CN101477657A - Personnel casualty probability prediction method for building fire disaster - Google Patents

Abstract

The invention discloses a method for forecasting the probability of casualties in a building fire. The method comprises the following steps: firstly, analyzing a possible fire scenario, and then, analyzing the appearance probability of the fire scenario with the time development of the fire; secondly, establishing a stochastic distribution function of the approaching time of the fire dangerous state and a stochastic distribution function of evacuation time, calculating to obtain the possible casualties caused by each fire scenario by comparing the relation between the two stochastic distribution time functions, and forecasting the probability of the casualties in the building fire according to possible casualties caused by each fire scenario. As more uncertain factors, stochastic factors, the characteristics of the building and the effect of fire prevention and extinguishing measures are considered in a fire risk assessment, the invention has the advantage that the probability of casualties in a fire of different functional buildings under different fire-fighting equipment can be forecast.

Description

The Forecasting Methodology of building fire personnel casualty probability

Technical field

The present invention relates to casualties risk analysis technology in a kind of building fire, relate in particular to a kind of Forecasting Methodology of building fire personnel casualty probability.

Background technology

Some superelevation, super large, futuramic building be modern city hyperchromic in, increasingly serious fire safety evaluating problem is thereupon also arranged.Simple existing " prescription formula " design specifications that relies on of fire prevention design during these are built can't solve, can only rely on the Performance-based Fire Protection Design method, and the fire risk assessment then is ten minutes the key link in the Performance-based Fire Protection Design process.Have only and carry out the fire risk assessment rationally, exactly, Performance-based Fire Protection Design just can reach the set goal.

As shown in Figure 1, ASET (Available Safety Egress Time, available safe escape time) and RSET (Required Safety Egress Time, essential safe escape time) timeline fire risk assessment synoptic diagram.In casualties calculated risk assessment in the building fire, a basic criterion is exactly the magnitude relationship of comparison fire hazard state arriving time and evacuating personnel time, promptly ASET and RSET is compared.If personnel failed total evacuation to the safety zone before fire arrives precarious position, remaining number is the number of casualties that may cause in buildings this moment under current fire scenario so.

In the prior art,, be mostly to determine that by the magnitude relationship of more required safe escape time RSET and available safe escape time ASET can personnel escape to the safety zone about the method and the model of evacuating personnel under the fire hazard environment and venture analysis.Correlation parameter in evacuating personnel and the fire development process all is taken as definite value.

There is following shortcoming at least in above-mentioned prior art:

Uncertainty and randomness rule to fire do not have to consider substantially, can accurately not predict the probability of casualties under the fire hazard environment.

Summary of the invention

The Forecasting Methodology that the purpose of this invention is to provide a kind of building fire personnel casualty probability of the probability that can accurately predict casualties under the fire hazard environment.

The objective of the invention is to be achieved through the following technical solutions:

The Forecasting Methodology of building fire personnel casualty probability of the present invention comprises:

At first, set up a plurality of fire scenarios, each fire scenario is in fire development from the state of original state to the fire hazard state, and analyzes the probability that described fire scenario occurs in time, and described fire scenario comprises following at least one factor:

Whether the water spray successfully starts, whether detection is successful, whether personnel find whether fire, machine smoke evacuation system start;

Then, relatively each scene arrives the time and the required time of evacuating personnel of described fire hazard state respectively, and calculates the number of casualties that each fire scenario may cause;

Afterwards, according to the number of casualties that each fire scenario may cause down, prediction building fire personnel casualty probability.

As seen from the above technical solution provided by the invention, the Forecasting Methodology of building fire personnel casualty probability of the present invention, owing to set up a plurality of fire scenarios, its time dependent probability of occurrence is analyzed, and analyze the number of casualties that may cause under each fire scenario, predict the building fire personnel casualty probability.Uncertainty and randomness rule to fire are considered, can accurately predict casualties under the fire hazard environment.

Description of drawings

Fig. 1 is an ASET/RSET timeline fire risk assessment synoptic diagram of the prior art;

Fig. 2 is based on the event tree of fire-fighting measure and possible fire scenario synoptic diagram in the specific embodiments of the invention;

Fig. 3 is the state transitions synoptic diagram between corresponding each state of fire scenario in the specific embodiments of the invention;

Fig. 4 is a fire heat release rate curve synoptic diagram in the specific embodiments of the invention;

Fig. 5 is evacuation time and the probability distribution synoptic diagram of fire hazard state arriving time in the specific embodiments of the invention.

Embodiment

The Forecasting Methodology of building fire personnel casualty probability of the present invention, its preferable embodiment is:

At first, set up a plurality of fire scenarios, each fire scenario is in fire development from the state of original state to the fire hazard state, and analyzes the probability that described fire scenario occurs in time, and described fire scenario comprises following at least one factor:

Whether the water spray successfully starts, whether detection is successful, whether personnel find whether fire, machine smoke evacuation system start;

Then, relatively each scene arrives the time and the required time of evacuating personnel of described fire hazard state respectively, and calculates the number of casualties that each fire scenario may cause;

Afterwards, according to the number of casualties that each fire scenario may cause down, prediction building fire personnel casualty probability.

