WO2021099264A1

WO2021099264A1 - A method of determining changes in stationary states of a signal

Info

Publication number: WO2021099264A1
Application number: PCT/EP2020/082255
Authority: WO
Inventors: Aliaksandr YAROMA; Andrei DUKHOUNIK; Aleh AKSIONAU
Original assignee: Octonion Sa
Priority date: 2019-11-18
Filing date: 2020-11-16
Publication date: 2021-05-27
Also published as: GB2588975B; GB2588975A; GB201916772D0

Abstract

The present disclosure relates to a method of determining changes in stationary states of a signal, the method comprising: receiving a plurality of sets of values, each set of values comprising at least one value of the signal; for each set of values among the plurality of sets of values, determining a respective first measure of statistical dispersion; determining a second measure of statistical dispersion for a subset of first measures of statistical dispersion among the determined first measures of statistical dispersion; and determining an exit from a stationary state of the signal by comparing the determined second measure with a predetermined threshold.

Description

A METHOD OF DETERMINING CHANGES IN STATIONARY STATES OF A

SIGNAL

BACKGROUND OF THE INVENTION

The present invention relates to the field of signal processing, and in particular, the signal processing applied to the monitoring or the security of a system.

Machine safety, reliability and efficiency of machines are major concerns in an industry. Condition monitoring of a machine allows detecting a significant change in the system, which may indicate that a failure has occurred, is occurring or will occur. Depending on the evolution of a parameter (or a set of parameters) of the system, maintenance may be scheduled, or other actions may be taken to avoid significant damages. As a result, condition monitoring is important to maintain the efficiency and performance of a machine at its optimum level.

In the context of rotating machines, most of the existing condition monitoring techniques rely on vibration analysis. Vibration analysis methods aim to monitor the vibration level of a machine and to detect whether this vibration level is abnormally increasing or exceeding a critical threshold. The vibration level may be determined based on physical parameter measurements obtained from sensors (e.g. proximity sensor, velocity and/or displacement transducer, accelerometer, etc.). For instance, casing vibrations of machine bearing casings may be measured with accelerometers (seismic or piezo-electric transducers), or eddy current transducers may be used on a rotating shaft to measure the radial (and axial) displacement of the shaft.

Some vibration analysis methods of the prior art are efficient and provide good results for extracting features and detecting faults, but generally have a high computational complexity.

Furthermore, most of these methods do not detect state changes in a system, for instance the transitions from a stationary state to a non-stationary state (and vice versa) for the measured signal, or the transitions from one first stationary state to another stationary state (having different properties, e.g. another frequency/period or another amplitude). By “stationary state” it is meant that the statistical properties (e.g. mean, variance, autocorrelation, etc.) of the measured signal are constant over time. On the contrary, a “non-stationary state” refers to the case wherein the statistical properties are variable with time.

However, determining whether the system is in a stationary state or in a non- stationary state provides essential information about the stability of the system, and therefore its reliability and its efficiency. For instance, when the system enters a non- stationary state, this may indicate a malfunction of the machine. On the contrary, a system that remains in a stationary state indicates normal and safe operation of the machine.

Determining a switch from a first stationary state to another stationary state, or the simple fact that the system is leaving a stationary state, is also an important task, since it provides information on the operation of a system (e.g. it may identify an operating mode of the system).

There is thus a need for a method for determining the state of a system, and in particular for determining non-stationary states of the system.

SUMMARY OF THE INVENTION The disclosure relates to a method of determining changes in stationary states of a signal, said signal being relative to a physical quantity associated with a system, the method being performed by a computing device. The method may comprise: receiving a plurality of sets of values, each set of values comprising at least one value of the signal; for each set of values among the plurality of sets of values, determining a respective first measure of statistical dispersion; determining a second measure of statistical dispersion for a subset of first measures of statistical dispersion among the determined first measures of statistical dispersion; and determining an exit from a stationary state of the signal by comparing the determined second measure with a predetermined threshold.

