CN106777913A - The new method that a kind of approximate entropy and Sample Entropy common optimized parameter m, r determine - Google Patents
The new method that a kind of approximate entropy and Sample Entropy common optimized parameter m, r determine Download PDFInfo
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Abstract
The new method that a kind of approximate entropy and Sample Entropy common optimized parameter m, r determine, including：Step one：The different scenes of the approximate entropy of setting time sequence and the parameter m and r of Sample Entropy；Step 2：Calculate the approximate entropy and sample entropy of different parameters m and r scene.Step 3：Determine the approximate entropy of certain time series different parameters m and the common optimized parameter r of Sample Entropy；Step 4：Size based on coefficient correlation and its absolute value sum determines common optimized parameter m, r of the approximate entropy and Sample Entropy suitable for all time serieses.The method has ensured two kinds of uniformity of different Complexity Measurement results, theoretically solves the problems, such as the nonuniformity of approximate entropy and sample entropy caused by different m and r parameters；The method is simple to operation, and computational efficiency is high, and calculating achievement is more accurate, more scientific, is not only suitable for single research object, is also applied for the situation of many research objects, there is important theory significance and practical value, has a extensive future.
Description
Technical field
The present invention relates to Complexity Measurement field, more particularly to a kind of approximate entropy and Sample Entropy common optimized parameter m, r it is true
Fixed new method.
Background technology
In thermokinetics, its expression can not be used for the part energy for doing work to the concept source of entropy.Entropy is often used in be retouched
State the complexity of time series, be directly or indirectly applied at present economics, social science, learn, life science, engineering
The ambits such as, information science, mathematics simultaneously obtain important research progress.Wherein Kolmogorov-Sinai entropys are a kind of applications
Relatively broad entropy, it can effectively analyze the complexity of short sequence as the basis of approximate entropy.Approximate entropy is a kind of non-linear ginseng
Number recognition methods, can be used for the scrambling of the complexity, dynamic and measurement dynamic sequence of reflecting time sequence.Approximate entropy
Value is bigger, and expression sequence is more random or more irregularly, is worth and smaller represents that the feature that be can recognize that in sequence or pattern are smaller.Therefore, closely
There is preferable robustness to some singular points like entropy, be usually used in Analyze noise signal, and show preferable performance.But,
Approximate entropy comes with some shortcomings, and such as lacks relative uniformity to the undue dependence of data length and result, so as to cause sample
The proposition of entropy.Relative to approximate entropy, Sample Entropy has computational efficiency higher, by judging different data lengths in time series
Repeat pattern, for the measurement of " ordered structure " provides useful instrument.Approximate entropy and Sample Entropy represent time series structure
Complexity：The conditional probability of two adjacent part similitudes is lower, and time series is more complicated, and approximate entropy and sample entropy are got over
Greatly.They are not only two nonlinear dynamic parameters, and extensive being applicable is respectively provided with random process and deterministic process
Property, therefore there is general meaning in terms of the complexity of description time series.
Approximate entropy and Sample Entropy are all printenv variables, and it has two important unknown parameters, i.e. dimension number m and content
Threshold value r.Parameter m is used for describing the sequence length of contrast, and parameter r is to receive the threshold value that two parts are parallel pattern.The two ginsengs
Number pairing approximation entropy and sample entropy have important influence, and the reasonability to time series result of calculation explains also there is important meaning
Justice.Therefore, correct selection parameter m and r seems abnormal important.Traditional way is that m and r is typically taken as 2 and 0.1~0.25 times
Sequence criteria it is poor.But, these values are mostly the empirical values in some fields, in other fields, even if take identical value also having
May result in different results.More seriously, to same or analogous research object, taking different m and r values can cause
The appearance of nonuniformity problem, coherence request when heavy damage both approximate entropy and Sample Entropy are contrasted so that near
There is no common reference point when being contrasted like entropy and Sample Entropy, so as to cause the invalid or nonsensical of contrast.Therefore, it is being
In system complexity analyzing, for identical research object, m, r parameter of approximate entropy and Sample Entropy are preferably applied to simultaneously for protecting
The uniformity for hindering result just seems abnormal important.But do not have any effective method currently to determine the near of identical research object
Like entropy and the common optimized parameter m and r of Sample Entropy, this largely constrains the application of both Complexity Measurements.Cause
This, finds a kind of approximate entropy and the method for optimizing of sample entropy parameter m and r suitable for identical research object, approximate for ensureing
The application field of the uniformity, expansion approximate entropy and Sample Entropy of entropy and Sample Entropy result has important theory significance and practical valency
Value, has a extensive future.
