WO2018141410A1

WO2018141410A1 - Method, electronic module and computer program product for detecting time delayed relationship between a first and at least a second sensor data stream of measurements

Info

Publication number: WO2018141410A1
Application number: PCT/EP2017/052521
Authority: WO
Inventors: Jonathan Christoph BOIDOL; Andreas Hapfelmeier
Original assignee: Siemens Aktiengesellschaft
Priority date: 2017-02-06
Filing date: 2017-02-06
Publication date: 2018-08-09

Abstract

A Method, electronic module and computer program product for detecting a time delayed relationship between a first and at least one second data stream of measurements, which are recorded on different sensors of a technical device, in particular in an energy generation device, wherein the method comprises the following steps: - Capturing (S1) the first and second streams of sensor data continuously over time, - Creating (S2) incrementally over the captured sensor data for each stream a sequence of more than one layer of data structures, - Determining (S3) for each layer a dependency value for the second data stream being delayed by a specified lag with respect to the first data stream by applying a dependency algorithm on the data structures of the first and a second data stream of the same level of layer, wherein a first stream' s data structures are correlated with a second stream' s data structures temporal shifted by a lag, wherein the lag increases geometrically in consecutive layers, and - Evaluating (S4) a lag of a maximum dependency value. Lagged dependency detection allows identifying interesting relationships of a system, which creates streams. Monitoring of the dependant sensor streams could, e. g., reveal changes in the system.

Description

Method, electronic module and computer program product for detecting time delayed relationship between a first and at least a second sensor data stream of measurements

The application is related to a method, an electronic module and a computer program for detecting a time delayed, i.e. lagged, relationship between a first and at least one second data stream of measurements, which are recorded on different sensors of a technical device, in particular an energy generation device.

Sensors detecting technical parameters like voltage, current, pressure and the like are usually applied in a large-scale wireless sensor network (WSN) . The sensor networks may be use for remote monitoring of technical devices and industrial plants. This progress has spurred the need for processes and applications that work on high dimensional streaming data. Streaming data analysis is concerned with applications where the records are processed in unbounded streams of

information. The nature and volume of this type of data makes traditional batch learning exceedingly difficult, and fit naturally to algorithms that work in one pass over the data, i.e. in an online-fashion. To achieve this transmission from batch to online algorithms, window-based and incremental algorithms are popular, often favoring heuristics over exact results . In many real-world applications streams of data from

different sensors from the same monitored system exhibit relationships, which we can try to detect and use to better understand the system. This gets vastly more complicated when the relationships between data streams exhibit a delay, i.e. changes in one stream effect another stream sometime in the future. Imagine e.g. relationships in weather data, where temperature changes have delayed effects on humidity or precipitation. In an energy generation device, e.g. a turbine, changes in vibration e.g. have an effect on the measured temperature or measured flow velocity of a fluid which is delayed by the same or different lags related to the occurrence of the vibration changes.

The relationships may only appear for a short time period or they may be stable for months and years. The relationships might appear with short or also possibly large delays. A straight forward approach for finding delayed dependencies would be to save all data streams and calculate a measure of dependency for every possible delay between the streams.

The article "Time delay estimation via minimum entropy" of Benesty, Jacob, Yiteng Huang, and Jingdong Chen, published in IEEE Signal Processing Letters 14.3 (2007): 157-160,

describes finding the optimal lag corresponding to a minimum entropy. This approach has been tried a specific application e.g. for finding a time delay in signals from several

microphones with different distances to the signal source. This, however, makes use of a specific model of speech signals, e.g Laplace-distribution. For more general

application a model-free measure of dependence is required to find the lag that optimizes the relationship.

