CN103150466A - Detection method and detection system for dynamics structural mutation - Google Patents
Detection method and detection system for dynamics structural mutation Download PDFInfo
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- CN103150466A CN103150466A CN2012105898341A CN201210589834A CN103150466A CN 103150466 A CN103150466 A CN 103150466A CN 2012105898341 A CN2012105898341 A CN 2012105898341A CN 201210589834 A CN201210589834 A CN 201210589834A CN 103150466 A CN103150466 A CN 103150466A
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Abstract
The invention provides a detection method and a detection system for system dynamics structural mutation. The system comprises a sliding time window definition module 1, a system state probability density distribution calculation module 2, a Fisher information value calculation module 3 and a mutation detection and observation module 4, wherein the sliding time window definition module 1 is used for defining a sliding time window on an observation data sequence set for describing the condition that the system state is changed along with time; the system state probability density distribution calculation module 2 is used for calculating the probability density distribution Pm (Zl) corresponding to a ZI interval in the sliding time window; the Fisher information value calculation module 3 is used for calculating the Fisher information value FI according to the probability density distribution Pm (Zl); and the mutation detection and observation module 4 is used for drawing a change curve of the FI value along with time, and according to the change curve, judging the system dynamics structural mutation situation. The detection system and the detection method disclosed by the invention have wide adaptability and certain antijamming capability, and do not depend on the length and the amplitude of an analyzed signal.
Description
Technical field
The present invention relates to the physics field, in particular to a kind of detection method and detection system of dynamical structure sudden change.
Background technology
The evolution of the many physical phenomenons of nature and development often show as non-linear, non-stationary and complicacy, and this is because its internal motivation structure along with the variation that forces effect outward, sudden change has occured.Therefore studying suitable dynamical structure sudden change detection method carries out determination and analysis to the observation sequence of system and just seems particularly important with the evolving trend in prognoses system future.Traditional sudden change detection method makes its description to physical process not too obvious as: filtering detection method, slip t-check, F detection method and Yamamoto signal to noise ratio (S/N ratio) method etc. because of statistical and the linearity of its method.Wherein there are certain methods such as slip t-check and F detection method some false catastrophe points often can be detected when detecting equal value mutation.In recent years, development along with nonlinear science, all multi index options in the nonlinear kinetics field are used to the dynamic characteristic of descriptive system, as correlation dimension, Lyapunov exponent, Kolmogorov entropy etc., yet want directly carry out concrete calculating and be not easy according to the definition of these indexes.In view of this, some scholar has worked out various detection methods based on a certain concrete research field such as weather system, and the document of delivering mainly contains: " a kind of dynamical structure sudden change new detecting method based on rescaled range analysis " of " Acta Physica Sinica " and " research of detecting abrupt climate change with approximate entropy " etc.The precondition that the former uses is that time series to be analyzed should have fractal characteristic, and this makes the scope of its application be restricted.And the latter's testing result depends on sub-sequence length, and the accurate position of positional mutation point, is merely able to provide a Sudden change region roughly, and this obviously can not satisfy the demand of practical application.Need to seek a kind of more effective, sane sudden change for this reason and detect new technology, the observation sequence of system is carried out determination and analysis, with the prognoses system evolving trend in future.
Tend to face univariate One-dimension Time Series in reality, obviously, the nonlinear mutation characteristic information of system is just contained in these sequences, and how effectively therefrom extracting this category information becomes a very crucial problem.
Fisher information provides for us the possibility that characterizes such class Characteristics of Mutation information just.Reason is that the data of any type and model can be converted to information and in essence no matter what initial subject is.Unlike other measuring methods of system information, thereby Fisher information provides a kind of state by monitoring system variable monitoring system and the method for state mutation.Yet by the practical computing formula of Fisher information as can be known, calculate Fisher information, first want the computational problem of the probability density distribution of resolution system state variable.Therefore the difficult point during the calculating of state variable probability density distribution is calculated as Fisher information is all the time perplexing people.In my previous research work, the method that employing is packaged into state to observed data is calculated the probability density distribution of variable, but this method only is only applicable to more single, the stable situation of system state, and the situation that those system states are shaken in a big way and inapplicable.
