Apparatus and computer-implemented method for machine learning
By constructing a hybrid model that combines physical and data models and utilizes control variables and measurement datasets, the selection of control variables for the technical system is optimized, thus solving the problem of avoiding unsafe states in machine learning and improving the system's security and operational reliability.
Patent Information
- Application Number
- CN202510564848.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2024-05-07
- Filing Date
- 2025-04-30
- Publication Date
- 2025-11-07
AI Technical Summary
Existing technologies struggle to effectively explore and avoid unsafe states of technical systems in machine learning, such as damaged or destroyed states, especially when control variables are unknown or unutilized.
By constructing a hybrid model that combines a physical model and a data-based model, and utilizing control variables and their associated measurement datasets, the parameters of the hybrid model are learned, the information gain and security of the control variables are determined, and the operation of the technical system is optimized.
This enables the optimization of control variable selection in the technical system, improves system security, avoids unsafe states, and ensures that the system operates under conditions where the probability of safety is higher than a threshold.
Smart Images
Figure CN120909112A_ABST
Abstract
Description
BACKGROUND
[0001] In machine learning, hybrid models can be used.
[0002] “Universal Differential Equations for Scientific Machine Learning” (Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, Alan Edelman (arXiv:2001.04385)) discloses an example of a hybrid model. SUMMARY
[0003] The apparatus and the computer-implemented method for machine learning enable an exploration of new measurement values in a technical system, wherein an unsafe state of the technical system, for example a state in which the technical system is damaged or destroyed, is avoided.
[0004] The method provides that a data set is provided in which each control variable of the technical system is associated with a measurement of an operating variable of the technical system, in particular a noisy measurement of the operating variable, wherein parameters of a hybrid model, in particular a hybrid differential equation, are learned from the data set, wherein the hybrid model comprises a physical model and a data-based model, wherein the physical model is configured to determine a first part of a temporal change of the operating variable of the technical system, wherein the data-based model is configured to determine a second part of the temporal change of the operating variable of the technical system, wherein a control variable of the technical system is determined from a measure of the information gain associated with the control variable when the operating variable of the technical system is measured in the case of operation of the technical system with the control variable, and from the probability that the technical system is safe when operated with the control variable, wherein a measurement of the operating variable associated with the control variable, in particular a noisy measurement of the operating variable, is detected when the technical system is operated with the control variable, wherein the control variable and the measurement associated with the control variable are added to the data set, and wherein the parameters of the hybrid model are learned using the data set to which the control variable and the measurement associated with the control variable have been added.
[0005] For example, it is provided that the technical system comprises a computer-controlled machine, in particular a robot, preferably a vehicle, a household appliance, a power tool, a production machine, a personal assistance system or an access control system, or that the technical system comprises a test bench, in particular for a computer-controlled machine, in particular a robot, preferably a vehicle, a household appliance, a power tool, a production machine, a personal assistance system or an access control system.
[0006] For example, the test bench is configured to operate an internal combustion engine, wherein the internal combustion engine is configured to combust an air-fuel mixture depending on a control variable, wherein a measurement associated with the control variable characterizes an operating variable of the internal combustion engine, in particular a noise emission or a pollutant emission of the internal combustion engine, in particular wherein the internal combustion engine is configured to ignite the air-fuel mixture with a pilot ignition and a main ignition, wherein the control variable comprises a time between the pilot ignition and the main ignition, and / or wherein the internal combustion engine is configured to provide fuel in a distribution pipe of the internal combustion engine with a pressure, wherein the control variable comprises the pressure, and / or wherein the internal combustion engine is configured to inject a fuel quantity, wherein the control variable comprises the fuel quantity.
[0007] For example, the technical system is operable in a first operating state in which the technical system is used for a set purpose according to the hybrid model, wherein the technical system is operable in a second operating state in which the technical system cannot be used for the set purpose, and wherein in the second operating state the control variable is determined, and / or the measurement associated with the control variable, and / or the data set comprising the control variable and the measurement associated with the control variable.
[0008] For example, in the second operating state, the parameters of the hybrid model are learned using the data set comprising the control variable and the measurement associated with the control variable.
[0009] For example, it is provided that in the first operating state the control variable and / or the measurement associated with the control variable and / or the data set comprising the control variable and the measurement associated with the control variable are not determined, and / or the parameters of the hybrid model are not learned using the data set comprising the control variable and the measurement associated with the control variable.
