CN108593557A - Based on TE-ANN-AWF mobile pollution source telemetry errors compensation methodes - Google Patents
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Abstract
The invention discloses one kind being based on TE ANN AWF mobile pollution source telemetry errors compensation methodes, the present invention carries out causal correlation analysis using TE transfer entropies to interference and measurement result, so that it is determined that uneven degree between Measuring origin and the more interference of measurement, and utilize the non-significant causal quantitative criteria of the directionality of TE transfer entropies extraction and determination method.Virtual observation method is proposed to realize the polynary destructing of unit observation sequence, the compensation of channel virtual observation sequence is disturbed by ANN error prediction model realizations single-trunk, then fusion reconstruct is carried out to the polynary virtual observation sequence after compensation using polynary adaptive weighted fusion method.For the weight convergence problem in blending algorithm, the advantages of Weight number adaptively that the good weights of TE are estimated ability and AWF by method that index forgetting is introduced in model adjusts, is combined, and improves the dynamic property of error compensation procedure.
Description
Technical field
The present invention designs a kind of mobile pollution source remote sensing detection error compensating method based on TE-ANN-AWF, belongs to pair
Mobile pollution source remote sensing detection instrument error compensation technical field, under external environmental disturbances to remote sensing detection instrument
Measurement result, which is corrected, is mended for target according to entropy estimate theory, the correlation theory of adaptive fusion and neural network
It repays and estimates, and then solve the problems, such as that remote sensing detection method is vulnerable to external environment interference.
Background technology
Mobile pollution source refers to that the source of air pollutants is not discharged with fixed apparatus, is such as discharged in moving process
Motor vehicle, Mobile engineering machine, ship and aircraft of exhaust gas etc..Moving source pollution especially heavy-duty diesel oil lorry, operation vapour
Oily vehicle, old automobile, engineering machinery vehicle have become the main source of atmosphere pollution, are to cause city superfine particulate matter, light
The major reason of chemical fumes pollution.Diesel exhaust has been promoted to bright by the World Health Organization in 2012 by suspecious carcinogen
True carcinogenic substance.In order to effectively be administered to mobile pollution source, the identification management and control of especially high blowdown motor vehicles needs
Effective detection in real time is carried out to the emission of mobile pollution source.
Currently, mobile pollution source detection technique type is various, such as by plant growth come reflect air pollution level or
The concentration of pollutant is measured using chemical detection, but these methods are difficult to carry out real-time online detection to mobile pollution source.It is distant
Sense detection method is a kind of rapidly and effectively method of detection mobile pollution source.This method is based on to other optical absorption spectrum
Rigorous analysis, according to gas componant in environment, in ultraviolet, visible and infrared spectrum wave band absorbent properties, come inverting, its is dense
Degree.1988, the first remote sense monitoring system using non-diffusing infrared technique (NondispersiveInfrared, NDIR)
(Remote Sensing Device, RSD) is developed by University of Denver of the U.S., which can detect in motor-vehicle tail-gas simultaneously
The concentration of emission of CO2, CO, HC.In the 1990s, University of Denver has developed using UV absorption technology (Ultra
Violet, UV) measure NO concentration remote sense monitoring system, overcome NDIR measure when water vapor absorption problem.Later, MD-
LaserTech companies have developed based on ultraviolet difference technology (Ultra-Violet Differential Optical
Absorption Spectrometry, UV-DOAS) NO and HC remote sensing systems.Due to tunable diode laser
(Tunable Diode Lasers, TDL) launch wavelength wave band is narrow, and the tested gas componant of difference can be selected not by dry
The wave band disturbed measures, and meets the real-time detection requirement such as high time resolution, high sensitivity, highly selective.Later, Massachusetts is managed
Engineering college has developed based on infrared laser difference absorption spectrum technology TDLAS (Tunable DiodeLaser
AbsorptionSpectrometer telemetry system), the detection for mobile pollution sources discharge beyond standards such as motor vehicles.Currently,
Remote sensoring technology has become the mainstream technology means of real-time online detection gas concentration.