In state of the art, several approaches are known to detect pair-wise dependencys or dependencies between pairs or groups of data streams. The best known indicator for pair-wise correlation is the Pearson's correlation coefficient

essentially the normalized covariance between two random variables. Direct computation of the Pearson's correlation coefficient, however, is prohibitively expensive and, more problematic it is only a suitable indicator for linear or linear transformed relationships. For Pearson's correlation coefficient, a Braid algorithm has been developed which allows a fast approximation of a cross-correlation, which is a function of lag versus correlation. It is described in "Braid: Stream mining through group lag correlations", by Sakurai, Yasushi, Spiros Papadimitriou, and Christos

Faloutsos, published in Proceedings of the 2005 ACM SIGMOD international conference on management of data, 2005.

Since data streams are unbounded and represent unlimited data, Braid would require infinite memory to process them. Also the correlation-coefficient is far from capable of detecting more complex relationships of data streams e.g. non-linear functions. Therefore an object of the present invention is to find the delay or lag between data streams that maximize the

dependence between them, to find the corresponding strength of this dependence and to monitor it continuously. The solution should allow determining the lag that optimizes the dependence fast and with limited memory.

Lagged dependency detection allows identifying interesting relationships of a system, which creates streams. Monitoring of the dependant sensor streams could, e. g., reveal changes in the system. In a predictive scenario the determined delay could be used to detect changes in the system before the effects appear in all streams since the delay relation is known . In this application we understand the term correlation to indicate a broad class of relationships, including but not limited to linear relationships. We explicitly refer to linear relationships as such, e.g. as linear correlation. According to a first aspect the present invention refers to a method for detecting a time delayed relationship between a first and at least one second data stream of measurements, which are recorded on different sensors of a technical device, in particular in an energy generation device, wherein the method comprises the following steps:

- Capturing the first and second streams of sensor data continuously over time, - Creating incrementally over the captured sensor data for each stream a sequence of more than one layer of data

structures ,

- Determining for each layer a dependency value for the second data stream being delayed by a specified lag with respect to the first data stream by applying a dependency algorithm on the data structures of the first and a second data stream of a same level of layer, wherein the first stream' s data structures are correlated with the second stream's data structures shifted temporal by a lag, wherein the lag increases geometrically in consecutive layers, and

- Evaluating a lag of a maximum dependency value.

This limits the number of determination steps which have to be performed in a processing unit, e.g. micro processor, also for long lags. In turn an online processing with continuously captured new sensor data is possible.

A data stream is a sequence of sensors measurement data. The sequence may be a sequence of digits or other values or digital or analog signals. Usually, a plurality of data streams is processed in parallel. In particular, at least two streams are compared and all streams may be compared pair- wise. The data stream may be captured directly from the sensor or may be read from memory storage. Each layer of data structure can be seen as a window encoding a number of data structures, which is moved over the data streams

simultaneously for each pair of sensors. Within a layer a dependency value is determined for data structures of the first and second data stream that are shifted to each other by a lag, especially a lag of one or several time intervals, by which the single data structures are spaced in time.

In a preferred embodiment each layer contains the same number of data structures with subsequent layers containing data structures captured further backwards in time.

This limits the storage capacity for historic data. In a specific preferred embodiment for each layer, adjacent data structures have a temporal distance of a specified fixed time interval, and the same specified time interval is applied in each layer of the same level of each stream, wherein the specified time interval corresponds to the lag considered for a level of layers, and

determining for each layer a dependency value, wherein the first stream' s data structures are correlated with a second stream's data structures shifted temporal by one time

interval .

This means that, if the time interval between the data structures in the first layer has a value 1 the time interval between two adjacent data structures in the second layer increases by a factor of two and is therefore 2*1. In the k- th layer the time interval between data structures in is ₂k-l * 1. Accordingly by determining a dependency value between a pair of layers of the same level shifted by at least one time interval means that the dependency algorithm is determined for a lag 1. Determining in the same manner the dependency value for all levels of layers, provides a

geometrically spaced sequence of dependency values. That way, errors will be small at small lags where accuracy is required most. Even for large lag the relative error is likely still small .

