Method for correcting aging-dependent deviations of sensor values of sensor system

Abstract

The invention relates to a computer-implemented method for recalibrating a trained data-based calibration model for use in a sensor system for measuring one or more physical quantities, the data-based calibration model being designed as a graph neural network, the invention relates to a method for outputting an output vector, comprising one or more output variables and a plurality of auxiliary variables, according to a sensor state diagram representing a sensor state, comprising the following steps: detecting a detection variable relating to a physical quantity and a state variable, the state variable being indicative of an environmental impact on the sensor system; determining a sensor state diagram on the basis of the detection variable and the state variable at the detection point in time; enhancing the sensor state diagram; -evaluating the enhanced sensor state diagram with a data-based calibration model in order to obtain an output vector; determining a loss from the output vector; -unsupervised training of the calibration model as a function of the determined loss.

Description

Technical Field

[0001] The invention relates to a sensor system for detecting at least one sensor variable. The invention also relates to measures for correcting aging effects by means of a data-based correction model which is adapted or trained in an unsupervised manner during operation of the sensor system. Background Art

[0002] Sensor systems are usually calibrated after their manufacture, since the components used have deviations within the permitted tolerances. The calibration can be performed on the basis of a mathematical calibration model, wherein the model parameters of the model are adapted to the individual sensor system during the calibration process. For this purpose, for example, measured values ​​of a reference state are recorded with the sensor system during the calibration process, and the model parameters are adjusted by means of an adaptation algorithm as a function of these measured values. The calibration model is integrated into the sensor system, so that detection variables corresponding to the sensor raw data are processed with the aid of the calibration model in order to provide measurement variables.

[0003] Depending on where the sensor system is used, after a certain operating time and / or due to cumulative effects in the case of changed environmental conditions, the original calibration may no longer be optimally adapted to the sensor system. Although the deviation can be compensated by means of recalibration, this is usually not sufficient due to the lack of knowledge about the exact operating principle of the sensor system and its calibration. In addition, due to aging effects, the behavior changes during the service life of the sensor system, so that the calibration model cannot correct the sensor values ​​well enough in the long term.

[0004] For calibration models, adaptive methods are known in order to adapt these calibration models to new conditions after the actual initial calibration process. These adaptive methods are so-called test-time training algorithms, such as are known from the publications "TTT++: When Does Self-Supervised Test-Time Training Fail or Thrive?" by Liu, Yuejiang et al., 2021 and "Test-Time Training for Out-of-Distribution Generalization" by Sun, Yu et al., 2019. In these test-time training algorithms, the training task is, for example, image classification by means of a neural network, wherein unsupervised retraining without labels is described. Summary of the invention

[0005] According to the invention, a method for adjusting a data-based calibration model for a sensor system is provided as claimed in claim 1 , and a sensor system is provided as claimed in the independent claim.

[0006] Further refinements are described in the dependent claims.

[0007] According to a first aspect, a method, in particular a computer-implemented method, for recalibrating a data-based calibration model for use in a sensor system for measuring one or more physical quantities is provided, wherein the data-based calibration model is designed as a graph neural network, which is trained to: output an output vector according to a sensor state graph representing a sensor state, the output vector comprising one or more output variables and a plurality of auxiliary variables, the method comprising the following steps:

[0008] - detecting one or more detection variables related to one or more physical variables and one or more state variables (or the one or more detection variables represent the one or more physical variables), the state variables being indicative of one or more sensor-internal variables and / or one or more environmental influences on the sensor system;

[0009] - determining a sensor state diagram based on the one or more detection variables and the one or more state variables at the detection time point;

[0010] -Enhance the sensor status diagram;

[0011] - evaluating an augmented sensor state diagram using a calibration model based on the data to obtain the output vector;

[0012] - Based on the output vector, determine the loss;

[0013] - Perform unsupervised training on the calibrated model based on the determined loss.

[0014] In sensor systems, for example in integrated sensor systems, such as acceleration sensors, gyroscopes, vibration sensors, radiation sensors, capacitive and piezoelectric sensors, etc., calibration is required, by means of which component-specific deviations from a standard behavior can be compensated. For this purpose, calibration models can be implemented in the sensor system, which output output variables as correction variables for application to detection variables (detected sensor raw data) (in order to determine the sensor output variable) or which immediately output corrected sensor output variables as a function of the detection variables.

