METHOD FOR PREDICTING A RESIDUAL SERVICE LIFE OF VEHICLE BATTERIES OF A FLEET OF ELECTRIC VEHICLES

Abstract

A computer-implemented method is introduced for predicting a residual service life of vehicle batteries of a fleet of electric vehicles. In the method, parameters of the vehicle batteries are measured during the operation of the electric vehicles and transmitted to a server; a conditional probability is determined that the residual service life of a specific vehicle battery undershoots a predefined limit value at a point in time lying in the past; and the residual service life of vehicle batteries of the fleet is predicted as a function of the conditional probability.

Claims

1-13. (canceled)

14. A computer-implemented method for predicting a residual service life of vehicle batteries of a fleet of electric vehicles, comprising the following steps: measuring parameters of the vehicle batteries during an operation of the electric vehicles, and transmitted the measured parameters to a server; determining a conditional probability that the residual service life of a specific vehicle battery of the vehicle batteries undershoots a predefined limit value at a point in time lying in the past; and predicting the residual service life of the vehicle batteries of the fleet as a function of the conditional probability.

15. The method as recited in claim 14, wherein the parameters measured during the operation of the electric vehicles for each vehicle battery are combined to a feature vector characterizing the specific vehicle battery.

16. The method as recited in claim 15, wherein the conditional probability is determined as a quotient whose denominator is a function of a probability that the specific vehicle battery has a specific feature vector at the point in time lying in the past.

17. The method as recited in claim 16, wherein the denominator is: estimated by an empirical distribution based on an event frequency, or determined based on a parametric distribution, or determined based on a normal distribution, or determined based on a uniform distribution.

18. The method as recited in claim 16, wherein the quotient has a numerator, which is a function of a joint probability that the specific vehicle battery having the specific feature vector has a residual service life that undershoots the predefined limit value at the point in time lying in the past.

19. The method as recited in claim 18, wherein the joint probability is modeled by a Bayesian network, that is, by a directed cyclic graph B = (v,g), where v is the set of vertices that represents the variables, and ε forms a set of edges that encode the dependencies between variables.

20. The method as recited in claim 19, wherein the Bayesian network has a vertex without parents.

21. The method as recited in claim 14, wherein the vehicle batteries are labeled by a binary classifier, which has a first value for those of the vehicle batteries whose residual service life is greater than a threshold value, and which has a second value that differs from the first value, for those of the vehicle batteries whose residual service life is less than a threshold value, wherein the first value is zero and the second value is 1.

22. The method as recited in claim 21, wherein a probability that the binary classifier has the second value at a point in time T that is later than a specific point in time t is described by a survival function which is estimated by a Kaplan-Meier estimator.

23. The method as recited in claim 22, wherein the probability of an event, that is, the probability that the binary classifier assumes the second value is calculated by a cumulative death distribution function from survival analysis.

24. The method as recited in claim 19, wherein the structure of the Bayesian network is determined using a criterion of a minimum description length.

25. A device configured to predict a residual service life of vehicle batteries of a fleet of electric vehicles, the device comprising: a sensor system configured to measure parameters of the vehicle batteries occurring during operation of the electric vehicles; and a transmitter configured to transmit the measured parameters to a server, the server being configured to: determine a conditional probability that the residual service life of a specific vehicle battery undershoots a predefined limit value at a point in time lying in the past; and predict the residual service life of the vehicle batteries of the fleet as a function of the conditional probability.

26. A non-transitory computer-readable medium on which is stored a computer program including instructions for predicting a residual service life of vehicle batteries of a fleet of electric vehicles, the instructions, when executed by a computer, causing the computer to perform the following steps: measuring parameters of the vehicle batteries during an operation of the electric vehicles, and transmitted the measured parameters to a server; determining a conditional probability that the residual service life of a specific vehicle battery of the vehicle batteries undershoots a predefined limit value at a point in time lying in the past; and predicting the residual service life of the vehicle batteries of the fleet as a function of the conditional probability.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] FIG. 1 shows the technical environment of the present invention.

[0032] FIG. 2 shows a flow diagram as an exemplary embodiment of a method according to an example embodiment of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0033] In detail, FIG. 1 shows a fleet 10 of electric vehicles 10.1, 10.2, ..., 10.n together with a server 12 of an operator of vehicle fleet 10. Every electric vehicle 10.1, 10.2, ..., 10.n has an electric vehicle battery 14.1, 14.2, ...,14.n and a sensor system 16.1, 16.2, ...16.n for acquiring parameters of vehicle battery 14.1, 14.2, ...,14.n such as its temperature, electrical voltage and electrical current strength. The vehicle batteries are preferably identical vehicle drive batteries.

