CN106096115B - A kind of crowd evacuation emulation method based on self-organizing sand ionization formula - Google Patents
A kind of crowd evacuation emulation method based on self-organizing sand ionization formula Download PDFInfo
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Abstract
The present invention relates to a kind of crowd evacuation emulation methods based on self-organizing sand ionization formula, the stability of crowd evacuation is obtained by establishing the dynamic 3 D self-organizing sand ionization formula emulation propagated towards crowd panic, this method includes the following steps: that evacuation individual 1) is mapped as the grains of sand, the dynamic 3 D self-organizing sand ionization formula that foundation is propagated towards crowd panic；2) crowd's unstability burst critical probability is determined according to sand avalanche scale；3) the current crowd's unstability average probability amount for seeking established dynamic 3 D self-organizing sand ionization formula is compared with the crowd's unstability burst critical probability determined in step 2), judges the state of the dynamic 3 D self-organizing sand ionization formula；4) crowd evacuation emulation verifying is carried out using dynamic 3 D self-organizing sand ionization formula of the crowd evacuation emulation software to foundation.Compared with prior art, the present invention has many advantages, such as that Consideration is comprehensive, accuracy is high, has scientific basis and with a high credibility.
Description
Technical field
The present invention relates to Simulation and Modeling Technology fields, more particularly, to a kind of crowd evacuation based on self-organizing sand ionization formula
Emulation mode.
Background technique
Currently, crowd evacuation stability study is still in infancy, usually by crowd evacuation model emulation or evacuation
It drills, and the crowd by emerging during observation crowd evacuation is overcrowding or tramples equal typical phenomenons to describe crowd
The stability of evacuation.The research method of crowd's emergency evacuation stability has the methods of crash analysis, evacuation drill and evacuation simulation.
Crash analysis method has convincingness, but because being influenced by the condition of a disaster (such as dense smoke), causes accident limited with image data.Evacuation
Manoeuvre has intuitive, but it is more difficult to study evacuation panic behavior, first is that because organizer itself fears to go out in evacuation drill
Existing safety accident, second is that because there is also larger differences for the psychology of personnel and behavior in evacuation participant and true accident.It is existing
Crowd evacuation simulation model is mostly the research focused in terms of crowd movement learns with dynamics, main to describe crowd evacuation behavior,
And analyze the pass of building evacuation element (stairs port and passageway for fire apparatus minimum widith etc.) and crowd's traffic capacity and evacuation time
System provides several contingency management strategies and suggestion that building prevention crowd tramples, but most existing model not yet system researches
The mechanism and evolutionary process of generation are trampled, is only taken in as the typical unstable phenomenon in existing evacuation model using trampling.
In recent years, fear is to crowd evacuation stability action during scholars' increasingly valuing researches evacuation, from fear
Propagation model angle carrys out study population's stability.But Psychological phobia have complexity, time variation and can not replicability, Er Qieren
It is one nonlinear that group's evacuation, which is developed again, non-structured and self-organizing complex process, especially to crowd in panic shape
Occur under state overcrowding and phenomenon is trampled, therefore, it is impossible to establish accurate mathematical model, made it difficult to classics
Lyapunov function analyzes its Instability and evolution mechanism.Therefore, researcher uses dynamic 3 D self-organizing sand drift mould
Type carrys out study population's stability.But the theoretical research is in the starting stage, and there are several deficiencies: micro-analysis is less, classical husky
The grains of sand space structure of heap model is complicated, and classical panic sand ionization formula of propagating lacks time variation, not yet formation strong operability
Analysis method.
Summary of the invention
The purpose of the present invention is providing regarding to the issue above, a kind of Consideration is comprehensive, accuracy is high, has scientific basis
And the crowd evacuation emulation method with a high credibility based on self-organizing sand ionization formula.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of crowd evacuation emulation method based on self-organizing sand ionization formula is moved by establishing towards what crowd panic was propagated
The emulation of state three-dimensional self-organizing sand ionization formula obtains the stability of crowd evacuation, and this method includes the following steps:
1) evacuation individual is mapped as the grains of sand, establishes the dynamic 3 D self-organizing sand ionization formula propagated towards crowd panic；
2) crowd's unstability burst critical probability is determined according to sand avalanche scale；
3) the current crowd's unstability average probability amount for seeking established dynamic 3 D self-organizing sand ionization formula, with step 2)
Crowd's unstability burst critical probability of middle determination is compared, and judges the state of the dynamic 3 D self-organizing sand ionization formula；
4) crowd evacuation emulation is carried out using dynamic 3 D self-organizing sand ionization formula of the crowd evacuation emulation software to foundation
Verifying.