[0010] For example, it is provided that the following control variable is determined for which the measure of information gain is greater than for other control variables and the probability that the technical system is safe to operate with this control variable is greater than a threshold value.
[0011] For example, it is provided that the measure of information gain comprises a first matrix comprising a time series of measurements and a set of change values of an operating variable of a data-based model, wherein the operating variable to be measured is determined depending on a determinant of a second matrix, wherein the determinant of the second matrix approximates the determinant of the first matrix.
[0012] For example, it is provided that the elements of the second matrix are defined by the covariances of the changed values of the operating variables with the values of the time series.
[0013] An apparatus for machine learning comprises at least one processor and at least one memory, wherein the at least one processor is configured to execute instructions which, when executed by the at least one processor, cause the apparatus to perform the method according to any one of the preceding claims, and wherein the at least one memory stores the instructions.
[0014] A computer program can be provided which comprises instructions executable by a computer which, when executed by the computer, cause the computer to perform the method. BRIEF DESCRIPTION OF DRAWINGS
[0015] Further advantageous embodiments can be derived from the following description and the attached drawings. In the drawings: Figure 1 A schematic diagram is shown which illustrates a first example of an apparatus for machine learning, Figure 2 A flow chart is shown which illustrates a first example of a method for machine learning, Figure 3 A schematic diagram is shown which illustrates a second example of an apparatus for machine learning, Figure 4 A flow chart is shown which illustrates a second example of a method for machine learning. DETAILED DESCRIPTION
[0016] An apparatus for machine learning comprises at least one processor 102 and at least one memory 104.
[0017] For the machine learning, an operating variable x of a technical system is used which is influenced by a control variable c of the technical system.
[0018] Mixed model for the temporal change dx / dt of the operating variable x of the technical system dx / dt = f(c, x) + g(c, x) The physical model f(c, x) for the part of the temporal change dx / dt of the operating variable x which is related to the control variable c and the data-based model g(c, x) for the part of the temporal change dx / dt of the operating variable x. The data-based model g(c, x) comprises, for example, a Gaussian process which is defined by hyperparameters of the Gaussian process.
[0019] For operating variables x for which the physical model f(c, x) is unknown, it can be provided that the part of the temporal change dx / dt of the operating variable x which is independent of the physical model f(c, x) is determined, for example, by f(c, x) = 0.
[0020] For a physical model f(c,x) with a known operating variable x, it can be stipulated that the part of the time change dx / dt of the operating variable x that is related to the physical model f(c,x) should be determined.
[0021] For machine learning, it can be stipulated that the physical model f(c, x) remains unchanged.
[0022] Machine learning is based on the existence of m initial time series. , ... , i=1, ..., m and the operating variables of the technical system Noise that is independent and uniformly distributed Measurement of additive application .
[0023] Measurement These are the operational variables of the technical system. The measurement with noise is generated when the operating variable is generated in the technical system as a control variable c during operation.
[0024] In machine learning, it is stipulated that new control variables are used. New measurement The exploration is conducted, and this exploration determines the running variables. How to determine the evolution of dx / dt=f(c, x)+g(c, x) over time.
[0025] In one example, the control variable c represents the initial state of the technical system x(t0)=c.
[0026] In one example, the control variable c represents the parameters of the controller that regulates the technology system.
[0027] In one example, the control variable c represents the control strategy or control function. In this example, the physical model f(x, c) is specified to implement the control strategy or control function.
[0028] When the physical model f(c, x) is unknown, i.e. f(x) = 0, for example when using M time series for machine learning, follow these steps: 1. For i = m + 1: M 2. Based on the dataset D={ , Learning differential equations A data-based model, the dataset including control variables and corresponding control variables Related measurements Among them, measurement In a real-world technical system, based on the corresponding control variables It is detected during evolution. For example, learning the hyperparameters of a Gaussian process.
[0029] 3 identifying control variables that enable the greatest possible information gain and possibly a safe operation of the technical system.
[0030] In this example, a measure of information gain is specified In this example, a measure of information gain is specified is a first matrix comprising n time series of measurements and changes in the operating variable determined using a data-based model from the variable c : where c denotes a possible control variable of the technical system to be evaluated.
[0031] In this example, the determinant of the first matrix is approximated by the determinant of the second matrix .
