Method for correcting deviation caused by change with time of sensor value of sensor system

Abstract

To provide a sensor system and a computer implemented method for performing retrospective calibration of a calibration model based on trained data in order to measure a physical variable.SOLUTION: In a sensor system, a calibration model is configured as a neural graph network trained to output an output vector including an output variable and a plurality of auxiliary variables depending on a sensor state graph representing a sensor state, and the sensor system captures a first capture variable related to a physical variable and a state variable indicating an influence of environment on the sensor system, determines the sensor state graph at the time of the capture depending on the capture variable and one state variable, expands the sensor state graph, evaluates the expanded sensor state graph by using a calibration model based on data in order to obtain the output vector, determines a loss depending on the output vector, and performs unsupervised training of the calibration model depending on the determines loss.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a sensor system for capturing at least one sensor variable, and further to means for compensating for ageing effects using data-based compensation models that are unsupervisedly adapted or trained during operation of the sensor system. [Background technology]

[0002] The sensor system is usually calibrated after its production, because the components used have deviations that lie within the tolerance range. The calibration can be carried out on the basis of a mathematical calibration model, the model parameters of which are adapted to the respective sensor system during the calibration process. For this purpose, for example, during the calibration process, the sensor system records measured values ​​for a reference state, and the model parameters are adapted via a comparison algorithm as a function of the measured values. The calibration model is integrated into the sensor system, so that the captured variables corresponding to the sensor raw data are processed with the aid of the calibration model to provide the measured variables.

[0003] Depending on where the sensor system is used, after some operating time and / or due to the cumulative effect of changing ambient conditions, the original calibration may no longer be optimally adapted for the sensor system. By using a post-calibration, this deviation can be compensated for, but this is often insufficient due to lack of knowledge about the exact functioning of the sensor system and its calibration. Furthermore, the calibration model is not always able to provide a sufficiently good correction of the sensor values, since the characteristics change over the life of the sensor system due to aging effects.

[0004] Adaptation methods are already known for calibration models to adapt them to new conditions after the original initial calibration process. These are so-called test-time training algorithms, which are known, for example, 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 such cases, the training task is, for example, image classification by neural networks, where unsupervised post-training is described without labels. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Liu, Yuejiang, et al., “TTT++: When Does Self-Supervised Test-Time Training Fail or Thrive?” (2021) [Non-Patent Document 2] Sun, Yu et al., “Test-Time Training for Out-of-Distribution Generalization” (2019) Summary of the Invention [Problem to be solved by the invention]

[0006] Disclosure of the Invention According to the invention a method for adapting a data-based calibration model for a sensor system according to claim 1 and a sensor system according to the parallel claim are envisaged.

[0007] Further embodiments are set forth in the dependent claims. [Means for solving the problem]

[0008] According to a first aspect, a method, in particular a computer-implemented method, is envisaged for post-calibrating a data-based calibration model for use in a sensor system for measuring one or more physical variables, the data-based calibration model being configured as a neural graph network, the neural graph network being trained to output an output vector comprising one or more output variables and a number of auxiliary variables in dependence on a sensor state graph representing the sensor states, the method comprising the following steps: - capturing one or more capture variables related to (or representative of) one or more physical variables and one or more sensor internal variables and / or one or more state variables indicative of one or more environmental influences on the sensor system; - determining a sensor state graph depending on one or more capture variables and on one or more state variables at the capture time; - expanding the sensor state graph; - evaluating the augmented sensor state graph with a data-based calibration model to obtain an output vector; determining a loss in dependence on the output vector; - unsupervised training of a calibration model depending on the determined losses; Includes.

[0009] Sensor systems, for example integrated sensor systems, such as acceleration sensors, gyroscopes, vibration sensors, radiation sensors, capacitive sensors and piezoelectric sensors, require a calibration that can compensate for deviations from the standard characteristics of the individual components. For this purpose, in the sensor system, a calibration model can be implemented that outputs an output variable as a correction variable for applying the captured variable (captured raw sensor data) (to determine the sensor output variable) or simultaneously outputs a modified sensor output variable depending on the captured variable.