[0034] Each electric vehicle also has calculation means (i.e., devices) 18.1, 18.2, ...,18.n, which calculate from the data supplied by sensor system 16.1, 16.2, ...,16.n an instantaneous SoH of the drive battery with the aid of machine learning using a calculation model. This calculation model is preferably independent of the prediction according to the present invention, less accurate and requires more measured values (i.e., a more complete parameter space).

[0035] In addition, each electric vehicle 10.1, 10.2, ...,10.n has a Cloud connectivity in the form of mobile radio communication means (i.e., devices) 20.1, 20.2, ...,20.n by which electric vehicle 10.1, 10.2, ...,10.n is able to exchange information with server 12 of vehicle fleet 10 and/or other components of a Cloud 22.

[0036] The present invention is realized by an interaction of the components of the distributed system illustrated in FIG. 1.

[0037] FIG. 2 shows a flow diagram as an exemplary embodiment of a method according to the present invention. In a first phase of the method, data are collected that map the measured parameters of the vehicle batteries 14.1, 14.2, ...,14.n. The collected data are transmitted to server 12. The first phase corresponds to step 100 in the flow diagram of FIG. 2.

[0038] With the aid of the parameters measured for one of vehicle batteries 14.1, 14.2, ...,14.n in each case, feature vectors are formed for respective vehicle battery 14.1, 14.2, ...,14.n. The measurements are undertaken at specific points in time. The variable to be determined is (initially) a remaining service life of a respective vehicle battery 14.1, 14.2, ...,14.n at an instantaneous point in time.

[0039] The variable to be determined is defined as the conditional probability that a certain event (such as reaching/undershooting a residual service life) occurs in a vehicle battery 14.1, 14.2, ...,14.n having a specific feature vector (x(t) at a specific point in time t.

[0040] Let it be assumed that data from n vehicle batteries 14.1, 14.2, ...,14.n, which are independent from one another and identical, are collected by m different data sensors of sensor system 16.1, 16.2, ...,16.n of vehicles 10.1, 10.2, ...,10.n that allow for a continual measurement in each case. Examples of such data are electrical voltages and temperatures of vehicle batteries 14.1, 14.2, ...,14.n, but the data are not restricted to these examples.

[0041] Despite continual measurements, only discretized measurements are considered for the evaluation. That means, the measurements received from an i.sup.th data source (e.g., a sensor of a vehicle battery) are transformed into a range R.sub.ic Q. The discretized data collected during the measurements are represented as feature vector x .Math. R.sub.i× ... × R.sub.m. The data are collected with discrete time stamps, which are denoted by t.sub.1 <t.sub.2...t.sub.K, that is, t.sub.i∈ ℤ for all 1 ≤i ≤ K. For all 1 ≤ i≤ n, T.sub.i £ Z is defined as the event time, and C¡E{t.sub.1...,tK} as the censor time (that is, the given object is no longer monitored). It is assumed that C.sub.i ≤ T.sub.i applies. However, T.sub.i >t.sub.K is also possible, which means that the event has occurred by the time of the last time stamp. The event status at instant t.sub.K is defined as δ.sub.ik = [T.sub.j ≤t.sub.k], where [.] is denoted as the Iverson bracket, that is,[true] = 1 and [false ] = 0.

[0042] A set of indexes T.sub.i<={1...,K} is introduced so that t.sub.k ≤ min(Ci,Ti) applies, and X.sub.ik are available for all k E Γ.sub.i.In this context, X.sub.ik is the feature vector of the i.sup.th vehicle battery at time t.sub.k. The data collected for the i.sup.th vehicle battery are represented as D.sub.i= {(x.sub.ik,δik)|k∈T.sub.i}. The entire dataset is denoted byD = D.sub.i U ... U D.sub.n .

[0043] A scenario is examined where data are available only for a few events at the instantaneous point in time t.sub.c = t.sub.K. The goal is the prediction of an event status at instant t.sub.f, where t.sub.f > t.sub.c and thus lies in the future. The event status for the vehicle battery i is denoted .sub.by y.sub.j(t.sub.c) .Math. {0.1} .

