DE102024204828A1 - Method and apparatus for creating a data-based or parametric functional model for the control or regulation of a technical system - Google Patents

Abstract

The invention relates to a computer-implemented method for providing a data-based model (41), in particular for operating a technical system, wherein the data-based model (41) is configured to output a model output depending on a provided input data point (M), which can be used for controlling or regulating the technical system or as a virtual sensor in the technical system, comprising the following steps:
- Provision (S1, S2, S4) of the data-based model (41) initially trained with initial measurement data points, wherein the initial measurement data points represent labeled input data points (M) obtained from a survey;
- Providing a number of query points (Q) that are equally distributed in an input data space of input data points,
- Determining (S3) a density value for each query point (Q) in the form of a point density, which depends on the number of nearest measurement data points to the query point (Q) in question that do not have a nearest query point (Q);
- Identify (S6, S7) at least one query point (Q) as the query point for which the density value indicates a point density around the identified query point that is too low;
- Acquisition (S8) of further measurement data points in a measurement data space around the at least one identified query point (Q); and
- Retraining (S9) the data-based model (41) based on the new measurement data points.

Description

Technical field

The invention relates to the training of data-based regression or classification models, in particular Gaussian process models. The invention further relates to the training of data-based models based on measurement data that are unevenly distributed in the input space.

Technical background

Technical systems are frequently operated with control units in which a microcontroller executes an algorithm implemented in hardware and/or software in the form of a computational model. Due to the complexity of the physical system, these models are often difficult to model physically. Therefore, data-driven models trained as computational models are used to represent or account for the real physical behavior of the system. These computational models can be evaluated at a specific evaluation data point to determine control variables directly or indirectly. Such data-driven models can include, for example, RBF networks, neural networks, Gaussian process models, and the like.

To create data-driven models, which can include regression or classification models, training datasets are required. These datasets represent pairs of input data points from one or more input variables and output values. Collectively, they define the desired model relationship that the data-driven model is intended to represent. Such training datasets are typically selected from measurement data points obtained by measurements on the technical system on a test bench. For example, technical systems on a test bench can be operated with trajectories of input data points, and a resulting variable can be recorded as a label. Thus, the measurement data points are derived from the traversed input data points of the trajectory and the recorded resulting variable as a label.

The previously selected or determined input data points define an input data space within which an evaluation/inference of the data-driven functional model trained with them is valid. Typically, the number of recorded measurement data points is much higher than the number of required training data sets, so suitable training data sets must be selected from the recorded measurement data points before training begins.

For the selection of training datasets, especially for Gaussian process models, it is essential that the training datasets are space-filling and uniformly distributed across the input data space with respect to their input vectors. Otherwise, difficulties often arise because the determination of length scales is dominated by areas of high data density, and the model quality suffers in areas of low data density.

If the measurement data points are acquired using a stationary experimental design, a sufficiently good data distribution can be ensured through the experimental design itself. However, if the measurement data points are determined for a transiently operated technical system, the resulting data distribution is often unevenly dense. Furthermore, the number of available measurement data points in the measurement data can be orders of magnitude too high for training a Gaussian process model.

Disclosure of the invention

According to the invention, a method for creating a data-based functional model using training data sets from measurement data according to claim 1 and a corresponding device according to the dependent claim are provided.

Further details are specified in the dependent claims.

• - Bereitstellen des mit initialen Messdatenpunkten initial trainierten datenbasierten Modells, wobei die initialen Messdatenpunkte aus einer Vermessung erhaltene, mit einem Label versehene Eingangsdatenpunkte darstellen;
• - Bereitstellen einer Anzahl von Abfragepunkten, die in einem Eingangsdatenraum der Eingangsdatenpunkte gleichverteilt sind,
• - Ermitteln einer Dichteangabe für jeden Abfragepunkt in Form einer Punktedichte, die jeweils von einer Anzahl von für den betreffenden Abfragepunkt nächstgelegenen Messdatenpunkten, die keinen nächstgelegeneren Abfragepunkt aufweisen, abhängt;
• - Identifizieren mindestens eines Abfragepunkts als der Abfragepunkt, für den die Dichteangabe eine zu geringe Punktdichte um den identifizierten Abfragepunkt angibt;
• - Erfassen von weiteren Messdatenpunkten in einem Messdatenraum um den mindestens einen identifizierten Abfragepunkt; und
• - Nachtrainieren des Modells basierend auf den neuen Messdatenpunkten.