By “changes in stationary states” it is meant either a transition from a stationary state to a non-stationary state, or a transition from a first stationary state to a second stationary state (having, for instance, different average amplitude and/or different average frequency). More generally, the transition to a first stationary state to another state (stationary or non-stationary) may correspond to an “exit” from the stationary state, which may be determined by the above method.

By “system” it is meant an element or a set of elements to be monitored. It is noted that the present disclosure may be advantageously applied to any system, whether in the industrial, agricultural, or health field. For instance, the disclosure may be used for monitoring the operation of a machine, in particular a rotating machine (e.g. electrical motor, turbine, pump, etc.), by analyzing a vibration signal or an acoustic signal. Such an analysis also makes it possible to detect and predict a machine failure, therefore increasing the security of the system. In other embodiments the disclosed method and device may be used for monitoring a human and/or animal activity (e.g. walking / running), for instance by analyzing an acceleration signal measured by an accelerometer. Of course, the signal may be of another type, for instance an electrical signal (e.g. representative of voltage or intensity), a velocity signal, etc.

For example, the exit from the stationary state of the signal may be determined when the determined second measure exceeds said threshold.

In one or several embodiments, the exit from the stationary state of the signal corresponds to a transition from a stationary state to a non-stationary state, or to a transition from a first stationary state to a second stationary state.

In one or several embodiments, the signal may be obtained from a sensor related to the system, said sensor measuring said physical quantity.

For instance, the sensor may be one among: a proximity sensor, a velocity transducer, a displacement transducer, and an accelerometer.

In one or several embodiments, the method may further comprise: upon determining that the signal is a non-stationary state, emitting an alert message.

Said message may be sent to a user, e.g. an administrator of the system, or to an external device, e.g. a monitoring device configured for taking specific actions (such as shutting down the system, performing further tests, switching into a different operating mode, etc.). This advantageously ensures the security and the proper functioning of the system. In one or several embodiments, the receiving of the plurality of sets of values, the determining of first measures of statistical dispersion and the determining of a second measure of statistical dispersion may be iteratively repeated.

Thus, the value of the second measure of statistical dispersion may be regularly updated based on newly received signal values. The evolution of the value of the second measure of statistical dispersion in function of time may therefore be obtained and analyzed for determining changes of states of the signal.

In one or several embodiments, the system may comprise a rotating machine and the signal may be a vibration signal of said rotating machine. In one or several embodiments, the plurality of set of values may correspond to values of the signal received during successive time-windows.

In particular, the successive time-windows may have a same length.

In addition or in complement, the length of the successive time-windows may be further function of a frequency of the signal in a normal operation of the system. In addition or in complement, the successive time-windows may start at regularly spaced times.

In one or several embodiments, the first measure of statistical dispersion and/or the second measure of statistical dispersion may be a function of a variance, or a function of a standard deviation. In one or several embodiments, the threshold may be function of a measure of statistical location of the determined first measures of statistical dispersion.

For instance, the measure of statistical location may be a mean of the determined first measures of statistical dispersion.

In particular, the threshold Th may be given by:

Th = α x μ_δ where: a is a constant such as 0 £ a £ 1 ; and μ_δ is the mean of the determined first measures of statistical dispersion. The constant a may be determined by an optimization method based on a plurality of sets of training signal data, each set comprising a respective plurality of sets of values of the signal.

By “training signal data”, it is meant values of the signal used for estimating a value of a that is suitable for a given situation (i.e. a specific type of signal measured in a specific system, such as a signal measured on an accelerometer located on a vibrating machine, or a sound signal measured by a microphone placed nearby a vibrating machine). Each set of training signal data may correspond to an example of the measured signal in one given situation. The “plurality of sets of training signal data” may therefore correspond to a plurality of examples of the measured signal in the same given situation. Based on these examples, it is possible to estimate the value of a that is appropriate for the considered situation.

For instance, the constant a may be determined by a machine learning method. For instance, a supervised learning method may be used on the plurality of sets of training signal data, e.g. support vector machines or neural networks.