Summary of the invention
For the deficiencies in the prior art and defective, the present invention aims to provide a kind of detection method and detection system of system dynamics structural mutation, by computing system state variable probability density distribution, bring the probability density that calculates into Fisher information computing formula, can judge whether the system dynamics structure sudden change has occured.
For reaching above-mentioned purpose, the present invention proposes a kind of detection method of system dynamics structural mutation, comprises the following steps:
(1) definition is used for the sliding time window of the sudden change of dynamical structure
Sliding time window of definition on the time dependent observed data sequence sets of descriptive system state, this window width depends on the behavior of available data volume and system;
(2) probability density distribution of system state calculates
The sliding time window of step 1 definition is divided into L mutually disjoint interval Z
l, and utilize in following formula calculation window corresponding to Z
lProbability density distribution P on the interval
m(Z
l):
(3) calculate the Fisher value of information
The P that step 2 is calculated
m(Z
l) evolution tries to achieve q
m(Z
l), that is:
With q
m(Z
l) in the practical computing formula of substitution Fisher information, calculate the Fisher value of information of m time window, i.e. FI value, FI value computing formula is as follows:
FI
m≈4∑[q
m(z
l)-q
m(z
1+1)]
2
(4) detect the dynamical structure sudden change
Make the time dependent curve of FI value according to the FI value of step 3, and judge the sudden change situation of system dynamics structure based on the variation tendency of this curve.
Further, in aforesaid step 1, the window width w of sliding time window should comprise 8 data points at least to guarantee that the every bit in window can the whole calculating of excessive influence.
Further, in aforesaid step 1, the slippage factor δ of sliding time window should be less than window width w so that occur overlapping between adjacent sliding time window.
Further, in abovementioned steps 2, the L value is the integer between 4～12.
Another aspect of the present invention proposes a kind of detection system of system dynamics structural mutation, and this system comprises:
The sliding time window definition module is in order to sliding time window of definition on the time dependent observed data sequence sets of descriptive system state;
The probability density distribution computing module of system state is in order to calculate in sliding time window corresponding to Z
lProbability density distribution P on the interval
m(Z
l);
Fisher value of information computing module is in order to according to aforementioned probability density distribution P
m(Z
l) calculating Fisher value of information FI; And
Sudden change detects and Observation Blocks, the sudden change situation that is used for drawing the time dependent curve of FI value and judges the system dynamics structure based on the variation tendency of this curve.
Further, the window width w of aforementioned sliding time window should comprise 8 data points at least to guarantee that the every bit in window can the whole calculating of excessive influence.
Further, the slippage factor δ of aforementioned sliding time window should be less than window width w so that occur overlapping between adjacent sliding time window.
Further, the probability density distribution computing module of aforementioned system state is divided into L mutually disjoint interval Z with sliding time window
l, and utilize in following formula calculation window corresponding to Z
lProbability density distribution P on the interval
m(Z
l):
Further, aforesaid L value is the integer between 4～12.
Further, aforementioned Fisher value of information computing module is with probability density distribution P
m(Z
l) evolution tries to achieve q
m(Z
l), that is:
According to q
m(Z
l) calculate the Fisher value of information of m time window, i.e. FI value, its computing formula is as follows:
FI
m≈4∑[q
m(z
l)-q
m(z
1+1)]
2
By above technical scheme of the present invention as can be known, beneficial effect of the present invention has been fully to analyze on the system dynamics structure undergos mutation physical essence basis, calculate the fisher value of information according to the system state variables probability density distribution, these characteristics of the probability density distribution generation subtle change of the sharp capture system variable of Fisher information energy have solved the test problems of dynamical structure sudden change well:
1. the present invention is applicable to detect the dynamical structure sudden change of any type, does not need sample size to defer to certain distribution, also is not subjected to the interference of minority exceptional value, suddenlys change all effective to parameter sudden change, nonparametric.