When the probability that the described fire scenario of analysis occurs in time, comprising:

At first, set up described fire scenario from the probability matrix of current state to other state transitions:

$P=\left(\begin{array}{cccc}{P}_{00}& P_{01}& \·\·\·& P_{09}\\ P_{10}& P_{11}& \·\·\·& P_{19}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ P_{90}& P_{91}& \·\·\·& P_{99}\end{array}\right)---\left(4\right)$

In the matrix, P _IjFor described fire scenario from the transition probability of state i to state j, work as P _Ij=0 o'clock, expression state i did not shift to state j; Work as P _Ij0 o'clock, expression existence i is to the transfer process of state j, i, j=1～9;

Afterwards, according to the different probability that constantly occur of each fire scenario of described matrix analysis at fire development.

Can set up the fire hazard state probability distribution function of arriving time:

$f\left(t_c\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_{\ln t_c}{t}_c}\exp [-\frac{{(\ln t_c-{\mathrm{\μ}}_{\ln t_c})}^2}{2{{\mathrm{\σ}}_{\ln t_c}}^2}]---\left(16\right)$

In the formula, t _cFor the fire hazard state arrives the time; F (t _c) mean value and variance be:

${\mathrm{\μ}}_{t_c}=\exp ({\mathrm{\μ}}_{\ln t_c}+\frac{1}{2}{\mathrm{\σ}}_{\ln t_c}^2)---\left(17\right)$

${\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="t\; c"\; filenames="A200910077913E00172.png"\; state="\{\{state\}\}">t</figure-callout>}}_c}^2=\exp ({\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="ln\; t\; c"\; filenames="A200910077913E00172.png"\; state="\{\{state\}\}">ln</figure-callout>}{t}_c{}_{}}^2+2{\mathrm{\&mu;}}_{\ln t_c})\&CenterDot;[\exp \left({\mathrm{\&sigma;}}_{\ln t_c}^2\right)-1]---\left(18\right)$

Can also set up the probability distribution function f (t of evacuating personnel time _e), it is a joint density function of considering that the fire detecting and alarm time probability distributes and evacuation setup time probability distribution obtains.

Wherein, evacuating the probability distribution function of setup time is:

$\begin{array}{cc}f\left(t_p\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_p}\exp [-\frac{{(t_p-{\mathrm{\&mu;}}_p)}^2}{2{{\mathrm{\&sigma;}}_p}^2}]& t_p>0\end{array}---\left(24\right)$

In the formula, f (t _p) for evacuating the probability distribution function of setup time; t _pFor evacuating setup time; μ _pFor evacuating the mean value of setup time; σ _pFor evacuating the standard deviation of setup time.

Afterwards, can calculate the number of casualties C that may cause under each fire scenario according to probability distribution function and the probability distribution function of described evacuating personnel time of described fire hazard state arriving time.

$C={\&Integral;}_0^{\&infin;}[(N\&CenterDot;{\&Integral;}_t^{\&infin;}f\left(t_e\right)\mathrm{dt})\&CenterDot;f\left(t_c\right)]\mathrm{dt}---\left(28\right)$

In the formula, N is the number in the buildings.

When calculating the building fire personnel casualty probability, the probability that can occur in time according to described fire scenario obtains constantly in i-1 and the i interval constantly the probability distribution vector P (S of described fire scenario _i)=(p (s _{I, 0}), p (s _{I, 1}) ..., p (s _{I, 9}));

And, obtain the number of casualties distribution vector C=(c that may cause under each fire scenario according to described fire hazard state arrive probability distribution function and the probability distribution function of described evacuating personnel time of time ₀, c ₁..., c _j) ^T

Afterwards, calculating described building fire personnel casualty probability is:

$\mathrm{Risk}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_i\&CenterDot;C_i---\left(32\right)$

Can also be according to described building fire personnel casualty probability, obtain construction personnel injures and deaths calculated risk probability and be:

$P_{\mathrm{fire}-\mathrm{life}}=\frac{P_{\mathrm{if}}\&CenterDot;\mathrm{Risk}\&CenterDot;A_f}{N}---\left(33\right)$

In the formula, P _IfBe the frequency of buildings breaking out of fire, 1/ (m ²Year); A _fBe the floor area of buildings, m ²

The present invention is based on fire dynamics, in the fire risk assessment, the feature of more uncertain and random factor and buildings and the influence of fire-fighting measure have been considered, calculate in conjunction with evacuating personnel, proposed the evaluation measures of the forecasting risk that fire causes personnel.By comparing fire hazard state arriving time and evacuating personnel time relation, calculate the number of casualties that each fire scenario may cause.Can predict the fire personnel casualty probability of difference in functionality building under the different preventing fire-fighting equipment.

The fire scenario and the time dependent probability of occurrence analytical approach thereof that comprise coupling fire dynamics and the anti-fire-fighting equipment usefulness of building; Consider the probability density function analytical approach of the fire hazard state arriving time of fire growth coefficient stochastic distribution rule; Consider the evacuation time probability density function analytical approach of evacuating personnel setup time stochastic distribution rule; And consider that difference in functionality builds the computing method etc. of the building fire personnel casualty probability of frequency on fire.