Other mathematical optimization methods may be used, e.g. a gradient descent method, or a brute-force search method for searching extrema of a predefined metric.

Another aspect of the disclosure relates to a device for determining changes in stationary states of a signal, said signal being relative to a physical quantity associated with a system. The device may comprise: an interface for receiving a plurality of sets of values, each set of values comprising at least one value of the signal; a circuit for determining, for each set of values among the plurality of sets of values, a respective first measure of statistical dispersion; a circuit for determining a second measure of statistical dispersion for a subset of first measures of statistical dispersion among the determined first measures of statistical dispersion; and a circuit for determining an exit from a stationary state of the signal by comparing the determined second measure with a threshold.

Yet another aspect of the disclosure relates to a non-transitory computer readable storage medium, having stored thereon a computer program comprising program instructions, the computer program being loadable into a data-processing unit and adapted to cause the data-processing unit to carry out the methods of any of claims 1 to 16 when the computer program is run by the data-processing device.

Other features and advantages of the method and apparatus disclosed herein will become apparent from the following description of non-limiting embodiments, with reference to the appended drawings. BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings, in which like reference numerals refer to similar elements and in which:

- Figure 1 represents an example of an observed signal in a possible embodiment of the invention;

- Figure 2 illustrates the determination of stationary and non-stationary states of the signal of interest, in a possible embodiment of the invention;

- Figure 3a and 3b illustrate the variation of the second measure of statistical dispersion in function of the signal state changes, in possible embodiments of the invention;

- Figure 4 is a flow chart of a method for determining stationary and/or non- stationary states of a system, in a possible embodiment;

- Figure 5 is a possible embodiment for a device that enables the present invention. DESCRIPTION OF PREFERRED EMBODIMENTS

Determining a change of state in a system is a significant problem in terms of monitoring and security. By change of state it is meant a transition from a stationary state to a non-stationary state (or vice versa), or a transition from a first stationary state to a second stationary state. It is proposed to perform such determination by analyzing the dispersion of a signal of interest associated to the system. More specifically, values of a parameter of statistical dispersion are determined for respective signal time frames, and the evolution of these values in time is analyzed by determining a second dispersion parameter based on these values, as described in detail below.

In the context of the present disclosure, the signal of interest is typically a signal representative of a physical quantity (e.g. a vibration signal, an acoustic signal, an acceleration signal, etc.). Such signal is generally a continuous signal of time t, which may be sampled to obtained a discrete signal (or “discrete-time” signal), which is referred to as the observed signal.

Figure 1 represents an example of such observed signal in a possible embodiment of the invention.

In Figure 1, the signal of interest s(t) is a continuous function of time t, which is sampled at different times t₁, t₂, t₃, t_n. The observed signal may therefore comprise values (also referred to as “observations”) s₁, s₂, s₃, ... , s_n of the signal s(t) that are acquired at respective times t_1; t₂, t₃,

In the example of Figure 1, the sampling times t₁, t₂, t₃, t_n are regularly spaced. In other embodiments, the spacing ( t_i+1 - ti) between two consecutive sampling times t_i and t_i+1 may be variable. In other words, in one or several embodiments, the observed signal may correspond to a time series of samples S = {s_j}_i=12,... .

Figure 2 illustrates the determination of stationary and non-stationary states of the signal of interest, in a possible embodiment of the invention. As depicted in Figure 2, sets of values 211, 212, 213, 214 may be formed based on the received values s₁, s₂, s₃, .... of the signal. More specifically, each set of values may comprise at least one respective value of the signal, and preferably at least two values. In the example of Figure 2, the first set 211 comprises values s_1, s₂ and s₃, the second set 212 comprises values s₃, s₄ and s₅, the third set 213 comprises values s₅, s₆ and s₇ and the fourth set 214 comprises values s₇, s₈ and s₉. Of course, the sets of values may comprise more than three values or less than three values. Also, two different sets of values may comprise a different respective number of values.

