JP2011002272A - System and program for analyzing time series data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for which it is widely recognized as being reasonable where the basic fluctuations obtained in analysis of time series data is decided as being an "optimum solution", and to provide a system for analyzing the time series data which can uniquely determine the basic fluctuations in time series which occurs in the order of a data length.SOLUTION: In the analytic system proposed herein, parameters of GTP corresponding to many lags, and amounts obtained from MEM-PSD, are compared on the basis of the total of power of each triangular term and that of power of a spectrum peak so as to select the lag of which the consistency is within tolerance. The power of each triangular term of the GTP, corresponding to the selected lag and that of the corresponding spectrum peak, is sequentially compared so as to select the triangular term of which the consistency lies within the tolerance, as the triangular term constituting the basic fluctuation, and the sum of the power of the triangular terms constituting the basic fluctuations, corresponding to the selected lag is compared so as to determine the lag expressing the optimum basic fluctuations.

Description

  The present invention relates to an analysis system and an analysis program for analyzing time series, particularly time series data that fluctuates in the order of data length.

  The inventor previously analyzed time-series data using a maximum entropy method (MEM) as shown in Patent Document 1 and Patent Document 2, for example, as an analysis system capable of analyzing time-series data with high accuracy. We propose a method and an analysis system that executes a computer program to which the analysis method is applied. Note that a method for analyzing time series data using the maximum entropy method is also described in Non-Patent Document 1 and Non-Patent Document 2, for example.

  The analysis method described above is to analyze the time series data to be analyzed by expressing it with a generalized trigonometric polynomial. Generally, the maximum entropy method is applied to the time series data, and the power spectral density ( In the following, the number of terms and the period value of each triangular term as an initial value for solving the generalized trigonometric polynomial (hereinafter also referred to as GTP) from the prominent spectral peak is obtained. Based on the initial value and the linearized nonlinear least squares method, the parameters of each triangular term are obtained, the residual time series data is obtained, and these are added together to regenerate the time series data. It consists of the process of configuring.

  This analysis method and the analysis system to which it is applied do not assume any numerical model and can perform high-precision analysis using only time-series data, and the analysis is sufficient even with the computational capability of a normal personal computer. It is characterized by being practical.

By the way, in time-series data analysis, there is a group of data that requires special handling. For example, ABPM data (blood pressure data measured for about 24 hours at intervals of about 30 minutes to 1 hour with a portable sphygmomanometer), and when viewed from the viewpoint of analyzing the data, the ABPM data shows the following characteristics.
(1) The measurement accuracy of individual data varies greatly.
(2) The sampling interval is long (cannot be shortened).
(3) The measurement period is short (cannot be long).
(4) There are very few data points (not many).
(5) The data structure corresponding to the measurement period length is important.

  The features (2) to (4) can be easily understood by considering a measurement method in which the upper arm is subjected to pressure reduction and then gradually reduced. Also, for example, systolic blood pressure (SBP, so-called higher blood pressure) and diastolic blood pressure (DBP, lower blood pressure) each appear after every 100,000 beats per day, and every beat Although it varies, it can understand the feature of (1) because it describes the change with only a few tens of points. In addition, in many cases, the fluctuation corresponding to the data length is an object of interest (feature (5)). This is the so-called circadian rhythm or circadian rhythm.

In addition to ABPM data, there are many data such as pulsation interval fluctuation data (RR data) and activity (acceleration) data that have an important data structure corresponding to the measurement period length at most.
In the case of RR data, about 100,000 points of data can be obtained by 24-hour measurement. However, when circadian rhythms are a problem, it is difficult to handle 100,000 points of data directly. Eventually, for example, data created by an average value every 5 minutes is constructed and the long-term structure is examined. As a result, the data has the feature (4) in the above table.

  FIG. 7 shows SBP data measured every hour for 48 hours. The measurement started at 12:15 on the first day and ended with the measurement at 11:15 on the following day (data score was 48 points). As shown in the figure, blood pressure is high during the day and low at night. And it often falls temporarily in the afternoon. The example in the figure also shows a low value around 2am to 6am on the second day and around 3am to 6am on the third day. In addition, a decrease in blood pressure is observed around 3:00 to 6:00 pm on the first day and around 2:00 to 5:00 pm on the second day. Including these features, the data in the figure is expected to change in the order of 24 hours (daily rhythm). Hereinafter, this variation is described as a base variation, which is a more general concept. The results of analyzing such time-series data using the above-described analysis method by the present inventor are shown below.

  FIG. 8 (a) shows only the first 24 points of the data shown in FIG. 7. The 48-hour ABPM measurement places a heavy burden on the subject, and usually the 24-hour measurement is performed. FIG. 8B shows the power spectral density obtained by applying the maximum entropy method, and the lag used in this calculation is 18.

  Spectral peaks in MEM-PSD in FIG. 8B are as shown in the table of FIG. 9, and there are seven main peaks from 20.82 hours to 2.37 hours when viewed from the reciprocal of the peak center frequency (Nyquist frequency). Excluding location peaks).

  (A) of FIG. 10 shows a time series reconstructed by a generalized triangular polynomial consisting of seven terms having seven periods corresponding to the above-described seven remarkable spectral peaks, and (b) shows a residual. Is.

  As can be seen from FIG. 10, the coincidence between the original time series data and the GTP description (fitting curve) is sufficient, and no time dependence is recognized in the residual.

  However, it is not possible to determine whether or not this GTP description optimally represents the base variation of the original time series data only by comparing the GTP description with the original time series data. Therefore, the MEM-PSD is calculated with lag 18 as to whether the above seven triangular terms are the modes that constitute the 24-point time-series basis fluctuations, and what criteria should be followed if short-period behavior is excluded. However, there has not been a method for answering questions such as how appropriate the value is for the purpose of extracting the base variation.