Remote sensing survey method high degree of automation, as long as after equipment frame is set to road side, so that it may to measure through the section
A large amount of vehicles.Meanwhile this method is smaller to traffic impact.Liverpool John Moores University: Liverpool, England, Technical Sourcing Internation of the U.S. etc. adopt
System is monitored with the Dao Bianshi that can detect the pollutants such as including CO, NOx based on technological development such as TDLAS, UV-DOAS.But
Be this measurement method use condition it is limited, it is big by environmental disturbances, such as environment temperature, humidity, air pressure, wind speed to detection
Data have a major impact.And the geographical environment in city is mostly complicated and changeable, such as：Urban canyon effect can cause the unexpected of air-flow
Variation.Due to the complexity of external environment, German Fraunhofer physical measurement techniques research institute is in detection pollutant parameter
On the basis of increase measurement to meteorologic parameters such as wind speed, wind direction, humiture, air pressures again, school is carried out to contaminant detection results
Just.
Invention content
The present invention is easy the interference problem by external environment for the remote sensing detection method of mobile pollution source, herein in conjunction with
The adaptive weighted fusion of TE transfer entropies, ANN artificial neural networks, AWF three kinds of methods propose a kind of new error compensation mould
Type TE-ANN-AWF.Wherein, the causal correlation with measurement is interfered using TE transfer entropy quantitative analysis in model, and drawn non-
Notable causal determination method.The thought of virtual observation is proposed in model to realize the polynary destructing of unit observation sequence, then
Polynary virtual observation sequence is reconstructed by polynary fusion method.The method that index is forgotten is introduced in model TE is good
Weights the advantages of estimating the Weight number adaptively adjustment of advantage and AWF be combined, improve the dynamic of error compensation procedure
Energy.
The technology of the present invention solution：
Step 1：The measurement sample obtained under disturbance effect is tested by environmental simulation；Sample is measured based on experiment
This, interference correlation analysis is carried out by TE transfer entropies, so that it is determined that between Measuring origin and the more interference of measurement not
Balanced degree；And draw non-significant causal quantitative criteria and determination method using the directionality of TE transfer entropies；
Step 2：The training sample set that single interfering channel is obtained using environmental simulation smog box experiment porch, passes through god
The measurement error prediction model of each interference is established through network A NN methods；
Step 3：The polynary destructing that unit observation sequence is realized by virtual observation method, by under disturbance
ANN error predictions model carries out error compensation to the polynary virtual observation sequence after destructing, then adaptive weighted is melted using polynary
Conjunction method carries out fusion reconstruct to the polynary virtual observation sequence after compensation；
For the weight convergence problem in blending algorithm, the method that index forgetting is introduced in model is pre- by the weights of TE
The advantages of Weight number adaptively adjustment for estimating ability and polynary adaptive weighted fusion method, is combined, and improves error compensation mistake
The dynamic property of journey.
In the step 1, detectable feature is interfered for external environment, and TE transfer entropies is introduced to do remote sensing survey
It disturbs and carries out correlation causality analysis, non-significant causal quantitative criteria and judgement side are drawn using the directionality of transfer entropy
Method；
Assuming that between interference to a certain extent independently of each other, being obtained by simulation experiment platform under the variation that control single-trunk is disturbed
Measurement sequence, with this calculate temperature interference to measured value transfer entropy TET->CO, humidity interferes with the transfer entropy of measured value
TEH->CO, air pressure interferes with the transfer entropy TE of measured valueP->CO, the transfer entropy TE of wind speed disturbing factor to measured valueW->CO, wherein
Take maximum back transfer entropy TE0Measurement standard as non-causality；
TE0=max { TECO->T、TECO->H、TECO->P、TECO->W} (1)。
In the step 3, using polynary adaptive weighted fusion method to the polynary virtual observation sequence after compensation into
Row fusion, which reconstructs, is specially：, the multivariate observation of each interfering channel is adaptively melted under the criterion of least mean-square error
It closes；By virtual observation method and index Forgetting Mechanism by TE transfer entropies, ANN artificial neural networks, AWF is adaptive weighted melts
Three kinds of methods are closed mutually to combine closely.
The good weights of TE are estimated ability and AWF by the method that index forgetting is introduced in the step 3, in model
The advantages of Weight number adaptively adjusts is combined, specially
In TE-ANN models, although transfer entropy has the ability that good weights are estimated, weights can not be according to error
It is adjusted so that gradually convergence, also keeps fluctuating, can not restrain so as to cause the distribution of error；And AWF is adaptive weighted
Blending algorithm has can be so that weights be gradually convergent excellent under the criterion of least mean-square error without any priori
Point；The advantages of Weight number adaptively in order to which the good weights of TE to be estimated to advantage and AWF adjusts is combined, and introduces Forgetting Mechanism；
The confidence weights K that obtained transfer entropy the is estimated and optimal weighted factor W according to minimum mean square error criterion*,
Choose weighting coefficient { βn, K and W are merged to obtainIt is shown below；
Wherein, n-th observation is merged in n expressions,Indicate the weighting coefficient of confidence weights K, KnIndicate n-th
Secondary observation carries out the confidence weights that transfer entropy is estimated,Indicate the weighting coefficient of optimal weighted factor W, Wn *Indicate n-th
Observation merged after AWF weights.