[0044] A binary classifier is generated by using .sub.Yi(t.sub.c) as a class label. If .sub.Yi(t.sub.c) = 1, then the event for vehicle battery i has occurred at instantaneous point in time t.sub.c. In contrast, if .sub.Yi(t.sub.c) = 0, then the event has not yet occurred at the instantaneous point in time t.sub.c.

[0045] The goal is to calculate the conditional probability

[00001]$\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1\left|\text{x, t}\le {\text{t}}_{\text{c}}\right)\right)=\frac{\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1,\text{x, t}\le {\text{t}}_{\text{c}}\right)}{\text{P}\left(\text{x, t}\le {\text{t}}_{\text{c}}\right)}$

where xrepresents the feature vector for a given vehicle battery. The determination of this probability is represented by a second step 200 of the flow diagram. An event prediction based on the evaluation of probabilities is described in the paper “A Bayesian Perspective on Early Stage Event Prediction in Longitudinal Data”, IEEE Transactions on Knowledge and Data Engineering, 28 (12):3126 - 3139, December 2016.

[0046] In the denominator of the fraction, the probability represents that the vehicle battery has the specific feature vector x at the specific point in time t.

[0047] The numerator of the fraction represents the joint probability

[00002]$\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1,\text{x,t}\le {\text{t}}_{\text{c}}\right)$

that the specific event has already occurred in a vehicle battery that has the specific feature vector x at the specific instant t.

[0048] The quotient thus is the probability that an individual vehicle battery has already undershot a residual service life of 80% of its expected total service life at an instant t in the past.

[0049] To model the joint probability P(y(t.sub.c),x,t≦t.sub.c), step 200 includes the definition of a Bayesian network, that is, a directed cyclic graph B = (v, .Math.),in which v is the set of vertices that the variables represent, and .Math. forms the set of edges that encode the dependencies between the variables. For example, a Bayesian network is described in paper “Bayesian network classifiers”, Machine Learning, 29(2-3): 131- 161, November 1997.

[0050] For this purpose, a random variable for each sensor measurement x.sub.i with t1 ≤ i ≤ is initially examined for each feature vector x, and an additional variable that corresponds to the class label y(t.sub.c) is examined. To this end, the notation .sub.π(x.sub.i)for the set of the parents of the vertex belonging to x.sub.¡ is used. It is assumed that π(y(t.sub.c)= ø applies, that is, that no parents exist for the vertex belonging to y(t.sub.c).

[0051] The joint probability may then be factorized to

[00003]$\text{p}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1,\text{x,t}\le {\text{t}}_{\text{c}}\right)=\text{p}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1,\text{t}\le {\text{t}}_{\text{c}}\right){\displaystyle \underset{\text{i =1}}{\overset{\text{m}}{.Math.}}\text{p}\left({\text{x}}_{\text{i}}\left|\pi \left({\text{x}}_{\text{i}}\right)\right)\right)}$

[0052] Therefore, the following is obtained: [..., sic]

[0053] The numerator P(x,t≤t.sub.c) is able to be estimated via the empirical distribution on the basis of the event frequencies, that is,

[00004]$\text{P}\left(\text{x,t}\le {\text{t}}_{\text{c}}\right)\approx \frac{\left|\left\{{\text{x}}_{\text{ik}}=\text{x}\right)\left({\text{x}}_{\text{ik}},{\delta }_{\text{ik}}\right)\in \mathcal{D},{\text{t}}_{\text{k}}\le \left({\text{t}}_{\text{c}}\right\}\right|}{\left|\mathcal{D}\right|}$

[0054] As an alternative, a parametric distribution may be assumed for p(x,t < t.sub.c) such as the normal distribution or the uniform distribution.

[0055] To calculate the probability for the vertex without parents, theory from the field of survival analysis is used, based on a survival analysis:

[0056] The present invention relates to a scenario in which only a limited set of data is available for estimating the a priori probability (prior probability) P(y(t.sub.c) = 1,t ≤ t.sub.c) of an event. Some of the available data are incomplete, that is, censored data are present.

[0057] For each time t.sub.i, all events are labeled either as event or as event-free. The survival function S(t) = P(T > t) is estimated to calculate the labeling. This function indicates the probability that the instant T of an event occurrence is later than an instant t indicated in the network.

