Method for predictive diagnosis of a device battery of a technical device using hybrid differential equations

Abstract

The invention relates to a computer-implemented method for detecting an anomaly of an electrical device battery (41) having at least one electrochemical unit, in particular a battery cell (45), in a technical device (4) using a data-based battery model (10) for determining internal electrochemical battery states (x), comprising the following steps: - Providing temporal operating variables of the device battery’s operating variables; - Determining the internal electrochemical battery states using the data-based battery model depending on the recorded temporal operating variable profiles of the operating variables of the device battery, wherein the data-based battery model (10) is designed with a hybrid differential equation system in order to model the internal electrochemical battery states (x) of the device battery (41) and / or their temporal gradients depending on the operating variable profiles (F(t)), wherein at least one of the differential equations (11) of the differential equation system has a sum of a deterministic model term (f1, f2, f3, f4, f5, f6) and a data-based correction term (g1, g2, g3, g4, g5, g6) which is formed by a sparse Gaussian process model; - Determining probability distributions of the determined internal electrochemical battery states (x) using a Monte Carlo approach; - Determining an anomaly of the device battery (41) depending on a predetermined interface (G) of the internal battery states and their probability distributions, wherein the interface (G) separates areas of anomalous and normal battery states in a data space of battery state vectors (x) from the determined internal electrochemical battery states (x).

Description

Technical FieldThe invention relates to methods for diagnosing device batteries for technical devices, in particular to methods for predictively diagnosing device batteries by abnormality detection.Background ArtThe power supply of electric devices and machines operated independently of the grid, such as electrically drivable motor vehicles, is generally effected using device batteries or vehicle batteries. These supply electrical energy for operating the devices.Device batteries degrade over their service life and depending on their load or use. This so-called aging leads to a continuously decreasing maximum power or storage capacity. The aging state corresponds to a measure for indicating the aging of device batteries. By convention, a new device battery may have a 100% state of aging (in terms of its capacity, SOH-C) that decreases markedly over its lifetime. A degree of deterioration of the device battery (change of the state of deterioration with time) depends on an individual load of the device battery, i.e., in vehicle batteries of automobiles, the driver's use behavior, external environmental conditions, and the vehicle battery type.In order to monitor device batteries from a plurality of devices for anomalies, operating variable data are generally continuously recorded and transmitted as operating variable profiles continuously or in blocks to a central unit external to the device. For evaluating the operating variable data, in particular in physical or electrochemical battery models, which can be based on differential equations, for example, the operating variable data can be sampled as curves with a comparatively high temporal resolution (sampling rates) of between 1 and 100 Hz, for example, and a battery state can be determined therefrom using a time integration method.For evaluating the operating variable data, in particular for ascertaining battery states which determine the state of aging, an electrochemical battery model can be used which is based on a differential equation system having a plurality of nonlinear differential equations. The operating variable data enables modeling of a current battery state using a time integration method. Electrochemical battery models of this type are known, for example, from the publications U.S. Pat. No. 2016 / 023,566, U.S. Pat. No. 2016 / 023,567 and U.S. Pat. No. 2020 / 150,185.The provision of the operating variable profiles in the central unit enables the use and adaptation of the electrochemical battery model for a multiplicity of device batteries with similar battery cells or with cells of similar cell chemistry. The calculation of the battery states with the aid of the differential equation system is computationally expensive, so that the capacity for computing in internal computing devices can be reduced by the removal from the central unit.In battery-operated technical devices, the proper functioning of the device battery used must regularly be monitored for faults for safety reasons, in particular at high energy densities. If a battery cell, a unit comprising a plurality of battery cells or the entire device battery fails, the technical device can become inoperative depending on the fault which has occurred and, if appropriate, the safety of the technical device and of the user can also be impaired in the event of malfunctions which lead to a strong temperature increase.On the basis of the usual rule-based abnormality detection, however, until now, errors in device batteries are only detected when applied error threshold values for operating variables such as the cell voltage, a module temperature, a current value or a state of charge value and an aging state value are exceeded or undershot.DE 10 2019 208 372 A1 discloses a computer-implemented method for detecting an abnormality in a technical system, comprising the following steps: detecting an operating variable vector which indicates an operating state of the technical system and comprises a number of operating state variables, wherein the operating state variables comprise at least one environmental state variable which indicates an environmental condition in which the technical system is operated and system state variables indicate internal system states of the technical system; providing an environment state model and an anomaly detection model, wherein the environment state model indicates a verification of the operating variable vector with respect to the presence of an anomaly using the anomaly detection model as a function of at least one of the environment state variables, and wherein the anomaly detection model indicates the presence of an anomaly to be expected as a function of the operating variable vector, signaling a presence of an anomaly or a non-anomaly as a function of an assessment of the at least one environment state variable of the operating variable vector as a function of the environment state model and as a function of an assessment of the operating variable vector as a function of the anomaly detection model.Disclosure of the InventionAccording to the invention, a method for detecting an abnormality of an electrical appliance battery and for diagnosing an appliance battery of a technical appliance having one or more battery cells according to Claim 1, and a device and a battery system according to the subordinate claims are provided.Further embodiments are given in the dependent claims.According to a first aspect, a computer-implemented method for detecting an abnormality of an electrical device battery having at least one electrochemical unit, in particular a battery cell, is provided in a technical device with the aid of a data-based battery model for determining internal electrochemical battery states, having the following steps:providing temporal operating variable characteristics of operating variables of the device battery;determining the internal electrochemical battery states with the