smaller than the predetermined threshold are assigned to a subset of the training data points.

Another variant in the classification is that only those subsets of the training data are taken into account whose variances are each below a predetermined variance threshold. The subsets thus selected become local function models 51 created. These local submodels 51 can be weighted and added according to their predictive variances.

According to the flowchart of FIG 9 According to certain methods, a data-based functional model, which is determined in a conventional manner or according to one of the above methods, can be further improved. For this purpose, in step S21 training data points are determined in functional areas of the created data-based function model whose variances are above a predetermined variance threshold value.

In step S22, for the training data points residing in the respective functional areas of the data-based functional model, as described in connection with the flowchart of FIG 4 described another data-based functional model determined. The original data-based function model and the further data-based function model are then suitably combined in step S23. The combining may occur as described in connection with step S5 by forming a weighted average, in particular with a variance-dependent weighting.

The creation of the additional data-based function model can be done with little effort, depending on which value the variance threshold is set. In particular, the variance threshold can be set such that between 10 and 50%, preferably between 10 and 20%, of the training data points are used to create the further data-based function model

Training data points, which are also located in the input space of the original data-based function model, provide an overlap between the two data-based function models in the originally provided data-based function model and the local submodel 51 , However, this overlap does not disturb the prediction because the model output y of the global model is weighted with the variance.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102010028259 A1 [0005]

Cited non-patent literature

• C. Plagemann, K. Kersting, W. Burgard, "Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness", ICML Proceedings, pages 204-2116, 2006 [0006]
• CE Rasmussen et al., Gaussian Processes for Machine Learning, MIT Press 2006 [0045]

Claims (15)

Method for creating a data-based function model, in particular a Gaussian process model, comprising the following steps: - providing (S1) training data; - dividing (S2) the training data into subsets of training data; - Create (S3) a data-based local submodel ( 51 ) based on each of the subsets of the training data; and - combining (S5) the local submodels ( 51 ) to obtain the data-based function model. The method of claim 1, wherein the training data comprises training data points, each training data point having a value of at least one measurand (u) of a current computation cycle, a value of at least one output (y) of a current computation cycle, at least one value of one of the measurands (u) from a previous one Calculation cycle and / or a value of the output variable (y) from a previous calculation cycle includes as input values The method of claim 1 or 2, wherein the subdivision (S2) of the training data manually or automatically, in particular by means of a k-means algorithm or a mean-shift algorithm is performed. The method of claim 1 or 2, wherein the subdividing (S2) of the training data is performed by forming subsets of training data points, wherein the training data points of a subset are selected to have a Euclidean distance from each other that is less than a predetermined threshold. Method according to one of claims 1 to 4, wherein the combining (S5) of the local submodels ( 51 ) by forming a weighted average of the local submodels ( 51 ) is carried out. Method according to claim 5, wherein the local submodels ( 51 ) are weighted depending on a measure of the model uncertainty, in particular depending on a predictive variance. Method according to one of claims 1 to 6, wherein in the created data-based function model new training data points (NTP) are taken into account by adding these to one of the subsets of the training data. Method according to one of claims 1 to 7, wherein in the created data-based function model a new training data point (NTP) is taken into account by adding it to one of the subsets of the original training data, the local submodel ( 51 ) is created from the corresponding subset of the original training data and the corresponding local sub-model ( 51 ) with the remaining local submodels ( 51 ) is combined. A method for providing a data-based functional model, wherein training data points are selected from one or more functional areas of the data-based functional model and another data-based functional model is determined based on the selected training data points according to a method of any one of claims 1 to 7, wherein the data-based functional model and the further data-based Functional model can be combined. The method of claim 9, wherein the training data points are selected from the training data if their predictive variance exceeds a predetermined variance threshold. The method of claim 9 or 10, wherein the data-based function model and the further data-based function model are combined by a weighted average is formed from the function models, wherein the function models are weighted in particular based on the predictive variance. Device, in particular a computing unit, for creating a data-based function model, in particular a Gaussian process model, wherein the device is designed to: provide training data; - subdivide the training data into subsets of training data; A data-based local sub-model ( 51 ) based on each of the subsets of the training data; and - the local submodels ( 51 ) to obtain the data-based function model. Computer program adapted to carry out all steps of a method according to one of Claims 1 to 11. Machine-readable storage medium on which a computer program according to claim 13 is stored. An electronic control device comprising an electronic storage medium according to claim 14.

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