CN107563017A - A kind of oil chromatography online monitoring data optimization length system of selection - Google Patents
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Abstract
The invention discloses a kind of oil chromatography online monitoring data optimization length system of selection of the on-line monitoring for belonging to transformer oil chromatographic and analysis technical field.This method obtains the oil chromatography online monitoring data of transformer as original oil chromatographic data collection, the phase space of original oil chromatographic data collection is reconstructed afterwards, calculate optimal embedding dimension and the optimal time delay of oil chromatography phase space, the relation of optimal embedding dimension and optimization length is analyzed according to the shrinkage of phase space, concentrated according to optimization length from original oil chromatographic data and obtain optimal oil chromatogram analysis data set, finally exported optimal oil chromatogram analysis data set.The present invention can obtain optimal analyze data collection from substantial amounts of oil chromatography online monitoring data so that analysis efficiency and analysis accuracy rate are higher.
Description
Technical Field
The invention belongs to the technical field of on-line monitoring and analysis of transformer oil chromatography. In particular to a method for selecting the optimal length of oil chromatogram on-line monitoring data.
Background
The transformer is one of the important pivotal devices of the power system, and the reliability of the operation of the transformer is related to the safe and stable operation of the power system. In order to ensure the normal operation of the transformer, the Dissolved gas in the transformer oil is measured in real time by using a Dissolved Gas Analysis (DGA) online monitoring technology, and according to the real-time monitoring value, the early fault of the transformer can be timely found, the type of the fault can be judged, and a maintenance plan and the like can be given. The transformer oil chromatogram on-line monitoring system obtains the data of the dissolved gas in the oil according to a certain collection period, and the collected oil chromatogram data change along with time to form an oil chromatogram on-line monitoring time sequence. In the existing research, the oil chromatogram on-line monitoring time sequence is widely applied to the aspects of state evaluation, fault prediction, oil chromatogram threshold value calculation, early warning and the like of the transformer. The oil chromatogram on-line monitoring time sequence is formed from the time of commissioning the transformer, so that the time span of the time sequence is long, the data volume is large, all data are taken for analysis or data in a fixed time period are taken for analysis in actual use, the selection of the length of the fixed time period mainly depends on the subjectivity of researchers, and no uniform standard exists. When the data is further analyzed, if the selected data is too much, that is, the selected time span is long, the previous part of the data may not reflect the operation condition of the transformer under the current working condition, and similarly, if the selected data is small, that is, the selected time span is short, the current operation condition of the transformer cannot be truly reflected due to the lack of the data amount. Therefore, the problem of selecting the length of the oil chromatographic analysis data is an urgent problem to be solved. However, in recent years, there is little research on the selection of optimal length of online monitoring data of oil chromatography.
Disclosure of Invention
The invention aims to provide a method for selecting the optimal length of oil chromatogram on-line monitoring data, which is characterized by comprising the following steps of: s102, acquiring transformer on-line monitoring data as an original oil chromatographic data set; s104, reconstructing an original oil chromatographic data set phase space; s106, calculating the optimal embedding dimension and the optimal time delay of the phase space; s108, analyzing the relation between the optimal embedding dimension and the optimal length according to the phase space contractibility; s110, calculating the optimal length of the original oil chromatogram data set according to the optimal embedding dimension; s112, acquiring an optimal oil chromatographic analysis data set from the original oil chromatographic data set according to the optimal length; and S114, outputting an optimal oil chromatographic analysis data set.
Step S102, acquiring transformer on-line oil chromatogram monitoring data as an original oil chromatogram data set; all monitoring data collected by the transformer oil chromatographic on-line monitoring system are used as an original chromatographic data set; specifically, acquiring transformer oil chromatogram online monitoring time sequence data, wherein each piece of monitoring data corresponds to one piece of monitoring time, and the monitoring times are arranged according to a descending order;
step S104, reconstructing an original oil chromatographic data set phase space; constructing an m' dimensional vector X (n) for the original oil chromatography data set X (n):
x (N) ═ X (N), X (N-t '), …, X (N- (m' -1) t ')), N ═ m' -1) t '+ 1, … N'; where the parameter N is 1,2, … N ', t ' is the preset delay time, and m ' is the preset embedding dimension.
