CN107506334A - A kind of hidden Markov model computational methods for describing electric automobile during traveling behavior - Google Patents

A kind of hidden Markov model computational methods for describing electric automobile during traveling behavior Download PDF

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CN107506334A
CN107506334A CN201710616945.XA CN201710616945A CN107506334A CN 107506334 A CN107506334 A CN 107506334A CN 201710616945 A CN201710616945 A CN 201710616945A CN 107506334 A CN107506334 A CN 107506334A
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state
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陈星莺
徐书洋
张玮
谢俊
余昆
金颋
钱科军
沈杰
潘雨晴
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State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
Hohai University HHU
Suzhou Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
Hohai University HHU
Suzhou Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/29—Graphical models, e.g. Bayesian networks
    • G06F18/295—Markov models or related models, e.g. semi-Markov models; Markov random fields; Networks embedding Markov models
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0637—Strategic management or analysis, e.g. setting a goal or target of an organisation; Planning actions based on goals; Analysis or evaluation of effectiveness of goals

Abstract

The invention discloses a kind of hidden Markov model computational methods for describing electric automobile during traveling pattern, including：Single electric automobile during traveling situation is modeled with HMM, describes the change of electric automobile travel situations within a period of time.This method can flexibly catch use situation of change of the electric automobile within a period of time, can be as needed, with state descriptions such as stroke start time, stroke finish time, stroke start position, stroke end positions；Since it is desired that the parameter amount of estimation is larger, by model conversation be generalized linear model with B-spline method, reasonable selection Spline Node, reduce the number of parameters that needs are estimated.

Description

A kind of hidden Markov model computational methods for describing electric automobile during traveling behavior
Technical field
A kind of hidden Markov model computational methods for describing electric automobile during traveling behavior of present invention design, belong to electronic vapour Car traveling behavioral techniques field.
Background technology
Electric automobile during traveling process can be realized " zero-emission ", and it can be charged with new energy, and consumption can be again The raw energy.The energy that can be charged to electric automobile, such as wind energy, solar energy, tide energy, all there is uncertainty, if not having There is the energy storage of vast capacity, while these generations of electricity by new energy, it is necessary to be consumed, just can guarantee that the stabilization of power grids.Electric automobile is such as Fruit can be charged at the time of generation of electricity by new energy, with regard to that can solve this problem, if instead electric automobile is in network load Charged during in peak value, it is likely that aggravate power network burden, bring the problem of new.It is thus impossible to be not added with studying, blindly let alone big The free discharge and recharge of electric automobile is measured, but needs to study rational electric automobile discharge and recharge strategy, studies electric automobile discharge and recharge , it is necessary to analyze electric automobile during traveling behavior before tactful, corresponding model is established.
The content of the invention
Goal of the invention：The present invention proposes that one kind is based on hidden horse to solve the deficiency of existing electric automobile during traveling behavior model Er Kefu electric automobile during traveling behavior model algorithm, can be with the optimal discharge and recharge policy development of auxiliary electric automobile.
Technical scheme：For the above-mentioned purpose, the technical solution adopted by the present invention is：One kind description electric automobile during traveling behavior Hidden Markov model computational methods, this method comprises the following steps：
Step 001. is by taking working day electric automobile service condition model as an example, the electric automobile during traveling data first to collection Carry out statistical analysis, daily using electric automobile number more than 3 times, using continuous time markov chain model, otherwise use from Dissipate the markov chain modeling of time；
Step 002. assumes all identical p of state transition probability of working day daily synchronizationjk(t)=pjk(t+1440)；
Step 003. establishes the electric automobile service condition state transition probability model of N-state
Step 004. is directed to the feature of continuous time markov chain, actual with reference to physics, carries out parameter reduction；
Step 005. uses B-spline method, is generalized linear model by model conversation, reduces parameter Estimation number；
Step 006. chooses suitable B-spline node, and model is calculated；
Step 007. output services day electric automobile usage behavior hidden Markov model；
Step 008. is calculated using same method day off data, goes to step 001；
Step 009. exports the hidden Markov model of day off electric automobile usage behavior.
Further, in the step 001, the nonhomogeneous Markov model of discrete time is established：With XtBecome to be random The sequence X of amount, wherein t ∈ 0,1,2 ... }, the value on finite aggregate S, S represents state space；Markov chain is the random mistake of description A kind of method of journey, following state determine according only to present state, and independent of past state, a markov chain is from shape The transition probability that state j is transferred to state k be it is unique, i.e.,：
pjk(t)=P (Xt+1=k | Xt=j) (1)
If this transition probability does not change with time t, for homogeneous markov chain, if transition probability can over time t and Change, be then Nonhomogeneous Markov Chain.
Further, in the step 002, it is assumed that state transition probability rule：
By taking working day as an example, consider that user uses the custom of vehicle, it is assumed that in working day every day synchronization from shape The transition probability that state j is transferred to state k is identical, further, it is assumed that working day, i.e. the week, the shape of synchronization State transition probability is all identical, if sampled with one minute as time interval, then assumed above to write：
pjk(t)=pjk(t+1440) (2)
Wherein 1440 be the minute sum of one day.