[0010] Model is generally understood herein to mean a data-based computational model that can be trained to represent a desired functional relationship.

[0011] Based on various influences, such as environmental influences, on the captured variables, the sensor output variables result from a combination of the captured variables and one or more state variables, which can be captured via further sensor elements, using a calibration model. These state variables can be indicative of one or more environmental influences on the sensor system, such as, for example, temperature, humidity, air pressure, pollution levels, the action of electromagnetic beams, the action of mechanical stresses, vibrations, etc. Alternatively or additionally, these state variables can be indicative of one or more sensor internal variables, such as, for example, the offset captured by the sensor or the sensitivity of the sensor for one or more captured variables, the signal of a dedicated stress sensor, the signal of a BITE (built-in test equipment), the signal from the amplitude or phase control of an actuator in the sensor system, the quality and / or frequency of the detection mode of the sensor, or features derived therefrom, etc.

[0012] For an inertial sensor, these state variables may be one or more of the following: The offset or sensitivity of the acceleration sensor or angular rate sensor, Signals from dedicated stress sensors, The captured (detection mode) phase value, Signals from BITE (built-in test equipment), A signal from the amplitude or phase control of the drive unit of the angular velocity sensor; The quality and frequency of the drive or detection modes of the angular velocity sensor; Accelerometer mode quality and frequency, The difference between the drive mode frequency and the detection mode frequency of the angular velocity sensor; Cross-axis sensitivity of the acceleration or angular rate sensor, Quadrature or angular velocity derivatives or dynamic responses upon application of preset quadrature or angular velocity stimuli Includes.

[0013] Depending on one or more state variables, correction of the captured variables for calibration can be performed.

[0014] The data-based calibration model can be adapted or trained once after the sensor system is manufactured, and possibly post-trained or fine-tuned again once immediately after installation in the end-use application. When the sensor system is used in the end-use application, it will be necessary to ensure that the sensor output variables provided can be provided reliably and accurately during the life of the sensor system, independent of aging and environmental effects. Periodic post-calibration is therefore usually necessary.

[0015] However, for these post-calibrations, usually no inspection level data / training data is available, since the sensor system is integrated into the end-use application and no inspection level measurements are possible. Therefore, the post-calibration process can only be performed without labeled data. According to the above method, this is performed using unsupervised training methods for the data-based calibration model.

[0016] To this end, the method envisages creating a mathematical graph having nodes and edges based on one or more captured variables and one or more state variables captured at a time step or capture instant.

[0017] The step of determining the sensor state graph is performed by assigning to the nodes of the sensor state graph node variables corresponding to one or more capture variables and one or more state variables at the capture time point, and by assigning to the edges of the sensor state graph interconnecting each two nodes of the sensor state graph one edge variable each indicating a correlation between the capture variables or state variables representing the nodes, where in particular this correlation is determined by evaluation of the time course of the capture variables or state variables within a pre-set time window.

[0018] Thus, the one or more capture variables and the one or more state variables are also referred to as node variables. The graph may have nodes that are assigned to each one of the node variables. As node values, the respective values ​​of the node variables at the time of capture are assumed. An edge connects two nodes, and the relationship between the two nodes is shown as an edge value, for example in the form of a correlation between the corresponding node variables. For example, instead of a correlation that can be determined from a comparison of the course of the two node variables in question, other functions in which each two of the node variables are related to each other can also be used. The mathematical sensor state graph thus formulated then reflects the captured sensor state, which is then shown by the values ​​of the capture variables as nodes and edge values ​​of the edges between the two nodes.

[0019] By using a neural graph network, the data structure of the sensor state graph can be converted into an output vector, which includes the output variables as correction variables for correcting the captured variables or as modified sensor output variables, and further includes additional auxiliary variables that can be used for a post-calibration process.

