CN107292447A - A kind of short-term wind speed forecasting method and system based on small data sets arithmetic - Google Patents
A kind of short-term wind speed forecasting method and system based on small data sets arithmetic Download PDFInfo
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Abstract
The invention discloses a kind of short-term wind speed forecasting method based on small data sets arithmetic and system, this method comprises the following steps：S1：Obtain the wind speed time series of preset length；S2：The time delay of the wind speed time series obtained is calculated using auto-relativity function method；S3：According to G P algorithms and the Embedded dimensions of Taken theorem calculation of wind speed time serieses；S4：According to the time delay of wind speed time series and Embedded dimensions phase space reconstruction；S5：The maximum Lyapunov exponent that small data sets arithmetic calculation of wind speed time series is passed through to the matrix of the phase space of reconstruct；S6：The forecast model of wind speed time series is set up based on maximum Lyapunov exponent, the short-term wind speed after wind speed time series is predicted using forecast model；The system includes：Acquisition module, time delay computing module, Embedded dimensions computing module, phase space reconfiguration module, Lyapunov indexes computing module, prediction module.The sample size that the present invention needs is relatively small, and prediction calculating speed is very fast.
Description
Technical field
The present invention relates to forecasting wind speed technical field, more particularly to a kind of short-term wind speed forecasting based on small data sets arithmetic
Method and system.
Background technology
Wind energy is a kind of extremely important and huge resource, and it is safe and clean, abundant and unlimited, can be provided in a steady stream not
Disconnected energy supply, the transition started for global economy based on regenerative resource provides good chance.
Because wind speed has the natural quality of random fluctuation, and large-scale Wind turbines do not have the work(of power storage
Can, therefore wind-powered electricity generation has inherent randomness and uncontrollability.Further, since the wind speed that different infields are caused is bright
Significant difference is different, the Wind turbines in same wind power plant, and the variation for the wind speed experienced in every typhoon group of motors is nor same
Step.Due to these characteristics of wind-power electricity generation, wind power generating set is caused to carry out the randomness of energy exchange with wind, and then cause
Wind turbines switching frequently, causes the impact to power network., will more to electric network influencing with the continuous increase of installed capacity of wind-driven power
Seriously, the principal element as restriction Wind Power Development, by the extensive concern of wind-powered electricity generation industry.And can to the Accurate Prediction of wind speed
To reduce the O＆M cost of Wind turbines, the timely plan for adjustment of complete set manufacturer is helped, so as to mitigate impact of the wind energy to power network.
In the prior art, the prediction to wind speed includes neural net method and support vector machine method etc..Chinese invention
Disclose a kind of based on the neural network short-term wind speed forecasting method for improving difference algorithm, middle promulgated by the State Council in patent CN106503793A
A kind of short-term wind speed forecasting method of wind farm, but the wind speed that above-mentioned Forecasting Methodology needs are disclosed in bright patent CN101793907A
The training sample amount of time series is relatively large, and substantial amounts of sample causes the calculating time of forecasting wind speed needs longer.
Therefore, a kind of short-term wind speed forecasting method based on small data sets arithmetic and system how are founded, makes the wind of its needs
The training sample amount of fast time series is relatively small, and predicts that the calculating time of needs is relatively short, as art technology
Personnel's urgent problem to be solved.
The content of the invention
It is an object of the invention to provide a kind of short-term wind speed forecasting method based on small data sets arithmetic and system, need it
Wind speed time series training sample amount it is relatively small, and predict that the calculating time of needs is relatively short, it is existing with client
The deficiency of wind speed forecasting method.
To achieve the above object, the present invention is adopted the following technical scheme that：
A kind of short-term wind speed forecasting method based on small data sets arithmetic, comprises the following steps：S1：Obtain the wind of preset length
Fast time series；S2：The time delay of the wind speed time series obtained is calculated using auto-relativity function method；S3：According to G-P algorithms
The Embedded dimensions of the wind speed time series are calculated with Taken theorems；S4：According to the time delay of the wind speed time series and
Embedded dimensions phase space reconstruction；S5：By small data sets arithmetic is calculated the wind speed time to the matrix of the phase space of the reconstruct
The maximum Lyapunov exponent of sequence；S6：The prediction of the wind speed time series is set up based on the maximum Lyapunov exponent
Model, is predicted using the forecast model to the short-term wind speed after the wind speed time series.