The content of the invention
Regarding to the issue above, determine it is an object of the invention to provide a kind of approximate entropy and Sample Entropy common optimized parameter m, r
New method.Its core is approximate entropy and Sample Entropy when being contrasted to same research object, it is necessary to meet one
Cause property requires that is, guarantee has common comparison basis or identical reference point, and reference point or common comparison basis are required
The approximate entropy and Sample Entropy of contrast have common m, r value.The difference of the present invention setting approximate entropy and sample entropy parameter m and r first
Scene value；Then the approximate entropy and sample entropy of each time series are calculated；And then determine the approximate entropy and sample of certain time series
The intersections of complex curve of this entropy, obtains the common optimized parameter r of the approximate entropy and Sample Entropy under time series parameter m；Last base
Optimal m, r value of the time series is obtained in the sign of the time series and the coefficient correlation of its complexity, and is further led to
All time serieses are crossed with the size of the absolute value sum of the coefficient correlation of its complexity to determine to be applied to all time serieses
Two kinds of complexities optimized parameter m and r value.
To solve the above problems, the present invention takes following technical scheme：
The new method that common optimized parameter m, r of a kind of approximate entropy and Sample Entropy determine, it be applied to different research fields,
The comparative analysis of the approximate entropy and Sample Entropy of different time sequence is calculated, and the method is comprised the following steps that：
Step one：The different scenes of the approximate entropy of setting time sequence and the parameter m and r of Sample Entropy；
Step 2：Calculate the approximate entropy and sample entropy under different parameters m and r scene.Pairing approximation entropy, if time series is
X (1), x (2) ..., x (N), N are sequence total length, and it is [x (i), x (i+1) ..., x (i+m-1)], i to define m n dimensional vector ns X (i)
=1,2 ..., N-m+1, the distance between vector X (i) and X (j) d [X (i), X (j)] isThen approximate entropy can be determined by following formula：
ApEn (m, r)=Cm(r)–Cm+1(r) (1)
In formula, CmR () represents the logarithm accumulation mean of the ratio factor determined by parameter m and r, its size isWhereinThe ratio factor less than parameter r apart from d [X (i), X (j)] is represented,
Its size is { d [X (i), X (j)]<The number of r }/(N-m+1), and i=1,2 ..., N-m+1.
To Sample Entropy, to identical time series x (1), x (2) ..., x (N), it is [x (i), x (i to define m n dimensional vector ns X (i)
+ 1) ..., x (i+m-1)], i=1,2 ..., N-m+1, the distance between vector X (i) and X (j) d [X (i), X (j)] isAnd j ≠ i, then Sample Entropy can be counted by following formula
Calculate：
SampEn (m, r)=ln [Cm(r)/Cm+1(r)] (2)
In formula, CmR () represents the accumulation mean of the ratio factor determined by parameter m and r, its size isWhereinThe ratio factor less than parameter r apart from d [X (i), X (j)] is represented, its
Size is { d [X (i), X (j)]<The number of r }/(N-m), and i=1,2 ..., N-m+1.
Step 3：Determine the common optimized parameter r of the approximate entropy and Sample Entropy under certain time series different parameters m.With certain
The approximate entropy and Sample Entropy of time series are ordinate, and parameter r is abscissa, and point paints the point (r, approximate entropy) under certain parameter m
(r, sample entropy), in the X-Y coordinate of each parameter m, approximate entropy and Sample Entropy curve will intersect at a point, this intersection point
The parameter r values at place are the common optimal value of this time sequence parameter m lower aprons entropy and Sample Entropy；
Step 4：Size based on coefficient correlation and its absolute value sum determines the approximate entropy suitable for all time serieses
With common optimized parameter m, r of Sample Entropy.The coefficient correlation of certain time series and its complexity sequence is calculated, based on this phase relation
Several signs determines the optimized parameter m and r of this time sequence, and further calculates all time serieses and its complexity sequence
Coefficient correlation absolute value sum, size based on this absolute value sum determine suitable for all time serieses approximate entropy and
Common optimized parameter m, r value of Sample Entropy.
