DE-102024210756-A1 - 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.

Inventors

• Sven Peter
• Xiahan Shi
• Felix Eberhard Hildebrand
• Markus Klinsmann

Assignees

• Robert Bosch Gesellschaft mit beschränkter Haftung

Dates

Publication Date

20260513

Application Date

20241108

Claims (10)

1. 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, depending on a multidimensional input variable from an input space, wherein the input space comprises several dimensions, wherein the method is 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 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. Procedure according to Claim 1 , characterized in that a validation data set is provided 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 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 one of the preceding claims, characterized in that a data set is provided (200) comprising 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 one of the preceding claims, characterized in 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 with the Gaussian process assigned to the selected end node (206), wherein, for at least one decision node, the dimension is selected depending on the deviation (202) which minimizes the deviation.
5. Method according to one of the preceding claims, characterized in that the input space is divided into different partitions, particularly in iterations using different decision tree candidates, in particular 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, in particular if at least one input variable is located 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. Procedure according to Claim 5 , characterized in 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 threshold for the storage space, or until it is determined that a change in the improvement of the predictions is less than a threshold for the improvement, or until it is determined that the number of end nodes exceeds a threshold for the maximum number of end nodes.
7. A method according to one of the preceding claims, characterized in that data points are provided, each of which assigns a target value for the 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 associated with the respective The training is performed using data points assigned to the Gaussian process.
8. Method according to one of the preceding claims, characterized in 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 in that the device is configured to perform the method according to one of the Claims 1 until 8 to execute.
10. Computer program, characterized in that the computer program comprises computer-readable instructions, the execution of which by the computer follows the method according to one of the Claims 1 until 8 expires.

Description

State of the art 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. 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, complex dependencies and/or numerous features sometimes require large datasets, i.e., many samples. In such cases, Gaussian processes exhibit scaling behavior with regard to memory requirements and computation time, which complicates their use on available computing infrastructure with limited memory or processing resources. Furthermore, it has been shown that some electrochemical systems exhibit behavior where the correlations between relevant variables change across the parameter range. This cannot be satisfactorily represented by classical Gaussian processes with stationary kernels. Disclosure of the invention 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. 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. 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. 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. 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. 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. In particular, for training to identify a number of decision nodes that lead to improvement, it may be intended that the input room is used, especially in iterations. The system is divided into different partitions using different decision tree candidates, in particular 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, in particular if there is at least one input variable 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. For example, the numbe