Day off can be equally using this hypothesis.
Further in the step 003, the state transition probability defined by formula (1) can be considered as using time s as change certainly Function diurnal periodicity of amount；State transition probability matrix is：
WhereinS ∈ { 1,2 ..., 1440 }, using minute as temporal resolution, obey condition Likelihood function, for there is the model of N kind states：
Wherein, njk(s) be from s to s+1 the moment observe from state j transfer quantity；
According to conditional likelihood, pjk(s) maximum likelihood probability is：
Based on P (1), P (2) ..., P (1440) estimate can establish the Markov model of a discrete time.
Further in the step 004, two state discrete Markov models and number of parameters are in two States Markov Chains In model, state transition probability matrix per minute is：
Now number of parameters is 2*1440；
Assuming that traveling duration is unrelated with forming the time started, i.e. p21(s)=p21, wherein, 2 represent traveling, and 1 represents Stop；So number of parameters is just reduced to 1440+1；
Two state models obey conditional likelihood：
And maximal possibility estimationIt can be calculated by formula (5)；
Establish the Markov model of continuous time：
(1) continuous time Markov model and transition intensity matrix
pjk(t, u)=P (X (u)=k | X (t)=j) (8)
Wherein t ＜ u；This model is based on it is assumed hereinafter that (Δ u → 0)：
pjj(u, u+ Δ u)=1-qjj(u)Δu+o(Δu) (9)
Same：0≤qjj(u)≤∞, and 0≤qjk(u)≤∞；Wherein qjj(u) transition intensity is represented；Two based on more than It is individual it is assumed that Andrei Kolmogorov forward difference equation can further be applied to Non-homogeneous：
Wherein P (t, u)={ pjk(t, u) }, i.e. P (t, u) is by pjkThe matrix of (t, u) composition；So transition intensity matrix It can be converted into：
BecauseWith formula (9)-(10) equallyI.e.
If Q (t) is constant within the period [t, t+T], then is obtained with simple Andrei Kolmogorov forward difference equation：
P (t, t+T)=eQ(t)TP (t, t)=eQ(t)T (13)
Wherein P (t, t) is the probability that is shifted between different conditions between moment t and t, i.e. when a length of zero situation Under, this matrix is unit battle array；Assuming that T=1, then transition probability per minute is：
P (t, t+1)=P (t)=eQ(t) (14)
(2) two state transition intensity matrixes
Wherein P (t) is the standard state transition probability matrix of discrete joint network model, if model is made up of two states, So transition intensity matrix is changed into：
Further, in the step 004, the Markov chain of continuous time can be reduced under some specific structures Parameter, further, picking out this class formation can make model more controllable in theory；Simple example explanation：Assuming that there is one four The model of state, i.e. N=4, state 1 represent that electric automobile is parked in family, and state 2 represents electric automobile under steam, starting point For in family, state 3 represents that electric automobile stops, that is, in staying out, state 4 represents that electric automobile is in traveling, and starting point is not It is in family；Assuming that electric automobile can not once be transformed into the state stopped at home from the state for being parked in other places, then, so that it may to mould Type carries out parameter reduction processing；Equally it can not can directly be changed between state 2,1 with reasonable assumption electric automobile；So transfer is strong Spending matrix is：
The state-transition matrix of discrete time can have formula (14) to be calculated, in the example above, it is necessary to the ginseng of identification Number is changed into 5 from N (N-1)=12, and model, rather than discrete time are established using continuous time；This model can be caught The stand of electric automobile, traveling duration, also can determine whether that electric automobile parks frequency at home at night；With in model The increase of number of states, because the number of parameters recognized using the method for continuous time and the needs of reduction also will increase.