As a modification of the present invention, the forming method of wind speed time series is in the step S1：Gather wind power plant
Air speed data, the air speed data of collection is arranged according to the sequencing of acquisition time and wind speed time series is formed.
Further improve, also include equalling the wind speed time series of acquisition using single step exponential smoothing in the step S1
The step of sliding processing.
Further improve, the step S3 is specifically included：S31：According to default Embedded dimensions and time delay reconstruct first
Phase space；S32：Calculate correlation integral；S33：The association product obtained according to the field radius of the first phase space of reconstruct and calculating
Point, calculate saturation correlation dimension using G-P algorithms；S34：The saturation correlation dimension obtained according to calculating, utilizes Taken theorem meters
Calculate the Embedded dimensions of wind speed time series.
Further improve, the step S33 is specifically included：The correlation integral C (r) obtained according to calculating and the first of reconstruct
The field radius r of phase space, calculates and corresponds to default Embedded dimensions m0=1 correlation dimension estimate d (m0=1), the association
Integration and the field radius of the first phase space have log-linear relation, and expression is as follows：
In formula, m0To preset Embedded dimensions, C (r, m0=1) it is correlation integral when Embedded dimensions are m0, r is phase space
Field radius；The default Embedded dimensions of increase, saturation correlation dimension is calculated using G-P algorithms.
A kind of short-term wind speed forecasting system based on small data sets arithmetic, including：Acquisition module, for obtaining preset length
Wind speed time series；Time delay computing module, for the time delay using auto-relativity function method calculation of wind speed time series；
Embedded dimensions computing module, for the Embedded dimensions according to G-P algorithms and Taken theorem calculation of wind speed time serieses；Phase space
Reconstructed module, for the time delay according to wind speed time series and Embedded dimensions phase space reconstruction；Lyapunov indexes are calculated
Module, the matrix for the phase space to reconstruct is referred to by the maximum Lyapunov of small data sets arithmetic calculation of wind speed time series
Number；Prediction module, the forecast model for setting up wind speed time series based on maximum Lyapunov exponent utilizes the prediction mould
Type is predicted to the short-term wind speed after the wind speed time series.
As a modification of the present invention, in addition to wind speed time series formation module, the wind speed for gathering wind power plant
Data, the air speed data of collection is arranged according to the sequencing of acquisition time and wind speed time series is formed.
Further improve, in addition to smoothing module, for using wind speed time series of the single step exponential smoothing to acquisition
It is smoothed.
Further improve, the embedded digit computing module includes：Reconfiguration unit, for according to default Embedded dimensions and when
Between the phase space of delay reconstruction first；Correlation integral computing unit, for calculating correlation integral；Saturation correlation dimension computing unit,
Correlation integral for being obtained according to calculating calculates saturation using G-P algorithms with the field radius of the first phase space of reconstruct and associated
Dimension；Embedded dimensions computing unit, for the saturation correlation dimension obtained according to calculating, during using Taken theorem calculation of wind speed
Between sequence Embedded dimensions.
Further improve, the saturation correlation dimension computing unit, for calculating saturation correlation dimension as follows：
The correlation integral C (r) and the field radius r of the first phase space of reconstruct obtained according to calculating, which is calculated, corresponds to default Embedded dimensions
m0=1 correlation dimension estimate d (m0=1), the field radius of the correlation integral and the first phase space has log-linear pass
System, expression is as follows：
In formula, m0To preset Embedded dimensions, C (r, m0=1) it is correlation integral when Embedded dimensions are m0, r is phase space
Field radius；The default Embedded dimensions of increase, saturation correlation dimension is calculated using G-P algorithms.
Due to using above-mentioned technical proposal, the present invention at least has advantages below：
1st, of the invention short-term wind speed forecasting method and system based on small data sets arithmetic, using small data algorithm to wind speed
Carry out short-term forecast, by this method and system can effectively capture wind speed time series feature, it is necessary to wind speed when
Between sequence training sample amount it is relatively small, and predict that the calculating time of needs is relatively short, can realize to the fast of wind speed
The purpose of fast Accurate Prediction, so as to reduce the O＆M cost of Wind turbines.
2nd, the wind speed time series of acquisition is smoothed using single step exponential smoothing, the shadow of accidentalia can be eliminated
Ring, improve the precision of short-term wind speed forecasting result.
Brief description of the drawings
Above-mentioned is only the general introduction of technical solution of the present invention, in order to better understand the technological means of the present invention, below
With reference to accompanying drawing, the present invention is described in further detail with embodiment.
