JP2010086398A - Device for analysis of time-series data - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain consistent and detailed information both in a time domain and a frequency domain about a structure which time series contains with respect to arbitrary finite length data (real data) measured in a discrete manner by using only the arbitrary finite length data without using additional information. <P>SOLUTION: The analyzing device combines time series data by the maximum entropy method and a nonlinear least square method to calculate a parameter and a residual of a generalized trigonometric polynomial, and also composites power spectral density obtained from the parameter with power spectral density of the residual to calculate a reconstruction spectrum of the time series data. The analyzing device divides the time series data into segments so as not to exceed the number of preset maximum data, and also divides segment data of a nonuniform data structure into multiple uniform segment data to define each of the divided uniform segments as a basic segment. Then the analyzing device sets a storage area for a storing means and performs analysis processing, to those segments. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to an apparatus for analyzing time series data.

  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 apparatus capable of analyzing time-series data with high accuracy. The analysis apparatus which executes the computer program which applied the method and its analysis method is proposed. 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 ( PSD), and the number of terms as the initial value for solving the generalized trigonometric polynomial and the periodic value of each triangular term from the prominent peak, and the nonlinear minimum self-linearized by these initial values. The method includes a process of obtaining parameters of each triangular term by using multiplication, obtaining residual time series data, and adding these to reconstruct time series data.

This analysis method and the analysis device 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.
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…”, 1st Edition, Hokkaido University Library Publications, June 25, 2002, p.79- 99

  By the way, when the analysis is performed by the above-described analysis device, it is difficult to process a large amount of time-series data in a lump because the computer capacity is limited in terms of calculation speed, calculation accuracy, storage capacity, and the like. In this case, it is necessary to divide and process long time-series data. On the other hand, time-series data includes data whose data structure is kept uniform over the entire data in the observation period, as well as those whose data structure changes from moment to moment within the observation period. In the latter case, It is difficult to process all the data in the observation period at once.

  The present invention was devised in view of the above points, that is, time series data to be analyzed is analyzed by appropriately segmenting and processing the time series data to be analyzed according to the number of data points and the data structure. The purpose is to enable appropriate and accurate analysis at all times regardless of the data.

  The time-series data targeted by the present invention is real time-series data, that is, data of a finite-length discrete time series with a certain number of points observed in a certain limited period, and is theoretically present. Infinite length data and continuous data are not included. The time-series data targeted by the present invention is not limited to normal time-series data as described above, but also includes data that is spatially continuous, such as a change in luminance with respect to the distance of the formation cross section.

  In order to solve the above-described problem, in the present invention, analysis sequence determination means for determining a sequence for analyzing time-series data to be analyzed, and analysis of data by a maximum entropy method and a nonlinear least square method according to the analysis sequence. Data analysis means for obtaining parameters and residuals of generalized trigonometric polynomials, analysis result evaluation means for evaluating the analysis results obtained by the data analysis means and storing them in the storage means when the conditions are met, and obtained from the above parameters A reconstructed spectrum calculating means for obtaining a reconstructed spectrum of time series data by synthesizing the power spectrum density and the residual power spectrum density obtained using the maximum entropy method, and taking out from the storage means using this calculating means Based on the above parameters and residuals, generalized triangles corresponding to the time series data to be analyzed An analysis result structuring unit that constitutes a term expression, and the analysis sequence determining unit divides the time series data to be analyzed into segments so as not to exceed a preset maximum number of data points, and each segment Based on the evaluation process for evaluating the uniformity of the data structure for the data, the division process for dividing the non-uniform segment data into a plurality of uniform segments, and the divided uniform segments. As a segment, we propose a time-series data analysis apparatus having a storage area setting process for setting a storage area in the storage means.

  Further, in the present invention, in the above analysis device, each segment is divided into two sequentially from the segment of the highest layer corresponding to the whole period data of the time series data to be analyzed, and each of the lower layers is configured. When it is composed of a power-of-two segment included and segments of sub-layers that are sequentially formed by dividing a segment whose data structure changes in the lowest layer at a location where the data structure changes A data analysis device is proposed.

但し、Bm(f)はラグ値m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)はバーグの係数である。 In the present invention, in the above analysis apparatus, the uniformity of the data structure is a time series evaluated by the transition of the Burg coefficient Pm with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation. A data analysis device is proposed.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients.

  Further, in the present invention, in the above analysis apparatus, it is proposed that the analysis sequence determination means is provided with an equal interval processing step for equal interval processing of unequal interval time series data.

但し、Bm(f)はラグ値m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)はバーグの係数である。 Further, in the present invention, in the above analysis apparatus, the data analysis means, for the segment data extracted from the time-series data to be analyzed, determines the Burg's value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation. The calculation process for determining the transition of the coefficient Pm with respect to the lag value, the lag value determining process for determining the lag value used for calculating the power spectral density by the maximum entropy method from the determined transition, and the power spectral density based on the determined lag value Calculate the parameters of the fitting curve by the nonlinear least square method from the power spectral density calculation process to find the frequency of the main peak from the obtained power spectral density, the extraction process to extract the power, and the extracted frequency and power The parameter derivation process and the obtained fitting curve and segment The degree of coincidence is evaluated by comparing with the data, and if the degree of coincidence is equal to or higher than the predetermined coincidence, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process, and the predetermined coincidence is reached. If not, an apparatus for analyzing time series data is provided that includes an evaluation process that discards the parameters of the fitting curve and shifts to a process of determining the lag value.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients.

  In the present invention, in the above analysis device, the analysis of the segment data in the data analysis means is performed sequentially from the highest layer to the lowest layer. At this time, the segment data of the upper layer segment is In addition, in order to prevent the number of data points per segment from exceeding the preset maximum number of data points, the processing is performed to reduce the number of data points of the time series data to be analyzed by bunching processing and configure segment data, A temporary storage area is configured corresponding to each segment of the layer, and the polynomial parameter obtained for the upper segment is stored in the temporary storage area of each segment of each lower layer, and is configured from the above polynomial parameter. By calculating the difference between the fitting curve and the corresponding part of the original time series data. The residual time series data that is to propose an analysis device of the time-series data to perform processing to set as the segment data of the next lower layer.

  In the present invention, in the above analysis apparatus, the analysis result evaluation means obtains a residual curve by comparing the corresponding range of the fitting curve obtained by the data analysis means with respect to the segment data and the time series data to be analyzed. The degree of agreement is evaluated by comparing the residual analysis process that performs the analysis with the residual curve analyzed by the residual analysis process and the time series data. And the residual is stored in a predetermined storage means, and the process proceeds to the next process.If the predetermined degree of coincidence is not reached, the data is discarded, and the evaluation process is performed to transfer the segment data to the next layer segment. We propose a time-series data analysis device.

  Also, in the present invention, in the above analysis apparatus, the analysis result configuration means obtains and stores a reconstructed spectrum for all data areas collectively from the parameters and residuals of the basic segments stored in all the storage areas. The basic analysis segment is composed of a batch analysis result configuration unit and a segment analysis result configuration unit that obtains and stores a reconstruction spectrum for each basic segment from the parameters and residuals of the basic segment stored in each storage area. Configure the top phase transition calculation means to analyze the frequency dependence of the top phase every time, and configure the segment analysis result for the frequency dependence of the top phase for each basic segment calculated by this top phase transition calculation means We propose a time series data analysis device that stores as a representative time attribute of the basic segment along with the reconstructed spectrum by means. .

  Further, in the present invention, in the above analysis device, the reconstructed spectrum calculating means uses the prototype of the δ function for each of the terms of the generalized triangular polynomial in the calculation for obtaining the power spectral density from the obtained parameters. By configuring a single spectrum peak that spreads in the entire frequency band to form a group of isolated peaks corresponding to each frequency obtained from parameters, and obtaining a reconstructed spectrum of time series data as its superposition A data analysis device is proposed. As the prototype of the δ function, for example, a spectrum obtained by calculating the spectral density of the maximum entropy method using lag 2 for a time series obtained by adding weak noise to the cosine function can be used.