In the step S106, the calculation method for calculating the optimal embedding dimension and the optimal time delay of the phase space includes: one or more of an autocorrelation function method, a mutual information method, a saturated correlation dimension method, an improved false near point method and a C-C method.
The step S108, according to the phase space contractibility, analyzes the relationship between the optimal embedding dimension and the optimal length,
the step S108 includes:
step S108A: since the raw oil chromatogram data set is bounded, assuming it is in [ -R, R ], the phase space of the raw oil chromatogram data is located in a hypercube bounded by 2R, in which the N points of the time series are equally distributed, and the average distance from each point to the boundary is:
wherein R is the boundary of the data value, m is the optimal embedding dimension, N is the optimal length,
step S108B, the volume corresponding to each point is: v. of0＝(2R)mand/N, wherein R is a boundary of a data value, m is an optimal embedding dimension, N is an optimal length, and the characteristic lengths of adjacent points are as follows:
rn＝(v0)1/m＝2R(1/N)1/m(2)
wherein, R is the boundary of the data value, m is the optimal embedding dimension, and N is the optimal length;
step S108C: when r isn＝rsThe phase space has the property of being contractible and saturated, otherwise it will always be contractible or saturated, so that the relation of the optimal embedding dimension to the optimal length can be obtained:
N1/m＝2(m+1) (3)
where m is the optimal embedding dimension and N is the optimal length.
The step S110, calculating the optimal length of the original oil chromatogram data set according to the optimal embedding dimension,
calculating the optimal length of the oil chromatographic analysis data: n is 2m(m+1)m；
Step S112, acquiring an optimal oil chromatographic analysis data set from the original oil chromatographic data set according to the optimal length, and selecting N data before the latest time as the optimal oil chromatographic analysis data set from the time sequence of the original oil chromatographic data set according to the optimal length;
and step S114, outputting the optimal oil chromatographic analysis data set, and outputting the optimal oil chromatographic analysis data set of the step S112.
The step S106 is explained by calculating an optimal embedding dimension and an optimal time delay by using a C-C method:
in step S106A, the correlation integral of the embedding time series of X (n) is defined as:
wherein τ is the time delay; m is the embedding dimension; m ═ N- (M-1) τ; n is the number of data; dij＝||yi-yj||∞Is an infinite function; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d); and theta (x) is a Heaviside function, and when x is larger than or equal to 0, theta (x) is 1, and when x is smaller than 0, theta (x) is 0. Step S106B, defining test statistics for X (n):
wherein τ is the time delay; m is the embedding dimension; n is the number of data; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d);
step S106C, defining a deviation statistic for X (n):
ΔS(m,N,r,τ)＝max{S(m,N,r,τ)}-min{S(m,N,r,τ)} (6)
wherein τ is the time delay; m is the embedding dimension; n is the number of data; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d); max { S (m, N, r, τ) } represents the maximum value of S (m, N, r, τ); min { S (m, N, r, τ) } represents the maximum value of S (m, N, r, τ). Step S106D, defining X (n) mean test statistics:
wherein τ is the time delay; m is the embedding dimension; n is the number of data; s (m, N, r, tau) represents the test statistic for X (N); n ismThe number of possible values for the embedding dimension m; n iskThe number of possible values of the search radius r. Step S106E, defining X (n) mean deviation statistic:
wherein τ is the time delay; m is the embedding dimension; n is the number of data; Δ S (m, N, r, τ) represents the deviation statistic of X (N); n ismThe number of possible values for the embedding dimension m.
Step S106F, defining X (n) mean index statistics:
wherein,represents the mean deviation statistic for X (n),mean index statistic representing X (n)
Step S106G, selecting the minimum value of two delay times corresponding to the first zero point of equation (7) and the first minimum value of equation (8) as the optimal delay time t,
step S106H, the global minimum point of the selection formula (9) is the optimal delay time window tauω，
Step S106I, according to tauωThe embedding dimension m is calculated as (m-1) τ.