The step 1) specifically:
11) sand grain shapes are determined: according to the individual statistics in physiologic factor and the key feature of social relationships factor of evacuation
With the quantized result of investigation and analysis, the key feature in physiologic factor and social factor is mapped to three Cartesian coordinates
On six space coordinate semiaxis, the rectangular pyramid grains of sand are formed, determine sand grain shapes；
12) it determines sand particle size: the evacuation individual for fleeing from outlet and while trampling being lost into locomitivity and information passes
The evacuation individual mapped sand particle size for broadcasting ability is denoted as 0, and the evacuation behavior of remaining evacuation individual is mapped as evacuation individual
Velocity vector and acceleration then calculate panic degree, and panic degree is mapped as sand particle size；
13) determine the grains of sand in the position in sand drift: according between the sand bed height and evacuation individual and extra exit of the grains of sand
The directly proportional principle of distance, determine position of the grains of sand in sand drift, specifically:
Li=Klround(die,2)
Wherein, LiFor the sand bed height of the grains of sand, KlIt is evacuation individual at a distance from extra exit, round is bracket function；
14) it determines sand drift ambient humidity: extracting disaster factors and space constraint, it is wet that sand drift is converted to by mapping function
Degree, specifically:
Hsand=CdisHdis+CarcHarc
Wherein, HsandFor sand drift ambient humidity, HarcFor space constraint radix, HdisFor disaster factors radix, CdisFor disaster
Factor, CarcFor space constraint.
It is described that panic degree is mapped as expression formula based on sand particle size are as follows:
fiw={ Ai exp[(ri-diw)/Bi]+kg(ri-diw)}niw-γg(ri-diw)(vi·tiw)tiw
Wherein, riFor the i.e. required sand particle size of diameter of i-th of evacuation individual, miTo evacuate Individual Quality,For reason
Think speed,For the direction of setting, viIt (t) is actual speed, τiIt is characterized time, fijFor the phase interaction between evacuation individual
Firmly, fiwFor evacuation individual and the interaction force between wall or isolation guardrail, Ai、BiFor constant, dijFor the matter of evacuation individual
Measure centre distance, rijFor the distance between two evacuation individuals, kg (rij-dij)nijWith kg (ri-diw)niwFor mass force,For the force of sliding friction between evacuation individual, γ g (ri-diw)(vi·tiw)tiwFor evacuation individual and wall
Or the force of sliding friction between isolation guardrail, k and γ are the blocking effect for determining the interaction between evacuation individual i and j
Parameter,It is the variable quantity of tangential velocity, diwIt is evacuation individual the distance between i and wall, niwRefer to Vertical Square
To tiwRefer to tangential direction, tijIt is nijTangential direction, nijIt is the standard vector that i is directed toward by evacuation individual j, function g (x) is fixed
Justice are as follows: if pedestrian impact, g (x)=0, otherwise g (x)=x.
The space constraint radix HarcExpression formula specifically:
Wherein, m=0,1,2,3,4 is each evacuation individual suffered general constraint during exercise, and n be the individual number of evacuation
Mesh, PkFor k type kinematic pair quantity, k=5,4,3,2,1 be the number of levels of kinematic pair.
The disaster factors radix HdisBased on expression formula are as follows:
Wherein, μDAWithRespectively DA and I0Membership function, DA be casualty loss degree, I0For for the strong of risk assessment
Angle value, subscript t are HdisSequence number, s is the serial number of i value, and i is the coordinate value in earthquake intensity, rstIt is the member in fuzzy relation matrix
Element, by I0Value is assigned on control point in the method that information is distributed to find out HdisValue, DA and I0Relationship are as follows:
DA=I0θR
Wherein, R is fuzzy relation matrix.
