CN104156594B - Dynamic flight station-crossing time estimation method based on Bayes network - Google Patents

Abstract

Disclosed is a dynamic flight station-crossing time estimation method based on a Bayes network. A data mining method is used for flight station-crossing time estimation. The dynamic flight station-crossing time estimation method comprises the steps of firstly extracting a few factors which have an obvious effect on flight station-crossing time, applying the Bayes network for obtaining a station-crossing time estimation model, and then obtaining station-crossing time estimated values under different conditions. When flight departure time estimation is carried out, the probability distribution of station-crossing time values can be obtained by applying the station-crossing estimation model under the condition that only the flight arrival information needs to the known, and the possible values of the station-crossing time are obtained by obtaining expected values on the basis of the probability distribution. In addition, according to the characteristic that flight data are increased continuously, the newly-added data can be learnt through the dynamic flight station-crossing time estimation method, the consistency between the learning result and the result of relearning of all the data is ensured, the station-crossing time estimation model can be dynamically adjusted, and the station-crossing time estimation values are updated periodically so as to adapt to the constantly-changing external environment.

Description

A kind of flight turnaround on airport method for dynamic estimation based on Bayesian network

Technical field

The invention belongs to civil aviaton's technical field of aerospace, more particularly to a kind of flight turnaround on airport based on Bayesian network moves State method of estimation.

Background technology

Flight is delayed, as the focus of Air transportation service dispute, in recent years with the continuous increasing of CAAC's freight volume Long, this problem receives more and more attention.Flight delay brings direct economic loss not only to airport, airline, Cause very big inconvenience to the normal trip of passenger, also can very disruptive airport normal order.Lead to delayed reason Varied, there are weather reason, air traffic control, mechanical breakdown, aircraft allotment, flight plan etc. the reason common.Prolong in flight Effectively predicted occur by mistake before, be a target expecting during Civil Aviation Industry to reach.For airline, Each airplane executed multiple flights within one day, was delayed situation to downstream flight in the case that upstream flight involves a delay Effectively predicted, for the service quality improving boat public company, the competitiveness of lifting airline has important reality Meaning.

Flyontime.us is the flight delay time at stop analysis system that one, the U.S. opens for free towards the public.This system to The whole society opens for free, and anyone can be by the delay rate of its each flight of the query analysis U.S., airport waiting time, boat Class's moment and Weather information.The data that this system uses is mainly derived from DOT, and the time that safety check is waited in line is then Submit to system by common travelling personnel to obtain.This system mainly adopt study of statistical methods within certain a period of time each Airport all of flight delay distribution.

Flightcaster company of the U.S. develops flight delay information service system, and this system adopts a kind of advanced algorithm Collect the data of each flight past few years domestic, then it is mated the delay situation to determine flight with real-time condition, can With the flight situation in the following several hours of look-ahead.Also provide terminal applies for iphone and blackberry simultaneously, Flight delay advance notice is provided.

Flight Information service is paid much attention in Europe.European Civil Aviation administrative organization (eurocontrol) implements research and development Europe The plan of science and technology of aeronautical information system turnaround on airport rule base (european ais database, ead), ead is integrated and integrates The information of member state's aeronautical information system turnaround on airport rule base, is centralized aviation information worldwide largest at present Service system, the online aviation information service area of ead has covered most of country in Europe.

Singapore's Zhangyi airport is one of Asia Large Aeronautic Hub the busiest, and the information issuing system on this airport can There is provided real-time, accurate flight dynamic information, its flight entering and leaving port multidate information (boarding broadcast, upper visitor, hatch door close, take off, The message such as landing) have been realized in real-time update and issue.

In recent years, part domestic airport such as Capital Airport, new White Cloud Airport etc. pass through set up a web site, telephone contact center Etc. means, provide Scheduled Flight inquiry service to passenger.Also have sets up the exclusive page in the social networking website such as microblogging, When Flights Delayed situation occurs, communication is explained to passenger by forms such as word, pictures.

It is free to passenger that winged friend's science and technology (civil aviaton's resource network) develops the Related product such as " very accurate ", " variflight " Scheduled Flight customization service is provided, also provides Flight Information service to some airparks.

But, there is following point in said system: generally speaking, information is imperfect, the randomness that each influence factor changes Larger etc., therefore lack a kind of with the method for data mining, flight historical data can study, in many factors at present Under the influence of estimate turnaround on airport, thus method turnaround on airport effectively estimated when running into same condition.