In the example of Figure 2, the sets of values 211 , 212, 213, 214 partially overlap two by two, i.e. each set of values shares at least one value with the next set of values. Such property is not mandatory: in one or several embodiments, the sets of values 211 , 212, 213, 214 may not overlap at all (i.e. a set of values does not share any value with the next set of values). In other embodiments, some sets of values 211 , 212, 213, 214 may (partially) overlap since other ones may not overlap.

Each set of values 211 , 212, 213, 214 may be characterized by two respective indexes: a start index and an end index. The start index may be, for instance, the time index corresponding to the “first” value of the set of values (i.e. the value having the lowest time index of the set of values). The end index may be, for instance, the time index corresponding to the “last” value of the set of values (i.e. the value having the highest time index of the set of values). For instance, in Figure 2, the third set of values 213 may have a start index equal to 5 and an end index equal to 7.

A current set of values (e.g. 211, 212 or 213) has a start index which is lower than or equal to the start index of the next set of values (e.g. 212, 213 or 214, respectively), and an end index which is greater than or equal to the end index of the next set of values (e.g. 212, 213 or 214, respectively).

In one or several preferred embodiments, the start index of a current set of values (e.g. 211 , 212 or 213) is strictly lower than the start index of the next set of values (e.g. 212, 213 or214, respectively), and the end index of a current set of values (e.g.

211 , 212 or 213) is strictly lower than the end index of the next set of values (e.g.

212, 213 or 214, respectively). For instance, as represented in Figure 2, the sets of values 211 , 212, 213, 214 may correspond to the observed values of the signal in a regular sliding time-window (in the particular example of Figure 2, the time samples s₁, s₂, s₃, ... are regularly spaced, and the sliding time-window has a length of three - i.e. each set of values comprises three values 211 , 212, 213, 214 - and a sliding period of two - which corresponds to the spacing between the start indexes of two consecutive sets of val ues 211 , 212, 213, 214).

Of course, in alternative embodiments, other configurations can be envisaged. For instance, two consecutive sets of values 211, 212, 213, 214 may have a same start index and two different end indexes, or two different start indexes and a same end index.

The set of values 211, 212, 213, 214 may be formed offline or online. In an offline processing, data is first collected and then processed in a later time. For instance, a plurality of values s₁, s₂, s₃, ...,s_n are received between time 1 to and time n, and the sets of values 211, 212, 213, 214 are then formed after time n. In an online processing (or “real-time processing”), data is received over time and processed as it is received. For instance, values s₁,s₂ , s₃, ... may be received as a data stream over time, and new sets of values 211, 212, 213, 214 may be formed as new values are received. With an online processing, the oldest data may be regularly deleted, keeping only the “most recent” values: in practice, a value Δt may be set, and only the values received between t_cur - Δ and t_cur are kept, t_cur being a current time. This advantageously reduces the number of data to be preserved, and avoids a saturation of the memory and a slowing down of the processing time.

Online processing advantageously makes it possible to detect a fault early, or to predict an error on the system. Offline processing may be used to retrospectively analyze a system where a fault has occurred. Offline processing may also be used in a predictive way, as the detection of a change in the signal may be the sign of a weakening of the system before the occurring of a fault.

Once sets of values 211, 212, 213, 214 are formed, a respective first measure of statistical dispersion δ_1, δ₂, δ₃, δ₄ may be computed for each set of values 211 , 212, 213, 214.

For instance, the first measure of statistical dispersion may be a variance or a standard deviation of the values of the sets 211, 212, 213, 214. It is recalled that the variance δ²(c₁, ...,x_N) and the standard deviation δ(x_1,...,x_N) of a set of values {x_1; ... , x_N} are parameters that quantify the dispersion of the values x_1, ...,x_N among their mean x = μ(x_1, ...,x_N). More the variance (or standard deviation) is high, more the values x_1; ...,x_N are spread out from their average value x.