aid of the data-based battery model as a function of the detected temporal operating variable characteristics of the operating variables of the device battery, wherein the data-based battery model is configured with a hybrid differential equation system in order to model the internal electrochemical battery states of the device battery and / or their temporal gradients as a function of the operating variable characteristics, wherein at least one of the differential equations of the differential equation system has a sum of a deterministic model term and a data-based correction term formed by a sparse (sparse) Gaussian process model,determining probability distributions of the determined internal electrochemical battery states, in particular with the aid of a Monte Carlo simulation;determining an anomaly of the device battery depending on a predefined multidimensional boundary surface of the internal battery states and their probability distributions, wherein the boundary surface separates regions of anomalous and normal battery states in a point space of internal electrochemical battery states.Conventional device batteries are generally constructed with a multiplicity of electrochemical battery cells and these change over the course of the operating period, which is evident from the outside only by reduced performance. However, the performance of the device battery is critically determined by internal battery conditions that are not readily determinable from the outside. These battery states are generally determined on the basis of models on the basis of operating variables.For the model-based determination of battery states, for example, an electrochemical battery model can be used which is based on a differential equation system which models the internal operating states, in particular equilibrium states and possibly kinetic states, with the aid of a time integration method on the basis of differential equations parameterized via model parameters. Such electrochemical battery models are known, for example, from the publications U.S. Pat. Nos. 2016 / 023,566, 2016 / 023,567 and U.S. Pat. No. 2020 / 150,185.The model parameters of such an electrochemical battery model are adapted by evaluating operating variable characteristics, i.e. time series of operating variables of the device battery, such as a battery current, a battery voltage, a battery temperature and a state of charge.The model parameters of the battery model are usually determined by chamfering, for example using a least-square method. This parameterization of the battery model can lead to inaccurate determination of the internal battery states during the evaluation of operating variable characteristics, since the model parameters are generally constant over all battery states.In order to compensate for the remaining error in the modeling of the internal battery states, data-based correction models are generally provided, which are trained on the residue and which are additively combined with the differential equations.Such a combination with a data-based correction model has the disadvantage that the data-based correction model only compensates modeling errors of the electrochemical battery model, but does not allow any influence on the calculation of the internal battery states based on the electrochemical battery model. By means of the correction with the aid of the correction model, which determines a separate correction variable for each of the battery states, implausible combinations of battery states can arise, which are technically impossible or do not occur. Furthermore, these implausible combinations may not be properly associated with a fault of a device battery when used for abnormality detection. Often, these implausible combinations of battery states result in the detection of false positives if not yet sufficient training data has been incorporated into the model parameterization.The above method therefore provides for providing a battery model in order to map an electrochemical battery model based on differential equations in an improved manner. The data-based battery model is based on hybrid differential equations, so that the time-variant differential equations of the electrochemical battery model, which are based on models of the internal battery state, are provided as hybrid differential equations. Hybrid differential equations correspond to differential equations in which the right-hand term is supplemented by a data-based correction term, i.e. in which the right-hand term has an additional variable portion which is operation variable and time-dependent.The hybrid differential equation can take the form in which the model term f(α, x, F, t) embodies the electrochemical battery model with respect to an internal system state x and values of the operating variables F that are valid at the time t and is parameterized with the parameter vector α on the basis of expert knowledge. Here, the state vector x may comprise, for example, equilibrium or kinetic parameters, and in particular one or more of the following electrochemical state variables as internal battery states or parameters:- amount of cyclable lithium,volume fraction of anode,volume fraction of cathode,reaction rate or reaction coefficient with respect to anode,diffusion coefficient of the anode,layer thickness with respect to anode,reaction rate or reaction coefficient with respect to cathode,diffusion coefficient of the cathode,porosities in anode,porosities in the cathode,Bruggeman coefficients in anode,Bruggeman coefficients in cathode,electrolyte concentration,contact resistors,mechanical particle loading.Further parameters for electrochemical or physical modeling can also be included. The battery model can be designed in particular as a performance model and can comprise equilibrium parameters and / or kinetic parameters which can describe electrochemical states. The parameters of the battery model are parameterized in such a way that the model quality is maximized. It is important that the data meet specific requirements: for the determination of the equilibrium parameters, the use of operating variable characteristics of a sufficient number of resting phases is important, and for the determination of kinetic parameters, the use of operating variable characteristics with sufficient load dynamics of the battery is important.In contrast to conventional electrochemical battery models, a data-based correction term is provided that allows adjustments to be made in the hybrid differential equation system and taken into account in integrating the differential equation.g(β, x, F, t) corresponds to a data-based correction model as a model component. The data-based correction model can basically be designed as a Gaussian process model. However, very large amounts of training data can be provided for large amounts of data, which can only be used with very great computational effort for the training of the conventional Gaussian process model, because the complexity in training the Gaussian process is cubic.Therefore, provision is made for g(β, x, F, t) to be designed as a sparse or sparse Gaussian process model, wherein β corresponds to a model parameter vector of the data-based correction term. The sparse or sparsely populated Gaussian process model is based on augmentation of the Gaussian process model with a reduced number of interpolation points. The model parameter vector includes model parameters and hyperparameters of the underlying data-based correction model. The model term f(α, x, F, t) includes electrochemical action chains modeled from non-linear state equations.Thus, the expansion of the electrochemical battery model into a hybrid differential equation is effected