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Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen Probabilistic CFD and Evacuation Simulation for Life Safety Assessment Cornelius Albrecht & D. Hosser i. BMB Fire Protection Engineering Division Technische Universität Braunschweig
Introduction & Motivation § Conventional empirical safety concept: § ASET/RSET > Arbitrary safety factor (usually chosen 2. 0 -3. 0) § Is that overly safe? § Or even too optimistic? § Does it provide the same safety level as “deemed-to-satisfy” (prescriptive) codes? § How do fire protection barriers (sprinklers etc. ) influence the safety level? § Are they worth their investment? § Client: Is my life safety design really cost-benefit optimized? Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 2
Introduction § Risk-informed design: § Risk = Sum of Probabilities x Consequences § What are the consequences if it fails? § What is the probability of failure of my life safety design? § Consequences: § People are “delayed” in their egress (visibility/optical density, walking speed) § People are severely harmed and/or incapacitated which can ultimately lead to death (toxic smoke, heat) § Quantification of the consequences in monetary terms? § Life quality index, ALARP, mortality rates, lost-life-years? § Data is missing almost entirely and ethically questionable! § Thus comparative design: How does my solution perform compared to the “deemed-to-satisfy” prescriptive code solution? § Probabilistic reliability analysis! Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 3
Introduction § Reliability analysis life safety design § State function: z(x) = t. ASET – t. RSET § Failure domain: Ωf ≡ z(x) ≤ 0 § “Design” point : z(x) = 0 § x is a vector of uncertain parameters, i. e. § Pre-movement time § Walking speed § Number of occupants § Max. heat release rate § Time to 1 MW tg or α, respectively § Soot and/or CO yield § etc. § t. ASET : complex and “expensive” numerical fire simulation (CFD) § t. RSET : (more or less) complex evacuation simulation + additional Δt‘s Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 4
Reliability analysis § Commonly used reliability algorithms § Classic FORM: not applicable to implicit state functions § Monte Carlo: required number of simulations simply not possible with CFD § Classic least square RSM: only coarse global approximation, results not accurate enough or overfitting § Fast and accurate response surface algorithm: § Preceding sensitivity analysis: reduces dimensionality (filters irrelevant par’ms) § Interpolating Moving Least Squares (IMLS): fast and locally accurate surrogate § Adaptive Importance Sampling to solve reliability problem using the surrogate § This allows for reliability analysis using complex numerical tools with § reasonable accuracy and § in a reasonable time (several 10 runs instead of several 1000, independent evaluation allows for crude parallelization on HP/HT clusters) § More information on the methodology in the paper! Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 5
Application example § 240 m² small-medium size assembly(1996) building From: Madrzykowski § Analysis with probabilistic FDS and FDS+evac § Visibility (optical density 0. 1/m, low pass filter to stabilize numerical results) § FED (1. 0 with lump sum of irritant gases of 0. 3 as they cannot be simulated) § Stochastic modeling based on the literature (partly educated guess) § Two scenarios loosely based on NFPA 101 (which actually requires no t²) § Fire in the bar area: t² with linear incubation phase § Ultra-fast fire on the dance floor: t² § Fire protection barrier analyzed: automatic detection & alarm system § Modeling: Warning/Premovement times are reduced from 180 s to 90 s on average – this is an assumption! § Failure probability: 10% (BS 7974) to “work as designed on demand” Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 6
Sensitivity analysis § Simple: linear or rank correlation and t-test or stepwise regression § What parameters are important? Which are not? Which can we omit to reduce dimensionality and thus numerical costs for the reliability analysis? Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 7
Reliability analysis § “Per hostile fire” – failure probabilities without detection system § For reference period “ 1 year” § Fire occurrence 0. 02 per year (simplified from BS 7974) § Manual intervention at fire start (~50%) Calculated pfs per hostile fire Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 8
Impact of a Detection & Alarm System § Re-running the model with reduced warning/premovement times § Additional sub-event tree to model potential failure of the system § Correlation effects are modeled within the scenarios, thus simple multiplication in horizontal direction is possible § Vertically it is a “random walk” through the system, thus summation of the probabilities denotes an upper bound of the system failure probability Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 9
Impact of a Detection & Alarm System § Results “per hostile fire” WITH and WITHOUT Detection & Alarm System § Results “per hostile fire” considering the previous event tree and 10% failure § Visibility: 0. 9 x 0. 2142 + 0. 1 x 0. 6819 = 0. 2610 § FED: 0. 9 x 0. 0174 + 0. 1 x 0. 0540 = 0. 0211 § Results per annum § Visibility: 0. 0013 per annum (compare to 0. 0034) § FED: 0. 000105 per annum (compare to 0. 0003) Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 10
Impact of a Detection & Alarm System § Absolute values have to be treated with care due to all the assumptions § Not comparable to structural reliability requirements § Thresholds, parameters, models, scenarios etc. are highly influential on the calculated probabilities and thus only those based on the same parameter set are comparable! § We call them “operational” probabilities and they usually are conservative § But: comparative design is possible: § Visibility: Increase of safety of a factor 2. 6 for the bar fire § FED: 2. 85 for the bar fire § That already includes the 10% probability of failure § As the costs of the systems are approx. known, similar analyses with other systems (sprinklers, smoke extraction) can yield the cost-benefit-optimal solution for the particular problem. Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 11
Conclusions & Outlook § Quantitative, risk-informed design using highly complex numerical tools becomes possible with the RSM approach presented! § Unfortunately, accurate data, scenarios, and models are still missing, but engineer tend to be conservative in their assumptions § Calculated probabilities are “operational” and likely to be conservative § Performing extensive calculations with various similar models for code-compliant buildings allows for the quantification of the currently acceptable safety levels based on the “deemed-to-satisfy” codes § The quantified values can then be used to validate non-code-compliant designs based on quantitative and thus objective comparison using numerical FPE tools § Effect of fire protection systems can be objectively considered and compared to find a cost-benefit optimized solution without (subjective) “gut feeling” § Future: Derivation of a semi-probabilistic safety concept (? ) Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 12
Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen Probabilistic CFD and Evacuation Simulation for Life Safety Assessment Cornelius Albrecht & D. Hosser i. BMB Fire Protection Engineering Division Technische Universität Braunschweig
- Slides: 13