Further, in the step 005, parameter is estimated with B-spline method：
Because the parameter amount to be estimated is very big, application technology method is needed to reduce number of parameters；B- spline functions can answer For in daily change estimation：
(1).B-Splines
Establish a B-spline function, it is necessary first to define node (vector) sequence τ：
τ1≤τ2≤…≤τM(16)
Sequence node is needed in the section for preparing estimation batten, that is, is needed in section [0,1440], that is one In it time；
Use Bi,m(x) i-th of sequence node τ m rank B-spline basic functions is represented, wherein m ＜ M；Basic function recurrence shape Formula is as follows：
I=1 in formula ..., M-m；These basic functions are in [τ1,τM] on value m-1 rank multinomials；
The piecewise polynomial of one m degree B-spline curves is defined as follows：
Wherein Ci, i={ 1 ..., M-m }, from controlling polygon；Bi,m(x) the B samples for the m ranks being defined on knot vector Bar basic function；
Because target is to establish the diurnal variation situation of electric automobile during traveling behavior, basic spline is in periodic；This 2m new nodes can be added in existing node by sample；New node is defined as follows：
τ1-h=τM-h-(τM-τ1) wherein h ∈ 1 ..., m } (20)
τM+h=τh+(τM-τ1) wherein h ∈ 1 ..., m } (21)
More precisely, with τ '={ τ1-m,...,τM+mRepresent new knot vector；For each B-spline basic function, M+1 node is at least needed, although it is possible to duplicate；B-spline function is uniquely determined by the position of node；Particularly, such as Fruit sequence node translate α (constant) individual unit, basic function will with sequence node translate before on the basis of add α；If the section of row Point vector is defined as τ ', and this basic function will have sequence node { τM,...,τM+mDetermine, in { τ1-m,...,τ1Determine base letter τ is translated on the basis of numberM-τ1Individual unit；
The basic function that all m ranks piecewise polynomials defined with knot vector sequence τ can have formula (17), (18) to define is asked ；So there will not be any restrictions to polynomial spline method with B-spline method；But it is with the advantage of B-spline, it is desirable to Batten can be written to the linear combination of several polynomial functions；This point can be estimated model conversation is generalized linear model Count state transition probability；Conventional method typically uses cubic B-spline, that is m=4, the present invention also use the method；
(2) generalized linear models
The nonhomogeneous state transition probability p changed over time can be calculated with B-spline methodj,k(s) ginseng in model is reduced Number, still, this method there is also some problems：First, it is impossible to ensure that all B-splines are always interior in section [0,1], this just gives The model for calculating probability makes troubles；In addition, if for some s,Now it is calculated by formula (5) pjk(s) will not define；So a more accurate method is that original method is substituted using generalized linear model；Below By selective analysis generalized linear model；
In certain daily minute, occur to state k transfer or do not occur from state j, that is, each in diurnal periodicity Each moment s, state transfer quantity, which may be considered, obeys bi-distribution；That is njk~B (zj,pjk(s)), wherein when The Bernoulli Jacob's experiment number for carving s can basisCalculate, and pjk(s) it is unknown；Data can use index Return to analyze, be converted into logarithm expression：
Unknown logarithm binomial probability ηjk(s) basic function B can be usedi,m(s) represent, i.e.,：
ηjk(s) linear predictor is：
Wherein estimateTried to achieve by weighted least-squares method iteration；
It can invert to obtain with logarithmic function in the hope of being transferred to state k probability from state j now：
The application program of generalized linear model is packaged as glm () in statistical analysis software R.
Further, in the step 006, selected on node：
Select node τ quantity extremely important for establishing a suitable model with position, select the tradition side of node Node is is evenly distributed in the period of one day by method, but this method can not pick out pjk(s) spike, so proposing New node selecting method below：
1) number of nodes, M are determined first；
2) start node quantity, M are determinedinit＜ M, node are uniformly distributed in section, use τinitRepresent node；
3) setting model and the likelihood probability of each node interval is calculated；
4) two minimum adjacent nodes of likelihood probability are found, are set as { τj,τj+1}；
5) in { τj,τj+1Centre position is put into a new node τ*；
If 6) M*＜ M, then step 3 is skipped to, if M*=M then end loops；
If the number of nodes M of selection is too small, if M number is too big, can be selected by increasing node come lift scheme It is excellent it is possible that parameter overflow；So suggest calculating a variety of models as test, when M values increase to a certain extent, increasing Then the improvement degree of model can be ignored, and select this value as number of nodes.
Technique effect：Compared with the prior art, beneficial effects of the present invention are：1. by electric car travel situations data, Travel situations Markov model is established, basis is provided for electric automobile discharge and recharge policy development；2. using B-spline method, do Parameter is cut down, and reduces computing dimension.
A kind of nonhomogeneous Markov model for catching vehicle and using Daytime varieties is proposed, collects the actual travel of vehicle Data, with the time-varying definition of probability of the beginning and end stroke model, rationally reflect the uncertainty used of vehicle.Because Need to recognize substantial amounts of parameter using nonhomogeneous Markov model, the parameter in proposed model is reduced using B-spline Quantity.
Brief description of the drawings
Fig. 1 is present invention description electric automobile during traveling behavior overall flow figure；
Fig. 2 is that B-spline node of the present invention selects flow chart；
Fig. 3 is specific embodiment of the invention electric automobile during traveling frequency statistics figure；
Fig. 4 is from halted state to transport condition transition probability figure in specific embodiment of the invention electric automobile one day.
Embodiment
The present invention is further described with reference to embodiment and accompanying drawing, it should be appreciated that be only used for for these embodiments Illustrate the present invention rather than limitation the scope of the present invention, after the present invention has been read, those skilled in the art are to the present invention The modifications of various equivalents fall within the application appended claims limited range.