Content of the invention

In order to solve the above problems, it is an object of the invention to provide a kind of flight turnaround on airport based on Bayesian network moves State method of estimation.

In order to achieve the above object, the flight turnaround on airport method for dynamic estimation bag based on Bayesian network that the present invention provides Include the following step carrying out in order:

Step one: pretreatment is carried out to history flight data, therefrom extract including before flight reach the delay time at stop, front boat The class's section time of advent, plan turnaround on airport, original base, type of airplane and actual turnaround on airport interior data as affect because Element；

Step 2: assume that above-mentioned each factor all has impact and affects to be separate, thus on actual turnaround on airport Determine Bayesian network topological structure；Then the data obtaining with previous step, obtains pattra leaves using maximum likelihood estimate This network parameters, thus obtains turnaround on airport and estimates model；

Step 3: model makes inferences to be estimated to turnaround on airport obtained above, obtains the turnaround on airport under different situations Estimated value；

Step 4: the Departure airport of the flight that approaches is predicted；

Step 5: through after a period of time, the method using step one carries out pretreatment to new history flight data, obtains To new training sample；Then using the model obtaining before as priori, in conjunction with new training sample, estimated using Bayes Meter method correction Bayesian network parameter；After having revised parameter, model makes inferences to be estimated to new turnaround on airport, and updated Stand time rule storehouse；

Step 6: repeat at periodic or other desired step 5, dynamically update time rule storehouse of missing the stop.

In step one, described flight historical data includes flight number, aircraft number, the flight planning departure time, plan Landing time, actual time of departure, Actual Time Of Fall, original base, destination airport and airline seat number；Front flight reaches and prolongs Be to deduct front flight planning time of advent the front flight actual time of arrival between mistaking, plan turnaround on airport be in flight planning table under The Proposed Departure time of one flight deducts the plan time of advent of a flight.

Described obtains Bayesian network parameter using maximum likelihood estimate, thus obtains the side that turnaround on airport estimates model Method is:

AssumeFor the vector of all parameters composition, n is node number, q_iFor π (x_i) valued combinations number, r_iFor node x_iValue number, θ_ijk=p (x_i=k/ π (x_i)=j) it is to work as x_iFather node Value is j-th value, x_iValue is the probability of k-th value, d_i, i=1,2 ..., m is sample data, then vectorRight Number likelihood function is:

$l(\stackrel{\→}{\mathrm{\θ}}/d)=\log \underset{l=1}{\overset{m}{\mathrm{\π}}}p(d_l/\stackrel{\→}{\mathrm{\θ}})=\underset{l=1}{\overset{m}{\mathrm{\σ}}}\log p(d_l/\stackrel{\→}{\mathrm{\θ}})---\left(1\right)$

Work as θ_ijkWhen taking following value, log-likelihood function acquirement maximum:

Wherein, m_ijkIt is in flight data, to meet x_i=k, π (x_iThe sample size of)=j, r_iFor node x_iValue number； If in history flight data sourceThen setting parameter is to be uniformly distributed；Bayesian network parameter is determined by formula (2), thus Obtain turnaround on airport and estimate model.

Model makes inferences to be estimated to the turnaround on airport obtaining, the method obtaining the turnaround on airport estimated value under different situations For:

3.1 pairs of turnaround on airport estimate that model makes inferences, and obtain the probability distribution of turnaround on airport under different situations；

3.2 pairs of turnaround on airport seek expected value:

$e\left(t\right)=\underset{i}{\mathrm{\σ}}p\left(i\right)*t_i---\left(3\right)$

Wherein e (t) is the turnaround on airport expected value when other conditions determine, t_iFor the intermediate value that i-th turnaround on airport is interval, P (i) be probability in i-th interval for the turnaround on airport, in the hope of turnaround on airport expected value e (t) descended as this kind of situation Stand the estimated value of time；

3.3 the turnaround on airport estimated value under different condition is inserted in turnaround on airport rule base, is the flight for putting forth time Prediction offer condition.

In step 4, to the method that Departure airport of the flight that approaches is predicted it is；If a upper flight does not enter Port delay or delay time at stop are less than 10 minutes, then the estimation departure time of Next Flight is planned time；If the delay time at stop is big In 10 minutes, then draw the estimation turnaround on airport under respective conditions from turnaround on airport rule base；If actual enter ETA estimated time of arrival add The upper plan turnaround on airport estimating that turnaround on airport is less than Next Flight, then when the estimation Departure airport of Next Flight is plan departure from port Between；If a upper flight actual enter ETA estimated time of arrival add estimate turnaround on airport be more than Next Flight the plan Departure airport, The estimation Departure airport of Next Flight be actual enter ETA estimated time of arrival add estimate turnaround on airport；If the delay time at stop is more than 10 minutes, And there is no corresponding turnaround on airport information in turnaround on airport rule base, then the turnaround on airport estimated is plan turnaround on airport, under The estimation Departure airport of one flight be actual enter ETA estimated time of arrival add plan turnaround on airport.

