Device and computer-implemented method for calculating a prediction for an operating characteristic of an electrochemical system, in particular a fuel cell, an electrolyzer or a battery

Abstract

Device and computer-implemented method for calculating a prediction for an operating characteristic of an electrochemical system, in particular a fuel cell, an electrolyzer or a battery, depending on a multidimensional input variable from an input space, wherein the input space comprises several dimensions, characterized in that a decision tree is provided (202) which divides the input space into subspaces along at least one dimension at decision nodes of the decision tree, wherein each subspace is assigned a Gaussian process, wherein, depending on the multidimensional input variable and the decision nodes, the subspace in which the multidimensional input variable lies is selected from the subspaces (204), and the prediction is determined with the Gaussian process that is assigned to the selected subspace.

Description

State of the art

[0001] The invention relates to a device and a computer-implemented method for calculating a prediction for an operating characteristic of an electrochemical system, in particular a fuel cell, an electrolyzer or a battery.

[0002] Gaussian processes are a machine learning method for regression or classification problems. They are suitable for virtual sensors of electrochemical systems, such as fuel cells, electrolyzers, and batteries. Besides accurately representing the behavior of the electrochemical system, particularly as a surrogate model for simulations, Gaussian processes offer the advantage of uncertainty estimation. However, with complex dependencies and / or numerous features, large datasets, i.e., many samples, are sometimes required. In such cases, Gaussian processes exhibit scaling behavior with regard to memory requirements and computation time, which can make their use difficult on available computing infrastructure with limited memory or processing resources.Furthermore, it has been shown that some electrochemical systems exhibit behavior in which the correlations between the relevant quantities change across the parameter range. This cannot be satisfactorily represented by classical Gaussian processes with stationary kernels. Disclosure of the invention

[0003] The computer-implemented method according to claim 1 provides a tree-based approach which significantly improves the scaling behavior with respect to memory requirements and computation time when using Gaussian processes.

[0004] This method reduces the memory requirements of Gaussian processes and shortens computation times for model predictions while maintaining or improving model quality. The method is particularly advantageous for approximating non-stationary problems, as the tree-based approach allows the use of different length-scale parameters typical of Gaussian processes in different regions of the input space.

[0005] The method allows the calculation of a prediction for an operating characteristic, in particular an indirect measurement of the operating characteristic, of an electrochemical system, especially a fuel cell, an electrolyzer, or a battery, depending on a multidimensional input variable from an input space, wherein the input space comprises several dimensions. The method provides a decision tree that divides the input space into subspaces along at least one dimension at decision nodes of the decision tree, with each subspace being assigned a Gaussian process. Depending on the multidimensional input variable and the decision nodes, the subspace containing the multidimensional input variable is selected from the available subspaces, and the prediction is determined using the Gaussian process assigned to the selected subspace.

[0006] In particular, for tree creation and validation, a validation dataset can be provided that assigns a target value for the prediction to each input variable. Depending on the input variables and target values ​​from the validation dataset, a metric value (in particular, mean squared error, root mean squared error, mean absolute error, or mean absolute percentage) is determined that quantifies the deviation of the respective prediction from the respective target value. The metric thus determined is suitable for identifying, when further subdividing the input space, the input variable that most improves the model.

[0007] In particular for training purposes, it may be provided that a data set is supplied which includes input variables, whereby at least one dimension, along which the input space is divided into subspaces at decision nodes of the decision tree, is determined depending on the input variables.

[0008] In particular, for training purposes, it can further be provided that a training data set is supplied which assigns a respective target value for the prediction to a respective input variable, wherein, depending on the input variables and target values ​​from the training data set, a value of a metric is determined which quantifies a deviation of the respective prediction from the respective target value, wherein the prediction is determined with the Gaussian process assigned to the selected end node, wherein for at least one decision node, the dimension is chosen depending on the deviation which minimizes the deviation.

[0009] In particular, for training to identify a number of decision nodes that lead to an improvement, it may be provided that the input space is divided into different partitions, especially in iterations using different decision tree candidates, particularly using decision tree candidates that have an increasing number of decision nodes with an increasing number of iterations, wherein a prediction is determined for each partition, especially if at least one input variable is contained in the partition, wherein, depending on the predictions determined for the partitions, the decision tree is selected from the decision tree candidates for which the prediction is better than for the other decision tree candidates.

