Method and device for providing a virtual sensor using machine learning

Abstract

The invention relates to a method for providing a virtual sensor which is designed to ascertain a state variable (x), which characterizes the state of a technical system, on the basis of an operational variable curve (u) of the technical system (200, 300), said operational variable curve being ascertained in particular on the basis of a measurement carried out on the technical system (200, 300), wherein training data (D) is provided which comprises pairs of time curves of the operational variable (u(t))), said pairs being ascertained empirically (i.e. in particular on the basis of measurements), and associated curves of the state variable (x(t)), and a first model (h 1) is ascertained on the basis of the training data (D), said model characterizing the evolution of the state variable (x(t)) on the basis of the operational variable (u(t)) and the state variable (x(t)). The first model (h 1) comprises a machine learning system (g), and a second model (h 2) is ascertained from the first model (h 1) in that the machine learning system (g) is replaced with an algebraic expression (g a) ascertained using symbolic regression of the learning system (g). The virtual sensor is provided such that the virtual sensor ascertains the operational variable (x) on the basis of the state variable (u) using the second model (h 2).

Description

[0001]R. 408520 Description Title Method and device for providing a virtual sensor with machine learning The invention relates to a method for providing a virtual sensor, the virtual sensor, a method for operating the virtual sensor, a computer program, a machine-readable storage medium, and a training device. State of the art From DE 102022200022 A1, a method for providing an aging state model for determining a modeled aging state SOH of a battery cell is known, comprising the following steps: ^ Providing training data sets, each of which assigns an empirically determined aging state to an operating variable profile of one or more operating variables at a specific point in time; ^ Providing a data-based aging model that is designed with a neural differential equation system,to model internal electrochemical states of the energy storage device, wherein the internal states are mappable to an aging state, wherein at least one of the differential equations of the differential equation system comprises a sum of a deterministic model term and a data-based correction term formed by a data-based correction model, ^ training the data-based aging model based on the training data sets so that model parameters of the data-based correction model R. 408520 are determined. It is then also known to use this aging state model as a virtual sensor. Therefore, a method for determining the modeled aging state (SOH) of the battery cell at a specific time is also known from the cited document.with the following steps: ^ Providing a business variable profile for one or more business variables; ^ Providing a trained, data-based aging state model based on a neural differential equation system and trained to associate a business variable profile with an aging state; ^ Determining or predicting the modeled aging state by evaluating the aging state model with the business variable profile in time steps. Neural differential equation systems are derived from Chen et al. Neural Ordinary Differential Equations,https: / / arxiv.org / pdf / 1806.07366.pdf. DE 102020215138 A1 discloses a method for generating physical equations using symbolic regression of trained machine learning systems. Advantages of the Invention Virtual sensors generally refer to the determination of a profile of a variable characterizing a state of a technical system as a function of an operating variable profile of the technical system (determined as a function of a measurement). The invention with the features of independent claim 1 has the advantage over what is known from the prior art thatthat the virtual sensor is particularly powerful. In particular, it is robustly capable of extrapolation. R. 408520 Further aspects of the invention are the subject of the independent claims. Advantageous developments are the subject of the dependent claims. Disclosure of the Invention In a first aspect, the invention relates to a method for providing a virtual sensor that is configured to determine a state variable characterizing a state of the technical system depending on an operating variable profile of a technical system determined in particular as a function of a measurement on a technical system, wherein training data are provided that comprise empirically (i.e., in particular as a function of measurements) determined pairs of temporal profiles of the operating variable and associated profiles of the state variable, wherein a first model is determined depending on this training data,which characterizes an evolution of the state variable depending on the operating variable) (and the state variable (x(t))), wherein the first model comprises a machine learning system, wherein a second model is determined from the first model by replacing the machine learning system with an algebraic expression determined by symbolic regression of the learning system, and wherein the virtual sensor is provided in such a way that it determines the operating variable depending on the state variable using the second model. This has the advantage of improving the extrapolation capability. In addition, the algebraic expression has a lower complexity than the machine learning system. This reduction in complexity leads to a more resource-efficient virtual sensor. In some developments, it is provided that the first model also comprises