In a further preferred embodiment a data structure of a subsequent layer of a sequence of layers is formed by

compression of all data structures of a previous layer in the respective time interval of the considered layer.

This optimizes the amount of storage data to be required for determining a dependency at a large lag. Generating a data structure of a subsequently layer by compressing or smoothing over the data structures of the data structures lying in the time interval of the subsequent layer takes all these

contributing data structures into account and provides the far more information than just selecting one of the actual data structures in the previous layers to be used in the subsequent layer. In a preferred embodiment of the present invention, the dependency algorithm is an entropy based algorithm,

especially using a mutual information based algorithm.

Mutual information, especially a Kraskov-estimator, as a measure of dependency produces good results and is applicable to a variety of data from different fields. It is a model- independent measure and not limited to certain types of relationships in the data or data drawn from a known

distribution. Therefore a model independent analysis of the data streams can be provided.

In a further embodiment of the present invention two of the number of layers, the time interval of the first layer, or the maximum lag is configured in a configuration phase.

Each pair of these settings specifies sufficiently the runtime of the method for providing a dependency value for each layer of the sequence of layers. In a preferred embodiment every layer of data structures is incrementally updated by new captured sensor data and

compressed data structures respectively.

This ensures the provision of dependency values of the continuously captured sensor data.

In a further embodiment dependency values between determined dependency values are estimated by interpolation, especially using the cubic spline method.

An interpolation of a function which provides a dependency value for continuous lag values allows approximating the maximum of the dependency function and therefore provides a better estimate for the actual maximum dependency between the data streams occurring at the resulting lag.

In a preferred embodiment a resolution of the dependency value for a dedicated lag is increased by applying the dependency algorithm on the data structures of the lower layer with a time interval smaller than the dedicated lag and data structures of the lower layers being shifted to each other by the dedicated lag.

In this case dependency values are determined within time intervals of the lower layer, e.g. layer i, instead of a time interval of the former evaluated layer i+k. In this case the refined resolution is 2¹ -1₀ instead of 2¹⁺k · l₀.

High resolution here means that the number of dependency values determined is higher with respect to the number of dependency values determined for the same lag in time

calculated by a layer of higher level.

In a further embodiment a method further comprises a step of estimating data of the first or second sensor of a similar device by applying the lag to a captured stream of only second sensor data or first sensor data of the similar device.

According to another aspect the invention refers to an electronic module (100) for detecting a time delayed

relationship between a first and at least a second sensor data stream of measurements, which are recorded on a

technical device (200), in particular in an energy generation device, comprising:

- An input interface (101) which is adapted for capturing the streams of sensor data from sensors (201, 201, 203,)

continuously over time,

- A first processing unit (102) which is adapted for creating (S2) incrementally over the captured sensor data for each stream a sequence of more than one layer of data structures, - A second processing unit (103), which is adapted for determining (S3) for each layer a dependency value for the second data stream being delayed by a specified lag with respect to the first data stream by applying a dependency algorithm on the data structures of the first and a second data stream of the same level of layer, wherein the first stream' s data structures are correlated with a second stream' s data structures shifted temporal by a lag, wherein the lag increases geometrically in consecutive layers, and - An output interface (104), which is adapted for evaluating a lag of a maximum dependency value.

In another aspect the invention refers to a computer program product, tangible embodying a program of machine readable instructions executable by a digital processing apparatus to perform a method according to one of the preceding claims, if the program is executed on the digital processing apparatus.

The provided method and respective electronic module detects lags in data streams using a model-free, entropy based measure for dependence. These features make the method applicable for all kinds of streaming data or doubts specific assumptions on the data. The probing technique, e.g. the described creation of

sequence of layers of data structures drastically reduces computation time and thereby allows the constant monitoring of an environment that produces many data streams in

parallel. In fact the described computation of dependency values in layers with a described time interval between data structures reduces computation time heavily from a factor linear to the size of the maximum lag that should be detected in a naive solution to a logarithmic factor. The data

compression allows performing the probing and a memory- efficient way, keeping only data in memory that is actually needed for the current calculations. The method also makes use of the special design data structures to speed up

frequent evaluation. Typically data structures for this task do not support frequent insertion and deletion of data which happens constantly in the streaming data setting.