[0020] The output vector obtained with the neural graph network is configured to provide, by means of the output variables on the one hand and the auxiliary variables on the other hand, an output suitable for determining a loss for training a neural graph model. This loss corresponds to a statement about the accuracy or prediction accuracy of the calibration model and is used for training the calibration model. The representation of the sensor states in the form of a sensor state graph and the use of the neural graph network by extension of the sensor state graph makes it possible to determine a loss suitable for a post-training unsupervised neural graph network.

[0021] The expansion of the sensor state graph can be performed by randomly removing one or more nodes, randomly removing one or more edges, randomly swapping node variables, and / or randomly swapping edge variables.

[0022] When expanding 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 removal or exchange of nodes and / or edges is performed randomly. Here, the possibilities can be restricted, so that only specific expansions are possible. It is also possible, for example, to realize random specific rotations of the graph. Furthermore, further possibilities of expansion, such as specific changes of numerical values, are also conceivable.

[0023] In this way, it is possible to calibrate the sensor system without asking for labels, since the individual influencing variables can be fed out and / or exchanged, for example, by extending the mathematical graph at the input side. Therefore, post-calibration can be performed in an efficient manner by combining the output of the correction variables with the auxiliary variables for unsupervised learning of the calibration model during the initial training process.

[0024] Once the sensor state is provided as a mathematical graph in the form of values ​​of one or more capture variables and one or more state variables versus capture time, this sensor state can be evaluated using a data-based calibration model to obtain an output variable, which is configured and trained as a neural graph network to provide an output vector having the output variable and the auxiliary variable.

[0025] A post-calibration can be performed at the same time or at pre-set time points, which can be regular. For this purpose, a calibration model is developed using an unsupervised training method to compensate for the growing deviations due to aging and environmental influences. The unsupervised training method takes advantage of the fact that in neural graph networks, evaluation can be performed despite the lack of input data. The unsupervised training method uses the augmented sensor state graph to determine the losses required for training.

[0026] According to one embodiment, the loss is: - providing an evaluation model using the calibration model, the evaluation model including one or more further neuronal layers or data-based models corresponding to the calibration model or additionally arranged downstream with respect to the calibration model; providing a twin model that is trained similarly to the evaluation model and has a different configuration with respect to the evaluation model; evaluating the augmented sensor state graph with a rating model to obtain a rating vector; evaluating the further extended sensor state graph by the twin model to obtain a further evaluation vector; -Loss is calculated as a measure of the difference between evaluation vectors It can be determined by:

[0027] Here, a first and a second augmented sensor state graph can be created for an unsupervised training method of a data-based calibration model.

[0028] Here, an estimation is performed using an estimation model to obtain a first output vector having auxiliary variables.

[0029] In addition to the evaluation model, a twin model is provided, which is constructed and trained as a neural graph network like the calibration model, but has a different configuration, in particular based on another set of hyperparameters. Thus, for example, the evaluation model can use the calibration model without modification, or can be supplemented with a first number of downstream neuron layers (for example in the form of a Fully connected Layern), while a twin model is provided that has a completely different configuration from the evaluation model. This twin model can be formed, for example, by a calibration model with a second number of downstream neuron layers that are different from the first (for example in the form of a Fully connected Layern). The evaluation model and the twin model are constructed such that the format of their output vectors is equivalent, so that a simple method can be used to evaluate the differences between the output vectors.

[0030] In this way, the first augmented sensor state graph is evaluated by the evaluation model, and the second augmented sensor state graph is evaluated by the twin model. The discrepancy between the resulting output vectors can be evaluated by a loss.

[0031] The loss L can be expressed as follows, for example: L=2-2{(y Kalmod y Zwilling ) / (||y Kalmod || 2 ||y Zwilling || 2 )} The two resulting output vectors y Kalmod ,y Zwilling can be calculated based on the Euclidean distance of Kalmod corresponds to the output vector of the evaluation model, and y Zwilling corresponds to the output vector of the twin model.