These parameters may be calculated as follows:

Of course, other parameters may be used for computing the first measures of statistical dispersion δ_1, δ₂, δ₃, δ₄. For instance, the first measure of statistical dispersion δ_1, δ₂, δ₃, δ₄ may be a function of the variance or the standard deviation. In particular, such function may correspond to the unbiased sample variance δ ² (or its square root δ):

Alternatively, the first measures of statistical dispersion δ_1, δ₂, δ₃, δ₄ may be computed by using weighted variance or weighted standard deviation. Such parameters are computed from a data set {x_1; ...,x_N) by associating each value x_i with a respective weight w_i:

where, for i ∈ {1, ...,N},0 ≤ w_i ≤ 1 and

Weighted parameters advantageously allow, for instance, to assign higher weights to the most recent observations, and smaller weights to the less recent observations.

In other embodiments, first measures of statistical dispersion δ_1, δ₂, δ₃, δ₄ may be computed by using other dispersion parameters, such as (non-exhaustively): interquartile range (IQR), mean absolute difference (or Gini mean absolute difference), median absolute deviation (MAD), average absolute deviation, coefficient of variation, quartile coefficient of dispersion, relative mean difference, or any function of these parameters.

Once a group of first measures of statistical dispersion δ_1, δ₂, δ₃, δ₄ are determined, a second measure M₁ may be computed: this second measure M₁ may quantify the dispersion of the values of the group { δ_1, δ₂, δ₃, δ₄} of first measures of statistical dispersion.

The second measure M₁ may be computed by using similar parameters than the first measure of statistical dispersion δ_1, δ₂, δ₃, δ₄, or other parameters. For instance, in one embodiment, the first measure δ_i corresponds to the standard deviation of the corresponding set of values 211, 212, 213, 214, and the second measure corresponds to the standard deviation of the group of first measures { δ_1, δ₂, δ₃, δ₄}; and in another embodiment, the first measure δ_i corresponds to the standard deviation of the corresponding set of values 211, 212, 213, 214, and the second measure corresponds to the coefficient of variation of the group of first measures { δ_1, δ₂, δ₃, δ₄}.

In other words, the second measure M₁ may be computed as follows:

where:

• m is the number of sets of values; · Gi is the i-th set of values ( i being an integer index);

• DM¹(G _i) is the first measure of statistical dispersion determined for the set of values Gi;

• DM²{. ) is the second measure of statistical dispersion (determined for the m values DM¹(G_i) in the above formula). DM¹(. ) can be seen as a “local” measure of the signal dispersion, since it quantifies a dispersion of a set of signal samples during a given period of time. DM²{. ) can be seen a measure of the signal stability in time: it indicates the changes in the signal (changes of amplitude and/or frequency or period). More specifically, the second measure DM²{. ) becomes higher when a change occurs. Therefore, it also indicates a change in the state: during a stationary state, the value of M₁ is low, and when the signal enters a non-stationary state, the value of M₁ becomes higher.

Therefore, by comparing the value of the second measure of statistical dispersion M₁ to a threshold, it is possible to detect a change in the state of the system. For instance, the following detection rule may be applied: while the second measure of statistical dispersion M₁ is under a threshold, the system is in a stationary state, and when the second measure of statistical dispersion M₁ exceeds this threshold, the system enters a non-stationary states. It is then possible to send an alert to an external system (e.g. system administrator) or to perform specific actions (e.g. automatically shut down the machine).

The value of the second measure of statistical dispersion may be regularly updated based on new received values of the signal. In other words, the second measure of statistical dispersion may be seen as a function M(t) of time t, where the values of M(t) may be calculated at different times t, based on values

received during a time interval preceding t,.

Figure 3a illustrates the variation of the second measure of statistical dispersion in function of the signal state changes, in another possible embodiment of the invention. In particular, the graph at the top of Fig. 3a represents a signal s measured by an accelerometer located on a rotating machine, in which three changes of regime are observed at three respective times t₁, and t₃. The signal s represented in Fig. 3a comprises four stationary states having different properties (in particular, different amplitudes): a first stationary state before t₁, a second stationary state between t₁ and t₂, a third stationary state between t₂ and t₃ and a fourth stationary state after tz. The graph at the bottom of Fig. 3a represents the variations of the values of the second measure M(t) in function of time t.