According to a first aspect, a computer-implemented method for providing a data-based model, in particular for operating a technical system, is provided, wherein the data-based model is designed to output a model output depending on a provided input data point, which can be used for controlling or regulating the technical system or as a virtual sensor in the technical system, with the following steps:

• - Providing the data-based model initially trained with initial measurement data points, where the initial measurement data points represent labeled input data points obtained from a survey;
• - Providing a number of query points that are equally distributed in an input data space of input data points,
• - Determining a density value for each query point in the form of a point density, which depends on the number of measurement data points nearest to the query point in question that do not have a nearest query point;
• - Identify at least one query point as the query point for which the density value indicates a point density around the identified query point that is too low;
• - Acquisition of further measurement data points in a measurement data space around the at least one identified query point; and
• - Retraining the model based on the new measurement data points.

It may be provided that for each of the query points to which one or more than one measurement data point is assigned, a model accuracy is determined as an error value using a predefined loss function, wherein the identification of the at least one query point includes sorting the query points according to the magnitude of the assigned density specification, performing a regression on the model inaccuracy with respect to the order of the sorted query points, and identifying the at least one query point if its model inaccuracy deviates from the regression curve of the model inaccuracy, in particular by more than a predefined threshold.

Alternatively, for each query point to which one or more measurement data points are assigned, a model inaccuracy can be determined as an error value using a predefined loss function. Identifying the at least one query point involves determining an error measure for each query point that depends on the model inaccuracy and the density value. The at least one query point is identified if its error measure exceeds a threshold. In particular, the threshold is determined by a predefined quantile value, e.g., the 90th percentile, of a distribution of the error measures. The error measure can be determined by or dependent on the model inaccuracy and, conversely, depend on an inverse value or a negative value of the density value. That is, the larger/smaller the model inaccuracy, the larger/smaller the error measure, and the smaller/higher the density value, the higher/smaller the error measure.

As described at the beginning, the data-based model to be created can be used in the control of technical systems, such as the control of electric machines, combustion engines, and the like, to support regulation, for example, by being used in an observer as a virtual sensor, such as a speed sensor, a temperature sensor, and so on. Fundamentally, the data-based model serves to provide a functional relationship that is crucial for the operation of technical systems.

The core of the above procedure involves analyzing the measurement data points from an initial survey to identify areas of input data points that must be considered during the subsequent training of the data-driven functional model. For example, after initial training of the data-driven functional model, the procedure envisages identifying areas of low-density input data points and high model uncertainty. This allows for the acquisition of new measurement data points within these areas to potentially increase the number of measurement points. This can be done, for instance, based on an error measure that depends on the model uncertainty and, for example, an inverse of the density value.

It is also possible to identify areas of input data points in the input data space with a high density of training data points and high model inaccuracy of the trained functional model, in order to determine if the capacity of the data-based functional model is insufficient, or the relevant area of input data points can be excluded from evaluation with the data-based functional model, e.g., rule-based, since it does not allow for better prediction there.

The above method involves training a data-driven functional model from training datasets selected from an initial set of measurement data points, each assigning a label to an input data point. This data-driven functional model can be implemented, for example, as a Gaussian process model, a deep neural network, or similar, and the training of the data-driven functional model can be performed using a conventional gradient-based training method with a predefined loss function.

Furthermore, a number of artificially generated query points are provided in an input data space, which contains the input data area defined by the input data points of the measurement data points. Here, the input data space is understood as the circumscribing hypercube of the given input data points. The term "input data area" subsequently refers to that part of the input data space that is actually covered by measurement points. In particular, the input data area can be defined as a spatial region (dimension n) defined by the connections (dimension n-1) is defined between each adjacent outer measuring points.