In step 5, the method using Bayes' assessment correction Bayesian network parameter is:

AssumeServe as reasonsThe subvector being formed, α_ijkMeet x in priori_i=k and π (x_i)=j Sample size,For the distribution of Di Li CrayObtained by Bayesian formula:

$p(\stackrel{\→}{\mathrm{\θ}}/d)=\frac{p\left(\stackrel{\→}{\mathrm{\θ}}\right)p(d/\stackrel{\→}{\mathrm{\θ}})}{\&integral;p\left(d\stackrel{\→}{\mathrm{\θ}}\right)d\stackrel{\→}{\mathrm{\θ}}}=\frac{p\left(\stackrel{\→}{\mathrm{\θ}}\right)p(d/\stackrel{\→}{\mathrm{\θ}})}{p\left(d\right)}---\left(4\right)$

WhereinFor vectorPrior probability distribution,For vectorPosterior probability distribution；Due toObey the distribution of Di Li Cray $d=[m_{\mathrm{ij}1}+{\mathrm{\α}}_{\mathrm{ij}1},m_{\mathrm{ij}2}+{\mathrm{\α}}_{\mathrm{ij}2},...,{m_{\mathrm{ijr}}}_i+{{\mathrm{\α}}_{\mathrm{ijr}}}_i],$ So:

$e({\mathrm{\θ}}_{\mathrm{ijk}}/d)=\frac{m_{\mathrm{ijk}}+{\mathrm{\α}}_{\mathrm{ijk}}}{\underset{k=1}{\overset{r_i}{\mathrm{\σ}}}(m_{\mathrm{ijk}}+{\mathrm{\α}}_{\mathrm{ijk}})}---\left(5\right)$

Bayesian network parameter, wherein m are revised using formula (5)_ijkMeet x in new samples_i=k and π (x_iThe sample number of)=j Amount.

The method of data mining is used by the flight turnaround on airport method for dynamic estimation based on Bayesian network that the present invention provides In flight turnaround on airport is estimated, several factors that flight turnaround on airport is had a significant impact are extracted first, with pattra leaves This net show that turnaround on airport estimates model, and then obtains turnaround on airport estimated value under different condition.Carrying out the flight for putting forth time It is only necessary to know under conditions of flight approaches information during estimation, estimate that model can draw turnaround on airport with turnaround on airport The probability distribution of value, on this basis, by seeking expected value, draws the possible value of turnaround on airport.In addition, being directed to flight number According to ever-increasing feature, the method that the present invention uses can constantly learn to the data newly increasing, and guarantees to learn Result and the result concordance that all data are relearned, enable turnaround on airport to estimate that model dynamically adjusts, and And regularly update turnaround on airport estimated value, to adapt to the extraneous circumstance being continually changing.

Brief description

The flight turnaround on airport method for dynamic estimation flow chart based on Bayesian network that Fig. 1 provides for the present invention.

In the flight turnaround on airport method for dynamic estimation based on Bayesian network that Fig. 2 present invention provides, the flight Departure airport is estimated Meter flow chart.

Specific embodiment

The flight turnaround on airport based on Bayesian network with specific embodiment, the present invention being provided below in conjunction with the accompanying drawings is dynamic Method of estimation is described in detail.

As shown in figure 1, the present invention provide included by suitable based on the flight turnaround on airport method for dynamic estimation of Bayesian network The following step that sequence is carried out:

Step one: pretreatment is carried out to history flight data, therefrom extract including before flight reach the delay time at stop, front boat The class's section time of advent, plan turnaround on airport, original base, type of airplane and actual turnaround on airport interior data as affect because Element；Wherein flight historical data includes flight number, aircraft number, the flight planning departure time, the plan landing time, actual when taking off Between, Actual Time Of Fall, original base, destination airport and airline seat number；It is actual for front flight that front flight reaches the delay time at stop Deduct front flight planning time of advent the time of advent, when plan turnaround on airport is the Proposed Departure of Next Flight in flight planning table Between deduct plan time of advent of a flight；

