JP2014170270A - Analysis device and analysis method for time series data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To detect a characteristic of a phase for time series data which has the characteristic in the period and the phase based on the period.SOLUTION: An analysis device 1 includes a sine wave superposition section 6, an attractor constitution section 7, and an orbit parallel measurement calculation section 8. The sine wave superposition section 6 acquires time series data accumulated in a time series data accumulation section 5, and superposes a sine wave of a preset frequency on the acquired time series data. The attractor constitution section 7 performs embedding processing in a preset delay time and an embedding dimension for sine wave superposition time series data on which the sine wave is superposed, and constitutes an attractor. The orbit parallel measurement calculation section 8 obtains an orbit parallel measurement of the constituted attractor. The time series data is evaluated on the basis of the attractor or the orbit parallel measurement.

Description

  The present invention relates to a chaos analysis technique for time series data.

  In order to ensure the sustainability of plant facilities and equipment in the industrial field, it is required to appropriately maintain and manage the plant equipment and equipment. In particular, detecting abnormalities and failures in plant facilities and equipment as soon as possible and taking appropriate measures is an indispensable element not only for reducing maintenance costs but also for ensuring the safety and security of users.

  In order to efficiently perform abnormality detection and abnormality prediction of these plant facilities and equipment, a method for analyzing based on chaos theory for time series data detected by the plant equipment and equipment has been proposed (for example, Patent Document 1, Non-Patent Document 1). In the analysis based on the chaos theory, the measured time series data is reconstructed by embedding it in the time delay coordinate system, and the attractor is drawn (for example, Non-Patent Document 2). As described in Non-Patent Document 2, there is a method for determining the delay time and the embedding dimension required for the reconstructed attractor to appropriately represent the original dynamic system, and the delay time used for embedding is usually It is determined based on the main period of the time series data and the autocorrelation function.

  Then, as described in Patent Document 1, the trajectory parallel measure is calculated by quantifying the degree of alignment of the trajectory direction of the time series data in the vicinity of each point of the reconstructed attractor, and the calculated trajectory parallel measure is calculated. Based on this, the time series data is evaluated.

  Time-series data measured by plant equipment and equipment may be characterized by a specific period determined from measurement conditions and a phase based on that period. For example, AE signals and UHF signals measured by electrical equipment to measure partial discharge are characterized by a phase based on the power supply frequency because environmental noise from partial discharge and electrical equipment is generated with voltage fluctuation. Get out. Further, the vibration data measured for diagnosing the bearing state of the rotating machine is characterized by a phase based on the rotation frequency because vibration is generated as the rotating machine rotates.

Japanese Patent No. 3785703

Tomoyuki Hamada, Takanori Hayashi, “Sequential orbit parallel measure method for detecting anomalies from time series data”, 2012 Annual Conference of the Institute of Electrical Engineers of Japan, March 2012, pp. 146-147 Kazuyuki Aihara, “Basics and Applications of Chaos Time Series Analysis”, Sangyo Tosho, November 2000

  However, in the analysis method based on the conventional chaos theory, since the measured time series data is reconstructed into the attractor, the reference frequency set in the external condition is not reflected in the attractor. Even if the delay time is set based on the reference frequency, points corresponding to the phases of the reference frequency are disturbed on the reconstructed attractor, and it is difficult to read and understand the phase characteristics. Since the phase feature is difficult to be reflected in the attractor, it is difficult to read the phase feature based on the orbit parallel measure even when the orbit parallel measure is calculated based on the attractor.

  In view of the above circumstances, an object of the present invention is to provide a chaos analysis technique that contributes to detecting a phase characteristic of time series data having a characteristic of a period and a phase based on the period. Yes.

  The time series data analysis apparatus of the present invention that achieves the above object, the analysis method by this analysis apparatus, and the program for causing a computer to function as each means of this analysis apparatus are provided for time series data having periodic characteristics. A feature is that a sine wave having the same frequency as the period that is characteristic of the time series data is superimposed, and the time series data on which the sine wave is superimposed is embedded in the n-dimensional state space.

  According to the present invention, in the time-series data analysis technique using the chaos analysis method, it contributes to detecting the phase feature of the time-series data having the phase and the phase based on the cycle. can do.

