Data processing: artificial intelligence – Machine learning
Reexamination Certificate
1997-10-30
2001-04-10
Powell, Mark (Department: 2122)
Data processing: artificial intelligence
Machine learning
C701S111000, C701S096000
Reexamination Certificate
active
06216118
ABSTRACT:
The contents of a Patent Application Heisei 8-289658, with a filing date of Oct. 31, 1996 in Japan, are herein incorporated by reference.
BACKGROUND OF THE INVENTION
a) Field of the invention
The present invention relates to a method and apparatus for discriminating a time series data, particularly and, relates to a method and apparatus for discriminating whether the time series data is based on a determinism (,e.g., deterministic signal) or based on a stochastic process (,e.g., random signal).
b) Description of the Related Art
For example, in a rotary mechanical system, when a shaft vibration is abnormal, the observed time series data is synthesized with those based on the determinism and with those based on a stochastic process such as random noises.
It is frequent that irregular-looking time series data may be caused by determining dynamics, and also well known that it is called deterministic chaos. Nowadays, even if the time series data observed from a system has a little noise, it is not always easy, by eye, to recognize whether or not it has some noise. To solve this issue, in general, there is a method of extracting some characteristic frequency by FFT (Fast Fourier Transformation) analysis. But chaotic time series is composed of an infinite number of frequency elements, and give rise to a broad continuous power spectrum.
The characteristic determining method described above using the FFT analyzing method will briefly be described below.
That is to say, at a first step, the time series data observed from the rotary mechanical system is derived from an observer.
At a second step, the observed time series data are analyzed using the FFT analyzer.
At a third step, from the result of spectrum analysis using the FFT analyzer, a characteristic frequency is selected.
At a fourth step, the selected characteristic frequency value is compared with an analyzed value of a normal data which is previously spectrum analyzed using the FFT analyzer.
Finally, the spectrum analyzer determines whether the selected value of the characteristic frequency at the third step is normal or abnormal according to the result of the comparison at the fourth step.
A U.S. Pat. No. 5,576,632 issued on Nov. 19, 1997 exemplifies the FFT analysis for a measurement for a motor current.
SUMMARY OF THE INVENTION
As described above in the BACKGROUND OF THE INVENTION, the method for extracting the characteristic frequency from the time series data through the spectrum analysis using the FFT analyzer cannot clearly discriminate whether the time series data is based on the determinism or based on the stochastic process.
For example, as a result that the spectrum analysis using the FFT analyzer is carried out after the characteristic data of the time series data on a Rössler chaos as a representative of the deterministic chaos (refer to
FIGS. 9A and 10A
) is compared with the characteristic data of the time series data on the Rössler chaos to which an element of a stochastic process system (10% of the white noise) is added (refer to FIGS.
9
B and
10
B), no clear difference between the results of the FFT spectrum analysis for the time series data to which no white noise is added or to which 10% white noise is added is obtained as shown in
FIGS. 11A and 11B
and
FIGS. 12A and 12B
.
Consequently, it was indicated that the discrimination between the time series data in the deterministic system and in the stochastic process system was clearly difficult.
Hence, the abnormality in the shaft vibration cannot clearly be detected even if the spectrum analysis using the FFT analyzer is carried out to detect the abnormality in the shaft vibration of the rotary mechanical system.
It is therefore an object of the present invention to provide a method and apparatus for discriminating the time series data which can accurately discriminate whether the time series data is based on the determinism or based on the stochastic process.
The above-described object can be achieved by providing a method for discriminating a time series data observed from a dynamical system, comprising the steps of:
a) embedding the time series data y(t) in an n-dimensional reconstructed state space;
b) selecting an arbitrary data vector Xi from trajectories of the embedded time series data;
c) selecting, in terms of Euclidian distance, m data vectors Xj (j=1, 2, - - - , m) neighboring to the selected data vector Xi;
d) deriving tangential unit vectors Ti and Tj with respect to the data vectors Xi and Xj;
e) calculating variations in directions relative to the tangential unit vectors Tj of the neighboring data vectors by referring to the tangential unit vectors Ti as follows:
γ
i
=
1/4
m
×
∑
j
m
&LeftDoubleBracketingBar;
Ti
-
Tj
&RightDoubleBracketingBar;
2
;
f) iterating the calculation of &ggr;; at the previous step for a predetermined sample number k which corresponds to subspaces to derive a mean value &Ggr;:
Γ
=
1/
k
∑
i
k
γ
i
;
g) determining whether &Ggr;≈0; and
h) discriminating whether the observed time series data is deterministic chaos or a stochastic process according to a result of determination on the mean value &Ggr;.
The above-described object can also be achieved by providing an apparatus for discriminating a time series data observed from a dynamical system, comprising:
a) means for embedding the time series data y(t) in an n-dimensional state space;
b) means for selecting an arbitrary data vector Xi from trajectories of the embedded time series data;
c) means for selecting, in terms of Euclidian distance, m data vectors Xj (j=1, 2, - - - , m) neighboring to the selected data vector Xi;
d) means for deriving tangential unit vectors Ti and Tj with respect to the data vectors Xi and Xj;
e) means for calculating variations in directions relative to the tangential unit vectors Tj of the neighboring data vectors by referring to the tangential unit vectors Ti as follows:
γ
i
=
1/4
m
×
∑
j
m
&LeftDoubleBracketingBar;
Ti
-
Tj
&RightDoubleBracketingBar;
2
;
f) means for iterating the calculation of &ggr;; at the calculating means for a predetermined sample number k which corresponds to subspaces to derive a mean value &Ggr;:
Γ
=
1/
k
∑
i
k
γ
i
;
g) means for determining whether &Ggr;≈0; and
h) means for discriminating whether the observed time series data is deterministic chaos or a stochastic process according to a result of determination on the mean value &Ggr;.
The above-described object can also be achieved by providing an apparatus for discriminating a time series data observed from a dynamical system constituting a vehicular automatic transmission, said apparatus comprising:
a) a detector for observing a shaft vibration sound of the automatic transmission;
b) a converter for converting the shaft vibration sound into a digital discrete signal;
c) a first processor for providing the time series data y(t) according to the digital discrete signal;
d) a second processor for embedding the time series data y(t) in an n-dimensional state space;
e) a first selector for selecting an arbitrary data vector Xi from trajectories of the embedded time series data;
f) a second selector for selecting, in terms of Euclidian distance, m data vectors Xj (j=1, 2, - - - , m) neighboring to the selected data vector Xi;
g) a first calculator for deriving tangential unit vectors Ti and Tj with respect to the data vectors Xi and Xj;
h) a second calculator for calculating variations in directions relative to the tangential unit vectors Tj of the neighboring data vectors by referring to the tangential unit vectors Ti as follows:
γ
i
=
1/4
m
×
∑
j
m
&LeftDoubleBracketingBar;
Ti
-
Tj
&RightDoubleBracketingBar;
2
;
i) a third calculator for iterating the calculation of &ggr;; at the seco
Fujimoto Yasunari
Iokibe Tadashi
Foley & Lardner
Kabushiki Kaisha Meidensha
Powell Mark
Starks Wilbert
LandOfFree
Apparatus and method for discriminating a time series data does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Apparatus and method for discriminating a time series data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Apparatus and method for discriminating a time series data will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-2520637