Method for detecting time dependent modes of dynamic systems

• US 7,277,831 B1
• Filed: 09/11/1998
• Issued: 10/02/2007
• Est. Priority Date: 09/15/1997
• Status: Expired due to Fees

• Current Assignee: Fraunhofer Gesellschaft Zur Foerderung Der Angewandten Forsching E.V.
• Original Assignee: Fraunhofer Gesellschaft Zur Foerderung Der Angewandten Forsching E.V.
• Inventors: Müller, Klaus-Robert, Pawelzik, Klaus, Kohlmorgen, Jens
• Primary Examiner(s): Knight; Anthony
• Assistant Examiner(s): STEVENS, THOMAS H
• Application Number:
  US09/508,042
• Time in Patent Office: 3,308 Days
• Field of Search: 703/2, 703/13, 703/6, 703/11, 706/6, 706/16, 706/22, 706/44, 706/41, 706/14
• US Class Current: 703/2
• CPC Class Codes: A61B 5/369 Electroencephalography [EEG] devices for psychotechnics A61B5/16
• CPC Class Codes: A61B 5/372 Analysis of electroencephalograms
• CPC Class Codes: A61B 5/7267 involving training the classification device
• CPC Class Codes: G05B 13/027 using neural networks only
• CPC Class Codes: G05B 13/048 using a predictor
• CPC Class Codes: G05B 17/02 electric
• CPC Class Codes: G10L 25/12 the extracted parameters being prediction coefficients
• CPC Class Codes: G10L 25/30 using neural networks

Abstract

In a method for detecting the modes of a dynamic system with a large number of modes that each have a set α (t) of characteristic system parameters, a time series of at least one system variable x(t) is subjected to modeling, for example switch segmentation, so that in each time segment of a predetermined minimum length a predetermined prediction model, for example a neural network, for a system mode is detected for each system variable x(t), whereby modeling of the time series is followed by drift segmentation in which, in each time segment in which there is transition of the system from a first system mode to a second system mode, a series of mixed prediction models is detected produced by linear, paired superimposition of the prediction models of the two system modes.

Claims

1. A method performed on a computer for detecting modes of a dynamic system in a physical, chemical or biological process with a multiplicity of modes s_i that each have a set α

(t) of characteristic system parameters comprising the steps of;

performing a switch segmentation of a time series of at least one system variable x(t), in which the switch segmentation is a simulation of a training time series of the system or of the time series to be investigated with several, competing prediction models,

detecting predetermined prediction models f_i for system modes s_i for each system variable x(t) in each time segment of a predetermined minimum length,

deriving a system model by performing a drift segmentation subsequent to said switch segmentation in which, in each time segment in which there is a transition of the system from a first system mode s_i to a second system mode s_j, a series of mixed prediction models g_i is detected and produced by linear, paired superimposition of prediction models f_i,j of the two system modes s_i,j,

detecting a current system mode corresponding to a current state of the dynamic system; and

applying the derived system model to the detected current system mode to determine a state of the dynamic system in the physical, chemical or biological process, that directly follows the current state.

2. The method according to claim 1 in which the prediction models are formed by neural networks or other models for estimating functions that are each characteristic of a mode s and compete for description of individual elements of the time series according to predetermined training rules.

3. The method according to claim 1 in which the series of mixed system modes g_i is determined from the prediction models f_i,j and interpolation parameters a, b according to g_i=a(s)f_i(s)(x)+b(s)f_j(s)(x).

4. The method according to claim 1 in which the series of mixed prediction models g_i is detected by determining a prediction for each time increment with each possible prediction models, resulting in a time-dependent prediction matrix from which a mean prediction error for randomly selected segmentations can be derived, whereby a sought series of mixed prediction models g_i is the segmentation with a smallest prediction error or a maximum probability.

5. The method according to claim 1 in which drift segmentation is followed by an additional step to reduce a number of prediction models used for modeling where the number of prediction models is reduced sequentially, associated with a determination of a mean prediction error, until a further reduction of a number of prediction models means an increase in the prediction error.

6. The method according to claim 1 in which the time series of at least one of the system variables x(t) comprises a time series of physiological parameters described by the Mackey-Glass delay differential equation dx(t)/dt=−

0.1x(t)+0.2x(t−

t_d)/1+x(t−

t_d)¹⁰.