It is a schematic diagram of a time series data analysis device concerning an embodiment of the present invention. It is a flowchart explaining the process sequence of the time series data analyzer which concerns on embodiment of this invention. (A) The figure which shows the time series data measured under an inverter noise environment, (b) The figure which shows the attractor which embedded the time series data measured under the inverter noise environment in the three-dimensional state space. It is a figure which shows the time series data containing the waveform based on inverter noise, (a) The figure which shows the time series data input into an analyzer, (b) The time series data input into an analyzer, and a to-be-measured object The figure which displayed the sine wave of the same frequency as the power supply frequency of the electric equipment superimposed, (c) The sine wave of the same frequency as the power supply frequency of the electric equipment to be measured is superimposed on the time series data input to the analysis device It is a figure which shows the time series data made to do. It is a figure which shows the attractor which embedded the time series data shown in FIG.4 (c) in the three-dimensional state space. It is a figure which shows the time series data containing the waveform based on partial discharge, (a) The figure which shows the time series data input into an analyzer, (b) The time series data input into an analyzer, and a to-be-measured object The figure which displayed the waveform of the same frequency as the power supply frequency of the electric equipment, (c) The waveform of the same frequency as the power supply frequency of the electric equipment to be measured was superimposed on the time series data input to the analysis device It is a figure which shows time series data. It is a figure which shows the attractor which embedded the time series data shown in FIG.6 (c) in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (amplitude 1 time), (b) The figure which shows the attractor which embedded the sine wave superposition time series data (amplitude 1 time) in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (2 times amplitude), (b) The figure which shows the attractor which embedded the sine wave superposition time series data (2 times amplitude) in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (amplitude 5 times), (b) The figure which shows the attractor which embedded the sine wave superposition time series data (amplitude 5 times) in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (amplitude 10 times), (b) The figure which shows the attractor which embedded the sine wave superimposition time series data (amplitude 10 times) in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (amplitude 20 times), (b) The figure which shows the attractor which embedded the sine wave superposition time series data (amplitude 20 times) in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (amplitude 50 times), (b) The figure which shows the attractor which embedded the sine wave superimposition time series data (amplitude 50 times) in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (amplitude 100 times), (b) The figure which shows the attractor which embedded the sine wave superposition time series data (amplitude 100 times) in the three-dimensional state space. (A) The figure which shows the sine wave superimposed on time series data, (b) The figure which shows the attractor which embedded the sine wave in the three-dimensional state space. (A) The figure which shows sine wave superimposition time series data (amplitude 1 time, frequency 25 times), (b) The attractor which embedded the sine wave superposition time series data (amplitude 1 time, frequency 25 times) in the three-dimensional state space. FIG. (A) The figure which shows sine wave superimposition time series data (amplitude 1 time, frequency 10 times), (b) The attractor which embedded the sine wave superposition time series data (amplitude 1 time, frequency 10 times) in the three-dimensional state space. FIG. (A) A diagram showing sinusoidal superimposed time series data (2 times amplitude, 10 times frequency), (b) an attractor in which sinusoidal superimposed time series data (2 times amplitude, 10 times frequency) is embedded in a three-dimensional state space. FIG.

  A time-series data analysis apparatus, analysis method, and program according to an embodiment of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a diagram showing an outline of a time-series data analysis apparatus 1 according to an embodiment of the present invention.

  As shown in FIG. 1, time-series data is input from the measurement target 2 to the analysis apparatus 1, and the analysis result of the analysis apparatus 1 is output to the output unit 3.

  The measurement target 2 is, for example, an electric device such as a transformer, a switchgear, or a rotating machine. A sensor or the like is installed in the measurement target 2, and time series data such as light emission, heat generation, pulse current, electromagnetic wave, and ultrasonic wave detected by the sensor or the like is transmitted to the analysis device 1. Note that the time series data input to the analysis apparatus 1 may be a file or the like in which time series data collected in advance is stored.

  The output unit 3 is, for example, a display or printer that outputs the analysis result of the analysis device 1, a storage that stores the analysis result of the analysis device 1, or the like. Based on the output of the output unit 3, the time series data is confirmed and evaluated, or the analysis result is used for another purpose (for example, output of an alarm notifying that an abnormality has occurred in the waveform).

  The analysis device 1 includes a time-series data collection unit 4, a time-series data storage unit 5, a sine wave superimposing unit 6, an attractor configuration unit 7, a trajectory parallel measure calculation unit 8, and a setting / control unit 9.

  The time series data collection unit 4 appropriately collects time series data from the measurement target 2.

  The time series data storage unit 5 stores the collected time series data. The accumulated time series data is used for analysis by sine wave superposition.