Weight number adaptively adjustment and the convergence feature of feature and AWF, the initial stage dynamic of weights are steadily estimated in view of transfer entropy
The discreet value of process should lay particular emphasis on Kn, and steady-state process should then lay particular emphasis on Wn *, and gradually converge on Wn *；It is above-mentioned in order to embody
Feature, weighting coefficient { βnNeed to meet following features：
I indicates natural number；
In order to meet above-mentioned condition, construction such as minor function；
dn=(1-b)/(1-abn), n=1,2,3L (4)
Wherein, b is forgetting factor, and a is decay factor, 0<b<1<a；Weighting coefficient is obtained by formula (3)：
Thus the weights in each channel are obtained, as shown in formula：
The advantages of present invention exists compared with prior art：
(1) present invention incorporates three kinds of TE transfer entropies, ANN artificial neural networks, the adaptive weighted fusions of AWF methods to carry
A kind of new error compensation model TE-ANN-AWF is gone out.Compared with traditional error compensating method, interfered without priori omniscient more
Measure sample, can measurement error caused by the interference of effective compensation external environment, improve the applicability of remote sensing survey and anti-dry
Disturb ability.
(2) present invention introduces TE transfer entropies to interfere progress phase to remote sensing survey for the detectable feature of external disturbance
The causality analysis of closing property draws non-significant causal quantitative criteria and determination method using the directionality of transfer entropy.
(3) invention introduces adaptive weight fusion estimated algorithm AWF, to each interference under the criterion of least mean-square error
The observation in channel is adaptively merged, to ensure the Long-term stability of error compensation.
(4) present invention is good by TE by introducing Forgetting Mechanism in order to further improve the dynamic property of error compensation procedure
Good weights are estimated the advantages of Weight number adaptively adjustment of advantage and AWF and are combined.
Description of the drawings
Fig. 1 is the method for the present invention flow chart；
Fig. 2 is that disturbance factor transfer entropy of the present invention compares figure；
Fig. 3 is that present invention single-trunk disturbs lower telemetry errors neural network prediction model figure；
Fig. 4 is CO measurement error distribution maps under temperature-concentration of the present invention；
Fig. 5 is CO measurement error distribution maps under wind speed-concentration of the present invention；
Fig. 6 is CO measurement error distribution maps under air pressure-concentration of the present invention；
Fig. 7 is that virtual observation observation sequence of the present invention reconstructs definition graph；
Fig. 8 is TE-ANN-AWF error compensation models figure of the present invention；
Specific implementation mode
To make the innovation point realized of the present invention it can be readily appreciated that with reference to Fig. 1, to the realization method of the present invention into
One step describes in detail, is as follows：
Step 1：The measurement sample obtained under disturbance effect is tested by environmental simulation, then is carried out to measuring sample
Pretreatment and normalized.Sample is measured based on experiment, interference correlation analysis is carried out by TE transfer entropies, so that it is determined that
Uneven degree between Measuring origin and the more interference of measurement.And using TE transfer entropies directionality draw it is non-significant because
The quantitative criteria and determination method of fruit relationship.
If Xn and Yn is the two environmental disturbances change sequences and remote sensing survey at the n moment with xn and yn discrete states
Observation sequence, and Xn and Yn can be approximated to be the stable state markoff process of k ranks and l ranks respectively, then from the transmission of Yn and Xn
Entropy definition is as follows：
Wherein, TY→XIndicate the transfer entropy (Transfer Entroy) of Y to X, un=(xn+1,xn,yn (l)), p (un) indicate
Status xn+1With sequence xn(k),yn (l)The probability occurred simultaneously；p(xn+1|xn (k),yn (l)) indicate at the n moment, it is known that xn (k),
yn (l)Under the premise of, xn+1Conditional probability；p(xn+1|xn (k)) indicate xn (k)X under the premise of knownn+1Conditional probability, work as xn
When state sometime is determined by the historic state of itself completely, transfer entropy zero.