Fig. 1 is the flow chart of the short-term wind speed forecasting method of the invention based on small data sets arithmetic；
Fig. 2 be the short-term wind speed forecasting method based on small data sets arithmetic of the invention a kind of illustrative embodiments in ln C
(r) with ln r relation schematic diagram；
Fig. 3 is associated in a kind of illustrative embodiments of the short-term wind speed forecasting method based on small data sets arithmetic of the invention
Dimension estimate is with the increased change matched curve figure of default Embedded dimensions；
Fig. 4 is short in a kind of illustrative embodiments of the short-term wind speed forecasting method based on small data sets arithmetic of the invention
Phase forecasting wind speed result schematic diagram；
Fig. 5 is the structural representation of the short-term wind speed forecasting system of the invention based on small data algorithm.
Embodiment
The invention provides a kind of short-term wind speed forecasting method based on small data sets arithmetic and system, by this method and it is
System can effectively capture the feature of wind speed time series, can realize the purpose quick and precisely predicted to wind speed, so that
Reduce the O＆M cost of Wind turbines.
As shown in figure 1, the short-term wind speed forecasting method based on small data sets arithmetic of the present invention, comprises the following steps：
S1：The wind speed time series of preset length is obtained, then using wind speed time series of the single step exponential smoothing to acquisition
It is smoothed, to eliminate the influence of accidentalia.The wind speed time series of acquisition is designated as { x (i), i=1,2 ..., N }, N
For the length of the wind speed time series of the preset length of acquisition.The forming method of above-mentioned wind speed time series is：Gather wind power plant
Air speed data, the air speed data of collection is arranged according to the sequencing of acquisition time and wind speed time series is formed.
S2：The time delay τ of the wind speed time series obtained is calculated using auto-relativity function method, specific method is as follows：
Wind speed time series to acquisition carries out auto-correlation computation, auto-correlation function RkExpression formula it is as follows：
Wherein, N is the number of elements of the wind speed time series of the preset length of acquisition, xiAnd xi+kFor wind speed time series
I-th and the i-th+k element in { x (i), i=1,2 ..., N }, k is constant；
Choose and cause RkLess than the minimum k value of predetermined threshold value, the time delay τ of wind speed time series is taken so that RkLess than pre-
If the minimum k value of threshold value.
S3：According to G-P algorithms and the Embedded dimensions of Taken theorem calculation of wind speed time serieses, following steps are specifically included：
S31：First phase space is reconstructed according to the time delay τ obtained in default Embedded dimensions and step S2；
S32：Calculate correlation integral C (r)；
S33：The correlation integral obtained according to the field radius of the first phase space of reconstruct and calculating, utilizes G-P algorithm meters
Saturation correlation dimension is calculated, is specifically included：
According to correlation integral C (r) and the field radius r of the first phase space, calculate and correspond to default Embedded dimensions m0=1
Correlation dimension estimate d (m0=1), the field radius of correlation integral and the first phase space has log-linear relation, specific table
It is as follows up to formula：
In formula, m0To preset Embedded dimensions, C (r, m0=1) be Embedded dimensions m0Correlation integral when=1, r is phase space
Field radius；
The default Embedded dimensions of increase, saturation correlation dimension is calculated using G-P algorithms；
S34：The Embedded dimensions of Taken theorem calculation of wind speed time serieses are utilized according to saturation correlation dimension.
S4：According to the time delay of wind speed time series and Embedded dimensions phase space reconstruction.
S5：The maximum Lyapunov that the matrix of the phase space of reconstruct extracts wind speed time series by small data sets arithmetic is referred to
Number.
S6：The forecast model of wind speed time series is set up based on maximum Lyapunov exponent, according to forecast model to wind speed
Short-term wind speed after time series is predicted.
Technical solution of the present invention is described in detail below in conjunction with specific embodiment：
S1：It has chosen the wind speed time series { x that the length that certain typhoon group of motors is gathered from certain wind power plant is N=672
(i), i=1,2 ..., N }；
S2：Utilize the time delay τ of auto-relativity function method calculation of wind speed time series：Wind speed time series to selection is entered
Row autocorrelation calculation, auto-correlation function RkExpression formula it is as follows：
τ takes so that RkLess than the minimum k value of predetermined threshold value, wherein given threshold is
For the wind speed time series chosen in the present embodiment, by calculating, time delay τ=5.