  The sine wave superimposing unit 6 acquires the time series data stored in the time series data storage unit 5 and superimposes a sine wave having a preset frequency on the acquired time series data. When the time series data has periodic characteristics, the sine wave superimposing unit 6 superimposes a sine wave having the same frequency as that period on the time series data. For example, when the measurement target 2 is an electrical device, a sine wave having the same frequency as the frequency of the power supply voltage of the electrical device is superimposed on the time-series data. Further, when the measurement target 2 is a rotary shaft, a sine wave having the same frequency as the rotation cycle of the rotary shaft is superimposed. Although it is desirable to match the frequency of the superimposed sine wave with the frequency of the original time series data as accurately as possible, the phase of the sine wave need not necessarily match the phase of the time series data. This is because the periodic feature can be grasped even when the phase is shifted. Moreover, the amplitude of the superimposed sine wave is, for example, about 1 to 100 times, more preferably 2 to 20 times the maximum amplitude of the time-series data that is the analysis target signal.

  The attractor constructing unit 7 performs embedding processing on the sine wave superimposed time series data on which the sine wave is superimposed by the sine wave superimposing unit 6 with a preset delay time and embedding dimension, thereby configuring the attractor. At this time, if the delay time is set to be a fraction of the number of samplings in one cycle of the power supply frequency, the analysis becomes easy. The embedded dimension n (n is a positive integer) can be 3 to 5 dimensions, for example, so that time-series data can be analyzed. In addition, when displaying an attractor on an output part, the attractor structure part 7 also produces | generates the projection expression to two dimensions or three dimensions.

  The track parallel measure calculation unit 8 obtains the track parallel measure from the attractor configured by the attractor configuration unit 7. The trajectory parallel measure calculation unit 8 obtains the tangent direction (unit tangent vector) of the trajectory in the arbitrary data vector selected from the attractor and the data vector in the vicinity of this data vector, and the degree of similarity in the direction of the obtained tangential direction Is calculated as a trajectory parallel measure. A detailed calculation method of the orbit parallel measure is described in Patent Document 1 and Non-Patent Document 1. For example, as described in Non-Patent Document 1, when acquiring a sequential data vector from acquired time series data and calculating a trajectory parallel measure in the acquired data vector, the average value within a predetermined range It is also possible to evaluate the orbital parallel measure of the attractor using a statistic such as the median.

  The setting / control unit 9 inputs and stores parameters set in each unit of the analysis apparatus 1. The setting / control unit 9 sets parameters stored in advance in each unit (the sine wave superimposing unit 6, the orbit parallel measure calculation unit 8, and the like), and controls each unit of the analysis apparatus 1.

[Example]
With reference to FIG. 2, the analysis procedure of the time series data by the analysis apparatus 1 will be described.

First, as preparation for analysis, analysis conditions of the analysis apparatus 1 are set in the setting / control unit 9. Examples of the setting items include the following items.
-Measurement cycle (frequency): Specify the measurement interval. In the example, it was set to 500 kHz.
• Sine wave frequency: Set the frequency of the sine wave to be superimposed. In the example, the frequency was set to 50 Hz, which is the frequency of the power supply voltage of the electrical device to be measured.
-Sine wave superposition ratio: The magnitude of the amplitude of the sine wave to be superposed on the time-series data input to the analysis apparatus 1 is determined.
-Embedding dimension: Sets the dimension used when constructing an attractor from sinusoidal superimposed time series data. The embedding dimension can be arbitrarily set as long as it is an integer of 2 or more. However, if the number of dimensions is too small, the structure of the phenomenon cannot be reflected, and if the number of dimensions is too large, the calculation load increases. In the embodiment, it is set to five dimensions. In addition, when outputting an attractor to the output part 3, the attractor was comprised in five dimensions, and the attractor was output by projecting in three dimensions by the output part 3. FIG.
・ Delay time: Set the delay time used when constructing an attractor from sine wave superimposed time series data. In the example, 1000 was set.
• Number of reference neighbors: Specify the number of reference neighbors used when calculating the orbital parallel measure. In the example, it was set to 5.
Output range: Sets the period of the attractor displayed on the output unit 3. For example, about 2 to 5 cycles are displayed in the cycle of the superimposed sine wave. In the example, three periods are displayed.
-Output axis: Determines the display dimension of the attractor. In the embodiment, it is set to three dimensions.