[0015] Herein, a model is generally understood to be a data-based computational model that can be trained to describe a desired functional relationship.

[0016] Due to various influences such as environmental influences on the detection variable, the sensor output variable is derived from the combination of the detection variable with one or more state variables detectable via other sensor elements using a calibration model. These state variables may, for example, indicate one or more environmental influences on the sensor system, such as temperature, humidity, air pressure, pollution level, influence of electromagnetic radiation, influence of mechanical stress, vibration, etc. Alternatively or additionally, these state variables may, for example, indicate one or more sensor internal variables, such as sensor-detected offsets or sensor sensitivity to one or more detection variables, signals from dedicated stress sensors, signals from BITE (built-in test equipment), signals from amplitude or phase adjustments of actuators in the sensor system, quality and / or frequency of the sensor's detection mode or features derived therefrom.

[0017] For inertial sensors, these state quantities may include one or more of the following state quantities: offset or sensitivity of the accelerometer or yaw rate sensor; signal from a dedicated stress sensor; detected (detection mode) phase value; signal from a BITE (built-in test equipment); signal from the amplitude or phase adjustment of the driver of the yaw rate sensor; quality and frequency of the drive or detection mode of the yaw rate sensor; quality and frequency of the mode of the accelerometer; difference in drive and detection mode frequencies of the yaw rate sensor; cross-axis sensitivity of the accelerometer or yaw rate sensor; and quadrature or yaw rate difference or dynamic response when a specified quadrature or yaw rate excitation is applied.

[0018] The detection variable can be corrected based on the one or more state variables for calibration.

[0019] The data-based calibration model is adjusted or trained once after the manufacture of the sensor system and can, if necessary, be retrained or fine-tuned again immediately after integration into the final application. If the sensor system is now used in the final application, it must be ensured during the service life that the sensor output variables provided can be provided reliably and precisely despite aging and environmental influences. Therefore, regular recalibration is usually necessary.

[0020] However, for these recalibrations, usually no bench data / training data is available, since the sensor system is embedded in the final application and bench measurements are not possible. Thus, the recalibration process can only be performed without labeled data. According to the above method, this is performed with the help of unsupervised training methods for the data-based calibration model.

[0021] For this purpose, the method provides for the creation of a mathematical graph having nodes and edges based on one or more detection variables and one or more state variables detected at a time step or detection time point.

[0022] It can be provided that the determination of the sensor state diagram is performed in the following manner: node parameters are assigned to the nodes of the sensor state diagram, which correspond to one or more detection parameters and one or more state parameters at the detection time point; and edge parameters are respectively assigned to the edges of the sensor state diagram which respectively connect two nodes of the sensor state diagram to each other, which edge parameters indicate the correlation between the detection parameters or state parameters representing the nodes, wherein, in particular, the correlation is determined by evaluating the change process of the detection parameters or state parameters over time within a specified time window.

[0023] Therefore, the one or more detection parameters and the one or more state parameters are referred to as node parameters. The graph can have nodes that are respectively assigned to one of these node parameters. The corresponding value of the node parameter at the detection time point is assumed to be the node value. The edge connects two nodes and indicates the relationship between the two nodes as an edge value, for example in the form of a correlation between the corresponding node parameters. Instead of a correlation that can be determined, for example, from a comparison of the course of changes of two related node parameters, other functions can also be used, with which two of these node parameters are respectively correlated to each other. Then, the mathematical sensor state diagram expressed in this way reflects the detected sensor state, which is then indicated by the value of the detection parameter as a node and the edge value of the edge between the two nodes.

[0024] With the aid of a graph neural network, the data structure of the sensor state graph can be converted into an output vector. The output vector contains output parameters as correction parameters for correcting the detection parameters or as corrected sensor output parameters. The output vector also includes other auxiliary parameters that can be used in the recalibration process.