Since remote sensing detection is the detection based on the completion of optical absorption principle to mobile pollution source blowdown gas, and light is believed
The problems such as number there are absorption, scattering process, light beam deviation, beam spreads.And detect be mostly in outdoor environment into
Row, measurement process are easy to be influenced by factors such as temperature, humidity, air pressure, wind speed, wind direction, airborne dusts, are one by Multiple factors
The Nonlinear Dynamics Problems of coefficient complexity.Transfer entropy can be between quantitative measurement system variable linear and nonlinear
Relationship, while there is preferable anti-noise ability, often it is applied to portray the kinematic nonlinearity feature inside complication system.Therefore,
In compensation model select transfer entropy come to measurement data carry out correlation analysis, this contribute to trace error generate source and
More rationally accurately error is compensated.
To verify the validity of compensation model, selects CO for target detection object, simulated by environmental simulation experiment porch
Temperature, humidity, the measuring environment of air pressure and wind speed variation, using remote-measuring equipment measure target object.Compensation model
Middle uneven degree between weighing more interference using transfer entropy.Assuming that between interference to a certain extent independently of each other, it is real by simulating
Test platform and obtain measurement sequence under the variation disturbed of control single-trunk, with this calculate temperature interference to measured value transfer entropy TET->
CO, humidity interfere with the transfer entropy TE of measured valueH->CO, air pressure interfere with the transfer entropy TE of measured valueP->CO, wind speed interference
Transfer entropy TE of the factor to measured valueW->CO, wherein taking maximum back transfer entropy TE0 as the measurement mark of non-causality
It is accurate.
TE0=max { TECO->T、TECO->H、TECO->P、TECO->W}
As seen from Figure 2, the transfer entropy TE that wind speed, temperature, air pressure to CO measureW->CO、TET->CO、 TEP->COAll obviously
More than the transfer entropy TE of humidity to CO measured valuesH->CO, and humidity is to the transfer entropy TE of CO measured valuesH->COWith back transfer entropy TE0
It is not much different.In terms of information theory view, the information contained measured in sequence can be obtained from wind speed, temperature, air pressure interference sequence
It significantly explains, and can obtain explaining that part is smaller from humidity sequence.Thus wind speed, temperature, air pressure have significantly measurement result
Causalnexus, i.e. three environmental factors are larger to the interference of measurement, the large percentage of three in measurement error.It can therefrom see
Go out humidity to the transfer entropy TE measuredH->COWith back transfer entropy TE0It is sufficiently close to, reflects that humidity does not have CO measurement results
Apparent causal connection.The influence for considering humidity can thus not had in the measurement compensation to CO.
Step 2：The training sample set that single interfering channel is obtained using environmental simulation smog box experiment porch, passes through god
The measurement error prediction model of each interference is established through network A NN methods；
According to Fig.3, it is CO gas remote measurement error neural network prediction models under temperature interference.Due to being missed in telemetering
The effect of the poor factor that is not only interfered, meanwhile, the actual concentration of under test gas can also influence the order of magnitude of error.Cause
This, the input data of neural network is standard gas concentration n, temperature t, and output data is measurement error e.According to feedforward network
The effect of hidden layer point choosing method and actual treatment data, hidden layer number selection 7.By smog box environmental simulation platform, it is fixed
His factor, is regulated and controled the temperature inside the box, the training sample under single temperature interference is obtained with this.Similarly, wind can also be established
Rapid-curing cutback disturbs down the gentle neural network prediction model pressed dry under disturbing.Fig. 4-6 is single temperature, single air pressure, single wind speed interference respectively
Under, the error of test sample is distributed.
It, then can be under certain temperature, wind speed, air pressure after establishing three temperature, wind speed, air pressure prediction models
Measured value carries out error prediction respectively, sums later to three prediction errors, obtains final offset.
Step 3：TE-ANN-AWF model structures according to Fig.8, pass through virtual observation destructing, index Forgetting Mechanism
Transfer entropy TE, neural network ANN, adaptive weighted fusion AWF triplicitys are disturbed to the final estimation of measured value for band.
1) the polynary destructing that unit observation sequence first, is realized by virtual observation method, by under disturbance
ANN error predictions model carries out corresponding error compensation to the polynary virtual observation sequence after destructing, then using polynary adaptive
Weighted Fusion method AWF carries out fusion reconstruct to the polynary virtual observation sequence after compensation.
For ANN error prediction models, direct influence is distributed on error in the actual concentration of under test gas.And it is practical
On, under test gas actual concentration can not be learnt, can only substantially be estimated by historical series, this also leads to the measurement of prediction
Error is inaccurate.Thus, the error compensation value in each channel is directly added, effect is not obvious.According to Fig. 7, in order to count
It is applied in the compensation model of error according to the method for fusion, needs to deconstruct observation sequence.For this purpose, drawing first virtual
The concept of observation.
