JP2010154998A - Device for time-series data analysis and computer readable recording medium having recorded with time-series data analysis program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that though the inventors have proposed that a brain wave data spectrum can serve as an index, and that brain data spectrum tilt value should be used as an index of the subject's conditions, no progress has been made yet so as to distinguish the conditions of a subject by using only the tilt values, since the tilt varies according to the subject's conditions. <P>SOLUTION: A device for time-series data analysis is provided to solve this problem, which includes a segmental conditions input part, an analytic conditions input part, an optimum analytic conditions deriving part that under both segmental and analytic conditions input to respective input parts, analyzes all respective segments by maximum entropy and nonlinear minimum square methods under all analytic conditions, selects an appropriate optimum segment and appropriate analytic conditions based on all the analysis results and derives optimum segment length and lag values corresponding to them, and an analysis execution part to execute an analysis by the maximum entropy method, by using the optimum analytic conditions derived. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a time-series data analysis device such as an electroencephalogram and a computer-readable recording medium on which a time-series data analysis program is recorded.

  The inventors found that the chaos time series according to the Lorentz, Wrestler, and Duffing model nonlinear motion equations are all exponential spectra, and reported to the European Physical Society of Japan (Non-patent Document 1). . Published in European journals in 1995. This Japanese translation of Non-Patent Document 1 was published as Non-Patent Document 2 in 1996.

  In addition, the inventors analyzed non-patent document 1 pulse wave (blood pressure waveform) data by a similar method, found that the spectrum was an exponential spectrum, and related to the chaos characteristics of physiological phenomena. Pointed out. Non-Patent Document 1 is a paper that triggered the attention of the exponential spectrum due to chaos time series and physiological phenomena.

  Non-Patent Document 1 is an important finding obtained for the first time by accurately calculating the spectrum of a chaotic time series using the highly accurate general-purpose time series analysis system MemCalc (registered trademark) created by the inventor for analysis. However, with the spread of this MemCalc (registered trademark) and its application system, various time series data, especially biological time series data, have been characterized by various researchers and groups including our group. It came to be examined in detail.

  Particularly interesting among them are the electroencephalogram data and analysis results described in Non-Patent Document 3. According to Non-Patent Document 3, the spectrum of the electroencephalogram data measured on the scalp is an exponential spectrum in the frequency band of interest (1 to 30 Hz or 0.5 to 30 Hz), and its inclination changes depending on the age and the condition of the subject. The fact that the slope of the electroencephalogram spectrum fluctuates according to the “sleep rhythm” of about an hour and a half during sleep, and that the slope of the spectrum changes with the introduction of anesthesia has been revealed.

Norio OHTOMO, Kazuo TOKIWANO, Yukio TANAKA, Ayako SUMI, Saburou TERACHI and Hidetoshi KONNO, "Exponential Characteristics of Power Spectral Densities Caused by ChaoticPhenomena", Journal of the Physical Society of Japan, Vol. 64, No. 4 (1995) pp. 1104-1113. Supervised by Junichi Hosoda, edited by Hiroshi Kasanuki and Ikuo Otomo, "New Development of Biological Time Series Data Analysis", Hokkaido University Library Publications, December 25, 1996, pp.139-155 Tomoko Tadami, “Actual analysis of biological time-series data using MemCalc”, published by Japan Perioperative Time Medical Society, March 10, 2001.

  Since the spectrum of the electroencephalogram data becomes an exponential spectrum and the slope of the exponential spectrum changes according to the state of the subject, it is expected to immediately use the slope value as an index of the subject's state.

  The inventor has developed simple systems Makin (trade name) and Makin 2 (trade name) for obtaining the slope of the exponential spectrum of the electroencephalogram in real time, and has been used in many research institutions. Various knowledge about the behavior of this tilt has been accumulated and reported.

However, at present, it is not possible to determine each state of the subject with only the value of the slope. For example, the slope of the exponential spectrum of the electroencephalogram under anesthesia and deep sleep is both steep, but it is impossible to determine whether the electroencephalogram is under anesthesia or during deep sleep only by the slope value. Further, in the determination of the sleep stage, the inclinations of a plurality of brain waves that are set to the same sleep stage by an engineer may remain largely varied, and the difference between subjects is also large. In order to use the remarkable characteristic that the spectrum of the electroencephalogram data shows an exponential shape widely and practically, technical ingenuity to overcome such a current situation is required.
The present invention aims to solve such problems.

In order to solve the above-mentioned problems, the present invention is composed of the shortest segment length, the longest segment length, the shortest / longest segment, and segments having different lengths between the segments that are cut out from the original time series data and analyzed. A segment condition input section with the total number of segments to be cut or the time increment between the shortest and longest segments as input items;
An analysis condition input unit having as input items a set interval of a series of lag values set between the minimum lag value and the maximum lag value and the minimum / maximum lag value;
Based on the segment conditions input to the segment condition input section and the analysis conditions input to the analysis condition input section, analysis is performed by the maximum entropy method and the nonlinear least squares method for all analysis conditions for all segments. Selecting an appropriate segment and an analysis condition from all analysis results, and deriving an optimum segment length and an optimum lag value correspondingly,
We propose a time-series data analysis device composed of an analysis execution unit that sets an optimal analysis condition derived in an optimal analysis condition deriving unit and executes an analysis by a maximum entropy method.

In the present invention, in the above analysis device, the optimum analysis condition derivation unit is
Based on the conditions input to the segment condition input unit, a plurality of segments having different lengths are cut out from the original time series data and set as sample segments, and the analysis conditions input to the analysis condition input unit are read and set. Setting processing means;
A first processing means for calculating a power spectral density using a maximum entropy method according to all analysis conditions for each of all sample segments set by the setting processing means;
For each of the power spectral densities obtained by the first processing means, a main spectral peak is extracted, and various quantities of the generalized trigonometric polynomial expression for the sample segment are calculated from them by the nonlinear least square method. Processing means,
The validity of the generalized trigonometric polynomial expression obtained by the second processing means with respect to the sample segment data and the consistency with respect to the power spectral density are judged, and one corresponding to the generalized trigonometric polynomial expression with high validity and consistency is obtained. A time-series data analyzing apparatus is proposed which comprises a third processing means for selecting one sample segment and deriving the corresponding segment length and lag value as the optimum segment length and optimum lag value.

  In the present invention, in the above analysis apparatus, the second processing means extracts the number, each peak frequency, and each peak power of main spectrum peaks from the power spectrum density calculated by the first processing means. Then, using the above number as the number of terms and the reciprocal of each peak frequency as the initial value of the period of each triangular term, the quantities of the generalized trigonometric polynomial expression are calculated by nonlinear least squares method that minimizes the sum of squares of the residuals. We propose a time-series data analysis device configured to calculate.

In the present invention, in the above analysis apparatus, the third processing means compares the standard deviation of the residual in various quantities of the generalized trigonometric polynomial expression for each sample segment with a set value, A first selection function that rejects the generalized trigonometric polynomial expression and selects other generalized trigonometric polynomial expressions as selection candidates;
Compare the period of each term of the polynomial determined by the nonlinear least squares method with its initial value set from the reciprocal of the peak frequency of the power spectral density, and reject the generalized triangular polynomial expression whose difference is greater than the set value And a second selection function using other generalized triangular polynomial expressions as selection candidates,
A generalized triangular polynomial expression that compares the power obtained from the amplitude of each term of the polynomial determined by the nonlinear least squares method with the power of the corresponding peak of the power spectral density one by one, and the difference has an amplitude greater than the set value And a third selection function with other generalized triangular polynomial expressions as selection candidates,
A time-series data analysis apparatus is proposed in which processing by the first, second, and third sorting functions is sequentially performed to select a generalized triangular polynomial expression having high validity and consistency.

  In the present invention, in the above analysis apparatus, the third processing means sequentially performs the processing by the first, second, and third selection functions, and then a plurality of generalized triangular polynomial expressions remain as selection candidates. In this case, a time-series data analyzing apparatus having a fourth selecting function for selecting a generalized triangular polynomial expression having the smallest standard deviation of the residual is proposed.

  In the present invention, in the above analysis apparatus, the third processing means is selected after performing the processing by the first, second and third or first, second, third and fourth sorting functions. A sample segment having a fifth sorting function for selecting the longest sample segment as the optimum sample segment when a plurality of sample segments having the generalized trigonometric polynomial representation remain, and selected by the fifth sorting function A time series data analysis device is proposed, in which the lag value calculated for the power spectrum density corresponding to the selected generalized trigonometric polynomial expression is selected as the optimal lag value for the sample segment. .

In the present invention, in the above analysis apparatus, the analysis execution unit is
Segment preparation means for cutting out segments from original time series data based on the optimum segment length derived by the optimum analysis condition derivation unit and set in the analysis condition setting means,
A power spectrum density calculating means for calculating a power spectrum density by a maximum entropy method using an optimum lag value derived in the optimum analysis condition derivation unit for the prepared segment and set in the analysis condition setting means;
Peak extraction means for extracting the number of main peaks of the calculated power spectral density, the center frequency and peak power of each peak;
A time-series data analysis device is proposed which comprises a feature quantity extraction means for extracting a feature quantity from an extracted peak sequence.

  Further, in the present invention, in the above analysis apparatus, the analysis condition setting means includes a function for setting the optimum analysis conditions derived by the optimum analysis condition derivation unit as it is, a function for setting the analysis conditions input by the input means, We propose a time-series data analysis device with the selection function.