[0032] The loss is used to post-train both the evaluation model and the twin model using gradient-based methods known per se, such as backpropagation, so that this loss can be used to determine the output variables during conventional operation of the sensor system.

[0033] In the initial calibration process, the evaluation model and the twin model are initially trained using jointly labeled data. For this purpose, the calibration model is trained based on the training data set in a conventional manner together with losses, which includes the sensor state graph representing the sensor state at a particular capture time point and the labels assigned as the output variables, so as to obtain the corresponding auxiliary variables of the output vector of the calibration model by unsupervised training by extending the mathematical sensor state graph while fitting the model output of the output variables in the output vector by the calibration model. In addition to classical training using the backpropagation method, Meta-Learning or Few-Shot-Learning can also be used for this. The twin model can also be initially trained in the same way. By alternately training the calibration model with the training data set and its modification to the evaluation model and the twin model using the unsupervised training method, a suitable combination of the output variables and auxiliary variables in the output vector can be achieved.

[0034] A common loss can be used for training the evaluation model (the corrected calibration model) and the twin model. Since the loss is calculated using two models, the gradients for both models can be calculated using one loss. For example, via backpropagation, the resulting loss is backcalculated and thus the gradients are calculated. This causes the backcalculation of the backpropagation to be done through the two models. Typically, the gradients have different learning rates for the two models, but here it may be the same learning rate.

[0035] In a further embodiment of the unsupervised training method for a data-based calibration model, it may be envisaged that the calibration model is provided such that the auxiliary variables indicate an output graph of the calibration model, where the loss is determined by evaluating the calibration model with the augmented sensor state graph to obtain a reconstructed sensor state graph, and determining the loss as a measure of the difference between the original sensor state graph and the reconstructed sensor state graph.

[0036] Here, the auxiliary variables of the output vector are a representation of the sensor state graph with the shape (number of nodes and connections by edges) of the original, unexpanded sensor state graph. The auxiliary variables can be considered as parameters for describing the sensor state graph.

[0037] These auxiliary variables can be determined by evaluation of a calibration model depending on the augmented sensor state graph, where these auxiliary variables should represent a reconstruction of the original sensor state graph. Training can be performed using a loss resulting from the difference between the original sensor state graph (before augmentation) and the reconstructed sensor state graph. This difference can be represented as the Euclidean distance between the original sensor state graph and a vector (or tensor) describing the reconstructed sensor state graph.

[0038] According to one embodiment, a data-based calibration model can be initially trained before the sensor system is put into operation by determining losses for a plurality of sensor states and further losses from a training dataset for supervised training, where a total loss is determined from the losses and the further losses, and where a calibration model is initially trained based on the total loss.

[0039] That is, after the sensor system is manufactured, the calibration model is initially trained using labeled training data that assigns the sensor state graph to the output variables of the output vector. This initial training is performed alternately or simultaneously (using a common loss) with the step of the unsupervised learning method based on the extended sensor state graph as described above, where the output vector of the calibration model indicates the output variables and auxiliary variables for determining the unsupervised loss. In this case, the auxiliary variables can describe the graph in the form of the sensor state graph.

[0040] Here, during operation, the loss based on the expanded sensor state graph is determined exclusively by unsupervised training, and the calibration model is then post-trained, for example, based on a gradient-based training method. This results in a corresponding adaptation of the output variables in the output vector during the evaluation of the calibration model, since this adaptation is directly connected with the auxiliary variables of the output vector via the calibration model. In this way, an improved means of performing post-calibration without a labeled training data set available during operation of the sensor system is created.