Below the specific embodiment of the present invention is carried out detail analysis:

1, the probability analysis method of fire scenario appearance

1.1, the fire scenario that may cause

When appraiser's expection fire risk, need to consider to influence the correlative factor of fire development and smoke movement.Except combustible characteristic and architectural environment, the reliability and the validity of the fire-fighting measure work in the buildings also are crucial influence factors.Fire-fighting measure will have influence on the consequence that fire development and flue gas spread, and then causes different fire scenarios.For example, fire alarm can be by the signal enabling of water spray action feedback, also can be linked by smoke detector or personnel manual.If water spray or smoke detector operate as normal, fire alarm just can send information automatically.If water spray or smoke detector break down, so just can only rely on personnel manually to carry out fire alarm.Generally speaking, influencing the main fire-fighting measure that fire development and flue gas spread has: water spray, detection, personnel find fire, mechanical smoke extraction etc. automatically.The fire scenario that may cause can obtain by the method for ETA.

As shown in Figure 2, be the specific embodiment of ETA.

1.2, time dependent fire scenario probability of occurrence

In the event tree as shown in Figure 2, the startup of each fire-fighting measure (effectively) probability is to change the time with fire development, so the probability that each fire scenario occurs is also along with the fire development time changes.In addition, for the prediction of personnel's fire injures and deaths, mainly be that comparison evacuating personnel and fire smoke spread the relation that changes along with the time, if the evacuating personnel time arrives the time less than the fire hazard state, personnel can safe escape so.If the evacuating personnel time arrives the time greater than the fire hazard state, in precarious position arrives, still there are some of the staff to fail escape so to the safety zone, escape personnel's threat that just may be subjected to fire does not cause injured even dead like this.Therefore, when analyzing each fire scenario probability of happening, its situation about changing of necessary consideration with the fire development time.

Each fire scenario can carry out stochastic analysis according to the method for Markov chain in difference variation constantly.Suppose that the fire development time is divided into n constantly, each the time be carved with j state, the state vector of so arbitrary moment i can be expressed as

S _i＝(s _i，0，s _i，1，...，s _i，j)，i＝1，2，...，n (1)

Because what the casualties risk profile was concerned about is each state probability at any time, the probability vector at moment i can be expressed as so

P(S _i)＝(p(s _i，0)，p(s _i，1)，...，p(s _i，j)) (2)

According to the character of discrete time Markov chain, can calculate by probability vector and the transition matrix of moment i in the probability vector of moment i+1

P(S _i+1)＝P(S _i)×P _i+1 (3)

In the formula, P _I+1Be i+1 transition matrix constantly.

Specific to the assessment of casualties calculated risk, the fire development time can be divided into some discrete moment, and state then can be divided according to fire scenario, and the corresponding relation of fire scenario and state as shown in Figure 2.

When fire takes place, because all fire-fighting measures all are not activated work in the buildings, and the incident that influences of fire scenario 10 correspondences is the failures of water spray, the detection failure, personnel find the fire failure, can think that fire scenario 10 pairing fire-fighting measures all do not have action, so the original state when fire scenario 10 taken place as fire.

As shown in Figure 3, the relation based between event tree shown in Figure 2 and each fire scenario can obtain the state transition diagram between each state.

In event tree shown in Figure 2, fire-fighting measure is implemented successful each state 9,7,4,2, promptly fire scenario 1,3, and the state of 6,8 correspondences is the last current state of this analysis process as absorbing state.Owing to be absorbing state, other states just might shift to them so.Original state 0 might be to other any one state transitions.Three kinds of transfer scenario all might appear in each state: the transfer of (1) oneself state; (2) from the transfer of other states; (3) be sent to the transfer of other states.For first kind of transfer scenario, think that here the state of each fire scenario correspondence all exists.For back two kinds of transfer scenario, total rule is the state transitions of the corresponding state of fire-fighting measure failure to fire-fighting measure success correspondence, but also needs to determine according to the practical situation of event tree correspondence.

Based on state transition diagram shown in Figure 3, can obtain transition probability matrix:

$P=\left(\begin{array}{cccc}{P}_{00}& P_{01}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{09}\\ P_{10}& P_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{19}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ P_{90}& P_{91}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{99}\end{array}\right)---\left(4\right)$

In the formula, P _IjBe the transition probability of state i to state j.Work as P _Ij=0 o'clock, expression state i did not shift to state j; Work as P _Ij0 o'clock, expression existence i is to the transfer process of state j.State i is that the i of formula (4) transition probability matrix is capable to the probability of other state transitions among Fig. 3.