  Further, in the present invention, in the above analysis apparatus, the peak extraction means obtains a locally prominent peak in a range several times the average interval between peaks obtained from all peaks of the power spectral density, and is obtained. A first process that forms a fusion peak by fusing a prominent peak with an interval shorter than the average interval to form a fusion peak, and making all peaks other than the prominent peak and the fusion peak the nearest prominent peak or fusion peak The main peak is extracted from the second process to be fused, and when multiple peaks are merged, the peak power before and after the fusion is preserved, and the peak power of the multiple peaks before fusion is proportionally distributed. We propose a time-series data analysis device that determines the center frequency of the fusion peak.

  Further, in the present invention, in the above analysis apparatus, the feature amount extracting means uses a so-called exponential spectrum by a linear least square method for a pair of log power and peak frequency of a plurality of main peaks extracted by the peak extracting means. The trend line calculation means for obtaining the slope and y intercept of the trend line, and for all the peaks obtained by the power spectrum density calculation means, the peak power value is divided by the power value indicated by the trend line and normalized. When it is composed of relative power calculation means for calculating trend line relative power, peaks discretely arranged on the frequency axis, and feature quantity extraction means for extracting the feature quantity of the relative peak power distribution from the relative peak power A data analysis device is proposed.

  In the present invention, in the above analysis device, the time-series data is brain wave data, and the feature amount extracted by the feature amount extraction unit is usually a relative peak in the attention frequency band of the brain wave spectrum of 1 to 30 Hz or 0.5 to 30 Hz. It is proposed that power is integrated from the low frequency side, and that the integrated value includes three frequencies that are 25%, 50%, and 75% of the total relative peak power of the frequency band of interest.

Next, in the present invention, regarding the segment to be cut and analyzed from the original time series data, the shortest segment length and the longest segment length and the shortest / longest segment and the total number of segments to be cut or the shortest segment Entering the time step between the longest segments as the segment condition,
A process of inputting a set interval of a series of lag values set between the minimum lag value and the maximum lag value and the minimum and maximum lag values as an analysis condition,
Based on the input segment conditions and analysis conditions, all segments are analyzed using the maximum entropy method and nonlinear least squares method under all analysis conditions. The process of selecting one analysis condition and deriving the analysis condition consisting of the optimal segment length and the optimal lag value,
A computer-readable recording medium recording a time-series data analysis program composed of the process of executing the analysis by the maximum entropy method by setting the derived optimal analysis condition as the analysis condition is proposed.

In the present invention, in the recording medium, the process of deriving the analysis condition is
A process of cutting out a plurality of segments of different lengths from the original time series data based on the input segment conditions and setting them as sample segments,
The process of setting analysis conditions,
A first processing step of calculating a power spectral density using a maximum entropy method according to all set analysis conditions for each of all set sample segments;
A main spectrum peak is extracted for each of the power spectral densities obtained by the first processing step, and various quantities of the generalized trigonometric polynomial expression for the sample segment are calculated from them by the nonlinear least square method. And the process of
The validity of the generalized trigonometric polynomial expression obtained by the second processing step with respect to the sample segment data and the consistency with respect to the power spectral density are judged, and one corresponding to the generalized trigonometric polynomial expression with high validity and consistency is obtained. A computer readable recording of a time series data analysis program consisting of a third process that selects one sample segment and derives the corresponding segment length and lag value as the optimum segment length and optimum lag value recoding media.

  In the present invention, in the above recording medium, the second processing step extracts the number, each peak frequency, and each peak power of main spectrum peaks from the power spectral density calculated by the first processing step. The generalized trigonometric polynomial expression is calculated by the non-linear least-squares method that minimizes the sum of squares of the residuals, with the number of terms as the number of terms and the reciprocal of each peak frequency as the initial value of the period of each triangular term. A computer-readable recording medium recording a time-series data analysis program having a process of calculating an amount is proposed.

In the present invention, in the above recording medium, the third processing step is to compare the standard deviation of the residual in various quantities of the generalized trigonometric polynomial expression relating to each sample segment with the set value, and to determine the general value greater than the set value. A first selection process of rejecting the generalized trigonometric polynomial expression and selecting other generalized trigonometric polynomial expressions as selection candidates;
Compare the period of each term of the polynomial determined by the nonlinear least squares method with its initial value set from the reciprocal of the peak frequency of the power spectral density, and reject the generalized triangular polynomial expression whose difference is greater than the set value And a second selection process using other generalized triangular polynomial expressions as selection candidates,
A generalized triangular polynomial expression that compares the power obtained from the amplitude of each term of the polynomial determined by the nonlinear least squares method with the power of the corresponding peak of the power spectral density one by one, and the difference has an amplitude greater than the set value And a third selection process with other generalized triangular polynomial expressions as selection candidates,
A computer-readable recording medium on which is recorded a time series data analysis program in which a generalized trigonometric polynomial expression having high validity and consistency is selected by sequentially performing processes according to the first, second and third selection processes. Propose.

  In the present invention, in the above recording medium, a plurality of generalized trigonometric polynomial expressions remain as selection candidates after sequentially performing the first, second, and third sorting processes in the third processing process. In this case, a computer-readable recording medium recording a time-series data analysis program having a fourth selection process for selecting a generalized triangular polynomial expression having the smallest standard deviation of the residual is proposed.

  In the present invention, in the above recording medium, the third processing step includes a plurality of steps after sequentially performing the first, second and third or first, second, third and fourth sorting steps. If the sample segment remains as a candidate for selection, it has a fifth sorting process for selecting the longest sample segment as the optimal sample segment, and the sample segment selected by the fifth sorting process is selected as the optimal segment. A computer-readable recording medium recording a time-series data analysis program having a process of selecting a lag value obtained by calculating a power spectral density corresponding to a selected generalized trigonometric polynomial expression as an optimum lag value for a sample segment Propose.

In the present invention, in the above recording medium, the analysis execution process is:
A segment preparation process for extracting a segment from original time series data based on the optimal segment length derived in the optimal analysis condition derivation process and set in the analysis condition setting means,
A power spectrum density calculation process for calculating a power spectrum density by a maximum entropy method using an optimum lag value set in the analysis condition setting means, which is derived in the optimum analysis condition derivation process for the prepared segment;
A peak extraction process for extracting the number of main peaks of the calculated power spectral density, the center frequency of each peak and the peak power;
A computer-readable recording medium recording a time-series data analysis program comprising a feature amount extraction process for extracting a feature amount from an extracted peak sequence is proposed.

  In the present invention, in the above recording medium, the analysis condition setting means includes a function for setting the optimum analysis condition derived in the optimum analysis condition derivation process as it is, a function for setting the analysis condition input by the input means, The computer-readable recording medium which recorded the time series data analysis program of Claim 18 characterized by comprising the selection function is proposed.

In the present invention, in the recording medium, the peak extraction process is
The process of obtaining the average interval between peaks from all the peaks of the power spectral density, the process of obtaining locally prominent peaks in the range of several times the obtained average interval, and the average interval between the obtained prominent peaks The first processing step, which consists of fusing adjacent peaks at shorter intervals to form a fusion peak, and fusing all peaks other than the prominent peak and the fusion peak into the nearest prominent peak or fusion peak And a second processing step
In the first processing step and the second processing step, when merging a plurality of peaks, the peak power before and after the fusion is preserved, and it is prorated according to the peak power of the plurality of peaks before the fusion. A computer-readable recording medium recording a time-series data analysis program for determining the center frequency is proposed.

  In the present invention, in the recording medium described above, the feature amount extraction process is performed by using a linear least square method for a pair of logarithmic values of peak powers and peak frequencies of a plurality of main peaks extracted in the peak extraction process. Trend line calculation process to find the slope and y-intercept of the trend line, and for all the peaks obtained by the power spectrum density calculation means, the peak power value is divided by the power value indicated by the trend line and normalized Time-series data consisting of a relative power calculation process for obtaining line relative power, a peak discretely arranged on the frequency axis, and a feature quantity extraction process for extracting the feature quantity of the relative peak power distribution based on the relative power. A computer-readable recording medium on which an analysis program is recorded is proposed.

  In the present invention, in the above recording medium, the time series data is brain wave data, and the feature amount extracted by the feature amount extraction process is usually a relative peak in the attention frequency band of the brain wave spectrum of 1 to 30 Hz or 0.5 to 30 Hz. A computer reading that records the time series data analysis program that integrates power from the low frequency side and includes three frequencies where the integrated value is 25%, 50%, and 75% of the total relative peak power of the frequency band of interest. A possible recording medium is proposed.

  According to the analysis apparatus and the analysis program according to the present invention, in the optimum analysis condition derivation unit or the optimum analysis condition derivation process, the segment that provides the generalized triangular polynomial expression that best reproduces the segment of the original time series data to be analyzed The length and lag values are derived, and these are used as the optimal segment length and optimal lag value for analysis by the maximum entropy method in the analysis execution unit or analysis execution process. It is expected that the output is from a system in a certain dynamic state (the brain when the time series data is brain wave data), and the behavior and frequency axis of the time series data such as brain wave data on the time axis The above MEM-PSD behavior is expected to be consistent.

  Therefore, as a result of the consistency ensured in this way, various quantities characterizing time-series data, such as the slope of the spectrum and the section power obtained in the analysis execution unit or analysis execution process, compared to the case of the conventional method, You can put more trust.