[0010] For example, the number of decision nodes is increased until an end criterion is reached, in particular until it is determined that the storage space required to store the Gaussian processes exceeds a predetermined storage space threshold, or until it is determined that the change in the quality of the predictions, for example based on a metric, when adding the next node is less than an improvement threshold, or until it is determined that the number of end nodes exceeds a threshold for the maximum number of end nodes.

[0011] It can be provided that data points are supplied, each assigning a target value for the prediction to an input variable. Depending on the value of the input variable from the data point in the selected dimension, the data points are assigned to a Gaussian process, which is then assigned to the Gaussian process by the decision tree. Each Gaussian process is trained on the data points assigned to it. Thus, for each subspace defined by the decision tree, one Gaussian process is provided, trained on a subset of the total number of samples. This increases efficiency, reduces the computational resource requirements for prediction, and, by allowing different length scales for each subspace, improves the prediction quality, particularly for non-stationary problems.

[0012] For example, it is envisaged that the multidimensional input variable, in particular at least two of the variables temperature, pressure, voltage, or current, are acquired in the electrochemical system, and the prediction, in particular of another of the variables or another internal variable of the electrochemical system, or an aging variable, is determined using the Gaussian process assigned to the selected subspace. The method can thus be used to indirectly measure the operating characteristic. The method can therefore be used as an indirect or virtual sensor.

[0013] A device for calculating a prediction of an operating characteristic of an electrochemical system, in particular a fuel cell, an electrolyzer, or a battery, using a Gaussian process as a function of a multidimensional input variable from an input space comprising several dimensions, is configured to perform the method. The device has properties that correspond to the properties of the method.

[0014] A computer program may be provided, wherein the computer program includes computer-readable instructions, the execution of which by the computer carries out the procedure.

[0015] Further embodiments can be found in the following description and the drawing. The drawing shows: Fig. 1 a schematic representation of a device for calculating a prediction for an operating characteristic of an electrochemical system, Fig. 2. A flowchart showing the steps of a procedure for calculating the prediction of the operating characteristic of the electrochemical system. Fig. 3. Exemplary tree structure of a decision tree with decision nodes and end nodes.

[0016] In Fig. 1 is a device 100 for calculating a prediction for an operating characteristic of an electrochemical system 102, shown schematically.

[0017] Electrochemical system 102 is, for example, a fuel cell, an electrolyzer, or a battery.

[0018] In the example, the electrochemical system 102 includes at least one sensor 104. The at least one sensor 104 is configured to detect a multidimensional input quantity 106.

[0019] The multidimensional input quantity 106 includes, for example, at least two of the quantities Temperature, Pressure, Tension, Electricity

[0020] The device 100 is designed to determine the prediction using a Gaussian process, which defines the prediction depending on the multidimensional input variable 106.

[0021] The operating characteristic is, for example, one of the variables. Temperature, Pressure, Tension, Electricity.

[0022] The predicted operating characteristic is, for example, a different quantity than the quantities from the multidimensional input. The prediction can also be one of the quantities detected by sensor 104, e.g., to verify one of the quantities.

[0023] The device 100 is configured to perform a method for calculating the prediction for the operating characteristic of the electrochemical system.

[0024] In Fig. Figure 2 shows a flowchart illustrating the steps of the procedure.

[0025] The procedure comprises one step 200.

[0026] In step 200, data points are provided that assign a target value for the prediction to each multidimensional input variable.

[0027] In step 200, the multidimensional input variable is provided. This multidimensional input variable is, for example, detected by at least one sensor 104.

[0028] For example, a dataset, a training dataset, or a validation dataset is provided that includes the data points.

[0029] The procedure includes step 202.

[0030] In step 202, the decision tree is provided.

[0031] The decision tree divides the input space into subspaces along at least one dimension of decision nodes of the decision tree.

[0032] The decision tree includes, for example, at least one decision node and one end node.

[0033] Each terminal node is assigned a Gaussian process.

[0034] At least one decision node is assigned a comparison value for the value of the input variable in the selected dimension.