[0041] In the following, the embodiments will be explained in more detail based on the attached drawings. [Brief description of the drawings]

[0042] [Figure 1] FIG. 1 illustrates an example sensor system for providing values ​​of sensor output variables having a post-trainable implemented calibration model. [Diagram 2] FIG. 2 is a schematic diagram showing a sensor state graph. [Diagram 3] FIG. 2 is a schematic diagram illustrating a method for unsupervised post-training of a calibration model according to a first embodiment. [Figure 4] 4 is a flow chart illustrating a method for unsupervised post-training of a calibration model according to the depiction of FIG. 3. [Diagram 5]FIG. 13 is a schematic diagram illustrating a model for unsupervised post-training of a calibration model according to a further embodiment. [Figure 6] 6 is a flow chart illustrating a method for post-training of a calibration model according to the depiction of FIG. 5. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0043] Description of the embodiments 1 shows a schematic diagram of a sensor system 1 with a sensor element 2 for capturing one or more physical variables, such as, for example, acceleration, radiation, vibration, filling level, etc., and providing one or more captured variables E, in particular electrical, that are dependent on the one or more physical variables. The one or more captured variables E are pre-processed, for example amplified and / or filtered, by a pre-processing unit 3. The captured variables E can also represent several homogeneous physical variables, such as, for example, acceleration in several spatial directions.

[0044] Furthermore, one or more state sensors 4 are provided for capturing state variables Z. These state variables Z can represent, for example, environmental conditions and can indicate, for example, temperature, humidity, air pressure, mechanical stress loads, for example bending loads, vibration loads, loads due to electromagnetic radiation, etc. Furthermore, the state variables can also be signals captured by internal sensors which indicate the state of the sensor system. For example, the state variables can indicate, for example, quadrature values ​​in the case of an acceleration sensor or the operating voltage of a laser diode, etc. The state variable or variables Z can likewise be preprocessed by a preprocessing unit 3, for example by being amplified and / or filtered.

[0045] In the graph creation unit 5, the captured variable(s) E and the state variable(s) Z are processed into a mathematical sensor state graph 10. Such a sensor state graph is exemplarily shown in Fig. 2. The captured variable(s) E and the state variable(s) Z, also referred to herein as node variables K, are assigned to nodes 11 of the sensor state graph. The nodes 11 of the sensor state graph are interconnected or related by edges 12, to which respective edge variables G are assigned herein.

[0046] Here, the edge variables G can represent edge relations between the node variables, for example in the form of correlations between the node variables. The correlations can be determined by comparison of the time courses of the respective node variables within a predefined time window, which can end in particular at the current time point (the last determined sample). Furthermore, the edge variables G can also represent the relationship between each two node variables K represented by the nodes 11 in other forms. The resulting mathematical sensor state graph 10 represents the state of the sensor system 1 at a particular time step, i.e. at the capture time point.

[0047] The edge variables can be determined once with a special measurement sequence, whereby a time series can be recorded under different environmental conditions in order to capture the time series within a time window and determine the correlation value. Furthermore, the edge variables can also be determined by prior supervised training, whereby the edge variables are varied during training in order to determine optimal values ​​in a kind of hierarchical training. This training can here often be repeated with different edge variables, which can be varied, for example, in a Bayesian manner.

[0048] The sensor state graph is now fed to an initially trained, data-based calibration model 6. At the output of the calibration model, an output vector is output with an output variable for each of the one or more capture variables E and further auxiliary variables. The one or more output variables may in particular correspond to a sensor output variable A which may be modified according to the calibration model 6 and which may be uniquely assigned to a measure of the physical variable represented by the respective capture variable E. Alternatively, each output variable may be a correction variable which may be applied, for example additively or multiplicatively, to the respective capture variable, for example in an optional application block 7, in order to calculate the sensor output variable A in dependence on the sensor state.

[0049] The calibration model 6 is initially trained based on a training data set in which a sensor state graph is assigned to one or more output variables that correspond to or can be derived from the measured physical variables. The initial training of the calibration model is described in more detail further below.

[0050] During operation of the sensor system 1, due to ageing and / or environmental influences, deviations of the sensor characteristics occur, so that the calibration model 6 fits less and less to the actual sensor system 1. The resulting sensor output variables may therefore map less and less sharply to the measured physical variables, which leads to falsification of the measurement results. For this purpose, a calibration control unit 8 is provided, which performs a post-calibration using unsupervised training methods during operation of the sensor system 1 regularly in the end use or at predefined times or triggered externally.