The step 2) specifically:
21) sand avalanche scale is calculated, specifically:
D (T)=AT-β
Wherein, A is sand avalanche scale, and D (T) is avalanche probability, and T is relaxation time, β=1.58 ± 0.15；
22) the sand avalanche scale according to required by step 21) determines crowd's unstability burst critical probability, specifically:
Qc=Ax-B
Wherein, QcFor crowd's unstability burst critical probability, x is that the i.e. evacuation individual of crowd size is total, and B is between 2.1 Hes
Positive real constant between 5.2.
The step 3) specifically:
31) P is measured in the mean field Hamilton for calculating dynamic 3 D self-organizing sand ionization formulai；
32) amount of the mean field Hamilton according to required by step 31) lists equilibrium condition；
33) it is acquired according to the equilibrium condition listed in the mean field Hamilton amount and step 32) in step 31) and works as forefathers
Group's unstability average probability amount Q；
34) comparison step 33) in current crowd's unstability average probability amount Q for acquiring and the crowd's unstability acquired in step 2)
Happen suddenly critical probability Qc, as Q < QcWhen, dynamic 3 D self-organizing sand ionization formula is in stable state；Work as Q=QcWhen, dynamic 3 D
Self-organizing sand ionization formula is in critical state；As Q > QcWhen, sand avalanche occurs for dynamic 3 D self-organizing sand ionization formula.
Measure P in the mean field HamiltoniSpecifically:
Wherein, i=0,1,2,3,0,1 is nonexcitation state, and 2,3 be excitation state, fijIt is mutual between two evacuation individuals
Active force, miTo evacuate Individual Quality,For vector, u is evacuation individual state.
The equilibrium condition specifically:
P2(1-h)I2=P0[(1-μh)I+hI2+(1-h)μ2+2hμI]
P0[2(1-h)μI+hI2]+P2[2(1-h)μI+hI2]+P3[2(1-h)μI+hI2]=P1[(1-h)μ2+2hμI+2(1-
h)μI+2hI2]
P0[(1-h)μ2+2hμI]+P1[2(1-h)μI+hI2]=P2[(1-h)I2+2(1-h)μI+hI2]
P1[(1-h)μ2+ 2h μ I]=P3[(1-h)I2]
μ=P2+P3
I=P0+P1
Wherein, I represents the probability that crowd is in nonexcitation state, and μ represents crowd and is in excitation probability of state, and h is excitation
Probability.
It is described to acquire current crowd's unstability average probability amount Q specifically:
α=0 × P0+1×P1+2×P2+3×P3
4Q2α=0 Q-h+(1-2 α+2h)
Wherein, α is average probability amount.
Compared with prior art, crowd evacuation stability is analyzed using the method for the present invention, consider comprehensively it is related because
Element, accuracy is high, has scientific basis and carries out simulating, verifying, with a high credibility.Specifically, the present invention has below beneficial to effect
Fruit:
(1) it is directed to crowd's stability analysis, the non-homogeneous partial size dynamic sand ionization formula propagated towards fear is constructed, by crowd
The stability problem of evacuation is converted into the stability problem of sand ionization formula, is convenient for studying.
(2) in the sand ionization formula built, the shapes of the grains of sand, partial size, the feature of position and evacuation individual, panic degree and
Range direction to outlet corresponds, and has fully described physiology, psychology and the social factor difference of evacuation individual.
(3) environmental factors such as disaster are corresponded into sand drift humidity, directly affects the stiction between the grains of sand, supplement sand drift
The factor not yet considered in computation model and physical model has fully demonstrated the environmental characteristic of evacuation.
(4) in the sand ionization formula built, it is contemplated that individual panic degree size dynamic change is corresponded to grains of sand grain
The variate when dynamic of diameter has objectively reacted the mental difference of evacuation individual, and easily ensures sand by partial size time-varying characteristics
The inhomogeneities of grain partial size, meets the necessary condition of sand drift critical behaviour.
(5) the criticality feature of crowd's instability condition and sand drift is corresponding, the sand avalanche of initiation and the thorough unstability of crowd are opposite
It answers, with uniformity and completeness, provides scientific basis for network analysis crowd's instability Mechanism.