An embodiment of the invention is described hereafter. In the drawing

Fig.lA shows a dependency values determined at equidistant lags ; Fig. IB shows dependency values determined at lags

according an embodiment of the inventive method;

Fig.2 shows a sequence of layers of data structures of one stream of sensor data stream as created in an embodiment of the invention;

Fig.3 shows exemplarily three pairs of layers of data

structures of two different sensors data streams used for determining dependency values in an embodiment of the invention;

Fig.4 shows the results of a lag determination of an

exemplarily data stream of sunspot activity

determined by an embodiment of the inventive method compared to a naive approach;

Fig.5 shows a flowchart of an embodiment of the inventive method; and Fig.6 shows an embodiment of the inventive electrical

module as block diagram.

In the following description same functional objects are labeled with the same reference sign.

Data streams appear in diverse environments, e.g., data streams of sensor data measurements detected and forwarded by sensors in, e.g., automation plants, energy grids, motion tracking or in the analysis of network traffic. Especially in energy generating devices like turbines many different sensors monitor parameters like temperature, pressure, flow velocity, which exhibit relationships and show similar chronological sequence with a certain delay in time. In this description the expression lag is used as a synonym for a delay .

The determination of lagged dependencies between such sensor data streams can help to get a deep understanding of a system and to explore by that the reason for a specific shape of sensor data streams. By determining the exact lag in which the dependency of two or more streams is strongest can be used for predicting e.g. for scenarios in a technical device.

The problem of lagged dependency is the analysis of two or more evolving sequence of data for dependence and for the lag at which the dependence is strongest. Since the streams evolve, this also becomes a continuing monitoring task. To solve this problem, a method needs a general measure for dependency in time series, has to work efficiently in linear time and at least sub-linear in space and provide accurate results over a wide range of time delays. The presented method finds the shifted dependency and the corresponding lag 1 on a pair or for all pairs of large numbers of data streams. In the following example a pair of streams X,Y are considered for simplicity, with obvious generalization to pairs between three and more streams.

In general, a lag 1 is the relative shift of two time series of e.g. data streams at which the behavior of one is most predictable from the other and vice versa. The difficulty in lag detection is the need to keep a large amount of historic data which can be shifted relative to each other. Also the computational cost to calculate the dependency for every shift is high. Given a time series X = ( x i , x ) with the newest element x at time t, and a second time series Y, we can naively calculate a measure of dependency for all lags as a function of the shifted series f( (x_lr x_n) ; (yi, y_n-i) ) · In signal processing this is known as cross-dependency where f is normalized covariance.

The inventive method finds the cross-dependency for a pair of time series which are the data streams of measurements collected over the time t . As a measure of dependency between the two time series, mutual information I is used. Estimating mutual information from sample data is a difficult problem.

However, it functions as model-independent measure and is not limited to certain types of relationship in the data or data drawn from known distribution. Mutual information is defined as m Y = S_x S_x /(*,ylog dxdy ( 1 ) where f(_.x,y),f(_.x),f(y) are the joint and marginal probability density functions, or it can be composed from entropy and joint entropy as

1(XY)=H(X)-H(X,Y) + H(Y) (2)

We define the cross-dependency between X and Y as

D(X, Y, 1) = I((xi x„); (yi y_n-i)) (3)

The task of cross-dependency monitoring is then to calculate D for all possible lags L and report the optimum lag with a maximum dependency of a pair our group of data streams. Since there can be periodic pattern in the data such as daily or seasonally dependencies, it is more adequate and practical to report the earliest local maximum above a specified

threshold .

