CN103500272A - Fuzzy information granulation method for time series trend prediction - Google Patents

Fuzzy information granulation method for time series trend prediction Download PDF

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CN103500272A
CN103500272A CN201310432741.2A CN201310432741A CN103500272A CN 103500272 A CN103500272 A CN 103500272A CN 201310432741 A CN201310432741 A CN 201310432741A CN 103500272 A CN103500272 A CN 103500272A
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time series
data
window
trend prediction
fuzzy
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CN103500272B (en
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赵云
吴响
盛文燕
孟彬
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XUZHOU CUMT DAHUAYANG COMMUNICATION EQUIPMENT CO Ltd
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Abstract

The invention discloses a fuzzy information granulation method for time series trend prediction and relates to the technical field of granular computation. The method includes the steps that first, a time series window is given, and the minimum value and the maximum value in a dataset are selected and used as parameters of a trapezoid model respectively; second, interpolation is carried out on an original time series window to form a new time series window; third, the sum of supporting boundaries of a trapezoid fuzzy set is determined for the newly-formed time series window with a data traversal method. The fuzzy information granulation method for time series trend prediction has the advantages that time series discrete data in lower-layer information granules can be completely contained, unknown data except the discrete data can be well supported, the time series trend prediction effect can be significantly improved in combination with an existing prediction method, and high practical significance and practical value are achieved.

Description

A kind of Fuzzy Information Granulation method towards the time series trend prediction
 
Technical field
The present invention relates to the Granular Computing technical field, specifically a kind of Fuzzy Information Granulation method towards the time series trend prediction.
Background technology
Utilize FUZZY SET APPROACH TO ENVIRONMENTAL to carry out Fuzzy Information Granulation to time series and mainly be divided into two steps: discretize and obfuscation.The discretize fundamental purpose is that time series is divided into to some subsequences, and the size of each subsequence is called window; Obfuscation is that the window that discretize is produced carries out obfuscation, generates the timing ambiguity information.The new time series now generated is called the granulation time series.Predict and can obtain the high layer information that former time series can not directly be obtained for the granulation time series.
The process of discretize and obfuscation is called Fuzzy Information Granulation, is designated as the f-granulation.The key of f-granulation is obfuscation, and obfuscation refers to subsequence preset time
Figure 2013104327412100002DEST_PATH_IMAGE001
on set up an obscure particle
Figure 464141DEST_PATH_IMAGE002
, determine one and can rationally describe
Figure 2013104327412100002DEST_PATH_IMAGE003
fuzzy set
Figure 311005DEST_PATH_IMAGE004
(with
Figure 2013104327412100002DEST_PATH_IMAGE005
fuzzy set for domain).Determined
Figure 573009DEST_PATH_IMAGE004
also just determined fuzzy example
Figure 828410DEST_PATH_IMAGE006
, that is:
Figure 2013104327412100002DEST_PATH_IMAGE007
The process of obfuscation is exactly to determine function
Figure 717999DEST_PATH_IMAGE002
process,
Figure 924596DEST_PATH_IMAGE002
it is fuzzy concept
Figure 298946DEST_PATH_IMAGE004
subordinate function,
Figure 910318DEST_PATH_IMAGE008
.Usually, at first determine the citation form of concept during granulation, then determine concrete subordinate function
Figure 899703DEST_PATH_IMAGE002
.The citation form of obscure particle comprises: triangle, trapezoidal, gaussian-shape, parabolic type etc.Wherein, this patent is mainly for trapezoidal obscure particle, and the subordinate function of trapezoidal obscure particle is:
Figure 2013104327412100002DEST_PATH_IMAGE009
At present, granulating method commonly used comprises: the Information Granulating method that W.Pedrycz proposes and dirt is non-, Dong Keqiang is to the improvement of the method.
The obscure particle of the Information Granulating method that W.Pedrycz proposes for setting up
Figure 721160DEST_PATH_IMAGE002
basic thought be:
(1) obscure particle can reasonably represent raw data, maximizes ;
(2) obscure particle will have certain singularity, namely minimizes fuzzy set
Figure 175198DEST_PATH_IMAGE002
support, minimize
Figure 2013104327412100002DEST_PATH_IMAGE011
, wherein with
Figure 2013104327412100002DEST_PATH_IMAGE013
it is respectively fuzzy set
Figure 515011DEST_PATH_IMAGE002
the support border.