Due to taking above technical scheme, it has advantages below to the present invention：
1. ensured two kinds of different Complexity Measurements --- the uniformity of approximate entropy and Sample Entropy result of calculation, make this two
Planting when Complexity Measurement is contrasted has common reference point, theoretically solves approximate entropy caused by different m and r parameters
With the nonuniformity problem of sample entropy.
2. the method is simple to operation, and orderliness understands, computational efficiency is high, and calculating achievement is more accurate, more scientific.
3. the method has more preferable applicability, is not only suitable for approximate entropy and Sample Entropy is applied to the feelings of single research object
Condition, is also applied for approximate entropy and Sample Entropy is applied to the situation of many research objects, there is important theory significance and practical value, should
With having a extensive future.
Brief description of the drawings
Fig. 1 is the FB(flow block) of the inventive method.
Fig. 2 is the approximate entropy and sample under the upper reaches of the Yellow River Guide hydrometric station 1960~nineteen ninety Inflow Sequence different parameters m
The common optimized parameter r of entropy.
Fig. 3 is approximate under the upper reaches of the Yellow River Guide hydrometric station above basin 1960~nineteen ninety precipitation different parameters m
The common optimized parameter r of entropy and Sample Entropy.
Fig. 4 is the approximate entropy and Sample Entropy optimized parameter m of runoff based on coefficient correlation absolute value sum and precipitation
Two kinds of preferred results of parameter r scenes when=6.
Specific embodiment
With reference to the accompanying drawings and detailed description, the present invention is described in further detail.
As shown in figure 1, the new method that a kind of approximate entropy of the invention and Sample Entropy common optimized parameter m, r determine, including set
The scene of determining the approximate entropy of different time sequence and the parameter m and r of Sample Entropy, the approximate entropy for calculating different parameters m, r scene and
Sample entropy, determined based on certain time series approximate entropy and Sample Entropy intersections of complex curve it is approximate under time series different parameters m
The optimized parameter r of entropy and Sample Entropy and determining is applied to the common optimal of the approximate entropy of all time serieses and Sample Entropy simultaneously
The part of parameter m and r tetra-.
By taking the runoff and Precipitation Time Series of Hydrology as an example, specific implementation of the invention is followed the steps below：
Step one：The approximate entropy and different parameters m, r scene of Sample Entropy of setting runoff and precipitation；
Step 2：Calculate the approximate entropy and sample entropy of the runoff and precipitation under different parameters m, r scene.Pairing approximation
Entropy, if runoff or Precipitation Time Series are x (1), x (2) ..., x (N), N is sequence length, and it is [x to define m n dimensional vector ns X (i)
(i), x (i+1) ..., x (i+m-1)], i=1,2 ..., N-m+1, the distance between vector X (i) and X (j) d [X (i), X (j)]
ForThen approximate entropy can be determined by following formula：
ApEn (m, r)=Cm(r)–Cm+1(r) (1)
In formula, CmR () represents the logarithm accumulation mean of the ratio factor determined by parameter m and r, its size isWhereinThe ratio factor less than parameter r apart from d [X (i), X (j)] is represented,
Its size is { d [X (i), X (j)]<The number of r }/(N-m+1), and i=1,2 ..., N-m+1.
To Sample Entropy, to identical runoff or Precipitation Time Series x (1), x (2) ..., x (N) define m n dimensional vector ns X (i)
It is [x (i), x (i+1) ..., x (i+m-1)], i=1,2 ..., N-m+1, the distance between vector X (i) and X (j) d [X (i), X
(j)] beAnd j ≠ i, then Sample Entropy can be by following formula
Calculated：
SampEn (m, r)=- ln [Cm+1(r)/Cm(r)] (2)
In formula, CmR () represents the accumulation mean of the ratio factor determined by parameter m and r, its size isWhereinThe ratio factor less than parameter r apart from d [X (i), X (j)] is represented, its
Size is { d [X (i), X (j)]<The number of r }/(N-m), and i=1,2 ..., N-m+1.