A kind of hidden Markov model computational methods for describing electric automobile during traveling behavior, this method comprise the following steps：
Step 001. is by taking working day electric automobile service condition model as an example, the electric automobile during traveling data first to collection Carry out statistical analysis, daily using electric automobile number more than 3 times, using continuous time markov chain model, otherwise use from Dissipate the markov chain modeling of time；
Step 002. assumes all identical p of state transition probability of working day daily synchronizationjk(t)=pjk(t+1440)；
Step 003. establishes the electric automobile service condition state transition probability model of N-state
Step 004. is directed to the feature of continuous time markov chain, actual with reference to physics, carries out parameter reduction；
Step 005. uses B-spline method, is generalized linear model by model conversation, reduces parameter Estimation number；
Step 006. chooses suitable B-spline node, and model is calculated；
Step 007. output services day electric automobile usage behavior hidden Markov model；
Step 008. is calculated using same method day off data, goes to step 001；
Step 009. exports the hidden Markov model of day off electric automobile usage behavior.
Further, in the step 001, the nonhomogeneous Markov model of discrete time is established：With XtBecome to be random The sequence X of amount, wherein t ∈ 0,1,2 ... }, the value on finite aggregate S, S represents state space；Markov chain is the random mistake of description A kind of method of journey, following state determine according only to present state, and independent of past state, a markov chain is from shape The transition probability that state j is transferred to state k be it is unique, i.e.,：
pjk(t)=P (Xt+1=k | Xt=j) (1)
If this transition probability does not change with time t, for homogeneous markov chain, if transition probability can over time t and Change, be then Nonhomogeneous Markov Chain.
Further, in the step 002, it is assumed that state transition probability rule：
Consider that user uses the custom of vehicle, it is assumed that synchronization every day in working day from state j is transferred to state k Transition probability be identical, further, it is assumed that working day, i.e. the week, state transition probability all phases of synchronization Together, if sampled with one minute as time interval, then assumed above to write：
pjk(t)=pjk(t+1440) (2)
Wherein 1440 be the minute sum of one day.
Further in the step 003, the state transition probability defined by formula (1) can be considered as using time s as change certainly Function diurnal periodicity of amount；State transition probability matrix is：
WhereinS ∈ { 1,2 ..., 1440 }, using minute as temporal resolution, obey condition Likelihood function, for there is the model of N kind states：
Wherein, njk(s) be from s to s+1 the moment observe from state j transfer quantity；
According to conditional likelihood, pjk(s) maximum likelihood probability is：
Based on P (1), P (2) ..., P (1440) estimate can establish the Markov model of a discrete time.
Further in the step 004, two state discrete Markov models and number of parameters are in two States Markov Chains In model, state transition probability matrix per minute is：
Now number of parameters is 2*1440；
Assuming that traveling duration is unrelated with forming the time started, i.e. p21(s)=p21, wherein, 2 represent traveling, and 1 represents Stop；So number of parameters is just reduced to 1440+1；
Two state models obey conditional likelihood：
And maximal possibility estimationIt can be calculated by formula (5)；
Establish the Markov model of continuous time：
(1) continuous time Markov model and transition intensity matrix
pjk(t, u)=P (X (u)=k | X (t)=j) (8)
Wherein t ＜ u；This model is based on it is assumed hereinafter that (Δ u → 0)：
pjj(u, u+ Δ u)=1-qjj(u)Δu+o(Δu) (9)
Same：0≤qjj(u)≤∞, and 0≤qjk(u)≤∞；Wherein qjj(u) transition intensity is represented；Two based on more than It is individual it is assumed that Andrei Kolmogorov forward difference equation can further be applied to Non-homogeneous：
Wherein P (t, u)={ pjk(t, u) }, i.e. P (t, u) is by pjkThe matrix of (t, u) composition；So transition intensity matrix It can be converted into：
BecauseWith formula (9)-(10) equallyI.e.
If Q (t) is constant within the period [t, t+T], then is obtained with simple Andrei Kolmogorov forward difference equation：
P (t, t+T)=eQ(t)TP (t, t)=eQ(t)T (13)
Wherein P (t, t) is the probability that is shifted between different conditions between moment t and t, i.e. when a length of zero situation Under, this matrix is unit battle array；Assuming that T=1, then transition probability per minute is：
P (t, t+1)=P (t)=eQ(t) (14)
(2) two state transition intensity matrixes
Wherein P (t) is the standard state transition probability matrix of discrete joint network model, if model is made up of two states, So transition intensity matrix is changed into：
Further, in the step 004, the Markov chain of continuous time can be reduced under some specific structures Parameter, further, picking out this class formation can make model more controllable in theory；Simple example explanation：Assuming that there is one four The model of state, i.e. N=4, state 1 represent that electric automobile is parked in family, and state 2 represents electric automobile under steam, starting point For in family, state 3 represents that electric automobile stops, that is, in staying out, state 4 represents that electric automobile is in traveling, and starting point is not It is in family；Assuming that electric automobile can not once be transformed into the state stopped at home from the state for being parked in other places, then, so that it may to mould Type carries out parameter reduction processing；Equally it can not can directly be changed between state 2,1 with reasonable assumption electric automobile；So transfer is strong Spending matrix is：
The state-transition matrix of discrete time can have formula (14) to be calculated, in the example above, it is necessary to the ginseng of identification Number is changed into 5 from N (N-1)=12, and model, rather than discrete time are established using continuous time；This model can be caught The stand of electric automobile, traveling duration, also can determine whether that electric automobile parks frequency at home at night；With in model The increase of number of states, because the number of parameters recognized using the method for continuous time and the needs of reduction also will increase.