[0025] The output vector obtained by means of the graph neural network is designed to: on the one hand, output the output parameter; and on the other hand, provide an output through these auxiliary parameters, which is suitable for determining the loss of training the graph neural model. The loss corresponds to an indication of the accuracy or prediction accuracy of the calibration model and is used to train the calibration model. The above method enables: by describing the sensor state in the form of a sensor state graph and using the graph neural network by enhancing the sensor state graph, a loss is determined, which is suitable for unsupervised retraining of the graph neural network.

[0026] Augmentation of the sensor state graph may be performed by randomly removing one or more of the nodes, by randomly removing one or more of the edges, by randomly swapping node parameters, and / or by randomly swapping edge parameters.

[0027] When enhancing the sensor state graph, one or more nodes and / or one or more edges can be removed or exchanged in a manner known per se. The deletion or exchange of nodes and / or edges is random. In this case, the options can be restricted so that only certain enhancements can be performed. For example, a random, specific rotation of the graph can also be achieved. In addition, other enhancement options are still conceivable, such as specific changes in numbers, etc.

[0028] In this way, the sensor system can be calibrated without specific markings by enhancing the mathematical diagram on the input side, for example, by hiding and / or exchanging individual influencing variables. In this way, recalibration can be performed efficiently by coupling the output of correction variables and auxiliary variables during the initial training process for unsupervised learning of the calibration model.

[0029] Once the sensor state is available as a mathematical graph in the form of one or more detection variables and the value of one or more state variables for a detection time point, it can be evaluated with the aid of a data-based calibration model in order to obtain an output variable. The data-based calibration model is designed as a graph neural network and is trained to provide an output vector with output variables and auxiliary variables.

[0030] At the same time or at specified points in time, which may be regular, a recalibration may be performed. To this end, the calibration model is further developed with the aid of an unsupervised training method in order to compensate for the increased deviations due to aging and environmental influences. The unsupervised training method exploits the advantage that in graph neural networks, missing input data is not important and can still be evaluated. The unsupervised training method uses an augmented sensor state diagram to determine the losses required for training.

[0031] According to one embodiment, the loss may be determined as follows:

[0032] - with the aid of the calibration model, providing an evaluation model, which corresponds to the calibration model or which includes in addition to the calibration model one or more downstream further neuronal layers or data-based models;

[0033] - providing a twin model that is trained in the same manner as the evaluation model and has an additional configuration relative to the evaluation model;

[0034] - evaluating the enhanced sensor state diagram by means of the evaluation model to obtain an evaluation vector;

[0035] - evaluating another enhanced sensor state diagram by means of the twin model to obtain another evaluation vector; and

[0036] The loss is determined as a measure of the difference between these evaluation vectors.

[0037] Here, first and second enhanced sensor state diagrams may be created for an unsupervised training method of a data-based calibration model.

[0038] An estimation is now carried out with the aid of the estimation model in order to obtain a first output vector with auxiliary variables.

[0039] In addition to the evaluation model, a twin model is provided, which is designed as a graph neural network and trained in the same way as the calibration model, but has a different configuration therefrom and is especially designed based on another set of hyperparameters. In this way, for example, the evaluation model can use the calibration model without change, or the evaluation model can be supplemented with a first number of downstream neuron layers (for example in the form of fully connected layers), while providing a twin model having a completely different configuration from the evaluation model. The twin model can be formed, for example, by the calibration model using a second number of downstream neuron layers (for example in the form of fully connected layers) that is different from the first number. The evaluation model and the twin model are designed so that the format of the corresponding output vectors is the same, so that the differences between the output vectors can be evaluated in a simple way.

[0040] In this way, the first augmented sensor state diagram is evaluated by the evaluation model, and the second augmented sensor state diagram is evaluated by the twin model. The difference between the resulting output vectors can be evaluated by the loss.

[0041] The loss L can be based on the cosine similarity of the two obtained output vectors y Kalmod ,y Zwilling The Euclidean distance is calculated as:

[0042]

[0043] Among them, y Kalmod corresponds to the output vector of the evaluation model and y Zwilling Corresponds to the output vector of the twin model.

[0044] This loss is used to retrain the evaluation model and the twin model by means of gradient-based methods known per se, such as backpropagation, so that they can be used to determine output variables during normal operation of the sensor system.