[0032] where where denotes the covariance, denotes the time point corresponding to the measurement .
[0033] In this example, is unknown.
[0034] In one example, is determined by mean field approximation, i.e. by solving using the data-based model with the currently learned hyperparameters .
[0035] In one example, it is determined where K trajectories of the control variable c are drawn where = and from the drawn trajectories is determined .
[0036] For example, the following control variable is determined, which produces a greater information gain than other possible control variables.
[0037] For example, from the technical system with the control variable Probability that the run is safe to determine the control variable .
[0038] For example, the control variable is determined that fulfills the following condition : where a threshold value is defined for the probability at which it is assumed that the technical system is safe in the run with the control variable .
[0039] For example, where and In this example, is unknown.
[0040] In one example, is determined by the described mean field approximation, where the uncertainty of the steps is taken into account by .
[0041] 4. The output control variable .
[0042] In response to the output of the control variable , a measurement is detected. The measurement is detected when the technical system is actually present in the run with the control variable . The measurement is detected, for example, automatically or by a user of the technical system.
[0043] 5. The data set is updated with the control variable and the measurement associated with the control variable , for example: 6. The cycle is ended In addition, further conditions can also be taken into account. For example, a condition for the control variable c can be preset, which is observed in the calculation. For example, a region is specified in which the exploration is too unsafe to be carried out. One example of a control variable as an initial value for the region is: where is a threshold value for the predicted variance along the trajectory from the mean field approximation may not exceed the threshold value. For example, the preset condition is a gradient condition, for example: wherein is a threshold value, the predicted gradient along the trajectory out of the mean field approximation may not exceed the threshold value.
[0044] correspondingly for the case that the physical model is considered to be deterministic, and wherein f is only considered for the mean field approximation.
[0045] A first example of an apparatus 100 for machine learning is schematically illustrated. Figure 1 The apparatus 100 according to the first example comprises at least one processor 102 and at least one memory 104. The at least one memory 104 comprises, for example, a non-volatile memory and a volatile memory.
[0046] The apparatus 100 comprises an interface 106 for communicating with a technical system 108. The interface 106 is configured to receive measurements
[0047] from the technical system 108. The interface 106 is configured to send control variables to the technical system 108.
[0048] In this example, the technical system 108 comprises a test bench.
[0049] In this example, the test bench is configured to test an internal combustion engine.
[0050] The internal combustion engine is configured to combust an air-fuel mixture in accordance with the control variables .
[0051] In one example, the internal combustion engine is configured to ignite the air-fuel mixture with pilot ignition and main ignition.
[0052] In one example, the control variables include a time between the pilot ignition and the main ignition.
[0053] In one example, the internal combustion engine is configured to provide fuel in a distribution pipe of the internal combustion engine at a pressure.
[0054] In one example, the control variables include the pressure.
[0055] In one example, the internal combustion engine is configured to inject an amount of fuel.
[0056] In one example, control variables This includes the amount of fuel.
[0057] In one example, control variables Defines the method for performing measurements The initial state x of the internal combustion engine.
[0058] For example, control variables It defines the initial time between pilot ignition and main ignition, or the initial pressure of fuel in the distribution pipe of the internal combustion engine, or the initial amount of fuel.
[0059] For example, control variables The controller parameters of the internal combustion engine controller are defined, which adjusts the internal combustion engine when performing measurements.
[0060] The test bench can be configured to test other technical systems, such as computer-controlled machines, especially robots, preferably vehicles, home appliances, power tools, production machines, personal assistance systems, or access control systems. An example of a vehicle is an excavator. For instance, at the end of an excavator manufacturing production line, the excavator is individually calibrated using the model created above. For calibration, measurements are performed, for example, on the parameters of the excavator to be calibrated. Based on these measurements, a hybrid model can be trained, which can then be used to assist in calibration.
[0061] The test bench is configured to measure the operating variables of an internal combustion engine. Measurement For example, it could be a noisy measurement of an operating variable. Operating variables, for instance, characterize the noise or pollutant emissions of an internal combustion engine.
[0062] exist Figure 2 The diagram shows a flowchart of a first example of a method for machine learning.
[0063] The method described in the first example is based on the test bench.
[0064] The method according to the first example includes step 202.
[0065] In step 202, a dataset D is provided, which contains each control variable of the technical system 108 (e.g., an internal combustion engine). All of these are related to the noisy measurement of the operating variable x of the technical system 108. Related.