JP-A-5-216195 JP-A-6-149863

Supervised by Koji Miyake, Nobuaki Takahashi, Akio Kamiyama, and Yasuo Otomo, “Biological Rhythm Structure: Analysis of Biological Time Series Data Using MemCalc”, 1st Edition, Fuji Shoin, January 15, 1992, p.19- 39 Kazuo Joban, Ikuo Otomo, Yukio Tanaka, “Time Series Analysis by Maximum Entropy Method… Theory and Practice of MemCalc…” Second Edition, Hokkaido University Press, December 25, 2008, p.45-52 , P.73-77, p.79-99

  The problem to be solved by the present invention can provide a method widely recognized as reasonable to judge that the basis variation obtained in the analysis of the time series data is the “optimal solution”, and To provide a time-series data analysis system and an analysis program capable of uniquely determining a time-series basis fluctuation that fluctuates in the order of data length.

In order to solve the above-described problems, the present invention is an apparatus for analyzing time-series data by a programmed computer, an input unit for analysis-target time-series data and analysis conditions, and a processing means for executing analysis. And an analysis result recording means for recording the analysis result,
A first process for calculating a parameter of a generalized trigonometric polynomial from a time series data to be analyzed using a maximum entropy method for a large number of lags and calculating a power spectral density from various quantities obtained therefrom. Process,
Compare the parameters of the generalized trigonometric polynomial corresponding to many lags obtained in the first process and the quantities obtained from the power spectral density, select the lag with the highest consistency, and handle the lag Selecting a highly consistent triangular term in the generalized trigonometric polynomial as a triangular term constituting the base variation;
Using the parameters of the generalized trigonometric polynomial obtained corresponding to the optimal lag obtained in the second processing step, the value of the base variation curve at each time point is calculated from the parameters of the triangular term constituting the base variation. And a third processing step for obtaining the value of the residual curve at each time point from the time series data, and a processing means for executing the third processing step.
In the second processing step, parameters of the generalized trigonometric polynomial corresponding to a large number of lags obtained in the first processing step, and various quantities obtained from the power spectral density, the sum of the power of each triangular term and the spectral peak are obtained. The first selection process for selecting lags whose consistency is within an allowable range as compared with the sum of the powers of the generalized trigonometric polynomials corresponding to the lag selected in the first selection process A second selection process in which the power of the term and the power of the corresponding spectrum peak are sequentially compared, and a triangular term whose consistency is within an allowable range is selected as a triangular term constituting the base variation; and a second selection The third selected in the process is to compare the sum of the powers of the triangular terms constituting the base variation corresponding to each lag, and obtain the lag that maximizes the power sum as the lag that expresses the optimal base variation. Suggest analysis system time-series data was configured to perform the selection process sequentially.

In the present invention, the power spectral density is calculated from the time series data to be analyzed using the maximum entropy method for a large number of lags, and the parameters of the generalized trigonometric polynomial are calculated from the quantities obtained therefrom using the fitting method. A first process to be sought;
Compare the parameters of the generalized trigonometric polynomial corresponding to many lags obtained in the first process and the quantities obtained from the power spectral density, select the lag with the highest consistency, and handle the lag Obtained by corresponding to the optimal lag obtained in the second processing step and selecting the triangular term having high consistency in the generalized trigonometric polynomial as the triangular term constituting the base variation. Using each parameter of the generalized trigonometric polynomial, the value of the base fluctuation curve at each time point is obtained from the parameters of the triangular term constituting the base fluctuation, and the value of the residual curve at each time point is obtained from the time series data. A program for causing a computer to execute a third processing step,
In the second processing step, parameters of the generalized trigonometric polynomial corresponding to a large number of lags obtained in the first processing step, and various quantities obtained from the power spectral density, the sum of the power of each triangular term and the spectral peak are obtained. The first selection process for selecting lags whose consistency is within an allowable range as compared with the sum of the powers of the generalized trigonometric polynomials corresponding to the lag selected in the first selection process A second selection process in which the power of the term and the power of the corresponding spectrum peak are sequentially compared, and a triangular term whose consistency is within an allowable range is selected as a triangular term constituting the base variation; and a second selection The third selected in the process is to compare the sum of the powers of the triangular terms constituting the base variation corresponding to each lag, and obtain the lag that maximizes the power sum as the lag that expresses the optimal base variation. We propose an analysis program of time series and configured to perform a selection process sequentially.

  According to the present invention, in the above configuration, the second processing step includes a fourth selection step for selecting a lag corresponding to a parameter having higher consistency after the first selection step, and the fourth selection step. Comparing the power of each triangular term of the generalized trigonometric polynomial corresponding to the lag selected in the process and the power of the corresponding spectral peak sequentially, the triangular term whose consistency is within an acceptable range constitutes the base variation A lag that maximizes the power sum by comparing the sum of the powers of the second selection process that is selected as a triangular term and the powers of the triangular terms that constitute the base fluctuations corresponding to the respective lags selected in the second selection process. A time-series data analysis system or analysis program is proposed in which a third selection process is sequentially performed as a lag that expresses the optimum base variation.

  According to the present invention, in the above configuration, in the second selection process, the consistency of the triangular term of the longest period of the data length order is within an allowable range, and the consistency is allowed continuously in descending order of the period. A time series data analysis system or program for selecting a series of triangular terms within a range as a triangular term constituting a base variation is proposed.

  The present invention also proposes a time-series data analysis system or analysis program for selecting a triangular term whose consistency is within an allowable range as a triangular term constituting a base variation in the second selection process in the above configuration. To do.

  In the present invention, in the above configuration, the analysis condition input to the input unit is a value that sets the fitting method to be used and the first selection process of the second processing process and the allowable range of the second selection process. We propose an analysis system or analysis program for certain time series data.

  According to the analysis system and the analysis program according to the present invention, it is possible to provide a method that is widely recognized as reasonable to judge that the base variation obtained in the analysis of the time series data is the “optimal solution”. Thus, it is possible to provide a time-series data analysis system and an analysis program capable of uniquely determining a time-series basis variation that varies in the order of the data length.