7. The method according to claim 1 in which the time series of at least one of the system variables x(t) comprises a time series of physiological parameters that are characteristic of a development of sleep and wake modes.

8. The method according to claim 1 in which the time series of at least one of the system variables x(t) comprises a time series of speech signals.

9. The method according to claim 3 in which the interpolation parameters are selected according to 0<

a(s)<

1 and b(s)=1−

a(s).

10. The method according to claim 9 in which the values a(s) are restricted to a certain resolution figure R.

11. The method according to claim 9 in which values a(s) are equidistant.

12. The method according to claim 4 in which a search for the segmentation with the smallest prediction error is made by a dynamic programming technique that is equivalent to a Viterbi algorithm for hidden Markov models, whereby an optimum sequence of prediction models is determined using a minimized cost function C* of the prediction and the segmentation is derived inductively from the sequence of prediction models.

13. The method according to claim 7 in which the physiological parameters comprise EEG signals.

14. A method performed on a computer for detecting modes of a dynamic system in a physical, chemical or biological process with a multiplicity of modes s_i that each have a set α

(t) of characteristic system parameters comprising the steps of;

performing a switch segmentation of a time series of at least one system variable x(t), in which the switch segmentation is a simulation of a training time series of the system or of the time series to be investigated with several, competing prediction models,

detecting predetermined prediction models f_i for system modes s_i for each system variable x(t) in each time segment of a predetermined minimum length,

deriving a system model by performing a drift segmentation subsequent to said switch segmentation in which, in each time segment in which there is a transition of the system from a first system mode s_i to a second system mode s_j, a series of mixed prediction models g_i is detected and produced by linear, paired superimposition of prediction models f_i,j of the two systems modes s_i,j, and

controlling said dynamic system in the physical, chemical or biological process, via determining a deviation of a current state of said dynamic system from a setpoint state using the derived system model and deriving a control strategy on the basis of said deviation.

15. The method according to claim 14 in which the prediction models are formed by neural networks or other models for estimating functions that are each characteristic of a mode s and compete for description of individual elements of the time series according to predetermined training rules.

16. The method according to claim 14 in which the series of mixed system modes g_i is determined from the prediction models f_i,j and interpolation parameters a, b according to g_i=a(s)f_i(s)(x)+b(s)f_j(s)(x).

17. The method according to claim 14 in which the series of mixed prediction models g_i is detected by determining a prediction for each time increment with each possible prediction models, resulting in a time-dependent prediction matrix from which a mean prediction error for randomly selected segmentations can be derived, whereby a sought series of mixed prediction models g_i is segmentation with a smallest prediction error or a maximum probability.

18. The method according to claim 14 in which drift segmentation is followed by an additional step to reduce a number of prediction models used for modeling where the number of prediction models is reduced sequentially, associated with a determination of a mean prediction error, until a further reduction of the number of prediction models means an increase in the prediction error.

19. The method according to claim 14 in which the time series of at least one of the system variables x(t) comprises a time series of physiological parameters described by a Mackey-Glass delay differential equation dx(t)/dt=−

0.1x(t)+0.2x(t−

t_d)/1+x(t−

t_d)¹⁰.

20. The method according to claim 14 in which the time series of at least one of the system variables x(t) comprises a time series of physiological parameters that are characteristic of a development of sleep and wake modes.

21. The method according to claim 14 in which the time series of at least one of the system variables x(t) comprises a time series of speech signals.

22. The method according to claim 16 in which the interpolation parameters are selected according to 0<

a(s)<

1 and b(s)=1−

a(s).

23. The method according to claim 17 in which a search for the segmentation with the smallest prediction error is made by a dynamic programming technique that is equivalent to a Viterbi algorithm for hidden Markov models, whereby an optimum sequence of prediction models is determined using a minimized cost function C* of the prediction and the segmentation is derived inductively from a sequence of prediction models.

24. The method according to claim 20 in which the physiological parameters comprise EEG signals.

25. The method according to claim 22 in which the values a(s) are restricted to a certain resolution figure R.

26. The method according to claim 22 in which values a(s) are equidistant.