The method has the advantages that the optimal analysis data set can be obtained from a large amount of oil chromatogram on-line monitoring data, so that the analysis efficiency and the analysis accuracy are higher.
Drawings
Fig. 1 is a flowchart of an alternative method for selecting an optimal length of online oil chromatography monitoring data according to an embodiment of the present invention.
FIG. 2C-C methodCurve line
FIG. 3C-C of the processCurve line
FIG. 4C-C Scor (. tau.) curves for the method
Detailed Description
Example 1
The invention aims to provide a method for selecting the optimal length of oil chromatography on-line monitoring data, which comprises the following steps: s102, acquiring transformer on-line monitoring data as an original oil chromatographic data set; s104, reconstructing an original oil chromatographic data set phase space; s106, calculating the optimal embedding dimension and the optimal time delay of the phase space; s108, analyzing the relation between the optimal embedding dimension and the optimal length according to the phase space contractibility; s110, calculating the optimal length of the original oil chromatogram data set according to the optimal embedding dimension; s112, acquiring an optimal oil chromatographic analysis data set from the original oil chromatographic data set according to the optimal length; and S114, outputting an optimal oil chromatographic analysis data set.
The following describes the implementation steps of the present invention with reference to the accompanying drawings.
FIG. 1 is a flow chart of an alternative method for selecting optimal length of online monitoring data of oil chromatography,
FIG. 1 shows the following steps, which are further described below:
step S102, acquiring transformer on-line oil chromatogram monitoring data as an original oil chromatogram data set; all monitoring data collected by the transformer oil chromatographic on-line monitoring system are used as an original chromatographic data set;
the step S102 specifically includes; acquiring transformer oil chromatogram on-line monitoring time sequence data, each monitor
The measured data corresponds to a monitoring time, and the monitoring times are arranged according to a descending order;
for example, in the present embodiment, 1095 pieces of time-series data of H2 in the online monitoring oil chromatogram from 2012 th 1 to 2014 th 12 th 31 of a certain transformer are obtained, and the data format is shown in table 1.
TABLE 1
Step S104, reconstructing an original oil chromatographic data set phase space; constructing an m' dimensional vector X (n) for the original oil chromatography data set X (n):
x (N) ═ X (N), X (N-t '), …, X (N- (m' -1) t ')), N ═ m' -1) t '+ 1, … N'; where the parameter N is 1,2, … N ', t ' is the preset delay time, and m ' is the preset embedding dimension.
Step S106, calculating the optimal embedding dimension and the optimal time delay of the phase space, wherein the calculating method comprises the following steps: one or more of an autocorrelation function method, a mutual information method, a saturated correlation dimension method, an improved false near point method and a C-C method;
the calculation of the optimal embedding dimension and the optimal time delay using the C-C method is explained below:
in step S106A, the correlation integral of the embedding time series of X (n) is defined as:
wherein τ is the time delay; m is the embedding dimension; m ═ N- (M-1) τ; n is the number of data; dij＝||yi-yj||∞Is an infinite function; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d); and theta (x) is a Heaviside function, and when x is larger than or equal to 0, theta (x) is 1, and when x is smaller than 0, theta (x) is 0.
Step S106B, defining test statistics for X (n):
wherein τ is the time delay; m is the embedding dimension; n is the number of data; r is the search radiusTake less than max (d)ij) Any real number of (d);
step S106C, defining a deviation statistic for X (n):
ΔS(m,N,r,τ)＝max{S(m,N,r,τ)}-min{S(m,N,r,τ)} (6)
wherein τ is the time delay; m is the embedding dimension; n is the number of data; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d); max { S (m, N, r, τ) } represents the maximum value of S (m, N, r, τ); min { S (m, N, r, τ) } represents the maximum value of S (m, N, r, τ). Step S106D, defining X (n) mean test statistics:
wherein τ is the time delay; m is the embedding dimension; n is the number of data; s (m, N, r, tau) represents the test statistic for X (N); n ismThe number of possible values for the embedding dimension m; n iskThe number of possible values of the search radius r.