S3：The Embedded dimensions m of wind speed time series is determined with G-P algorithms and Taken theorems, is comprised the following steps that：
Step 1：It is a less positive integer m just to preset Embedded dimensions surely0=1, when then using wind speed
Between calculate obtained time delay τ reconstruct one phase space, i.e. the first phase space in sequence and step S2I=[1,2 ..., N- (m0-1)τ]；
Step 2：Correlation integral is calculated, specific expression formula is as follows：
In formula：||Yi-Yj| | represent phase point YiAnd YjThe distance between；θ (z) is Heaviside functions, the θ when z is more than 0
θ is equal to 0 when being less than 0 for 1, z；R is field radius；C (r) is a cumulative distribution function, represents 2 points in phase space of spacing
From the probability less than r.
Step 3：Calculate correlation dimension：For r some interval range, correlation integral C (r) and field radius r satisfactions pair
Number linear relationship, so as to be obtained by fitting corresponding to default Embedded dimensions m0=1 correlation dimension estimate d (m0=1), specifically
Expression formula it is as follows：
Then increase default Embedded dimensions, compute repeatedly step 2 and 3 in step S3, until the estimation of corresponding correlation dimension
Value d is no longer with the m of default Embedded dimensions0Increase and increase, and changed in the range of certain error.Now, correlation dimension is estimated
Value d is saturation correlation dimension dc, and Embedded dimensions m chooses (2d according to Taken theoremsc+ 1) minimum positive integer value；
For the wind speed time series chosen in the present embodiment, Fig. 2 shows default Embedded dimensions m030 are increased to from 1
Logarithmic relationship figure between correlation integral C (r) and field radius r, i.e. ln C (r) and ln r graph of a relation, as can be known from Fig. 2：
When ln r change between [0.4,1.4], ln C (r) and ln r meet log-linear relation.Fig. 3 be fitted ln C (r) with
Ln r meet the interval correlation dimension of log-linear relation, and depict with correlation dimension estimate during default Embedded dimensions increase
Change matched curve, as seen from Figure 3：When default Embedded dimensions increase to 23, correlation dimension estimate d starts to reach full
With, when default Embedded dimensions further increase, correlation dimension estimate d substantially remains in 5 or so, variable error for ±
Between 0.5%, now d=5 is saturation correlation dimension dc, according to Taken theorems：M chooses (2dc+ 1) minimum positive integer value, institute
With m=11.
S4、S5：According to the time delay and Embedded dimensions phase space reconstruction of the wind speed time series, to the reconstruct
The matrix of phase space extracts the maximum Lyapunov exponent of the wind speed time series, specific calculation procedure by small data sets arithmetic
It is as follows：
Step 1：Fourier transformation is carried out to time series { x (i), i=1,2 ..., N }, fourier function F (k) is obtained：
Used frequency is in conversion：
Finally with power F2(k) to period weightings and weighted average is sought, calculating obtains P average period：
In the present embodiment, obtained P=7 average period is calculated by the method.
Step 2：Weighed using calculating obtained time delay τ in step S2 and obtained Embedded dimensions m being calculated in step S3
Structure phase space Yn,
Yn=[xn,xn+τ,…xn+(m-1)τ], n=[1,2 ..., M], M=n+ (m-1) τ (7)
Step 3：Look for each point Y in phase spacenClosest to pointAnd limit of short duration separation, i.e.,：
Step 4：For each point Y in phase spacen, this is calculated closest to pointI discrete time step after apart from dn
(i)。
Step 5：Calculate each dn(i) logarithm value ln dn(i) all ln d, are then calculatedn(i) average value y (i),
I.e.：
Wherein, △ t are the sampling interval durations of wind speed time series, and q is non-zero dn(i) number, and use least square
Method makes regression straight line, and the slope of the straight line is exactly maximum Lyapunov exponent λ1。
In the present embodiment, the matrix of phase space reconstruction calculates obtained maximum Lyapunov exponent by small data sets arithmetic
λ1=0.081.
S6：The wind speed time series predicting model based on maximum Lyapunov exponent is set up, is comprised the following steps that：
If YMFor the central point of prediction, YkFor Y in phase spaceMNearest point of proximity, namely closest point, are designated as dM
(0), expression formula is as follows：
dM(0)=| | YM-Yk|| (11)
According to YM、YkBe further evolved into YM+1、Yk+1, there is following formula establishment：
In formula (12), phase point YM+1In only last component x (tn+1) unknown, therefore x (tn+1) be it is predictable, in advance
Measured value x (tn+1) ' be following expression：
x(tn+1) '=YM+1(m) (13)
Above formula is namely based on the wind speed time series predicting model of maximum Lyapunov exponent, can be to wind speed based on the model
Short-term wind speed after time series is predicted.