Further, in the step 005, parameter is estimated with B-spline method：
Because the parameter amount to be estimated is very big, application technology method is needed to reduce number of parameters；B- spline functions can answer For in daily change estimation：
(1).B-Splines
Establish a B-spline function, it is necessary first to define node (vector) sequence τ：
τ1≤τ2≤…≤τM(16)
Sequence node is needed in the section for preparing estimation batten；；Node is needed in section [0,1440], that is In the time of one day；
Use Bi,m(x) i-th of sequence node τ m rank B-spline basic functions is represented, wherein m ＜ M；Basic function recurrence shape Formula is as follows：
I=1 in formula ..., M-m；These basic functions are in [τ1,τM] on value m-1 rank multinomials；
The piecewise polynomial of one m degree B-spline curves is defined as follows：
Wherein Ci, i={ 1 ..., M-m }, from controlling polygon；Bi,m(x) the B samples for the m ranks being defined on knot vector Bar basic function；
Because target is to establish the diurnal variation situation of electric automobile during traveling behavior, basic spline is in periodic；This 2m new nodes can be added in existing node by sample；New node is defined as follows：
τ1-h=τM-h-(τM-τ1) wherein h ∈ 1 ..., m } (20)
τM+h=τh+(τM-τ1) wherein h ∈ 1 ..., m } (21)
More precisely, with τ '={ τ1-m,...,τM+mRepresent new knot vector；For each B-spline basic function, M+1 node is at least needed, although it is possible to duplicate；B-spline function is uniquely determined by the position of node；Particularly, such as Fruit sequence node translate α (constant) individual unit, basic function will with sequence node translate before on the basis of add α；If the section of row Point vector is defined as τ ', and this basic function will have sequence node { τM,...,τM+mDetermine, in { τ1-m,...,τ1Determine base letter τ is translated on the basis of numberM-τ1Individual unit；
The basic function that all m ranks piecewise polynomials defined with knot vector sequence τ can have formula (17), (18) to define is asked ；So there will not be any restrictions to polynomial spline method with B-spline method；But it is with the advantage of B-spline, it is desirable to Batten can be written to the linear combination of several polynomial functions；This point can be estimated model conversation is generalized linear model Count state transition probability；Conventional method typically uses cubic B-spline, that is m=4, the present invention also use the method；
(2) generalized linear models
The nonhomogeneous state transition probability p changed over time can be calculated with B-spline methodj,k(s) ginseng in model is reduced Number, still, this method there is also some problems：First, it is impossible to ensure that all B-splines are always interior in section [0,1], this just gives The model for calculating probability makes troubles；In addition, if for some s,Now it is calculated by formula (5) pjk(s) will not define；So a more accurate method is that original method is substituted using generalized linear model；Below By selective analysis generalized linear model；
In certain daily minute, occur to state k transfer or do not occur from state j, that is, each in diurnal periodicity Each moment s, state transfer quantity, which may be considered, obeys bi-distribution；That is njk~B (zj,pjk(s)), wherein when The Bernoulli Jacob's experiment number for carving s can basisCalculate, and pjk(s) it is unknown；Data can be with referring to Number is returned to analyze, and is converted into logarithm expression：
Unknown logarithm binomial probability ηjk(s) basic function B can be usedi,m(s) represent, i.e.,：
ηjk(s) linear predictor is：
Wherein estimateTried to achieve by weighted least-squares method iteration；
It can invert to obtain with logarithmic function in the hope of being transferred to state k probability from state j now：
The application program of generalized linear model is packaged as glm () in statistical analysis software R.
Further, in the step 006, selected on node：
Select node τ quantity extremely important for establishing a suitable model with position, select the tradition side of node Node is is evenly distributed in the period of one day by method, but this method can not pick out pjk(s) spike, so proposing New node selecting method below：
1) number of nodes, M are determined first；
2) start node quantity, M are determinedinit＜ M, node are uniformly distributed in section, use τinitRepresent node；
3) setting model and the likelihood probability of each node interval is calculated；
4) two minimum adjacent nodes of likelihood probability are found, are set as { τj,τj+1}；
5) in { τj,τj+1Centre position is put into a new node τ*；
If 6) M*＜ M, then step 3 is skipped to, if M*=M then end loops；
If the number of nodes M of selection is too small, if M number is too big, can be selected by increasing node come lift scheme It is excellent it is possible that parameter overflow；So suggest calculating a variety of models as test, when M values increase to a certain extent, increasing Then the improvement degree of model can be ignored, and select this value as number of nodes.
Embodiment
Certain the electric automobile running data of 150 days is collected, data include：Date, stroke start time, at the end of stroke Carve.Statistics finds that stroke includes 799 strokes.Data collection interval is 1 minute.