Obtain following majorized function by above basic thought:
Figure 57594DEST_PATH_IMAGE014
The target of granulation is to make function obtain maximal value.For given time series granulation window
Figure 564930DEST_PATH_IMAGE016
, the fuzzy granulation algorithm concrete steps of W.Pedrycz are:
Step 1, determine the core of trapezoidal fuzzy set
Figure 2013104327412100002DEST_PATH_IMAGE017
,
Figure 670288DEST_PATH_IMAGE018
.Will
Figure 401090DEST_PATH_IMAGE016
by the sequence of ascending order, the time series that might as well establish after sequence is still
Figure 983250DEST_PATH_IMAGE016
, when N is even number,
Figure 2013104327412100002DEST_PATH_IMAGE019
,
Figure 849487DEST_PATH_IMAGE020
; When N is odd number, .
Step 2, determine that trapezoidal fuzzy set supports lower bound
Figure 750578DEST_PATH_IMAGE013
.Adopt the method for data traversal to calculate
Figure 765414DEST_PATH_IMAGE015
, make
Figure 823369DEST_PATH_IMAGE015
get peaked data value and be the support lower bound
Figure 242980DEST_PATH_IMAGE013
, that is: make function
Figure 181549DEST_PATH_IMAGE022
get peaked
Figure 296398DEST_PATH_IMAGE013
for
Figure 423623DEST_PATH_IMAGE002
the support lower bound, wherein
Figure 2013104327412100002DEST_PATH_IMAGE023
for
Figure 694811DEST_PATH_IMAGE024
degree of membership.
Step 3, determine that trapezoidal fuzzy set supports the upper bound
Figure 485175DEST_PATH_IMAGE012
.Adopt the method for data traversal to calculate
Figure 851434DEST_PATH_IMAGE015
, make
Figure 83482DEST_PATH_IMAGE015
get peaked data value and be the support upper bound
Figure 586007DEST_PATH_IMAGE012
, that is: make function get peaked
Figure 937485DEST_PATH_IMAGE012
for
Figure 23997DEST_PATH_IMAGE002
the support lower bound, wherein
Figure 493024DEST_PATH_IMAGE023
for
Figure 617100DEST_PATH_IMAGE024
degree of membership.
Through above-mentioned steps, can determine 4 parameters of trapezoidal fuzzy message particle:
Figure 638732DEST_PATH_IMAGE026
.
Can carry out the granulation operation to any one time series by the W.Pedrycz method; yet the support less of the fuzzy set that the method obtains; be embodied in too much data message and lose, make set up particle lose the alternative meaning to raw data.The reason that causes loss of data is not consider that particle supports the negative effect of data in addition to particle integral body, the degree of membership of the data beyond particle supports is 0, for this situation, dirt is non-, Dong Keqiang improves the method, makes the subordinate function of original trapezoidal fuzzy set into following form:
Improved fuzzy granulation algorithm concrete steps are:
Step 1, determine the core of trapezoidal fuzzy set ,
Figure 612821DEST_PATH_IMAGE018
.Will
Figure 588474DEST_PATH_IMAGE016
by the sequence of ascending order, the time series that might as well establish after sequence is still
Figure 452394DEST_PATH_IMAGE016
, when N is even number,
Figure 516427DEST_PATH_IMAGE019
,
Figure 264940DEST_PATH_IMAGE020
; When N is odd number,
Figure 163276DEST_PATH_IMAGE021
.Write down
Figure 339042DEST_PATH_IMAGE028
with
Figure 952688DEST_PATH_IMAGE030
, wherein
Figure 2013104327412100002DEST_PATH_IMAGE031
,
Figure 862482DEST_PATH_IMAGE032
.
Step 2, determine that trapezoidal fuzzy set supports lower bound
Figure 314192DEST_PATH_IMAGE013
.Computing method are: .