FIG. 1 is a system diagram of an overall configuration schematically showing an embodiment of an analysis system according to the present invention. FIG. 2 is a system diagram of the overall configuration of the embodiment of the analysis system according to the present invention. FIG. 3 is an explanatory diagram schematically showing a partial configuration of an analysis system according to an embodiment of the present invention and a processing flow thereof. FIG. 4 is an explanatory view schematically showing another part of the configuration of the embodiment of the analysis system according to the present invention and the flow of the processing. FIG. 5 is an explanatory view schematically showing still another part of the configuration of the embodiment of the analysis system according to the present invention and the flow of the processing. FIG. 6 is an explanatory view schematically showing still another part of the configuration of the embodiment of the analysis system according to the present invention and the flow of the processing. FIG. 7 shows SBP data measured every hour for 48 hours. FIG. 8A shows 24-hour SBP data (data score: 24), and FIG. 8B shows the MEM-PSD. FIG. 9 shows various amounts of spectral peaks in the MEM-PSD of FIG. FIG. 8B shows a time series reconstructed by a generalized trigonometric polynomial (GTP) consisting of seven terms having seven periods corresponding to the spectral peaks of the seven main terms in the MEM-PSD of FIG. Indicates the residual. It shows various quantities of each term of GTP in FIG. It is MEM-PSD in the lag value 20 of 24 hour SBP data (data points: 24) of Fig.8 (a). FIG. 13 shows various amounts of spectral peaks in the MEM-PSD of FIG. 12. 14A shows a GTP curve having triangular terms corresponding to the nine main peaks of the MEM-PSD in FIG. 12, and FIG. 14B shows a residual curve. FIG. 15 shows the parameters of the GTP curve of FIG. FIG. 16 shows the analysis result of the single condition analysis unit corresponding to the lag value 20. FIG. 17 shows the calculation results of TPP _L and TMP _L corresponding to lag values 16-23. FIG. 18 shows the number of modes calculated for each of the lag values 16 to 23 and the power of each triangular term. FIG. 19 shows FIG. 17 with the ratio of TMP _L and TPP _L added. FIG. 20 shows a comparison between the power of each triangular term at a lag value of 20 and the peak power of MEM-PSD. FIG. 21 shows a comparison of the power of each triangular term at the lag value 21 and the peak power of the MEM-PSD. It shows the size of FMP _{L at} each lag value. (A) of FIG. 23 shows a base fluctuation curve calculated from the triangular term parameter of the base fluctuation, and (b) shows a residual curve composed of a difference between the original time series data and the base fluctuation curve. It is.

  In the time series data analysis system and analysis program according to the present invention, in the process of obtaining the parameters of the generalized trigonometric polynomial from the time series data to be analyzed, a large number of lags are used for the calculation, and the fitting is the main of MEM-PSD. All the peaks are used, and the quality is based only on the consistency between the MEM-PSD on the frequency axis and the GTP description on the time axis. Here, as a feature of the present invention, a standard deviation of a portion (residual curve) that cannot be described by a stable triangular term is not used as a criterion.

In the present invention, the following points are the main points.
1. First, in the present invention, the base fluctuation is regarded as a sum of vibration modes that exist stably during a time-series observation period.
2. In the present invention, the maximum entropy method (MEM) is used as the processing of the main processing steps. As shown in Non-Patent Document 2, MEM is a method that directly relies on the principle of maximum entropy (ME principle). MEM handles only given time-series data and does not assume any structure before or after the data. And extract the maximum data structure. As a limit, MEM-PSD converges to a Dirac δ function sequence.
3. In the present invention, a generalized triangular polynomial (GTP) is adopted as an equation for reconstructing and expressing a time series. As shown in Non-Patent Document 2, GTP is an equation having the widest application range among equations expressing time-series fluctuations. And more importantly, the spectrum becomes Dirac's δ function sequence. That is, the description by MEM on the frequency axis and the description by GTP on the time axis constitute a pair that is consistent with each other.
4). In the present invention, the base variation to be taken out when the time series is reconstructed and expressed in GTP is the sum of triangular terms (stable triangular terms or stable terms) that exist stably during the time series observation period. In addition, for the purpose of capturing fluctuations in the order of the data length, a triangular term having a period of the order is a stable triangular term, and a series of stable triangular terms that are continuous in the periodic order is regarded as a base fluctuation component. In addition, a stable term that appears after an unstable term can also be regarded as a base fluctuation component. Even in that case, there will be no inconsistency in the analysis procedure.
5). As a rational criterion for determining the optimum solution, the MEM-PSD and GTP are consistent, and the curve that maximizes the sum of the powers of the stable triangular terms is set as the optimum solution. At this time, the sum of the stable triangular terms of the curve is the optimum base variation to be obtained.
6). The following procedure is used to determine whether MEM-PSD and GTP are consistent and which are stable terms.
6-1. Using all the main peaks of MEM-PSD calculated by many lags, GTP with the number of triangular terms as the number and the reciprocal of the peak frequency as the period of the triangular term is applied to the time series data. (All modes are applied), time series data is reconstructed by GTP.
6-2. It is determined whether or not the sum of the powers of the main peaks matches the sum of the powers of all the triangular terms of the GTP, selects the matching ones, and performs the following determination processing. The power of the triangular term is 1/2 of the square of the amplitude.
6-3. For a pair of spectral peak and GTP triangular terms, those whose peak power and triangular term power match are stable terms, and those that are not are unstable terms.

Next, one embodiment of an analysis system according to the present invention will be described with reference to the accompanying drawings.
First, FIG. 1 is an explanatory diagram showing the relationship between the analysis system of the present invention and inputs and outputs.
In FIG. 1, reference numeral 1 denotes an analysis system using a computer. Time series data 2 and analysis conditions 3 to be analyzed are input to the analysis system 1, and analyzed by the analysis system 1 to output an analysis result 4. The

  As the time-series data 2 to be analyzed input to the analysis system 1, not only data that is sampled at equal intervals and not missing, but also data that is irregularly spaced or missing can be applied. In the latter case, analysis can be performed with equal intervals using a known equal interval processing method.

  The analysis condition 3 to be input to the analysis system 1 includes two methods for setting a fitting method used for processing to be described later, and a first selection process and a permissible range of the second selection process to be described later. Is the value of

  As the fitting method, the least square method is usually set, but a method of minimizing the absolute value of the deviation and a more robust method such as the M estimation method can also be set.

