1、PD CEN/TR 16988:2016Estimation of uncertainty inthe single burning item testBSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06PD CEN/TR 16988:2016 PUBLISHED DOCUMENTNational forewordThis Published Document is the UK implementation of CEN/TR16988:2016.The UK participati
2、on in its preparation was entrusted to TechnicalCommittee FSH/21, Reaction to fire tests.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for
3、its correctapplication. The British Standards Institution 2016. Published by BSI StandardsLimited 2016ISBN 978 0 580 90291 8ICS 17.200.01Compliance with a British Standard cannot confer immunity fromlegal obligations.This Published Document was published under the authority of theStandards Policy an
4、d Strategy Committee on 31 August 2016.Amendments issued since publicationDate Text affectedPD CEN/TR 16988:2016TECHNICAL REPORT RAPPORT TECHNIQUE TECHNISCHER BERICHT CEN/TR 16988 July 2016 ICS 17.200.01 English Version Estimation of uncertainty in the single burning item test Messunsicherheit - The
5、rmische Beanspruchung durch einen einzelnen brennenden Gegenstand (SBI) This Technical Report was approved by CEN on 4 July 2016. It has been drawn up by the Technical Committee CEN/TC 127. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic,
6、Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMI
7、TTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2016 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. CEN/TR 16988:2016 EPD CEN/TR
8、16988:2016CEN/TR 16988:2016 (E) 2 Contents Page European foreword . 4 1 Scope 5 1.1 General 5 1.2 Calculation procedure . 5 1.2.1 Introduction 5 1.2.2 Synchronization of data 5 1.2.3 Heat output 5 2 Uncertainty 9 2.1 Introduction 9 2.2 Elaboration of terms and concepts 11 2.2.1 Mean and variance . 1
9、1 2.2.2 Estimation of the confidence interval for the population mean . 12 2.2.3 Sources of uncertainty 12 2.2.4 Standard uncertainties for different distributions 12 2.2.5 Combined uncertainty 15 2.2.6 Expanded uncertainty 16 2.2.7 Uncorrected bias 16 2.3 Combined standard uncertainties . 17 2.3.1
10、Combined standard uncertainty on sums . 17 2.3.2 Combined standard uncertainty on averages 18 2.3.3 Combined standard uncertainty of a product and a division . 19 2.3.4 Combined standard uncertainty on the heat release rate (Q) . 20 2.3.5 Combined standard uncertainty on the depletion factor () 22 2
11、.3.6 Combined standard uncertainty on the initial O2-concentration (XDO2) . 22 2.3.7 Combined standard uncertainty on the volume flow rate (VD298) 23 2.3.8 Combined standard uncertainty on the air density (air) 24 2.3.9 Combined standard uncertainty on specimen heat release rate (Qspecimen) 24 2.3.1
12、0 Combined standard uncertainty on the average heat release rate (Qav) . 24 2.3.11 Combined standard uncertainty on FIGRA . 25 2.3.12 Combined standard uncertainty on THR600s . 25 2.3.13 Combined standard uncertainty on the volume flow (V(t) . 25 2.3.14 Combined standard uncertainty on the smoke pro
13、duction rate (SPR) 25 2.3.15 Combined standard uncertainty on specimen smoke production rate (SPR) . 26 2.3.16 Combined standard uncertainty on the average smoke production rate (SPRav) 26 2.3.17 Combined standard uncertainty on SMOGRA 26 2.3.18 Combined standard uncertainty on TSP600s 27 2.4 Confid
14、ence interval classification parameters 27 2.5 Standard uncertainty on the different components 28 2.5.1 Uncertainty on the data acquisition (DAQ). 28 2.5.2 Transient error . 28 2.5.3 Aliasing error . 28 2.5.4 Uncertainty on data synchronicity 29 2.5.5 Uncertainty on the component E and E . 30 2.5.6
15、 Uncertainty on the component . 36 2.5.7 Uncertainty on the component patm. 36 2.5.8 Uncertainty on the component Troom. 36 2.5.9 Uncertainty on the component 38 PD CEN/TR 16988:2016CEN/TR 16988:2016 (E) 3 2.5.10 Uncertainty on the component c . 38 2.5.11 Uncertainty on the component A and L 39 2.5.