One main idea of the presented method is to reconstruct the cross-dependency function from a geometrically spaced probing. Probing means the selection of adjacent data

structures which are evaluated and taken into account by the described function of mutual information. Fig.l visualizes the idea. Instead of naively calculating the dependency for every possible lag, as shown in Fig. 1A, we take a subset of every 2¹ lag up to a maximum lag m. The distance, or in other word the time interval t_lr t₂, t₃, t₄, .. between the actually calculated points increases

geometrically with the lag.

That way, errors will be small at small lags where accuracy matters most. Even for a large lag the relative error is likely still small. We can fill in the lag values between the probed points, i.e. lags, with any interpolation method. Our method of choice is cubic splines to get a smooth and

efficient interpolation. The probing, i. e. the selected time interval between data structures, reduces computation time greatly to O(log(m)) compared to 0 (m) in the naive solution.

With respect to the accuracy of this method, the Nyquist-

Shannon samplings theorem states that a signal can be

perfectly reconstructed from a uniform sampling, if the sampling is spaced at most 2-fg Hertz apart and the signal contains no frequency higher then Fg . Even for non-uniform sampling, we can reconstruct the full cross-dependency from the sampling, if the average sampling rate is at least 2-fg.

For the proposed geometric sampling, this means that the cross-dependency D can be perfectly determined up to a lag 1, if 1 < 2/fp and the highest frequency in the signal D is at most f-Q. Intuitively, we capture D accurately, if the

dependency does not change too fast from one distance to the other . To get the dependency at all sampled points, we still would need to save historic data up to the largest lag value we want to compute. Instead of that we only save a compressed, smoothed version of the sequence in increasing compressed layers. Every layer stores the same number of data points over a window with the endpoint increasingly further

backwards in time, but spaced so that the number of points stay constant. The word data point or point is used here as a synonym for data structure.

Fig.2 shows an example of a data stream of measurements 11 of which a sequence of n layers L1.0, .., Ll.n comprising eight data points or data structures each, e.g. see layer LI.2 comprises data x₂i, X22_/ χ₂3_/ · ·_/ ^χ28 · Adjacent data structures in one layer are spaced by a specified time interval t₂ which is fixed or constant in that layer LI.2. From layer to layer the time interval between adjacent data structures is doubled so that the time interval of the sequence of layers provides a geometrical series. As the number of data points is in each layer the same, the data structures used in one layer are further apart from each other and therefore the layer itself expands over the double length in time to the preceding layer .

To get the dependency at all sample points, we still would need to save historic data up to the larges lag value we want to compute. Instead, we only save a compressed smoothed version of the sequence 12, 13, 14 in increasingly compressed layers. In Fig.2 the data structures of data stream 12 are formed by compressing at least two data structures of the previous data stream 11, which is comprises e.g. the

uncompressed data structure sampled at a sensor. This holds for all succeeding streams of data structures 12, 13, 14 and further.

In the example depicted in Fig. 2, we refer to increasingly compressed layers as Ll.h where LI .0 stores the last eight of the original, uncompressed data points of a stream. Every higher layer averages 0=2^ consecutive data points. Figure 2 shows the smoothening for the single streams 12, 13, 14. To calculate a lag of we use the smoothed stream of Layer

Ll.h and calculate the lag 1^ = 1 corresponding to 1 = 2h.

Accordingly, we use \log₂(r)] layers. This also has the desirable effect that large lags are calculated from larger slices of the data. While the effect of small lag might only be detectable in the most recent data, the effect of a dependency with a large delay could also be detectable over a large time frame. Maintaining the layers requires a constant number of

operations every steps or

∑log(m) \

„₌„ ^≤2 in total, so we can update them in amortized time 0(1) of 1.

The error introduced by the smoothing in the sequence is small for streams with low frequencies. Given the original data X†- and the smoothed X_t in the stream X and the Haar wavelet coefficients w-j_ of X, the faithfulness of the

smoothing depends on the highest frequencies.