2, the probability distribution function f (t of fire hazard state arriving time _c)

In fire casualties risk profile, have only and comparatively scientifically set fire and choose the suitable time dependent curve of fire HRR, just might obtain rational fire hazard state and arrive the time, and then obtain the desired value of rational casualties risk.Related fire is a kind of artificial hypothesis in the fire risk assessment, but hypothesis is reasonable more, and the resulting result of analog computation who carries out according to it is just true more.Usually describe the fire development situation with the HRR of fire, HRR is determined the situation more complicated by many factors such as the quantity delivered of the chemical energy of combustible, geometry state, air and architectural environments.For the fire risk assessment that personnel face, what we were concerned about only is that fire development arrived personnel escape's time required to the safety zone in adventurous time of people's life and the buildings.

The HRR of fire initial stage is pressed t substantially ²Rule increases:

Q＝αt ² (5)

In the formula, α is fire growth coefficient (kW/s ²); T is the time (s) after lighting a fire.Initial stage of fire increase can be divided at a slow speed, middling speed, quick, supper-fast etc. four types, corresponding fire growth coefficient Q is followed successively by 0.002931,0.01127,0.04689,0.1878.The value of α obtains when 600s, 300s, 150s and 75s reach 1055kW respectively according to the burning things which may cause a fire disaster HRR.

As shown in Figure 4, be fire heat release rate curve synoptic diagram.

During risk that the prediction fire causes personnel, the deviation that the fire growth coefficient is chosen probably causes personnel to face the difference of fire risk value, therefore, in the fire risk evaluation process, the uncertainty of necessary consideration fire growth coefficient.Holborn et al. shows by a large amount of fire data statisticses, fire growth coefficient obeys logarithm normal distribution.

Because the assessment of personnel's fire risk is mainly towards some large public buildings, and these buildings mostly are the volumed space building structure, are example with large space type building here, analyze the fire hazard state randomness of arriving time.Naturally fill under the smoke condition, the burning things which may cause a fire disaster initial stage is t ²When rule increases, fill accounting equation based on the flue gas of regional model thought and be:

$Z={[0.075{\left(\frac{\mathrm{\&alpha;g}}{{\mathrm{\&rho;}}_0{C}_p{T}_0{A}^3}\right)}^{\frac{1}{3}}{t}^{\frac{5}{3}}+H^{-\frac{2}{3}}]}^{-\frac{3}{2}}---\left(6\right)$

In the formula, Z is the height (m) of flue gas layer lower surface apart from ground; G is acceleration of gravity (m/s ²); ρ ₀Density (kg/m for surrounding air ³); C _PSpecific heat at constant pressure (kJ/ (kgK)) for air; T ₀Temperature (K) for surrounding air; A is floor area (m ²); T is a fire initial stage development time (s); H is room height (m).

Formula (6) can be converted into

$Z^{-\frac{2}{3}}-H^{-\frac{2}{3}}=0.075{\left(\frac{g}{{\mathrm{\&rho;}}_0{C}_p{T}_0{A}^3}\right)}^{\frac{1}{3}}{\mathrm{\&alpha;}}^{\frac{1}{3}}{t}^{\frac{5}{3}}---\left(7\right)$

During hot flue gas layer is reduced to human body directly contacts height, promptly the flue gas layer interface is lower than the human eye feature height, is precarious position this moment and arrives constantly.The feature height of human eye is generally 1.2～1.8m, and the height of getting flue gas layer usually drops to 1.5m height, i.e. Z _c=1.5.

$\frac{{Z_c}^{-\frac{2}{3}}-H^{-\frac{2}{3}}}{0.075{\left(\frac{g}{{\mathrm{\&rho;}}_0{C}_p{T}_0{A}^3}\right)}^{\frac{1}{3}}}={\mathrm{\&alpha;}}^{\frac{1}{3}}{t_c}^{\frac{5}{3}}---\left(8\right)$

Wherein, t _cFor the fire hazard state arrives the time.

Order

$\frac{{Z_c}^{-\frac{2}{3}}-H^{-\frac{2}{3}}}{0.075{\left(\frac{g}{{\mathrm{\&rho;}}_0{C}_p{T}_0{A}^3}\right)}^{\frac{1}{3}}}=k_c,$ Under certain architectural environment, k is a constant, then has

$k_c={\mathrm{\&alpha;}}^{\frac{1}{3}}{t_c}^{\frac{5}{3}}---\left(9\right)$

Formula (9) both sides are taken from right logarithm and can be got,

$\ln t_c=-\frac{1}{5}\ln \mathrm{\&alpha;}+\frac{3}{5}\ln k_A---\left(10\right)$

Because fire growth factor alpha obeys logarithm normal distribution, ln α Normal Distribution so is by the character of normal distribution, lnt _cAlso Normal Distribution.If the mean value and the standard deviation of the fire growth factor alpha of obeys logarithm normal distribution are respectively μ _αWith σ _α, mean value and the standard deviation of normal distribution f (ln α) are respectively so

${\mathrm{\&mu;}}_{\ln \mathrm{\&alpha;}}=\ln \frac{{\mathrm{\&mu;}}_{\mathrm{\&alpha;}}}{\sqrt{1+\frac{{\mathrm{\&sigma;}}_{\mathrm{\&alpha;}}^2}{{\mathrm{\&mu;}}_{\mathrm{\&alpha;}}^2}}}---\left(11\right)$