[0045] During the initial calibration process, the evaluation model and the twin model are initially trained together with the aid of labeled data. To this end, the calibration model is trained together with the loss in a conventional manner based on a training data set, which includes a sensor state diagram describing the sensor state at a specific detection time point and the assigned labels as output parameters, so as to: adjust the model output of the output parameter in the output vector by unsupervised training through the calibration model and on the other hand by enhancing the mathematical sensor state diagram to obtain the corresponding auxiliary parameters of the output vector of the calibration model. In addition to classical training with the aid of backpropagation, meta-learning or few-shot learning can also be used for this purpose. The twin model can be initially trained in a similar manner. By using these training data sets to alternately train the calibration model and its modification to the evaluation model and the twin model with the aid of unsupervised training methods, appropriate coupling of the output parameters and auxiliary parameters in the output vector can be achieved.

[0046] The evaluation model (modified calibration model) and the twin model can be trained using a joint loss. Since the loss is calculated using two models, the gradients of the two models can be calculated using the loss. For example, via back propagation, the resulting loss is calculated backwards, and the gradient is calculated therefrom. Thereby, the backward calculation of the back propagation is performed through the two models. Typically, gradients with different learning rates are applied at the two models, but the same learning rate can also be used.

[0047] In another embodiment of the unsupervised training method for a data-based calibration model, it can be provided that the calibration model is provided such that the auxiliary parameter indicates an output diagram of the calibration model, wherein the loss is determined in the following manner: the calibration model is evaluated with the aid of an enhanced sensor state diagram in order to obtain a reconstructed sensor state diagram, and the loss is determined as a measure of the difference between the original sensor state diagram and the reconstructed sensor state diagram.

[0048] In this case, the auxiliary parameters of the output vector are a representation of the sensor state graph, which has the shape of the original non-augmented sensor state graph (number of nodes and links made by edges). The auxiliary parameters can be assumed to be parameters for describing the sensor state graph.

[0049] The auxiliary quantities may be determined by evaluating the calibration model based on the enhanced sensor state graph, wherein the auxiliary quantities should indicate a reconstruction of the original sensor state graph. Training may be performed using a loss derived from the difference between the original sensor state graph (before enhancement) and the reconstructed sensor state graph. The difference may be indicated as the Euclidean distance between the vectors (or tensors) describing the original sensor state graph and the reconstructed sensor state graph.

[0050] According to one embodiment, a data-based calibration model can be initially trained before the sensor system is put into operation by determining the loss for multiple sensor states and determining another loss from a training data set used for supervised training, wherein a total loss is determined based on the loss and the other loss, and the calibration model is initially trained based on the total loss.

[0051] Therefore, after manufacturing the sensor system, the calibration model is initially trained using labeled training data, which assign the sensor state diagram to the output parameters of the output vector. This initial training is performed alternately or simultaneously (in the case of a joint loss) with the steps of the unsupervised training method based on the enhanced sensor state diagram as described above, wherein the output vector of the calibration model indicates the output parameters and auxiliary parameters for determining the unsupervised loss. In this case, these auxiliary parameters can be described in the format of the sensor state diagram.

[0052] During operation, the losses are now determined based on the augmented sensor state diagram by means of unsupervised training alone, and the calibration model is thereby retrained, for example, according to a gradient-based training method. Thus, when evaluating the calibration model, one or more output variables in the output vector are correspondingly adjusted, since the one or more output variables are directly linked to the auxiliary variables of the output vector via the calibration model. In this way, the option of performing a recalibration in an improved manner is obtained, which can be used during the operation of the sensor system without the need for labeled training data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Subsequently, the embodiments are described in more detail with reference to the accompanying drawings, wherein:

[0054] Figure 1 An exemplary sensor system for providing a value of a sensor output parameter utilizing a retrainable implemented calibration model is shown;

[0055] Figure 2 A schematic diagram of a sensor state diagram is shown;

[0056] Figure 3 A schematic diagram of a method for unsupervised retraining of a calibration model according to a first embodiment is shown;

[0057] Figure 4 Shows the explanation according to Figure 3 A flowchart of a method for unsupervised retraining of a calibration model;

[0058] Figure 5A schematic diagram showing a model for unsupervised retraining of a calibration model according to another embodiment; and