  In the present invention, the time series data 2 and the analysis conditions 3 to be analyzed are input to the analysis system 1 and analyzed by the analysis system 1 to obtain an analysis result 4 including a base variation curve that is uniquely determined. In the analysis system of the present invention, as will be described later, it may be determined that “there is no optimal basis fluctuation curve”. In this case, the above-described allowable range of the analysis condition 3 is widened and recalculation is performed. You can also.

FIG. 2 is a system diagram showing the configuration of the analysis system and the flow of processing according to the present invention.
Reference numeral 5 denotes an input unit, which takes in the time series data 2 and the analysis condition 3 described above. Reference numeral 6 denotes a calculation condition setting unit. The calculation condition setting unit 6 determines the number of repetitive calculations based on the time series data 2 and the analysis condition 3 taken in via the input unit 5. As will be described later, the analysis system of the present invention is to repeatedly apply the maximum entropy method (MEM) to obtain the optimum base variation. When the score of the time series data 2 is N, the number of iterations and the condition are MEM. Is determined by the lag value L and its range (1 to N−1).

  That is, if there are sufficient calculation resources in the analysis system 1, the lag value L is changed from 1 to N-1, that is, N-1 iterations are performed corresponding to all the lag values L. In the following description, for simplicity, the number of repetitions is N−1. However, lag 1 may be excluded because its MEM spectrum (MEM-PSD) has no peak. In addition, even when computational resources are not sufficient, it is preferable to perform operations on a large number of lags.

  Reference numeral 7 denotes a control unit, and the control unit 7 controls the above-described N-1 iterations in the single condition analysis unit 8. The single condition analysis unit 8 performs the first process described above, calculates the MEM-PSD with the lag value L specified by the control unit 7, and extracts the number of main spectral peaks and the center frequency. Applying GTP, where the number of peaks is the number of triangular terms and the reciprocal of each center frequency is the period of the triangular terms to the time series data, the level value of the polynomial, the amplitude and top phase (top time) of each triangular term Ask for. Note that the top phase is any time at which the triangular term shows a maximum value.

  In the present invention, the above-described fitting in the single condition analysis unit 8 is performed using all the main peaks extracted from the MEM-PSD, and thus the single condition analysis unit 8 is necessary for the subsequent processing. A spectrum feature amount is extracted and recorded as an analysis result A in the analysis result recording means 9 as an attribute of the lag value L.

  Reference numeral 10 denotes an evaluation criterion calculation unit. This evaluation criterion calculation unit 10 uses GTP descriptions (GTP parameters) at each lag value L, as will be described later, from the feature value as the analysis result A of the single condition analysis unit 8. ) And the amount of induction to be described later for determining the base variation portion of GTP. The induction amount is calculated for each lag value L, and is recorded as the analysis result B in the analysis result recording means 9.

  Reference numeral 11 denotes a comparison / selection unit. The comparison / selection unit 11 uses an amount of guidance obtained by the evaluation criterion calculation unit 10 to obtain an optimal GTP expression describing the time-series data 2 to be analyzed and its base variation part. Is used as an analysis result, and the second processing step described above is executed together with the evaluation criterion calculation unit 10 described above, and is a main element of the present invention. As an analysis result in the comparison / selection unit 11, an optimum lag value L *, therefore, one GTP, and one or a plurality of triangular terms constituting the base variation are determined. This analysis result is recorded as an analysis result C in the analysis result recording means 9.

  Reference numeral 12 denotes an additional information configuration unit. The additional information configuration unit 12 calculates a base variation curve, a residual curve, and the like from the GTP parameters determined by the comparison / selection unit 11, and the analysis result is an analysis result recording means. 9 is recorded as the analysis result D.

  Reference numeral 13 denotes an output unit. The analysis results recorded in the analysis result recording means 9 are collected and output as analysis results of the analysis system 1.

Next, the above-described elements of the analysis system 1 will be described in more detail.
First, FIG. 3 is a system diagram showing the configuration of the single condition analysis unit 8.
Reference numeral 15 denotes a calculation / feature quantity extraction unit. The calculation / feature quantity extraction unit 15 is set in the time-series data 2 input via the input unit 5 of the analysis system 1 and the analysis condition 3. From the fitting method and the lag value L (14) given from the control unit 7, the MEM-PSD is calculated by the Burg method represented by the following equation.

Here, P _m (f) is a spectral density at a frequency f at a lag value m, Δt is a sampling interval, and P _m and γ _m (k) are Burg coefficients.

The calculation / feature extraction unit 15 calculates the MEM-PSD according to the above equation, and then obtains the number of main peaks, the center frequency and power of each peak. And the following features related to base variation:
M _L : number of main peaks f _{L, i} : center frequency of each peak (i = 1 to M _L )
P _{L, i} : Power of each peak (i = 1 ~ _ML )
Are extracted, and the extracted feature quantity related to the base variation is recorded in the analysis result recording means 9 as the analysis result E.

Next, reference numeral 16 denotes a generalized trigonometric polynomial fitting unit. This generalized triangular polynomial fitting unit 16 performs generalized trigonometric polynomial fitting from the time series data 2 and the above-described feature quantity related to the base variation according to the set fitting method 3. A polynomial parameter is calculated and recorded in the analysis result recording means 9.
The following equation shows a generalized triangular polynomial applied in the present invention.

Where x (t) is the GTP value at time t, a ₀ is the level value, M is the number of terms, a _i , T _i , and φ _i are the amplitude, period, and top phase of the i-th triangular term, respectively. . The number of terms M is given by the number of main peaks of the MEM-PSD, and the period T _i is given by the reciprocal of the peak frequency of the MEM-PSD.

  As described above, the least square method (LSF) is usually used as the fitting method, but a more robust method can be selected by specifying the analysis conditions. In the embodiment of the analysis system 1, in addition to the method of least squares, a method of minimizing the absolute value of the deviation is arranged in advance so that it can be selected in advance. It can be configured to be able to.