  In the present invention, the analysis sequence determination procedure for determining the sequence for analyzing the time series data to be analyzed, and the analysis of the data by the maximum entropy method and the nonlinear least square method according to the analysis sequence, the parameters of the generalized triangular polynomial and the remaining A data analysis procedure for obtaining the difference, an analysis result obtained by the data analysis procedure, an analysis result evaluation procedure stored in the storage means when the conditions are met, a power spectral density obtained from the above parameters, and a maximum entropy method The reconstructed spectrum calculation procedure for obtaining the reconstructed spectrum of the time series data by synthesizing the power spectrum density of the residual obtained using, and using the calculation procedure and the parameter and the residual extracted from the storage means, Analysis result structure that constitutes a generalized trigonometric polynomial corresponding to the time series data to be analyzed The analysis sequence determination procedure includes a division processing procedure for dividing the time-series data to be analyzed into segments so as not to exceed the preset maximum number of data points, and the uniformity of the data structure for each segment Based on this evaluation, based on this evaluation, a division processing procedure for dividing non-uniform segment data into a plurality of uniform segments, and each of the divided uniform segments as basic segments, A computer-readable recording medium recording a time-series data analysis program for causing a computer to execute each procedure including a storage area setting processing procedure for setting a storage area in a storage means is proposed.

  Further, according to the present invention, in the recording medium, the segment is divided into two in order from the segment of the highest layer corresponding to the whole period data of the time-series data to be analyzed. It is composed of the power-of-two segments included and the sub-layer segments that are sequentially formed by dividing the segment whose data structure changes in the lowest layer at the location where the data structure changes. The computer-readable recording medium which recorded the analysis program of the time series data of Claim 8 characterized by these is proposed.

但し、Bm(f)はラグ値m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)はバーグの係数である。 Further, in the present invention, in the above recording medium, the uniformity of the data structure is a time series evaluated by the transition of the Burg coefficient Pm with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation. A computer-readable recording medium recording a data analysis program is proposed.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients.

  In the present invention, it is proposed that in the recording medium described above, the analysis sequence determination procedure is provided with an equal interval processing step for equal interval processing of unequal interval time series data.

但し、Bm(f)はラグ値m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)はバーグの係数である。 In the present invention, in the recording medium described above, the data analysis procedure is performed on the segment data extracted from the time-series data to be analyzed, in the calculation of the spectral density of the maximum entropy method up to the maximum lag value according to the following equation. The calculation process for determining the transition of the coefficient Pm with respect to the lag value, the lag value determining process for determining the lag value used for calculating the power spectral density by the maximum entropy method from the determined transition, and the power spectral density based on the determined lag value Calculate the parameters of the fitting curve by the nonlinear least square method from the power spectral density calculation process to find the frequency of the main peak from the obtained power spectral density, the extraction process to extract the power, and the extracted frequency and power The parameter derivation process and the obtained fitting curve and segment The degree of coincidence is evaluated by comparing with the data, and if the degree of coincidence is equal to or higher than the predetermined coincidence, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process, and the predetermined coincidence is reached. If not, a computer-readable recording medium recording a time-series data analysis program composed of an evaluation process in which the parameters of the fitting curve are discarded and the lag value is determined is proposed.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients.

  In the present invention, in the recording medium, the segment data analysis in the data analysis procedure is performed sequentially from the highest layer to the lowest layer. At this time, the segment data of the upper layer segment is In addition, in order to prevent the number of data points per segment from exceeding the preset maximum number of data points, the processing is performed to reduce the number of data points of the time series data to be analyzed by bunching processing and configure segment data, A temporary storage area is configured corresponding to each segment of the layer, and the polynomial parameter obtained for the upper segment is stored in the temporary storage area of each segment of each lower layer, and is configured from the above polynomial parameter. By calculating the difference between the fitting curve and the corresponding part of the original time series data. The residual time series data suggest the following computer-readable recording medium storing an analysis program of time-series data consisting of a process of setting a lower layer of the segment data to be.

  In the present invention, in the above recording medium, the analysis result evaluation procedure obtains a residual curve by comparing the corresponding range of the time series data to be analyzed with the fitting curve obtained by the data analysis procedure for the segment data. The degree of agreement is evaluated by comparing the residual analysis process that performs the analysis with the residual curve analyzed by the residual analysis process and the time series data. The residual is stored in a predetermined storage means, and the process proceeds to the next process. If the predetermined degree of coincidence is not reached, the data is discarded and the segment data is transferred to the next layer segment. A computer-readable recording medium on which a time-series data analysis program is recorded is proposed.

  Further, in the present invention, in the above configuration, the analysis result configuration procedure is a batch in which all the data areas are collectively obtained from the parameters and residuals of the basic segments stored in all the storage areas and a reconstructed spectrum is obtained and stored. The analysis result configuration procedure and the segment analysis result configuration procedure for obtaining and storing the reconstructed spectrum for each basic segment from the parameters and residuals of the basic segment stored in each storage area. The top phase shift calculation procedure for analyzing the frequency dependence of the top phase is configured, and the frequency dependence of the top phase for each basic segment calculated by this top phase shift calculation procedure is configured as a segment analysis result configuration procedure Together with the reconstructed spectrum according to, and the procedure to store as the attribute of the representative time of the basic segment The analysis program proposes a computer-readable recording medium having recorded.

  In the present invention, in the above configuration, the reconstruction spectrum calculation procedure is performed by using the prototype of the δ function for each of the terms of the generalized trigonometric polynomial in the calculation for obtaining the power spectral density from the obtained parameters. By configuring each spectrum peak that spreads in the frequency band, a group of isolated peaks corresponding to each frequency obtained from the parameters is formed, and the time series used as a procedure to obtain the reconstructed spectrum of the time series data as its superposition A computer-readable recording medium recording a data analysis program is proposed. As the prototype of the δ function, for example, a spectrum obtained by calculating the spectral density of the maximum entropy method using lag 2 for a time series obtained by adding weak noise to the cosine function can be used.

  According to the inventions of claims 1 and 11, the time sequence data to be analyzed is divided according to the total number of data points by the analysis sequence determination means or procedure, and is adapted to the calculation capability of the analysis device, and the data structure By dividing the segment where the data is changing into segments and eliminating the part where the data structure is changing in the segment, these uniform segments can be analyzed with high precision using data analysis means or procedures. Can do.

  According to the second and twelfth aspects of the present invention, the segment is configured by being sequentially divided into two from the segment of the highest layer corresponding to the whole period data of the time series data to be analyzed by the analysis sequence determining means or procedure. Sub-layers that are sequentially formed by dividing the segment of the power of 2 included in each of the lower layers and the segment whose data structure changes in the lowermost layer at the location where the data structure changes. Since each segment is composed of segments, the time series data can be rationally segmented in accordance with both the computing capability of the analysis apparatus and the data structure of the time series data, and automation is easy.

  According to the third and thirteenth aspects, the uniformity of the data structure can be easily evaluated.

  According to the inventions of claims 4 and 14, even when the original time series data is unequal, the spectral density of the maximum entropy method can be calculated by equalization. On the other hand, in the derivation of the parameters for obtaining the parameters of the fitting curve by the non-linear least square method, it is possible to use time-series data with equal intervals or original time-series data with unequal intervals as necessary.

  According to the inventions of claims 5 and 15, in the data analysis means or procedure, the degree of coincidence is evaluated by comparing the obtained fitting curve with the segment data. An evaluation process in which the parameter is stored in the storage means corresponding to the segment and the process proceeds to the next process, and when the predetermined degree of coincidence is not reached, the parameter of the fitting curve is discarded and the process proceeds to a process of determining the lag value. By repeating the derivation of parameters and the evaluation thereof, a more accurate fitting curve can be obtained.

  According to the sixth and sixteenth aspects of the present invention, it is possible to process all the data points of the time-series data to be analyzed at once by the bunching process even when the analysis device has insufficient computing power. By reducing the number of points, the segment data of the highest layer, that is, the entire time-series data to be analyzed can be collectively analyzed, and therefore the long-period analysis over the entire time-series data is possible. At the same time, set the residual time series data obtained by calculating the difference between the fitting curve obtained by the analysis of the upper layer and the corresponding part of the original time series data as the segment data of the next lower layer, and analyze sequentially. As a result, the solution for the time-series data as it is without the reduction in the number of data points due to the bunching process due to the segment data of the lowest or sublayer. It can be carried out.

  According to the inventions of claims 7 and 17, in the analysis result evaluation means or procedure, when the obtained fitting curve does not reach the corresponding range of the time series data to be analyzed and a predetermined coincidence, the data is discarded. Since the segment data is transferred to the next layer segment for processing, even if a fitting curve with a high degree of coincidence is not found in the upper layer, there is no inconvenience, and the lower layer By the process, a fitting curve with a high degree of coincidence can be obtained.