  Further, according to the analysis apparatus and the analysis program according to the present invention, in addition to the various quantities in the conventional electroencephalogram analysis, the most basic features of the spectrum, along with the inclination of the trend line, the relative peak power (trend line) in the frequency band of interest. Since the integrated value of the relative intensity of each peak power) is described in more detail by adding a set of frequencies that are 1/4, 1/2, 3/4 of the sum in the frequency band of interest, it can be distinguished by the conventional method. It is possible to obtain knowledge about the dynamic state of a non-system (brain).

Next, the best mode of an apparatus for analyzing time series data according to the present invention will be described with reference to the accompanying drawings.
First, FIG. 1 is an explanatory diagram schematically showing the overall configuration of an analysis apparatus according to the present invention. The analysis apparatus generally includes a shortest segment length and a longest segment with respect to a segment that is cut out from the original time series data 1 and analyzed. Segment condition input unit 2 with the total number of segments to be cut out consisting of long and shortest / longest segments and segments of different lengths between them or the time increment between shortest / longest segments as input items, minimum lag value and maximum lag Analysis condition input unit 3 having as input items a set interval of a series of lag values set between the minimum and maximum lag values, the segment condition input to segment condition input unit 2, and the input to analysis condition input unit 3 Based on the analysis conditions specified, analysis is performed by the maximum entropy method and the nonlinear least squares method under all analysis conditions for each segment. Then, an appropriate segment and an analysis condition are selected from all the analysis results, and an optimum analysis condition derivation unit 4 for deriving an optimum segment length and an optimum lag value, and an optimum analysis condition derivation unit 4 And an analysis execution unit 5 that executes an analysis by the maximum entropy method based on the optimal analysis condition derived in FIG.

  In this embodiment, the optimum analysis condition deriving unit 4 cuts out a plurality of segments having different lengths from the original time series data 1 based on the conditions input to the segment condition input unit 2 as sample segments. Setting processing means 6 for reading and setting the analysis condition input to the analysis condition input unit 3 and setting the maximum entropy method for all sample segments set by the setting processing means 6 according to all analysis conditions The first processing means 7 for calculating the power spectral density by using the above and the main spectral peak for each of the power spectral densities obtained by the first processing means 7 are extracted, and the nonlinear least square method is extracted therefrom. Second processing means 8 for calculating various quantities of the generalized trigonometric polynomial expression for the sample segment, and The validity of the generalized trigonometric polynomial expression obtained by the second processing means 8 with respect to the sample segment data and the consistency with respect to the power spectral density are judged, and one corresponding to the generalized trigonometric polynomial expression having high validity and consistency. It comprises third processing means 9 for selecting one sample segment and deriving the corresponding segment length and lag value as the optimum segment length and optimum lag value.

  Furthermore, in this embodiment, the analysis execution unit 5 is prepared with segment preparation means 10 for cutting out segments from the original time series data 1 based on the optimum segment length derived by the optimum analysis condition deriving unit 4 Power spectrum density calculating means 11 for calculating the power spectral density by the maximum entropy method using the optimum lag value derived by the optimum analysis condition deriving unit 4 for the segment, the number of main peaks of the calculated power spectral density, The peak extraction unit 12 extracts the center frequency and peak power of each peak, and the feature amount extraction unit 13 extracts a feature amount from the extracted peak train.

  Although not shown, the analysis execution unit 5 includes an analysis condition setting unit, and the analysis condition setting unit sets the optimum analysis condition derived by the optimum analysis condition deriving unit 4 as it is. A function, a function for setting an analysis condition input by an input means (not shown), and a selection function thereof can be configured.

  Next, the operation of the time-series data analysis apparatus according to the present invention having the above-described configuration will be described in the case where the time-series data to be analyzed is brain wave data.

  First, the slope of the spectrum means the “slope” of the trend line of the frequency distribution of the power constituting the time series. In the case of the exponential spectrum described above, when the spectrum is displayed semilogarithmically, the trend line is a straight line, and literally, the slope of this straight line is the slope of the spectrum.

  FIG. 4 shows an example of electroencephalogram data for 2 seconds and its spectral density. (A) is the electroencephalogram data, and (b) is the spectral density. As can be seen, the electroencephalogram fluctuates significantly in just 2 seconds, and its spectrum consists of many peaks, which are exponentially attenuated in the frequency band of interest (1-30Hz or 0.5-30Hz) To do. This figure shows the result of cutting out and analyzing 2-second data as segments from long-term electroencephalogram data as original time series data.

  Conventionally, there is no clear problem awareness as to how to determine the data length to be analyzed as a segment, and the data length (data points) is determined exclusively for the convenience of analysis. That is, since FFT is mainly used for the calculation of the spectrum, the data to be analyzed is determined to be data of a power of 2 suitable for it.

  On the other hand, to determine the slope of the spectrum of time series data in the first place is to obtain the most basic and fundamental index regarding the dynamic state of the system that generated the time series data. It should be assumed that the dynamic state of the system is constant over the segment length (time). For example, in an extreme example, even if the data of a segment that includes both data immediately before and after a seizure is collectively analyzed, it is necessary to obtain positive meaning for the slope of the spectrum as the analysis result. I can't. FIG. 5 shows an example of electroencephalogram data in such a case, and it can be seen that the state is clearly different between the first half and the second half of the 20-second data.

  If the inclination of the spectrum of the time series data is to be used effectively, the time series data to be analyzed, in this case, the electroencephalogram data, is required to be in the same dynamic state in the section for obtaining the spectrum, that is, the segment. In the analysis apparatus of the present invention, the optimum analysis conditions including the optimum segment length that is considered to be in a certain dynamic state can be obtained and the optimum analysis can be performed by the following operations. .

  First, in FIG. 2 showing the operation of the optimum analysis condition deriving unit 4, the segment condition input unit 2 includes the shortest length of the segment to check whether it is in the same state, the longest length, and these shortest / longest segments. And the total number N of segments to be cut out composed of segments of different lengths between them or the time increment between the shortest and longest segments is input in advance.

  In the electroencephalogram analysis, the frequency band of interest is 1 to 30 Hz or 0.5 to 30 Hz. Therefore, the length of the order of the reciprocal of the lower limit frequency, for example, 2 seconds is input as the shortest segment length. In general, when the brain wave is visually determined, it is performed every 30 seconds, but the brain wave varies in various ways and does not show the same state throughout the entire time of 30 seconds. For the length, enter a fraction of 30 seconds, for example, 5 seconds. Further, the total number N of segments to be cut out is set to 2 to 5 seconds when the number of segments set to 2 to 5 seconds is 7 for example. Therefore, the segment condition input unit 2 may be input with the total number N of segments, or may be input with time increments.

  Next, in the analysis condition input unit 3, a plurality of sample segments set according to the segment condition input in the segment condition input unit 2 are analyzed in the analysis execution unit 5 by any analysis condition, that is, the maximum entropy method. Whether to analyze with the lag value at is input in advance.

  The lag value as the analysis condition can be input by obtaining the range and the like from the knowledge obtained from the analysis results of a large number of time series data by the maximum entropy method. For example, in the case of EEG data, the lag value is changed in the range of 50 to 75% of the data length. In this case, the minimum lag value (ratio to the number of segment data points) is 0.5, and the maximum lag value is 0.75. input. If the lag value is calculated in increments of 5%, the lag value setting interval is input as 0.05.

  Note that the original time series data 1 in FIG. 2 may be the whole or a part of the collected electroencephalogram data and should be at least longer than the longest segment length.

  Next, in the optimum analysis condition deriving unit 4, first, in step S6 corresponding to the setting processing means 6, a plurality of segments having different lengths are derived from the original time series data 1 based on the conditions input to the segment condition input unit 2. Is extracted and set as a sample segment, and the analysis condition input to the analysis condition input unit 3, that is, the lag value condition is read and set.

Reference numeral D1 indicates the contents set in the setting processing means 6, and a total of N sample segments (1 to N) cut out from the original time series data 1 and set, and a plurality of lags for each sample segment. Values (1-1 to ₁ -M ₁ , 1-1 to ₁ -M ₂ ,..., 1-1 to 1-M _N ) are set.

  Here, the sample segment is set by being cut out from the original time series data so that the long one includes the short one. In that case, the sample segments of different lengths can be cut out together with either the start point, the central portion or the end point.

ここで、Bm(f)はラグ値mにて計算した周波数fにおけるスペクトル密度、Δtはサンプリング間隔、Pmとγm(k)はm次のバーグの係数である。 Next, in the optimal analysis condition deriving unit 4, in step S7 corresponding to the first processing means 7, a plurality of set lag values (1-1 to 1) are set for each of the sample segments (1 to N) of D1. -M ₁ , 1-1 to ₁ -M ₂ ,..., 1-1 to 1-M _N ), MEM-PSD calculation processing by the maximum entropy method is performed according to the following equation.

Here, Bm (f) is a spectral density at the frequency f calculated with the lag value m, Δt is a sampling interval, and Pm and γm (k) are m-th order Burg coefficients.

For example, as shown in Non-Patent Document 4, the prior application by the applicant of the present application, and the specification and drawings of Japanese Patent Application No. 2008-256418, the maximum entropy method (MEM) can analyze data of an arbitrary score, Therefore, unlike the analysis by FFT, the setting of the sample segment is not limited by the original time-series data, in this case, the sampling frequency or the number of data points of the electroencephalogram data.
Kazuo Joban, Ikuo Otomo, Yukio Tanaka, “Time Series Analysis by Maximum Entropy Method… Theory and Practice of MemCalc…”, 1st Edition, Hokkaido University Library Publications, June 25, 2002

Thus, as indicated by reference numeral D2 by the processing in step S7, a plurality of power spectral densities (PSD1-1, PSD1-2,..., PSD1-M ₁ ); (PSD1-1, PSD1-2,..., PSD1-M ₂ );... (PSD1-1, PSD1-2,..., PSD1-M _N ) are obtained.