Step 3：Determine the common optimal ginseng of the approximate entropy and Sample Entropy under runoff or Precipitation Time Series different parameters m
Number r.As ordinate, parameter r is abscissa to approximate entropy and sample entropy with runoff or precipitation, and point paints Inflow Sequence and drop respectively
Point (r, approximate entropy) and (r, sample entropy) under water sequence parameter m in the X-Y coordinate of each parameter m, runoff or drop
The approximate entropy and Sample Entropy curve of water will intersect at a point, and the parameter r values of this point of intersection are runoff or precipitation ginseng
The common optimal value of number m lower aprons entropy and Sample Entropy；
Step 4：Size based on coefficient correlation and its absolute value sum is determined suitable for the approximate of runoff and precipitation
Common optimized parameter m, r of entropy and Sample Entropy.Runoff or the coefficient correlation between precipitation and its complexity are calculated, it is related based on this
The sign of coefficient selects the optimized parameter m and r of the approximate entropy and Sample Entropy suitable for runoff or precipitation, and further counts
The absolute value sum of runoff and the coefficient correlation between precipitation and its complexity is calculated, is determined based on the size of this absolute value sum
It is applied to the approximate entropy and common optimized parameter m, r value of Sample Entropy of runoff and precipitation simultaneously.
Case study on implementation
The present invention is with the moon runoff and Guide hydrometric station above basin of the upper reaches of the Yellow River Guide 1960~nineteen ninety of hydrometric station
The average moon precipitation in face is research object, and setup parameter m is that 2~6, parameter r is 0.01~1.5SD, and wherein SD is the standard of sequence
Difference, step-length is taken as 0.01, calculates the approximate entropy and sample entropy of the runoff and precipitation under different parameters m and r scene, obtains difference
The common optimized parameter r values of two kinds of complexities of runoff or precipitation under parameter m, then based on coefficient correlation and coefficient correlation
Absolute value sum, it is determined that common optimized parameter m, r value of the approximate entropy and Sample Entropy suitable for runoff and precipitation.
As a result, seeing Fig. 2, Fig. 3, Fig. 4 respectively.
Fig. 2 is the approximate entropy and sample under the upper reaches of the Yellow River Guide hydrometric station 1960~nineteen ninety Inflow Sequence different parameters m
The common optimized parameter r of entropy.
Fig. 3 is approximate under the upper reaches of the Yellow River Guide hydrometric station above basin 1960~nineteen ninety precipitation different parameters m
The common optimized parameter r of entropy and Sample Entropy.
Fig. 4 is the approximate entropy and Sample Entropy optimized parameter m of runoff based on coefficient correlation absolute value sum and precipitation
Two kinds of preferred results of parameter r scenes when=6.
From examples detailed above as can be seen that a kind of new approximate entropy and the common optimized parameter m and r of Sample Entropy of present invention offer
The method of determination, it is adaptable to the determination of a kind of approximate entropy of time series and the common optimized parameter m and r of Sample Entropy, is also suitable
In the determination of the common optimized parameter m and r of the approximate entropy and Sample Entropy of various time serieses, for ensureing approximate entropy and Sample Entropy
The application field of the uniformity, expansion approximate entropy and Sample Entropy of result has important theory significance and practical value, using preceding
Scape is wide.
Embodiment described above only expresses several embodiments of the invention, and its description is more specific and detailed, but simultaneously
Therefore the limitation to the scope of the claims of the present invention can not be interpreted as.It should be pointed out that for one of ordinary skill in the art
For, without departing from the inventive concept of the premise, various modifications and improvements can be made, these belong to guarantor of the invention
Shield scope.Therefore, the protection domain of patent of the present invention should be determined by the appended claims.
Claims (5)
1. the new method that a kind of approximate entropy and Sample Entropy common optimized parameter m, r determine, comprises the following steps：
Step one：The different scenes of the approximate entropy of setting time sequence and the parameter m and r of Sample Entropy；
Step 2：Calculate the approximate entropy and sample entropy under different parameters m and r scene；
Step 3：Determine the common optimized parameter r of the approximate entropy and Sample Entropy under certain time series different parameters m；And
Step 4：Size based on coefficient correlation and its absolute value sum determines the approximate entropy and sample suitable for all time serieses
Common optimized parameter m, r of this entropy.