  According to the eighth and eighteenth aspects of the present invention, time series data to be analyzed can be output as a batch analysis result and an analysis result for each segment by the analysis result configuration means or procedure.

  According to the ninth, tenth, nineteenth, and twentyth aspects of the present invention, the spectrum of the time series data, which is a line spectrum sequence that cannot be configured by a computer that handles finite discrete values in the theoretical format, continuously decreases as the distance from the peak frequency increases. By reconstructing a function, for example, a time series obtained by adding weak noise to a cosine function and calculating the spectral density of the maximum entropy method at lag 2 as the prototype of the δ function, Can be used to analyze time-series data consistent with theory.

Next, the best mode of the time-series data analysis apparatus according to the present invention will be described with reference to FIGS.
The analysis apparatus 1 according to the present invention performs analysis by expressing time series data to be analyzed (hereinafter referred to as original time series data as necessary) by a generalized triangular polynomial in order to apply the above-described analysis method. In general, the maximum entropy method is applied to the original time series data to obtain a highly accurate power spectral density (PSD), and the initial value for solving the generalized trigonometric polynomial from its prominent peaks The process of obtaining the number of terms and the period value of each triangular term, and using these initial values, the linearized nonlinear least squares method is used to obtain the parameters of each triangular term and the residual time series data And adding these to reconstruct time-series data.

ここで、x(t)は原時系列データ、即ち、有限長離散時系列のデータを示し、Lは項数、ajは振幅、Tjは周期、φjは頂位位相、εx(t)は雑音成分を示しており、上述した一般化三角多項式のパラメータは、これらの項数(モード数)、各項の振幅aj、周期Tj及び頂位位相φjから成る。尚、頂位位相とは、そのモードの値が極大を示す時刻で、そのモードの周期ごとに現れる時刻のうちの一つを示している。 That is, in the analysis apparatus 1 according to the present invention, the original time series data is represented by the following generalized triangular polynomial.

Where x (t) indicates original time series data, that is, finite length discrete time series data, L is the number of terms, aj is the amplitude, Tj is the period, φj is the top phase, and εx (t) is the noise The parameters of the generalized trigonometric polynomial described above are composed of the number of terms (number of modes), the amplitude aj of each term, the period Tj, and the top phase φj. Note that the top phase is a time at which the value of the mode has a maximum, and indicates one of the times that appear for each cycle of the mode.

FIG. 1 is an explanatory diagram of an overall configuration schematically showing an embodiment of an analysis apparatus 1 according to the present invention, and a processing flow is schematically shown by arrows in the drawing.
As shown in the figure, the analysis apparatus 1 according to this embodiment includes an analysis sequence determination unit 2 that determines a sequence for analyzing original time series data, and a maximum according to the analysis sequence determined by the analysis sequence determination unit 2. When analyzing the data by the entropy method and the nonlinear least square method to obtain the parameters and residuals of the generalized trigonometric polynomial, the analysis result obtained by the data analysis means 3 is evaluated, and when the conditions are met, The analysis result evaluation means 4 stored in the preset storage means, the analysis sequence determination means 2, the data analysis means 3, and the analysis result evaluation means 4 are controlled in an integrated manner so that necessary repetitive calculations and the like are performed. The control means 5 for performing, the power spectral density obtained from the above parameters and the power of the residual obtained using the maximum entropy method Reconstructed spectrum calculating means 6 for obtaining a reconstructed spectrum of time series data by synthesizing spectrum density, top phase transition calculating means 7 for calculating the transition of the top phase, and calculation related to preparation of output data, etc. The other calculation means 8 to be performed and the analysis result construction means 9 that constitutes the analysis result of the data analysis means 3 to be output using these calculation means 6 to 8 are configured.

  As will be described later, the analysis sequence determination means 2 has a uniform data structure that is configured as a plurality of layers according to the number of data points, the data structure, etc. of the whole period data of the original time series data as one of the analysis sequences And dividing each of the divided uniform segments into basic segments, and setting a storage area in the storage means corresponding to them, and the original captured in the divided segments. The time series data is analyzed by the data analysis means 3. The analysis results obtained for the original time-series data of each segment in the data analysis means 3 are configured as a batch analysis result for collecting the entire target time-series data and a segment analysis result. The analysis result configuring unit 9 includes a collective analysis result configuring unit 9a corresponding to the former and a segment analysis result configuring unit 9b corresponding to the latter.

  FIG. 2 schematically shows an analysis result output from the analysis apparatus 1 according to the present invention. The batch analysis result 10 in which the data structure is maintained over the entire period of the original time series data, and the original time The data structure fluctuates from time to time within the period of the series data, and is composed of analysis results 11 obtained for each of a plurality of segments covering the entire period of the original time series data. Therefore, the former analysis result 10 is not time-dependent, and the latter analysis result 11 is time-dependent.

  In the analysis result 10, the generalized trigonometric polynomial parameter a is the number of terms, amplitude, period, and top phase of the generalized trigonometric polynomial described above. From these parameters a, a periodically varying curve, that is, a polynomial parameter The optimal fitting curve 4 and its spectrum, that is, the reconstructed spectrum 5 by the polynomial parameter, are constructed, and the residual time and the residual component of the residual spectrum 6 are added to this, thereby reconstructing the original time series data Is done.

  On the other hand, in the analysis result 11, the generalized triangular polynomial parameter e, the reconstruction spectrum f based on the polynomial parameter, and the top phase g based on the polynomial parameter are configured for each segment. A time variation of the phase g is constructed.

Next, the operation of each component described above of the analysis apparatus 1 will be described.
3 and 4 are flowcharts showing the flow of processing in the analysis sequence determination means 2, and FIG. 5 schematically shows a configuration example of layers and segments determined by the analysis sequence determination means 2.

  First, when original time series data is input to the analysis apparatus 1 in step S1, the analysis sequence determination means 2 first sets a layer in which one segment is arranged in step S2. Since the layer in which this one segment is arranged is always set, the setting time may not be the time of step S2.

Next, in step S3, it is determined whether or not the total number of data points of the input original time series data exceeds the preset maximum number of data points.
This maximum number of data points is the maximum number of data points that can be analyzed by importing into the basic segment, which will be described later. Generally, if the number of data points that are imported into each segment and analyzed at the same time is too small, it will be difficult to extract the structure of the data. If it is too large, an excessive data structure is extracted. Therefore, it is preferable to obtain an optimal number of data points in order to obtain a highly accurate analysis result. On the other hand, the optimal number of data points for analysis differs depending on whether the periodicity of the acquired data is strong, and the number of data points is also limited by the calculation speed and calculation accuracy of the calculation means constituting the analysis apparatus 1.
For this reason, as the maximum number of data points, a value obtained from knowledge accumulated by analysis of a large number of time series data so far is set. Note that this maximum data score can be changed by feeding back the results of evaluation by each evaluation means to be described later, and step S3 and subsequent processing can be performed based on the changed maximum data score. The maximum number of data points can be set by the operator.

  Note that the step of equalizing the unequal-interval original time series data by using interpolation, interpolation, or the like in order to automatically analyze the unequal interval original time-series data. Can be provided at or before step S3.

  If it is determined in step S3 that the total number of data points of the input time-series data does not exceed the preset maximum number of data points, one layer in which one segment is arranged is set. In this state, the process proceeds to step S6 in FIG.

  On the other hand, if it is determined in step S3 that the total number of data points of the input time-series data exceeds the preset maximum number of data points, the process proceeds to step S4. In step S4, A layer is added to the lower layer of the upper layer set so far, and a segment twice as many as the number of segments of the upper layer is arranged in the lower layer, and the process proceeds to step S5.

  In step S5, whether the number of data points for each segment when the whole period data of the input original time series data is equally divided into all the segments arranged in step S4 exceeds the maximum number of data points. Determine whether or not.

  If it is determined in step S5 that the number of data points of each segment exceeds the maximum data point, the process proceeds to step S4, where a lower layer is added, while the number of data points of each segment is If it is determined that the maximum number of data points has not been exceeded, the process proceeds to step S6 in FIG.