As it appears on Fig. 3a, the graph of the function M : t → M(t) has three peaks, which corresponds to the changes of regime of the signal s. This graph illustrates how the second measure of statistical dispersion M(t) may be used for determining changes of stationary states of a signal of interest. Figure 3b illustrates the variation of the second measure of statistical dispersion in function of the signal state changes, in another possible embodiment of the invention. In particular, the graph at the top of Fig. 3b represents a signal s provided by a microphone placed nearby a rotating engine and measuring the sound produced by this engine. The signal s of Fig. 3b comprises several different regimes, as it can be seen on the graph. The middle graph of Fig. 3b represents the variations of the values of the first measure DM¹(t) in function of time t. In other words, the middle graph of Fig. 3b represents a statistical dispersion of the values of the signal s(t) in function of time t. Finally, the graph on the bottom of Fig. 3b represents the variations of the values of the second measure M(t) in function of time t.

As it appears on the middle graph of Fig. 3b, it is not possible to determine the changes of regime directly from the first measure of statistical dispersion DM¹. On the contrary, these changes appear on the graph of the second measure DM(t), in the form of peaks. In other words, when the second measure DM(t) exceeds a predetermined threshold, it may indicate a change of regime of the signal of interest.

Figure 4 is a flow chart of a method for determining stationary and/or non- stationary states of a system, in a possible embodiment.

At step 401, a plurality of sets of values G_i are received, each set of values G_i comprising at least one value of the signal of interest. These sets of values G_i correspond to references 211, 212, 213, 214 of Figure 2. For instance, as described with reference to Figure 2, the set of values G_i may be formed based on a sliding- windowing of the signal of interest.

At step 402, for each set of value G_i, a respective first measure DM¹(G_i) of statistical dispersion is computed as described above.

Then, at step 403, a second measure M₁ = DM²(DM¹(G₁),DM¹(G₂), ...) of statistical dispersion of a plurality of values G_i is computed as described above.

The computed second measure M₁ may then be compared to a threshold Th. If M₁ is below the threshold Th (arrow “N” in Figure 4), then no specific action is taken. New values of the second measure may be computed on a new set of observations, i.e. more recent observations than those use for computing the previous value of M₁). If M₁ is above the threshold Th (arrow Ύ” in Figure 4), then a specific action may be taken, for instance shutting down the machine or sending an alert message to an external system (step 405). In one or several embodiments, new values of the second measure may then be computed on a new set of observations as represented in Fig. 4.

It is noted that, in one or several embodiments, steps 401 - 402 - 403 may be iteratively repeated. Indeed, as new signal values are received, new set of values may be formed and received (step 401) for computing respective first measures of dispersion (step 402). A new value of the second measure may then be computed based on these new first measures of dispersion (step 403).

In one or several embodiments, the threshold Th may be a function of a parameter of statistical location of the first measures. For instance, Th may be function of a mean μ(DM¹(G₁), DM¹(G₂), ... ) of the first measures of dispersion. In one or several embodiments, the threshold may be given by:

Th = α x μ(DM¹(G¹)(G²), ... ) where α is a constant such as 0 < α ≤ 1.

In one or several embodiments, a may further be determined based on the nature of the signal of interest. For instance, it has been determined, in some examples, that a value a = 0.1 is particularly suitable for a vibration signal of an electrical motor or an electrical water pump. For a sound signal, a value a = 0.25 is more appropriate.

The value of a may be determined by using a mathematical optimization method. For instance, for a given situation (i.e. a specific type of signal measured in a specific system, such as a signal measured on an accelerometer located on a vibrating machine, or a sound signal measured by a microphone placed nearby a vibrating machine), a set of examples may be generated. It is therefore possible, based on this set of examples, to find extrema of a predefined metric.