[0066] The method according to the first example includes step 204.
[0067] In step 204, the hybrid model (especially the hybrid differential equations) of the learning technology system 108 is learned based on the dataset D. The parameters of ).
[0068] This hybrid model includes the physical model of technology system 108. and data-based models .
[0069] Physical Model The time variation of the operating variable x of the determined technical system 108 is constituted. The first part.
[0070] Data-based models The time variation of the operating variable x of the determined technical system 108 is constituted. The second part.
[0071] The method according to the first example includes step 206.
[0072] In step 206, the control variables of the technical system 108 are determined. .
[0073] Control variables of technical system 108 According to the measurement of information gain To determine.
[0074] Control variables of technical system 108 According to the technical system 108, the control variable The probability that the operation is safe To determine.
[0075] In this example, the control variable is determined. For the control variable, and the control variable Related information gain metrics It is greater than other possible control variables c, and the technical system 108 uses this control variable The probability that the operation is safe The value exceeds a preset threshold. This threshold, for example, is between 95% and 99.999% for the probability that the operation is safe, specifically 95%, 97%, or 99%.
[0076] The method according to the first example includes step 208.
[0077] In step 208, in the technical system 108, control variables are used. At runtime, the runtime variable x is checked against the control variable. Noisy measurements associated with .
[0078] The method according to the first example includes step 210.
[0079] In step 210, the control variables are... and measurement are added to the dataset D in association with each other.
[0080] Subsequently, step 204 is re-executed.
[0081] This means that, upon re-execution of step 204, the parameters of the mixture model are learned using the dataset D comprising the control variables and the measurements associated with the control variables of the respective technical system 108.
[0082] A second example of an apparatus 100 for machine learning is schematically shown in Figure 3 .
[0083] The apparatus 100 according to the second example is constituted as described for the first example.
[0084] Unlike the apparatus 100 according to the first example, the interface 106 of the apparatus 100 according to the second example is constituted to communicate with a multitude of technical systems 108 in order to send control variables to the respective technical system 108 and to receive respective measurements detected at the respective technical system 108 when the respective technical system 108 is operated with the respective control variable .
[0085] The respective technical system 108 is constituted to receive the respective control variable , to detect the respective measurement when the respective technical system 108 is operated with the respective control variable , and to send the respective measurement to the interface 106.
[0086] The technical systems 108 according to the second example are computer-controlled machines.
[0087] The technical systems 108 according to the second example can comprise robots.
[0088] The technical systems 108 according to the second example can comprise vehicles, household appliances, power tools, production machines, personal assistance systems, or access control systems.
[0089] The respective technical system 108 can be operated on site.
[0090] For example, the respective technical system 108 can be operated in a first operating state in which the respective technical system 108 is used for a set purpose according to the mixture model.
[0091] For example, the respective technical system 108 can be operated in a second operating state in which the respective technical system 108 is not used for the set purpose.
[0092] For example, the corresponding technical system 108 is configured to receive control variables in the second operating state. .
[0093] For example, the corresponding technical system 108 is configured such that it does not receive control variables in the first operating state. .
[0094] For example, the corresponding technical system 108 is configured to measure and control variables in the second operating state. Related measurements .
[0095] For example, the corresponding technical system 108 is configured not to be based on control variables in the first operating state. Take measurements.
[0096] For example, the corresponding technical system 108 is configured to send and control variables in the second operating state. Measurement of the connection .
[0097] For example, the corresponding technical system 108 is configured such that no control variables are sent in the first operating state. Related measurements .
[0098] The corresponding technical system 108 can be configured to not receive control variables. Rather, it is to determine the control variables, especially in the second operating state. For example, the corresponding technical system 108 is configured such that the control variable is uncertain in the first operating state. .
[0099] The corresponding technical system 108 can be configured to send and control variables without being in the second operating state. Related measurements Instead, control variables and control variables Related measurements The data is added to a local dataset. The corresponding technical system 108 can be configured, for example, to send the local dataset to device 100 after multiple measurements have been performed on multiple control variables to be measured. Device 100 can be configured to receive the corresponding local dataset and add it to dataset D.
[0100] The apparatus 100 according to the second example is configured, for example, to learn the parameters of a hybrid model using a dataset D.