by supplementing a part or each of the differential equations of the differential equation system with the data-based correction term, which is determined as a sparse Gaussian process model and which depends on the model parameter vector β and the internal state variables, i.e. the internal battery states, and furthermore also on the operating variable characteristics.The differential terms of the left side of the differential equations define the changes in the internal battery states of the device battery.For modeling battery states using the hybrid differential equation system, operating variable profiles of the operating variables are evaluated, which must be present in the form of high-resolution time series. The calculation of such a hybrid, data-based battery model is complicated and, because of limited computing capacities, generally cannot be carried out with the control device of the technical device. In this regard, it can be provided to carry out the evaluation of the data-based battery model in a central unit which is in communication connection with the technical device.In contrast to conventional physical battery models, which are more precisely or corrected by a suitable data-based correction model learned on the residues, the data-based correction term in the above approach for a hybrid differential equation system accesses deeper in the battery model and is carried along in the integration of the differential equation, which is not possible in conventional data-based battery models.The data-based correction model is designed as a sparse Gaussian process model, wherein the training is carried out with the aid of a gradient-based method by maximizing a lower bound of the log likelihood and thus allowing a probabilistic modeling to be taken into account.A probabilistic generative model is thus used to transform time-series data into a latent state space. To do this, a GP prioris placed over each correction term, i.e., g(β, x, F, t) ~ GP(0, k((β, x, F, t), (β, x, F, t)). The kernel function k is usually determined by two ways. Firstly, a universal kernel function k is used (such as the squared exponential kernel), which is capable of realizing each correction term with a sufficiently large model size and data. On the other hand, the initial parameterization of the kernel function can still be scaled with respect to plausible expectable effects.During training, a sparse approximation to the posterior Gaussian process is learned. The Gaussian process posterior corresponds to a probability distribution over the function g(β, x, F, t) and each train from the Gaussian process posterior corresponds to a realization of the function g(β, x, F, t). In order to obtain probabilistic prediction, a plurality of functions are extracted from the posterior and the relevant distribution is determined via the state vector x(t).During training, the Gaussian process is iteratively learned. For each training iteration, in particular a subset of the complete training dataset can be used.The state vector x(t) can now be evaluated in each dimension with respect to confidence, so that a probability density function can be assigned to each state.Training data sets are used for training the hybrid differential equation, which assign operating variable characteristics, starting from a known internal state of the device battery, e.g. during its startup, to an aging state reached after an operating time.With the aid of the training data sets, the parameter vector α can be parameterized together with the physical parameters α and the model parameters of the model parameter vector β in the training process.Training the data-based state of health model may be performed byparameters of the model term and model parameters of the data-based correction model can be simultaneously optimized using a gradient-based optimization method, orwherein in a first step parameters of the model term are adapted and in a second step model parameters of the sparse Gaussian process model of the at least one differential equation are trained with fixed parameters of the model term.Thus, the training method can provide for a simultaneous training of the parameters α and β. Alternatively, the training method can also be carried out in two steps, according to which the parameter vector α is initially parameterized with the physical parameters α on the basis of a set of training data sets and the physical parameters α are subsequently fixed and only the model parameter vector β of the sparse Gaussian process model is trained with the same or a further training set of training data.For reliable anomaly detection based on battery states, knowledge about the probability distribution of the modeled internal battery states is necessary. This makes it possible to evaluate the totality of the battery states for each dimension with respect to their confidence, i.e. a probability density function is assigned to each battery state.The probability density function is determined using a Monte Carlo simulation.In order to obtain quantified model uncertainties of the modeled internal battery states, which make it possible to evaluate the reliability of the model predictions, different methods for determining a probability distribution can fundamentally be used.The probability density function is estimated with the aid of the Gaussian process model, since Gaussian process models are particularly suitable for learning calibrated uncertainties. This property is especially important for anomaly detection.In the following, a state space analysis of the electrochemical inner battery states is carried out in which at least one dimension of the battery state vector x(t) is evaluated and a comparison with a plurality of device batteries takes place using the data of the plurality of technical devices. In particular, the entire battery state vector can be evaluated. When evaluating a plurality of dimensions, i.e. a plurality of battery states, this dimensional manner can be carried out and it can be required that a certain number of dimensions is recognized as normal, or alternatively that all dimensions are jointly recognized as normal.Using a limit model, an interface in the state space of the modeled internal battery states (n-1 dimensional interface in the n-dimensional state space with n battery state variables) can be defined, by means of which it can be differentiated whether the combination, i.e. a battery state vector formed from the internal battery states, is normal (fault-free) or abnormal. This boundary surface can be designed in particular simulatively, i.e. for example on the basis of validated fault modes to which a prediction model has been calibrated. The advantage here is that the boundary surface thus has a higher ability to be elucidated or interpreted.The limit model can be created, for example, on the basis of data records which each assign a label to the modeled battery states which are ascertained from operating variable characteristics using the trained data-based battery model described above, said label indicating the occurrence of a fault or an anomaly or a loss of performance within a past time duration of, for example, in the past six months. For example, if a fault occurs, the battery conditions may be considered abnormal within the past time period before the fault occurs.It may be provided that the interface is determined by a clustering method of battery state vectors in which a cluster of battery state vectors of a plurality of normal device batteries of technical devices that had no fault within the period of time is formed, wherein the interface may be defined by a predefined distance from a centroid of a "normal" cluster that contains