Step 2: assume that above-mentioned each factor all has impact and affects to be separate, thus on actual turnaround on airport Determine Bayesian network topological structure；During determining Bayesian network topological structure, the node representing type of airplane is according to boat Class's seating capacity difference has four kinds of value states, and less than 90 is type a, and 90 160 is type b, and 160 230 is type C, more than 230 is type d；Before representative, the node value of the flight section time of advent has 24 states, each status representative when Between span be a hour, such as before h13 represents, flight time of advent is between 13:00 13:59；Front flight reaches delay Time, plan turnaround on airport, each state of actual turnaround on airport are with 10 minutes for a segment；The node representing airport is every Individual one airport of status representative.After having determined Bayesian network topological structure, the data that obtains with previous step, using maximum seemingly So the estimation technique obtains Bayesian network parameter, thus obtains turnaround on airport and estimates model:

AssumeFor the vector of all parameters composition, n is node Number, q_iFor π (x_i) valued combinations number, r_iFor node x_iValue number, θ_ijk=p (x_i=k/ π (x_i)=j) it is to work as x_iFather Node value is j-th value, x_iValue is the probability of k-th value, d_i, i=1,2 ..., m be sample data, then parameter to AmountLog-likelihood function be:

$l(\stackrel{\→}{\mathrm{\θ}}/d)=\log \underset{l=1}{\overset{m}{\mathrm{\π}}}p(d_l/\stackrel{\→}{\mathrm{\θ}})=\underset{l=1}{\overset{m}{\mathrm{\σ}}}\log p(d_l/\stackrel{\→}{\mathrm{\θ}})---\left(1\right)$

Work as θ_ijkWhen taking following value, log-likelihood function acquirement maximum:

Wherein, m_ijkIt is in flight data, to meet x_i=k, π (x_iThe sample size of)=j, r_iFor node x_iValue number； If in history flight data sourceThen setting parameter is to be uniformly distributed.Bayesian network parameter is determined by formula (2), thus Obtain turnaround on airport and estimate model；

Step 3: model makes inferences to be estimated to turnaround on airport obtained above, obtains the turnaround on airport under different situations Estimated value, specifically comprises the following steps that

3.1 pairs of turnaround on airport estimate that model makes inferences, and obtain the probability distribution of turnaround on airport under different situations；

3.2 pairs of turnaround on airport seek expected value:

$e\left(t\right)=\underset{i}{\mathrm{\σ}}p\left(i\right)*t_i---\left(3\right)$

Wherein e (t) is the turnaround on airport expected value when other conditions determine, t_iFor the intermediate value that i-th turnaround on airport is interval, P (i) be probability in i-th interval for the turnaround on airport, in the hope of turnaround on airport expected value e (t) descended as this kind of situation Stand the estimated value of time；

3.3 the turnaround on airport estimated value under different condition is inserted in turnaround on airport rule base, is the flight for putting forth time Prediction offer condition.

Step 4: the Departure airport of the flight that approaches is predicted；During prediction, the delay if a upper flight does not approach Or the delay time at stop is less than 10 minutes, then the estimation departure time of Next Flight is planned time；If the delay time at stop is more than 10 points Clock, then draw the estimation turnaround on airport under respective conditions from turnaround on airport rule base；If actual enter ETA estimated time of arrival add estimate Turnaround on airport is less than the plan turnaround on airport of Next Flight, then the estimation Departure airport of Next Flight is the plan Departure airport；As The upper flight of fruit actual enter ETA estimated time of arrival add that the turnaround on airport estimated is more than the plan Departure airport of Next Flight, then next navigates Class the estimation Departure airport be actual enter ETA estimated time of arrival add estimate turnaround on airport；If the delay time at stop is more than 10 minutes, and mistake Standing does not have corresponding turnaround on airport information in time rule storehouse, then the turnaround on airport estimated is plan turnaround on airport, Next Flight The estimation Departure airport be actual enter ETA estimated time of arrival add plan turnaround on airport.