Fig. 4 is the figure that predicts the outcome to the short-term wind speed after wind speed time series.In Fig. 4, actual value is from sample
The length of middle selection is 10 wind speed time series, and sample frequency is 1 hour, then using the present invention based on maximum
To wind speed time series, further development is predicted the wind speed time series predicting model of Lyapunov indexes, is as a result shown：
Method proposed by the present invention is no more than ± 3.5% to the predicated error of the short-term wind speed after wind speed time series.
In addition, coordinating shown in Fig. 5, the invention also provides a kind of above-mentioned short-term wind speed forecasting method of use is based on decimal
According to the short-term wind speed forecasting system of amount method, including：
Wind speed time series formation module, the air speed data for gathering wind power plant, by the air speed data of collection according to adopting
The sequencing at collection time point arranges and forms wind speed time series；
Acquisition module 1, the wind speed time series for obtaining preset length；
Time delay computing module 2, for the time delay using auto-relativity function method calculation of wind speed time series；
Embedded dimensions computing module 3, for being tieed up according to G-P algorithms and the embedded of Taken theorem calculation of wind speed time serieses
Number；
Phase space reconfiguration module 4, for the time delay according to wind speed time series and Embedded dimensions phase space reconstruction；
Lyapunov indexes computing module 5, the matrix for the phase space to reconstruct passes through small data sets arithmetic calculation of wind speed
The maximum Lyapunov exponent of time series；
Prediction module 6, the forecast model for setting up wind speed time series based on maximum Lyapunov exponent, utilizes prediction
Model is predicted to the short-term wind speed after wind speed time series.
The system also includes smoothing module, for being put down using single step exponential smoothing to the wind speed time series of acquisition
Sliding processing.
Wherein, Embedded dimensions computing module 3 includes：
Reconfiguration unit, for reconstructing the first phase space according to default Embedded dimensions and time delay；
Correlation integral computing unit, for calculating correlation integral；
Saturation correlation dimension computing unit, for the correlation integral and the neck of the first phase space of reconstruct obtained according to calculating
Domain radius calculates saturation correlation dimension using G-P algorithms；
Embedded dimensions computing unit, for the saturation correlation dimension obtained according to calculating, utilizes Taken theorem calculation of wind speed
The Embedded dimensions of time series.
The short-term wind speed forecasting method based on small data sets arithmetic and system of the present invention, is entered using small data algorithm to wind speed
Row short-term forecast, by this method and system can effectively capture wind speed time series feature, it is necessary to the wind speed time
The training sample amount of sequence is relatively small, and predicts that the calculating time of needs is relatively short, can realize to the quick of wind speed
The purpose of Accurate Prediction, so as to reduce the O＆M cost of Wind turbines.
The above described is only a preferred embodiment of the present invention, any formal limitation not is made to the present invention, this
Art personnel make a little simple modification, equivalent variations or modification using the technology contents of the disclosure above, all fall within this hair
In bright protection domain.
Claims (10)
1. a kind of short-term wind speed forecasting method based on small data sets arithmetic, it is characterised in that comprise the following steps：
S1：Obtain the wind speed time series of preset length；
S2：The time delay of the wind speed time series obtained is calculated using auto-relativity function method；
S3：The Embedded dimensions of the wind speed time series are calculated according to G-P algorithms and Taken theorems；
S4：According to the time delay and Embedded dimensions phase space reconstruction of the wind speed time series；
S5：The maximum of the wind speed time series is calculated by small data sets arithmetic to the matrix of the phase space of the reconstruct
Lyapunov indexes；
S6：The forecast model of the wind speed time series is set up based on the maximum Lyapunov exponent, the prediction mould is utilized
Type is predicted to the short-term wind speed after the wind speed time series.
2. the short-term wind speed forecasting method according to claim 1 based on small data sets arithmetic, it is characterised in that the step
The forming method of wind speed time series is in S1：The air speed data of wind power plant is gathered, during by the air speed data of collection according to collection
Between the sequencing put arrange and form wind speed time series.