2. the present invention not only can detect the sudden change of system dynamics structure, the degree of stability of the system that also can provide before and after undergoing mutation, and do not rely on length and the amplitude of analyzed signal, and have certain antijamming capability.
Description of drawings
Fig. 1 is the module diagram of the detection system of preferred embodiment system dynamics of the present invention structural mutation.
Fig. 2 a is two kinds of ideal time sequence schematic diagram with system of steady dynamic mechanical structure.
Fig. 2 b is for adopting method of the present invention to two kinds of sudden change testing result schematic diagram with system of steady dynamic mechanical structure of Fig. 2 a.
The time series schematic diagram of Fig. 3 a for adopting method of the present invention that sudden change between a kind of chaos system and stochastic system is detected.
Fig. 3 b is the data sequence schematic diagram after the data normalization before and after Fig. 3 a sudden change is processed.
Fig. 3 c is for adopting data after method of the present invention is processed for the data normalization before and after Fig. 3 a sudden change testing result schematic diagram that suddenlys change.
Embodiment
In order more to understand technology contents of the present invention, especially exemplified by specific embodiment and coordinate appended graphic being described as follows.
As shown in Figure 1, according to preferred embodiment of the present invention, the detection system of system dynamics structural mutation, this system comprises: sliding time window definition module 1, in order to sliding time window of definition on the time dependent observed data sequence sets of descriptive system state; The probability density distribution computing module 2 of system state is in order to calculate in sliding time window corresponding to Z
lProbability density distribution P on the interval
m(Z
l); Fisher value of information computing module 3 is in order to according to aforementioned probability density distribution P
m(Z
l) calculating Fisher value of information FI; And suddenly change and detect and Observation Blocks 4, the sudden change situation that is used for drawing the time dependent curve of FI value and judges the system dynamics structure based on the variation tendency of this curve.
Sliding time window definition module 1 defines a sliding time window on the time dependent observed data sequence sets of descriptive system state D.Window width depends on the behavior of available data volume and system.Window width comprises 8 data points at least to guarantee that the every bit in window can the whole calculating of excessive influence.The slippage factor of sliding time window should be less than window width, will occur between adjacent like this window one overlapping, can make sliding time window can catch the sudden change that might extend to the dynamical structure outside this window edge.For periodic system, sliding time window should be got a complete cycle or ideally several cycle at least.
Note observed data sequence sets be D=d (k), k=1 ..., N }, wherein N is the sequence total length, and window width is w ∈ N, and slippage factor is δ ∈ N, can be described below sliding window W with mathematical formulae:
W(m,w，δ)=｛d(k),k=1+m*δ,…,w+m*δ｝ (1)
M=1 in formula, 2 ..., M, M are the window number, M=(N-w)/δ.
The probability density distribution computing module 2 of system state is divided into following L interval with sliding time window:
{ Z in formula
l=[S
l-1, S
l), l=1,2 ..., L }, and mutually disjoint.
S
0＜S
1＜S
2＜…＜S
L (3)
S
0=min[W(m,w，δ)]=min[｛d(k),k=1+m*δ,…,w+m*δ｝] (4)
S
L=max[W(m,w，δ)]=max[｛d(k),k=1+m*δ,…,w+m*δ｝] (5)
Data d (k) ∈ W (m, w, δ) falls into interval Z
lProbability P
m(Z
l) equal d (k) ∈ W (m, w, δ) and fall into interval Z
lNumber and sliding time window W (m, w, δ) in the ratio of total data number.
Namely use in following formula calculation window corresponding to Z
lProbability density distribution P on the interval
m(Z
l):
In above-mentioned calculating, in sliding time window, the value of interval number L is larger, and the interval is narrower, and under the same terms, the window probability density distribution that calculates is milder, thereby the Fisher value of information is less, and this makes its reaction to sudden change more blunt.Otherwise the L value is less, and the interval is wider, under the same terms, and the window probability density distribution steeper that calculates, thus the Fisher value of information is larger, and this makes it easily be subject to the interference of noise and causes erroneous judgement.Through repetition test, the integer that in the present embodiment, L gets between 4～12 is advisable.