Step S106E, defining X (n) mean deviation statistic:
wherein τ is the time delay; m is the embedding dimension; n is the number of data; Δ S (m, N, r, τ) represents the deviation statistic of X (N); n ismThe number of possible values for the embedding dimension m.
Step S106F, defining X (n) mean index statistics:
wherein,represents the mean deviation statistic for X (n),representing mean index statistics
Step S106G, selecting the minimum value of two delay times corresponding to the first zero point of equation (7) and the first minimum value of equation (8) as the optimal delay time t,
step S106H, the global minimum point of the formula (8) is selected as the optimal delay time window tauω，
Step S106I, according to tauωThe embedding dimension m is calculated as (m-1) τ.
In this embodiment, values of expressions (7), (8), and (9) are calculated for the phase space X (n), and a value change map is drawn as shown in fig. 2, 3, and 4. As can be seen from the figure, since the first zero point of equation (7) is 10, the first extreme point of equation (9) is 6, the delay time is 6, and since the global minimum point of equation (9) is 12, the embedding dimension m is (12/6) +1 is 3.
Step S108, according to the phase space contractibility, analyzing the relation between the optimal embedding dimension and the optimal length,
since the raw oil chromatogram dataset is bounded, it is assumed that]In the method, the phase space of the original oil chromatogram data is located in a hypercube with a 2R boundary, N points of the time series are evenly distributed in the hypercube, and the average distance from each point to the boundary is as follows:wherein, R is the boundary of data value, m is the optimal embedding dimension, N is the optimal length, and the volume that each point corresponds is: v. of0＝(2R)mN, the characteristic length of the neighboring points is: r isn＝(v0)1/m＝2R(1/N)1/mWhen r isn＝rsThe time phase space has the characteristics of shrinkage and saturation, otherwise, the time phase space is always shrinkage or always saturation; thus can beTo obtain the relationship between the optimal embedding dimension and the optimal length: n is a radical of1/m＝2(m+1)；
The step S108 includes:
step S108A: since the raw oil chromatogram data set is bounded, assuming it is in [ -R, R ], the phase space of the raw oil chromatogram data is located in a hypercube bounded by 2R, in which the N points of the time series are equally distributed, and the average distance from each point to the boundary is:
wherein R is the boundary of the data value, m is the optimal embedding dimension, N is the optimal length,
step S108B, the volume corresponding to each point is: v. of0＝(2R)mand/N, wherein R is a boundary of a data value, m is an optimal embedding dimension, N is an optimal length, and the characteristic lengths of adjacent points are as follows:
rn＝(v0)1/m＝2R(1/N)1/m(2)
wherein, R is the boundary of the data value, m is the optimal embedding dimension, and N is the optimal length;
step S108C: when r isn＝rsThe phase space has the property of being contractible and saturated, otherwise it will always be contractible or saturated, so that the relation of the optimal embedding dimension to the optimal length can be obtained:
N1/m＝2(m+1) (3)
where m is the optimal embedding dimension and N is the optimal length.
In this embodiment, the optimal embedding dimension m is 3, so the relationship between the optimal embedding dimension and the optimal length is:
N1/3＝2(3+1)
step S110, calculating the optimal length of the original oil chromatogram data set according to the optimal embedding dimension,
calculating the optimal length of the oil chromatographic analysis data: n is 2m(m+1)m；
And calculating the optimal length of the original oil chromatogram data set according to the optimal embedding dimension:
N＝23(3+1)3＝512
step S112, obtaining an optimal oil chromatographic analysis data set from the original oil chromatographic data set according to the optimal length,
according to the optimal length, selecting N data from the time sequence of the original oil chromatographic data set from the latest time backward as an optimal oil chromatographic analysis data set;
512 data after the last time 2014, 12 months and 31 days, are used as the optimal oil chromatographic data set, and the data and date of the obtained optimal oil chromatographic data set are shown in table 2.
TABLE 2
In step S114, the data in table 2 is output as the optimal analysis data set.
Through the steps S102-S114, the phase space reconstruction can be performed on the transformer on-line monitoring data, the optimal embedding dimension and the delay time are calculated, the relationship between the optimal embedding dimension and the optimal length is analyzed, and the optimal oil chromatography data set is selected from the original oil chromatography monitoring data according to the optimal length.