(6) since Consideration is complete, thus can be by adjusting all kinds of evacuation scenario factors, the analysis crowd of system dredges
Dissipate stable condition, Instability and unstability evolution mechanism.
(7) the panic degree after quantization is mapped as sand particle size, belongs to piecewise linear maps, method is simple and feasible.
(8) sand ionization formula that evacuation crowd panic can be clearly analyzed in sand ionization formula, which reaches, " stablizes-critical-sand
Collapse-new stablize " overall process of state, this is consistent with crowd's Instability feature.
(9) by the method for the invention can from the Large-sized Communication pivot building model data of city directly analysis and extraction loop
Border feature, data are comprehensively reliable, and method is simple and feasible.
(10) panic propagation model and stability analysis are verified with crowd evacuation emulation software in the method for the present invention as a result,
Emulator is high, and confidence level is big.
Detailed description of the invention
Fig. 1 is to consider the panic crowd's emergency evacuation stability study technical schematic diagram propagated；
Fig. 2 is Shanghai Hongqiao Integrative Transport Hub evacuation emulation trajectory diagram；
Fig. 3 is that Shanghai Hongqiao Integrative Transport Hub evacuates 3D simulating sports scene figure；
Wherein, 1 is evacuates individual physiology and social factor, and 2 is evacuate individual physiology, psychology and social factor, and 3 be evacuation
Individual physiology and social characteristic, 4 be evacuation individual behavior feature, and 5 be the three-dimensional grains of sand, 6 dynamics propagated for crowd evacuation fear
Three-dimensional self-organizing sand ionization formula, 7 be colony intelligence crowd evacuation model, and 8 be environmental factor, and 9 propagate self-organizing sand drift mould to be panic
Type, the 10 sand ionization formula critical behaviours propagated for crowd evacuation fear, 11 be crowd evacuation unstability evolution mechanism, and 12 dredge for emergency
Tread event preventive suggestions library is dissipated, 13 be Urban Transport Terminals personnel emergency evacuation analogue system.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention
Premised on implemented, the detailed implementation method and specific operation process are given, but protection scope of the present invention is not limited to
Following embodiments.
As shown in Figure 1, the present embodiment provides a kind of crowd evacuation emulation method based on self-organizing sand ionization formula, this method
By analyzing the individual physiology of evacuation, psychology and social factor, evacuation individual behavior feature is obtained, to establish the consideration heart
The panic dynamic 3 D self-organizing sand ionization formula propagated of reason, the critical behaviour for the sand ionization formula that study population's fear is propagated, thus
The stability of the dynamic 3 D self-organizing sand ionization formula of foundation is analyzed.This method includes the following steps:
(1) dynamic 3 D self-organizing sand ionization formula is established, specifically:
(11) determine sand grain shapes: research evacuation Feature Mapping relationship is closed according to evacuation individual in physiologic factor and society
Be the statistics of the key feature of factor and the quantized result of investigation and analysis, by physiologic factor age, gender, disability degree,
The key features such as the strange degree in agility, weight and social factor are respectively mapped to six skies of three Cartesian coordinates
Between on coordinate semiaxis, form the rectangular pyramid grains of sand, thereby determine that the shape of the grains of sand.
(12) it determines sand particle size: choosing the various evacuations that evacuation individual mind, physiology and social factor are emerged
Behavior, the integrated velocity vector and acceleration for being presented as evacuation individual.According to Helbing, D. fear " psychology-behavior "
Volatility model considers that guidance calms to fear from individual tensity and velocity variations retrospectively calculate its panic degree is evacuated
Effect, reduces the active force between pedestrian, so that fear degree reduces；And panic degree is mapped as sand particle size, determine the grains of sand
Partial size.Panic degree may be expressed as:
Wherein, miIt is pedestrian's mass,It is ideal velocity,It is the direction of setting, viIt (t) is actual speed, τi
It is characteristic time, fijIt is the interaction force between pedestrian and pedestrian, fiwIt is the phase interaction between pedestrian and wall or isolation guardrail
Firmly,
fiw={ Ai exp[(ri-diw)/Bi]+kg(ri-diw)}niw-γg(ri-diw)(vi·tiw)tiw (3)
Ai、BiFor constant, dijMass centre's distance of pedestrian, rijThe distance between two pedestrians, kg (rij-dij)nijFor matter
It measures one's own ability,To slide frictional force, riThe diameter of i-th of pedestrian, parameter k and γ are determined between pedestrian i and j
Active blocking effect of meeting,It is the variable quantity of tangential velocity, diwIt is between evacuation individual i and wall
Distance, niwRefer to vertical direction, tiwRefer to tangential direction, tijIt is nijTangential direction, nijIt is that i is directed toward by evacuation individual j
Standard vector, function g (x) is defined as: if pedestrian impact, g (x)=0, otherwise g (x)=x.