[0059] Figure 6 Shows the explanation according to Figure 5 Flowchart of a method for retraining a calibration model. DETAILED DESCRIPTION

[0060] Figure 1 A schematic diagram of a sensor system 1 is shown, which has a sensor element 2 for detecting one or more physical quantities, such as acceleration, radiation, vibration, material level, etc., and for providing one or more, in particular electrical, detection variables E, which depend on the one or more physical quantities. The one or more detection variables E are preprocessed, such as amplified and / or filtered, by a preprocessing unit 3. By means of the detection variable E, a plurality of similar physical quantities, such as acceleration in a plurality of spatial directions, can also be described.

[0061] Furthermore, one or more state sensors 4 are provided in order to detect state variables Z. These state variables Z can represent environmental conditions, for example, and can indicate temperature, humidity, air pressure, mechanical stress loads (such as bending loads), vibration loads, loads due to electromagnetic radiation, etc. Furthermore, state variables can also be internal signals detected in a sensor manner, which indicate the state of the sensor system. For example, these state variables can indicate, for example, the operating voltage of an orthogonal or laser diode in an acceleration sensor, etc. One or more state variables Z can also be preprocessed by the preprocessing unit 3, such as amplification and / or filtering.

[0062] In the diagram creation unit 5, one or more detection variables E and one or more state variables Z are processed to form a mathematical sensor state diagram 10. Such a sensor state diagram is Figure 2 Here, one or more detection parameters E and one or more state parameters Z are referred to as node parameters K, which are assigned to nodes 11 of the sensor state diagram. The nodes 11 of the sensor state diagram are connected or related to each other via edges 12, wherein corresponding edge parameters G are assigned to these edges 12.

[0063] Here, these edge parameters G can indicate the edge relationship between these node parameters, for example in the form of correlation between these node parameters. This correlation can be determined by comparing the time-dependent changes of the corresponding node parameters within a predetermined time window, which can especially end at the current time point (the most recently determined sample). In addition, these edge parameters G can also indicate the relationship between two node parameters K described by the nodes 11 in other forms. The resulting mathematical sensor state diagram 10 indicates the state of the sensor system 1 at a specific time step, i.e., at the detection time point.

[0064] These side parameters can be determined once in a special measurement series. In this case, time series can be recorded under different environmental conditions in order to detect the time series within a time window and determine the correlation value. In addition, these side parameters can also be determined by previous supervised training, in that the side parameters are varied during the training in order to determine the optimal value in the manner of a hierarchical training. In this case, the training can be repeated more frequently with different side parameters, which can be varied, for example, in a Bayesian manner.

[0065] The sensor state diagram is now fed to a trained data-based calibration model 6, which is initially trained. On the output side of the calibration model, an output vector is output, which has: an output variable for each of one or more detection variables E; and other auxiliary variables. One or more output variables can correspond to a sensor output variable A, which can be corrected in particular according to the calibration model 6, and which can be uniquely assigned to a measure of the physical quantity represented by the corresponding detection variable E. Alternatively, the corresponding output variable can also be a correction variable, which can be applied to the corresponding detection variable, for example in an optional application block 7, for example by addition or multiplication, in order to calculate the sensor output variable A according to the sensor state.

[0066] The calibration model 6 is initially trained based on a training data set in which the sensor state diagram is assigned to one or more output variables, which correspond to the measured physical quantity or can be determined from the output variable / variables. The initial training of the calibration model is described in more detail below.

[0067] During the operation of the sensor system 1, deviations in the sensor behavior occur due to aging effects and / or environmental influences, so that the calibration model 6 becomes less and less adapted to the real sensor system 1. As a result, the resulting sensor output variable can increasingly poorly describe the measured physical quantity, thereby falsifying the measurement result. For this purpose, a calibration control unit 8 is provided, which during the operation of the sensor system 1 in the end application regularly or at predetermined points in time or triggered from the outside performs a recalibration by means of an unsupervised training method.

[0068] Subsequently, an embodiment for performing a recalibration of the calibration model 6 is described in more detail.