[0051] In the following, an embodiment for performing the post-calibration of the calibration model 6 will be described in more detail.

[0052] In post-calibration, the data-based calibration model 6 or its model parameters are modified, thereby modifying one or more captured variables. The training of the data-based calibration model 6 has the objective of providing one or more output variables that correspond to the sensor output variables as the modified captured variables, respectively, or that correspond to correction variables for subsequently modifying the captured variables, and that are suitable or contribute to providing the sensor output variables assigned to the corresponding physical variables.

[0053] The method for post-training a calibration model will now be described in more detail based on the schematic diagram of Figure 3 and the flow chart of Figure 4. The method starts in step S1 with providing an initially trained calibration model 6 based on a training data set.

[0054] In step S2, the sensor state is captured for a particular time step or capture time point, and in step S3, a sensor state graph is created as described above. The sensor state is represented by one or more capture variables and one or more state variables.

[0055] In a subsequent step S4, a first expanded sensor state graph and a second expanded sensor state graph are generated from the sensor state graph. The expansion of the sensor state graph can be performed by omitting nodes and / or edges or by exchanging nodes and edges, as is shown diagrammatically in Fig. 3. This expansion is performed randomly and in particular independently of the values ​​of the capture variables and / or of one or more state variables.

[0056] 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 first neuron layers 22 arranged downstream in the form of a Fully Connected Layern (MLP), which further process the output vector of the calibration model and provide an evaluation vector from the output side. Other extensions with one or more neuron layers or models based on further data are also conceivable.

[0057] Additionally, a twin model 23 is provided, which is trained in the same manner as the evaluation model 21, but has a different configuration 24. The twin model 23 may include a calibration model 6 and may be modified in a different manner than the evaluation model 21 to account for the differences in configuration 24.

[0058] During the initial training of the evaluation model 21, the twin model 23 is likewise trained with the aim that the twin model 23 provides an evaluation vector B identical to that of the evaluation model 21. The evaluation model 21 and the twin model 23 are each adapted to process a graph as an input variable and to output an evaluation vector B having the same format.

[0059] The twin model 23 is also constructed as a neural graph network, like the calibration model, but may have other structures based on other choices of hyper-parameters.

[0060] The evaluation model 21 and the twin model 23 may be configured identically, but may be extended with a different number of subsequent Fully Connected Layers, so that the two data-based neural graph network models do not represent 1:1 copies of each other and have different configurations.

[0061] Within the framework of an unsupervised training step for post-training the calibration model, in step S5, an evaluation model 21 with the extended first sensor state graph and a twin model 23 with the extended second sensor state graph are evaluated to obtain an evaluation vector B.

[0062] In step S6, the evaluation model 21 and the twin model 23 are trained using a loss L. This loss is generated by comparing the evaluation vector B of the evaluation model 21 with the evaluation vector B of the twin model 23 as the difference between the respective resulting evaluation vectors B. For this purpose, the evaluation vectors B can be examined in terms of Euclidean distance or cosine similarity to determine the loss L. The loss L essentially evaluates the distance between the evaluation vectors B.

[0063] The post-training is performed based on a gradient-based training method for both the evaluation model 21 and the twin model 23. Since the evaluation model 21 includes a calibration model 6, the calibration model 6 is adapted to the sensor state in the process. The calibration model 6 is then used to correct the captured signal and improve the performance of the sensor system 1.

[0064] According to a further embodiment, the post-training can be performed without the use of a twin model 23. Now, the method for post-training the calibration model 6 will be explained in more detail based on the schematic diagram of Fig. 5 and the flow chart of Fig. 6. The method starts in step S11 with providing an initially trained calibration model 6 based on a training data set.

[0065] In step S12, the sensor state is captured for a particular time step or capture time point and a sensor state graph 10 is created as described above. The sensor state is represented by one or more capture variables E and one or more state variables Z.