${\mathrm{\&sigma;}}_{\ln \mathrm{\&alpha;}}=\sqrt{\ln (1+\frac{{\mathrm{\&sigma;}}_{\mathrm{\&alpha;}}^2}{{\mathrm{\&mu;}}_{\mathrm{\&alpha;}}^2})}---\left(13\right)$

According to the character of normal distribution, f (lnt _c) functional expression and mean value and standard deviation be respectively

$f\left(\ln t_c\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_{\ln t_c}}\exp [-\frac{{(\ln t_c-{\mathrm{\&mu;}}_{\ln t_c})}^2}{2{{\mathrm{\&sigma;}}_{\ln t_c}}^2}]---\left(13\right)$

${\mathrm{\&mu;}}_{\ln t_c}=-\frac{1}{5}\ln \frac{{\mathrm{\&mu;}}_{\mathrm{\&alpha;}}}{\sqrt{1+\frac{{\mathrm{\&sigma;}}_{\mathrm{\&alpha;}}^2}{{\mathrm{\&mu;}}_{\mathrm{\&alpha;}}^2}}}+\frac{3}{5}\ln k_A---\left(14\right)$

${\mathrm{\&sigma;}}_{\ln t_c}=\frac{1}{5}\sqrt{\ln (1+\frac{{\mathrm{\&sigma;}}_{\mathrm{\&alpha;}}^2}{{\mathrm{\&mu;}}_{\mathrm{\&alpha;}}^2})}---\left(15\right)$

By formula (13), can get f (t _c) obeys logarithm normal distribution, promptly fire development is to constituting dangerous marginal time obeys logarithm normal distribution to personnel's life, and its functional expression is

$f\left(t_c\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_{\ln t_c}{t}_c}\exp [-\frac{{(\ln t_c-{\mathrm{\&mu;}}_{\ln t_c})}^2}{2{{\mathrm{\&sigma;}}_{\ln t_c}}^2}]---\left(16\right)$

F (t _c) mean value and variance be

${\mathrm{\&mu;}}_{t_c}=\exp ({\mathrm{\&mu;}}_{\ln t_c}+\frac{1}{2}{\mathrm{\&sigma;}}_{\ln t_c}^2)---\left(17\right)$

${\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="t\; c"\; filenames="A200910077913E00172.png"\; state="\{\{state\}\}">t</figure-callout>}}_c}^2=\exp ({\mathrm{\&sigma;}}_{\ln t_c}^2+2{\mathrm{\&mu;}}_{\ln t_c})\&CenterDot;[\exp \left({\mathrm{\&sigma;}}_{\ln t_c}^2\right)-1]---\left(18\right)$

If get H=3.5m, g=9.8m/s ², ρ ₀=1.2kg/m ³, C _p=1kJ/kgK, T ₀=300K, A=500m ², k so _A=7286.8.

3, the random distribution function f (t of evacuating personnel required time _e)

3.1, the stochastic distribution of fire detecting and alarm time

Detection time and time of fire alarming mainly are subjected to the architectural environment in fire development initial stage dynamic characteristic, zone on fire and the influence of detection alarm device characteristic, can calculate and predict according to the characteristic of fire spread model and detection system.With the smoke fire detector is example, and engineering calculation often is deposited to the flue gas height room height time in response below 5%.Fire smoke height experimental formula has following some hypothesis: the ceiling area in (1) room, floor area and absolute altitude is identical everywhere;

(2) the fire initial stage is according to t ²Rule increases.

$Z={[0.075{\left(\frac{\mathrm{\&alpha;g}}{{\mathrm{\&rho;}}_0{C}_p{T}_0{A}^3}\right)}^{\frac{1}{3}}{t}^{\frac{5}{3}}+{H_r}^{-\frac{2}{3}}]}^{-\frac{3}{2}}---\left(19\right)$

Work as Z=0.95H _rThe time,

${\mathrm{\&alpha;}}^{\frac{1}{3}}{t_d}^{\frac{5}{3}}=\frac{{\left(0.95H_r\right)}^{-\frac{2}{3}}-{H_r}^{-\frac{2}{3}}}{0.075{\left(\frac{g}{{\mathrm{\&rho;}}_0{C}_p{T}_0{A_r}^3}\right)}^{\frac{1}{3}}}---\left(20\right)$

In the formula, t _dBe detection time (s); H _rBe stud (m); A _rBe room floor area (m ²).