[0069] During recalibration, the data-based calibration model 6 or its model parameters are changed so that one or more detection variables are corrected in a changed manner. The purpose of training the data-based calibration model 6 is to provide one or more output variables, which correspond to the sensor output variables as corrected detection variables or to the correction variables for subsequent correction of the detection variables, and are suitable for or contribute to providing the sensor output variables assigned to the corresponding physical quantities.

[0070] Now, according to Figure 3 Schematic diagram and Figure 4 The method for retraining a calibration model is described in more detail in the flowchart of FIG. 1 . The method starts in step S1 by providing a calibration model 6 which is initially trained based on a training data set.

[0071] In step S2, for a specific time step or detection time point, the sensor state is detected, and in step S3, a sensor state diagram is created as described above. The sensor state is indicated by one or more detection parameters and one or more state parameters.

[0072] In the subsequent step S4, a first enhanced sensor state graph and a second enhanced sensor state graph are generated from the sensor state graph. The enhancement of the sensor state graph can be achieved by deleting nodes and / or edges or exchanging nodes and edges, such as Figure 3 The enhancement is random and is performed mainly independently of the value of the detection parameter and / or one or more state parameters.

[0073] An evaluation model 21 is provided, which corresponds to the calibration model and can provide an output vector as an evaluation vector B. Alternatively, the evaluation model can include the calibration model 6 and one or more further downstream first neuron layers 22 in the form of fully connected layers (MLP), which further process the output vector of the calibration model and provide the evaluation vector on the output side. Further extensions with one or more neuron layers or other data-based models are also conceivable.

[0074] Furthermore, a twin model 23 is provided, which is trained in the same way as the evaluation model 21, but has a further configuration 24. The twin model 23 may include the calibration model 6 and may be modified in a different way than the evaluation model 21 in order to achieve the difference in configuration 24.

[0075] When the evaluation model 21 is initially trained, the twin model 23 is also trained, with the goal that the twin model provides the same evaluation vector B as the evaluation model 21. The evaluation model 21 and the twin model 23 are respectively adapted to process a graph as an input vector and output an evaluation vector B having a similar format.

[0076] Like the calibration model, the Siamese model23 is designed as a graph neural network, but can have different structures based on different choices of hyperparameters.

[0077] The evaluation model 21 and the twin model 23 may also be designed to be identical, but may be extended by a different number of subsequent fully connected layers, so that the two data-based graph neural networks are not 1:1 copies of each other and have different configurations.

[0078] Within the framework of an unsupervised training step for retraining the calibration model, in step S5 the evaluation model 21 is evaluated with the first augmented sensor state diagram and the twin model 23 is evaluated with the second augmented sensor state diagram in order to obtain an evaluation vector B.

[0079] In step S6, the evaluation model 21 and the twin model 23 are trained with the aid of a loss L. The loss is obtained by comparing the evaluation vectors B of the evaluation model 21 and the twin model 23 as the difference between the respectively obtained evaluation vectors B. To this end, the evaluation vectors B can be checked with respect to the Euclidean distance or the cosine similarity in order to determine the loss L. The loss L essentially evaluates the distance between the evaluation vectors B from each other.

[0080] This retraining is performed according to a gradient-based training method both in the evaluation model 21 and in the twin model 23. Since the calibration model 6 is included in the evaluation model 21, it is adapted to the sensor state in the process. The calibration model 6 is then used to correct the detection signal and improve the performance of the sensor system 1.

[0081] According to another embodiment, the retraining can be performed without using the twin model 23. Figure 5 Schematic diagram and Figure 6 The flowchart of FIG. 1 describes in more detail the method for retraining the calibration model 6. The method starts in step S11 by providing a calibration model 6, which is initially trained based on a training data set.

[0082] In step S12, for a specific time step or detection time point, the sensor state is detected and a sensor state diagram 10 is created as described above. The sensor state is indicated by one or more detection variables E and one or more state variables Z.

[0083] To this end, in step S13 an enhanced sensor state diagram 10 is determined in the above-described manner from the sensor state diagram 10 of the current sensor state or the sensor state at a certain point in time. This sensor state diagram 10 is enhanced and fed to the calibration model 6 .