[0101] According to the second example, the corresponding technical system 108 can be configured to learn the corresponding local parameters of the corresponding local hybrid model using a local dataset. The apparatus 100 can be configured to receive the corresponding local parameters and determine the parameters of the hybrid model based on the local parameters.
[0102] According to the second example, the apparatus 100 is configured to send the learned parameters of the hybrid model to the corresponding technical system 108. The corresponding technical system 108 is configured, for example, to replace the local parameters of the local hybrid model with the parameters received from the apparatus 100, especially in the second operating state.
[0103] In this example, the corresponding technical system 108 is configured such that the local parameters are not determined in the first operating state. In this example, the corresponding technical system 108 is configured such that the local parameters are not replaced by parameters received from the device 100 in the first operating state.
[0104] exist Figure 4 The diagram shows a flowchart of a second example of a method for machine learning.
[0105] The method according to the second example is described using multiple technical systems 108 as examples.
[0106] The method according to the second example includes step 402.
[0107] In step 402, a dataset D is provided, in which the initial values of the control variable c for each technical system 108 (e.g., an internal combustion engine) are provided. All of these are related to the noisy measurement of the operating variable x of the technical system 108. Related.
[0108] The method according to the second example includes step 404.
[0109] In step 404, a mixture model (especially mixture differential equations) is learned based on dataset D. The parameters of ). In this example, the hybrid model models the corresponding technical system 108.
[0110] The hybrid model includes a physical model of at least a portion of the technical system 108. and at least a part of the data-based model of the technology system 108 .
[0111] Physical Model The time variation of the operating variable x of the determined technical system 108 is constituted. The first part.
[0112] Data-based models The time variation of the operating variable x of the determined technical system 108 is constituted. The second part.
[0113] In this example, the same hybrid model and the same physical model are used. and the same data-based model Modeling is performed for each technical system 108. This means learning hybrid models, each of which models at least a portion of the technical system 108. The technical systems 108 themselves do not need to be identical, but can be of the same type, i.e., similar enough to be modeled using the same hybrid model. It can be specified that a separate hybrid model is trained for each technical system 108 or for multiple technical systems 108, or a common hybrid model is trained for multiple technical systems 108.
[0114] The method according to the second example includes step 406.
[0115] In step 406, the control variables of the corresponding technical system 108 are determined. Different control variables can be specified for multiple or all technical systems 108. Or determine the same control variables .
[0116] In this example, the corresponding control variables Initial values were defined. .
[0117] The information gain is measured based on the control variable c during operation in the corresponding technical system 108. Determine the control variables .
[0118] Based on the probability that the corresponding technical system 108 operates safely with control variable c, Determine the control variables of the corresponding technical system 108 .
[0119] In this example, the control variable is determined. Regarding this control variable, and the control variable Related information gain metrics It is greater than other possible control variables c, and the corresponding technical system 108 uses this control variable. The probability that the operation is safe The value exceeds a preset threshold. This threshold, for example, is between 95% and 99.999% for the probability that the operation is safe, specifically 95%, 97%, or 99%.
[0120] It can be stipulated that the same metric and the same probability are determined for technical systems 108 and applied to all or multiple technical systems 108.
[0121] The method according to the first example comprises a step 408.
[0122] In step 408, the technical system 108 is operated with the control variable The measurement associated with the control variable is detected.
[0123] This means that the respective technical system 108 receives from the device 100 the control variable set for the respective technical system 108, determines the measurement when the respective technical system 108 is operated with the respective control variable and sends the measurement to the device 100.
[0124] It can be provided that a plurality of control variables to be measured is sent and a plurality of measurements respectively associated therewith is measured when the respective technical system 108 is operated with the respective control variable to be measured.
[0125] The method according to the first example comprises a step 410.
[0126] In step 410, the respective control variable c* and the measurement associated with the respective control variable c* are added to the data set D in mutual association.
[0127] It can be provided that the measurement is received separately or that the measurement is received in the respective local data set.
[0128] It can be provided that the respective local data set is added to the data set D.
[0129] Subsequently, step 404 is re-executed.
[0130] This means that, when step 404 is re-executed, the parameters of the mixture model are learned with the data set D comprising the control variables and the measurements associated with the control variables .
[0131] It can be provided that the locally learned parameters are determined by the respective technical system 108 and that these parameters are received by the device. It can be provided that the parameters of the mixture model are determined in accordance with the locally learned parameters.