After setting the setting items in the setting / control unit 9, time series data was input to the analysis apparatus 1, and the input time series data was analyzed according to the steps S1 to S7 shown below.
<Step S1> Analysis of time series data is started for each designated measurement cycle.
<Step S <b>2> The time series data collection unit 4 acquires time series data from the measurement target 2. Then, the acquired time series data is stored in the time series data storage unit 5.
<Step S3> The sine wave superimposing unit 6 obtains newly measured time series data from the time series data storage unit 5, superimposes the sine wave at the set frequency and superposition ratio, and newly added sine wave The sine wave superimposed time series data including the superimposed time series data is updated. Here, superimposing means adding a value of a sine wave at a corresponding phase to each value in time series. This phase is determined from the measurement frequency, the sine wave frequency, and the sine wave phase at the start of measurement. Here, the sine wave phase at the start of measurement is set to zero.
<Step S4> The attractor constructing unit 7 acquires the newly added sine wave superimposed time series data, performs the embedding process with the set embedding dimension and delay time, and updates the attractor reflecting the additional data.
<Step S5> The track parallel measure calculation unit 8 calculates and updates the track parallel measure from the attractor reflecting the additional data. When the sequential orbit parallel measure method is used, the orbit parallel measure of the portion corresponding to the newly added data is calculated.
<Step S6> The attractor configuration unit 7 updates the projection of the attractor according to the specified output shaft and output range. The orbit parallel measure calculation unit 8 outputs time series data of the calculated orbit parallel measure according to the designation of the output range. The output format output to the output unit 3 is easy to understand visually if the attractor is a two-dimensional or three-dimensional plot, and the orbital parallel measure is a time-series line graph, but the output format is not limited to this. .
<Step S7> If time-series data still remains in the output range (in the case of arrow NO in the figure), steps S1 to S6 are repeated again to analyze the time-series data. If all the time series data within the output range has been analyzed (in the case of arrow YES in the figure), the analysis result is output to the output unit 3. Examples of the analysis result to be output include an attractor, an orbit parallel measure, an alarm when the orbit parallel measure exceeds a threshold, and the like.

  Next, a specific analysis example will be shown, and the time series data analysis apparatus and analysis method of the present invention will be described in detail. In the analysis example, an AE sensor is provided in an electrical device (transformer), and time series data detected by the AE sensor is analyzed by a chaos analysis technique. Examples of signals detected by the AE sensor include a signal based on partial discharge and a signal based on inverter noise. It is known that the partial discharge signal and the inverter noise signal vary according to the power supply frequency of the electric device.

  When an attractor is constructed from time-series data (envelope processed) detected by an electric device under an inverter noise environment shown in FIG. 3A, the attractor is intricately entangled as shown in FIG. 3B. It is difficult to find periodic feature points based on attractors.

  Therefore, as shown in FIGS. 4A to 4C, the time series data detected by the electric equipment under the inverter noise environment (FIG. 4A) has the same frequency as the power supply frequency of the electric equipment. When a sine wave (FIG. 4B) is superimposed, sine wave superimposed time series data (FIG. 4C) is obtained. When the attractor is constructed from the sine wave superimposed time series data, as shown in FIG. 5, the attractor is drawn in a deformed circle.

  The attractor shown in FIG. 5 is configured based on time-series data having a power supply frequency of slightly more than 3 cycles. One round of the attractor represents one cycle of the power supply frequency, and it can be seen from the drawn attractor that the trajectories of these three cycles are almost overlapped. That is, it can be easily understood that the time series data shown in FIG. 4A has periodicity only by looking at the shape of the attractor.

  Also, as shown in FIGS. 6A to 6C, the time series data (FIG. 6A) detected by the electrical device in which the partial discharge has occurred is the same as the power supply frequency of the electrical device. When a frequency sine wave (FIG. 6B) is superimposed, sinusoidal superimposed time series data (FIG. 6C) is obtained. When the attractor is constructed from the sine wave superimposed time series data, as shown in FIG. 7, the attractor is drawn in a deformed circle.

  As shown in FIG. 7, the time-series data based on the partial discharge fluctuates according to the power supply frequency of the electric equipment, but the orbits of the respective periods do not overlap like the inverter noise shown in FIG. It is understood that has occurred. Therefore, based on the shape of the attractor, it can be easily determined from the time series data that partial discharge has occurred. This cannot be easily determined by simply comparing the time series data shown in FIG. 4A and the time series data shown in FIG.

  In this way, by configuring the attractor after superimposing the sine wave, it is possible to obtain information on the phase at a specific period that cannot be found with the same attractor configuration.