[0084] The calibration model 6 is designed to provide, by evaluating the enhanced sensor state diagram, an output vector which comprises, on the one hand, one or more output variables A and auxiliary variables which represent a sensor state diagram 10 whose format corresponds to the original sensor state diagram.

[0085] Therefore, the calibration model 6 can be designed to, in addition to outputting the output variables, also reconstruct a sensor state graph 10 corresponding to the original sensor state graph from the enhanced sensor state graph, described by the auxiliary variables. By comparing the original sensor state graph with the reconstructed sensor state graph, the loss L can be determined as an evaluated difference between the sensor state graphs 10. The difference can be determined based on parameters of the sensor state graphs, which can be described as graph vectors, for example, in particular by determining the Euclidean distance or cosine similarity of the two graph vectors.

[0086] In step S14, the calibration model 6 is trained based on the loss L.

[0087] The advantage of this implementation is that only a single enhancement of the sensor state diagram is required, and only one data-based graph neural network model needs to be trained.

[0088] In this way, the model parameters of the data-based calibration model 6 can also be adjusted accordingly and can be applied online, ie, during operation of the sensor system 1 .

[0089] Before using the sensor system 1, it is necessary to initially train the calibration model 6. In this case, the elements of the output vector, i.e. one or more output variables A and the auxiliary variables are related to one another in such a way that in the case of unsupervised training during operation of the sensor system 1 - as described above - the model parameters of the calibration model 6 are changed so that an optimal adjustment or correction of the detection variables can be carried out.

[0090] During the initial training of the calibration model, one or more output variables to be determined need to be associated in a suitable manner with the auxiliary variables that are also output. For this purpose, a joint training is provided, which alternately or in parallel performs supervised training based on a training data set and supervised training based on a loss, which loss is determined, for example, using one of the above-mentioned training methods. Preferably, the training is performed for a plurality of different physical quantity values ​​in the case of changes in environmental conditions (i.e. changes in the state variables), so that a mapping of the input data space that fills the space as much as possible is achieved by the calibration model.

[0091] The training data sets for supervised training are derived from measurements of the sensor system on a test bench, where one or more applied physical quantities to be measured by the sensor system are recorded in a targeted manner and the corresponding detection variables are detected. The applied physical quantities are assigned to sensor output variables to be output by the sensor system when the corresponding physical quantity is present. The training data sets thus correspond to input vectors consisting of one or more detection variables and one or more state variables (for a specific applied physical quantity), which are labeled with corresponding sensor output variables assigned to the corresponding physical quantity.

[0092] The loss L used for unsupervised training unsupervised It is mainly based on the evaluation of auxiliary parameters at the output of the calibration model 6, while the supervision loss L supervised The determination of is based on a corresponding evaluation of these training data sets, in particular a comparison of the labels from the training data sets with one or more output variables output by the calibration model.

[0093] The two loss values ​​L derived from unsupervised , L supervised The total loss L can be calculated as follows total :

[0094] L total =λ1·L unsupervised +λ2·L supervised

[0095] Here, λ1 and λ2 are weighting factors that can be predefined. In this way, the calibration model 6 can be initially trained to jointly solve two tasks, namely, output one or more correct output variables and output auxiliary variables that enable unsupervised retraining of the calibration model.

[0096] The recalibration can be performed during each detection time step before determining one or more output variables, so that the latest state of the sensor system can be taken into account when determining the one or more output variables.

[0097] It can also be provided that, in addition to the retraining step, at each detection time point of the sensor system 1, the calibration model 6 is reset, i.e., the model parameters of the calibration model 6 are reset to the initial values ​​which were obtained by the initial training. This has the advantage that the recalibration can make the deviations of the model parameters of the calibration model 6 not too great and the performance thus becomes worse again over time. In contrast, only a predictable parameter space of the variation of the model parameters of the calibration model can be achieved, which parameter space can already be controlled and specified during the training phase for safety applications.