Data set is divided into：Working day, day off two large divisions, by taking working day as an example, are calculated electric automobile during traveling Frequency statistics, see accompanying drawing 3.
According to the daily frequency of use statistical result of electric automobile, discrete horse is cooked to date of the frequency of usage less than 3 times respectively Er Kefu is modeled, and the continuous markov of the frequency doing more than or equal to 3 times is modeled.
Assuming that there is the model of four states, i.e. state 1 represents that electric automobile is parked in family, and state 2 represents electric automobile Under steam, starting point is in family, and state 3 represents that electric automobile stops (in staying out), and state 4 represents that electric automobile is in row In sailing, starting point is not in family.Assuming that electric automobile can not once be transformed into the state stopped at home from the state for being parked in other places, So, so that it may which parameter reduction processing is carried out to model.Equally it can not can directly be turned between state 2,1 with reasonable assumption electric automobile Change.So transition intensity matrix is：
The state-transition matrix of discrete time can have formula (14) to be calculated, in the example above, it is necessary to the ginseng of identification Number is changed into 5 from individual.
With B-spline node selecting method, it be 21 to select nodes, estimated in one day from dead ship condition to travelling shape The transition probability of state is with representing, as a result such as accompanying drawing 4.
Embodiments of the present invention are explained in detail above in conjunction with accompanying drawing, but the present invention is not limited to above-mentioned implementation Mode, can also be on the premise of present inventive concept not be departed from those of ordinary skill in the art's possessed knowledge Make a variety of changes.

Claims (8)

  1. A kind of 1. hidden Markov model computational methods for describing electric automobile during traveling behavior, it is characterised in that：This method includes Following steps：
    Step 001. is carried out to the electric automobile during traveling data of collection first by taking working day electric automobile service condition model as an example Statistical analysis, daily using electric automobile number more than 3 times, using continuous time markov chain model, otherwise using it is discrete when Between markov chain modeling；
    Step 002. assumes all identical p of state transition probability of working day daily synchronizationjk(t)=pjk(t+1440)；
    Step 003. establishes the electric automobile service condition state transition probability model of N-state
    Step 004. is directed to the feature of continuous time markov chain, actual with reference to physics, carries out parameter reduction；
    Step 005. uses B-spline method, is generalized linear model by model conversation, reduces parameter Estimation number；
    Step 006. chooses suitable B-spline node, and model is calculated；
    Step 007. output services day electric automobile usage behavior hidden Markov model；
    Step 008. is calculated using same method day off data, goes to step 001；
    Step 009. exports the hidden Markov model of day off electric automobile usage behavior.
  2. 2. the hidden Markov model computational methods of description electric automobile during traveling behavior according to claim 1, its feature It is：In the step 001, the nonhomogeneous Markov model of discrete time is established：With XtFor the sequence X of stochastic variable, its Middle t ∈ 0,1,2 ... }, the value on finite aggregate S, S represents state space；Markov chain is one kind side for describing random process Method, following state determine that, independent of past state, a markov chain is transferred to from state j according only to present state State k transition probability be it is unique, i.e.,：
    pjk(t)=P (Xt+1=k | Xt=j) (1)
    If this transition probability does not change with time t, for homogeneous markov chain, if transition probability can over time t and change, It is then Nonhomogeneous Markov Chain.
  3. 3. the hidden Markov model computational methods of description electric automobile during traveling behavior according to claim 1, its feature It is：In the step 002, it is assumed that state transition probability rule：
    By taking working day as an example, consider that user uses the custom of vehicle, it is assumed that synchronization every day in working day turns from state j The transition probability for moving on to state k is identical, further, it is assumed that working day, i.e. the week, the state transfer of synchronization Probability is all identical, if sampled with one minute as time interval, then assumed above to write：
    pjk(t)=pjk(t+1440) (2)
    Wherein 1440 be the minute sum of one day.
    Day off can be equally using this hypothesis.
  4. 4. the hidden Markov model computational methods of description electric automobile during traveling behavior according to claim 1, its feature It is：In the step 003, the state transition probability defined by formula (1) can be considered as letter diurnal periodicity using time s as independent variable Number；State transition probability matrix is：
    WhereinS ∈ { 1,2 ..., 1440 }, using minute as temporal resolution, obey conditional likelihood letter Number, for there is the model of N kind states：
    <mrow> <mi>L</mi> <mrow> <mo>(</mo> <mi>P</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> <mo>,</mo> <mi>P</mi> <mo>(</mo> <mn>2</mn> <mo>)</mo> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>P</mi> <mo>(</mo> <mn>1440</mn> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>1440</mn> </munderover> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mrow> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, njk(s) be from s to s+1 the moment observe from state j transfer quantity；
    According to conditional likelihood, pjk(s) maximum likelihood probability is：
    <mrow> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    Based on P (1), P (2) ..., P (1440) estimate can establish the Markov model of a discrete time.