(13) positioning of the grains of sand in sand drift: according to the sand bed height and its of the corresponding grains of sand of evacuation individual from extra exit
Directly proportional principle is answered apart from size, particles spatial is distributed in crowd's model to determine, determines position of the grains of sand in sand drift.It can
It indicates are as follows:
Li=Klround(die,2) (4)
Wherein, LiFor sand bed height, KlIt is individual with a distance from extra exit, KlFor bracket function.
(14) it determines the ambient humidity of sand drift: exporting the mould of the typical disasters such as fire and toxic gas leakage from hazard model library
Type data extract disaster to the key influence factor of evacuation；Relevant building is evacuated in export from building model library
Space-filling model data extract space constraint (exit width and wall locations etc.) to the key influence factor of evacuation.By calamity
Noxa element and space constraint are converted into sand drift humidity by mapping function.It may be expressed as:
Hsand=CdisHdis+CarcHarc (5)
Wherein, HsandFor sand drift humidity, HarcFor space constraint radix, HdisFor disaster factors radix, CdisFor disaster because
Element, CarcFor space constraint.Definition rule θ are as follows:
I in formula0It is the earthquake intensity value for risk assessment, subscript t is (Hdis) sequence number, s is the serial number of i value, and i is strong
Coordinate value on degree, rstIt is the element in fuzzy relation matrix.μDAWithRespectively DA and I0Membership function, wherein DA is
Casualty loss degree, I0It is the earthquake intensity value for risk assessment, using inference formula:
DA=I0θR (7)
By the I of risk analysis0On the control point that value is assigned in the method that information is distributed, H is finally found outdisValue.According to
Constraint theory can obtain HarcFormula:
Wherein, m is each individual suffered general constraint (m=0,1,2,3,4) during exercise, and n is evacuation individual amount,
PkFor k type kinematic pair quantity, k is the number of levels (k=5,4,3,2,1) of kinematic pair.
Will evacuation individual it is corresponding with the grains of sand, evacuation individual physiology, society and the panic characteristics for pouring into outlet be mapped as falling to
The grains of sand of sand drift, fleeing from sand particle size corresponding to the evacuation individual of outlet is zero, i.e., disappears from sand drift；If it happens it steps on
It steps on, the corresponding sand of evacuation individual (severely injured or the dead in such as tread event) of loss of athletic ability and information propagation capabilities
Grain partial size is also zero, this is just to analyze panic " stabilization-critical-sand avalanche-is newly stablized " evolutionary process providing method for propagating sand drift
Support, by determining the crowd panic mapping network model established in sand particle size, obtain crowd panic propagation finite dimensional,
The dynamic 3 D self-organizing sand ionization formula of non-homogeneous partial size.
(2) critical behaviour for the dynamic 3 D self-organizing sand ionization formula that study population's fear is propagated: sand avalanche scale A is calculated
(such as 1 × 107), the power rate relationship of the burst probability and scale of crowd's unstability is provided, the burst probability for group unstability of asking for help can indicate
For
Qc=Ax-B (9)
Wherein QcFor the burst probability of crowd's unstability, x is scale (crowd), and B is positive real constant (between 2.1-5.2)；It adopts
With the mean field analysis method of sand ionization formula, the G-bar of sand drift is defined as " the thermodynamics drive volume " of broad sense, from probability
Angle lists the kinetics and kinematical equation that sand flows at all kinds of lattice points, sends out from panic sand ionization formula is macroscopically analyzed
Raw first order phase change (discontinuous phase transition) the i.e. mean field value of sand avalanche (seeing below Q value) can be measured with mean field Hamilton to indicate:
Wherein, fijFor the interaction force between two individuals, miFor some Individual Quality, i and j are respectively i-th
Body and j-th of individual,WithFor vector, the state for evacuating individual is u.