The query points are typically generated or provided as space-filling elements within the relevant input data space. For example, the query points can be generated from a pseudo-random sequence, such as a Sobol sequence. These pseudo-randomly generated query points are evenly distributed as random points within the input data space, but do not form a regular grid.

To determine the initial training datasets as a selection from the measurement data points, each query point is assigned the nearest input data point, provided that the respective measurement data point is not closer to another query point. "Nearest" can be understood as a Euclidean distance that takes into account the value range of the respective input dimension or can be normalized to it. Preferably, the dimensions of the input data points are normalized to values between 0 and 1; however, the Euclidean distances can also be determined for unnormalized data points, taking into account the corresponding length scale. Other definitions of distance measures can also be applied here.

Based on the measurement data points, a mapping is created that assigns each query point a set of measurement data points that are closer to that query point than to other query points, so that each measurement data point is assigned to the query point to which it is closest. The number of measurement data points assigned to a query point corresponds to a density value for the density of measurement data points at the query point.

Now, for each query point, the average value of the model inaccuracy at the associated measurement data points is determined according to the loss function. The loss function can be calculated as a mean squared difference between the outputs of the functional model trained with the initial training datasets at the corresponding input data points associated with the respective query point and the corresponding label assigned to that measurement data point. Each query point can have one or more input data points, so that the mean squared difference of the labels and the evaluations for the associated measurement data points results in a local model inaccuracy as an evaluation error.

For each of the query points, an analysis point can now be determined from the local density value and the local model uncertainty.

The query points can be sorted according to their assigned model uncertainty, and the density value can be assigned to the sorting of the query points, and vice versa. Normally, a higher data density correlates with a lower model uncertainty, i.e., better model accuracy, resulting in a roughly monotonically decreasing density value across query points sorted with decreasing model accuracy. If a regression reveals deviations from this trend that exceed a predefined threshold, a query point with excessively high model uncertainty can be identified. If the point density for the query point in question is too low, a more targeted measurement can be performed in that region to capture additional data points. These data points can then be used to determine alternative or additional training datasets for retraining the model.

The acquisition of further measurement data points in a measurement data space around the at least one identified query point can be carried out by selecting for further measurement only input data points that have a distance from the at least one identified query point that does not exceed a specified threshold.

It may be possible to perform retraining by adding the additional measurement data points to the initial measurement data points and training the model based on the combined measurement data points.

• - Identifizieren mindestens eines Abfragepunkts als der Abfragepunkt, für den die Dichteangabe eine zu hohe Punktdichte um den identifizierten Abfragepunkt angibt;
• - Ausschließen der Anwendung und Anwendbarkeit des datenbasierten Modells in dem Bereich um den identifizierten mindestens einen Abfragepunkt. Dies kann beispielsweise durch regelbasiertes Abfragen eines Messdatenpunkts vor dem Auswerten des Modells erfolgen.

The procedure may include the following further steps:

• - Identify at least one query point as the query point for which the density value indicates a point density around the identified query point that is too high;
• - Excluding the application and applicability of the data-based model in the area around the identified at least one query point. This can be achieved, for example, by rule-based querying of a measurement data point before evaluating the model.

If the point density in the area of the relevant query point is average or above average with respect to the course of the regression of the analysis points, then the area of the The relevant query point will be excluded from the model evaluation.

According to another aspect, the technical system is intended to be operated based on the trained data-based functional model.

According to another aspect, a device for carrying out the above procedure is provided.