  The same can be said for the case of analyzing time-series data based on the trajectory parallel measure. That is, the trajectory parallel measure calculated from attractors that draw nearly overlapping trajectories is small, and the periodicity appears as a small trajectory parallel measure. Further, as shown in FIG. 7, when there is a “fluctuation” in the phase in a periodic attractor, the trajectories intersect and the trajectory parallel measure increases. That is, it is possible to detect the time series data “fluctuation” (that is, detect the partial discharge) based on the orbit parallel measure calculated from the sine wave superimposed time series data.

  Here, the amplitude of the sine wave superimposed on the time series data will be examined. If the amplitude of the sine wave is much larger than the amplitude of the time-series data, the characteristics of the original time-series data are almost hidden, which is not preferable. Further, if the amplitude of the sine wave is smaller than the amplitude of the time series data, the time series data and the orbit of the sine wave may intersect, which is not preferable. Therefore, we examined the amplitude of the sine wave superimposed on the time series data in the chaos analysis technology.

  In FIG. 8A, a sine wave having the same amplitude as the maximum amplitude value of the time series data is superimposed on the time series data detected in the inverter noise environment (time series data shown in FIG. 4A). FIG. 8B shows an attractor obtained from this sine wave superimposed time series data. As shown in FIG. 8B, it can be seen that when a sine wave having the same amplitude as the maximum amplitude value of the time-series data is superimposed, attractors that overlap periodically can be obtained.

  9 (a) to 14 (a), the time series data detected in the inverter noise environment (time series data shown in FIG. 4 (a)) is doubled the maximum amplitude value of this time series data, Sine wave superimposed time series data when sine waves having amplitudes of 5 times, 10 times, 20 times, 50 times, and 100 times are superimposed are respectively shown in FIGS. 9B to 14B. The attractor obtained from sine wave superimposition time series data is shown. As shown in FIGS. 9B to 14B, by increasing the amplitude of the sine wave superimposed on the time-series data, the attractor when the drawn shape of the attractor is only a sine wave (FIG. 15 ( As shown in b).

  Depending on the type of time-series data, even when a sine wave having the same amplitude as the maximum amplitude value of the time-series data is superimposed, the attractors cross and visually understand the periodicity of the time-series data. May be difficult to do. Even in such a case, the amplitude of the superimposed sine wave can be increased so that the time series data can be easily analyzed. For example, as shown in FIGS. 16A and 16B, an attractor (FIG. 16B) obtained from time-series data obtained by superimposing a sine wave having the same amplitude on time-series data does not have overlapping trajectories. Time series data can be analyzed. On the other hand, as shown in FIG. 17 (a), even with an attractor (FIG. 17 (b)) obtained from time-series data obtained by superimposing a sine wave of the same amplitude on time-series data, the trajectories overlap and the time-series data It may be difficult to analyze the data. Also in this case, as shown in FIGS. 18A and 18B, it is easy to grasp the periodic characteristics by increasing the amplitude of the superimposed sine wave.

  As apparent from the analysis results shown in FIGS. 8 to 18, the amplitude of the sine wave superimposed on the time series data is 1 to 100 times, more preferably 2 times the maximum amplitude value of the original time series data. By setting the magnification to 20 times, it is possible to detect the periodic characteristics of the time series data.

  As described above, according to the time-series data analysis apparatus and analysis method of the present invention, in the technique for analyzing time-series data by the chaos analysis method, the periodic characteristics of the time-series data are reflected in the attractor or the orbit parallel measure. Can be made.

  That is, in the conventional chaos analysis technology, the attractor did not have a viewpoint for obtaining the characteristics related to the phase of the specific frequency reference, but according to the time series data analysis device and the analysis method of the present invention, the characteristics related to the phase of the specific frequency reference are provided. It can be expressed visually. In addition, characteristics relating to the phase of the specific frequency reference can be evaluated based on the orbit parallel measure.

  As a result, it is possible not only to clearly distinguish between periodic features and non-periodic features, but also to compare periodic features.

  Note that the analysis apparatus according to the embodiment configured as described above is realized by, for example, reading a predetermined program into a computer including a ROM, a RAM, a CPU, and the like, and executing the program by the CPU. Is.

  Each unit in the apparatus may be configured by executing a predetermined program on a computer, or at least a part of the processing contents may be realized in hardware. For example, the time-series data storage unit 5 is constructed as storage means / storage means such as a hard disk or RAM.