a physical model and in particular as a link, for example a sum or a product,consisting of a physical model and a machine learning system. This allows a priori knowledge of the desired behavior to be incorporated, which can lead to a more robust and extrapolation-capable virtual sensor. R. 408520 In further developments of this aspect, it can be checked whether the algebraic expression corresponds to a neutral element of the connection, and the virtual sensor is provided depending on whether the algebraic expression corresponds to the neutral element or not. This makes it particularly easy to check whether the a priori modeling of the physical model is correct. It can then be provided that the virtual sensor is only provided if the algebraic expression corresponds to the neutral element. This ensures in a particularly simple way that the provided sensor corresponds to the correct a priori model. Advantageously, in these aspects,that the first model and / or the second model describe the evolution of the state variable as a neural differential equation. Such neural differential equations are known, for example, from Chen et al., Neural Ordinary Differential Equations, 2019, https: / / arxiv.org / pdf / 1806.07366.pdf. These are particularly well suited for modeling dynamic systems and thus for virtual sensors, as they exhibit high model accuracy and robustness. The state variable can then advantageously be determined by integrating the neural differential equation. In an exemplary concrete application, the technical system is an electrical energy storage device, in particular a battery.and the state variable characterizes in particular an aging state of the electrical energy storage device. In a further exemplary application, the technical system is an electrical machine and the state variable characterizes in particular a temperature of a rotor of the electrical machine. In a further aspect, the invention relates to a virtual sensor which is configured to determine the state variable characterizing the state of the technical system as a function of an operating variable profile of the technical system determined by a measurement on a technical system, in particular as a function of a measurement on a technical system, which was provided using one of the aforementioned methods. In a further aspect, the invention relates to a method for operating this virtual sensor, in which the operating variable profile of the technical system is determined, in particular measured,and the state variable characterizing the state of the technical system is determined. Embodiments of the invention are explained in more detail below with reference to the accompanying drawings. In the drawings: Figure 1 schematically shows an exemplary first application of a virtual sensor; Figure 2 schematically shows an exemplary second application of a virtual sensor; Figure 3 shows a flowchart of an embodiment of the method for providing a virtual sensor, with subsequent optional operation of the virtual sensor; Figure 4 schematically shows a device for carrying out the method for providing the virtual sensor. Figure 1 shows a motor vehicle (100) with a sensor (110), which in the exemplary embodiment is connected to an electrical energy storage device (200), in particular a battery, which can comprise at least one battery cell, or a fuel cell.measures the applied voltage. This electrical energy storage device (200) can, for example, be used to supply a drive unit (130) of the motor vehicle (100) with energy. A measured value from the sensor (110) is transmitted to a computer (120), which, using the virtual sensor provided with the R. 408520 method illustrated in Figure 3, determines a variable therefrom, which in some embodiments determines a state of health (SOH) of the electrical energy storage device (200). Depending on this determined state of health, it is possible for the drive unit (130) to be controlled accordingly. In some embodiments, it can be provided that the computer (120) is located in the motor vehicle (100). In alternative embodiments, it can be provided that the computer (120) is located outside the motor vehicle (100). For example, it is possiblethat the drive unit (130) is controlled with an optimal operating strategy. Alternatively or additionally, it is possible that maintenance measures on the electrical energy storage device (200) are displayed predictively depending on the predicted aging state. In other embodiments, in which the electrical energy storage device (200) is provided by a battery, it is possible that a charging strategy for the battery is controlled optimally. Figure 2 illustrates further embodiments for the application of virtual sensors. A motor vehicle (100) with a sensor (111) which, in the exemplary embodiment, measures a voltage applied to an electrical machine (300), in particular a generator or an electric motor, in particular a voltage,which is applied to a winding of a stator or to a winding of a rotor (310) of the electric machine (300). This electric machine (300) can, for example, be part of the drive unit (130) shown in Figure 1 and can receive energy from the electrical energy storage device (200) also shown in Figure 1. A measured value from the sensor (111) is transmitted to the computer (120), which, using the virtual sensor provided by the method illustrated in Figure 3, determines therefrom a variable that characterizes a temperature in a rotor (310) of the electric machine (300). Depending on this determined temperature, it is possible for an actuator (135) of the R. 408520 motor vehicle (100) to be controlled accordingly. In some embodiments, it can be provided that the computer (120) is located in the motor