Step 5: through after a period of time, the method using step one carries out pretreatment to new history flight data, obtains To new training sample；Then using the model obtaining before as priori, in conjunction with new training sample, estimated using Bayes Meter method correction Bayesian network parameter；

AssumeServe as reasonsThe subvector being formed, α_ijkMeet x in priori_i=k and π (x_i)= The sample size of j,For the distribution of Di Li CrayObtained by Bayesian formula:

$p(\stackrel{\→}{\mathrm{\θ}}/d)=\frac{p\left(\stackrel{\→}{\mathrm{\θ}}\right)p(d/\stackrel{\→}{\mathrm{\θ}})}{\&integral;p\left(d\stackrel{\→}{\mathrm{\θ}}\right)d\stackrel{\→}{\mathrm{\θ}}}=\frac{p\left(\stackrel{\→}{\mathrm{\θ}}\right)p(d/\stackrel{\→}{\mathrm{\θ}})}{p\left(d\right)}---\left(4\right)$

WhereinFor vectorPrior probability distribution,For vectorPosterior probability distribution；Due toObey the distribution of Di Li Cray $d=[m_{\mathrm{ij}1}+{\mathrm{\α}}_{\mathrm{ij}1},m_{\mathrm{ij}2}+{\mathrm{\α}}_{\mathrm{ij}2},...,{m_{\mathrm{ijr}}}_i+{{\mathrm{\α}}_{\mathrm{ijr}}}_i],$ So:

$e({\mathrm{\θ}}_{\mathrm{ijk}}/d)=\frac{m_{\mathrm{ijk}}+{\mathrm{\α}}_{\mathrm{ijk}}}{\underset{k=1}{\overset{r_i}{\mathrm{\σ}}}(m_{\mathrm{ijk}}+{\mathrm{\α}}_{\mathrm{ijk}})}---\left(5\right)$

Bayesian network parameter, wherein m are revised using formula (5)_ijkMeet x in new samples_i=k and π (x_iThe sample number of)=j Amount.After having revised parameter, model makes inferences to be estimated to new turnaround on airport, and updates time rule storehouse of missing the stop.

Step 6: repeat at periodic or other desired step 5, dynamically update time rule storehouse of missing the stop.

Claims (6)

1. a kind of flight turnaround on airport method for dynamic estimation based on Bayesian network it is characterised in that: described method include by The following step that order is carried out:

Step one: pretreatment is carried out to history flight data, therefrom extract including before flight reach delay time at stop, front flight and arrive Reach time period, plan turnaround on airport, original base, type of airplane and actual turnaround on airport in interior data as influence factor；

Step 2: assume that above-mentioned each factor all has impact and affects to be separate on actual turnaround on airport, thereby determine that Go out Bayesian network topological structure；Then the data obtaining with previous step, obtains Bayesian network using maximum likelihood estimate Parameter, thus obtains turnaround on airport and estimates model；

Step 3: model makes inferences to be estimated to turnaround on airport obtained above, obtains front flight and reach delay time at stop, front flight The time of advent section, plan turnaround on airport, original base, this five variables of type of airplane take turnaround on airport during different value to estimate respectively Evaluation；

Step 4: the Departure airport of the flight that approaches is predicted；

Step 5: through after a period of time, the method using step one carries out pretreatment to new history flight data, obtains new Training sample；Then using the model obtaining before as priori, in conjunction with new training sample, using Bayes' assessment Revise Bayesian network parameter；After having revised parameter, model makes inferences to be estimated to new turnaround on airport, and update when missing the stop Between rule base；

Step 6: repeat at periodic or other desired step 5, dynamically update time rule storehouse of missing the stop.

2. the flight turnaround on airport method for dynamic estimation based on Bayesian network according to claim 1 it is characterised in that: In step one, described flight historical data includes flight number, aircraft number, the flight planning departure time, plan landing time, reality The border departure time, Actual Time Of Fall, original base, destination airport and airline seat number；The front flight arrival delay time at stop is front The flight actual time of arrival deducts front flight planning time of advent, and plan turnaround on airport is the meter of Next Flight in flight planning table Drawing the departure time deducts plan time of advent of a flight.

3. the flight turnaround on airport method for dynamic estimation based on Bayesian network according to claim 1 it is characterised in that: In step 2, described obtains Bayesian network parameter using maximum likelihood estimate, thus obtains turnaround on airport and estimates model Method is:

AssumeFor the vector of all parameters composition, n is node number, q_iFor π(x_i) valued combinations number, r_iFor node x_iValue number, θ_ijk=p (x_i=k/ π (x_i)=j) it is to work as x_iFather node value For j-th value, x_iValue is the probability of k-th value, d_i, i=1,2 ..., m is sample data, then vectorLogarithm seemingly So function is:

$l(\stackrel{\→}{\mathrm{\θ}}/d)=log\underset{l=1}{\overset{m}{\π}}p(d_l/\stackrel{\→}{\mathrm{\θ}})=\underset{l=1}{\overset{m}{\σ}}\log p(d_l/\stackrel{\→}{\mathrm{\θ}})---\left(1\right)$

Work as θ_ijkWhen taking following value, log-likelihood function acquirement maximum:

Wherein, m_ijkIt is in flight data, to meet x_i=k, π (x_iThe sample size of)=j；If in history flight data sourceThen setting parameter is to be uniformly distributed；Bayesian network parameter is determined by formula (2), thus obtains turnaround on airport and estimate mould Type.