Claims

1. A method, in particular a computer-implemented method, for recalibrating a trained data-based calibration model (6) for use in a sensor system (1) for measuring one or more physical quantities, wherein: The data-based calibration model (6) is designed as a graph neural network, and the graph neural network is trained to: output an output vector according to a sensor state diagram (10) representing the sensor state, wherein the output vector includes one or more output parameters (A) and a plurality of auxiliary parameters, and the method comprises the following steps: - at a detection time, detecting (S2) one or more detection variables (E) which are correlated with the one or more physical variables and one or more state variables (Z), the state variables being indicative of one or more environmental influences on the sensor system (1); - determining (S3) a sensor state diagram (10) based on the one or more detection variables (E) and the one or more state variables (Z); - enhancing (S4) the sensor state diagram (10); - evaluating (S5) an enhanced sensor state diagram (10) using said data-based calibration model (6) in order to obtain said output vector; - determining a loss (L) based on the output vector; - Based on the determined loss (L), the calibration model (6) is trained unsupervised (S6).

2. The method according to claim 1, wherein: The determination of the sensor state diagram (10) is performed in the following manner: node parameters are assigned to the nodes of the sensor state diagram (10), the node parameters corresponding to the one or more detection parameters (E) and the one or more state parameters (Z) at the detection time point; and edge parameters are assigned to the edges of the sensor state diagram (10) that respectively connect two nodes of the sensor state diagram (10) to each other, the edge parameters indicating the correlation between the detection parameters (E) or the state parameters (Z) representing the nodes connected by the corresponding edges, wherein, in particular, the correlation is determined by evaluating the time-dependent change process of the detection parameters (E) or the state parameters (Z) within a specified time window.

3. The method according to claim 2, wherein: The enhancement of the sensor state graph (10) is performed by randomly removing one or more of the nodes, by randomly removing one or more of the edges, by randomly swapping node parameters and / or by randomly swapping edge parameters.

4. The method according to any one of claims 1 to 3, wherein: The loss (L) is determined as follows: - With the aid of the calibration model (6), providing an evaluation model, which corresponds to the calibration model (6) or which includes one or more downstream further neuronal layers or data-based models in addition to the calibration model (6); - providing a twin model (23), which is trained in the same way as the evaluation model (21) and has a different configuration (24) relative to the evaluation model (21); - evaluating the enhanced sensor state diagram (10) by means of the evaluation model (21) in order to obtain an evaluation vector (B); - evaluating another enhanced sensor state diagram (10) by means of the twin model (23) in order to obtain another evaluation vector (B); and - The loss is determined as a measure of the difference between these evaluation vectors (B).

5. The method according to claim 4, wherein: According to the loss (L), the evaluation model and the twin model are retrained.

6. The method according to claim 4 or 5, wherein: The loss (L) is determined as cosine similarity or Euclidean distance.

7. The method according to any one of claims 1 to 3, wherein: The calibration model (6) is provided such that the auxiliary variable is indicative of an output map of the calibration model (6), The loss (L) is determined in the following manner: - evaluating the calibration model (6) with the aid of the enhanced sensor state diagram (10) in order to obtain a reconstructed sensor state diagram (10); - determining the loss (L) as a measure of the difference between the original sensor state map (10) and the reconstructed sensor state map.

8. The method according to any one of claims 1 to 7, wherein: The data-based calibration model (6) is initially trained (S1) before the sensor system (1) is put into operation by: The loss (L) is determined for a plurality of sensor states, and another loss (L) is determined from a training data set used for supervised training, wherein a total loss (L) is determined based on the loss (L) and the other loss, thereby initially training the calibration model (6).

9. The method according to any one of claims 1 to 8, wherein: The one or more output parameters include one or more correction parameters for application to the one or more detection parameters (E) so as to obtain one or more sensor output parameters based on the one or more correction parameters, or wherein the one or more output parameters correspond to the one or more sensor output parameters.

10. The method according to any one of claims 1 to 9, wherein: The calibration model (6) is used in that the sensor state diagram is determined as a function of the one or more detection variables (E) and the one or more state variables (Z), wherein the one or more output variables are determined as a function of the sensor state diagram. 11 . A device comprising a data processing device, wherein the data processing device is designed to execute the method according to claim 1 . 12 . A computer program product comprising instructions which, when executed by at least one data processing device, cause the data processing device to perform the steps of the method according to claim 1 .

13. A machine-readable storage medium comprising instructions which, when executed by at least one data processing device, cause the data processing device to perform the steps of the method according to any one of claims 1 to 10.

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