2. the new method that approximate entropy according to claim 1 and Sample Entropy common optimized parameter m, r determine, it is characterised in that
In step：The different scenes of the approximate entropy of setting time sequence and the parameter m and r of Sample Entropy.Because parameter m is that non-negative is whole
Number, general arrange parameter m is the integer more than 2, such as m is 2,3,4,5,6 five kind of scene, scene is more, it is necessary to the work for calculating
Measure bigger；For the setting of parameter r, traditional way is that the general sequence criterias for being taken as 0.1~0.25 times of parameter r are poor.But
It is not necessarily accurate, therefore, the setting scope of r can be expanded, the sequence criteria that r is set to 0.01~2.5 times is poor, and step-length is set to
0.01。
3. the new method that approximate entropy according to claim 2 and Sample Entropy common optimized parameter m, r determine, it is characterised in that
In step 2：Calculate the approximate entropy and sample entropy under different parameters m and r scene.Pairing approximation entropy, if time series is x (1), x
(2) ..., x (N), N are sequence total length, define m n dimensional vector ns X (i) for [x (i), x (i+1) ..., x (i+m-1)], i=1,
The distance between 2 ..., N-m+1, vector X (i) and X (j) d [X (i), X (j)] isThen approximate entropy can be determined by following formula：
ApEn (m, r)=Cm(r)–Cm+1(r) (1)
In formula, CmR () represents the logarithm accumulation mean of the ratio factor determined by parameter m and r, its size isWhereinThe ratio factor less than parameter r apart from d [X (i), X (j)] is represented,
Its size is { d [X (i), X (j)]<The number of r }/(N-m+1), and i=1,2 ..., N-m+1.
To Sample Entropy, to identical time series x (1), x (2) ..., x (N), it is [x (i), x (i+ to define m n dimensional vector ns X (i)
1) ..., x (i+m-1)], i=1,2 ..., N-m+1, the distance between vector X (i) and X (j) d [X (i), X (j)] isAnd j ≠ i, then Sample Entropy can be counted by following formula
Calculate：
SampEn (m, r)=ln [Cm(r)/Cm+1(r)] (2)
In formula, CmR () represents the accumulation mean of the ratio factor determined by parameter m and r, its size isWhereinThe ratio factor less than parameter r apart from d [X (i), X (j)] is represented, its
Size is { d [X (i), X (j)]<The number of r }/(N-m), and i=1,2 ..., N-m+1.
4. the new method that approximate entropy according to claim 3 and Sample Entropy common optimized parameter m, r determine, it is characterised in that
In step 3：Determine the common optimized parameter r of the approximate entropy and Sample Entropy under certain time series different parameters m.With certain time sequence
The approximate entropy and Sample Entropy of row are ordinate, and parameter r is abscissa, and point paints point (r, approximate entropy) and (r, sample under certain parameter m
This entropy) in the X-Y coordinate of each parameter m, approximate entropy and Sample Entropy curve will intersect at a point, the parameter of this point of intersection
R values are the common optimal value of this time sequence parameter m lower aprons entropy and Sample Entropy.
5. the new method that approximate entropy according to claim 4 and Sample Entropy common optimized parameter m, r determine, it is characterised in that
In step 4：Size based on coefficient correlation and its absolute value sum determines the approximate entropy and sample suitable for all time serieses
Common optimized parameter m, r of entropy.The coefficient correlation of certain time series and its complexity sequence is calculated, based on this coefficient correlation just
Negative sign determines the optimized parameter m and r of this time sequence, and it is related to its complexity sequence further to calculate all time serieses
The absolute sum of coefficient, size based on this absolute value sum determines the approximate entropy and Sample Entropy suitable for all time serieses
Common optimized parameter m, r value.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107870893A (en) * | 2017-10-24 | 2018-04-03 | 顺特电气设备有限公司 | A kind of daily load similitude quantitative analysis method of intelligent transformer |
| CN107977505A (en) * | 2017-11-28 | 2018-05-01 | 兰州大学 | The new method that a kind of antecedent precipitation decline coefficient k determines |
-
2016
- 2016-11-29 CN CN201611068909.6A patent/CN106777913A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107870893A (en) * | 2017-10-24 | 2018-04-03 | 顺特电气设备有限公司 | A kind of daily load similitude quantitative analysis method of intelligent transformer |
| CN107977505A (en) * | 2017-11-28 | 2018-05-01 | 兰州大学 | The new method that a kind of antecedent precipitation decline coefficient k determines |
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