  Through the processing in each of the above steps, the structure of layers and segments for obtaining original time series data into a segment so as not to exceed the preset maximum number of data points is obtained, and the configured single or sequential Multiple segments cover the entire period of the original time series data. Therefore, the process of the above steps corresponds to the above-described division process.

  Next, in step S6, the corresponding portion of the original time series data is taken into the segment of the lowest layer, and segment data is configured.

ここで、Bm(f)はラグ値m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)はバーグの係数である。 Next, in step S7, the spectral density of the maximum entropy method of the following equation is calculated for the segment data from the minimum lag value to the maximum lag value, and the transition of the Berg coefficient Pm with respect to the lag value is evaluated in step S8.

Here, Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients.

  As will be exemplified later, the coefficient Pm is an amount that monotonously decreases as the lag value increases. In white noise time-series data, this decrease is very gradual, whereas a constant amount in the trigonometric function wave. In the time-series data on which the noise is superimposed and other time-series data including a component having periodicity as normally observed, the decrease in the coefficient Pm is slightly large. In addition, in the time series data with extremely high periodicity, which is described as a trigonometric wave which contains no noise or very little in addition to the component having periodicity, the coefficient Pm decreases very rapidly, The ratio of the coefficient Pm to the minimum lag value and the coefficient Pm to the maximum lag value (number of data points of segment data −1) reaches 7 to 10 digits or more.

  The data structure does not change over the entire period of the segment data, and for uniform time-series data, the coefficient Pm first decreases rapidly when increasing from the minimum lag value, then reaches the plateau region and reaches the maximum lag. In the case of non-uniform time series data in which the data structure changes within the period of the segment data while gradually decreasing to a value, a rapid change of the coefficient Pm occurs in the plateau region.

  Therefore, in step S8, as the evaluation of the segment data, a: the ratio of the coefficient Pm to the minimum lag value and the ratio of the coefficient Pm to the maximum lag value are calculated, and the value is compared with the set value to determine the cycle of the segment data. Evaluation of the strength of sex and b: detecting a sudden change in value in the plateau region to detect a change in data structure.

  If it is determined in step S8 that the data structure is uniform, the process proceeds to step S9, the segment for which the data structure has been evaluated is set as a basic segment, and then the process proceeds to step S10 for all segments. Then, it is determined whether or not the evaluation of the data structure of the segment data is completed. If the evaluation is not completed, the process proceeds to step S6, and the above-described processing is performed for the next segment.

  On the other hand, if it is determined in step S8 that the data structure is non-uniform, the process proceeds to step S11. In step S11, a sublayer is configured below the segment layer evaluated in step S8. In the sublayer, a segment divided into two is arranged at a location where the data structure is changed.

  Next, the process proceeds to step S6, and the same processing as described above is performed on the two segments arranged in the sublayer configured in step S11. That is, if it is determined in step S8 that the data structure of the sub-layer segment is uniform, this segment is also set as a basic segment in step S10, while the data structure is determined to be non-uniform. In this case, a sub-layer is further formed below the sub-layer, and a segment divided into two at the location where the data structure is changed is arranged in this sub-layer, and the process proceeds to step S6 and the same processing as described above. Is done.

  Thus, in step S10, it is determined whether or not the evaluation of the data structure of the segment data has been completed for all segments including the sublayer segment. If it is determined that the segment data has been completed, the process proceeds to step S12. Corresponding to all the segments set as basic segments in S9, storage areas are set in the storage means, initialization is performed, and the analysis sequence is completed.

  FIG. 5 schematically shows the structure of layers and segments determined by the analysis sequence determination means 2 for certain time-series data to be analyzed, and the layers correspond to the entire period data of the time-series data. N + 1 layers are configured up to layer N (N: natural number) below layer 0 where one segment is arranged, and sublayer 1 is configured corresponding to segment 3 of layer N. Yes. In this way, all the segments of layer N except segment 3 are set as basic segments, and two segments of sub-layer 1 obtained by dividing segment 3 of segment N are set as basic segments. A storage area is set in the storage means corresponding to all of these basic segments.

  The data analysis unit 3 analyzes the original time series data taken into the segment, that is, the segment data, based on the layer and segment configuration determined by the analysis sequence determination unit 2 as described above.

The analysis of the segment data by the data analysis means 3 is performed in the same processing flow sequentially from the highest layer 0 to the lowest layer N and the sublayer 1, but at this time, the segment of the upper layer segment As described above, the data is processed by configuring the segment data by reducing the number of data points of the original time series data by bunching processing so that the number of data points per segment does not exceed the preset maximum data number. . For example, for the segment of layer 0, data obtained by reducing the number of data points of the original time series data to ½ ^N by bunching processing is taken as segment data, and for the segment of layer 1, all of the original time series data is imported. Data in which the number of data points in the period is reduced to 1/2 ^N-1 is taken as a segment.

  Further, in the analysis result of each segment in the upper layer, the parameters obtained for the upper segment are sequentially stored in the storage areas of all the basic segments corresponding to the upper segment. On the other hand, the residual time series data obtained by calculating the difference between the fitting curve composed of the above parameters and the corresponding portion of the original time series data is set and analyzed as segment data of the next lower layer.

Therefore, the flow of analysis processing of each segment in the data analysis means 3 and the analysis result evaluation means 4 will be described with reference to the flowcharts of FIGS.
First, in step S101, the corresponding portion of the original time series data is taken into the segment to form segment data. At this time, in the case of segments of layers 0 to N-1, as described above, the number of data points is reduced by the bunching process.

  Next, in step S102, the spectral density (MEM-PSD) of the maximum entropy method is calculated from the minimum lag value to the maximum lag value for the segment data captured in step S101, as in step S8 described above. Calculate the transition of Berg's coefficient Pm with respect to the lag value.

  Next, in step S103, as in step S9 described above, the transition of the Berg coefficient Pm with respect to the lag value is evaluated, and M lag values used for calculation of the power spectral density by the maximum entropy method are determined based on the transition. This lag value may be singular or plural.

  This lag value is determined by, for example, a: data having strong periodicity, that is, when the ratio of the coefficient Pm to the minimum lag value and the coefficient Pm to the maximum lag value is large, the lag value is set to 50% or less. If the number of points is large, the lag value should be smaller. B: If the periodicity is weak, the lag value should be 50% or more, and up to 75% to efficiently extract the time-series structure. If there are few, the conditions for determining the lag value, such as a larger lag value, and other knowledge obtained from the analysis of many time-series data are stored as a knowledge base, and the above-mentioned Berg It is possible to adopt a configuration in which one or a plurality of lag values are automatically determined from the evaluation result of the coefficient Pm using a knowledge base. In addition, a person can determine the lag value by interactive operation of the analysis apparatus 1.

  Next, for each of the M lag values determined in step S103, in step S104, the power spectral density (MEM-PSD) is calculated by the maximum entropy method disclosed in the above-described literature.

  Next, in step S105, an appropriate number of main peaks and their powers are extracted from each of the M power spectral densities calculated in step S104. Also in the extraction operation of the main peak and its power, the person determines the lag value by interactive operation of the analysis apparatus 1 in addition to the automatic extraction using the knowledge base similarly to the determination operation of the lag value in step S103. It is also possible to perform.

  Next, in step S106, a plurality of fitting curves and their parameters are calculated by the nonlinear least square method using the reciprocal of the main peak frequency extracted in step S105 as the initial value of the period.

  Next, in step S107, the degree of coincidence is evaluated by comparing the parameters of the fitting curve obtained in step S106 with initial values. For example, the degree of coincidence is evaluated by a value obtained by dividing the power (1/2 of the square of the amplitude) of the mode of each cycle of the fitting curve by the power of the main peak.

  In this way, in step S107, the fitting curve having the highest degree of coincidence is selected as the optimum fitting curve.

  Next, in step S108, it is determined whether or not the degree of coincidence of the parameters of the optimum fitting curve selected in step S107 is equal to or higher than a preset degree of coincidence. In step S103, the process proceeds to step S103. If the degree of coincidence is equal to or higher than the preset matching degree, the process proceeds to step S109, and the optimum fitting curve selected in step S107 is analyzed. Evaluation is performed by the evaluation means 4.