normal battery state vectors for functional device batteries, wherein the predefined distance is selected such that the interface surrounds a region of the data space that contains a predefined proportion of all battery state vectors of the normal device batteries.The limit model thus defines an interface that separates regions of normal battery state vectors (for fault-free device batteries) from regions of abnormal battery state vectors (for abnormal device batteries). The limit model can generally be designed as a data-based model that defines the n-1 dimensional boundary surface (limit curve at n=2) in an n-dimensional battery state space depending on the training datasets at least for normal (fault-free, anomaly-free or performance-loss-free) device batteries.When a clustering method such as k-means clustering is used, the boundary surface for distinguishing between normal and abnormal device batteries may be determined based on the centroid of the normal cluster.The boundary surface can be determined unuputrified (e.g. cluster method, Gaussian mixture models, isolation forest, autoencoder, variational autoencoder or Ausubstantial detections) on the basis of laboratory measurements and / or states which were measured out in the normal state within the specification and subsequently validated for normality e.g. via plausibility checks, in particular:based on validated labels, wherein only simulated states are used, andbased on opened cells, wherein internal states (such as SEI thickness, cyclable lithium, etc.) are detected by measurement technology. Additionally or alternatively, equilibrium parameters or kinetic parameters of an electrochemical battery model can be included here or derived on the basis of these, e.g. via a parameter estimate, wherein the at least one internal electrochemical state is subsequently updated.The functionality of a device battery is now evaluated on the basis of the battery states modeled with the aid of the above battery model and the associated probability density functions. The battery states define a battery state vector. For this purpose, a position of the battery state vector with respect to the n-1 dimensional boundary surface and the distance between the battery state vector and the boundary surface are determined. The distance measure may be calculated as Mahalanobis distance, or alternatively as Euclidean distance (in normalized battery state space or taking length scales into account, if not normalized).Furthermore, a confidence range for the battery state vector can be determined by integration depending on the probability density distributions, wherein the confidence range is determined depending on a predefined quantile value, wherein an anomaly is detected if the battery state vector is located outside a "normal" cluster which contains normal battery state vectors for functional device batteries or the confidence range intersects the boundary surface.A functional device battery is present if the battery state vector is in the range of the normal battery state vectors and a predefined confidence interval (e.g. indicated by a specific quantile value of, for example, 95% with respect to the probability distributions) does not have an intersection point with the boundary surface.An anomaly may be determined if the battery state vector is in the range of the anomalous battery state vectors and a predefined confidence interval (e.g. indicated by a specific quantile value of e.g. 95% with respect to the probability distributions) does not have an intersection point with the boundary surface.In an intermediate region, if a predetermined confidence interval (e.g., indicated by a particular quantile value of, e.g., 95% relative to the probability distributions) has an intersection with the boundary surface, a potential anomaly is detected.The confidence interval of a battery state vector may be determined by presetting a quantile value by integration over a multi-dimensional probability density function.It can be provided that after a fault has been detected, a fault type and / or a criticality of the fault is detected depending on at least one predefined rule, wherein a warning is signaled depending on the fault type and / or the criticality of the fault.If an anomaly or a potential anomaly is detected, it can be detected with the aid of a rule-based check whether or not the detected device battery has a critical fault. In the event of a critical fault, a corresponding warning to the user of the technical device or a planning of a workshop stay can be provided for the diagnosis or predictive maintenance of the device battery.In the case of a potential anomaly, for example, a measure for preferred maintenance can be derived or a function in the digital twin can be modified: for example, the execution frequency of the anomaly evaluation can be increased, that is to say, for example, doubled, in order to be able to directly ascertain possible changes in a more critical range or deteriorating states, in order to be able to intervene directly as a result thereof.The rule-based check can comprise, for example, carrying out a comparison of ageing states of the device battery estimated to be abnormal with other device batteries having similar operating state vectors. If the aging state of the device battery found to be abnormal is inferior to that of the other similar device batteries, the abnormality can be judged to be critical. The state of aging can be determined in a manner known per se by evaluating operating variable characteristics of the relevant device battery with the aid of a suitable state of aging model or determination methodIn particular, the fault type and / or the criticality of the fault can be detected depending on the result of a threshold comparison of a battery temperature, a state of charge loss with a high temporal gradient, and an extreme value of the incremental capacity dQ / dU.The above method makes it possible to quickly ascertain a deviation of the data-based battery model from real battery states by uncertainty quantification, in order either to improve the model or to detect an abnormality of the device battery.It can be provided that the device battery is used for operating a device, such as a motor vehicle, a pedelec, an aircraft, in particular a drone, a machine tool, a device of entertainment electronics, such as a mobile telephone, an autonomous robot and / or a household appliance.Furthermore, the method can be carried out in a central unit external to the device, wherein the temporal operating variable profiles are determined in the technical device and transmitted to the central unit external to the device.Brief Description of the DrawingsEmbodiments are explained in more detail below with reference to the attached drawings. The following are shown: FIG. 1 shows a schematic illustration of a system for providing driver- and vehicle-specific operating variables for determining battery states of a vehicle battery in a central unit for abnormality detection; FIG. 2 is a schematic illustration of a functional configuration of a hybrid data-based battery model; and FIG. 3 is a diagram illustrating a data space of battery state vectors for illustrating detection of abnormality of a vehicle battery.DESCRIPTION OF EMBODIMENTSThe method according to the invention is described below with reference to vehicle batteries as device batteries in a multiplicity of motor vehicles as similar devices. In the motor vehicles, a data-based battery model for the respective vehicle battery can be implemented in a control unit. The battery model can be continuously updated or retrained from the fleet of vehicles in a central unit external to the vehicle, as