For example, the remote sensing detection of CO is interfered by temperature, air pressure, wind speed three in environment, it is assumed that three disturbing factors
The mutual coupling influenced on measurement result is smaller, then the composition of error may be considered additive noise.Thus, measured value can be seen
It is expressed from the next, wherein Y is measured value, and yr is actual value, and Wt, Ww, Wp are environmental disturbances noise, and θ is to measure to make an uproar at random
Sound.
Y=yr+Wt+Ww+Wp+θ
Wherein, Wt, Ww, Wp are the measurement error that single-trunk is disturbed, and can disturb ANN model by single-trunk and be predicted.
If the measured value under temperature single-trunk is disturbed is Yt, it is believed that it is the value excluded after Ww, Wp the two, such as following formula.
Yt=yr+Wt+ θ=Y-Ww-Wp
Obviously, temperature is gone alone the measured value Yt under disturbing in practice and is not present.Actually it is one kind to original observation
The destructing again of value, thus it is referred to as " virtual observation ".The measured value Yp and wind speed single-trunk that can similarly obtain under air pressure single-trunk is disturbed are disturbed
Under measured value Yw, be shown below.
Yw=yr+Ww+ θ=Y-Wt-Wp
Yp=yr+Wp+ θ=Y-Wt-Ww
After being deconstructed to observation by the concept of virtual observation, it is also necessary to be reconstructed.Compared to temperature, air pressure,
Wind speed has measurement result the influence of bigger, especially when wind speed is more than 5m/s.Obviously, measured value at this time is credible
Degree then should be minimum.In order to show the size of this confidence level, transfer entropy is introduced to express the confidence level of three virtual observations.
If being analyzed by transfer entropy it is found that interfering transfer entropy bigger, the causality of interference measurement is stronger, then interference is to measurement result
Interference is stronger.Thus the confidence level of virtual observation is inversely proportional with transfer entropy.Meanwhile in order to keep weights summation be 1, need to count
The weights that different virtual observation confidence levels account for three's totality are calculated, as following formula can obtain the confidence level of three virtual observations.
Wherein, TET、TEP、TEWIt can be estimated according to Entropy principle is transmitted, and KT、KP、KWMeet following formula.
Kt+Kp+Kw=1
It is reconstructed using the confidence level for the different virtual observations estimated, and as the weights of virtual observation.
Measurement result after reconstruct is shown below.
2) secondly, for the weight convergence problem in blending algorithm, method that index is forgotten is introduced by the good weights of TE
The advantages of Weight number adaptively adjustment for estimating ability and AWF, is combined, and improves the dynamic property of error compensation procedure.
In TE-ANN models, although transfer entropy has the ability that good weights are estimated, weights can not be according to error
It is adjusted so that gradually convergence, also keeps fluctuating, can not restrain so as to cause the distribution of error.And AWF is adaptive weighted
Blending algorithm has can be so that weights be gradually convergent excellent under the criterion of least mean-square error without any priori
Point.The advantages of Weight number adaptively in order to which the good weights of TE to be estimated to advantage and AWF adjusts is combined, and introduces Forgetting Mechanism.
The confidence weights K that obtained transfer entropy the is estimated and optimal weighted factor W according to minimum mean square error criterion,
Weighting coefficient { β n } is chosen, K and W are merged, are shown below.
Wherein, n-th observation is merged in n expressions.
Weight number adaptively adjustment and the convergence feature of feature and AWF, the initial stage dynamic of weights are steadily estimated in view of transfer entropy
The discreet value of process should lay particular emphasis on Kn, and steady-state process should then lay particular emphasis on Wn*, and gradually converge on Wn*.It is above-mentioned in order to embody
The characteristics of, weighting coefficient { β n } needs to meet following features：
In order to meet above-mentioned condition, construction such as minor function.
dn=(1-b)/(1-abn), n=1,2,3L
Wherein, b is forgetting factor, and a is decay factor, 0<b<1<a.Weighting coefficient can be obtained by condition 28：
βn K=dn, βn W=1-dn
It is hereby achieved that the weights in each channel, as shown in formula：
Wherein, Wn^ meets following formula, and replaces original Wn* using obtained new weights Wn^ as new weights.