Brief description of the drawings

• 1 eine schematische Darstellung eines technischen Systems mit einem Steuergerät, in dem ein datenbasiertes Modell implementiert ist;
• 2 ein Flussdiagramm zur Veranschaulichung eines Verfahrens zum Optimieren eines datenbasierten Funktionsmodells basierend auf einer Performance-Analyse anhand der zur Verfügung stehenden Trainingsdatensätze;
• 3 ein Diagramm zur Veranschaulichung eines Verfahrens zur Paarbildung zur Bestimmung von Punktepaaren;
• 4 die Darstellung einer Zuordnung von Trainingsdatenpunkten zum nächstgelegenen Abfragepunkt;
• 5 eine Darstellung einer resultierenden Datendichte basierend auf der Anzahl der Eingangsdatenpunkte, die einem Abfragepunkt zugeordnet sind; und
• 6 eine Darstellung der Verteilung der Punktedichte für Messdaten mit Trainingsdatensätzen und einer Verteilung der lokalen Modellungenauigkeit mit nach Höhe der Modellungenauigkeit sortierten Abfragepunkten.

The embodiments are explained in more detail below with reference to the accompanying drawings. These show:

• 1 a schematic representation of a technical system with a control unit in which a data-based model is implemented;
• 2 a flowchart to illustrate a procedure for optimizing a data-driven functional model based on a performance analysis using the available training datasets;
• 3 a diagram illustrating a procedure for pair formation to determine pairs of points;
• 4 the representation of an assignment of training data points to the nearest query point;
• 5 a representation of a resulting data density based on the number of input data points associated with a query point; and
• 6 a representation of the distribution of the point density for measurement data with training datasets and a distribution of the local model uncertainty with query points sorted by the level of model uncertainty.

Description of embodiments

1 Figure 1 schematically shows a technical system 1 with an actuator 2 in the form of one or more position sensors, for example, electromechanical position sensors and the like. The actuator 2 acts on a technical device 5 and thereby controls it directly, e.g., mechanically. Furthermore, a sensor 3 is provided to detect state variables of the technical device 5 and transmit the corresponding state variables to a control unit 4.

Technical system 1 can be, for example, a machine tool, a robotics application, a motor vehicle, or the like, in which, for instance, electromechanical actuators are provided that execute a movement depending on state variables of system 1. Furthermore, technical system 1 can include a virtual sensor, e.g., for temperature determination, in order to control processes based on a modeled temperature or to implement over-temperature shutdown.

The control unit 4 comprises a data-based functional model 41, which evaluates a predefined evaluation point during the operation of the technical system 1 and provides a corresponding model output. The model output can, for example, represent a value from a virtual sensor implemented with the functional model 41 and/or be used directly or indirectly to control the actuator 2. The evaluation point can be formed, for example, from one or more setpoint variables provided externally or from a sequence controller and/or one or more state variables, for example, sensor-acquired.

The functional model 41 can be designed as a neural network, RBF network, Gaussian process model or the like and trained with training data sets that correspond to labeled input data points.

The data-based functional model 41 must be trained with training data sets before commissioning so that the corresponding function of the control unit 4 can be implemented. For this purpose, the system 1 can be measured on a test bench in a known manner, and labels for input data points can be determined directly or indirectly from the measurement. The input data points and the assigned labels correspond to the measurement data points. The training data sets are generated by selecting from the measurement data points.

The input data points can result from a direct specification of one or more static control variables, such as current, voltage, and the like, or from predefined variables, such as ambient temperature and the like. Alternatively, in transient technical systems, the measurement can be carried out by specifying one or more trajectories of static control variables, and the input data points can be formed using the static control variables and one or more resulting state variables that can be sensorily determined at the control time.

In 2 A flowchart is used to describe the process for creating and improving a data-based functional model.

In step S1, measurement data is first acquired using a test bench measurement to obtain measurement data points. Each of these has an input data point consisting of one or more measured state and/or measurement and/or setpoint variables and at least one assigned label that can be used within the framework of a control or regulation of the technical system or as a virtual sensor.

In step S2, suitable training data sets are selected from the measurement data points.

For this purpose, a number of artificially generated query points are provided in an input data space, which contains the input data area defined by the input data points of the measurement data points. Subsequently, a set of spatially uniformly distributed query points is provided, having dimensions corresponding to the dimension of the input data points. The query points can correspond to Sobol points and are arranged such that they do not define a regular grid, but are nevertheless uniformly distributed within the input data space.