described below, based on operating variables of the vehicle batteries. The battery model is operated in the central unit and used for determining internal battery states.The above example represents a multiplicity of stationary or mobile devices with a network-independent energy supply, such as vehicles (electric vehicles, pedelecs, etc.), systems, machine tools, household appliances, IOT devices and the like, which are connected to a central unit (cloud) external to the device via a corresponding communication connection (e.g. LAN, Internet).FIG. 1 shows a system 1 for collecting fleet data in a central unit 2 for creating and operating and for evaluating a battery model. The battery model is designed as a hybrid differential equation system and is used to determine internal battery states of a vehicle battery in a motor vehicle. FIG. 1 shows a vehicle fleet 3 with a plurality of motor vehicles 4.One of the motor vehicles 4 is illustrated in more detail in FIG. 1. The motor vehicles 4 each have a vehicle battery 41, an electric drive motor 42 and a control unit 43. The control unit 43 is connected to a communication module 44, which is suitable for transmitting data between the respective motor vehicle 4 and a central unit 2 (a so-called cloud).The motor vehicles 4 transmit to the central unit 2 the operating variables F which indicate at least variables which influence the internal battery states of the vehicle battery 41 or depend thereon. The operating variables F can comprise time series of a battery current, a battery voltage, a battery temperature and a state of charge (SOC) in the case of a vehicle battery 41 both at the pack, module and / or cell level. The operating variables F are recorded in a fast time pattern from 1 Hz to 100 Hz and can be transmitted regularly to the central unit 2 in uncompressed and / or compressed form.Furthermore, the time series can be transmitted block by block to the central unit 2 using compression algorithms to minimize the data traffic to the central unit 2 at a distance of several hours up to several days.The central unit 2 comprises a data processing unit 21 in which the method described below can be carried out and a database 22 for storing data points, model parameters, states and the like.In the central unit 2, a battery model is implemented, which is implemented as a hybrid differential equation system. The hybrid data-based battery model can be used to determine a determination of internal battery states as a battery state vector of the relevant vehicle battery 41 on the basis of the time curves of the operating variables.As for the time series, compression algorithms can be used for the transmission in order to minimize the data traffic to the central unit 2. Furthermore, an event-based transmission can take place, so that the data transfer is triggered and takes place, for example, when a stable or known WLAN network connection has been identified.FIG. 2 shows a schematic illustration of the functional structure of the hybrid differential equation system 10, wherein this is solved at each time step with the provided operating variables F(t) and subsequently evaluated in order to signal an error.The differential equation system 10 realizes a plurality of differential equations dependent on each other and includes a model block 11 for providing the right-hand side model terms for each of the differential equations. The model terms correspond to the physical model equations [f1(α, x, F, t), f2(α, x, F, t), f3(α, x, F, t),... which embody the electrochemical battery model with respect to an internal battery state x and values of the operating variables that apply at the time t and are parameterized with the parameter vector α on the basis of expert knowledge.The parameter vector α of the model parameters of the electrochemical model is parameterized by fitting the model to operating variable profiles and represent, for example, geometric parameters, dimensioning, design and / or design parameters of the battery and electrochemical variables which characterize materials and their electrochemical properties.Furthermore, a correction block 12 is provided, which provides a data-based correction term g(β, x, F, t) in the form of a sparse Gaussian process model. In each time step, the result of the model block and the correction block 12 is added in a summing block 13. The result represents the rate of change ẋ t of the state vector x t. The rate of change is integrated by means of a numerical algorithm in an integration block 14 which provides the updated state. Furthermore, a model uncertainty can be provided on the basis of the sparse Gaussian process model.The internal battery states x can comprise, for a device battery, inter alia the following state variables: SEI layer thickness x SEI, amount of cyclable lithium x cLi, amount of cyclable solvent x csol1,2, amount of cathode material x Li, loss of active material x AML-, and amount of active material x AML+.In the exemplary case of these six internal state variables, the differential equation system has the following structure, wherein the functions g1 to g6 each correspond to a sparse Gaussian process modelThe resulting state vector x(t) can now be evaluated in a probability block 15 and a subsequent anomaly detection block 17 in order to detect an anomaly A.Furthermore, a fault detection model 16 is provided which, when an anomaly A is detected on the basis of heuristic rules which evaluate the battery states, can detect and signal a fault type and / or a criticality of the fault.Training data sets are specified for training the hybrid differential equation system, these training data sets associating operating variable characteristics, starting from a known internal battery state of the vehicle battery, for example during its startup, in each case with a battery state vector reached after an operating time. The internal battery states of the training data sets can result, for example, as the model parameters of an electrochemical physical aging model, which result from starting based on operating variable characteristics and measured aging states of the vehicle battery. Training can be performed with the lower bound of the log likelihood as a target function and gradient-based methods. In this case, the model parameters of the model parameter vector β are adapted for the sparse Gaussian process model in order to minimize loss.With the aid of the training data sets, the parameter vector α can be parameterized together with the physical parameters α and the model parameters of the model parameter vector β in the training process.Training of the battery model 10 may be performed byparameters α of the model term f and model parameters β of the sparse Gaussian process model g can be optimized simultaneously using a gradient-based optimization method, orby adapting parameters α of the model term f in a first step and training model parameters β of the sparse Gaussian process model g of the at least one differential equation with fixed parameters α of the model term f in a second step.The training can be carried out on the basis of a differentiable quality function which evaluates the probability that the parameterized sparse Gaussian process model produces a specific time series in the evaluation of the differential equation system.Thus, the training method can provide for a simultaneous training of the parameters α and β. Alternatively, the training method can also be carried out in two steps, according to which the parameter vector α is initially parameterized with the physical parameters α on the basis of a set of training data sets and the physical parameters α are subsequently fixed and only the model parameter