[0035] For example, for at least one decision node, the comparison value is determined depending on the values ​​of the input variables in the selected dimension. For example, the comparison value is determined as the mean or median of the values ​​of the input variables in the selected dimension.

[0036] The procedure includes step 204.

[0037] In step 204, depending on the multidimensional input variable and the decision nodes, the subspace in which the multidimensional input variable lies is selected from the subspaces.

[0038] For example, a terminal node is selected. The terminal node is selected, for example, depending on the result of comparing the value with the comparison value at at least one decision node of the decision tree.

[0039] The procedure includes step 206.

[0040] In step 206, the prediction is determined using the Gaussian process assigned to the selected subspace.

[0041] For example, the forecast is determined using the Gaussian process, which is assigned to the selected end account.

[0042] It may be possible to repeat steps 202 to 206 for the data points from the validation dataset and, depending on the input variables and target values ​​from the validation dataset, to determine a value of a metric that quantifies a deviation of the respective prediction from the respective target value.

[0043] The prediction is determined using the Gaussian process assigned to the selected terminal node.

[0044] The metric is, for example, a means squared error, a root mean squared error, a mean absolute error, or a mean absolute percentage error between the prediction for the input variable from a given data point and the target value from the given data point.

[0045] It may be provided that at least one dimension along which the input space is subdivided into subspaces at decision nodes of the decision tree is determined depending on the input variables.

[0046] It may be possible to repeat steps 202 to 206 for the data points from the training dataset, determining a metric value based on the input and target values ​​from the training dataset. Optionally, for at least one decision node, the comparison value is determined based on the deviation, such that the deviation is minimal, i.e., smaller than for all other comparison values.

[0047] For example, for at least one decision node, the dimension is chosen depending on the deviation, which minimizes the deviation.

[0048] Depending on the value of the input variable from the data point in the selected dimension, the data points are assigned to the Gaussian process, to which the value of the input variable from the data point in the selected dimension is assigned by the decision tree.

[0049] The respective Gaussian process is trained using the data points assigned to the respective Gaussian process.

[0050] In this example, the decision tree is determined by playing through different decision tree candidates.

[0051] Steps 202 to 206 are repeated for a data point, whereby the input space with different decision tree candidates is divided into different partitions and, depending on the predictions determined for partitions, the decision tree is selected from the decision tree candidates for which the prediction is better than for the other decision tree candidates.

[0052] This means that the entrance space is divided into different partitions in iterations using different decision tree candidates.

[0053] For example, the entrance space is subdivided using decision tree candidates, which have an increasing number of decision nodes with an increasing number of iterations.

[0054] The number of decision nodes is increased, for example, until a final criterion is reached.

[0055] The final criterion is reached, for example, when it is determined that the storage space required for storing the Gauss processes exceeds a predefined threshold for the storage space.

[0056] The final criterion is reached, for example, when it is determined that the number of end nodes exceeds a threshold for the maximum number of end nodes.

[0057] The prediction for the captured input variable is determined, for example, using the selected Gaussian process.

[0058] The Gaussian process for the recorded input variable is determined, for example, using the selected decision tree candidate.

[0059] In Fig. Figure 3 shows an exemplary tree structure of a decision tree 300 with decision node 302 and end node 304.

[0060] The decision tree 300 is applied, for example, to input variables 306.

[0061] The input variables 306 are, for example, subdivided per decision node 302 according to whether a value of the input variable 306 in a selected dimension falls below a comparison value or not.

[0062] In Fig. Figure 3 is an example of a two-dimensional input quantity that includes the quantities i and T.

[0063] The input variables 306 are, for example, subdivided by means of a first decision node 302 based on the selected dimension T according to whether the value of the input variable in dimension T falls below a first comparison value T* (T <T*) oder nicht (T≥T*).

[0064] The input variables T with a value T <T* sind einer ersten Partition und die anderen Eingangsgrößen T sind einer zweiten Partition in der ausgewählten Dimension T zugeordnet.

[0065] In the example, the input variables from the first partition are subdivided by means of a second decision node 302 based on the selected second dimension i, according to whether the value of the input variable in dimension i falls below a second comparison value i* (i <i*) oder nicht (i≥i*).