[0058] The conventional Kaplan-Meier estimator is used for the estimation

[00005]$\widehat{\text{S}}\left(\text{t}\right)={\displaystyle \underset{\text{i}:{\text{t}}_{\text{i}}<\text{t}}{.Math.}\left(1-\frac{{\text{d}}_{\text{i}}}{{\text{n}}_{\text{i}}}\right)}$

where, d.sub.i represents the number of events at instant t.sub.i, and n.sub.i is the number of objects that remain in the study at time t.sub.i. The probability of an event F.sub.e(t) is calculated with the aid of the cumulative death distribution function

[00006]$\text{F}\left(\text{t}\right)=\text{P}\left(\text{T}\le \text{t}\right)=1-\text{P}\left(\text{T}>\text{t}\right)=1-\text{S}\left(\text{t}\right),\text{that is,}\widehat{{\text{F}}_{\text{e}}}=1-\widehat{\text{S}}\left(\text{t}\right)$

[0059] In addition, let it be assumed that Q(t) = P(C > t), which indicates the probability that time C of the censoring is later than a specific time t. The Kaplan-Meier estimator for Q(t) takes the form of

[00007]$\widehat{\text{Q}}\left(\text{t}\right)={\displaystyle \underset{{\text{i:t}}_{\text{i}}<\text{t}}{.Math.}\left(1-\frac{{\text{n}}_{\text{i}}-{\text{d}}_{\text{i}}}{{\text{n}}_{\text{i}}}\right)={\displaystyle \underset{{\text{i:t}}_{\text{i}}<\text{t}}{.Math.}\frac{{\text{d}}_{\text{i}}}{{\text{n}}_{\text{i}}}}}$

[0060] The censoring probability is calculated as

[00008]$\widehat{{\text{F}}_{\text{c}}}\left(\text{t}\right)=1-\widehat{\text{Q}}\left(\text{t}\right)$

[0061] At point in time t, the event label is assigned to all instances if

[00009]$\widehat{{\text{F}}_{\text{e}}}\left(\text{t}\right)\ge \widehat{{\text{F}}_{\text{c}}}\left(\text{t}\right).$

In the other case, all instances are labeled as event-free.

[0062] The use of the labeling makes it possible to collect instances that are labeled as an event, and the experimental probability distribution

[00010]$\widehat{\text{F}}\left(\text{t}\right)$

is able to be calculated.

[0063] However, a parametric distribution F(t) is used instead. A popular example is the conventional Weibull distribution having two parameters a and b, that is,

[00011]$\text{F}\left(\text{t}\right)=1-{\text{e}}^{-{\left(\frac{\text{t}}{\text{b}}\right)}^{\text{a}}}.$

[0064] This parametric distribution is dependent on data.

[0065] To learn the structure, that is, the edge quantity of the Bayesian network, the criterion of the minimum description length

[00012]$\text{MDL}\left(B\left|\mathcal{D}\right)\right)=\frac{\log \text{N}}{2}\text{d}-\mathcal{l}\left(\left(B\right|\mathcal{D}\right)$

Is able to be used, where

[00013]$\text{N =}\left|\mathcal{D}\right|,\text{d =}{\displaystyle \underset{\text{i = 1}}{\overset{\text{m}}{.Math.}}{\text{R}}_{\text{i}}}$

is the number of free parameters in the network. The log-likelihood function may be defined as

[00014]$\mathcal{l}\left(B\left|\mathcal{D}\right)\right)=\log \left({\displaystyle \underset{\text{i=1}}{\overset{\text{n}}{.Math.}}{\displaystyle \underset{\text{k}\in T_{\text{i}}}{.Math.}{\text{p}}_{\text{B}}\left({\text{x}}_{\text{ik}}\right)}}\right)$

[00015]$\mathcal{l}\left(B\left|\mathcal{D}\right)={\displaystyle \underset{\text{i=1}}{\overset{\text{n}}{.Math.}}{\displaystyle \underset{Ek\in {\mathcal{J}}_{\text{i}}}{.Math.}\log \left({\text{P}}_{\text{B}}\left({\text{x}}_{\text{ik}}\right)\right)}}\right)$

[00016]$\mathcal{l}\left(B\left|\mathcal{D}\right)\right)={\displaystyle \underset{\text{i = 1}}{\overset{\text{n}}{.Math.}}{\displaystyle \underset{\text{k}\in T_{\text{i}}}{.Math.}\log \left({\displaystyle \underset{j=1}{\overset{m}{.Math.}}{\theta }_{{\left(x_{ik}\right)}_j\left|\pi \left({\left(x_{ik}\right)}_j\right)\right)}}\right)}}$

where Type equation here,

[00017]${\theta }_{\left(x_{ik}\right)j\left|\pi \left(\left(x_{ik}\right)j\right)\right)}=\text{P}\left({\left(x_{ik}\right)}_j\left|\pi \left({\left(x_{ik}\right)}_j\right)\right)\right)$