By the processing of the above calculation / feature amount extraction unit 15 and generalized trigonometric polynomial fitting unit 16, the parameters shown below as the generalized trigonometric polynomial parameters, that is,
a _{L, 0} : Level value M _L : Number of terms in polynomial = number of main peaks a _{L, i} : Amplitude of each term (i = 1 to _ML )
T _{L, i} : period of each term = 1 / f _{L, i} (i = 1 to M _L )
φ _{L, i} : Top phase of each term (i = 1 to M _L )
Is recorded in the analysis result recording means 9 as the analysis result F.

In this way, the analysis result recording means 9 includes the above-described feature quantities (M _L , f _{L, i} and P _{L, i} ) related to the base variation, and parameters (a _{L, 0} , a _{L, i} , T _{L, i} , φ _{L, i} ) is recorded as the analysis result A.

Next, FIG. 4 is a system diagram showing the configuration of the evaluation criterion calculation unit 10 and the flow of processing.
This evaluation criterion calculation unit 10 is analyzed by the single condition analysis unit 8 and is measured by MEM-PSD on the frequency axis of the time-series data 2 using various quantities 17 described later recorded in the analysis result recording means 9. An evaluation criterion for evaluating the consistency between the expression and the expression by GTP on the time axis is calculated.

The analysis results by the single condition analysis unit 8 used for calculation of the evaluation criteria are as follows.
M _L : Number of polynomial terms = number of main peaks
P _{L, i} : Power of each peak (i = 1 ~ _ML )
a _{L, i} : Amplitude of each triangular term (i = 1 to M _L )

The evaluation criterion calculation unit 10 calculates the analysis result for each lag value L value by the following calculation formula, and calculates the following evaluation criterion 19 by the evaluation criterion calculation processing unit 18.
TPP _L : Total peak power (sum of the power of each peak)
TMP _L : Total mode power (1/2 of the sum of the square of the amplitude of each triangular term)
MP _{L, i} : Power of each triangular term (1/2 of the square of the amplitude of each triangular term)

  The evaluation criteria calculated in this way are added and recorded as the analysis result B in the analysis result recording means 9.

Next, FIG. 5 is a system diagram showing the configuration and processing flow of the comparison / selection unit 11.
As described above, the comparison / selection unit 11 determines the optimal GTP expression describing the time-series data 2 to be analyzed and the base variation portion thereof as an analysis result. The above-described second processing process is executed together with the evaluation criterion calculation unit 10 to obtain the optimum lag value L *, thus one GTP, and one or more triangular terms constituting the base variation. .

First, the comparison / selection unit 11 performs comparison / selection processing according to the following flow using the following analysis result 20 and analysis condition 3 among the analysis results A to B by each unit described above.
・ Analysis result 20
TPP _L : Total peak power (sum of the power of each peak)
TMP _L : Total mode power (1/2 of the sum of the square of the amplitude of each triangular term)
MP _{L, i} : Power of each triangular term (1/2 of the square of the amplitude of each triangular term)
P _{L, i} : Power of each peak (i = 1 ~ _ML )
・ Analysis condition 3
CT− and CT +, CM− and CM +, where CT− and CM− are positive values of 1 or less (0.8, 0.95, etc.), and CT + and CM + are values of 1 or more (1.05, 1.2, etc.).

First, in the first step 21, the total mode power (TMP _L ) and the total peak power (TPP _L ) of the analysis results (N−1 sets) corresponding to each lag value match within an allowable range. Select the analysis result (and hence the lag value).

As specific processing of the first step 21, an analysis result in which the value of TMP _L ÷ TPP _L is within the range of CT− to CT + as an allowable range is selected, and an analysis result outside the range is excluded. To do.

  The number of analysis results selected and left by the processing in the first step 21 is N ′ :( N ′ ≦ N−1) as shown in the frame of reference numeral 22.

On the other hand, in the process of the first step 21, when there is no analysis result in which the value of TMP _L ÷ TPP _L is within the range of CT− to CT +, the process proceeds to the second step 23, where the optimal solution is obtained. If not, a predetermined output such as an alarm is performed and the process is terminated. The second step 23 and the first step 21 correspond to the first selection process in the second process described above.

Next, in the third step 24, good analysis results whose TMP _L ÷ TPP _L value is relatively close to 1 are extracted from the N ′ sets of analysis results selected in the processing of the first step 21. Analysis results are excluded. As a result of the processing in the third step 24, the number of analysis results selected and left is N ″ :( N ″ ≦ N ′ ≦ N−1) as shown in the frame of reference numeral 25. The third step 24 corresponds to the fourth selection process in the second process described above.

  Note that the processing of the third step 24 may be performed by narrowing the range of CT− to CT + in order to extract a better analysis result closer to 1, or closest to 1. Then, a selection process of selecting a preset number may be performed.

Next, in the fourth step 26, for each of the N ″ sets of analysis results remaining selected in the third step 24, in order from the triangular term of the longest period of the data length order, MP _{L, i} ÷ Search and select a triangular term whose value of P _{L, i} is within the range of CM− to CM + as an allowable range. In the present invention, the triangular term within the allowable range is regarded as constituting a base variation as a triangular term that exists stably during a time-series observation period, a so-called stable triangular term.

  In the fourth step 26, if any analysis result does not have the corresponding triangular term, the process proceeds to the fifth step 27, and a predetermined output such as an alarm is given and processing is performed assuming that there is no optimal solution. finish.

Through the processing in the fourth step 26, analysis results satisfying the above-described conditions are selected, and the number of terms FM _L continuous from the longest cycle of the data length order is obtained for each. In this embodiment, these triangular terms are considered as modes constituting the base variation. In the third process, the number of remaining analysis results is N ′ ″ :( N ′ ″ ≦ N ″ ≦ N ′ ≦ N−1) as shown in the frame of reference numeral 28. The fourth step 26 corresponds to the second selection process in the second process described above.

  In this embodiment, the triangular term of the longest cycle in the order of the data length is a stable triangular term, and a series of stable triangular terms that are continuous in descending order of the cycle is regarded as a base fluctuation component. Depending on the purpose of the analysis, the stable term appearing after the unstable term can be regarded as a base fluctuation component.