[0066] The input variables i in the range T <T* mit einem Wert i<i* sind einer ersten Partition und die anderen Eingangsgrößen sind einer zweiten Partition in der ausgewählten Dimension i zugeordnet.

[0067] In the example, the input variables from the second partition are subdivided by means of a third decision node 302 based on the selected first dimension T, according to whether the value of the input variable in dimension T falls below a third comparison value T* (T <T*) oder nicht (T≥T*).

[0068] The third comparison value T* is, for example, the median of the values ​​of the input variables from the second partition in the selected first dimension T.

[0069] This means that the decision limit or comparison value for a dimension for inserting another node is the median of the values ​​of this dimension in the subspace to be divided by the node in the dataset.

[0070] The input variables T with a value T

Claims

[1] Computer-implemented method for calculating a prediction for an operating characteristic of an electrochemical system, in particular a fuel cell, an electrolyzer or a battery, depending on a multidimensional input variable from an input space, wherein the input space comprises several dimensions, wherein the method characterized by is that a decision tree is provided (202) which divides the input space into subspaces along at least one dimension of decision nodes of the decision tree, wherein each subspace is assigned a Gaussian process, wherein, depending on the multidimensional input variable and the decision nodes, the subspace is selected from the subspaces (204) in which the multidimensional input variable lies, and the prediction is determined with the Gaussian process assigned to the selected subspace (206). [2] Method according to claim 1, characterized by, that a validation data set is provided which assigns a respective target value for the prediction to a respective input variable, whereby, depending on the input variables and target values ​​from the validation data set, a value of a metric is determined which quantifies a deviation of the respective prediction from the respective target value. [3] Method according to any one of the preceding claims, characterized by , that a data set is provided (200) which includes input variables, wherein at least one dimension along which the input space is subdivided into subspaces at decision nodes of the decision tree is determined depending on the input variables (202). [4] Method according to any one of the preceding claims, characterized by, that a training data set is provided (200) which assigns a respective target value for the prediction to a respective input variable, wherein, depending on the input variables and target values ​​from the training data set, a value of a metric is determined which quantifies a deviation of the respective prediction from the respective target value, wherein the prediction is determined using the Gaussian process assigned to the selected end node (206), wherein, for at least one decision node, the dimension is chosen depending on the deviation (202) which minimizes the deviation. [5] Method according to any one of the preceding claims, characterized by, that the input space is divided into different partitions, particularly in iterations using different decision tree candidates, especially using decision tree candidates which have an increasing number of decision nodes with an increasing number of iterations (202), wherein a prediction is determined for each partition, particularly if at least one input variable is in the partition (206), wherein, depending on the predictions determined for partitions, the decision tree is selected from the decision tree candidates for which the prediction is better than for the other decision tree candidates. [6] Method according to claim 5, characterized by, that the number of decision nodes is increased until an end criterion is reached, in particular until it is determined that the storage space required for storing the Gaussian processes exceeds a predetermined storage space threshold, or until it is determined that a change in the improvement of the predictions is less than a threshold for improvement, or until it is determined that the number of end nodes exceeds a threshold for the maximum number of end nodes. [7] Method according to any of the preceding claims, characterized by, that data points are provided, each assigning a target value for prediction to an input variable, wherein the data points are assigned to the Gaussian process depending on the value of the input variable from the data point in the selected dimension, to which the value of the input variable from the data point in the selected dimension is assigned by the decision tree, wherein the respective Gaussian process is trained with the data points assigned to the respective Gaussian process. [8] Method according to any one of the preceding claims, characterized by , that the multidimensional input quantity, in particular at least two of the quantities temperature, pressure, voltage, current, are detected in the electrochemical system, and the prediction, in particular another of the quantities, or another internal quantity of the electrochemical system, or an aging quantity, is determined with the Gaussian process assigned to the selected subspace. [9] Device for calculating a prediction for an operating characteristic of an electrochemical system, in particular a fuel cell, an electrolyzer or a battery, using a Gaussian process depending on a multidimensional input variable from an input space comprising several dimensions, characterized by that the device is configured to perform the method according to any one of claims 1 to 8. [10] Computer program, characterized by that the computer program comprises computer-readable instructions, the execution of which by the computer results in the procedure according to one of claims 1 to 8.

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