In most real datasets, most of those coefficients are small and only a few contribute significantly to the dynamic of the data, so we can expect the error introduced by the smoothing to be small.

Fig. 3 shows an example for concrete determination of the dependency value at geometrically spaced lags for each first and second stream, which shall be compared. We apply

dependency algorithm on the data structures of each pair of layers L_]_ , L2 for each level of layer Li.l, Li.2, Li .3. In each layer the adjacent data structures have a temporal distance of a specified fixed time interval, see time

interval t₂ in Layer Li.2, which is the considered lag 1₂. Accordingly data structures of the two layers are shifted by one time interval t₂ and therefore determination of the dependency value of all data structures in a pair of layers provides the dependency value for a lag 1₂ which is the same as time interval t₂ between adjacent data structures in the respective layer LI.2. The method can be refined in the resolution between two adjacent determined lags by g lags per layer, if every layer is extended by 2g steps. On the basic layer, we calculate 2-g dependency values up to the specified lag 1 =2g. On every subsequent higher layer, we calculate g lags from

2^h(g+l) to 2^h+1g. At the expense of 2glog (m) additional memory, we achieve a finer sampling and consequently more accurate results.

Another improvement is possible, if we realize that not all the layers are actually necessary to calculate all lags.

Further on a resolution of the dependency values for a dedicated lag is increased by applying the dependency

algorithm under data structures of a lower layer with a time interval or lag smaller than the dedicated lag and the data structures of the lower layers of the first and second stream being shifted to each other by the dedicated lag.

Fig.4 shows the determined dependency value over lag. The solid line is determined by a naive solution evaluating all possible lags. It is compared to the dependency values determined by the inventive method determined at

geometrically spaced lags, see the dashed line, and to dependency values determined by the described high resolution approach, see spotted it line.

The single steps of the method are shown in Fig.5 as a flowchart. The first method step SI is to capture the streams of sensor data continuously over time. And a subsequent step S2 dependency values for the second data stream being delayed by a specified lag with respect to the first data stream are determined by applying dependency algorithm on the data structures of each pair of layers of the first and the second data stream of the same level, wherein first stream's data structures are correlated with the second stream' s data structures temporal shifted by a lag which increases

geometrically in consecutive layers. In step S4 a dependency value for each layer of the sequence of layers are provided and a lag of a maximum dependency value is evaluated. In a further step S5 the data of the first and second sensor of a similar device can be estimated by applying the lag to a captured stream of only second sensor data or first sensor data of the similar device.

Fig.6 shows an electronic module 100 for detecting a time delayed relationship between a first and at least a second sensor 201, 202, 203 of a technical device 200. The technical device can be e.g. a turbine of a power generation plant or one or several field devices in an automation network or sensors capturing traffic flow or any other measured

parameters .

The electronic module 100 comprises an input interface 101, a first processing unit 102, a second processing unit 103 as well as an output interface 104, which all are interconnected by e.g. a data bus. The input interface 101 is adapted for capturing the streams of sensor data from the sensors 201, 202, 203 continuously over time. With a first processing unit 102 the layers of data structures are created and for all layers but the first data structures are composed by

compressing more than one data structure of the previous layer . The second processing unit 103 the dependency values are determined as described in step 3 of Fig.4. The output interface 104 is adapted to provide a dependency value for each layer of the sequence of layers respectively and evaluate a lag of a maximum dependency value and therefore detecting the time delayed relationship between the first and one second data stream. The output interface 104 is connected to a output device 300, which is adapted to estimate data of the first and second sensor of a similar device by applying e.g. the lag of a captured stream to only second sensor data or first sensor data of a similar device.