ここで、x(t)は時刻におけるサンプルセグメントデータ(観測値)、a₀は水準値、Mは項数、a_jはj番目の三角項の振幅、T_jは周期、φ_jは頂位位相、ε(t)は残差(最小自乗あてはめ誤差)である。 Next, the optimum analysis condition deriving unit 4 extracts main spectral peaks for each of the power spectral densities D2 obtained in step S7 in step S8 corresponding to the second processing means 8, and performs nonlinear minimum self-conversion from them. Various quantities of the generalized trigonometric polynomial expression shown in the following equation are calculated for the sample segment by multiplication.

Where x (t) is the sample segment data (observed value) at the time, a ₀ is the level value, M is the number of terms, a _j is the amplitude of the j-th triangular term, T _j is the period, φ _j is the top The phase, ε (t), is the residual (least square fitting error).

The calculation for obtaining the generalized trigonometric polynomial expression is described in the above document and the like, but is performed by the following procedure.
(1) First, the number, each peak frequency, and each peak power of main spectrum peaks are extracted from the MEM-PSD.
(2) Put the number of terms M of the generalized trigonometric polynomial equal to the number of main spectral peaks, take the initial value of the period T _j of each triangular term as the reciprocal of the peak frequency of the corresponding peak, and from this initial value First, sample segment data is described by generalized trigonometric polynomials by nonlinear least square method (nonlinear LSF) that minimizes the sum of squares of ε (t), and various quantities a ₀ , a _j , T _{j of} generalized trigonometric polynomial expressions , phi _j can be obtained (j = 1~M).

By the above procedure, a plurality of MEM-PSDs for each sample segment are calculated, and a plurality of generalized triangular polynomial expressions are obtained for each sample segment. 2 is obtained for each of N sample segments, a plurality of generalized triangular polynomial expressions (GTP1-1, GTP1-2,..., GTP1-M ₁ ); (GTP1-1, GTP1-2) , ..., GTP1-M ₂ ); ...; (GTP1-1, GTP1-2, ..., GTP1-M _N ).

  Next, in the optimum analysis condition deriving unit 4, in step S9 corresponding to the third processing means 9, the validity and power spectral density for the sample segment data for each of the plurality of generalized triangular polynomial expressions D3 obtained in step S8. A generalized trigonometric polynomial expression having high validity and consistency is selected.

  Step S9 corresponding to the third processing means 9 first compares the standard deviation of the residual in various quantities of the generalized trigonometric polynomial expression for each sample segment with the set value, and generalized trigonometric polynomials greater than the set value. While rejecting the expression, the period of each term of the polynomial determined by the first selection process using other generalized triangular polynomial expressions as selection candidates and the nonlinear least squares method is the reciprocal of the peak frequency of the power spectral density. A second selection process in which a generalized trigonometric polynomial expression whose difference is equal to or greater than the set value is rejected, and a generalized trigonometric polynomial expression other than that is selected as a selection candidate, and a nonlinear minimum Each power obtained from the amplitude of each polynomial term determined by the square method is compared with the corresponding peak power of the power spectral density one by one, and the difference is greater than the set value. And a third selection process in which other generalized trigonometric polynomial expressions are selected as candidates for selection, and sequentially performs the processes of the first, second, and third selection processes. Go to select a generalized trigonometric polynomial representation that is highly relevant and consistent.

  Further, step S9 corresponding to the third processing means 9 includes a case where a plurality of generalized trigonometric polynomial expressions remain as selection candidates after sequentially performing the processes according to the first, second and third selection processes. A fourth screening process can be configured to select a generalized triangular polynomial representation with the smallest standard deviation of the residual.

  Further, step S9 corresponding to the third processing means 9 includes the first, second and third or first, second, third and fourth sorting processes, and then the selected generalized triangle. When a plurality of polynomial expressions remain, a fifth sorting process is selected to select the longest sample segment as the optimum sample segment, and the sample segment selected by the fifth sorting process is set as the optimum segment. On the other hand, the lag value obtained by calculating the power spectral density corresponding to the selected generalized trigonometric polynomial expression is selected as the optimum lag value, and thus the analysis condition D4 composed of the optimum segment length and the optimum lag value can be derived. .

  In the above processing, the maximum segment length is set to 5 seconds, but this segment length is a practical length for EEG data, and the segment conditions and analysis conditions including this maximum segment length are It can be set as appropriate according to the series data. It is expected that the longer the sample segment length that is considered to be in a certain dynamic state, the more stable the obtained analysis result will be. This selection is made by the above-described fifth selection process. Done.

  FIG. 6 shows an example in which the electroencephalogram data having a length of 5 seconds is expressed by a generalized trigonometric polynomial, (a) is an electroencephalogram data, (b) is a generalized trigonometric polynomial expression, and (c) is a triangular term. This is the residual that could not be expressed as a sum.

  As shown in this figure, the generalized trigonometric polynomial representation of (b) reproduces the electroencephalogram data of (a) well, the residual of (c) is small and distributed around the value zero, And there is no time dependency. Thus, it can be seen that the power spectral density (MEM-PSD) that gives the initial value of the nonlinear least squares method is accurately calculated by the processing of the present invention.

  In the present invention, the optimum analysis condition derivation unit 4 derives the segment length and lag value from which the generalized trigonometric polynomial expression that best reproduces a part of the original time series data is derived. The segment of the original time series data to be analyzed is expected to be the output from the system (in this case, the brain) in a certain dynamic state over its entire length. In step S9 corresponding to the third processing means 9 of the optimum analysis condition deriving unit 4, the validity for the sample segment data and the consistency for the power spectral density are judged, and the generalized triangle having high validity and consistency is obtained. This is because the polynomial expression is selected, and from this, it can be expected that all the triangular terms of the generalized triangular polynomial continue to exist with a constant amplitude over the segment data length.

This will be specifically described below by way of example.
First, when the mode with a certain period T and amplitude a (Sankakuko) is present in the entire region of the segment, the power of that mode is a ^2/2, also the power of the corresponding spectral peak of MEM-PSD it is expected to become a ^2/2. On the other hand, only the first half of the segment data, when this mode is present, the power of the spectral peak is expected to be a ^2/4 by half. In addition, the amplitude of this mode cannot be accurately predicted from the balance with other modes, but at least it is a value different from a and coincides with the value expected from the peak power by chance. The possibility is extremely small. Therefore, by determining whether the amplitude of each mode corresponds to the peak power of the corresponding MEM-PSD, can the EEG data be regarded as an output from the same dynamic state system (= brain) over the entire segment length? You can give an indication of whether or not.

  7 and 8 show an example in which artificial time-series data having a length of 2 seconds and 201 points are expressed by generalized trigonometric polynomials, (a) is time-series data, and (b) is generalized triangles. Polynomial expression, (c) is a residual that could not be expressed as a sum of triangular terms.

  The time-series data in FIG. 7 is data obtained by superimposing noise on four triangular terms of 5, 10, 15, and 20 Hz, and the amplitude of each mode is 10, 7, 5, and 3 over the entire length. is there. On the other hand, the time series data of FIG. 8 is data in which the 10 Hz mode is missing from the data of FIG.

  When FIG. 7 is compared with FIG. 8, in the case of FIG. 7, as in the case of FIG. 6, the generalized trigonometric polynomial expression of (b) reproduces the time series data of (a) well, and (c ) Is small, distributed around the value zero, and is not time-dependent. On the other hand, in the time series data of FIG. As shown in b), the fitting of the mode is not successful, and a large residual remains as shown in (c).

  FIGS. 9A and 9B relate to the time-series data of FIGS. 7 and 8, respectively, and four triangular terms as processing results in step S9 corresponding to the third processing means 9 of the optimum analysis condition deriving unit 4. FIG. These parameters are shown.

  As can be seen from the figure, when the 10 Hz mode is missing in the second half, the value is as small as 3.62 (power 6.55) with respect to the original amplitude 7.0 (power 24.5) of the mode. The peak power of the 10 Hz MEM-PSD is calculated to be 25.6 in the case of time series data without omission in FIG. 7, and 12.9 in the case of time series data with omission in FIG.

  From the above, in the present invention, as described above, the segment of the original time series data analyzed by the analysis execution unit is expected to be output from the system in a certain dynamic state over the entire length. The In other words, the present invention provides a method for determining the dynamic stability of the electroencephalogram data over the segment length based on the consistency between the amplitude of each term of the generalized trigonometric polynomial and the peak power of the MEM-PSD.

Next, the operation of the analysis execution unit 5 will be described below with reference to FIG.
First, in step S10 corresponding to the segment preparation means 10, the analysis execution unit 5 selects the original time-series data 1 based on the optimum segment length in the optimum analysis condition D4 derived by the optimum analysis condition derivation unit 4, that is, a long A segment D5 to be analyzed is cut out from the electroencephalogram data. As described above, the segment D5 thus cut out is expected to be an output from the system in a certain dynamic state over its entire length.

  Next, in step S11 corresponding to the power spectrum density calculating means 11, the segment D5 extracted based on the optimum lag value in the optimum analysis condition D4 derived by the optimum analysis condition deriving unit 4 is subjected to the maximum entropy method. The power spectral density (MEM-PSD) D6 is calculated.