In particular, the value of a may be determined based on machine learning methods. The set of examples represents the “learning set” from which the value of a suitable for this given situation is determined.

The determination of α may be performed by using a supervised learning method, such as Support Vector Machines (SVM) or Neural Networks. In this case, an expert may associate to each example of the learning set a label indicating a change of regime, e.g. a switch to a dangerous non-stationary state. Unsupervised or semi- supervised learning methods may also be used.

Other mathematical optimization methods may be used, e.g. a gradient descent method, or a brute-force search method.

For the determination of the threshold, parameters of statistical location other than the mean m may be used, such as mode, median, etc.

An implementation of a possible embodiment of the method of Figure 4 is given below:

1. Store a newly received sample s_n into a buffer buffer_s of signal samples; 2. Repeat step 1 while the number of samples in buffer_s is lower than a size max_buffer_s_size ;

3. Calculate the first measure of dispersion (for instance the standard deviation) on the values of buffer_s: std_i = std(buffer_s );

4. Store std_i into a second buffer buffer_std; 5. Repeat steps 1 to 4 until the number of values in buffer_std is lower than a size max_buffer_std_size ;

6. Calculate the second measure of dispersion (for instance the standard deviation) on the values of the second buffer: std_std = std(buffer_std);

7. If std_std is lower than or equal to a threshold Th, then the portion of signal observed during a time frame corresponding to the samples used for calculating std_std is stationary; and if std_std is greater than Th, then the portion of signal observed during a time frame corresponding to the samples used for calculating std_std is not stationary

In the above implementation, threshold Th may be determined as follows:

Th = α x mean(buffer_std ) where 0 < α ≤ 1. In case of a rotating machine, the value of max_buffer_s_size may be determined based on the frequency (or the period) of rotation, or the rotational speed of the machine. For instance, this frequency may correspond to a frequency in a “normal operation” of the system, which may be determined based on historical data or based on training observations.

For a signal having a “high” frequency / “low” period, the value of max_buffer_s_size may be chosen between 0.5 second to 3 seconds. For a signal having a “low” frequency / “high” period, the value of max_buffer_s_size may be chosen between 10 and 20 seconds. Also, the value of max_buffer_std_size may be chosen between 10 and 20 samples.

The categories “high / low frequency” (or equivalently “low / high period”) may be predetermined based on the type of the machine considered. For instance, for electrical motors, electrical pumps or similar rotating machines, frequencies between 0 and 10 Hz may be considered as low frequencies, and frequencies above 30 Hz may be considered as high frequencies. For example, in case of an electrical motor having a 3000 rpm (revolutions per minute) speed, which corresponds to a frequency of rotation equal to 50 Hz, the value of max_buffer_s_size may be chosen 0.5 second to 3 seconds, e.g. 1.5 seconds.

Figure 5 is a possible embodiment for a device that enables the present invention.

In this embodiment, the device 500 comprise a computer, this computer comprising a memory 505 to store program instructions loadable into a circuit and adapted to cause circuit 504 to carry out the steps of the present invention when the program instructions are run by the circuit 504. The memory 505 may also store data and useful information for carrying the steps of the present invention as described above.

The circuit 504 may be for instance:

- a processor or a processing unit adapted to interpret instructions in a computer language, the processor or the processing unit may comprise, may be associated with or be attached to a memory comprising the instructions, or

- the association of a processor / processing unit and a memory, the processor or the processing unit adapted to interpret instructions in a computer language, the memory comprising said instructions, or

- an electronic card wherein the steps of the invention are described within silicon, or

- a programmable electronic chip such as a FPGA chip (for « Field- Programmable Gate Array »). This computer may comprise an input interface 503 for the reception of values of the signal that are used for the above method according to the invention, and an output interface 506 for providing values of the second measure of dispersion. Optionally, the output interface 506 may be configured for transmitting an alert signal to an external system 507. To ease the interaction with the computer, a screen 501 and a keyboard 502 may be provided and connected to the computer circuit 504.