vehicle (100). In alternative embodiments, it can be providedthat the computer (120) is located outside the motor vehicle (100). In some embodiments, it is possible for a cooling strategy of the electric machine (300) to be adapted depending on the determined temperature. Figure 3 describes in a flowchart the sequence of embodiments for providing and subsequently operating virtual sensors. First, the virtual sensor is provided. For this purpose, training data, provided (1000). These comprise a temporal profile of an operating variable (u) of a technical system, and an associated state variable (x) characterizing a state of the technical system. In the embodiments illustrated in Figure 1 and Figure 2, the operating variable (u) corresponds to the variable determined by the sensor (110, 111). These associated values ​​from profiles of the operating variable (u) and state variable (x) can, for example, have been determined on test benches. Then, a first model (ℎ^ ) is provided (1100), which in some embodiments has the following form: This first model (ℎ ^ ) comprises, in some embodiments, a physical model (f), e.g., a 1- or 2-node model (e.g., rotor temperature model) or an electrochemical battery cell model. This physical model (f) R. 408520 determines an approximation of the state vector x depending on the operating variable (u) (for the battery illustrated in Figure 1, this can, for example, be curves of the operating variable (u) during cycles using requested currents for charging or discharging the battery). The physical model is parameterized with parameters ^. The first model (ℎ ^) further comprises a machine learning system (g), for example an artificial neural network or a Gaussian process. The machine learning system (g) describes the data-based part of the modeling, which serves to improve the purely physical modeling. The machine learning system is parameterized with parameters ϕ. The physical model (^) and the machine learning system (^) are thus linked by an addition. In some embodiments, the physical model (^) and the machine learning system (^) are linked by a multiplication, and the first model (ℎ ^ ) has the following form: ℎ ^ (^(^), ^(^), ^, ^, ^) = ^(^(^), ^(^), ^, ^) ⋅ ^(^(^), ^(^), ^, ^) (B) In some embodiments, physical model (^) and machine learning system (^) are linked by an exponentiation, and the first model (ℎ ^ ) has the following form: In some embodiments, the first model (ℎ ^) completely given by the machine learning system: ℎ ^ ( ^ ( ^ ) , ^ ( ^ ) , ^, ^, ^ ) = ^ ( ^ ( ^ ) , ^ ( ^ ) , ^, ^ ) (D) R. 408520 This first model (ℎ ^ ) is calculated using the training data^ ( ^ ) Now in some embodiments trained as a neural differential equation system in a known manner, ie according to the equation In some embodiments, the state variable (x) describes a state vector and includes physically measurable or interpretable variables such as the temperature of the rotor (310) of the electric machine (300) or characterizes a thickness of an SEI or a quantity of cyclable lithium in the battery (200). A symbolic regression (1200) of the trained machine learning system (^) is then performed, and thus an algebraic expression (^ ^) is obtained, which is determined from a predeterminable number of predeterminable function blocks with predeterminable links in order to best represent the input-output behavior of the machine learning system (^). The data required to perform the symbolic regression can, for example, be easily generated in large numbers by providing data such as the training data ^ and feeding it to the machine learning system (^), and the associated output variable of the machine learning system (^) is then determined with little effort. In some of the embodiments in which the first model (ℎ ^ ) is given by a combination of physical model (^) and machine learning system (^) (compare equations (A), (B) and (C) above), it is now checked (1250) whether the algebraic expression (^ ^) corresponds to the neutral element of the operation; that is, a "0" in the case of an addition, a "1" in the case of a multiplication, a "1" in the case of an exponentiation, etc. If this is not the case, the provision of the virtual sensor is aborted (1251), otherwise step (1300) follows. R. 408520 In this, a second model ℎ ^ ( ^ ( ^ ) , ^ ( ^ ) , ^, ^, ^ ) provided which is derived from the first model (ℎ ^ ) by substituting the machine learning system (^) for the algebraic expression (^ ^ ). In some embodiments, it is possible for the resulting expression to be further simplified, for example, by using a link to the algebraic expression (^ ^) is omitted if it is equal to or approximately equal to the neutral element within specified tolerances. Now the virtual sensor is comprehensively the second model (ℎ ^) is provided (1400). The virtual sensor is configured to feed a curve of the operating variable (u) supplied to it to the second model and to determine the curve of the state variable (x) by integration (in some embodiments numerical integration) of equation (2) and to provide it at its output. This ends the method for providing the virtual sensor. Subsequently, in some embodiments, it can be provided that the virtual sensor (1500) is now operated, for example as illustrated in the embodiments in Figures 1 and 2. Figure 4 illustrates a training device (400) which is configured to carry out the method shown in Figure 3 (with the exception of the optional step 1500).In some embodiments, the method is embodied as a computer program stored on a computer-readable storage medium (420) and containing instructions that cause a computer (410) of the training device (400) to execute the method when the computer (410) plays the computer program.