vector β is trained with the same training set or a further training set of training data.The hybrid differential equation system of the battery model 10 can now be solved numerically for evaluating the internal battery states x(t), for example.For reliable anomaly detection based on battery states, knowledge about the probability distribution of the modeled internal battery states is necessary. This makes it possible to evaluate the totality of the battery states for each dimension with respect to their confidence, i.e. a probability density function is assigned to each battery state. The probability density function can be determined from the data-based battery model using a Monte Carlo simulation.By coupling the terms f(α, x, F, t) and g(β, x, F, t) in the equation, the time integration for solving the system states now takes place, wherein the probability density of the posterior of the sparse Gaussian process model is taken into account in order to be able to model the system modelling as accurately as possible.In a probability block 15, for each of the internal battery states, an uncertainty in the form of a probability density function can be determined based on the trained battery model 10. For this purpose, the probability block 15 is connected to the numerical integration algorithm of the integration block 14, which in turn queries the battery model 10. The probability block 15 can optionally implement a Monte Carlo approach in conjunction with the battery model 10. Assuming a Gaussian distribution for each of the battery states, the uncertainty may be given as variance.In the following, a method for estimating uncertainties of a prediction of the hybrid differential equation system will be generally described.Advantageously, the differential equation system comprises one or more differential equations in which the right side, the vector field, is parameterized by a function hθwith weights θ. θ can describe here either the totality / combination of all parameters α and β, or focus on only one part, wherein the uncertainty is usually calculated on the basis of the model parameters β of the data-based term.In our case, hθ=f(α, x, F, t)+g(β, x, F, t). In general, differential equations cannot be solved analytically. To solve differential equations, a numerical method is used, which is referred to here as ODESolve. A known numerical method is, for example, the explicit Euler method: wherein t n denotes the time of a particular output. The model is trained for predicting one or more continuous values of the variable of the technical system on a data record which comprises the relationship between values of an input variable and reference values for the variable respectively assigned to these values.Y n is an output, F n is an operation, and t n is a time point. For better readability, the training data set is limited to one time series here, but an extension to a plurality of time series is easily possible.The dynamics of the model are modeled in a latent space, since, on the one hand, the latent states are not observed directly and, on the other hand, the measurements are corrupted by noise. Therefore, the states are treated as latent variables resulting in the following generative model: wherein a standard Gaussian prior is introduced over the initial latent state x 1 and the data-based correction term g with an independent GP per output dimension.An approximate inference method is then derived that provides a high degree of accuracy and model flexibility. Since the exact posterior p(g,x 1| y 1,..., y N) is difficult to determine in nonlinear ODE models, the shape of the approximate posterior is first described (David M Lead, Alp Kucukelbir, and Jon D McAuliffe, "Variational inference: A review for statistics", Journal of the American statistical Association, 2017,9. The model parameters are then optimized.The located inference is determined for the initial values x 1 ∼ qφ(x 1| y 1:N) where φ is the parameters of a neural network encoder that outputs a diagonal covariance Gaussian distribution. For the unknown time differentials g, the standard sparse GP approximation is used, in which each output dimension d ∈[1,D] has its own independent set of interpolation nodes U d ∈R D and kernel output variances. The inputs of the interpolation nodes Z and the length scales l are divided by all output dimensions. The mean field variation posteriori is obtained: the mean values and covariances being variation parameters that are optimized during training.The following variation approximation q(x 1, g, U)=q(x 1) p(g|U)q(U) results, wherein K ZZ is the covariance matrix between all the nodes U, K XZ is the covariance between the extended inputs X≅={x n, F n, t n} and the nodes Z and K XX is the covariance between the extended inputs.The same independence assumptions are made for the approximate posterior as for the prior, resulting in a mean field solution. The interpolation nodes U acquire the buffered statistics of the training data, which allows the use of the prior p(g|U) in the approximate posterior.The approximate posterior q parameters are optimized by maximizing a lower bound on evidence: (see David M Lead, Alp Kucukelbir, and Jon D McAuliffe. Variational inference: A review for statistics. Journal of the American statistical Association, 2017) This integral can be simplified as follows: where KL denotes Kullback-Leibler divergence.The calculation of the conditional log likelihood log p(y 1:N| x 1, g, U) requires a forward sweep in time with the differential equation that can be solved with any standard ODE solver. The difficulty lies in the margining via the approximate posterior of the initial latent states q(h 1) and the approximate GP posterior q(g, U).Each individual marginalization step is already analytically inextricable per se, to be silent about its combination. It is therefore possible to perform Monte Carlo integration, i.e. the expected value E q is approximated, by randomly determining samples from q(x 1, U, g) and evaluating the log likelihood q(y 1:N| x 1, g, U) for each sample. This yields an undistorted estimate of the expected log likelihood.For Monte Carlo integration, first L random samples are extracted from the approximate post-point locations, where l denotes the sample index and g (l)( ·) is a function obtained from the sparse GP posterior. Explicitly selecting an entire function randomly from the GP posterior is not technically possible. The GP posterior can always only be evaluated at a finite number of points. This random determination of the samples from the GP posterior g (l)( ·) scales cubically with the number of data points.Since it is not known a priori at which points the ODE solver evaluates the function, points must be sampled from the posterior in chronological succession.This can still be done cubically in time by performing low rank updates of the posterior.Instead of calculating (x 1,..., x K) ~q(x 1,..., x K| U) (K is the number of steps in the ODE solve) directly, sampling is carried out sequentially:(x 1,..., x K) ~ q(x 1| U)q(x 2| U, x 1) ·...