In this process, each query point is assigned zero, one, or multiple measurement data points, and only the assigned measurement data points are selected as training data sets. A measurement data point is used as a training data set if it is the closest measurement data point to a query point and no other query point is closer. Preferably, at least one measurement data point can be included as a training data set for each query point.

“Nearest” corresponds to a minimum Euclidean distance, in particular based on a mutually normalized range of values for the input dimensions, such that each partial distance is weighted equally with respect to an input dimension.

3 The diagram illustrates the location of input data points M (represented as crosses) using a two-dimensional input data region (with feature x1 and feature x2). The query points Q correspond to the points represented as circles. Pairs of points are indicated by the dashed connecting lines. It can be seen that the distribution of the data points is uniform due to the spatial distribution of the query points across the entire depicted area, which completely surrounds the point cloud of input data points and includes the edge of the point cloud. This allows for the selection of measurement data points.

In step S3, a density value in the form of a point density is determined for each query point by identifying the nearest measurement data points (all measurement data points are considered) that do not have a closer query point. The number of measurement data points thus determined represents a density value for each query point, indicating the local point density in the area of the query point.

This is illustrated in the 4 and 5 This is illustrated. It is assumed, by way of example, that the measurement data points have two dimensions. 4 shows an arrangement of input data points (x) to a respective query point (o), and 5 shows a diagram illustrating the density information for the respective query points, where for each query point the density information is illustrated as the size of the query point represented as a circle.

In step S4, a data-driven functional model is trained using the training datasets selected from the measurement data points, each of which assigns a label to an input data point. This data-driven functional model can be implemented, for example, as a Gaussian process model, a deep neural network, or similar. The training of the data-driven functional model can be performed using a conventional gradient-based supervised training method with a predefined loss function. The training can weight the training datasets according to the density specification relative to the point density around the corresponding query point.

In step S5, for each query point to which one or more measurement data points are assigned, a model uncertainty is determined. This uncertainty can correspond to the mean of the loss values (by evaluating the loss function) of the loss function used for training the data-driven functional model for all measurement data points assigned to the respective query point. Thus, for each query point, information about the local point density and an indication of the local model uncertainty are available.

In step S6, the query points are now sorted in ascending order according to the inverse measure (reciprocal, negated value, etc.) of the local model uncertainty G, and the density value is displayed accordingly. The data is assigned to a specific group. An increasing trend in point density should result. This trend can be functionally represented by regression, allowing local outliers in point density to be identified at the sorted query points where the point density deviates from the regression trend by more than a predetermined tolerance amount.

The resulting distribution corresponds to the diagram of 6 It can be seen that the overall model accuracy M decreases with decreasing point density D. Low values are shown in darker shades, and higher values in lighter shades. The x-axis represents the point density D around the query points. The y-axis represents the model uncertainty M (e.g., inversely proportional to the model accuracy) with respect to the input data points assigned to a query point. As already described, the areas with low point density D and higher model uncertainty M (top left) are important here. In this area of query points, the acquisition of further measurement data is necessary; this can be improved, for example, through augmentation or test bench experiments. Overweighting the input data points assigned to this area can also be implemented.

In contrast, the top right section groups query points that exhibit a high point density but low model accuracy. These are challenging areas that require further investigation to determine, for example, whether the capacity of the regression or classification model is sufficient, or whether the measurement data in this area simply does not allow for better prediction. The input data points in this area can also be marked as out-of-distribution, and an (independent) classifier can be trained to recognize this area as out-of-distribution at runtime and accordingly refuse to make a prediction.

The query points identified as outliers represent areas in the measurement data space that need to be treated separately.

If the point density is higher than the regression curve of the point density, it is observed that, despite a large number of measurement data points, the model accuracy is below average in the area of the query point. This indicates that the capacity of the data-based functional model may be insufficient or that the feature space of the measurement data space does not allow for better prediction.