  5. 5. the hidden Markov model computational methods of description electric automobile during traveling behavior according to claim 1, its feature It is：In the step 004, two state discrete Markov models and number of parameters are in two States Markov Chains models, every point The state transition probability matrix of clock is：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>p</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>p</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>p</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>p</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>p</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Now number of parameters is 2*1440；
    Assuming that traveling duration is unrelated with forming the time started, i.e. p21(s)=p21, wherein, 2 represent traveling, and 1 represents to stop； So number of parameters is just reduced to 1440+1；
    Two state models obey conditional likelihood：
    <mrow> <mi>L</mi> <mrow> <mo>(</mo> <mi>P</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> <mo>,</mo> <mi>P</mi> <mo>(</mo> <mn>2</mn> <mo>)</mo> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>P</mi> <mo>(</mo> <mn>1440</mn> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>1440</mn> </munderover> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>2</mn> </munderover> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>2</mn> </munderover> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mrow> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    And maximal possibility estimationIt can be calculated by formula (5)；
    Establish the Markov model of continuous time：
    (1) continuous time Markov model and transition intensity matrix
    pjk(t, u)=P (X (u)=k | X (t)=j) (8)
    Wherein t ＜ u；This model is based on it is assumed hereinafter that (Δ u → 0)：
    pjj(u, u+ Δ u)=1-qjj(u)Δu+o(Δu) (9)
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>u</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>q</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mi>&amp;Delta;</mi> <mi>u</mi> <mo>+</mo> <mi>o</mi> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>&amp;ForAll;</mo> <mi>j</mi> <mo>&amp;NotEqual;</mo> <mi>k</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    Same：0≤qjj(u)≤∞, and 0≤qjk(u)≤∞；Wherein qjj(u) transition intensity is represented；It is false based on two above If Andrei Kolmogorov forward difference equation can be further applied to Non-homogeneous：
    <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>P</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>u</mi> </mrow> </mfrac> <mo>=</mo> <mi>P</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein P (t, u)={ pjk(t, u) }, i.e. P (t, u) is by pjkThe matrix of (t, u) composition；So transition intensity matrix can be with It is converted into：
    BecauseWith formula (9)-(10) equallyI.e.
    If Q (t) is constant within the period [t, t+T], then is obtained with simple Andrei Kolmogorov forward difference equation：P(t, T+T)=eQ(t)TP (t, t)=eQ(t)T (13)
    Wherein P (t, t) is the probability that is shifted between different conditions between moment t and t, i.e. when a length of zero in the case of, this Matrix is unit battle array；Assuming that T=1, then transition probability per minute is：
    P (t, t+1)=P (t)=eQ(t) (14)
    (2) two state transition intensity matrixes
    Wherein P (t) is the standard state transition probability matrix of discrete joint network model, if model is made up of two states, then Transition intensity matrix is changed into：
    <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>q</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>q</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>q</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>q</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  6. 6. the hidden Markov model computational methods of description electric automobile during traveling behavior according to claim 5, its feature It is：In the step 004, the Markov chain of continuous time can reduce parameter under some specific structures, further, distinguish Know and this class formation and can make model more controllable in theory；Simple example explanation：Assuming that there are the model of four states, i.e. N =4, state 1 represents that electric automobile is parked in family, and state 2 represents electric automobile under steam, and starting point is the table of state 3 in family Show that electric automobile stops, that is, in staying out, state 4 represents that electric automobile is in traveling, and starting point is not in family；It is assuming that electronic Automobile can not once be transformed into the state stopped at home from the state for being parked in other places, then, so that it may parameter reduction is carried out to model Processing；Equally it can not can directly be changed between state 2,1 with reasonable assumption electric automobile；So transition intensity matrix is：
    <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>q</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>23</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>q</mi> <mn>23</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>34</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>q</mi> <mn>34</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>q</mi> <mn>41</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>q</mi> <mn>43</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>q</mi> <mn>43</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>q</mi> <mn>41</mn> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    The state-transition matrix of discrete time can have formula (14) to be calculated, in the example above, it is necessary to identification parameter from N (N-1)=12 is changed into 5, and model, rather than discrete time are established using continuous time；This model can catch electronic The stand of automobile, traveling duration, also can determine whether that electric automobile parks frequency at home at night；With state in model The increase of quantity, because the number of parameters recognized using the method for continuous time and the needs of reduction also will increase.