The evaluation by the analysis result evaluation means 4 shown as step S109 in FIG. 6 is performed according to the flow shown in the flowchart of FIG.
First, in step S112, an optimal fitting curve is reconstructed using the parameters selected in step S107, and a difference from the original time series data corresponding to the data period is calculated to obtain a residual curve. In addition, various quantities for evaluating the reproducibility of the fitting curve, here, the time dependence of the standard deviation and the residual power are required.

  Next, in step S113, it is determined whether or not the optimum fitting curve and the corresponding portion of the original time series data are sufficiently matched based on various amounts for evaluating the reproducibility of the fitting curve obtained in step S112.

  If it is determined in step S113 that they are sufficiently matched, the process proceeds to step S114, and the obtained parameters are sequentially stored in the storage areas of all the basic segments corresponding to the segment. On the other hand, after the residual time series data obtained by calculating the difference between the fitting curve composed of the above parameters and the corresponding portion of the original time series data is set as the segment data of the next lower layer, the process of step S109 is performed. Ends.

  On the other hand, if it is determined in step S113 that they do not match sufficiently, the process proceeds to step S115, the segment analysis result is discarded, and the segment data is set as it is to the segment of the next layer, and then step S109. This process ends.

  By performing such processing, segment data for which a fitting curve that sufficiently matches cannot be obtained in the batch analysis processing is sequentially divided into two lower segments, and the next segment data is set. Since it is analyzed as segment data, even if it is segment data that does not provide a fitting curve that matches well due to fluctuations in the data structure in the batch analysis process, it will eventually be sufficient in the basic segment of the sublayer. A matching fit curve can be determined.

  When the process of step S109 is completed, the process proceeds to step S110, where it is determined whether or not the analysis of all segments has been completed. If not, the process proceeds to step S101, and the next segment is determined. If all the segments have been analyzed, the segment analysis is completed.

  Next, as described above, the collective analysis result configuration unit 9a uses the reconstructed spectrum calculation unit 6 and the other calculation unit 8 to configure the analysis result 10 as shown in FIG. 2, and the segment analysis result configuration unit 9b. Is to construct an analysis result 11 as shown in FIG. 2 using the reconstructed spectrum calculating means 6, the top phase shift calculating means 7, and the other calculating means 8, and these calculating means 6, Next, the operation of No. 7 will be described.

  First, FIG. 8 is a schematic flowchart for explaining the operation of the reconstructed spectrum calculating means 6 when it is used by the collective analysis result constituting means 9a. First, in step S201, all the storage areas 1 to 2N are stored. All parameters (amplitude aj and period Tj) and residual time series data εx (t) are extracted. The number of extracted parameters is set to L for convenience as shown in the figure.

  Next, in step S202, in order to save the energy of the time-series data, L parameters, that is, L amplitudes aj and periods Tj are normalized. In this normalization, when no sub-layer is configured from the analysis sequence determination means 2, and when the data periods of all the basic segments have the same length, the square of the amplitude aj of all the modes is the number of basic segments. By dividing by 2N and making the square root a new amplitude aj, normalization can be performed. On the other hand, if a sub-layer is configured and therefore a basic segment with a different data period length is included, the amplitude aj of all modes recorded in the corresponding storage area is squared for all the basic segments. Then, normalization can be performed by multiplying this value by the ratio of the length of the basic segment to which the mode belongs and the length of the entire period and setting the square root of the obtained product as a new amplitude aj.

  According to each of the L parameters (amplitude aj and period Tj) normalized in this manner, in step S203, an isolated peak train Pj having a peak at the center frequency 1 / Tj, that is, an isolated peak train (shown in the figure). P1 ... Pj ... PL).

  In this case, the isolated peak sequence (P1 ... Pj ... PL) uses the prototype of the δ function to form one spectral peak that spreads in the entire frequency band, and thus the isolated peak corresponding to each frequency obtained from the parameters. Construct a peak group. In this way, the time series data spectrum, which is a line spectrum sequence that cannot be configured by a computer that handles finite discrete values in the theoretical form, adds a faint noise to a continuous function that rapidly decreases as it goes away from the peak frequency, such as a cosine function. By using the computer to reconstruct the spectrum obtained by calculating the spectral density of the maximum entropy method at lag 2 using lag 2 as the prototype of the δ function, A reconstructed spectrum of sequence data can be obtained.

  On the other hand, for the residual time series data εx (t), the spectral density (MEM-PSD) of the maximum entropy method is calculated in step S204, and the obtained spectral density and the isolated peak sequence obtained in step S203 are calculated. Are superimposed and combined in step S205 to calculate a reconstructed spectrum.

  Next, FIG. 9 is a schematic flowchart for explaining the operations of the reconstructed spectrum calculating means 6 and the top phase transition calculating means 7 when used by the segment analysis result constituting means 9b.

  First, in step S301, one of the storage areas 1 to 2N corresponding to the basic segment is selected, and the representative time, parameters, and residual data of the corresponding basic segment stored therein are extracted. First, the storage contents of the storage area 1 of the earliest representative time are taken out, and then the contents of the storage areas corresponding to the basic segments whose time has passed are sequentially taken out by the repetitive processing described later, and the contents of all the storage areas Is taken out.

  Among the extracted data in the storage area, the parameters (amplitude aj and period Tj) and residual time series data εx (t) are input to the reconstruction spectrum calculation means 6, and the parameters (period Tj and top phase φj) are It is input to the top phase shift calculation means 7 and used for processing.

  The parameters (amplitude aj and period Tj) input to the reconstructed spectrum calculation unit 6 are not subjected to the above-described amplitude normalization process in step S202 when used by the collective analysis result configuration unit 9a, and step S203 is performed. Similarly to step S302, an isolated peak train Pj having a peak at the center frequency 1 / Tj, that is, an isolated peak train (P1... Pj... PL) shown in FIG.

  On the other hand, for the residual time series data εx (t), the spectral density (MEM-PSD) of the maximum entropy method is calculated in step S303, and the obtained spectral density and the isolated peak sequence obtained in step S302 Are synthesized in step S304, a reconstructed spectrum is calculated.

  On the other hand, the parameters (period Tj and top phase φj) input to the top phase transition calculation means 7 are analyzed in step S305, and the peak time relative to the representative time of the basic segment is determined from the correspondence between the frequency and the top phase. The frequency dependence of the phase is obtained.

  These obtained analysis results are recorded in the predetermined recording area as attributes of the representative time of the basic segment in step S306.

  Next, in step S308, it is determined whether or not the data in the storage area corresponding to all the basic segments has been analyzed. If a storage area that has not been analyzed remains, the process proceeds to step S301 via the connector B. Thus, the next storage area is analyzed. On the other hand, if the data in the storage area corresponding to all the basic segments has been analyzed in step S308, an end process is performed.

Next, the operation of the analysis apparatus of the present invention described above will be described with reference to a specific example.
The time-series data to be analyzed is shown in FIG. 10, and the data is time-series data of 48 points and 201 points. As can be seen from the figure, in the 24-hour mode, the phase is inverted at 24:00.

  First, when the time-series data shown in FIG. 10 is input to the analysis apparatus 1, the analysis sequence determination means 2 determines the analysis sequence through the processing steps shown in FIGS. 3 and 4 as described above.

  In the analysis apparatus 1, if the maximum number of data points is set to 300, for example, for accuracy of arithmetic processing, the number of data points of the input original time series data is 201 points, and the number of data points of the original time series data is Is less than the maximum number of data points, and through step S3 in FIG. 3, only one layer is set, and one segment is arranged in this layer.

  Next, in step S6, the whole period data of the original series data is taken into the segment. Next, in step S7, the transition of the Burg coefficient Pm is calculated up to the maximum lag value (200 points). FIG. 11 shows the transition of the coefficient Pm.

  Next, in step S8, the behavior of the coefficient Pm is analyzed. First, the ratio of the first coefficient Pm and the last coefficient Pm is calculated. As a result, since it exceeds 10 digits, it is determined that the data is “strongly periodic”.

  Next, the analysis sequence determination means 2 analyzes the transition of the coefficient Pm. Normally, the coefficient Pm gradually decreases to the maximum lag value after first rapidly decreasing, whereas in the input original time series data, the lag value The coefficient Pm hardly decreases in the region of 3 to 100 (corresponding data points are 4 to 101 points), decreases rapidly immediately afterwards, and then forms a plateau region again until the maximum lag value, so 101 points Detect that the data structure has changed in the vicinity of.