4. the flight turnaround on airport method for dynamic estimation based on Bayesian network according to claim 1 it is characterised in that: In step 3, model makes inferences to be estimated to the turnaround on airport obtaining, when obtaining front flight arrival delay time at stop, the arrival of front flight Between section, plan turnaround on airport, original base, this five variables of type of airplane take turnaround on airport estimated value during different value respectively Method is:

3.1 pairs of turnaround on airport estimate that model makes inferences, and obtain front flight and reach delay time at stop, the front flight section time of advent, meter Draw turnaround on airport, original base, this five changes of type of airplane measure the probability distribution of turnaround on airport during a certain definite value；

3.2 pairs of turnaround on airport seek expected value:

$e\left(t\right)=\underset{i}{\σ}p\left(i\right)*t_i---\left(3\right)$

Wherein e (t) is to reach delay time at stop, the front flight section time of advent, plan turnaround on airport, original base, fly in front flight This five changes of machine type measure turnaround on airport expected value during a certain definite value, t_iFor the intermediate value that i-th turnaround on airport is interval, p (i) is Probability in i-th interval for the turnaround on airport, in the hope of turnaround on airport expected value e (t) as front flight reach the delay time at stop, The estimation of turnaround on airport when the front flight section time of advent, plan turnaround on airport, original base, this five variables of type of airplane determine Value；

3.3 the turnaround on airport estimated value under different condition is inserted in turnaround on airport rule base, is flight for putting forth time prediction Offer condition.

5. the flight turnaround on airport method for dynamic estimation based on Bayesian network according to claim 1 it is characterised in that: In step 4, to the method that Departure airport of the flight that approaches is predicted it is；If a upper flight does not approach and being delayed or prolongs It is less than between mistaking 10 minutes, then the estimation departure time of Next Flight is planned time；If the delay time at stop is more than 10 minutes, The estimation turnaround on airport under respective conditions is drawn from turnaround on airport rule base；If actual enter ETA estimated time of arrival when missing the stop plus estimation Between less than Next Flight plan turnaround on airport, then the estimation Departure airport of Next Flight be plan the Departure airport；If upper one Flight actual enter ETA estimated time of arrival add that the turnaround on airport estimated is more than the plan Departure airport of Next Flight, then the estimating of Next Flight Meter the Departure airport be actual enter ETA estimated time of arrival add estimate turnaround on airport；If the delay time at stop is more than 10 minutes, and turnaround on airport There is no corresponding turnaround on airport information, then the turnaround on airport estimated is plan turnaround on airport, the estimation of Next Flight in rule base Departure airport be actual enter ETA estimated time of arrival add plan turnaround on airport.

6. the flight turnaround on airport method for dynamic estimation based on Bayesian network according to claim 1 it is characterised in that: In step 5, the method using Bayes' assessment correction Bayesian network parameter is:

AssumeIt is by θ_ij1,θ_ij2,...,The subvector being formed, α_ijkMeet x in priori_i=k and π (x_i)=j Sample size,For the distribution of Di Li CrayObtained by Bayesian formula:

$p(\stackrel{\→}{\mathrm{\θ}}/d)=\frac{p\left(\stackrel{\→}{\mathrm{\θ}}\right)p(d/\stackrel{\→}{\mathrm{\θ}})}{\&integral;p\left(d\stackrel{\→}{\mathrm{\θ}}\right)d\stackrel{\→}{\mathrm{\θ}}}=\frac{p\left(\stackrel{\→}{\mathrm{\θ}}\right)p(d/\stackrel{\→}{\mathrm{\θ}})}{p\left(d\right)}---\left(4\right)$

WhereinFor vectorPrior probability distribution,For vectorPosterior probability distribution；Due to Obey the distribution of Di Li CraySo:

$e({\mathrm{\θ}}_{ijk}/d)=\frac{m_{ijk}+{\mathrm{\α}}_{ijk}}{\underset{k=1}{\overset{r_i}{\σ}}(m_{ijk}+{\mathrm{\α}}_{ijk})}---\left(5\right)$

Bayesian network parameter, wherein m are revised using formula (5)_ijkMeet x in new samples_i=k and π (x_iThe sample size of)=j.