Next, in a sixth step 29, for each of the N ′ ″ sets of analysis results remaining selected in the fourth step 26, the power (the square of the amplitude) of the selected number of consecutive terms FM _L triangular terms. ), That is, the sum FMP _L of the powers of the triangular terms constituting the base variation is obtained as shown in the frame 30.

Next, in a seventh step 31, the magnitudes of N ′ ″ FMP _L are compared, an analysis result indicating the maximum FMP _L is obtained, and a corresponding lag value L * is obtained. As shown in the figure, the lag value indicates the optimum base variation. The seventh step 31 and the sixth step 29 correspond to the third selection process in the second process described above.

In this way, in the comparison / selection unit 11, the following quantities are obtained as analysis results, added to the analysis result recording means 9 as analysis results C, and recorded.
L *: Lag value indicating the optimal base variation
FM _{L *} : Number of terms constituting the base variation
FMP _{L *} : Sum of the powers of the triangular terms that make up the base variation

  Next, FIG. 6 is a system diagram showing the configuration of the additional information configuration unit 12 and the flow of processing. This additional information configuration unit 12 calculates a base variation curve and a residual curve using various amounts obtained as analysis results by the above processing and accumulated in the analysis result recording means 9 and the time series data 2. The unit calculates residual standard deviation and residual absolute deviation as required, and these calculation results are recorded as an analysis result D in the analysis result recording means 9 as an output from the additional information configuration unit 12. .

Reference numeral 33 denotes a base fluctuation curve calculation unit. The base fluctuation curve calculation unit 33 obtains a base fluctuation curve, that is, a value F (t _j ) (where j = 1 to N) of a base fluctuation curve at time t _j. . This calculation is performed only from the triangular term of the number of terms FM _L * constituting the base variation using each parameter of the generalized triangular polynomial obtained by the optimum lag L *.

This calculation is performed using the following various quantities 34 including parameters of the generalized trigonometric polynomial recorded in the analysis result recording means 9.
TSD: Time series data (N data points)
L *: Lag value indicating optimal base variation M _{L *} : Number of polynomial terms = number of main peaks
FM _{L *} : Number of terms constituting the base variation a _{L *, 0} : Level value a _{L *, i} : Amplitude of each term (i = 1 to FM _{L *} )
T _{L *, i} : Period of each term = 1 / FM, i (i = 1 to FM _{L *} )
φ _{L *, i} : Top phase of each term (i = 1 to FM _{L *} )

Next, reference numeral 35 denotes a residual curve calculation unit. This residual curve calculation unit 35 is a process for calculating a residual curve between the base fluctuation curve calculated by the base fluctuation curve calculation unit 33 and the time series data. Yes, that is, the value R (t _j ) (where j = 1 to N) of the residual curve at time t _j is obtained.

  Next, reference numeral 36 denotes an auxiliary calculation unit that performs a calculation for reference as necessary. This calculation unit 36 uses a residual curve obtained by the residual curve calculation unit 35 to calculate a residual standard deviation ( σ) and residual absolute deviation (D) are calculated.

As a result of the calculation in the additional information constituting unit 12 described above, the analysis result recording unit 9 stores the value F (t _j ) of the base fluctuation curve, the value R (t _j ) of the residual curve, the residual standard deviation σ, and the residual absolute value. The deviation D is added and recorded as the analysis result D.

Next, an analysis example of the time series data analysis system according to the present invention will be described.
The time series data to be analyzed in this analysis example is the 24-hour SBP data (data score: 24) shown in FIG.
First, the time series data 2 and the analysis condition 3 are input to the analysis system via the input unit 5. In this analysis example, the analysis condition 3 selects the least square method as the fitting method, CT + and CT− are 1.05 and 0.95, and CM + and CM− are 1.2 and 0.8.

Such analysis condition 3 and time-series data 2 are input via the input unit 5, and the calculation condition setting unit 6 sets a repetitive calculation from lag values 1 to 23 (maximum lag value) as a calculation condition. Note that the spectrum with a lag value of 1 has a peak at zero frequency or Nyquist frequency, which is not used for GTP calculation.For example, when the time series data is data consisting only of cosine function terms that do not contain noise. Can be used to check such time-series data by performing calculations because the Burg coefficient P _m value decreases rapidly with lag.

  The control unit 7 calls the single condition analysis unit 8 23 times based on the above-described calculation conditions set by the calculation condition setting unit 6, and the calculation processing in the single condition analysis unit 8 is performed.

First, the calculation / feature quantity extraction unit 15 performs MEM-PSD calculation processing by the maximum entropy method for each of the lag values 1 to 23. FIG. 12 shows MEM-PSD as a result of calculation with a lag value 20 as an example of the calculation result, and FIG. 13 shows various amounts of all major spectral peaks of MEM-PSD in a table. . As shown in FIG. 13, the number M ₂₀ of main peaks excluding two of the frequency zero and the Nyquist frequency is 9, and the feature amount related to these nine peaks is the next generalized triangular polynomial fitting unit 16. Used. That is, in the calculation / feature amount extraction unit 15, as described above, the feature amounts related to the base variation, that is, M _L, f _{L, I} (i = 1 to M _L ) and P _{L, i} (i = 1 to M). _L ) is extracted for each of the lag values 1 to 23 and recorded in the analysis result recording means 9.

For example, the calculation result of the lag value 20, M ₂₀ is 9, the feature amount f _{20, i} and P ₂₀ to 30.083 to 0.565 in the first row from 0.0481 to 0.4490 and the third column of the table of Figure 13 is involved in basal variation _{, i} (i = 1 to 9). Incidentally, the sum of the powers (areas) of nine spectrum peaks calculated by the evaluation reference calculation unit 10 described later, that is, TPP ₂₀ is 61.275 mmHg × mmHg.