16、12 Uncertainty on the component qgas40 2.5.13 Uncertainty on the component kt40 2.5.14 Uncertainty on the component kp. 43 2.5.15 Uncertainty on the component p 44 2.5.16 Uncertainty on the component Tms. 44 2.5.17 Uncertainty on the component I 46 Annex A (informative) List of symbols and abbreviat
17、ions . 48 PD CEN/TR 16988:2016CEN/TR 16988:2016 (E) 4 European foreword This document (CEN/TR 16988:2016) has been prepared by Technical Committee CEN/TC 127 “Fire Safety in Buildings”, the secretariat of which is held by BSI. Attention is drawn to the possibility that some of the elements of this d
18、ocument may be the subject of patent rights. CEN shall not be held responsible for identifying any or all such patent rights. This document has been prepared under a mandate given to CEN by the European Commission and the European Free Trade Association. PD CEN/TR 16988:2016CEN/TR 16988:2016 (E) 5 1
19、 Scope 1.1 General The measuring technique of the SBI (single burning item) test instrument is based on the observation that, in general, the heats of combustion per unit mass of oxygen consumed are approximately the same for most fuels commonly encountered in fires (Huggett 12). The mass flow, toge
20、ther with the oxygen concentration in the extraction system, suffices to continuously calculate the amount of heat released. Some corrections can be introduced if CO2, CO and/or H2O are additionally measured. 1.2 Calculation procedure 1.2.1 Introduction The main calculation procedures for obtaining
21、the HRR and its derived parameters are summarized here for convenience. The formulas will be used in the following clauses and especially in the clause on uncertainty. The calculations and procedures can be found in full detail in the SBI standard 1. 1.2.2 Synchronization of data The measured data a
22、re synchronized making use of the dips and peaks that occur in the data due to the switch from primary to main burner around t = 300 s, i.e. at the start of the thermal attack to the test specimen. Synchronization is necessary due to the delayed response of the oxygen and carbon dioxide analysers. T
23、he filters, long transport lines, the cooler, etc. in between the gas sample probe and the analyser unit, cause this shift in time. After synchronization, all data are shifted so that the main burner ignites by definition at time t = 300 s. 1.2.3 Heat output 1.2.3.1 Average heat release rate of the
24、specimen (HRR30s) A first step in the calculation of the HRR contribution of the specimen is the calculation of the global HRR. The global HRR is constituted of the HRR contribution of both the specimen and the burner and is defined as +=)(105,01)()()(HRRa_O2298totalttxtVEtD(1) where totalHRR ( )t i
25、s the total heat release rate of the specimen and burner (kW); Eis the heat release per unit volume of oxygen consumed at 298 K, = 17 200 (kJ/m3); 298()DVtis the volume flow rate of the exhaust system, normalized at 298 K (m3/s); a_O2xis the mole fraction of oxygen in the ambient air including water
26、 vapour; ()tis the oxygen depletion factor. The last two terms a_O2x and + )(105,01)(ttexpress the amount of moles of oxygen, per unit volume, that have chemically reacted into some combustion gases. Multiplication with the volume flow gives the PD CEN/TR 16988:2016CEN/TR 16988:2016 (E) 6 amount of
27、moles of oxygen that have reacted away. Finally this value is multiplied with the Huggett factor. Huggett stated that regardless of the fuel burnt roughly a same amount of heat is released. The volume flow of the exhaust system, normalized at 298 K, VD298(t) is given by )()()(ms298tTtpkkcAtVtDD=(2)
28、where c0,5 1,5 0,500(2 / ) 22,4 K m kg T = A is the area of the exhaust duct at the general measurement section (m2); tkis the flow profile correction factor; converts the velocity at the height of the bi-directional probe in the axis of the duct to the mean velocity over the cross section of the du
29、ct; kis the Reynolds number correction for the bidirectional probe, taken as 1,08; ()ptDis the pressure difference over the bi-directional probe (Pa); ms()Ttis the temperature in the measurement section (K). The oxygen depletion factor ()t is defined as )(O)(CO1)s90.s30(O)s90.s30(CO1)(O)(CO1)s90.s30
30、(O)(2222222txtxxxtxtxxt= (3) where 2O()xtis the oxygen concentration in mole fraction; 2CO ( )xtis the carbon dioxide concentration in mole fraction; Ys.Zs mean taken over interval Y s to Z s. The mole fraction of oxygen in ambient air, taking into account the moisture content, is given by =46)s90.s
31、30(81632,23exp1001s)s.9030(Oms2a_O2TpHxx (4) where 2O()xtis the oxygen concentration in mole fraction; H is the relative humidity (%); p is the ambient pressure (Pa); Tms(t) is the temperature in the general measurement section (K). Since we are interested in the HRR contribution of the specimen onl
32、y, the HRR contribution of the burner should be subtracted. An estimate of the burner contribution HRRburner(t) is taken as the HRRtotal(t) during the base line period preceding the thermal attack to the specimen. A mass flow controller ensures an identical HRR through the burners before and after s