If, in step S7, it is determined that a query point has a lower point density than indicated by the regression curve (alternative: Yes), it can be determined that additional measurement data points for the area of the query point in question must be determined in a further test bench measurement. This is carried out in step S8, and in step S9 the data-based functional model is retrained with the new measurement data points.

For retraining, the new measurement data points can be assigned to the corresponding query points in the manner described above. To do this, the new measurement data points can be added to the original measurement data points, and the procedure can be repeated.

As an alternative to steps S6 and S7, identifying the at least one query point can involve determining an error measure for each query point that depends on the model uncertainty and the density value. The at least one query point is identified if its error measure exceeds a threshold, where, in particular, the threshold is determined by a predefined quantile value, e.g., the 90th percentile, of a distribution of all error measures. The error measure can be determined by or dependent on the model uncertainty, and conversely, it can depend on an inverse value of the density value or its negative value. That is, the larger/smaller the model uncertainty, the larger/smaller the error measure, and the smaller/higher the density value, the larger/smaller the error measure.

Claims (10)

A computer-implemented method for providing a data-based model (41), in particular for operating a technical system, wherein the data-based model (41) is configured to output a model output, depending on a provided input data point (M), which can be used for controlling or regulating the technical system or as a virtual sensor in the technical system, comprising the following steps: - providing (S1, S2, S4) the data-based model (41) initially trained with initial measurement data points, wherein the initial measurement data points represent labeled input data points (M) obtained from a survey; - providing a number of query points (Q) that are uniformly distributed in an input data space of the input data points; - determining (S3) a density value for each query point (Q) in the form of a point density, which depends on the number of measurement data points nearest to the query point (Q) in question that do not have a nearest query point (Q); - Identify (S6, S7) at least one query punkts (Q) as the query point for which the density value indicates a point density that is too low around the identified query point; - Acquisition (S8) of further measurement data points in a measurement data space around the at least one identified query point (Q); and - Retraining (S9) the data-based model (41) based on the new measurement data points. Procedure according to Claim 1 , wherein for each of the query points to which one or more than one measurement data point is assigned, a model uncertainty is determined using a predefined loss function (S5), wherein identifying the at least one query point includes sorting the query points according to the magnitude of the assigned density value, performing a regression on the model uncertainty with respect to the order of the sorted query points, and wherein the at least one query point is identified if its model accuracy deviates from the regression curve of the model uncertainty, in particular by more than a predefined threshold. Procedure according to Claim 1 , wherein for each of the query points to which one or more than one measurement data point is assigned, a model accuracy is determined using a predefined loss function (S5), wherein the identification of the at least one query point comprises determining for each query point an error measure which depends on the model accuracy and the density specification, and identifying the at least one query point if its error measure exceeds a threshold, wherein in particular the threshold is determined by a predefined quantile value of a distribution of the error measures. Procedure according to one of the Claims 1 until 3 , wherein retraining is carried out by adding the additional measurement data points to the initial measurement data points and training the model (41) based on the combined measurement data points. Procedure according to one of the Claims 1 until 4 , wherein the model accuracy for each query point is determined by aggregating the loss values of the specified loss function for the measurement data points associated with the query point in question, in particular by providing them as a mean of the loss values. Procedure according to one of the Claims 1 until 5 with the further steps: - Identifying at least one query point as the query point for which the density indication shows an excessively high point density around the identified query point; - Excluding the application and applicability of the data-based model (41) in the area around the identified at least one query point. Procedure according to one of the Claims 1 until 6 , whereby the technical system is operated based on the trained data-based functional model. Device for carrying out one of the above methods according to one of the Claims 1 until 7 . A computer program product comprising instructions which, when executed by at least one data processing device, cause it to perform the steps of the procedure according to one of the Claims 1 until 6 to execute. Machine-readable storage medium comprising instructions which, when executed by at least one data processing unit, cause it to perform the steps of the procedure according to one of the Claims 1 until 6 to execute.