Claims

R. 408520 Claims 1. Method for providing a virtual sensor which is set up to determine a state variable (x) characterising a state of the technical system as a function of a determined operating variable profile (u) of a technical system (200, 300), wherein training data (D) are provided which comprise empirically (i.e. in particular as a function of measurements) determined pairs of temporal profiles of the operating variable (u(t)) and associated profiles of the state variable (x(t)), wherein as a function of these training data (D) a first model (ℎ ^ ) is determined, which characterizes an evolution of the state variable (x(t)) depending on the operating variable (u(t)) (and the state variable (x(t))), where the first model (ℎ ^ ) comprises a machine learning system (g), wherein a second model (ℎ ^ ) from the first model (ℎ ^), is determined by substituting the machine learning system (g) for an algebraic expression (^ ^ ), and wherein the virtual sensor is provided in such a way that it can be replaced by the second model (ℎ ^ ) determines the operating variable (x) as a function of the state variable (u).

2. Method according to claim 1, wherein the first model (ℎ ^ ) also comprises a physical model (^), and in particular as a combination, for example a sum or a product, of the physical model (^) and the machine learning system (^).

3. The method according to claim 2, wherein it is checked whether the algebraic expression (^ ^ ) corresponds to a neutral element of the link, and the virtual sensor is provided depending on whether the algebraic expression (^ ^ ) corresponds to the neutral element or not. R. 408520 4. The method according to claim 3, wherein the virtual sensor is provided only if the algebraic expression (^ ^ ) corresponds to the neutral element.

5. Method according to one of the preceding claims, wherein the first model (ℎ ^ ) and / or the second model (ℎ ^) describe the evolution of the state variable (x(t)) as a neural differential equation.

6. The method according to one of the preceding claims, wherein the technical system is an electrical energy storage device (200), in particular a battery, and the state variable (x(t)) characterizes in particular an aging state (SOH) of the electrical energy storage device (200).

7. The method according to one of claims 1 to 6, wherein the technical system is an electrical machine (300) and the state variable (x(t)) characterizes a temperature of a rotor (310) of the electrical machine (300).

8. A virtual sensor which is configured to determine the state variable (x) characterizing the state of the technical system (200, 300) as a function of an operating variable profile (u) of the technical system, which was provided with the method according to one of claims 1 to 6.A method for operating the virtual sensor according to claim 8, wherein the operating variable profile (u) of the technical system (200, 300) is determined, in particular measured, and the state variable (x) characterizing the state of the technical system (200, 300) is determined.

10. A computer program configured to contain instructions that cause a computer to execute the method according to one of claims 1 to 7 or 9 when the computer (410) executes the computer program. R. 408520 11. Machine-readable storage medium (420) on which the computer program according to claim 10 is stored.

12. Training device (400) comprising a computer (410) which is configured to carry out the method according to one of claims 1 to 7.

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