  As described above, the segment length of the time series data analyzed by the analysis execution unit 5 and the analysis conditions thereof use the optimum analysis condition D4 derived by the optimum analysis condition derivation unit 4 as described above, If sufficient knowledge has already been accumulated for similar time-series data by the operation of the optimum analysis condition deriving unit 4, these values can also be directly specified.

  Next, in step S12 corresponding to the peak extraction unit 12, the analysis execution unit 5 extracts various amounts D7 characterizing the power spectral density, that is, the number of main peaks of the power spectral density, the center frequency of each peak, and the peak power. .

  Next, feature amounts are extracted by steps S13a, S13b, and S13c corresponding to the feature amount extraction means 13.

  First, in step S13a corresponding to the trend line calculating means, a so-called exponent is obtained by a linear least square method for a set of logarithmic values of peak powers and peak frequencies of a plurality of main peaks extracted in step S12 corresponding to the peak extracting means 12. The inclination of the spectrum trend line and the y-intercept D8 are obtained.

  Next, in step S13b corresponding to the relative power calculation means, for all the peaks obtained in step S11 corresponding to the power spectral density calculation means 11, the peak power values are divided by the power value indicated by the trend line and normalized. To obtain a series D9 of trend line relative powers.

  In step S13c corresponding to the feature quantity extraction means 13, the feature quantity D10 of the relative peak power distribution is obtained from the peaks discretely arranged on the frequency axis and the relative peak power, and then the feature quantity is obtained in step S13d. D11 is output.

  It should be noted in the above process that the calculation in step S11 corresponding to the power spectrum density calculating means 11 is the optimum analysis condition D4 derived by the optimum analysis condition deriving unit 4 or the optimum value by accumulating sufficient knowledge. Since a possible value is directly specified, a series of main peaks of the spectrum as a result of calculation is regarded as each term of a generalized trigonometric polynomial expression describing segment data. In other words, in the present invention, the main peak sequence of the MEM-PSD calculated using the optimum segment length and the optimum lag value obtained by the optimum analysis condition derivation unit 4 is represented by a generalized trigonometric polynomial describing the segment data. Providing a procedure for each item.

  That is, in step S13a corresponding to the above-described trend line calculation means, the trend line is calculated for a series of main peaks (center frequency, peak power), that is, each term of the generalized triangular polynomial. However, it does not calculate the trend line of the power spectral density that is continuously distributed in all frequency bands. Thus, as a result of the processing in step S13, the trend line and inclination of the code D8 and the y-intercept are obtained, and the value of this inclination corresponds to the value of the inclination of the electroencephalogram spectrum according to the conventional method.

  Here, in the processing in step S13c described above, as will be described later, the relative peak power included in the target frequency band (1 to 30 Hz or 0.5 to 30 Hz) is integrated from the low frequency side, and the integrated value is obtained in the target frequency band. The result D10 can be obtained by extracting three frequencies that are 25%, 50%, and 75% of the total relative peak power. The process of step S13c is a so-called quintuplet summarization excluding the minimum value and the maximum value. This feature amount is proposed for the first time in the analysis apparatus of the present invention, and a series of results D11 including these are output by the output processing in step S13d.

In addition, although not clearly shown in FIG. 3, in the present invention, since a highly accurate MEM-PSD can be obtained, it is possible to calculate all the feature amounts of the conventional method related to the electroencephalogram spectrum. it can. Specifically, δ, θ, α, β each frequency (1-4Hz, 4-8Hz, 8-13Hz, 13-30Hz) division power (unit: μV ² ), SMF (Spectral
Mid Frequency, the frequency at which the integrated value of power is 50% at 1 to 30 Hz), SEF ⁹⁰ (Spectral Edge Frequency, the frequency at which 90% is the same), etc., and these quantities are also important in determining the electroencephalogram .

  When the analysis execution unit 5 completes the analysis of one segment that has been cut out as described above, the analysis processing for the next segment is performed in accordance with an instruction from a higher-level control unit that is not shown. Normally, the control means controls so that the segment sequentially analyzed by the analysis execution unit 5 covers the original time series data 1, but depending on the time series data to be analyzed, processing that opens an interval may be possible. it can.

  On the other hand, in order to perform analysis with higher accuracy, it is desirable to obtain the optimum segment length and the optimum lag value by the optimum analysis condition derivation unit 4 for each analysis of the segment, and analyze it accordingly. However, the processing to find the optimal segment length and optimal lag value requires a lot of CPU power, etc., and the brain wave is usually measured simultaneously over 20 channels or more, so the optimal segment length and the optimal It is virtually impossible to update the lag value every time.

  Therefore, the upper control means is configured to intermittently operate the optimum analysis condition deriving unit 4 within a range not to interfere with the continuous processing of the analysis execution unit 5 and to pass the result to the analysis execution unit 5 as necessary. Is realistic.

In addition, when performing analysis by sequentially segmenting segments from original time series data, the segmentation method is (a) segment segment without gaps, (b)
Various methods can be applied, such as cutting out a segment partially overlapping, or (c) regardless of the presence / absence of a gap, for example, cutting out so that the segment center times are arranged at regular intervals. In the present invention in which the segment length is variable, the method (c) is easy to handle.

  As a result of applying the method of (c), even if a gap is created between the segments, as long as a segment of several seconds is analyzed at intervals of several seconds and the fluctuation of the system on the order of seconds is a problem, there is no practical inconvenience. Does not occur. This is because, for example, blood pressure is determined every beat, but even if you do not know the blood pressure of all the pulses that reach 100,000 beats per day (maximum blood pressure and minimum blood pressure), you can determine the approximate blood pressure of the day. It corresponds to what can be done.

且つ、MEM-PSDの主要なピークについて、その個数が上式の項数Mに、各ピークの中心周波数(の逆数)とピークパワーがそれぞれ上式各項の周期Tjとパワーa_j ²/2に対応し得ると期待される。 Next, in the operation of the analysis execution unit 5, a specific example in which the procedure for obtaining the feature quantity D10 from the MEM-PSD is applied to the electroencephalogram data in the same manner as described above will be described.
First, FIG. 10 shows an example of the MEM-PSD obtained in step S11 of the analysis execution unit 5.
In FIG. 10, the horizontal axis represents the frequency (Hz), the vertical axis represents the spectral density (μV ² / Hz), and the spectrum is semilogarithmically displayed in the frequency band of 0 to 30 Hz.
As described above, the calculation in step S11 corresponding to the power spectrum density calculation means 11 directly specifies the optimum analysis condition D4 derived by the optimum analysis condition deriving unit 4, or a value that is considered to be the optimum value by accumulating sufficient knowledge. Therefore, the MEM-PSD in FIG. 10 can be expected to extract a dynamic structure that exists stably over the segment data length from the long electroencephalogram data as the original time series data 1. That is, the electroencephalogram data x (t) to be analyzed is described as

And, the major peak of MEM-PSD, the number of terms M of the number is above formula, the center frequency (the inverse of) of the peaks and peak power and the period Tj of each term on the type each power a _j ^2/2 It is expected that it can respond to.

Next, a series D7 of the number of main peaks, the center frequency of each peak and the power is extracted by the processing in step S12. This process is performed from the viewpoint of determining a series of the number M of terms of x (t), the period T _j , and the amplitude a _j . At this time, it is necessary to be able to describe the dynamic structure up to 30 Hz existing in the segment data without being biased to a specific frequency band by superimposing M triangular terms of the generalized triangular polynomial. Here, the reason for limiting to 30 Hz is that the structure of 1 to 30 Hz or 0.5 to 30 Hz is usually a problem in brain wave spectrum analysis. this is,
A. Extract locally prominent peaks.
B. Combine prominent peaks and adjacent peaks into a fusion peak.
C. Summarize the weak peaks into the most prominent or fused peaks.
Is executed. The sum of the number of prominent peaks and fused peaks is M.

The specific procedure is explained below.
1. Peak extraction The above MEM-PSD has 40 peaks in the frequency band up to 30Hz (except for the zero frequency peak). First, for all peaks, the center frequency and peak power are extracted. The peak power is an integral value of MEM-PSD from the frequency that gives the minimum value immediately before the peak to the same frequency immediately after the peak. Table 1 is a table showing a series of peaks thus obtained.

2. Discrimination between locally prominent peaks and adjacent peaks Next, find the average peak interval for the spectral peaks in Table 1, and find locally prominent peaks in the range several times the average interval. Peaks marked with “*” following the peak numbers in Table 1 (peak numbers 2, 5, 7, etc.) are locally prominent peaks thus found.
Further, regarding all of the prominent peaks, if there is an adjacent peak located at a position shorter than the average interval, it is set as a proximate peak. Peaks in Table 1 followed by “N” (peak numbers 8, 11, 14, etc.).

3. Fusion of locally prominent peaks and proximate peaks Next, consolidate prominent peaks into prominent peaks. If there are proximate peaks before and after the prominent peaks, combine them all together. At this time, the power of the fusion peak is the sum of the plurality of peak powers. The center frequency of the fusion peak is a frequency obtained by adding the weights of the respective peak powers to the center frequencies of the plurality of peaks. When the power of the prominent peak and the proximate peak is 9 to 1, the center frequency of the fusion peak is a frequency that is 1/10 of the frequency interval to the proximate peak from the prominent peak center frequency to the proximate peak side.
Table 2 is a list of peaks obtained in this manner, with adjacent peaks removed. The number of peaks has decreased from 40 to 29.