Claims
1. A computer-implemented method for machine learning, characterized in that, A data set is provided (202, 402) in which each control variable of a technical system (108) is associated with a measurement of an operational variable of the technical system (108), in particular a noisy measurement of the operational variable; wherein parameters of a hybrid model, in particular of a hybrid differential equation, are learned (204, 404) from the data set; wherein the hybrid model comprises a physical model and a data-based model; wherein the physical model is configured to determine a first part of a temporal change of the operational variable of the technical system (108); wherein the data-based model is configured to determine a second part of the temporal change of the operational variable of the technical system (108); wherein a control variable of the technical system (108) is determined (206, 406) from a measure of information gain associated with the control variable in a measurement of the operational variable of the technical system when the technical system (108) is operated with the control variable, and from a probability that the technical system (108) is safe when operated with the control variable; wherein, in the technical system (108) operated with the control variable, a measurement of the operational variable associated with the control variable, in particular a noisy measurement of the operational variable, is detected (208, 408); wherein the control variable and the measurement associated with the control variable are added (210, 410) to the data set; and wherein the parameters of the hybrid model are learned (204, 404) using the data set to which the control variable and the measurement associated with the control variable are added.
2. The method of claim 1, wherein, The technical system (108) comprises a computer-controlled machine, in particular a robot, preferably a vehicle, a household appliance, a power tool, a production machine, a personal assistance system or an access control system; or the technical system (108) comprises a test bench, in particular a test bench for a computer-controlled machine, in particular a robot, preferably a vehicle, a household appliance, a power tool, a production machine, a personal assistance system or an access control system.
3. The method of claim 2, wherein, The test bench is configured to test an internal combustion engine, wherein the internal combustion engine is configured to combust an air-fuel mixture in accordance with the control variable, wherein the measurement associated with the control variable characterizes an operational variable of the internal combustion engine, in particular a noise emission or a pollutant emission of the internal combustion engine, in particular wherein the internal combustion engine is configured to ignite the air-fuel mixture using a pilot ignition and a main ignition, wherein the control variable comprises a time between the pilot ignition and the main ignition; and / or wherein the internal combustion engine is configured to provide fuel at a pressure in a distribution pipe of the internal combustion engine, wherein the control variable comprises the pressure; and / or wherein the internal combustion engine is configured to inject a fuel quantity, wherein the control variable comprises the fuel quantity.
4. The method according to any of the preceding claims, characterized in that, The technical system (108) is capable of operating in a first operating state in which the technical system (108) is used for a set purpose in accordance with the hybrid model; wherein the technical system (108) is capable of operating in a second operating state in which the technical system (108) is not available for the intended purpose; and wherein in the second operating state the control variable and / or a measurement associated with the control variable and / or a data set comprising the control variable and a measurement associated with the control variable is determined (408).
5. The method according to any of the preceding claims, characterized in that, In the second operating state, parameters of the mixture model are learned using the data set comprising the control variable and a measurement associated with the control variable.
6. The method according to claim 4 or 5, characterized in that, In the first operating state, the control variable and / or a measurement associated with the control variable and / or a data set comprising the control variable and a measurement associated with the control variable is not determined and / or parameters of the mixture model are not learned using the data set comprising the control variable and a measurement associated with the control variable.
7. The method according to any of the preceding claims, characterized in that, The control variable is determined for which the measure of the information gain is greater than the measure of the information gain of other control variables and the probability that the technical system (108) operates with the control variable is greater than a threshold value.
8. The method according to any of the preceding claims, characterized in that, The measure of the information gain comprises a first matrix containing a time series of measurements and a set of change values of an operating variable of the data-based model, wherein the control variable is determined from a determinant of a second matrix, wherein the determinant of the second matrix approximates the determinant of the first matrix.
9. The method of claim 8, wherein, The elements of the second matrix are defined by a covariance of the change values of the operating variable and the time series values.
10. An apparatus (100) for machine learning, characterized in that The apparatus (100) comprises at least one processor (102) and at least one memory (104), wherein the at least one processor (102) is configured to execute instructions, which when executed by the at least one processor (102) cause the apparatus (100) to perform the method according to any one of the preceding claims, and wherein the at least one memory (104) stores the instructions.
11. A computer program, characterized in that, The computer program comprises instructions executable by a computer, which when executed by the computer cause the computer to perform the method according to any one of claims 1 to 9.