Order

$k_d=\frac{{\left(0.95H_r\right)}^{-\frac{2}{3}}-{H_r}^{-\frac{2}{3}}}{0.075{\left(\frac{g}{{\mathrm{\&rho;}}_0{C}_p{T}_0{A_r}^3}\right)}^{\frac{1}{3}}},$ Right logarithm is taken from formula (20) two ends can be got:

$\ln t_d=-\frac{1}{5}\ln \mathrm{\&alpha;}+\frac{3}{5}\ln k_d---\left(21\right)$

By fire growth factor alpha obeys logarithm normal distribution as can be known, ln α Normal Distribution.For specific building scene, k _dBe constant, lnt _dAlso Normal Distribution.F (lnt _d) mean value and standard deviation be respectively

${\mathrm{\&mu;}}_{\ln t_d}=-\frac{1}{5}{\mathrm{\&mu;}}_{\ln \mathrm{\&alpha;}}+\frac{3}{5}\ln k_d---\left(22\right)$

${\mathrm{\&sigma;}}_{\ln t_d}=\frac{1}{5}{\mathrm{\&sigma;}}_{\ln \mathrm{\&alpha;}}---\left(23\right)$

3.2, evacuate the setup time stochastic distribution

Evacuating setup time is the crucial ingredient of evacuating personnel time, the data presentation that survey behind a lot of fire and the evacuation drill of failing to give notice in advance obtain, evacuate setup time and occupy suitable ratio in the time, and its value also can be greater than run duration sometimes at evacuating personnel.In addition, evacuate the human behavior of preparatory stage run duration is had fundamental influence.Evacuating setup time is made up of understanding time and reaction time two parts.The understanding time is after fire alarm or the prompting clearly of other fire, recognize the time that emergency conditioies such as fire occurred and begun to make a response to personnel, personnel's waking state in main and building type, the building is familiar with the factors such as degree, warning system type of buildings and is correlated with.Reaction time is after personnel recognize fire alarm or other promptings, to the time that beginning is moved to the fire exit.Personnel's behavior varies in this stage, as seeking burning things which may cause a fire disaster, attempting fire extinguishing; Notice or helping others are withdrawn; Report to the police to fire brigade, the request fire extinguishing is supported; Tidy up property, prepare to flee from; Directly flee the scene; Panic behavior occurs, can't independently take action or blindly comform etc.Forefathers' The experimental results shows, evacuates setup time for obeying the stochastic variable of probability distribution.

In order to obtain the rational more required safe escape time, evacuate setup time should be taken as probability distribution, as when getting normal distribution, its probability density function can be represented with following formula:

$\begin{array}{cc}f\left(t_p\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_p}\exp [-\frac{{(t_p-{\mathrm{\&mu;}}_p)}^2}{2{{\mathrm{\&sigma;}}_p}^2}]& t_p>0\end{array}---\left(24\right)$

In the formula, f (t _p) for evacuating the probability density function of setup time; t _pFor evacuating setup time; μ _pFor evacuating the mean value of setup time; σ _pFor evacuating the standard deviation of setup time.

3.3, the random distribution function of evacuating personnel required time

The evacuating personnel required time is detection time, evacuating personnel setup time and personnel movement time sum, i.e. t _e=t _p+ t _m+ t _dSo, the random distribution function f (t of evacuating personnel required time _e) be the joint density function of considering that the fire detecting and alarm time probability distributes and evacuation setup time probability distribution obtains.

4, the number of casualties that may cause under the single fire scenario

In traditional personnel's fire risk assessment, all do not consider fire hazard state arriving time and the randomness of evacuating personnel in the time.Fire detecting and alarm time, evacuating personnel setup time and fire hazard state arriving time all are thought of as definite value.Basic criterion of casualties calculated risk assessment is exactly the magnitude relationship of comparison fire hazard state arriving time and evacuating personnel time.As preceding shown in Figure 1.

By top analysis as can be known, because the fire growth coefficient is the stochastic variable of obeys logarithm normal distribution, fire detecting and alarm time t so _dBe lognormal distribution.Owing to evacuate the setup time Normal Distribution, so evacuation time (t _e=t _p+ t _m) also Normal Distribution and to value of right translation.Work as t _dObeys logarithm normal distribution, t _eNormal Distribution so just can obtain the probability density function f (t of total evacuation time _e).F (t _e) consider that just the joint density function that the fire detecting and alarm time probability distributes and evacuation setup time probability distribution obtains, concrete expression formula also need to determine according to actual conditions.

By the fire hazard state arrive the time the randomness analysis as can be known, under the situation of the fire growth coefficient of lognormal distribution, the fire hazard state arriving time is the stochastic variable of obeys logarithm normal distribution.So the fire hazard state arrive time and number of evacuation over time situation all can represent by probability density function.

As shown in Figure 5, be evacuation time in the specific embodiments of the invention and the probability distribution synoptic diagram of fire hazard state arriving time.

Among Fig. 5, f (t _e) be the probability density function of personnel's evacuation time, f (t _c) be the arrive probability density function of time of fire hazard state.If f is (t _e) and f (t _c) the probability density distribution curve of expression has lap, represents that so then the fire hazard critical conditions comes temporarily, still has some of the staff not escape to the safety zone in the buildings.