(3) analyze crowd evacuation Instability evolution mechanism: crowd (is stepped on after a period of time after tread event occurs
Event is stepped on to occur to the traffic capacity to restore), it can develop to self-organizing to a new stable state, sand ionization formula is pushed " stablize-to face
Boundary-sand avalanche-is newly stablized " evolutionary process.I represents crowd's status and is in nonexcitation state (probability), and μ represents crowd's status and is in excitation
State (probability), 0,1 is nonexcitation state, and 2,3 be excitation state.Since each excitation state transits to the probability P of nonexcitation stateoutIt is equal to
The probability P of excitation state is transitted to from nonexcitation statein, it is as follows:
Pout=Pin (16)
Equilibrium condition is listed respectively for 0,1,2,3 4 states:
P2(1-h)I2=P0[(1-μh)I+hI2+(1-h)μ2+2hμI] (17)
P0[2(1-h)μI+hI2]+P2[2(1-h)μI+hI2]+P3[2(1-h)μI+hI2]=P1[(1-h)μ2+2hμI+2(1-
h)μI+2hI2] (18)
P0[(1-h)μ2+2hμI]+P1[2(1-h)μI+hI2]=P2[(1-h)I2+2(1-h)μI+hI2] (19)
P1[(1-h)μ2+ 2h μ I]=P3[(1-h)I2] (20)
μ=P2+P3 (21)
I=P0+P1 (22)
The value of h is obtained by above-mentioned formula, h is the probability of excitation.Average probability amount α at each lattice point is
α=0 × P0+1×P1+2×P2+3×P3 (23)
α and h value is substituted into following formula,
4Q2+ (1-2 α+2h) α=0 Q-h (24)
To obtained Q value and QcValue is compared: when Q reaches critical probability amount QcBefore, entire sand drift, which is in, stablizes shape
State；Work as Q=Qc, sand drift is in critical state；When Q is more than critical probability amount Qc, there is sand avalanche phenomenon.
(4) verify and optimize the dynamic 3 D self-organizing sand ionization formula that crowd panic is propagated: from tread event data bank
Export history evacuation data simultaneously carry out Comparative result, to verify the sand ionization formula of evacuation stability, and can be from model structure and mould
The constructed crowd evacuation stability sand ionization formula of two aspect optimizations of shape parameter.
Shanghai Hongqiao Integrative Transport Hub is one of the comprehensive transportation hub of scale the biggest in the world, and simulation Hongqiao in Shanghai is comprehensive
The crowd evacuation situation of transport hub has certain representativeness, therefore verifies by taking Hongqiao in Shanghai as an example above-mentioned husky based on self-organizing
The crowd evacuation emulation method of heap model, as shown in Figures 2 and 3.
By extracting Shanghai Hongqiao Integrative Transport Hub construction example data, analysis and extraction environmental characteristic, Shanghai is established
Hongqiao Integrative Transport Hub buildings model simulates the truth at scene.Firstly, establishing the finite dimension of crowd panic propagation
The dynamic 3 D self-organizing sand ionization formula of degree, non-homogeneous partial size, wherein the weight m of pedestriani=80kg,Simple gate
Width is 2.0m, τ=0.5s, Ai=2 × 103N, Bi=0.08m, k=1.2105kgs-2, γ=2.4105kgm-1s-1It can be with
Obtain riIt is 0.6.Then, it calculates the burst probability of crowd's unstability and the power rate relationship of scale finds out the burst probability of crowd's unstability
P0=0.08, P1=0.15, P2=0.23, P3=0.28, average probability amount Q=1.45 is calculated, average probability amount Q is less than at this time
Critical probability amount Qc, state of the crowd in safety.Finally, it is imitative to carry out crowd evacuation on computers using known data
Very, Shanghai Hongqiao Integrative Transport Hub evacuation emulation track is obtained.Wherein, dispersed site is that 12m magnetic floats Transfer Hall, shares 15
A extra exit, number of evacuation are that 2109 people (can be calculated 723 people of man, woman according to State Statistics Bureau's population ratio data
686 people, 131 people of 348 people of children, 221 people of old man and physical disabilities), evacuation time be 7 points 3 seconds, verify the crowd evacuation stablize
Property analysis method is feasible, easy-operating.