3. the short-term wind speed forecasting method according to claim 2 based on small data sets arithmetic, it is characterised in that the step
The step of also including being smoothed the wind speed time series of acquisition using single step exponential smoothing in S1.
4. the short-term wind speed forecasting method according to claim 1 based on small data sets arithmetic, it is characterised in that the step
S3 is specifically included：
S31：First phase space is reconstructed according to default Embedded dimensions and time delay；
S32：Calculate correlation integral；
S33：The correlation integral obtained according to the field radius of the first phase space of reconstruct and calculating, calculates full using G-P algorithms
And correlation dimension；
S34：The saturation correlation dimension obtained according to calculating, utilizes the Embedded dimensions of Taken theorem calculation of wind speed time serieses.
5. the short-term wind speed forecasting method according to claim 4 based on small data sets arithmetic, it is characterised in that the step
S33 is specifically included：
The correlation integral C (r) and the field radius r of the first phase space of reconstruct obtained according to calculating, is calculated corresponding to default embedding
Enter dimension m0=1 correlation dimension estimate d (m0=1), the field radius of the correlation integral and the first phase space has logarithm
Linear relationship, expression is as follows：
<mrow>
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<mrow>
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<mi>m</mi>
<mn>0</mn>
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<mo>=</mo>
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<mo>=</mo>
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In formula, m0To preset Embedded dimensions, C (r, m0=1) it is that Embedded dimensions are m0When correlation integral, r be phase space field
Radius；
The default Embedded dimensions of increase, saturation correlation dimension is calculated using G-P algorithms.
6. a kind of short-term wind speed forecasting system based on small data sets arithmetic, it is characterised in that including：
Acquisition module, the wind speed time series for obtaining preset length；
Time delay computing module, for the time delay using auto-relativity function method calculation of wind speed time series；
Embedded dimensions computing module, for the Embedded dimensions according to G-P algorithms and Taken theorem calculation of wind speed time serieses；
Phase space reconfiguration module, for the time delay according to wind speed time series and Embedded dimensions phase space reconstruction；
Lyapunov index computing modules, the matrix for the phase space to reconstruct passes through small data sets arithmetic calculation of wind speed time sequence
The maximum Lyapunov exponent of row；
Prediction module, the forecast model for setting up wind speed time series based on maximum Lyapunov exponent utilizes the prediction
Model is predicted to the short-term wind speed after the wind speed time series.
7. the short-term wind speed forecasting system according to claim 6 based on small data sets arithmetic, it is characterised in that also including wind
Fast time series formation module, the air speed data for gathering wind power plant, by the air speed data of collection according to acquisition time
Sequencing arranges and forms wind speed time series.
8. the short-term wind speed forecasting system according to claim 7 based on small data sets arithmetic, it is characterised in that also including flat
Sliding processing module, for being smoothed using single step exponential smoothing to the wind speed time series of acquisition.
9. the short-term wind speed forecasting system according to claim 6 based on small data sets arithmetic, it is characterised in that the insertion
Dimension computing module includes：
Reconfiguration unit, for reconstructing the first phase space according to default Embedded dimensions and time delay；
Correlation integral computing unit, for calculating correlation integral；
Saturation correlation dimension computing unit, for the correlation integral obtained according to calculating and the field half of the first phase space of reconstruct
Footpath calculates saturation correlation dimension using G-P algorithms；
Embedded dimensions computing unit, for the saturation correlation dimension obtained according to calculating, utilizes the Taken theorem calculation of wind speed times
The Embedded dimensions of sequence.
10. the short-term wind speed forecasting system according to claim 9 based on small data sets arithmetic, it is characterised in that described full
With correlation dimension computing unit, for calculating saturation correlation dimension as follows：
The correlation integral C (r) and the field radius r of the first phase space of reconstruct obtained according to calculating, which is calculated, corresponds to default insertion
Dimension m0=1 correlation dimension estimate d (m0=1), the field radius of the correlation integral and the first phase space has logarithm line
Sexual intercourse, expression is as follows：
<mrow>
<mi>d</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>ln</mi>
<mi> </mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>r</mi>
<mo>,</mo>
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>ln</mi>
<mi> </mi>
<mi>r</mi>
</mrow>
</mfrac>
</mrow>
In formula, m0To preset Embedded dimensions, C (r, m0=1) it is that Embedded dimensions are m0When correlation integral, r be phase space field
Radius；
The default Embedded dimensions of increase, saturation correlation dimension is calculated using G-P algorithms.
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