The output device 300 can also be applied to generate signals depending on the maximum dependency value and use it as input to the device 200 for control measures of device 200. In the above description, a processor can be an integrated circuit, a digital signal processor, a virtual processor, which can also include a memory unit e.g. as random access memory or any other form of memory. The claimed computer program product can be e.g. computer program means which is e.g. a storage card, a USB-stick, a CD-ROM, a DVD or also a retrievable file, which can be provided by servers in a network or which is delivered or provided by another means .

The invention is not limited to the described examples. The invention also comprises all combinations of any of the described or depicted features.

Claims

Patent Claims

1. Method for detecting a time delayed relationship between a first and at least one second data stream of measurements, which are recorded on different sensors of a technical device, in particular in an energy generation device, wherein the method comprises the following steps:

- Capturing (SI) the first and second streams of sensor data continuously over time,

- Creating (S2) incrementally over the captured sensor data for each stream a sequence of more than one layer of data structures ,

- Determining (S3) for each layer a dependency value for the second data stream being delayed by a specified lag with respect to the first data stream by applying a dependency algorithm on the data structures of the first and a second data stream of the same level of layer, wherein a first stream' s data structures are correlated with a second

stream' s data structures shifted temporal by a lag, wherein the lag increases geometrically in consecutive layers, and

- Evaluating (S4) a lag of a maximum dependency value.

2. Method according to any of the preceding claims, wherein each layer contains the same number of data structures with subsequent layers containing data structures captured further backwards in time.

3. Method according to any of the preceding claims, wherein for each layer, adjacent data structures have a temporal distance of a specified fixed time interval, and the same specified time interval is applied in each layer of the same level of each stream, wherein the specified time interval corresponds to the lag considered for the level of layers, and

determining for each layer a dependency value, wherein a first stream' s data structures are correlated with a second stream' s data structures temporal shifted by one time

interval .

4. Method according to any of the preceding claims, wherein a data structure of a subsequent layer of the sequence of layers is formed by compression of all data structures of the previous layer in the respective time interval of the

considered layer.

5. Method according to any of the preceding claims, wherein the dependency algorithm is an entropy based algorithm, especially using a Mutual Information based algorithm.

6. Method according to any of the preceding claims, wherein two of: the number of layers, the time interval of the first layer or the maximum lag is configured in a configuration phase.

7. Method according to any of the preceding claims, wherein every layer of data structures is incrementally updated by new captured sensor data and compressed data structures respectively.

8. Method according to any of the preceding claims, wherein dependency values between determined dependency values are estimated by interpolation, especially using a cubic spline function.

9. Method according to any of the preceding claims, wherein a resolution of the dependency values for a dedicated lag is increased by applying the dependency algorithm on the data structures of a lower layer with a time interval smaller than the dedicated lag and the data structures of the lower layers of the first and second stream being shifted to each other by the dedicated lag.

10. Method according to any of the preceding claims, wherein the method further comprises:

Estimating data of the first or second sensor of a similar device by applying the lag to a captured stream of only second sensor data or first sensor data of the similar device .

11. Electronic module (100) for detecting a time delayed relationship between a first and at least a second sensor data stream of measurements, which are recorded on a

continuously over time,

- A first processing unit (102) which is adapted for creating (S2) incrementally over the captured sensor data for each stream a sequence of more than one layer of data structures, - A second processing unit (103), which is adapted for

Determining (S3) for each layer a dependency value for the second data stream being delayed by a specified lag with respect to the first data stream by applying a dependency algorithm on the data structures of the first and a second data stream of the same level of layer, wherein a first stream' s data structures are correlated with a second stream' s data structures shifted temporal by a lag, wherein the lag increases geometrically in consecutive layers, and

- An output interface (104), which is adapted for evaluating a lag of a maximum dependency value.

12. Electronic module according to claim 11, further

comprises :

- An output device (300), which is adapted to estimate data of the first or second sensor of a similar device by applying the lag to a captured stream to only second sensor data or first sensor data of the similar device.

13. A computer program product, tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus to perform a method according to one of the preceding claims, if the program is executed on the digital processing apparatus.