If during breaking out of fire, the number in the buildings is N.If t constantly arbitrarily, the fire hazard critical conditions is arrived, and is so at moment t, following and evacuate to the number of safety zone and be:

$N\&CenterDot;{\&Integral;}_t^{\&infin;}f\left(t_e\right)\mathrm{dt}---\left(25\right)$

In like manner, the probability of fire hazard critical conditions arriving is:

f(t _c)(t+dt)-f(t _c)t＝f(t _c)dt (26)

Under actual fire condition, the evacuating personnel process is subjected to the influence of fire development situation, and fire hazard state the mobile closely related of spreading of then main and fire of time and flue gas that arrive is subjected to the influence of evacuating personnel less.Therefore, can think that it is separate that the fire hazard critical conditions is arrived, precarious position still has personnel not evacuate these two incidents temporarily.So, being with a toll of that moment t may cause:

$(N\&CenterDot;{\&Integral;}_t^{\&infin;}f\left(t_e\right)\mathrm{dt})\&CenterDot;f\left(t_c\right)\mathrm{dt}---\left(27\right)$

By getting formula (27) integration, the number of casualties C that fire may cause when taking place is:

$C={\&Integral;}_0^{\&infin;}[(N\&CenterDot;{\&Integral;}_t^{\&infin;}f\left(t_e\right)\mathrm{dt})\&CenterDot;f\left(t_c\right)]\mathrm{dt}---\left(28\right)$

According to the definition of probability density function, the cumulative distribution function F of evacuating personnel time _E(t) be:

$F_E\left(t\right)={\&Integral;}_0^{t}f\left(t_e\right)\mathrm{dt}---\left(29\right)$

Again ${\&Integral;}_0^{t}f\left(t_e\right)\mathrm{dt}+{\&Integral;}_t^{\&infin;}f\left(t_e\right)\mathrm{dt}=1---\left(30\right)$

So, formula (28) is converted into:

$C=N\&CenterDot;{\&Integral;}_0^{\&infin;}[(1-F_E\left(t\right))\&CenterDot;f\left(t_c\right)]\mathrm{dt}---\left(31\right)$

5, building fire personnel casualty probability Forecasting Methodology

In case if after certain building breaking out of fire, a plurality of fire scenarios may occur, but the probability of occurrence of each fire scenario not only according to the usefulness that has that it's too late of the anti-fire-fighting equipment of this building, and changes in time.Based on event tree and discrete Markov link analysis, can obtain the probability distribution vector P (S of fire scenario in moment i-1 and the moment i interval _i)=(p (s _{I, 0}), p (s _{I, 1}) ..., p (s _{I, 9})).According to f (t _e) and f (t _c) expression the probability density distribution curve, according to formula (31), the number of casualties that can obtain may causing under each fire scenario also can be expressed as a vectorial C=(c ₀, c ₁..., c _j) ^TFire casualties value-at-risk can be quantified as so

$\mathrm{Risk}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_i\&CenterDot;C_i---\left(32\right)$

Because the characteristic of combustible and the difference of architectural environment, dissimilar buildings probability difference on fire is bigger.If introduce the fire occurrence frequency, (Expected Risk to Life ERL) is can to obtain casualties calculated risk probability

$P_{\mathrm{fire}-\mathrm{life}}=\frac{P_{\mathrm{if}}\&CenterDot;\mathrm{Risk}\&CenterDot;A_f}{N}---\left(33\right)$

In the formula, P _IfFrequency (1/ (m for the buildings breaking out of fire ²Year)); A _fFloor area (m for buildings ²).

The present invention is based on fire dynamics, in the fire risk assessment, the feature of more uncertain and random factor and buildings and the influence of fire-fighting measure have been considered, can obtain rational prediction personnel fire risk more, for fire safety evaluating design provides reliable support.

The present invention is when determining the probability that fire scenario occurs, and this research focuses on the understanding uncertain problem when considering this variable-value of fire-fighting measure enforcement probability.The value of probability is not to represent with determined value simply, but reduces its uncertainty with the form of probability distribution function;

When the number of casualties that each fire scenario of assessment may cause, consider the many random factors in fire and the equal process of evacuating personnel.Therefore, when determining the probability that fire scenario occurs, the present invention considers in the evacuating personnel Time Calculation process, the detection time, the arrive randomness of time of the randomness of evacuating personnel setup time, fire hazard state is so that the assessment number of casualties that may cause more reasonably;

For the calculating of evacuating personnel time,, the fire detecting and alarm time is taken as probability distribution based on fire growth coefficient randomness; Consider to evacuate the randomness of setup time, it is taken as probability distribution.For the calculating of arriving time of fire hazard state, the uncertainty of fire is set in consideration based on fire growth coefficient randomness, is probability distribution with fire hazard state arriving time representation.By comparing fire hazard state arriving time and evacuating personnel time relation, calculate the number of casualties that each fire scenario may cause.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.

Claims (7)

1, a kind of Forecasting Methodology of building fire personnel casualty probability is characterized in that, comprising:

At first, set up a plurality of fire scenarios, each fire scenario is in fire development from the state of original state to the fire hazard state, and analyzes the probability that described fire scenario occurs in time, and described fire scenario comprises following at least one factor:

Whether the water spray successfully starts, whether detection is successful, whether personnel find whether fire, machine smoke evacuation system start;

Then, relatively each scene arrives the time and the required time of evacuating personnel of described fire hazard state respectively, and calculates the number of casualties that each fire scenario may cause;

Afterwards, according to the number of casualties that each fire scenario may cause down, prediction building fire personnel casualty probability.