The probability density distribution P that Fisher value of information computing module 3 calculates the probability density distribution computing module 2 of system state
m(Z
l) evolution tries to achieve q
m(Z
l), that is:
And with q
m(Z
l) in the following practical computing formula of Fisher information of substitution, calculate the Fisher value of information (FI value) of m time window.That is:
FI
m≈4∑[q
m(z
l)-q
m(z
l+1)]
2 （8）
Sudden change detects with Observation Blocks 4 and draws the time dependent curve of FI value according to the FI value that Fisher value of information computing module 3 calculates, and judges the sudden change situation of system dynamics structure based on the variation tendency of this curve.
According to the abovementioned embodiments of the present invention, occur in two kinds of situations between the system with steady dynamic mechanical structure for a kind of sudden change, be constructed as follows an ideal time sequence y (t):
Fig. 2 (a) has provided the time dependent situation of this ideal sequence y (t).Obviously, when t=1000, system sports another kind of stable dynamical structure from a kind of stable dynamical structure.Fig. 2 (b) wherein gets window width w=50 for adopting the resulting sudden change testing result of the inventive method, slippage factor δ=10, and piecewise interval is counted L=4.Can find out from Fig. 2 (b), at the t=1000 place, significantly sudden change has occured once in the FI value, and the FI value before sudden change is generally greater than the FI value after sudden change, after showing that Systems balanth is better than sudden change before sudden change.
According to the abovementioned embodiments of the present invention, sudden change occurs in the situation between chaos system and stochastic system for another kind, seasonal effect in time series length to be analyzed is 20000, front 10000 data points are produced by nonlinear system Logistic insect, and rear 10000 data are by equally distributed random number simulation.Logistic insect equation is as follows:
x
n+1=ux
n(1-x
n),x∈[0,1] (10)
X in formula
nBe n for population number, x
n+1Be that n+1 is for population number; U be one greater than 0 and less than 4 control parameter, when 3.569945672＜u＜4.0, system enters chaos state.Population number initial value x
0=0.8, parameters u=3.8.The data sequence temporal evolution situation of Fig. 3 (a) for adopting the inventive method to produce wherein got window width w=1000, slippage factor δ=100, and piecewise interval is counted L=9.As can be seen from the figure, sudden change has occured in t=10001 prescription journey form in this sequence, and the difference due to serial variance before and after sudden change causes the catastrophe point in Fig. 3 (a) too obvious.For fear of this defective, the data before and after suddenling change are respectively carried out standardization.Provide in Fig. 3 (b) through the ideal time sequence after standardization.As can be seen from the figure, the catastrophe point in the time series after standardization is not difficult to identify by the sudden change testing tool, and standardization can not affect the probability density distribution feature of data substantially.Fig. 3 (c) has provided corresponding sudden change testing result.As can be seen from the figure, obviously greater than the FI value after sudden change, meaning is Systems balanth is better than sudden change before sudden change after to the FI value before sudden change.
Although the present invention discloses as above with preferred embodiment, so it is not to limit the present invention.The persond having ordinary knowledge in the technical field of the present invention, without departing from the spirit and scope of the present invention, when being used for a variety of modifications and variations.Therefore, protection scope of the present invention is as the criterion when looking claims person of defining.
Claims (9)
1. the detection method of a system dynamics structural mutation, is characterized in that, comprises the following steps:
(1) definition is used for the sliding time window of the sudden change of dynamical structure
Sliding time window of definition on the time dependent observed data sequence sets of descriptive system state, this window width depends on the behavior of available data volume and system;
(2) probability density distribution of system state calculates
The sliding time window of step 1 definition is divided into L mutually disjoint interval Z
l, and utilize in following formula calculation window corresponding to Z
lProbability density distribution P on the interval
m(Z
l):
(3) calculate the Fisher value of information
The probability density distribution P that step 2 is calculated
m(Z
l) evolution tries to achieve q
m(Z
l), that is:
With q
m(Z
l) in the practical computing formula of substitution Fisher information, calculate the Fisher value of information of m time window, i.e. FI value, FI value computing formula is as follows:
FI
m≈4Σ[q
m(z
l)-q
m(z
l+1)]
2
(4) detect the dynamical structure sudden change
Draw the time dependent curve of FI value according to the FI value of step 3, and judge the sudden change situation of system dynamics structure based on the variation tendency of this curve.