Claims (9)
1. a kind of crowd evacuation emulation method based on self-organizing sand ionization formula, by establishing the dynamic propagated towards crowd panic
Three-dimensional self-organizing sand ionization formula emulation obtains the stability of crowd evacuation, which is characterized in that this method includes the following steps:
1) evacuation individual is mapped as the grains of sand, establishes the dynamic 3 D self-organizing sand ionization formula propagated towards crowd panic, specifically
Are as follows:
11) sand grain shapes are determined: according to the individual statistics and tune in physiologic factor and the key feature of social relationships factor of evacuation
Key feature in physiologic factor and social factor is mapped to six of three Cartesian coordinates by the quantized result for grinding analysis
On space coordinate semiaxis, the rectangular pyramid grains of sand are formed, determine sand grain shapes；
12) it determines sand particle size: the evacuation individual for fleeing from outlet and while trampling being lost into locomitivity and information propagates energy
The evacuation individual mapped sand particle size of power is denoted as 0, and the evacuation behavior of remaining evacuation individual is mapped as to the speed of evacuation individual
Degree vector sum acceleration then calculates panic degree, and panic degree is mapped as sand particle size；
13) determine the grains of sand in the position in sand drift: according to the grains of sand sand bed height and evacuation individual and extra exit between away from
From directly proportional principle, position of the grains of sand in sand drift is determined, specifically:
Li=Klround(die,2)
Wherein, LiFor the sand bed height of the grains of sand, KlIt is evacuation individual at a distance from extra exit, round is bracket function；
14) it determines sand drift ambient humidity: extracting disaster factors and space constraint, sand drift humidity is converted to by mapping function, have
Body are as follows:
Hsand=CdisHdis+CarcHarc
Wherein, HsandFor sand drift ambient humidity, HarcFor space constraint radix, HdisFor disaster factors radix, CdisFor disaster factors,
CarcFor space constraint；
2) crowd's unstability burst critical probability is determined according to sand avalanche scale；
3) the current crowd's unstability average probability amount for seeking established dynamic 3 D self-organizing sand ionization formula, in step 2) really
Fixed crowd's unstability burst critical probability is compared, and judges the state of the dynamic 3 D self-organizing sand ionization formula；
4) crowd evacuation emulation verifying is carried out using dynamic 3 D self-organizing sand ionization formula of the crowd evacuation emulation software to foundation.
2. the crowd evacuation emulation method according to claim 1 based on self-organizing sand ionization formula, which is characterized in that described
Panic degree is mapped as expression formula based on sand particle size are as follows:
fiw={ Aiexp[(ri-diw)/Bi]+kg(ri-diw)}niw-γg(ri-diw)(vi·tiw)tiw
Wherein, riFor the i.e. required sand particle size of diameter of i-th of evacuation individual, miTo evacuate Individual Quality,For ideal speed
Degree,For the direction of setting, viIt (t) is actual speed, τiIt is characterized time, fijFor the interaction between evacuation individual
Power, fiwFor evacuation individual and the interaction force between wall or isolation guardrail, Ai、BiFor constant, dijFor the quality of evacuation individual
Centre distance, rijFor the distance between two evacuation individuals, kg (rij-dij)nijWith kg (ri-diw)niwFor mass force,For the force of sliding friction between evacuation individual, γ g (ri-diw)(vi·tiw)tiwFor evacuation individual with wall or
Force of sliding friction between isolation guardrail, k and γ are the ginseng for determining the blocking effect of the interaction between evacuation individual i and j
Number,It is the variable quantity of tangential velocity, diwIt is evacuation individual the distance between i and wall, niwRefer to vertical direction,
tiwRefer to tangential direction, tijIt is nijTangential direction, nijIt is the standard vector that i is directed toward by evacuation individual j, function g (x) definition
If are as follows: pedestrian impact, g (x)=0, otherwise g (x)=x.