  Therefore, the analysis sequence determination means 2 moves to the process of step S11, constitutes a sublayer, and constitutes a segment divided into two at locations where the data structure is changed.

  Next, the process proceeds to step S6, and the uniformity of the data structure is sequentially evaluated in step S8 for each of the segments divided in step S11.

  In addition, since the data is located at the boundary of the segment of the divided sublayer, this data is duplicated and captured in the adjacent segment. As a result, the data score of each segment of the sublayer is 101 points. Become.

  First, in the evaluation of step S8 for the segment data with the earlier time, the change of the coefficient Pm is calculated as shown in FIG. 12, and the value of the coefficient Pm is attenuated by 14 digits from the lag value 0 to 7, The presence of the abrupt attenuation region in the plateau region as described above is not detected. Therefore, the analysis sequence determination means 2 sets this segment as a basic segment in step S9. The same evaluation is performed for the segment data having a later time through steps S10 to S6, and this segment is also set as a basic segment in step S9.

  Next, in step S10, it is determined that the evaluation is complete, the process proceeds to step S12, and a storage area is set in the storage means and initialized in correspondence with all the segments set as basic segments in step S9. The analysis sequence is completed. In the initialization of the storage area, when it is determined that the corresponding basic segment is “very periodic” in step S8, the information is written in the storage area.

  FIG. 13 schematically shows the structure of the layers and segments determined by the analysis sequence determination means 2, and the layers are located below layer 0 where one segment 1 corresponding to the entire period of the time-series data is arranged. Sublayer 1 is configured, and two segments of this sublayer 1 are set as basic segments 1 and 2. In correspondence with these basic segments 1 and 2, storage areas 1 and 2 are set in the storage means.

  Next, the data analysis means 3 analyzes each segment by the process shown in the flowchart of FIG. In this embodiment, segment analysis is first performed on the segment of layer 0, but the two basic segments 1 and 2 of the sublayer included in segment 1 of layer 0 are both extremely periodic data. Since it is determined, the analysis of the segment of layer 0 can be omitted. However, in the following description, the analysis of the segment 1 of layer 0 is also performed.

  First, the data analysis means 3 takes in the data corresponding to the original time series data into the segment 1 in step S101 and sets it as segment data. In this embodiment, the data of segment 1 is original time series data itself and has 201 data points.

  Here, in step S102, the spectral density (MEM-PSD) of the maximum entropy method is calculated from the minimum lag value to the maximum lag value, and the transition of the Burg coefficient Pm with respect to each lag value is calculated. In this embodiment, the same calculation is performed in the analysis sequence determination means 2 to obtain a result as shown in FIG. 11, so that the executed calculation is appropriately held for a period in the analysis apparatus 1 of the present invention. Such a configuration eliminates the need for recalculation.

  Next, in step S103, a plurality of lag values indicating characteristic behavior are selected from the transition shown in FIG. In FIG. 11, the greatest feature is the presence of a plateau region with a lag value of 2 to 101, which is highly periodic data. Therefore, the data analysis means 3 is reduced by a selection means using a knowledge base or the like that is configured in itself. For example, three lag values of lag values 2, 50, and 101 are selected, and in step S104, three MEM-PSDs corresponding to these lag values are calculated. The results are as shown in FIG. 14, and the results with lag values of 2, 50, and 101 are shown in order from the left.

  Next, in step S105, as the main peak, the initial value of the period is 24.66 hours (power 49.80) at lag value 2; 28.06 hours (49.76) at lag value 50; 34.48 hours (29.81) and 18.63 hours at lag value 101 in 2 modes. (31.31) is extracted and used as the initial value of the calculation by the following nonlinear least square method.

  Next, in step S106, the optimum fitting curve and the curve parameter in each case are searched for by the nonlinear least square method with respect to the above three sets of initial values. In this case, in the non-linear least squares analysis, a region for searching for the period value is set in the vicinity of the period of the initial value in advance, the initial value is in the vicinity of the true value, and the residual sum of squares is in the vicinity. Calculations are performed in the hope of having only one local minimum.

  That is, in step S106, the search process is monitored, and when the departure from the neighboring region is made during the search or when there are a plurality of minimum values, it is determined that the initial value itself is inappropriate, and the result is obtained. do not use. Therefore, it is determined that the initial values of the lag values 2 and 50 are inappropriate, and the optimal fitting curve and its curve parameters are calculated only using the calculation result for the initial value of the lag value 101. . FIG. 15A shows the calculated optimum fitting curve, and FIG. 15B shows a residual curve with the original time series data.

  Next, in step S107, the matching curve parameter is compared with an initial value to evaluate the degree of coincidence, and the validity of the optimum fitting curve calculated in step S106 is determined. That is, FIG. 16 compares the reciprocal of the peak frequency of the initial value and the power with the period and amplitude of the curve parameter finally obtained. In this case, the degree of coincidence shown in the figure is a value obtained by dividing the mode power (1/2 of the square of the amplitude) by the peak power, as described above.

  As can be seen from FIG. 16, the degree of coincidence is 0.967 in the 36-hour mode and 0.803 in the 18-hour mode. Although the degree of coincidence in the 18-hour mode is not so high, since it is the only optimum fitting curve calculated in step S106 and its parameter, the data analysis means 3 gives the result to step S109, that is, the analysis result evaluation means 4 Output to the process of evaluation by.

  First, in step S112, the optimum fitting curve obtained through steps S106 to S108 is reconstructed, the difference with the original time series data corresponding to the data period is calculated, a residual curve is obtained, and the fitting curve is obtained. The amount of evaluation of the reproducibility of the image, here, the time dependence of the standard deviation and the residual power is required.

  FIG. 17 compares the original time series data (dotted line) and the optimum fitting curve (solid line), and FIG. 18 shows the average of the residual curve for each of the 20 segment areas. The standard deviation of the residual is as large as 0.836, and it can be seen from FIG. 16 that the fit is not good. And from FIG. 18, the residual is not uniformly distributed around zero, and time dependence is recognized.

  Due to the magnitude of the standard deviation value, the time dependency of the residual, and the like, the data analysis unit 3 determines that the optimum fitting curve and the corresponding portion of the original time series data do not sufficiently match in step S113. Determination is made and the process proceeds to step S115. That is, the segment data of segment 1 of layer 0, which has been the object of analysis up to that point, is carried forward as it is as analysis object data of segments 1 and 2 of the next layer 1.

  As described above, when the segment data is configured by reducing the number of data points of the original time series data by bunching processing, the data set for the segment of the lower layer is not necessarily the same as the segment data of the upper layer. Not necessary.

  Next, the data analysis means 3 goes from step S109 to step S110 to step S101, and then the basic segments 1 and 2 of the sublayer 1 are sequentially analyzed.

  First, for basic segment 1, data of 1 to 101 points of original time series data is fetched as segment data in step S101.

  Next, the transition of the coefficient Pm as shown in FIG. 12 is obtained by the calculation in step S102. In this case, the transition to the lag value 7 is required for the accuracy of numerical calculation.

  Next, in step S103, two of 3 and 7 are determined as lag values, and MEM-PSD is calculated with the lag value determined in step S104. The result is as shown in FIG. 19 and is a result of the lag value and the lag value 7 in order from the left.

  Next, in step S105, an initial period value of 24.00 hours (power 49.66) is extracted with a lag value of 2, and an initial period value of 24.00 hours (50.14) is extracted with a lag value of 7, using these two sets of initial values, step S106. The two optimum fitting curves and curve parameters are calculated by the nonlinear least square method. In this case, a period of 24.00 hours, an amplitude of 10.00, and a top phase of 6.00 are obtained.

  Next, in step S107, the plurality of curve parameter sets described above are compared. In this embodiment, since all the parameters match and the fit is good, the optimum fit curve and its parameters are It inputs into step S109 through step S108.

Since the standard deviation of the residual obtained in step S112 is sufficiently small as 10 ⁻¹⁰ and the power transition of the residual is not time-dependent, in step S113, this time, the optimum fitting curve and the original time series data Are determined to match sufficiently, and the process proceeds to step S114.

  In step S114, the parameter of the analysis result is stored in the storage area 1. Unlike this embodiment, if there are further sublayers in the lower layer, the residual is calculated and saved to set it in the lower sublayer.

  Subsequently, the process proceeds to step S101 through step S110, and the same analysis processing is performed for the next basic segment 2, and thus the original time series data is described in the storage areas 1 and 2 by a generalized trigonometric polynomial, In addition, all the quantities necessary for the subsequent analysis are accumulated.