FIGS. 14 and 15 show the result of the fitting process in the generalized triangular polynomial fitting unit 16, and FIG. 14 (a) has triangular terms corresponding to the nine main peaks of the MEM-PSD with a lag value of 20. A GTP curve, (b) is a residual curve, and ◯ in (a) is original time series data. FIG. 15 shows GTP parameters, that is, the first column is the period T _{20, i} of each term, the second column is the amplitude a _{20, i} of each term, and the third column is the top phase φ _{20, i} of each term. Yes, and the total power in the upper right (61.941) is TMP ₂₀ . On the other hand, the GTP level a _20,0 was 124.94 mmHg. Thus, the above various quantities and the number of major peaks (= mode number) 9 at the lag value 20 are output as a part of the analysis result A from the single condition analysis unit 8 and recorded in the analysis result recording means 9. Is done. That is, the control unit 7 controls the single condition analysis unit 8 to perform the same calculation process as the above-described lag value 20 on the lag values 1 to 23 to obtain the same analysis result, and as the analysis result A The result is output and recorded in the analysis result recording means 9. FIG. 16 shows the analysis result A at the lug 20 (excluding _P20 and _i ).

Next, the evaluation criterion calculation unit 10 calculates TPP _L , TMP _L and MP _{L, i} for each lag value from the above-mentioned various amounts recorded in the analysis result recording means 9. FIG. 17 is a table showing the calculation results of TPP _L and TMP _L , and FIG. 18 is a table showing the number of modes and the power of each triangular term obtained for each of the lugs 16 to 23. In these tables, the results of the lag values 1 to 15 are omitted for simplicity, and only the calculation results of the lag values 16 to 23 are shown.

Various quantities calculated in this way by the evaluation criterion calculation unit 10 are additionally recorded in the analysis result recording means 9 as an analysis result B and used for calculation in the comparison / selection unit 11. That is, in the comparison / selection unit 11, the lag value L * that gives the optimal solution, the number of terms FM _{L *} that constitutes the base variation, and the sum of the powers of the triangular terms that constitute the base variation FMP _{L *} Determine.

First, in the first step 21 of the comparison / selection unit 11, the ratio of TMP _L to TPP _L is calculated for each lag value L, and the result is out of the range of CT− (0.95) to CT + (1.05) as candidates. Excluded from.

FIG. 19 is a table obtained by adding the ratio to the table of TMP _L and TPP _L shown in FIG. 17. In the first step 21, the result of the lag 23 is excluded. The number of analysis results that remain selected is in the range of lag values 16 to 23, and the candidate N = 8 is reduced to N ′ = 7. Next, in the third step 24, from the seven sets of analysis results selected in the process of the first step 21, a good analysis result in which the value of TMP _L ÷ TPP _L is relatively close to 1, in this case, FIG. From these tables, two analysis results of lag values 20 and 21 are left as candidates.

Next, in the fourth step 26, the two sets of analysis results (lag values 20 and 21) selected and left in the third step 24 are sequentially applied from the triangular term of the longest cycle of the data length order. , MP _{L, i} ÷ P _{L, i} is searched and selected for a triangular term in the range of CM− (0.80) to CM + (1.20) as an allowable range.

FIG. 20 shows the processing results for a lag value of 20, which continuously falls in the range of CM− (0.80) to CM + (1.20) until the fourth mode (cycle 4.81 hours), but the fifth mode with a cycle of 3.98 hours. Is outside this range. That is, the stable term is the first four terms (FM ₂₀ = 4).

  On the other hand, FIG. 21 shows the processing result for the lag value 21, which continuously falls in the range of CM− (0.80) to CM + (1.20) until the fourth mode (cycle 4.81 hours), but with a cycle of 3.98 hours. The 5 mode is outside this range. Therefore, the stable term is the first four terms for this lag value 21 as well.

Next, in a sixth step 29, for each processing result of the lag value 20 and the lag value 21, the sum FMP _L of the power of the triangular terms having the number of consecutive terms FM _L , that is, the triangular terms constituting the base variation. Calculate FIG. 22 shows the calculation results. In this figure, the calculation results are also shown for the lag values excluded in the previous steps for reference.

In the seventh step 31, the magnitudes of FMP _L are compared, and a lag value indicating the maximum FMP _L , L * = 20, is selected as shown in FIG. That is, FMP ₂₀ is 49.861, which is greater than any result of lag values excluded so far, as well as L = 21.

The various quantities calculated by the comparison / selection unit 11, that is, the values L *, FM _{L *} and FMP _{L *} are additionally recorded in the analysis result recording means 9 as the analysis result C, and are used for the calculation in the additional information configuration unit 12. used.

  That is, the additional information configuration unit 12 configures various amounts of analysis results recorded in the analysis result recording means 9 so far, that is, lag values, generalized trigonometric polynomial parameters, and base fluctuations that constitute an optimal solution. Based on various quantities such as a triangular term, additional information as shown in FIG. 23 is configured. That is, (a) of FIG. 23 shows a base fluctuation curve calculated from a triangular term parameter of base fluctuation, and a circle in the figure is original time series data. (B) shows a residual curve composed of the difference between the original time series data and the base fluctuation curve. Here, the basis variation curve in (a) is not the result of fitting the original time series data using only the stable term, but fitting for all modes using all the main peaks obtained by MEM-PSD. Among the curves, it is a so-called component curve reconstructed with only the level value and the stable term.

  In addition to the calculation of the base variation curve and the residual curve, the additional information configuration unit 12 can calculate the standard deviation and absolute deviation of the residual curve. In this example, the standard deviation was 5.36 and the absolute deviation was 4.37.

  Since the present invention is as described above, it can of course be used for analysis of normal appropriate time-series data. In particular, when the time fluctuates in the order of the data length, such as the above-described ABPM data. It is very effective for analyzing series data.