[0066] For this purpose, in step S13, as described above, an augmented sensor state graph 10 is determined from the sensor state graph 10 of the current sensor state or the sensor state at a particular point in time in the manner described above. This sensor state graph 10 is augmented and fed to the calibration model 6.

[0067] The calibration model 6 is configured, by evaluation of the extended sensor state graph, to provide, on the one hand, an output vector comprising one or more output variables A and auxiliary variables representing a sensor state graph 10 whose format corresponds to the original sensor state graph.

[0068] Thus, the calibration model 6 may be configured to reconstruct the sensor state graph 10 described by the auxiliary variables from the extended sensor state graph corresponding to the original sensor state graph besides the output of the output variables. A comparison of the original and the reconstructed sensor state graphs may determine a loss L as an estimated difference between the sensor state graphs 10. This difference may be determined based on parameters of the sensor state graphs, which may for example be described as graph vectors, in particular by determining the Euclidean distance or the cosine similarity of two graph vectors.

[0069] In step S14, the calibration model 6 is trained based on the loss L.

[0070] This embodiment has the advantage that only a single expansion of the sensor state graph needs to be performed and only a neural graph network model based on the data needs to be trained.

[0071] In this way, the model parameters of the data-based calibration model 6 can likewise be adapted accordingly and applied online, i.e. while the sensor system 1 is in operation.

[0072] Prior to use of the sensor system 1, it is necessary to initially train the calibration model 6. Here, the elements of the output vector, in particular the output variable or variables A and the auxiliary variables, are interrelated in an unsupervised training such that during operation of the sensor system 1 (as described above) the model parameters of the calibration model 6 are modified to allow an optimal adaptation or correction of the captured variables.

[0073] In the initial training of the calibration model, it is necessary to combine one or more output variables to be determined in a suitable manner with auxiliary variables that are also output. For this purpose, a combined training is provided, which alternates or parallels a supervised training based on a training data set and a supervised training based on losses, for example determined using one of the training methods described above. This training is preferably performed for a number of different values ​​of the physical variables in order to achieve a space-filling mapping of the input data space by the calibration model as much as possible when the ambient conditions change (i.e. when the state variables change).

[0074] A training data set for supervised training originates from measurements of a sensor system on a test bench, where one or more applied physical variables to be measured by the sensor system and corresponding captured variables are captured in a planned manner. The applied physical variables are assigned to sensor output variables that the sensor system should output when the corresponding physical variables are present. Thus, the training data set corresponds to an input vector from one or more captured variables and one of a number of state variables labeled with the sensor output variable assigned to the corresponding respective physical variable (when the particular physical variable is applied).

[0075] On the other hand, the loss L for unsupervised training unsupervised is based almost entirely on the evaluation of auxiliary variables at the output of the calibration model 6, whereas the supervised loss L supervisedThe calculation of is based on the evaluation of each of the training data sets, in particular on a comparison of the labels of the training data set with one or more output variables of the output calibration model.

[0076] The two resulting loss values ​​L unsupervised , L supervised will be written as follows: L total = λ 1 L unsupervised +λ 2 L supervised Total loss L total where λ 1 and λ 2 are weighting coefficients that can be determined in advance. In this way, the calibration model 6 can be initially trained to jointly solve two tasks, specifically, the output of one or more correct output variables and the output of auxiliary variables that allow unsupervised post-training of the calibration model.

[0077] Post-calibration can be performed during each acquisition time step prior to determining one or more output variables, thereby allowing the current state of the sensor system to be taken into account when determining the output variables.

[0078] Furthermore, additionally to the post-training step, it may be assumed that at each acquisition time 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 ​​obtained by the initial training. This has the advantage that the post-calibration does not cause the model parameters of the calibration model 6 to deviate too much, which would again deteriorate the performance over time. Instead, only a predictable parameter space for the evolution of the model parameters of the calibration model can be achieved, which can already be controlled and determined during the training phase for safe applications.