Expressions such as "comprise", "include", "incorporate", "contain", "is" and "have" are to be construed in a non-exclusive manner when interpreting the description and its associated claims, namely construed to allow for other items or components which are not explicitly defined also to be present. Reference to the singular is also to be construed in be a reference to the plural and vice versa.

A person skilled in the art will readily appreciate that various parameters disclosed in the description may be modified and that various embodiments disclosed may be combined without departing from the scope of the invention.

Claims

1. A method of determining changes in stationary states of a signal, said signal being relative to a physical quantity associated with a system, the method being performed by a computing device and comprising: receiving a plurality of sets of values, each set of values comprising at least one value of the signal; for each set of values among the plurality of sets of values, determining a respective first measure of statistical dispersion of said set of values; determining a second measure of statistical dispersion for a subset of first measures of statistical dispersion among the determined first measures of statistical dispersion; and determining an exit from a stationary state of the signal by comparing the determined second measure with a predetermined threshold.

2. The method of claim 1 , wherein the exit from the stationary state of the signal is determined when the determined second measure exceeds said threshold.

3. The method of claim 1 or 2, wherein the exit from the stationary state of the signal corresponds to a transition from a stationary state to a non-stationary state, or to a transition from a first stationary state to a second stationary state.

4. The method of any of the preceding claims, wherein the signal is obtained from a sensor related to the system, said sensor measuring said physical quantity.

5. The method of claim 4, wherein the sensor is one among: a proximity sensor, a velocity transducer, a displacement transducer, and an accelerometer.

6. The method of any of the preceding claims, further comprising: upon determining that the signal is a non-stationary state, emitting an alert message.

7. The method of any of the preceding claims, wherein the receiving of the plurality of sets of values, the determining of first measures of statistical dispersion and the determining of a second measure of statistical dispersion are iteratively repeated.

8. The method of any of the preceding claims, wherein the system comprises a rotating machine and the signal is a vibration signal of said rotating machine.

9. The method of any of the preceding claims, wherein the plurality of set of values correspond to values of the signal received during successive time-windows.

10. The method of claim 9, wherein the successive time-windows have a same length.

11. The method of claim 10, wherein the length of the successive time-windows is further function of a frequency of the signal in a normal operation of the system.

12. The method of any of claims 9 to 11, wherein the successive time-windows start at regularly spaced times.

13. The method of any of the preceding claims, wherein the first measure of statistical dispersion and/or the second measure of statistical dispersion is a function of a variance, or a function of a standard deviation.

14. The method of any of the preceding claims, wherein the threshold is function of a measure of statistical location of the determined first measures of statistical dispersion.

15. The method of claim 14, wherein the measure of statistical location is a mean of the determined first measures of statistical dispersion.

16. The method of claim 15, wherein the threshold Th is given by:

Th = α x μ_δ where: a is a constant such as 0 £ a £ 1 ; and μ_δ is the mean of the determined first measures of statistical dispersion.

17. The method of claim 16, wherein the constant a is determined by an optimization method based on a plurality of sets of training signal data, each set comprising a respective plurality of sets of values of the signal.

18. The method of claim 17, wherein the constant a is determined by a machine learning method.

19. A device for determining changes in stationary states of a signal, said signal being relative to a physical quantity associated with a system, the device comprising: an interface for receiving a plurality of sets of values, each set of values comprising at least one value of the signal; a circuit for determining, for each set of values among the plurality of sets of values, a respective first measure of statistical dispersion of said set of values; a circuit for determining a second measure of statistical dispersion for a subset of first measures of statistical dispersion among the determined first measures of statistical dispersion; and a circuit for determining an exit from a stationary state of the signal by comparing the determined second measure with a threshold.

20. A non-transitory computer readable storage medium, having stored thereon a computer program comprising program instructions, the computer program being loadable into a data-processing unit and adapted to cause the data-processing unit to carry out the methods of any of claims 1 to 18 when the computer program is run by the data-processing device.