4. Fusion of weak peaks into prominent peaks / fused peaks Next, all of weak peaks (peaks other than prominent peaks / fused peaks) are marked (with close distance on the frequency axis). Summarize into peaks. At this time, as in the case of the fusion of adjacent peaks, the peak power is preserved before and after the fusion, and the center frequency of the fused peaks is determined from the center frequency and power of all the peaks to be fused.
Table 3 shows the result D9 thus obtained. As shown in Table 3, the number of peaks finally obtained is 14. In Table 3, common logarithmic values of each peak power are added.

Next, the inclination is obtained from the 14 main peaks obtained in the above manner (in this case, significant peaks not fused with the fusion peak). Table 4 shows the trend lines, slopes, and y-intercepts determined by the linear least squares method for the 14 pairs (common logarithm of frequency and power).

Next, in step S13b, the series of peaks in Table 1 is divided by the value of the trend line at each peak frequency position to obtain a series of trend line relative peak powers. Here, since the trend line in Table 4 is a straight line in semi-logarithmic display, it is noted that the value of the trend line at the peak center frequency is multiplied by 10 to divide each peak power by that value. Table 5 corresponds to the result D9. In addition to the prominent peaks in Table 1, the results in Table 5 are also calculated for all adjacent peaks and weak peaks.

Inventors, RSEF ^25, RSMF, introduced three new feature quantity that RSEF ⁷⁵ in the present invention. These are obtained as frequencies whose values exceed 25%, 50%, and 75% in the percentages of Table 5, respectively. From Table 5, that is, 4.2 Hz, 4.2 Hz, and 19.1 Hz. In this way, the frequency at which the relative peak power integrated value of the result D10 is 1/4, 1/2, 3/4 of the total integrated value is obtained. Since the relative peak power is discretely localized on the frequency axis, the values of RSEF ²⁵ and RSMF may coincide with 4.2 Hz in this way.
Thus, it is important that the new feature quantities RSEF ²⁵ , RSMF, and RSEF ⁷⁵ are calculated using peaks and peak powers that are discretely present on the frequency axis. On the other hand, the conventional feature amounts SMF and SEF ⁹⁰ are amounts calculated for a spectrum that continuously varies on the frequency axis.

  In the above processing, an important point is a procedure for obtaining a main peak (in this case, a fusion peak and a prominent peak that has not been fused) and a power for obtaining a trend line. That is, as a result of analyzing a large number of electroencephalogram time series, and as a result of analyzing a chaotic model time series such as wrestler, duffing, and Lorentz, these spectra are locally significant over the entire frequency band. The knowledge that the peaks are almost uniformly arranged was obtained, and the above procedure was constructed based on this knowledge.

  For example, peak numbers 3 and 40 in Table 1 are considered to be weak peaks in this procedure and peak 40 is the most prominent peak in this procedure. A weak peak is a peak with weak power with respect to a locally remarkable peak. By distinguishing the prominent peak and the weak peak in this way, it is possible to extract locally main peak groups that are distributed almost evenly in the entire frequency band up to 30 Hz.

Next, an analysis example according to the present invention will be described.
First, we analyzed four types of EEG data: resting eyes, deep sleep, sleep awakening, and anesthesia. In the following, for easy comparison, after searching for the optimum segment length and optimum lag value for each data, the segment data length is unified to 3 seconds and the lag value to 70% as a value satisfying all data. Analysis. Even when a different segment data length and a different lag value are used for each data type, the following conclusions are not changed as long as they are the optimum segment length and the optimum lag value.
(A) in FIG. 11 is EEG data at resting eyes, (b) is the MEM-PSD, (a) in FIG. 12 is EEG data during deep sleep (sleep stage 3 or 4), (b) That MEM-PSD.
13A shows brain wave data during sleep arousal (Arousal), FIG. 13B shows its MEM-PSD, FIG. 14A shows EEG data under anesthesia, and FIG. 13B shows its MEM-PSD. PSD.
Table 6 is a list of analysis results according to the present invention.

“Spectral slope”, “RSMF”, “RSEF ^75- RSEF ²⁵ ”, “RSEF ²⁵ ”, and “RSEF ⁷⁵ ” in the top five rows of the table body are particularly characteristic amounts of analysis for the analyzer of the present invention. Various quantities such as “SMF” and “SEF ⁹⁰ ” calculated from the high-precision MEM-PSD in the analysis apparatus of the present invention are also useful. As described above, according to the present invention, it can be expected that the segment data is an output from a system (= brain) in the same state, and therefore all feature values can be evaluated as values that correctly reflect the state of the system.

This is the analysis result of EEG data when the eyes are resting. First, the slope of the spectrum is -0.060, which is gentle. RSMF is 10.0 Hz, and the center of the relative peak power train is located in the α band (8 to 13 Hz). Around this center frequency, 50% of the relative peak power is concentrated with a width of 0.1 Hz (value of RSEF ⁷⁵ -RSEF ²⁵ ). If assumed relative peak power is evenly distributed to all frequency bands (1~30Hz), because RSEF ⁷⁵ -RSEF ²⁵ becomes 14.5 Hz, a value of 0.1Hz width is relative power around the center frequency at rest closed eyes It means being concentrated. SMF is 10.1 Hz and SEF ⁹⁰ is 11.0 Hz. The difference between the two is only 0.9 Hz, and it can be seen that the α peak bears most of the power. The power in the α frequency band is 83% of the total power (1 to 30 Hz), which is more prominent than the values in the δ · θ · β frequency band.

On the other hand, at the time of deep sleep determined as sleep stage 3 or 4, the slope of the spectrum becomes steep -0.170. RSMF is 17.7 Hz and RSEF ⁷⁵ -RSEF ²⁵ is 12.8 Hz, and these values indicate that the relative peaks are almost uniformly distributed in the entire frequency band (1 to 30 Hz). That is, it shows a state in which a large number of spectral peaks are arranged on a steep spectral gradient and there are no protruding peaks. Since the spectral gradient is steep, SMF moves to the low frequency side of 3.3Hz. In addition, the power ratio in the δ, θ, α, and β frequency bands rapidly decreases to 57.3%, 31.3%, 10.0%, and 1.1% in order of increasing frequency.

Therefore, it is examined whether or not it is possible to distinguish between resting eyes closed and sleep awakening. The slope of the spectrum of the electroencephalogram data determined to be sleep-wake in the table is -0.070, which is gentle, close to the value of -0.060 when the eyes are at rest. On the other hand, RSEF ⁷⁵ -RSEF ²⁵ is 11.2 Hz, which is a value when the relative peaks are uniformly distributed in the entire frequency band, and is completely different from that at resting eyes (0.1 Hz). That is, the two are strictly distinguished. This can also be seen from the power ratio in the δ to β frequency band. This is in contrast to the situation in which the power ratio in the α frequency band is almost the same, but the section power gradually decreases in order of frequency from δ to β, and the power ratio in the α frequency band when the eyes are at rest is prominent. SMF is on the low frequency side at 4.6 Hz, and the difference between SEF ⁹⁰ and SMF is clearly different from 9.1 Hz and 0.9 Hz at resting eyes.

On the other hand, the slope of the electroencephalogram data under anesthesia is as steep as -0.194, RSMF is 6.6 Hz, and RSEF ⁷⁵ -RSEF ²⁵ is 10.1 Hz. Similarly, when compared to a deep sleep with a steep slope (-0.170), RSMF is characterized by a large shift from 17.7 Hz (deep sleep) to 6.6 Hz on the low frequency side. The power ratio in the δ frequency band is prominent at 83.4%, and the SMF is also as small as 2.5 Hz, but these tendencies are similar during deep sleep. That is, the most significant difference was found in RSMF between anesthesia and deep sleep.

  Next, after the introduction of anesthesia, it will be examined whether or not changes according to the degree of anesthesia can be grasped from these feature amounts. Additional analyzes were performed to confirm this. FIGS. 15 and 16 show data immediately after anesthesia introduction and during anesthesia introduction, respectively, where (a) is electroencephalogram data and (b) is their MEM-PSD. Each of these is followed by the electroencephalogram data under anesthesia shown in FIG.

Table 7 is a list of results of analysis by the analyzer of the present invention of data in which the depth of anesthesia gradually increases from the start of introduction of anesthesia in the second row to under anesthesia in the fourth row.

Regarding Table 7, first, the slope of the spectrum is -0.020 immediately after the induction of anesthesia, -0.078 during the induction of anesthesia, and the slope is gradually increased to finally reach a steep value -0.194 under anesthesia.
The analysis results of RSMF and RSEF ⁷⁵ -RSEF ²⁵ are characteristic for changes in the slope of the spectrum. RSMF shows a large value of 12.7 Hz immediately after the induction of anesthesia, passes through 11.5 Hz during induction of anesthesia, and reaches a low frequency of 6.6 Hz under anesthesia. RSEF ⁷⁵ -RSEF ²⁵ has almost constant values of 8.6Hz, 12.6Hz and 10.1Hz. That is, the relative peak train is evenly distributed over the entire frequency band immediately after the induction of anesthesia, and RSMF moves to the low frequency side under sufficient anesthesia.
On the other hand, the behavior from δ to SMF ⁹⁰ that is not normalized by the trend (curved) line varies depending on the degree of anesthesia. SMF moves from 9.5Hz after induction of anesthesia to 7.6Hz, 2.5Hz in order to the low frequency side. SEF ⁹⁰ also moves to the lower frequency side, and finally reaches 5.6 Hz under anesthesia. These changes can be understood as reflecting changes in the slope of the spectrum.
Similarly, the power ratio in the δ to β frequency band also fluctuates from a state having main power in the vicinity of the α frequency band to a state having overwhelming power in the δ frequency band, as estimated from changes in the slope of the spectrum.