· q(x K| U,x 1,..., x K-1). The posterior q(x k| x 1,..., x k-1, U) can be determined recursively from q(x k-1| x 1,..., x k-2, U). The computation-intensive step is the calculation of the inverse, and this step can be accelerated using the Sherman-Morison formula (rank-one update). However, this approach often leads to numerical instabilities in small step sizes.To overcome this challenge, a decoupled sampling method can be used, which is proposed in James Wilson, Vacheslav Borovitskiy, Alexander Terenin, Peter Mostowsky, and Marc Deisenroth, "Efficiently sampling functions from Gaussian process posteriors", International Conference on Machine Learning, 2020, in which the sampling is first drawn from a set of random Fourier features and then updated with the aid of the Matheron rule in order to obtain samples for the posterior. After the triplet has been sampled, the trajectory can be deterministically determined by forward integration of.The Monte Carlo estimate of the log likelihood is where the log likelihood term decays between times, allowing a twice stochastic variation inference (see Michalis Titsias and Miguel Lezaro-Gredilla, "Doubly stochastic variational Bayes for non-conjugate interference", International Conference on Machine Learning, 2014.). This means that the bound is stochastic because log is calculated via Monte Carlo samples. For each training step, it is not necessary to use the entire trajectory, but it can also be based on sub-trajectories. This makes the algorithm more efficient and results in re-stochasticity (sub-trajectory selection).The prior distributions across the interpolation nodes follow the Gaussian Since, moreover, a standard Gaussian prior with suitable dimensions is assumed for the initial values, all KL terms can be calculated in closed form.Monte carlo predictions can also be made by first randomly selecting L samples from the approximate posteriors and then applying the Matheron rule to determine posterior trajectories in the latent space.This results in an empirical risk minimization task of the form wherein l is the loss function. In regression tasks, a quadratic loss function or an absolute value loss function may be used.In principle, the predictive distribution of ODESolvcan be determined over a temporal development of the model by sampling the parameters for the sparse Gaussian process model and by linearization. In this case, the linearization of ODESolv is advantageous in order to approximate the predictive distribution.Thus, a probability density function is available for each of the battery states, which makes it possible to determine a confidence range around each of the battery state vectors x given a quantile value of, for example 95%. The confidence range B may be determined by integration over the multidimensional probability density function of the battery state vectors x.This is made possible by setting a limit model in the abnormality detection block 17 that defines an interface between normal battery state vectors indicating normal, i.e., functional, vehicle batteries and abnormal battery state vectors indicating abnormal vehicle batteries. The limit model that specifies the boundary surface can be ascertained, for example, on the basis of fleet data, i.e. operating variable characteristics of a plurality of vehicle batteries. The boundary surface is defined as an n-1 dimensional area in an n-dimensional data space / point space of the battery state vectors.For this purpose, an unuputrified trained data-based limit model can be trained with training data sets that defines the interface based on normal clusters and anomaly clusters by a clustering method of battery state vectors. The training data sets comprise data sets of battery state vectors of vehicle batteries for which no anomaly, no fault and / or no failure and / or no performance loss has been determined within a predefined period of time of, for example, 6 months and to which a label "normal" is assigned and of battery state vectors of vehicle batteries which have shown an anomaly within the predefined period of time (6 months) and to which a label "anomalous" is assigned.The limit model thus defines an interface that separates regions of normal battery state vectors (for fault-free device batteries) from regions of abnormal battery state vectors (for abnormal device batteries). The limit model may generally be configured as a data-based model that defines the n-1 dimensional interface (limit curve at n=3) in an n-dimensional battery state space depending on the training datasets, at least for normal (fault-free, anomaly-free or performance-loss-free) device batteries.Also, if additional fault cases of device batteries have been detected, they can be used for validation or as a test data set in order to validate the limit model.Alternatively, a clustering method may be performed on the training datasets determined as above, which associate battery state vectors of a vehicle battery with a classification label that indicates whether the respective vehicle battery is faulty or proper. Two clusters are obtained, wherein the boundary surface between the two clusters is determined as boundary surface.This is illustrated, for example, in FIG. 3 for two exemplary battery states x 1, x 2 as illustrative. However, the battery state vector may include more than two, namely n battery states, so that the interface is determined as an n-1-dimensional interface G. FIG. 3 shows, by way of example, for a two-dimensional battery state vector for a multiplicity of vehicle batteries, battery state vectors as points together with their surrounding confidence range (surrounding circle), which results from the probability distribution determined.The interface G may be determined, for example, by a distance measure from the centroid Z of the "normal" cluster comprising the functional vehicle batteries 41, the distance measure being calculated, for example, based on the probability density functions of each of the battery states as a Mahalanobis distance or, alternatively, as a Euclidean distance.In the anomaly detection block 17, it is now possible to detect a vehicle battery 41 on the basis of its battery state vector x and the associated confidence range B, which results from the probability density function of each of the battery states, whether the vehicle battery 41 is normal, i.e. functional, potentially has an anomaly or is anomalous, i.e. has an anomalous behavior.The functional vehicle battery 41 is detected when the confidence range B of the normal battery state vector x norm does not have an intersection with the boundary surface G and the distance measure of the normal battery state vector x norm from the centroid of the "normal" cluster CN is less than the distance measure of the limit curve.A potential anomaly is detected when the predetermined confidence range of a potential anomalous battery state vector x pot has an intersection with the interface.Abnormal behavior of the vehicle battery 41 is detected when the confidence range B of the abnormal battery state vector x anom does not have an intersection with the boundary surface G, and the distance measure of the normal battery state vector x norm from the centroid of the "normal" cluster CN is larger than the distance measure of the boundary surface G.Subsequently, it can be detected in the fault detection model 16 for the vehicle batteries 41 detected as potentially abnormal and for the vehicle batteries detected as abnormal by means of a rule-based check whether the battery state is critical. For example, a critical anomaly may be detected if a comparison with a plurality of vehicle batteries is found to be less performant. For example, a state of aging for vehicle batteries having mutually similar battery state vectors may be determined on the basis of a comparable load profile, and a critical anomaly may be detected when the resulting state of aging is poorer than the average of the considered vehicle batteries 41.According to one embodiment, after detecting one or a predetermined minimum number of anomalies, a heuristic model may be applied to identify, based on rules, whether a critical fault is present, such as an imminent thermal runaway event or the like. This rule-based heuristic model can provide, for example, threshold value comparisons of cell temperatures of battery cells 45, a charge state loss with high gradients and an extreme value of the incremental capacitance dQ / dU in order to detect the type of abnormality that has occurred and to signal it with an abnormality signal S. In the case of critical anomalies, corresponding warnings can be output to the drivers of the vehicles. In addition, functions in the battery management system of the vehicle battery 41 may be activated to bring them into a safe state.References included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Patent Literature citedUS 2016 / 023,566 [0005, 0014]US 2016 / 023,567 [0005, 0014]US 2020 / 150,185 [0005, 0014]DE 10 2019 208 372 A1