3. the crowd evacuation emulation method according to claim 1 based on self-organizing sand ionization formula, which is characterized in that described
Space constraint radix HarcExpression formula specifically:
Wherein, m=0,1,2,3,4 is each evacuation individual suffered general constraint during exercise, and n be the individual number of evacuation, Pk
For k type kinematic pair quantity, k=5,4,3,2,1 be the number of levels of kinematic pair.
4. the crowd evacuation emulation method according to claim 1 based on self-organizing sand ionization formula, which is characterized in that described
Disaster factors radix HdisBased on expression formula are as follows:
Wherein, μDAWithRespectively DA and I0Membership function, DA be casualty loss degree, I0For the earthquake intensity for risk assessment
Value, subscript t is HdisSequence number, s is the serial number of i value, and i is the coordinate value in earthquake intensity, rstIt is the member in fuzzy relation matrix
Element, by I0Value is assigned on control point in the method that information is distributed to find out HdisValue, DA and I0Relationship are as follows:
DA=I0θR
Wherein, R is fuzzy relation matrix, θ, that is, disaster factors radix HdisBased on expression formula.
5. the crowd evacuation emulation method according to claim 1 based on self-organizing sand ionization formula, which is characterized in that described
Step 2) specifically:
21) sand avalanche scale is calculated, specifically:
D (T)=AT-β
Wherein, A is sand avalanche scale, and D (T) is avalanche probability, and T is relaxation time, β=1.58 ± 0.15；
22) the sand avalanche scale according to required by step 21) determines crowd's unstability burst critical probability, specifically:
Qc=Ax-B
Wherein, QcFor crowd's unstability happen suddenly critical probability, x be crowd size i.e. evacuate individual sum, B be between 2.1 and 5.2 it
Between positive real constant.
6. the crowd evacuation emulation method according to claim 1 based on self-organizing sand ionization formula, which is characterized in that described
Step 3) specifically:
31) P is measured in the mean field Hamilton for calculating dynamic 3 D self-organizing sand ionization formulai；
32) amount of the mean field Hamilton according to required by step 31) lists equilibrium condition；
33) current crowd is acquired according to the equilibrium condition listed in the mean field Hamilton amount and step 32) in step 31) to lose
Steady average probability amount Q；
34) comparison step 33) in current crowd's unstability average probability amount Q for acquiring and the crowd's unstability acquired in step 2) burst
Critical probability Qc, as Q < QcWhen, dynamic 3 D self-organizing sand ionization formula is in stable state；Work as Q=QcWhen, dynamic 3 D is from group
It knits sand ionization formula and is in critical state；As Q > QcWhen, sand avalanche occurs for dynamic 3 D self-organizing sand ionization formula.
7. the crowd evacuation emulation method according to claim 6 based on self-organizing sand ionization formula, which is characterized in that described
Measure P in mean field HamiltoniSpecifically:
Wherein, i=0,1,2,3,0,1 is nonexcitation state, and 2,3 be excitation state, fijFor the interaction between two evacuation individuals
Power, miTo evacuate Individual Quality,For vector, u is evacuation individual state.
8. the crowd evacuation emulation method according to claim 7 based on self-organizing sand ionization formula, which is characterized in that described
Equilibrium condition specifically:
P2(1-h)I2=P0[(1-μh)I+hI2+(1-h)μ2+2hμI]
P0[2(1-h)μI+hI2]+P2[2(1-h)μI+hI2]+P3[2(1-h)μI+hI2]=P1[(1-h)μ2+2hμI+2(1-h)μI
+2hI2]
P0[(1-h)μ2+2hμI]+P1[2(1-h)μI+hI2]=P2[(1-h)I2+2(1-h)μI+hI2]
P1[(1-h)μ2+ 2h μ I]=P3[(1-h)I2]
μ=P2+P3
I=P0+P1
Wherein, I represents the probability that crowd is in nonexcitation state, and μ represents crowd and is in excitation probability of state, and h is the probability of excitation.
9. the crowd evacuation emulation method according to claim 8 based on self-organizing sand ionization formula, which is characterized in that described
Acquire current crowd's unstability average probability amount Q specifically:
α=0 × P0+1×P1+2×P2+3×P3
4Q2α=0 Q-h+(1-2 α+2h)
Wherein, α is average probability amount.
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