  When the processing means in the above apparatus is realized by a computer, the processing contents of the functions that each apparatus should have are described by a program. Then, by executing this program on the computer, the processing means in each apparatus is realized on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. Examples of the computer-readable recording medium include a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory. Specifically, a hard disk device, a flexible disk, a magnetic tape or the like as a magnetic recording device, and a DVD (Digital Versatile Disc), a DVD-RAM (Random Access Memory), or a CD-ROM (Compact Disc Read Only Memory) as an optical disk. , CD-R (Recordable) / RW (ReWritable), etc. can be used as magneto-optical recording media, MO (Magneto Optical disc) can be used, and flash memory can be used as semiconductor memory.

  The program is distributed via a portable recording medium such as a DVD or a CD-ROM on which the program is recorded. Alternatively, the program may be distributed by storing the program in a recording device of the server computer and transferring the program from the server computer to another computer via a network.

  Note that the time-series data analysis apparatus and analysis method of the present invention are not limited to the above-described embodiment, and can be appropriately designed and modified without departing from the operation and effect thereof. The form also belongs to the technical scope of the time series data analysis apparatus and analysis method of the present invention.

  For example, in the embodiment, the sine wave superimposed time series data is configured in the attractor, the periodic characteristics of the time series data are grasped based on the attractor, and the trajectory parallel measure of the attractor is calculated. The calculation of the measure is optional, and the time series data may be evaluated based only on the attractor. Further, the time series data may be evaluated based on the calculation result of the orbit parallel measure without displaying the attractor.

  Also, every time series data is added, the display on the output unit is updated, and old data is removed from the display on the output unit. Attractor) can be drawn on the output section.

  In the description of the embodiment, the example of analyzing time-series data detected from plant facilities and equipment has been described. However, the time-series data analysis apparatus and analysis method of the present invention have periodic characteristics. The analysis can be performed by applying to any time-series data.

  In the description of the embodiment, the attractor in which the time series data is embedded in the five-dimensional state space is projected in three dimensions and output to the output unit. Alternatively, an attractor obtained by embedding in a three-dimensional state space may be directly output to the output unit.

DESCRIPTION OF SYMBOLS 1 ... Analysis apparatus 2 ... Measurement object 3 ... Output part 4 ... Time series data collection part 5 ... Time series data storage part 6 ... Sine wave superimposition part (superimposition means)
7: Attractor component (embedding processing means)
8 ... orbit parallel measure calculation part (detection means)
9 ... Setting / control section

Claims (6)

Superimposing means for superimposing a sine wave having the same frequency as the period that is a feature of the time-series data on the time-series data having a periodic characteristic;
Embedding processing means for performing embedding processing in the n-dimensional state space for the time-series data on which the sine wave is superimposed;
A detection means for measuring a trajectory parallel measure of the embedded time-series data, and detecting a period characteristic of the time-series data or a phase characteristic based on the period based on the trajectory parallel measure;
An apparatus for analyzing time-series data, comprising: Superimposing means for superimposing a sine wave having the same frequency as the period that is a feature of the time-series data on the time-series data having a periodic characteristic;
Embedding processing means for performing embedding processing in the n-dimensional state space for the time-series data on which the sine wave is superimposed;
Display means for displaying the attractor obtained by the embedding process in a two-dimensional or three-dimensional state space;
An apparatus for analyzing time-series data, comprising: 3. The time-series data analysis apparatus according to claim 1, wherein the amplitude of the sine wave is 1 to 100 times the maximum amplitude of the time-series data. A method for analyzing time series data by an analysis device for analyzing time series data,
A superimposition step of superimposing a sine wave having the same frequency as the period that is a feature of the time-series data on the time-series data having a periodic characteristic;
An embedding step of embedding the time series data on which the sine wave is superimposed in an n-dimensional state space;
A step of measuring an orbital parallel measure of the time-series data subjected to the embedding process, and detecting a period characteristic of the time-series data or a phase characteristic based on the period based on the orbital parallel measure;
A method for analyzing time-series data, comprising: A method for analyzing time series data by an analysis device for analyzing time series data,
A superimposition step of superimposing a sine wave having the same frequency as the period that is a feature of the time-series data on the time-series data having a periodic characteristic;
An embedding step of embedding the time series data on which the sine wave is superimposed in an n-dimensional state space;
A display step of displaying the attractor obtained by the embedding process in a two-dimensional or three-dimensional state space;
A method for analyzing time-series data, comprising:   The program for functioning a computer as each means of the time series data analysis apparatus of any one of Claim 1 to 3.

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