33、witching from primary to the main burner. The average HRR of the burner is calculated as the average HRRtotal(t) during the base line period with the primary burner on (210 s t 270 s): PD CEN/TR 16988:2016CEN/TR 16988:2016 (E) 7 )s270.s210(HRRHRR totalav_burner= (5) where HRRav_burner is the average
34、 heat release rate of the burner (kW); HRRtotal(t) is the total heat release rate of specimen and burner (kW). HRR of the specimen In general, the HRR of the specimen is taken as the global HRR, HRRtotal(t), minus the average HRR of the burner, HRRav_burner: For t 312 s: av_burnertotalHRR)(HRR)(HRR
35、= tt (6) where: HRR(t) is the heat release rate of the specimen (kW); HRRtotal(t) is the global heat release rate of specimen and burner (kW); HRRav_burner is the average heat release rate of the burner (kW). During the switch from the primary to the main burner at the start of the exposure period,
36、the total heat output of the two burners is less than HRRav_burner(it takes some time for the gas to be directed from one burner to the other). Formula (24) gives negative values for HRR(t) for at most 12 s (burner switch response time). Such negative values and the value for t = 300 s are set to ze
37、ro, as follows: For t = 300 s: HRR(300) 0 kW= (7) For 300 s 3 kW) and (THR(t) 0,2 MJ) and (300 s 3 kW) and (THR(t) 0,4 MJ) and (300 s cckuku(46) And +=0ckuU if 00+cckuku(47) Note that the expanded uncertainty shall be re-computed if the coverage factor is changed, and in particular, that U (k = 2) 2
38、*U (k = 1). The combined standard uncertainty ucis calculated out of the standard uncertainty associated with the bias uband the standard uncertainty u that accounts for the combination of all other uncertainty sources not directly associated with the bias. ( )2122bcuuu += (48) The proposed approach
39、 can somewhat overestimate the uncertainty. In the case of a coverage factor k = 2, the method maintains the 95 % confidence interval until the ratio of the bias to the combined standard uncertainty becomes larger than the coverage factor. For such large bias values, the method produces uncertainty
40、intervals that are slightly conservative. Note that the sign of the sensitivity coefficient is important to know the effect on the global uncertainty. As an example, suppose x1and x2both have uncorrected bias and the expanded uncertainty is given by +111UUx (49) +222UUx (50) The uncertainty interval
41、 on x defined as 21xxx = (51) then becomes ( )+=+222211222211xUxUxUxUxxu(52) assuming x1 0 and x2 0. An underestimation of x1leads to an underestimation of x, while an underestimation of x2leads to an overestimation of x. 2.3 Combined standard uncertainties 2.3.1 Combined standard uncertainty on sum
42、s Since the discussion on the uncertainty of a data acquisition system often requires the standard uncertainty on the sum of N independent variables/measurements, a short review is as follows. PD CEN/TR 16988:2016CEN/TR 16988:2016 (E) 18 Assume the sum =Niixay (53) Taking the partial derivative to t
43、he different components xiresults in the corresponding sensitivity coefficients ci= a. The standard uncertainty of y is obtained by appropriately combining the standard uncertainties of the input estimates xi. This combined standard uncertainty uc(y) is the positive square root of the combined varia
44、nce u2c(y) and is given by =NiiNiiicxuaxucyu1212)()()( (54) Note that for correlated measurements this is no longer true as will be discussed in the next clause. 2.3.2 Combined standard uncertainty on averages If xiis a repetitive independent measurement of a measurand X, the uncertainty on the aver
45、age is given by NxuNxNuNxuxuiiNiic)()()()(212=(55) If however the uncertainty of a component is related to an effect with periodicity exceeding the weighing interval (tN t1 30 s). A similar statement is true for the calculation of the total heat release in the first 10 min of a test (600 s). Suppose
46、 the measurements are perfectly correlated (r = 1) the uncertainty on the sum becomes (ci= 1): = +=+=NiiNiNijjijiNiiicxuxuxuccxucu111 112)()()(2)( (58) which is higher than Formula (55). In this case, events with a periodicity of approximately 10 minutes or less will be dampened out while events wit
47、h a longer periodicity will not be dampened out (r goes to 1). For parameters like MARHE, which is also based on total heat release, the behaviour with respect to uncertainty will depend upon the integration time which is variable. On the other hand however, uncertainties related to very slow proces
48、ses ( 10 times test run) hardly contribute to the uncertainty on the oxygen depletion since it is a relative measurement, i.e. the actual status is compared with the initial status at the start of the test. This document therefore considers measurements as being independent, include the uncertainty
49、related to slow processes ( 10 times test run) in the zero calibration (= daily calibration of zero points), include the uncertainty related to drift over one test run in the uncertainty related to the actual measurement point. 2.3.3 Combined standard uncertainty of a product and a division Throughout the document, often the uncertainty has to be calculated for a product and for a divis