Above example is provided merely to describing the purpose of the present invention, and be not intended to limit the scope of the present invention.This hair
Bright range is defined by the following claims.It does not depart from spirit and principles of the present invention and the various equivalent replacements made and repaiies
Change, should all cover within the scope of the present invention.
Claims (4)
1. being based on TE-ANN-AWF mobile pollution source telemetry errors compensation methodes, this method specifically includes following steps：
Step 1：The measurement sample obtained under disturbance effect is tested by environmental simulation；Sample is measured based on experiment, is passed through
TE transfer entropies carry out interference correlation analysis, so that it is determined that the uneven journey between Measuring origin and the more interference of measurement
Degree；And draw non-significant causal quantitative criteria and determination method using the directionality of TE transfer entropies；
Step 2：The training sample set that single interfering channel is obtained using environmental simulation smog box experiment porch, passes through nerve net
Network ANN methods establish the measurement error prediction model of each interference；
Step 3：The polynary destructing that unit observation sequence is realized by virtual observation method is missed by the ANN under disturbance
Poor prediction model carries out error compensation to the polynary virtual observation sequence after destructing, then uses polynary adaptive weighted fusion method
Fusion reconstruct is carried out to the polynary virtual observation sequence after compensation；
For the weight convergence problem in blending algorithm, the weights of TE are estimated ability by the method that index forgetting is introduced in model
The advantages of being adjusted with the Weight number adaptively of polynary adaptive weighted fusion method is combined, and improves the dynamic of error compensation procedure
Performance.
2. according to claim 1 be based on TE-ANN-AWF mobile pollution source telemetry errors compensation methodes, it is characterised in that：
In the step 1, detectable feature is interfered for external environment, and TE transfer entropies is introduced to interfere progress phase to remote sensing survey
The causality analysis of closing property draws non-significant causal quantitative criteria and determination method using the directionality of transfer entropy；
Assuming that between interference to a certain extent independently of each other, the measurement under the variation that control single-trunk is disturbed is obtained by simulation experiment platform
Sequence, with this calculate temperature interference to measured value transfer entropy TET->CO, humidity interferes with the transfer entropy TE of measured valueH->CO, gas
Pressure interferes with the transfer entropy TE of measured valueP->CO, the transfer entropy TE of wind speed disturbing factor to measured valueW->CO, wherein taking maximum anti-
To transfer entropy TE0Measurement standard as non-causality；
TE0=max { TECO->T、TECO->H、TECO->P、TECO->W} (1)。
3. according to claim 1 be based on TE-ANN-AWF mobile pollution source telemetry errors compensation methodes, it is characterised in that：
In the step 3, fusion reconstruct is carried out to the polynary virtual observation sequence after compensation using polynary adaptive weighted fusion method
Specially：, the multivariate observation of each interfering channel is adaptively merged under the criterion of least mean-square error；By virtual
Observation procedure and index Forgetting Mechanism are by TE transfer entropies, ANN artificial neural networks, AWF three kinds of method phases of adaptive weighted fusion
Mutually combine closely.
4. according to claim 1 be based on TE-ANN-AWF mobile pollution source telemetry errors compensation methodes, it is characterised in that：
The weights that the good weights of TE are estimated ability and AWF by the method that index forgetting is introduced in the step 3, in model are adaptive
The advantages of should adjusting, is combined, specially：
The confidence weights K that obtained transfer entropy the is estimated and optimal weighted factor W according to minimum mean square error criterion*, choose and add
Weight coefficient { βn, K and W are merged to obtainIt is shown below；
Wherein, n-th observation is merged in n expressions,Indicate the weighting coefficient of confidence weights K, KnIndicate n-th observation
Value carries out the confidence weights that transfer entropy is estimated,Indicate the weighting coefficient of optimal weighted factor W, Wn *Indicate n-th observation
The weights of AWF after being merged；
Weight number adaptively adjustment and the convergence feature of feature and AWF, the Initial Dynamic Process of weights are steadily estimated in view of transfer entropy
Discreet value should lay particular emphasis on Kn, and steady-state process should then lay particular emphasis on Wn *, and gradually converge on Wn *；In order to embody above-mentioned feature,
Weighting coefficient { βnNeed to meet following features：
I indicates natural number；
In order to meet above-mentioned condition, construction such as minor function；
dn=(1-b)/(1-abn), n=1,2,3L (4)
Wherein, b is forgetting factor, and a is decay factor, 0<b<1<a；Weighting coefficient is obtained by formula (3)：
Thus the weights in each channel are obtained, as shown in formula：
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