2. the detection method of system dynamics structural mutation according to claim 1, is characterized in that, in abovementioned steps 1, the window width w of sliding time window comprises 8 data points at least to guarantee that the every bit in window can the whole calculating of excessive influence.
3. the detection method of system dynamics structural mutation according to claim 1, is characterized in that, in aforesaid step 1, the slippage factor δ of sliding time window less than window width w so that occur overlapping between adjacent sliding time window.
4. the detection method of system dynamics structural mutation according to claim 1, is characterized in that, in abovementioned steps 2, the L value is the integer between 4～12.
5. the detection system of a system dynamics structural mutation, is characterized in that, this system comprises:
The sliding time window definition module is in order to sliding time window of definition on the time dependent observed data sequence sets of descriptive system state;
The probability density distribution computing module of system state is in order to calculate in sliding time window corresponding to Z
lProbability density distribution P on the interval
m(Z
l);
Fisher value of information computing module is in order to according to aforementioned probability density distribution P
m(Z
l) calculating Fisher value of information FI; And
Sudden change detects and Observation Blocks, the sudden change situation that is used for drawing the time dependent curve of FI value and judges the system dynamics structure according to the variation tendency of this curve.
6. the detection system of system dynamics structural mutation according to claim 5, is characterized in that, the window width w of aforementioned sliding time window comprises 8 data points at least to guarantee that the every bit in window can the whole calculating of excessive influence.
7. the detection system of system dynamics structural mutation according to claim 5, is characterized in that, the slippage factor δ of aforementioned sliding time window should be less than window width w so that occur overlapping between adjacent sliding time window.
8. the detection system of system dynamics structural mutation according to claim 5, is characterized in that, the probability density distribution computing module of aforementioned system state is divided into L mutually disjoint interval Z with sliding time window
l, the L value is the integer between 4～12, and utilizes in following formula calculation window corresponding to Z
lProbability density distribution P on the interval
m(Z
l):
9. the detection system of system dynamics structural mutation according to claim 5, is characterized in that, aforementioned Fisher value of information computing module is with probability density distribution P
m(Z
l) evolution tries to achieve q
m(Z
l), that is:
According to q
m(Z
l) calculate the Fisher value of information of m time window, i.e. FI value, its computing formula is as follows:
FI
m≈4Σ[q
m(z
l)-q
m(z
l+1)]
2。
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN105302945A (en) * | 2015-09-26 | 2016-02-03 | 长安大学 | Scaling exponent based dynamic structure mutation detection method and detection system |
| CN108982106A (en) * | 2018-07-26 | 2018-12-11 | 安徽大学 | A kind of effective ways of quick detection of complex system dynamics mutation |
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2012
- 2012-12-29 CN CN201210589834.1A patent/CN103150466B/en not_active Expired - Fee Related
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| US4428237A (en) * | 1980-11-13 | 1984-01-31 | Electric Power Research Institute, Inc. | System and method for measuring ultrasonic return signals |
| CN102542561A (en) * | 2011-11-23 | 2012-07-04 | 浙江工商大学 | Active contour synthetic aperture radar (SAR) image segmentation method based on Fisher distribution |
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| 何文平 等: "滑动去趋势波动分析与近似熵在动力学结构突变检测中的性能比较", 《物理学报》 * |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105302945A (en) * | 2015-09-26 | 2016-02-03 | 长安大学 | Scaling exponent based dynamic structure mutation detection method and detection system |
| CN108982106A (en) * | 2018-07-26 | 2018-12-11 | 安徽大学 | A kind of effective ways of quick detection of complex system dynamics mutation |
| CN108982106B (en) * | 2018-07-26 | 2020-09-22 | 安徽大学 | Effective method for rapidly detecting kinetic mutation of complex system |
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