  Then, as described above, various quantities necessary for the analysis of the original time series data stored in the storage areas 1 and 2 are processed by the collective analysis result construction unit 9a or the segment analysis result construction unit 9b, as shown in FIG. Such an analysis result 11 can be configured.

As an example, the flow of calculation of the reconstructed spectrum by the reconstructed spectrum calculating means 6 when used by the collective analysis result configuring means 9a will be described.
First, in FIG. 8, in step S201, parameters (generalized triangular polynomial parameters) are extracted from the storage areas 1 and 2. At this time, two parameters are taken out, each of which has a period of 24 o'clock, an amplitude of 10 and an apex phase of 6 o'clock.
Next, in step S202, the amplitude is normalized. This normalization is performed by dividing the square of amplitude = 100 by the number of basic segments (= 2) and setting the square root (= √50) to a new amplitude for each of the two parameters.
Next, two peak spectra having the same peak frequency (= 1/24 hours) are obtained by calculating the PSD of the isolated peak in step S203. The calculation of the isolated peak is realized by normalizing a trigonometric MEM-PSD in advance and matching the area with the power of each mode. FIG. 20 shows the obtained cosine function MEM-PSD.
As described above, in the present invention, the isolated peak sequence is formed by using one prototype of the δ function to form one spectral peak having a base extending over the entire frequency band, thereby obtaining an isolated peak group corresponding to each frequency obtained from the parameters. In this way, the spectrum of time series data, which is a line spectrum sequence that cannot be configured by a computer that handles finite discrete values in the theoretical form, is a continuous function that rapidly decreases as it goes away from the peak frequency, for example, noise that is weak to cosine function By using the computer to reconstruct the spectrum obtained by calculating the spectral density of the maximum entropy method at lag 2 using lag 2, and using the computer as a prototype, it is consistent with the theory. A reconstructed spectrum of the original time series data can be obtained.
On the other hand, a residual curve over the entire measurement length is obtained from the residual components of the basic segments 1 and 2 extracted from the storage areas 1 and 2, and then in step S204, the residual MEM-PSD is calculated. Next, in step S205, the isolated peak group spectrum and the residual MEM-PSD are superimposed to finally obtain a reconstructed spectrum that matches the generalized triangular polynomial representation of the original time series data.

  As described above, the analysis apparatus according to the present invention mechanically calculates the generalized trigonometric polynomial expression on the time axis and the reconstructed spectrum expression on the frequency axis for real time series data. . At this time, the theoretical consistency between the time series data, generalized trigonometric polynomial expression, and reconstructed spectrum expression is completely guaranteed under the limitations of the numerical processing system built on the computer. Is done. That is, the most consistent and transparent understanding on the time axis and the frequency axis can be mechanically obtained for arbitrary actual data.

  In addition, the analysis apparatus according to the present invention can perform high-precision analysis using only time-series data without assuming any numerical model, and the analysis is sufficiently practical even with a computation capability comparable to that of a normal personal computer. In particular, the time series data to be analyzed is appropriately segmented according to the number of data points and the data structure and processed, so that it is always appropriate regardless of the time series data to be analyzed. There is a special effect that high-precision analysis can be performed.

  In addition to real time-series data, that is, finite-length discrete time-series data of a certain number of points observed in a certain limited period, the present invention provides spatial data such as a change in brightness with respect to the distance of the geological section. It can also be used for analysis of continuous data.

It is explanatory drawing of the whole structure which represented typically the embodiment of the analyzer which concerns on this invention. The analysis result output from the analyzer which concerns on this invention is shown typically. It is a flowchart which shows the flow of the process in an analysis sequence determination means. It is a flowchart which shows the flow of the process in an analysis sequence determination means. 3 schematically shows an example of the structure of layers and segments determined by an analysis sequence determination unit. It is a flowchart of the analysis process of each segment in a data analysis means. It is a flowchart of the analysis process of each segment in an analysis result evaluation means. It is a typical flowchart explaining operation | movement of the reconstruction spectrum calculation means when it is utilized by the collective analysis result structure means. It is a typical flowchart explaining operation | movement of the reconstruction spectrum calculation means when used by the segment analysis result structure means, and a top phase transition calculation means. It is explanatory drawing which shows an example of the time series data to analyze. It is explanatory drawing which shows transition of the coefficient Pm of Burg. It is explanatory drawing which shows transition of the Berg coefficient Pm about the segment data whose sublayer time is earlier. It is explanatory drawing which shows typically the structure of the determined layer and segment. It is explanatory drawing which shows a part of three MEM-PSD calculated corresponding to three lag values. (A) is the calculated optimal fitting curve, (b) is explanatory drawing which shows a residual curve with original time series data. It is explanatory drawing which compared the reciprocal number and power of the peak frequency of an initial value with the period and amplitude of the curve parameter finally obtained. It is explanatory drawing which compared the original time series data (dotted line) and the optimal fitting curve (solid line). It is explanatory drawing which averages a residual curve for every 20 division area. It is explanatory drawing which shows two MEM-PSD calculated corresponding to two lag values. It is explanatory drawing which shows MEM-PSD of a cosine function utilized as a prototype of (delta) function.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Analysis apparatus 2 Analysis sequence determination means 3 Data analysis means 4 Analysis result evaluation means 5 Control means 6 Reconstructed spectrum calculation means 7 Top phase transition calculation means 8 Other calculation means 9a Collective analysis result construction means 9b Segment analysis result construction means 10 Batch analysis result 11 Segment analysis result

Claims (20)