2, according to the Forecasting Methodology of the described building fire personnel casualty probability of claim 1, it is characterized in that, analyze the probability that described fire scenario occurs in time and comprise:

At first, set up described fire scenario from the probability matrix of current state to other state transitions:

$P=\left(\begin{array}{cccc}{P}_{00}& P_{01}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{09}\\ P_{10}& P_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{19}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ P_{90}& P_{91}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{99}\end{array}\right)---\left(4\right)$

In the matrix, P _IjFor described fire scenario from the transition probability of state i to state j, work as P _Ij=0 o'clock, expression state i did not shift to state j; Work as P _Ij ⁰The time, expression existence i is to the transfer process of state j, i, j=1～9;

Afterwards, according to the different probability that constantly occur of each fire scenario of described matrix analysis at fire development.

3, according to the Forecasting Methodology of the described building fire personnel casualty probability of claim 2, it is characterized in that, comprise and set up the fire hazard state probability distribution function f (t of arriving time _c):

$f\left(t_c\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_{\ln t_c}{t}_c}\exp [-\frac{{(\ln t_c-{\mathrm{\&mu;}}_{\ln t_c})}^2}{2{{\mathrm{\&sigma;}}_{\ln t_c}}^2}]---\left(16\right)$

In the formula, t _cFor the fire hazard state arrives the time; F (t _c) mean value and variance be:

${\mathrm{\&mu;}}_{t_c}=\exp ({\mathrm{\&mu;}}_{\ln t_c}+\frac{1}{2}{\mathrm{\&sigma;}}_{\ln t_c}^2)$ (17)

${\mathrm{\&sigma;}}_{t_c}^2=\exp ({\mathrm{\&sigma;}}_{\ln t_c}^2+2{\mathrm{\&mu;}}_{\ln t_c})\&CenterDot;[\exp \left({\mathrm{\&sigma;}}_{\ln t_c}^2\right)-1]---\left(18\right).$

4, according to the Forecasting Methodology of the described building fire personnel casualty probability of claim 3, it is characterized in that, comprise the probability distribution function f (t that sets up the evacuating personnel time _e), comprise the probability distribution function of fire detecting and alarm time and evacuate the probability distribution function of setup time;

The probability distribution function of described fire detecting and alarm time is:

$\ln t_d=-\frac{1}{5}\ln \mathrm{\&alpha;}+\frac{3}{5}\ln k_d---\left(21\right)$

In the formula, α is the fire growth coefficient, obeys logarithm normal distribution, then ln α Normal Distribution; k _dBe constant; The described probability distribution function of evacuating setup time is:

$\begin{array}{cc}f\left(t_p\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_p}\exp [-\frac{{(t_p-{\mathrm{\&mu;}}_p)}^2}{2{{\mathrm{\&sigma;}}_p}^2}]& t_p>0\end{array}---\left(24\right)$

In the formula, f (t _p) for evacuating the probability distribution function of setup time; t _pFor evacuating setup time; μ _pFor evacuating the mean value of setup time; σ _pFor evacuating the standard deviation of setup time;

Random distribution function f (the t of described evacuating personnel required time _e) be the joint density function of considering that the fire detecting and alarm time probability distributes and evacuation setup time probability distribution obtains.

5, according to the Forecasting Methodology of the described building fire personnel casualty probability of claim 4, it is characterized in that, comprising:

Probability distribution function and the probability distribution function of described evacuating personnel time according to the described fire hazard state arriving time calculate the injures and deaths people C number that may cause under each fire scenario.

$C={\&Integral;}_0^{\&infin;}[(N\&CenterDot;{\&Integral;}_t^{\&infin;}f\left(t_e\right)\mathrm{dt})\&CenterDot;f\left(t_c\right)]\mathrm{dt}---\left(28\right)$

In the formula, N is the number in the buildings.

6, according to the Forecasting Methodology of the described building fire personnel casualty probability of claim 5, it is characterized in that, comprising:

According to the probability that described fire scenario occurs in time, obtain in moment i-1 and the moment i interval probability distribution vector P (S of described fire scenario _i)=(p (s _{I, 0}), p (s _{I, 1}) ..., p (s _{I, 9}));

Probability distribution function and the probability distribution function of described evacuating personnel time according to the described fire hazard state arriving time obtain the number of casualties distribution vector C=(c that may cause under each fire scenario ₀, c ₁..., c _j) ^T

Described building fire personnel casualty probability is:

$\mathrm{Risk}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_i\&CenterDot;C_i---\left(32\right)$

In the formula, n is the fire scenario number, and i is an i fire scenario.

7, according to the Forecasting Methodology of the described building fire personnel casualty probability of claim 6, it is characterized in that, comprising:, obtain construction personnel injures and deaths calculated risk probability and be according to described building fire personnel casualty probability:

$P_{\mathrm{fire}-\mathrm{life}}=\frac{P_{\mathrm{if}}\&CenterDot;\mathrm{Risk}\&CenterDot;A_f}{N}---\left(33\right)$

In the formula, P _IfBe the frequency of buildings breaking out of fire, 1/ (m ²Year); A _fBe the floor area of buildings, m ²

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