[0009] Cited Non-Patent LiteratureDavid M lead, Alp Kucukelbir, and Jon D McAuliffe, "Variational inference: A review for statistics", Journal of the American statistical Association, 2017,9

[0095] David M lead, Alp Kucukelbir, and Jon D McAuliffe. Variational inference: A review for statistics. Journal of the American Statistical Association, 2017

[0099] James Wilson, Vacheslav Borovitskiy, Alexander Terenin, Peter Mostowsky, and Marc Deisenroth, "Efficiently sampling functions from Gaussian process posteriors", International Conference on Machine Learning, 2020

[0106] Michalis Titsias and Miguel Lezaro-Gredilla, "Doubly stochastic variational Bayes for non-conjugate interference", International Conference on Machine Learning, 2014

[0107]

Claims

Computer-implemented method for detecting an abnormality of an electrical device battery (41) having at least one electrochemical unit, in particular a battery cell (45), in a technical device (4) with the aid of a data-based battery model (10) for determining internal electrochemical battery states (x), having the following steps: - providing temporal operating variable profiles of operating variables of the device battery; determining the internal electrochemical battery states with the aid of the data-based battery model as a function of the acquired temporal operating variable characteristics of the operating variables of the device battery, wherein the data-based battery model (10) is configured with a hybrid differential equation system in order to model the internal electrochemical battery states (x) of the device battery (41) and / or their temporal gradients as a function of the operating variable characteristics (F(t)), wherein at least one of the differential equations (11) of the differential equation system has a sum of a deterministic model term (f1, f2, f3, f4, f5, f6) and a data-based correction term (g1, g2, g3, g4, g5, g6) formed by a sparse Gaussian process model; determining probability distributions of the determined internal electrochemical battery states (x) using a Monte Carlo approach; determining an anomaly of the device battery (41) depending on a predefined interface (G) of the internal battery states and their probability distributions, wherein the interface (G) separates regions of anomalous and normal battery states in a data space of battery state vectors (x) from the determined internal electrochemical battery states (x).The method of claim 1, wherein the operating variables comprise a battery voltage, a battery current, a battery temperature and / or a state of charge, and / or wherein the internal battery states (x) comprise one or more of the following electrochemical states: an amount of cyclable lithium, a volume fraction of the anode, a volume fraction of the cathode, a reaction rate or a reaction coefficient with respect to the anode, a diffusion coefficient of the anode, a layer thickness with respect to the anode, a reaction rate or a reaction coefficient with respect to the cathode, a diffusion coefficient of the cathode, a porosity in the anode, a porosity in the cathode, a Bruggemann coefficient in the anode, a Bruggemann coefficient in the cathode, an electrolyte concentration, a contact resistance, and a mechanical particle load.Method according to claim 1 or 2, wherein the interface (G) is determined by a clustering method of battery state vectors (x), in which a cluster of battery state vectors (x) of a plurality of normal device batteries (41) of technical devices (4) which had no fault within a period of time is formed, wherein the interface is defined by a predefined distance from a centroid of a "normal" cluster which contains normal battery state vectors (x) for functional device batteries, wherein the predefined distance is selected such that the interface surrounds a region of the data space which contains a predefined proportion of all battery state vectors (x) of the normal device batteries (41).Method according to one of Claims 1 to 3, wherein a confidence range for the battery state vector (x) is determined as a function of the probability distributions by integration over the probability distributions, wherein the confidence range is determined as a function of a predefined quantile value, wherein an anomaly is detected if the battery state vector (x) is located outside a "normal" cluster which contains normal battery state vectors (x) for functional device batteries (41) or the confidence range intersects the boundary surface.The method of any one of claims 1 to 4, wherein the sparse Gaussian process model is trained with a subset of a provided training dataset.Method according to one of Claims 1 to 5, wherein after detection of an error, an error type and / or a criticality of the error is detected as a function of at least one predefined rule, wherein a warning is signaled as a function of the error type and / or the criticality of the error.Method according to claim 6, wherein the fault type and / or the criticality of the fault is detected depending on the result of a threshold comparison of a battery temperature, a state of charge loss with a high temporal gradient and an extreme value of the incremental capacity dQ / dU.The method according to any one of claims 1 to 7, wherein the hybrid differential equation system is parameterized with training data sets formed from a time series of operating variable characteristics of a device battery and with a label that indicates whether an anomaly or a fault or no anomaly or no fault of the device battery has occurred after a predefined time period after the end of the time series.Method according to one of Claims 1 to 8, wherein the method is carried out in a central unit (2) external to the device, wherein the operating variable profile (F(t)) is determined in the technical device (4) and is transmitted to the central unit (2) external to the device.Method according to one of Claims 1 to 9, wherein the device battery (41) is used for operating a device, such as a motor vehicle, a pedelec, an aircraft, in particular a drone, a machine tool, a device for entertainment electronics, such as a mobile telephone, an autonomous robot and / or a domestic appliance.Method according to one of Claims 1 to 10, wherein the determination of the anomaly of the device battery (41) is carried out as a function of probabilistic modelling of the at least one battery state by integration over the probability density function.An apparatus for performing any of the methods of any of claims 1 to 11.A computer program product comprising instructions which, when the program is executed by at least one data processing device, cause the program to carry out the steps of the method according to any one of claims 1 to 11.A machine readable storage medium comprising instructions which, when executed by at least one data processing device, cause the at least one data processing device to carry out the steps of the method according to any one of claims 1 to 11.

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