Step 3, determine that trapezoidal fuzzy set supports the upper bound
Figure 349275DEST_PATH_IMAGE012
.Computing method are:
Figure 113532DEST_PATH_IMAGE034
.
The method has enlarged the supporting degree to time series data than the W.Pedrycz method; improved the accommodation of degree of membership; in the time series Fuzzy Information Granulation, use at present comparatively general; yet the method is the same with the W.Pedrycz method; definite support upper bound and support lower bound can not comprise all data in window fully, can not guarantee:
Figure 2013104327412100002DEST_PATH_IMAGE035
Figure 892264DEST_PATH_IMAGE036
An important evaluating standard of time series trend prediction is whether the scope of prediction can comprise following measurement data fully, obviously, adopts at present existing Fuzzy Information Granulation method to carry out trend prediction to time series and can not meet preferably this standard.
The time series trend prediction has been brought into play vital role in numerous industry fields, for example, in the mine safety field, carry out the granulation trend prediction to take the gas density discrete data that per minute gathers as interval, the gas density interval of predict future after 1 hour, judge whether the safety problems such as gas explosion, coal and Gas Outburst that there will be gas density to transfinite and shine; At medicine and hygiene fields, the time series data of patient's cardiogram (ECG) is carried out to trend prediction, the ecg wave form interval in predict future 5 minutes, for severe case's Real-Time Monitoring, patients with coronary heart disease health prevent etc. plays an important role.
Summary of the invention
In order to overcome the shortcoming of above-mentioned prior art, the invention provides a kind of Fuzzy Information Granulation method towards the time series trend prediction, the definite support bound of the method can comprise the discrete data under existing time series window fully.
The present invention realizes with following technical scheme: a kind of Fuzzy Information Granulation method towards the time series trend prediction, a given time series window
Figure 198480DEST_PATH_IMAGE016
, concrete steps are as follows:
Step 1, determine the core of trapezoidal fuzzy set
Figure 276901DEST_PATH_IMAGE017
,
Figure 301358DEST_PATH_IMAGE018
, computing formula is:
Figure 2013104327412100002DEST_PATH_IMAGE037
，
Figure 618201DEST_PATH_IMAGE038
。
Step 2, to the time series window
Figure 283318DEST_PATH_IMAGE016
carry out interpolation, form new time series window
Figure 2013104327412100002DEST_PATH_IMAGE039
; Will
Figure 660204DEST_PATH_IMAGE039
by the sequence of ascending order, the time series that might as well establish after sequence is still
Figure 906378DEST_PATH_IMAGE039
.
Step 3, determine that trapezoidal fuzzy set supports lower bound
Figure 899348DEST_PATH_IMAGE013
; At the new time series data collection built
Figure 180157DEST_PATH_IMAGE039
the method of middle employing data traversal is calculated
Figure 603310DEST_PATH_IMAGE015
, make
Figure 336780DEST_PATH_IMAGE015
get peaked data value and be the support lower bound
Figure 885440DEST_PATH_IMAGE013
, that is: make function
Figure 20755DEST_PATH_IMAGE022
get peaked
Figure 614810DEST_PATH_IMAGE013
for
Figure 835575DEST_PATH_IMAGE002
the support lower bound, wherein
Figure 170348DEST_PATH_IMAGE023
for
Figure 425749DEST_PATH_IMAGE024
degree of membership.
Step 4, determine that trapezoidal fuzzy set supports the upper bound
Figure 190705DEST_PATH_IMAGE012
; At the new time series data collection built
Figure 633188DEST_PATH_IMAGE039
the method of middle employing data traversal is calculated
Figure 777511DEST_PATH_IMAGE015
, make
Figure 887418DEST_PATH_IMAGE015
get peaked data value and be the support upper bound
Figure 823276DEST_PATH_IMAGE012
, that is: make function
Figure 753054DEST_PATH_IMAGE025
get peaked
Figure 491947DEST_PATH_IMAGE012
for
Figure 456361DEST_PATH_IMAGE002
the support lower bound, wherein
Figure 563119DEST_PATH_IMAGE023
for
Figure 245773DEST_PATH_IMAGE024
degree of membership.