  From the above, the analysis device of the present invention can discriminate each state under resting eyes, sleep awakening, deep sleep, and anesthesia from the electroencephalogram data, and can accurately discriminate changes with time due to the introduction of anesthesia. I understand.

The present invention is as described above, and differs from the analysis apparatus according to the conventional method in the following items.
1. Segment data to be analyzed (present invention)
2-5 seconds long data expected to be in the same state. Variable length or fixed. When fixing, examine a series of optimum segment lengths in advance and set the shorter one.
(Conventional method)
Length consisting of data of 2 power points determined by sampling frequency and analysis method (FFT). Fixed length.

2. Spectral calculation method (present invention)
Maximum entropy method (MEM). By adopting MEM, the segment length (= number of data points) can be set arbitrarily.
(Conventional method)
FFT. Because it is a method that assumes high-speed but infinite length data, it is inevitable that the spectrum contains many false peaks derived from the segment length.

3. Method of calculating the slope of the exponential spectrum For the main peak of the MEM-PSD obtained from the optimum segment length and optimum lag value, obtain a series of slopes of center frequency and peak power. As described above, this corresponds to finding the slope of the power frequency distribution of each term when segment data is described by a generalized triangular polynomial by optimizing the segment length and lag value.
(Conventional method)
No processing is carried out, or it is obtained from all peak points including a false peak derived from the segment length, or obtained from all calculation points.

4). Other features of the extracted electroencephalogram spectrum.
(Invention)
In addition to all the features by the conventional method, in addition to the relative peak power sequence normalized by the trend (curved) curve of the exponential spectrum, the frequency RSEF ²⁵ (the integrated value of the relative peak power is 1/4 of the total integrated value) Relative Spectral Edge Frequency 25), 1/2 frequency RSMF (Relative
Spectral Mid Frequency), a frequency RSEF ^{75 of} 3/4. These three quantities are introduced in the present invention and correspond to the integrated values of the powers of the respective terms of the generalized triangular polynomial describing the segment data.
(Conventional method)
δ, θ, α, β Frequency bands (1 to 4, 4 to 8, 8 to 13, 13 to 30 Hz), segmented power, SMF (Spectral Mid Frequency, frequency at which the integrated value of spectrum is 50% at 1 to 30 Hz ), SEF ⁹⁰ (Spectral
Edge Frequency 90, also the frequency at which the integrated value is 90%).

And in this invention, since it has the difference as mentioned above compared with the conventional method, it has the following characteristics.
(1) By dealing with electroencephalogram data of the optimal segment length, it is expected that analysis of “dynamically stable data” that is always assumed to be in a constant dynamic state will be performed.
(2) In addition, since the spectrum is calculated with the optimal lag value, the obtained MEM-PSD is expected to correspond to the generalized trigonometric polynomial representation of the original segment data. That is, it is expected that the behavior of EEG data on the time axis matches the behavior of MEM-PSD on the frequency axis.
(3) As a result of the consistency ensured in this way, it is possible to place more confidence in various quantities such as the slope of the obtained spectrum and the segmental power than in the conventional method.
(4) In addition to the quantities in the conventional electroencephalogram analysis, in the present invention, the most fundamental feature of the spectrum is not only the inclination of the trend (curved) line, but also the quantities created by the slope and the relative peak sequence (relative peak power Since it is described as a set of frequencies at which the integrated values are 1/4, 1/2, and 3/4), knowledge about the dynamic state of the system (= brain) that cannot be distinguished conventionally can be obtained.

It is explanatory drawing of the whole structure which represented typically Embodiment of the analyzer which concerns on this invention. It is explanatory drawing which shows typically the one part structure of the analyzer which concerns on this invention, and the flow of the process. It is explanatory drawing which shows typically the structure of the other part of the analyzer which concerns on this invention, and the flow of the process. It is explanatory drawing which shows an example of an electroencephalogram and its spectrum. It is explanatory drawing which shows the electroencephalogram data of 20 seconds from which a state clearly differs in the first half and the second half. It is explanatory drawing which shows the electroencephalogram data of 5 second length, its generalized trigonometric polynomial expression, and a residual. It is explanatory drawing which shows the artificial time series data and the analysis result by this invention. FIG. 8 is an explanatory diagram showing artificial time-series data in which some modes are lost in the second half of the data in FIG. 7 and the analysis results according to the present invention. FIG. 9 is an explanatory diagram illustrating triangular term parameters for each of the data in FIG. 7 and FIG. 8. It is explanatory drawing which shows the example of MEM-PSD obtained in the analysis execution part. It is explanatory drawing which shows the example of the electroencephalogram data at the time of resting eyes closed, and its MEM-PSD. It is explanatory drawing which shows the example of the electroencephalogram data at the time of deep sleep and its MEM-PSD. It is explanatory drawing which shows the example of the electroencephalogram data at the time of sleep awakening, and its MEM-PSD. It is explanatory drawing which shows the example of the electroencephalogram data under anesthesia, and its MEM-PSD. It is explanatory drawing which shows the example of the electroencephalogram data immediately after anesthesia introduction, and its MEM-PSD. It is explanatory drawing which shows the example of the electroencephalogram data during anesthesia induction, and its MEM-PSD.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Original time series data 2 Segment condition input part 3 Analysis condition input part 4 Optimal analysis condition derivation part 5 Analysis execution part 6 Setting processing means 7 First processing means 8 Second processing means 9 Third processing means 10 Segment preparation Means 11 Power spectral density calculation means 12 Peak extraction means 13 Feature quantity extraction means

Claims (22)