Claims (9)
1. The optimal length selection method for the online monitoring data of the oil chromatogram is characterized by comprising the following steps of:
s102, acquiring transformer on-line monitoring data as an original oil chromatographic data set;
s104, reconstructing an original oil chromatographic data set phase space;
s106, calculating the optimal embedding dimension and the optimal time delay of the phase space;
s108, analyzing the relation between the optimal embedding dimension and the optimal length according to the phase space contractibility;
s110, calculating the optimal length of the original oil chromatogram data set according to the optimal embedding dimension;
s112, acquiring an optimal oil chromatographic analysis data set from the original oil chromatographic data set according to the optimal length;
and S114, outputting an optimal oil chromatographic analysis data set.
2. The method for selecting the optimal length of the oil chromatogram on-line monitoring data according to claim 1, wherein in the step S102, the transformer on-line oil chromatogram monitoring data is obtained as an original oil chromatogram data set; all monitoring data collected by the transformer oil chromatographic on-line monitoring system are used as an original chromatographic data set; specifically, transformer oil chromatogram online monitoring time sequence data are obtained, each piece of monitoring data corresponds to one piece of monitoring time, and the monitoring times are arranged according to a descending order.
3. The method for selecting the optimal length of the on-line oil chromatography monitoring data according to claim 1, wherein in the step S104, an original oil chromatography data set phase space is reconstructed; constructing an m' dimensional vector X (n) for the original oil chromatography data set X (n):
x (N) ═ X (N), X (N-t '), …, X (N- (m' -1) t ')), N ═ m' -1) t '+ 1, … N'; where the parameter N is 1,2, … N ', t ' is the preset delay time, and m ' is the preset embedding dimension.
4. The method for selecting the optimal length of the online monitoring data of the oil chromatogram according to claim 1, wherein the step S106 of calculating the optimal embedding dimension and the optimal time delay of the phase space comprises the following steps: one or more of an autocorrelation function method, a mutual information method, a saturated correlation dimension method, an improved false near point method and a C-C method.
5. The method for selecting the optimal length of the on-line oil chromatography monitoring data according to claim 1, wherein the step S108 is to analyze the relationship between the optimal embedding dimension and the optimal length according to the phase space shrinkage,
the method comprises the following steps:
step S108A: since the raw oil chromatogram data set is bounded, assuming it is in [ -R, R ], the phase space of the raw oil chromatogram data is located in a hypercube bounded by 2R, in which the N points of the time series are equally distributed, and the average distance from each point to the boundary is:
<mrow> <msub> <mi>r</mi> <mi>s</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&Integral;</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <mi>x</mi> <mo>)</mo> </mrow> <msup> <mi>dN</mi> <mo>&prime;</mo> </msup> </mrow> <mrow> <mo>&Integral;</mo> <msup> <mi>dN</mi> <mo>&prime;</mo> </msup> </mrow> </mfrac> <mo>=</mo> <mi>R</mi> <mo>/</mo> <mrow> <mo>(</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
wherein R is the boundary of the data value, m is the optimal embedding dimension, N is the optimal length,
step S108B, the volume corresponding to each point is: v. of0＝(2R)mand/N, wherein R is a boundary of a data value, m is an optimal embedding dimension, N is an optimal length, and the characteristic lengths of adjacent points are as follows:
rn＝(v0)1/m＝2R(1/N)1/m(2)
wherein, R is the boundary of the data value, m is the optimal embedding dimension, and N is the optimal length;
step S108C: when r isn＝rsThe phase space has the property of being able to contract and saturate, whether or notIt will either shrink or saturate all the time, so the relation of the optimal embedding dimension to the optimal length can be obtained:
N1/m＝2(m+1) (3)
where m is the optimal embedding dimension and N is the optimal length.
6. The method for selecting the optimal length of the on-line oil chromatography monitoring data according to claim 1, wherein in the step S110, the optimal length of the original oil chromatography data set is calculated according to the optimal embedding dimension, and the optimal length of the oil chromatography data is calculated: n is 2m(m+1)m；
7. The method as claimed in claim 1, wherein in step S112, an optimal oil chromatography data set is obtained from the original oil chromatography data set according to the optimal length, and N data before the latest time in the time series of the original oil chromatography data set are selected as the optimal oil chromatography data set according to the optimal length.