Claims

1. A method, in particular a computer-implemented method, for post-calibrating a trained data-based calibration model (6) for use in a sensor system (1) for measuring one or more physical variables, the data-based calibration model (6) being configured as a neural graph network trained to output an output vector comprising one or more output variables (A) and a number of auxiliary variables in dependence on a sensor state graph (10) representing the sensor state, the method comprising: - a step (S2) of capturing, at a capture time, one or more capture variables (E) related to one or more physical variables and one or more state variables (Z) representative of one or more environmental influences on the sensor system (1); - determining (S3) a sensor state graph (10) depending on said one or more capture variables (E) and said one or more state variables (Z); - a step (S4) of expanding said sensor state graph (10); - evaluating (S5) said augmented sensor state graph (10) using a data-based calibration model (6) to obtain an output vector; - determining a loss (L) depending on said output vector; - a step (S6) of unsupervised training of said calibration model (6) depending on said determined losses (L); The method includes:

2. 2. The method according to claim 1, wherein the step of determining the sensor state graph (10) is performed by assigning to the nodes of the sensor state graph (10) node variables corresponding to the one or more captured variables (E) and the one or more state variables (Z) at the capture time point and assigning to the edges of the sensor state graph (10) interconnecting each two nodes of the sensor state graph (10) one edge variable each indicative of the captured variables (E) or the state variables (Z) representing a correlation between the nodes connected by the respective edges, in particular the correlation being determined by evaluation of the time course of the captured variables (E) or the state variables (Z) within a predefined time window.

3. 3. The method of claim 2, wherein the step of expanding the sensor state graph (10) is performed by randomly removing one or more nodes, randomly removing one or more edges, randomly swapping node variables, and / or randomly swapping edge variables.

4. The loss (L) is - using said calibration model (6) to provide an evaluation model comprising one or more further neuronal layers or data-based models corresponding to said calibration model (6) or additionally arranged downstream with respect to said calibration model (6), - providing a twin model (23) trained similarly to said evaluation model (21) and having another configuration (24) with respect to said evaluation model (21); - evaluating the extended sensor state graph (10) by said evaluation model (21) to obtain an evaluation vector (B), - evaluating a further extended sensor state graph (10) by said twin model (23) to obtain a further evaluation vector (B), - The loss is determined as a measure of the difference between the evaluation vectors (B) The method of claim 1 , wherein the difference is determined by:

5. The method of claim 4 , wherein both the evaluation model and the twin model are post-trained depending on the loss (L).

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

7. The calibration model (6) is provided such that the auxiliary variables represent an output graph of the calibration model (6); The loss (L) is - evaluating said calibration model (6) with said augmented sensor state graph (10) to obtain a reconstructed sensor state graph (10); - determining said loss (L) as a measure of the difference between the original sensor state graph (10) and the reconstructed sensor state graph The method of claim 1 , wherein the difference is determined by:

8. 8. The method according to claim 1, wherein the data-based calibration model (6) is initially trained (S1) before the start of operation of the sensor system (1) by determining the losses (L) for a plurality of sensor states and further losses (L) from a training data set for supervised training, and a total loss (L) is determined from the losses (L) and the further losses, thereby initially training the calibration model (6).

9. 9. The method according to claim 1, wherein the one or more output variables include one or more correction variables for application to the one or more capture variables (E) to obtain one or more sensor output variables in dependence on one or more correction variables, or the one or more output variables correspond to the one or more sensor output variables.

10. 10. The method according to claim 1, wherein the calibration model (6) is used to be determined depending on the one or more captured variables (E) and the one or more state variables (Z) of the sensor state graph, and the one or more output variables are determined depending on the sensor state graph.

11. Apparatus comprising a data processing device configured to carry out a method according to any one of claims 1 to 10.

12. A computer program product comprising instructions which, when executed by at least one data processing apparatus, cause said data processing apparatus to carry out the steps of the method according to any one of claims 1 to 9.

13. A machine-readable storage medium storing 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 9.

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