Analysis sequence determination means for determining the sequence for analyzing the time series data to be analyzed, and data analysis for determining parameters and residuals of generalized trigonometric polynomials by analyzing the data by the maximum entropy method and nonlinear least square method according to the analysis sequence And an analysis result evaluation means for evaluating the analysis result obtained by the data analysis means and storing it in the storage means when the condition is met, and a residual obtained by using the power spectral density obtained from the above parameters and the maximum entropy method A reconstructed spectrum calculating means for obtaining a reconstructed spectrum of time series data by synthesizing the power spectral density of the data, and using this calculating means, the time series to be analyzed is calculated from the parameters and residuals extracted from the storing means. And an analysis result construction means for reconstructing a generalized trigonometric polynomial corresponding to the data The analysis sequence determination means includes a division process for dividing the time-series data to be analyzed into segments so as not to exceed a preset maximum number of data points, and an evaluation process for evaluating the uniformity of the data structure for each segment And a division process for dividing the non-uniform segment data into a plurality of uniform segments based on the evaluation, and each of the divided uniform segments as a basic segment, and a storage area in the storage means. A time-series data analysis apparatus comprising a storage area setting process for setting the time series data. Segments are divided into two powers in the lower layer, each of which is composed of the uppermost layer segment corresponding to the whole period data of the time series data to be analyzed, and the lowermost layer. 2. The time series according to claim 1, wherein a segment whose data structure changes in a layer is composed of segments of sub-layers which are sequentially formed by dividing the segment where the data structure changes. Data analysis device. 2. The time series according to claim 1, wherein the uniformity of the data structure is evaluated by a transition of the Burg coefficient Pm with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation. Data analysis device.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients. 2. The time-series data analysis apparatus according to claim 1, wherein the analysis sequence determination means is provided with an equal-interval processing step for performing equal-interval processing on the time-series data with unequal intervals. The data analysis means is a calculation process to determine the transition of the Burg coefficient Pm with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following formula for the segment data extracted from the time series data to be analyzed And a lag value determination process for determining a lag value used for calculation of power spectral density by the maximum entropy method from the obtained transition, and a power spectrum density calculation process for determining the power spectral density based on the determined lag value. The frequency of the main peak from the power spectral density, the extraction process to extract the power, the parameter derivation process to obtain the parameters of the fitting curve by the nonlinear least square method from the extracted frequency and power, the obtained fitting curve and segment Compare the data and evaluate the degree of agreement If the degree of coincidence is equal to or higher than the degree of coincidence, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process. If the degree of coincidence is not reached, the parameters of the fitting curve are discarded. The time-series data analysis device according to claim 1, further comprising an evaluation process that shifts to a process of determining a lag value.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients. The segment data analysis in the data analysis means is performed sequentially from the highest layer to the lowest layer. At this time, the segment data of the upper layer segment is preset with the number of data points per segment. In order not to exceed the maximum number of data points, the number of data points of the time-series data to be analyzed is reduced by bunching processing to form segment data, and a temporary storage area corresponding to each segment of each layer The polynomial parameters obtained for the upper segment are stored in the temporary storage area of each segment of each lower layer, and the fitting curve composed of the above polynomial parameters is associated with the original time series data. The residual time series data obtained by the difference calculation with the part is used as the next lower layer. Analyzer time series data according to claim 5, characterized in that performing the process of setting as the segment data. The analysis result evaluation means is a residual analysis process in which the corresponding curve obtained by the data analysis means for the segment data is compared with the corresponding range of the time series data to be analyzed to obtain a residual curve and perform analysis thereof, The residual curve analyzed by the residual analysis process is compared with the time series data to evaluate the degree of coincidence. If the degree of coincidence is equal to or higher than the predetermined coincidence, the parameters of the fitting curve and the residual are stored in a predetermined storage means. And an evaluation step of discarding the data when the predetermined degree of coincidence is not reached and shifting the segment data to the segment of the next layer. Analyzing device for time series data described in 1. The analysis result configuration means includes collective analysis result configuration means for obtaining and storing a reconstructed spectrum in a batch from all the data areas from the basic segment parameters and residuals stored in all the storage areas, and each storage area. It consists of segment analysis result configuration means that calculates and stores the reconstruction spectrum for each basic segment from the stored basic segment parameters and residuals, and analyzes the frequency dependence of the top phase for each basic segment The top phase transition calculating means for performing the calculation, and the frequency dependence of the top phase for each basic segment calculated by the top phase transition calculating means together with the reconstructed spectrum by the segment analysis result constituting means and the representative of the basic segment The time-series data analyzing apparatus according to claim 1, wherein the time-series data analyzing apparatus is stored as a time attribute. The reconstruction spectrum calculation means calculates the power spectral density from the obtained parameters. For each term of the generalized trigonometric polynomial, each spectrum with a base spread over the entire frequency band using the prototype of the δ function. 2. The time according to claim 1, wherein an isolated peak group corresponding to each frequency obtained from a parameter is formed by configuring a peak, and a reconstructed spectrum of time series data is obtained as a superposition thereof. Series data analysis device. 10. The spectrum obtained by calculating the spectral density of the maximum entropy method using lag 2 from a time series obtained by adding weak noise to the cosine function is used as a prototype of the δ function. Time series data analysis device. Analytical sequence determination procedure to determine the sequence to analyze the time series data to be analyzed, and data analysis to find parameters and residuals of generalized trigonometric polynomials by analyzing data by maximum entropy method and nonlinear least square method according to analysis sequence The procedure, the analysis result obtained by the data analysis procedure, and the analysis result evaluation procedure stored in the storage means when the conditions are met, the power spectrum density obtained from the above parameters and the residual obtained using the maximum entropy method The reconstruction spectrum calculation procedure for obtaining the reconstruction spectrum of the time series data by synthesizing the power spectrum density of the time series, and the time series of the analysis target by using the calculation procedure and the parameters and residuals extracted from the storage means An analysis result composition procedure for constructing a generalized trigonometric polynomial corresponding to the data, The analysis sequence determination procedure consists of a division processing procedure that divides the time series data to be analyzed into segments so as not to exceed the preset maximum number of data points, and an evaluation process that evaluates the uniformity of the data structure for each segment A procedure, a division processing procedure for dividing the non-uniform segment data into a plurality of uniform segments based on this evaluation, and each of the divided uniform segments as a basic segment, and a storage area in the storage means The computer-readable recording medium which recorded the analysis program of the time series data for making a computer perform each procedure which consists of a storage area setting process procedure which sets up. The segment is composed of the segment of the highest layer corresponding to the whole period data of the time-series data to be analyzed, and is divided into two in order, the power of 2 included in each of the lower layers, and the lowest 12. The layer according to claim 11, wherein each segment of the data layer is composed of segments of sub-layers that are sequentially formed by dividing a segment whose data structure changes at a location where the data structure changes. A computer-readable recording medium on which a series data analysis program is recorded. 12. The time series according to claim 11, wherein the uniformity of the data structure is evaluated by a transition of the Burg coefficient Pm with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation. A computer-readable recording medium on which a data analysis program is recorded.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients. 12. The computer-readable recording of the time-series data analysis program according to claim 11, wherein the analysis sequence determination procedure includes an equal-interval processing step of performing equal-interval processing on the time-series data of unequal intervals. Possible recording media. The data analysis procedure calculates the transition of the Burg coefficient Pm with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following formula for the segment data extracted from the time series data to be analyzed A lag value determining process for determining the lag value used for calculating the power spectral density by the maximum entropy method from the obtained transition, and a power spectral density calculating process for determining the power spectral density based on the determined lag value. The frequency of the main peak from the measured power spectral density and the extraction process for extracting the power, the parameter derivation process for obtaining the parameters of the fitting curve by the nonlinear least square method from the extracted frequency and power, and the obtained fitting curve Compare the segment data and evaluate the degree of match, If the degree of coincidence is equal to or higher than the above, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process. If the predetermined degree of coincidence is not reached, the parameters of the fitting curve are discarded. The computer-readable recording medium recording the time-series data analysis program according to claim 11, comprising: an evaluation process that shifts to a process of determining the lag value.

Where Bm (f) is the spectral density at the lag value m, Δt is the sampling interval, and Pm and γm (k) are Burg's coefficients. The segment data analysis in the data analysis procedure is performed sequentially from the top layer to the bottom layer. At this time, the segment data of the upper layer segment is preset with the number of data points per segment. In order not to exceed the maximum number of data points, the number of data points of the time-series data to be analyzed is reduced by bunching processing to form segment data, and a temporary storage area corresponding to each segment of each layer The polynomial parameters obtained for the upper segment are stored in the temporary storage area of each segment of each lower layer, and the fitting curve composed of the above polynomial parameters is associated with the original time series data. The residual time series data obtained by the difference calculation with the part is used as the next lower layer. A computer-readable recording medium an analysis program of the time series data according to claim 15, characterized in that it is composed of a process of setting as the segment data. The analysis result evaluation procedure includes a residual analysis process in which a fitting curve obtained by the data analysis procedure for the segment data is compared with the corresponding range of the time series data to be analyzed to obtain a residual curve and analyze it. The residual curve analyzed by the residual analysis process is compared with the time series data to evaluate the degree of coincidence. If the degree of coincidence is equal to or higher than the predetermined coincidence, the parameters of the fitting curve and the residual are stored in a predetermined storage means. 16. The method according to claim 15, further comprising: an evaluation step of moving to the next step, discarding the data if the predetermined degree of coincidence is not reached, and moving the segment data to the segment of the next layer. A computer-readable recording medium on which the time-series data analysis program described in 1 is recorded. The analysis result composition procedure includes a collective analysis result composition procedure for obtaining and storing a reconstructed spectrum all at once from the parameters and residuals of the basic segments stored in all the storage areas, and each storage area. From the stored basic segment parameters and residuals, it consists of a segment analysis result configuration procedure that calculates and stores the reconstruction spectrum for each basic segment, and analyzes the frequency dependence of the top phase for each basic segment The top phase transition calculation procedure for the basic segment is calculated, and the frequency dependence of the top phase for each basic segment calculated by this top phase transition calculation procedure is represented together with the reconstructed spectrum by the segment analysis result configuration procedure and the representative of the basic segment. The time-series data solution according to claim 11, wherein the time-series data solution is configured to store the time attribute as a procedure. A computer-readable recording medium a program. The reconstruction spectrum calculation procedure is to calculate the power spectral density from the obtained parameters. For each term of the generalized trigonometric polynomial, one spectrum that spreads in the whole frequency band using the prototype of δ function for each term. The time according to claim 11, wherein by forming a peak, an isolated peak group corresponding to each frequency obtained from a parameter is formed, and a reconstructed spectrum of time series data is obtained as a superposition thereof. A computer-readable recording medium on which a series data analysis program is recorded. 20. The spectrum obtained by calculating the spectral density of the maximum entropy method using lag 2 for a time series obtained by adding weak noise to the cosine function is used as a prototype of the δ function. A computer-readable recording medium on which a time series data analysis program is recorded.

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