8. The method for selecting the optimal length of the online oil chromatography monitoring data according to claim 1, wherein the optimal oil chromatography data set is output in step S114, and the optimal oil chromatography data set in step S112 is output.
9. The method for selecting the optimal length of the on-line oil chromatography monitoring data according to claim 4, wherein the step S106 of calculating the optimal embedding dimension and the optimal time delay by using the C-C method is described as follows:
in step S106A, the correlation integral of the embedding time series of X (n) is defined as:
<mrow> <mi>C</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>N</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>2</mn> <mrow> <mi>M</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <munder> <mo>&Sigma;</mo> <mrow> <mn>1</mn> <mo>&le;</mo> <mi>i</mi> <mo>&le;</mo> <mi>j</mi> <mo>&le;</mo> <mi>M</mi> </mrow> </munder> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mo>></mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
wherein τ is the time delay; m is the embedding dimension; m ═ N- (M-1) τ; n is the number of data; dij＝||yi-yj||∞Is an infinite function; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d); and theta (x) is a Heaviside function, and when x is larger than or equal to 0, theta (x) is 1, and when x is smaller than 0, theta (x) is 0. Step S106B, defining test statistics for X (n):
<mrow> <mi>S</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>N</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>&tau;</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>&tau;</mi> </munderover> <mo>&lsqb;</mo> <msub> <mi>C</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mfrac> <mi>N</mi> <mi>&tau;</mi> </mfrac> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mi>s</mi> <mi>m</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mi>N</mi> <mi>&tau;</mi> </mfrac> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
wherein τ is the time delay; m is the embedding dimension; n is the number of data; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d);
step S106C, defining a deviation statistic for X (n):
ΔS(m,N,r,τ)＝max{S(m,N,r,τ)}-min{S(m,N,r,τ)} (6)
wherein τ is the time delay; m is the embedding dimension; n is the number of data; r is the search radius, and is taken to be less than max (d)ij) Any real number of (d); max { S (m, N, r, τ) } represents the maximum value of S (m, N, r, τ); min { S (m, N, r, τ) } represents the maximum value of S (m, N, r, τ). Step S106D, defining X (n) mean test statistics:
<mrow> <mover> <mi>S</mi> <mo>&OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>n</mi> <mi>m</mi> </msub> <msub> <mi>n</mi> <mi>k</mi> </msub> </mrow> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <msub> <mi>n</mi> <mi>m</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>n</mi> <mi>k</mi> </msub> </munderover> <mi>S</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>N</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
wherein τ is the time delay; m is the embedding dimension; n is the number of data; s (m, N, r, tau) represents the test statistic for X (N); n ismThe number of possible values for the embedding dimension m; n iskThe number of possible values of the search radius r. Step S106E, defining X (n) mean deviation statistic:
<mrow> <mi>&Delta;</mi> <mover> <mi>S</mi> <mo>&OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>n</mi> <mi>m</mi> </msub> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <msub> <mi>n</mi> <mi>m</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </munderover> <mi>&Delta;</mi> <mi>S</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>N</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
wherein τ is the time delay; m is the embedding dimension; n is the number of data; Δ S (m, N, r, τ) represents the deviation statistic of X (N); n ismThe number of possible values for the embedding dimension m.
Step S106F, defining X (n) mean index statistics:
<mrow> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&Delta;</mi> <mover> <mi>S</mi> <mo>&OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>+</mo> <mo>|</mo> <mover> <mi>S</mi> <mo>&OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
wherein,represents the mean deviation statistic for X (n),mean index statistic representing X (n)
Step S106G, selecting the minimum value of two delay times corresponding to the first zero point of equation (7) and the first minimum value of equation (8) as the optimal delay time t,
step S106H, the global minimum point of the selection formula (9) is the optimal delay time window tauω，
Step S106I, according to tauωThe embedding dimension m is calculated as (m-1) τ.
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