The invention has the beneficial effects as follows: this method is in conjunction with concrete time series application scenarios; the high layer information grain that the Fuzzy Information Granulation trapezoid model towards the time series trend prediction proposed is sought the generation of ginseng method can comprise the sequential discrete data in the bottom-up information grain fully; support preferably the unknown data that discrete data is outer; coordinate existing Forecasting Methodology; can significantly improve the time series trend prediction effect, there is higher realistic meaning and practical value.
The accompanying drawing explanation
Fig. 1 is flow chart of steps of the present invention;
Fig. 2 is trapezoidal Fuzzy Information Granulation figure;
Fig. 3 is the granulation effect curve figure of the Information Granulating trapezoid model of existing W.Pedrycz proposition;
Fig. 4 is the granulation effect curve figure of the Fuzzy Information Granulation trapezoid model of the existing non-proposition of dirt;
Fig. 5 is the granulation effect curve figure that the granulating method that proposes of the present invention produces;
Fig. 6 is the overall flow figure that the present invention is applied to the time series trend prediction.
Embodiment
For making purpose of the present invention, technical method and advantage clearer, the present invention is described in further detail below in conjunction with the accompanying drawings and the specific embodiments.
As shown in Figure 1, a kind of given time series window of Fuzzy Information Granulation method towards the time series trend prediction
Figure 454601DEST_PATH_IMAGE016
, the Fuzzy Information Granulation trapezoid model towards the time series trend prediction of the present invention is sought ginseng method tool
Body comprises the steps:
Step 1, determine the core of trapezoidal fuzzy set
Figure 539101DEST_PATH_IMAGE017
,
Figure 816761DEST_PATH_IMAGE018
.Computing formula is:
Figure 721132DEST_PATH_IMAGE037
Figure 739510DEST_PATH_IMAGE038
Time series data in practical application is discrete value, the core that its maximal value and minimum value are trapezoidal fuzzy set, and
Figure 678516DEST_PATH_IMAGE040
, can guarantee that actual acquisition sample data in existing time series window is all on fuzzy granulation border
Figure 127077DEST_PATH_IMAGE013
with
Figure 518744DEST_PATH_IMAGE012
between (
Figure DEST_PATH_IMAGE041
).
Step 2, to the time series window
Figure 471306DEST_PATH_IMAGE016
carry out interpolation, form new time series window .Will
Figure 884281DEST_PATH_IMAGE039
by the sequence of ascending order, the time series that might as well establish after sequence is still
Figure 261780DEST_PATH_IMAGE039
.
In practical application, adopt the fitting of a polynomial interpolation method.Fitting of a polynomial interpolation method commonly used has 4 kinds, is respectively: closest approach, linearity, batten and cube method of interpolation.Adopt spline method relatively evenly the time if the time window size is less and data distribute.
Step 3, determine that trapezoidal fuzzy set supports lower bound
Figure 389004DEST_PATH_IMAGE013
.At the new time series data collection built
Figure 538488DEST_PATH_IMAGE039
the method of middle employing data traversal is calculated , make
Figure 709760DEST_PATH_IMAGE015
get peaked data value and be the support lower bound
Figure 375096DEST_PATH_IMAGE013
, that is: make function get peaked
Figure 665318DEST_PATH_IMAGE013
for
Figure 253294DEST_PATH_IMAGE002
the support lower bound, wherein
Figure 223787DEST_PATH_IMAGE023
for
Figure 580819DEST_PATH_IMAGE024
degree of membership.
Step 4, determine that trapezoidal fuzzy set supports the upper bound
Figure 981494DEST_PATH_IMAGE012
.At the new time series data collection built
Figure 56766DEST_PATH_IMAGE039
the method of middle employing data traversal is calculated
Figure 565370DEST_PATH_IMAGE015
, make
Figure 42488DEST_PATH_IMAGE015
get peaked data value and be the support upper bound
Figure 608205DEST_PATH_IMAGE012
, that is: make function
Figure 170773DEST_PATH_IMAGE025
get peaked for
Figure 814692DEST_PATH_IMAGE002
the support lower bound, wherein for
Figure 595316DEST_PATH_IMAGE024
degree of membership.