DESCRIPTION OF SYMBOLS 1 Analysis system 2 Time series data 3 Analysis condition 4 Analysis result 5 Input unit 6 Calculation condition setting unit 7 Control unit 8 Single condition analysis unit 9 Analysis result recording means 10 Evaluation reference calculation unit 11 Comparison / selection unit 12 Additional information configuration unit 13 Output unit 14 Lag value 15 Calculation / feature amount extraction unit 16 Generalized trigonometric polynomial fitting unit 17 Recorded quantities 18 Evaluation standard calculation processing unit 19 Evaluation standard 20 Analysis result 21 First steps 22, 25, 28 , 30, 32 Processing result 23 2nd step 24 3rd step 26 4th step 27 5th step 29 6th step 31 7th step

Claims (10)

An apparatus for analyzing time series data by a programmed computer, comprising: time series data to be analyzed and an input unit for analysis conditions; a processing means for executing analysis; and an analysis result recording means for recording the analysis result,
A first process for calculating a parameter of a generalized trigonometric polynomial from a time series data to be analyzed using a maximum entropy method for a large number of lags and calculating a power spectral density from various quantities obtained therefrom. Process,
Compare the parameters of the generalized trigonometric polynomial corresponding to many lags obtained in the first process and the quantities obtained from the power spectral density, select the lag with the highest consistency, and handle the lag Selecting a highly consistent triangular term in the generalized trigonometric polynomial as a triangular term constituting the base variation;
Using the parameters of the generalized trigonometric polynomial obtained corresponding to the optimal lag obtained in the second processing step, the value of the base variation curve at each time point is calculated from the parameters of the triangular term constituting the base variation. And a third processing step for obtaining the value of the residual curve at each time point from the time series data, and a processing means for executing the third processing step.
In the second processing step, parameters of the generalized trigonometric polynomial corresponding to a large number of lags obtained in the first processing step, and various quantities obtained from the power spectral density, the sum of the power of each triangular term and the spectral peak are obtained. The first selection process for selecting lags whose consistency is within an allowable range as compared with the sum of the powers of the generalized trigonometric polynomials corresponding to the lag selected in the first selection process A second selection process in which the power of the term and the power of the corresponding spectrum peak are sequentially compared, and a triangular term whose consistency is within an allowable range is selected as a triangular term constituting the base variation; and a second selection The third selected in the process is to compare the sum of the powers of the triangular terms constituting the base variation corresponding to each lag, and obtain the lag that maximizes the power sum as the lag that expresses the optimal base variation. Analysis system of the time-series data, characterized in that it has a configuration for executing the selection process sequentially. In the second processing process, after the first selection process, a fourth selection process for selecting a lag corresponding to a parameter having higher consistency is provided, and a general process corresponding to the lag selected in the fourth selection process is performed. Selection process in which the power of each triangular term of the generalized trigonometric polynomial and the power of the corresponding spectrum peak are sequentially compared to select a triangular term whose consistency is within an allowable range as a triangular term constituting the base variation And the sum of the powers of the triangular terms constituting the base variation corresponding to each lag selected in the second selection process, and the lag that maximizes the power sum is represented by the lag that expresses the optimal base variation. The time-series data analysis system according to claim 1, wherein the third selection process obtained as follows is sequentially executed. In the second selection process, a series of triangular terms in which the consistency of the triangular term of the longest period in the order of the data length is within the allowable range, and the consistency is continuously within the allowable range in descending order of the period, 3. The time-series data analysis system according to claim 1, wherein the system is selected as a triangular term that constitutes a base variation. 3. The time-series data analysis system according to claim 1, wherein, in the second selection process, a triangular term whose consistency is within an allowable range is selected as a triangular term constituting a base variation. The analysis condition input to the input unit is a value that sets a fitting method to be used and an allowable range of the first selection process and the second selection process of the second processing process. The time-series data analysis system according to 2. A first process for calculating a parameter of a generalized trigonometric polynomial from a time series data to be analyzed using a maximum entropy method for a large number of lags and calculating a power spectral density from various quantities obtained therefrom. Process,
Compare the parameters of the generalized trigonometric polynomial corresponding to many lags obtained in the first process and the quantities obtained from the power spectral density, select the lag with the highest consistency, and handle the lag Obtained by corresponding to the optimal lag obtained in the second processing step and selecting the triangular term having high consistency in the generalized trigonometric polynomial as the triangular term constituting the base variation. Using each parameter of the generalized trigonometric polynomial, the value of the base fluctuation curve at each time point is obtained from the parameters of the triangular term constituting the base fluctuation, and the value of the residual curve at each time point is obtained from the time series data. A program for causing a computer to execute a third processing step,
In the second processing step, parameters of the generalized trigonometric polynomial corresponding to a large number of lags obtained in the first processing step, and various quantities obtained from the power spectral density, the sum of the power of each triangular term and the spectral peak are obtained. The first selection process for selecting lags whose consistency is within an allowable range as compared with the sum of the powers of the generalized trigonometric polynomials corresponding to the lag selected in the first selection process A second selection process in which the power of the term and the power of the corresponding spectrum peak are sequentially compared, and a triangular term whose consistency is within an allowable range is selected as a triangular term constituting the base variation; and a second selection The third selected in the process is to compare the sum of the powers of the triangular terms constituting the base variation corresponding to each lag, and obtain the lag that maximizes the power sum as the lag that expresses the optimal base variation. Analysis program time series data, characterized in that it has a configuration for executing the selection process sequentially. In the second processing process, after the first selection process, a fourth selection process for selecting a lag corresponding to a parameter having higher consistency is provided, and a general process corresponding to the lag selected in the fourth selection process is performed. Selection process in which the power of each triangular term of the generalized trigonometric polynomial and the power of the corresponding spectrum peak are sequentially compared to select a triangular term whose consistency is within an allowable range as a triangular term constituting the base variation And the sum of the powers of the triangular terms constituting the base variation corresponding to each lag selected in the second selection process, and the lag that maximizes the power sum is represented by the lag that expresses the optimal base variation. 7. The time-series data analysis program according to claim 6, wherein the third selection process obtained as follows is sequentially executed. In the second selection process, a series of triangular terms in which the consistency of the triangular term of the longest period in the order of the data length is within the allowable range, and the consistency is continuously within the allowable range in descending order of the period, The time series data analysis program according to claim 6 or 7, wherein the time series data analysis program is selected as a triangular term constituting a base variation. The time-series data program according to claim 6 or 7, wherein, in the second selection process, a triangular term whose consistency is within an allowable range is selected as a triangular term constituting a base variation. The analysis condition input to the input unit is a value that sets a fitting method to be used and an allowable range of the first selection process and the second selection process of the second processing process. 7. The time series data analysis program according to 7.