For the segment that is cut out from the original time series data and analyzed, the total number of segments to be cut or the time increment between the shortest and longest segments, consisting of the shortest and longest segment lengths, the shortest and longest segments, and segments of different lengths between them The segment condition input part with
An analysis condition input unit having as input items a set interval of a series of lag values set between the minimum lag value and the maximum lag value and the minimum / maximum lag value;
Based on the segment conditions input to the segment condition input section and the analysis conditions input to the analysis condition input section, analysis is performed by the maximum entropy method and the nonlinear least squares method for all analysis conditions for all segments. Selecting an appropriate segment and an analysis condition from all analysis results, and deriving an optimum segment length and an optimum lag value correspondingly,
An analysis device for time-series data, characterized in that it comprises an analysis execution unit for executing an analysis by a maximum entropy method by setting an optimum analysis condition derived in an optimum analysis condition deriving unit as an analysis condition. The optimal analysis condition derivation unit
Based on the conditions input to the segment condition input unit, a plurality of segments having different lengths are cut out from the original time series data and set as sample segments, and the analysis conditions input to the analysis condition input unit are read and set. Setting processing means;
A first processing means for calculating a power spectral density using a maximum entropy method according to all analysis conditions for each of all sample segments set by the setting processing means;
For each of the power spectral densities obtained by the first processing means, a main spectral peak is extracted, and various quantities of the generalized trigonometric polynomial expression for the sample segment are calculated from them by the nonlinear least square method. Processing means,
The validity of the generalized trigonometric polynomial expression obtained by the second processing means with respect to the sample segment data and the consistency with respect to the power spectral density are judged, and one corresponding to the generalized trigonometric polynomial expression with high validity and consistency is obtained. 3. The time series according to claim 1, wherein the sample sequence is composed of third processing means for selecting one sample segment and deriving the corresponding segment length and lag value as the optimum segment length and optimum lag value. Data analysis device. The second processing means extracts the number, each peak frequency, and each peak power for the main spectrum peak from the power spectral density calculated by the first processing means, and the number is the number of terms and each peak frequency. The amount of the generalized triangular polynomial expression is calculated by calculating the nonlinear least square method that minimizes the sum of the squares of the residuals with the reciprocal of Item 3. The time-series data analysis device according to Item 2. The third processing means compares the standard deviation of the residual in various quantities of the generalized trigonometric polynomial expression for each sample segment with the set value, rejects the generalized trigonometric polynomial expression greater than the set value, and otherwise A first selection function using a generalized trigonometric polynomial expression of
Compare the period of each term of the polynomial determined by the nonlinear least squares method with its initial value set from the reciprocal of the peak frequency of the power spectral density, and reject the generalized triangular polynomial expression whose difference is greater than the set value And a second selection function using other generalized triangular polynomial expressions as selection candidates,
A generalized triangular polynomial expression that compares the power obtained from the amplitude of each term of the polynomial determined by the nonlinear least squares method with the power of the corresponding peak of the power spectral density one by one, and the difference has an amplitude greater than the set value And a third selection function with other generalized triangular polynomial expressions as selection candidates,
4. The time series according to claim 2, wherein a generalized trigonometric polynomial expression having high validity and consistency is selected by sequentially performing processing by the first, second, and third sorting functions. Data analysis device. The third processing means has the smallest standard deviation of the residual when a plurality of generalized triangular polynomial expressions remain as selection candidates after sequentially performing the processing by the first, second, and third selection functions 5. The time-series data analysis apparatus according to claim 4, wherein the apparatus has a fourth selection function for selecting a generalized triangular polynomial expression. The third processing means performs processing by the first, second and third or first, second, third and fourth sorting functions, and then the sample segment having the selected generalized trigonometric polynomial expression is obtained. When there are multiple remaining samples, it has a fifth sorting function that selects the longest sample segment as the optimal sample segment, and the sample segment selected by the fifth sorting function is selected as the optimal segment for that sample segment. 6. The time-series data analyzing apparatus according to claim 4, wherein a lag value obtained by calculating a power spectral density corresponding to the generalized trigonometric polynomial expression is selected as an optimum lag value. The analysis execution unit
Segment preparation means for cutting out segments from original time series data based on the optimum segment length derived by the optimum analysis condition derivation unit and set in the analysis condition setting means,
A power spectrum density calculating means for calculating a power spectrum density by a maximum entropy method using an optimum lag value derived in the optimum analysis condition derivation unit for the prepared segment and set in the analysis condition setting means;
Peak extraction means for extracting the number of main peaks of the calculated power spectral density, the center frequency and peak power of each peak;
The time-series data analysis apparatus according to any one of claims 1 to 6, wherein the time-series data analysis apparatus includes: feature quantity extraction means for extracting a feature quantity from the extracted peak sequence. The analysis condition setting means comprises a function for setting the optimum analysis condition derived by the optimum analysis condition deriving unit as it is, a function for setting the analysis condition input by the input means, and a selection function thereof. The time-series data analysis device according to claim 7. The peak extraction means obtains a locally significant peak in the range of several times the average interval between peaks obtained from all the peaks of power spectral density, and the shorter than the average interval, the obtained remarkable peak is obtained. The main peak from the first process of fusing adjacent peaks to form a fused peak and the second process of fusing all the peaks other than the prominent peak and the fused peak to the nearest prominent peak or fused peak When combining multiple peaks, the peak power before and after the fusion is preserved, and the center frequency of the fusion peak is determined by dividing the peak power before the fusion. The time-series data analysis device according to claim 7. The feature quantity extraction means tends to obtain the slope and y intercept of the so-called exponential spectrum trend line by the linear least square method for the pair of log power and peak frequency of the plurality of main peaks extracted by the peak extraction means. Line power calculating means, and relative power calculating means for obtaining a trend line relative power by dividing the peak power value by the power value indicated by the trend line for every peak obtained by the power spectral density calculating means, And a feature amount extracting means for extracting a feature amount of a relative peak power distribution from the peaks discretely arranged on the frequency axis and the relative peak power thereof. The time-series data analysis device according to any one of the above items. The time series data is brain wave data, and the feature quantity extracted by the feature quantity extraction means is the sum of the relative peak powers from the low frequency side, usually in the frequency band of interest of the brain wave spectrum of 1 to 30 Hz or 0.5 to 30 Hz. 8. The time-series data analysis apparatus according to claim 7, comprising: three frequencies that are 25%, 50%, and 75% of the total relative peak power of the frequency band of interest. For the segment that is cut out from the original time series data and analyzed, the total number of segments that are composed of the shortest and longest segment lengths, the shortest and longest segments, and segments of different lengths between them, or the time increment between the shortest and longest segments As a segment condition,
A process of inputting a set interval of a series of lag values set between the minimum lag value, the maximum lag value, and the minimum / maximum lag value as an analysis condition,
Based on the input segment conditions and analysis conditions, all segments are analyzed by the maximum entropy method and nonlinear least squares method under all analysis conditions. The process of selecting one analysis condition and deriving the analysis condition consisting of the optimal segment length and the optimal lag value,
A computer-readable recording medium on which a time series data analysis program is recorded, characterized in that it comprises a process of executing analysis by a maximum entropy method by setting the derived optimum analysis conditions as analysis conditions. The process of deriving analysis conditions is
A process of cutting out a plurality of segments of different lengths from the original time series data based on the input segment conditions and setting them as sample segments,
The process of setting analysis conditions,
A first processing step of calculating a power spectral density using a maximum entropy method according to all set analysis conditions for each of all set sample segments;
A main spectrum peak is extracted for each of the power spectral densities obtained by the first processing step, and various quantities of the generalized trigonometric polynomial expression for the sample segment are calculated from them by the nonlinear least square method. And the process of
The validity of the generalized trigonometric polynomial expression obtained by the second processing step with respect to the sample segment data and the consistency with respect to the power spectral density are judged, and one corresponding to the generalized trigonometric polynomial expression with high validity and consistency is obtained. 13. The time series according to claim 12, comprising a third processing step of selecting one sample segment and deriving the corresponding segment length and lag value as the optimum segment length and optimum lag value. A computer-readable recording medium on which a data analysis program is recorded. The second processing step is a step of extracting the number, each peak frequency and each peak power of the main spectrum peak from the power spectral density calculated in the first processing step, A process of calculating various quantities of a generalized triangular polynomial expression by calculating a nonlinear least-squares method that minimizes the sum of squares of the residuals, using an inverse of the peak frequency as an initial value of the period of each triangular term. A computer-readable recording medium on which the time-series data analysis program according to claim 13 is recorded. The third processing step compares the standard deviation of the residual in various quantities of the generalized trigonometric polynomial expression for each sample segment with the set value, rejects the generalized trigonometric polynomial expression greater than the set value, and otherwise A first selection process using a generalized trigonometric polynomial expression of
Compare the period of each term of the polynomial determined by the nonlinear least squares method with its initial value set from the reciprocal of the peak frequency of the power spectral density, and reject the generalized triangular polynomial expression whose difference is greater than the set value And a second selection process using other generalized triangular polynomial expressions as selection candidates,
A generalized triangular polynomial expression that compares the power obtained from the amplitude of each term of the polynomial determined by the nonlinear least squares method with the power of the corresponding peak of the power spectral density one by one, and the difference has an amplitude greater than the set value And a third selection process with other generalized triangular polynomial expressions as selection candidates,
The time series data analysis according to claim 12 or 13, wherein the generalized trigonometric polynomial expression having high validity and consistency is selected by sequentially performing the processes of the first, second and third selection processes. A computer-readable recording medium on which a program is recorded. In the third processing step, the standard deviation of the residual is the smallest when a plurality of generalized triangular polynomial expressions remain as selection candidates after sequentially performing the processing in the first, second, and third selection steps. The computer-readable recording medium recording the time series data analysis program according to claim 15, further comprising a fourth selection process of selecting a generalized trigonometric polynomial expression. In the third processing step, a plurality of selected generalized trigonometric polynomial expressions remain after processing by the first, second and third or first, second, third and fourth sorting steps If there is a fifth sorting process in which the longest sample segment is selected as the optimal sample segment, the sample segment selected by the fifth sorting process is selected as the optimal segment, and the selected general segment is selected for the sample segment. 17. The time-series data analysis device according to claim 15, wherein a lag value obtained by calculating a power spectral density corresponding to a generalized trigonometric polynomial expression is selected as an optimum lag value. The analysis execution process
A segment preparation process for extracting a segment from original time series data based on the optimal segment length derived in the optimal analysis condition derivation process and set in the analysis condition setting means,
A power spectrum density calculation process for calculating a power spectrum density by a maximum entropy method using an optimum lag value set in the analysis condition setting means, which is derived in the optimum analysis condition derivation process for the prepared segment;
A peak extraction process for extracting the number of main peaks of the calculated power spectral density, the center frequency of each peak and the peak power;
18. A computer-readable recording program for analyzing time-series data according to any one of claims 12 to 17, characterized by comprising a feature quantity extraction process for extracting a feature quantity from the extracted peak sequence. recoding media. The analysis condition setting means comprises a function for setting the optimum analysis condition derived in the optimum analysis condition derivation process as it is, a function for setting the analysis condition input by the input means, and a selection function thereof. A computer-readable recording medium on which the time-series data analysis program according to claim 18 is recorded. The peak extraction process is
The process of obtaining the average interval between peaks from all the peaks of the power spectral density, the process of obtaining locally prominent peaks in the range of several times the obtained average interval, and the average interval between the obtained prominent peaks The first processing step, which consists of fusing adjacent peaks at shorter intervals to form a fusion peak, and fusing all peaks other than the prominent peak and the fusion peak into the nearest prominent peak or fusion peak And a second processing step
In the first processing step and the second processing step, when a plurality of peaks are fused, the peak power before and after the fusion is preserved, and the peak powers of the plurality of peaks before the fusion are prorated and distributed. The computer-readable recording medium recording the time-series data analysis program according to claim 18, wherein a center frequency is obtained. The feature extraction process is a trend line for determining the slope and y-intercept of the so-called exponential spectrum trend line by the linear least squares method for the combination of the logarithmic value and peak frequency of the peak power of the plurality of main peaks extracted in the peak extraction process A calculation process and a relative power calculation process for calculating a trend line relative power by dividing the peak power value by the power value indicated by the trend line for all peaks obtained by the power spectral density calculation means, 21. The method according to any one of claims 18 to 20, comprising a peak discretely arranged on the frequency axis and a feature amount extraction step of extracting a feature amount of a relative peak power distribution based on the relative power. A computer-readable recording medium on which the time series data analysis program described in 1 is recorded. The time series data is brain wave data, and the feature quantity extracted by the feature quantity extraction process is the sum of the relative peak power from the low frequency side, usually in the target frequency band of the brain wave spectrum of 1 to 30 Hz or 0.5 to 30 Hz. 19. The computer-readable record recording the time-series data analysis program according to claim 18, characterized in that includes three frequencies that are 25%, 50%, and 75% of the total relative peak power of the frequency band of interest. Medium.

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