As shown in Figure 2, the scope of the functional value that trapezoidal left and right hypotenuse is corresponding is between [0,1], shows that the numerical value mapping relations are fuzzy; The functional value perseverance of trapezoidal upper edge is 1, shows that the numerical value mapping relations determine.For the time series window , its value is the concrete actual value gathered, so its FUZZY MAPPING relation should perseverance be 1, i.e. determinacy mapping.To the time series window
Figure 897433DEST_PATH_IMAGE016
carry out difference, form new time series
Figure 539373DEST_PATH_IMAGE039
, the data of two seasonal effect in time series difference sets are the data that newly increase, and these data are the fitting data to original time series, and data have inaccuracy, so the membership function of these data should be between [0,1].Trapezoidal each angle is respectively m, n, a, b in the mapping of transverse axis.
Superiority with an example explanation this method with respect to classic method, for a data set X={141.77,142.72,141.81; 140.00,139.57,139.95,137.39; 135.24,135.30,137.49,136.26; 138.61,138.83,139.72,142.18; 140.77,141.24,140.33,140.64; 138.34} it carries out granulation the Information Granulating method that adopts W.Pedrycz to propose, the particle obtained is respectively:
a?=?137.3900
m?=?139.7200
n?=?139.9500
b?=?140.3300
Specifically as shown in Figure 3.
Adopt the granulating method of the non-proposition of dirt to carry out granulation to it, the particle obtained is respectively:
a?=?135.6300
m?=?139.7200
n?=?139.9500
b?=?142.3320
Specifically as shown in Figure 4.
By Fig. 3 and Fig. 4, can be found out, the data after existing two kinds of granulating method granulations can not comprise existing time series data fully, can not guarantee
Figure 76534DEST_PATH_IMAGE035
Figure 730631DEST_PATH_IMAGE036
An important evaluating standard of time series trend prediction is whether the scope of prediction can comprise following measurement data fully, obviously, adopts at present existing Fuzzy Information Granulation method to carry out trend prediction to time series and can not meet preferably this standard.
It carries out granulation the Information Granulating method that adopts patent of the present invention to propose, and the particle obtained is respectively:
a?=?134.8793
m?=?135.2400
n?=?142.7200
b?=?142.7200
Specifically as shown in Figure 5, the upper line boundary a of granulation value and b can comprise existing granulation data fully as can be seen from Figure, and n=b in this example, and the granulating method obviously proposed in the present invention is better than existing granulating method.
Be more than the application of single window, if, in a true application, should choose corresponding window value, time series be divided into to the different time periods.Detailed process as shown in Figure 6.
As shown in Figure 6, for original time series to be predicted
Figure 36848DEST_PATH_IMAGE042
, the trend prediction that it is carried out based on Fuzzy Information Granulation comprises the steps:
Step 1, selected window value
Figure DEST_PATH_IMAGE043
, original time series is carried out to discretize, form the window time series
Figure 245762DEST_PATH_IMAGE044
, wherein
Figure DEST_PATH_IMAGE045
, the window seasonal effect in time series length formed is original time series length
Figure 630738DEST_PATH_IMAGE046
with window
Figure 820017DEST_PATH_IMAGE043
take off round values after the phase division operation.
Step 2, for each time series, adopt the Fuzzy Information Granulation trapezoid model towards the time series trend prediction of the present invention to seek the ginseng method series of windows to be carried out to obfuscation one by one, form high layer information grain time series
Figure DEST_PATH_IMAGE047
with , wherein
Figure DEST_PATH_IMAGE049
, .Wherein
Figure 510126DEST_PATH_IMAGE047
be exactly to support upper rank b,
Figure 506026DEST_PATH_IMAGE048
support exactly lower bound a.
Step 3, the existing forecast model of employing are predicted the granulation data.Existing be usually used in the seasonal effect in time series forecast model and comprise neural network, SVM etc.
Step 4, draw time series variation trend and numerical value interval.The effect of prediction depends on the forecast model of choosing.