[0066] If the empirical distribution P(.) is assumed, which is defined by the frequency of the events in the training set, that is

[00018]$\text{P}\left(\text{X}\right)=\frac{I}{\text{N}}{\displaystyle .Math.{}_{\text{i =1}}^{\text{n}}}{\displaystyle .Math.{}_{\text{k}\in T_{\text{i}}}}〚{\text{x}}_{\text{ik}}\in \text{X}〛$

for each event

[00019]$\text{X}\in {\text{R}}_1\times .Math..Math.\times {\text{R}}_{{\text{m}}^{\prime }}$

the log-likelihood function is able to be written as

[00020]$\mathcal{l}\left(B\left|\mathcal{D}\right)\right)=\text{N}{\displaystyle \underset{\text{i =1}}{\overset{\text{n}}{.Math.}}{\displaystyle \underset{\text{k}\in {\mathcal{J}}_{\text{i}}}{.Math.}{\displaystyle \underset{\text{j = 1}}{\overset{\text{m}}{.Math.}}{\displaystyle \underset{\underset{\pi \left({\left({\text{x}}_{\text{ik}}\right)}_{\text{j}}\right)\in {\text{R}}_{\pi \left({\left({\text{x}}_{\text{ik}}\right)}_{\text{j}}\right)}}{{({\text{x}}_{\text{ik}})}_{\text{j}}\in {\text{R}}_{\text{j}},}}{.Math.}\widehat{\text{P}}\left({\left({\text{x}}_{\text{ik}}\right)}_{\text{j}},\pi \left({\left({\text{x}}_{\text{ik}}\right)}_{\text{j}}\right)\right)log\left({\theta }_{\left(x_{ik}\right)j|\pi \left({\left(x_{ik}\right)}_j\right)}\right)}}}}$

which is maximized as

[00021]$\widehat{\text{P}}\left({\left({\text{x}}_{\text{ik}}\right)}_{\text{j}},\pi \left({\left({\text{x}}_{\text{ik}}\right)}_{\text{j}}\right)\right)={\Theta }_{{\left({\text{x}}_{\text{ik}}\right)}_{\text{j}}}|\pi \left({\left({\text{x}}_{\text{ik}}\right)}_{\text{j}}\right)$

[0067] This criterion MDL(B|D) may be minimized by a local search algorithm (e.g., by the conventional hill climbing algorithm).

[0068] With the aid of the Bayesian network determined in this way, the numerator of the conditional probability

[00022]$\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1|\text{x,t}\le {\text{t}}_{\text{c}}\right)=\frac{\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1,\text{x,t}\le {\text{t}}_{\text{c}}\right)}{\text{P}\left(\text{x}\left(\text{t}\right)\le {\text{t}}_{\text{c}}\right)}$

is able to be calculated.

[0069] The resulting knowledge of the conditional probability

[00023]$\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1|\text{x,t}\le {\text{t}}_{\text{c}}\right)$

allows for a prediction of the residual service life of vehicle batteries of the fleet, which occurs in step 300, as a function of the conditional probability, as will be described in the following text.

[0070] The value of the probability P(y(t.sub.c) = 1|x,t ≤ t.sub.c) that an event has occurred by the instantaneous point in time t.sub.c amounts to between 0 and 1 according to the definition.

[0071] Probability P(y(t.sub.c) = 0|x,t ≤ t.sub.c) complementary thereto is able to be calculated on the basis of general characteristics of the probability as

[00024]$\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=0|\text{x,t}\le {\text{t}}_{\text{c}}\right)=1-\text{P}\left(\text{y}\left({\text{t}}_{\text{c}}\right)=1|\text{x,t}\le {\text{t}}_{\text{c}}\right).$

[0072] Therefore, if the probability that an event has occurred by the instantaneous point in time t.sub.c can be calculated, then it is also possible to calculate the probability that the event has not occurred by instantaneous point in time t.sub.c. In the present case, the latter probability is of interest, on the one hand. On the other hand, the training data for the complementary probability P(y(t.sub.c) = 0|x,t≤ t.sub.c) are available. For that reason, this probability is calculated at the outset, for instance. The calculated value may then be used to calculate the probability actually of interest in that t.sub.c is replaced by t.sub.f.