  7. 7. the hidden Markov model computational methods of description electric automobile during traveling behavior according to claim 1, its feature It is：In the step 005, parameter is estimated with B-spline method：
    Because the parameter amount to be estimated is very big, application technology method is needed to reduce number of parameters；B- spline functions can be applied to In daily change estimation：
    (1).B-Splines
    Establish a B-spline function, it is necessary first to define node (vector) sequence τ：
    τ1≤τ2≤…≤τM(16)
    Sequence node is needed in the section for preparing estimation batten, that is, is needed in section [0,1440], that is at one day In time；
    Use Bi,m(x) i-th of sequence node τ m rank B-spline basic functions is represented, wherein m ＜ M；Basic function recursive form is such as Under：
    <mrow> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>if&amp;tau;</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mi>x</mi> <mo>&lt;</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>x</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;tau;</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>x</mi> </mrow> <mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
    I=1 in formula ..., M-m；These basic functions are in [τ1,τM] on value m-1 rank multinomials；
    The piecewise polynomial of one m degree B-spline curves is defined as follows：
    <mrow> <msub> <mi>S</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mi>m</mi> </mrow> </munderover> <msub> <mi>C</mi> <mi>i</mi> </msub> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>
    Wherein Ci, i={ 1 ..., M-m }, from controlling polygon；Bi,m(x) the B-spline base for the m ranks being defined on knot vector Function；
    Because target is to establish the diurnal variation situation of electric automobile during traveling behavior, basic spline is in periodic；So may be used So that 2m new nodes to be added in existing node；New node is defined as follows：
    τ1-h=τM-h-(τM-τ1) wherein h ∈ 1 ..., m } (20)
    τM+h=τh+(τM-τ1) wherein h ∈ 1 ..., m } (21)
    More precisely, with τ '={ τ1-m,...,τM+mRepresent new knot vector；For each B-spline basic function, at least M+1 node is needed, although it is possible to duplicate；B-spline function is uniquely determined by the position of node；Particularly, if section Point sequence translate α (constant) individual unit, basic function will with sequence node translate before on the basis of add α；If row node to Amount is defined as τ ', and this basic function will have sequence node { τM,...,τM+mDetermine, in { τ1-m,...,τ1Determine basic function base τ is translated on plinthM-τ1Individual unit；
    The basic function that all m ranks piecewise polynomials defined with knot vector sequence τ can have formula (17), (18) to define is tried to achieve；Institute Will not have any restrictions to polynomial spline method with B-spline method；But be with the advantage of B-spline, it is desirable to batten can To be written to the linear combination of several polynomial functions；Model conversation can be that generalized linear model carrys out estimated state by this point Transition probability；Conventional method typically uses cubic B-spline, that is m=4, the present invention also use the method；
    (2) generalized linear models
    The nonhomogeneous state transition probability p changed over time can be calculated with B-spline methodj,k(s) parameter in model is reduced, But this method there is also some problems：First, it is impossible to ensure that all B-splines are always interior in section [0,1], this is just to meter The model for calculating probability makes troubles；In addition, if for some s,The p being now calculated by formula (5)jk (s) will not define；So a more accurate method is that original method is substituted using generalized linear model；Below will Selective analysis generalized linear model；
    In certain daily minute, occur to state k transfer or do not occur from state j, that is, each in diurnal periodicity At each moment s, state transfer quantity, which may be considered, obeys bi-distribution；That is njk~B (zj,pjk(s)), wherein in moment s Bernoulli Jacob's experiment number can basisCalculate, and pjk(s) it is unknown；Data can be returned with index Come back analysis, be converted into logarithm expression：
    <mrow> <mi>log</mi> <mi> </mi> <mi>i</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mfrac> <mi>p</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>p</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow>
    Unknown logarithm binomial probability ηjk(s) basic function B can be usedi,m(s) represent, i.e.,：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;eta;</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>C</mi> <mrow> <mi>j</mi> <mi>k</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>B</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>j</mi> <mi>k</mi> <mo>,</mo> <mi>M</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>B</mi> <mrow> <mi>M</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow>
    ηjk(s) linear predictor is：
    <mrow> <msub> <mover> <mi>&amp;eta;</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>C</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mi>k</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>B</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mover> <mi>C</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mi>k</mi> <mo>,</mo> <mi>M</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>B</mi> <mrow> <mi>M</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>
    Wherein estimateTried to achieve by weighted least-squares method iteration；
    It can invert to obtain with logarithmic function in the hope of being transferred to state k probability from state j now：
    <mrow> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&amp;eta;</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>exp</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&amp;eta;</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>
    The application program of generalized linear model is packaged as glm () in statistical analysis software R.
  8. 8. the hidden Markov model computational methods of description electric automobile during traveling behavior according to claim 1, its feature It is：In the step 006, selected on node：
    Select node τ quantity extremely important for establishing a suitable model with position, select the conventional method of node for Node is evenly distributed in the period of one day, but this method can not pick out pjk(s) spike, so proposing following New node selecting method：
    1) number of nodes, M are determined first；
    2) start node quantity, M are determinedinit＜ M, node are uniformly distributed in section, use τinitRepresent node；
    3) setting model and the likelihood probability of each node interval is calculated；
    4) two minimum adjacent nodes of likelihood probability are found, are set as { τj,τj+1}；
    5) in { τj,τj+1Centre position is put into a new node τ*；
    If 6) M*＜ M, then step 3 is skipped to, if M*=M then end loops；
    If the number of nodes M of selection is too small, if M number is too big, can preferentially may be used by increasing node come lift scheme It can occur that parameter is overflowed；So suggest calculating a variety of models as test, when the increase of M values to a certain extent, increasing then mould The improvement degree of type can be ignored, and select this value as number of nodes.
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