Adopt the Fuzzy Information Granulation trapezoid model towards the time series trend prediction of the present invention to seek the ginseng method and predict that the time series variation trend obtained has significant lifting compared to the conventional information granulating method prediction effect that adopts identical Forecasting Methodology, and have more realistic meaning and practical value.
In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (1)

1. the Fuzzy Information Granulation method towards the time series trend prediction, is characterized in that a given time series window , concrete steps are as follows:
Step 1, determine the parameter of trapezoidal fuzzy set
Figure 589951DEST_PATH_IMAGE002
,
Figure 2013104327412100001DEST_PATH_IMAGE003
; Computing formula is:
Figure 75421DEST_PATH_IMAGE004
，
Figure 2013104327412100001DEST_PATH_IMAGE005
；
Step 2, to the original time series window
Figure 494376DEST_PATH_IMAGE001
carry out interpolation, form new time series window
Figure 464606DEST_PATH_IMAGE006
, will
Figure 101386DEST_PATH_IMAGE006
by the sequence of ascending order, the time series that might as well establish after sequence is still
Figure 193976DEST_PATH_IMAGE006
;
Step 3, determine that trapezoidal fuzzy set supports lower bound
Figure 2013104327412100001DEST_PATH_IMAGE007
, at the new time series data collection built
Figure 32051DEST_PATH_IMAGE006
the method of middle employing data traversal is calculated
Figure 369754DEST_PATH_IMAGE008
, make
Figure 359576DEST_PATH_IMAGE008
get peaked data value and be the support lower bound
Figure 121602DEST_PATH_IMAGE007
, that is: make function
Figure 2013104327412100001DEST_PATH_IMAGE009
get peaked
Figure 455762DEST_PATH_IMAGE007
for
Figure 33374DEST_PATH_IMAGE010
the support lower bound, wherein
Figure 2013104327412100001DEST_PATH_IMAGE011
for
Figure 569048DEST_PATH_IMAGE012
degree of membership;
Step 4, determine that trapezoidal fuzzy set supports the upper bound
Figure 2013104327412100001DEST_PATH_IMAGE013
, at the new time series data collection built
Figure 691856DEST_PATH_IMAGE006
the method of middle employing data traversal is calculated
Figure 323432DEST_PATH_IMAGE008
, make
Figure 501472DEST_PATH_IMAGE008
get peaked data value and be the support upper bound
Figure 967351DEST_PATH_IMAGE013
, that is: make function
Figure 572645DEST_PATH_IMAGE014
get peaked
Figure 833729DEST_PATH_IMAGE013
for
Figure 549881DEST_PATH_IMAGE010
the support lower bound, wherein
Figure 807949DEST_PATH_IMAGE011
for
Figure 912040DEST_PATH_IMAGE012
degree of membership.
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CN105590023A (en) * 2015-12-08 2016-05-18 三峡大学 Fuzzy granulation prediction method of performance degradation of rolling bearing on the basis of information entropy
CN105956380A (en) * 2016-04-25 2016-09-21 东北林业大学 Construction method of leaf area prediction model
CN108846057A (en) * 2018-06-01 2018-11-20 山东师范大学 A kind of time series long-range forecast method based on band-like time-varying blurring information

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CN103150610A (en) * 2013-02-28 2013-06-12 哈尔滨工业大学 Fuzzy information granulation and support vector machine-based heating load prediction method

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Publication number Priority date Publication date Assignee Title
CN105590023A (en) * 2015-12-08 2016-05-18 三峡大学 Fuzzy granulation prediction method of performance degradation of rolling bearing on the basis of information entropy
CN105956380A (en) * 2016-04-25 2016-09-21 东北林业大学 Construction method of leaf area prediction model
CN105956380B (en) * 2016-04-25 2019-01-08 东北林业大学 A kind of construction method of leaf area prediction model
CN108846057A (en) * 2018-06-01 2018-11-20 山东师范大学 A kind of time series long-range forecast method based on band-like time-varying blurring information
CN108846057B (en) * 2018-06-01 2021-02-23 山东师范大学 Time series long-term prediction method based on banded time-varying fuzzy information particles

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