Interval Entropy Measurement Method in Risk Analysis and Its Application to Metro Construction

Transcription

1 ISGSR2007 Frst Iteratoal Symposum o Geotechcal Safety & Rsk Oct. 8~9, 2007 Shagha Togj Uversty, Cha Iterval Etropy Measuremet Method Rsk Aalyss ad Its Applcato to Metro Costructo J.W. LI Bejg Urba Egeerg Desg & Research Isttute Co., Ltd., Bejg, 00037, Cha L.Q. LI Rsk Maagemet Isttute, Jagta Isurace Broker Co., Ltd., Bejg, 00875, Cha X.R.YANG Bejg Urba Egeerg Desg & Research Isttute Co., Ltd., Bejg, 00037, Cha ABSTRACT: Rsk s related to ucertaty of potetal evets. Etropy s defed as the measure of ucertaty of a system. I udergroud egeerg, oe of deftos of rsk s the probablty of a evet occurrg. So, usg etropy theory for rsk measuremet s a good way to evaluate the probablty of a hazard geotechcal rsk system. I ths paper based o the real practce of rsk assessmet ad the dffculty quattatve rsk measuremet, the terval etropy measuremet method has bee put forward. As a example, the rsk of a sheld tuellg costructo stage s evaluated ad determed usg proposed method. I the ed some coclusos had bee draw as well. INTRODUCTION Urba metro egeerg s comprehesve system egeerg wth huge vestmet, log costructo stage, may specalty combatos ad volvg may cotractors. I costructo stage, adequacy of geotechcal formato, geologcal ad hydrogeologcal codtos locally dfferet from those foresee for the desg, approprate choce of the costructo method, o deal performace or behavour of the sheld mache tself or devato of the actual groudmache system behavour from the theoretcal oe, ufavourable groud evromet, such as busy traffc, exstg buldgs/utltes ad costructo parameter ad costructo maagemet ad other ucerta factors, they result may costructo evets or hazards (Grasso, et.al, 2007). Buldg ower ad cotractors bear much loss ad how to evaluato rsk ad maage the rsk metro egeerg to decrease the hazards loss s the ma topc of urba tuel works costructo. Sce 970 s, udergroud egeerg rsk has bee recogzed ad some research results have bee obtaed (Este, 974). But, these results maly focused o establshg cocepto of rsk ad some qualtatve aalyss. However the quattatve research work always focused o relablty calculato. I fact, relablty ad rsk geotechcal egeerg has heret dfferece. Except these, other rsk measuremet method seldom volved. I recet years, the mportace of geotechcal costructo rsk has bee realzed creasgly. As Sr Mchael Latham (994) sad No costructo project s rsk free. Rsk ca be maaged, mmzed, shared, trasferred or accepted. It caot be gored (Hu, 2006). Ad may commo rsk aalyss method cludg Delph Method, Aalytcal Herarchy Process, Ifluece Dagram Method, Mote-Carlo Smulato Method, CIM Model, Expected Value, Decso Tree Method, Fault Tree Method, Sestvty Aalyss Method etc ad ther combato have bee developed(che, 2004). But, a sutable measuremet method udergroud egeerg rsk aalyss has ot bee establshed. Thus, how to measure the rsk usg these commo methods or 657

2 establsh ew quattatve measuremet method s a mportat work rsk measuremet ow. I ths paper, based o the dea of etropy ad ts geeralzato ad exteso, the terval etropy measuremet method based o expert vestgato was proposed. 2 CHARACTERISTICS OF URBAN SHIELD TUNNELLING RISK Rsk s related to ucertaty of potetal evets. Etropy s defed as the measure of ucertaty of a system. I udergroud egeerg, oe of deftos of rsk s the probablty of a evet occurrg, so usg etropy theory for rsk measuremet s a good way to evaluate the probablty of a hazard geotechcal rsk system. I rsk aalyss practce of tuellg costructo of metro egeerg, take sheld tuellg costructo for example, because the lkelhood of hazards occurrece s always dffcult to determe owg to the lack of statstc data, the expert vestgato method ad Delph method are wdely used practce. As for expert vestgato, gvg a sgle probablty value of a certa rsk factor s dffcult for a expert. However, gvg a terval value s less dffcult tha gvg a sgle value to descrbe the probablty occurrece of detfed rsk factor. Moreover, the terval value could reflect the dyamc rsk maagemet process that cotues throughout the costructo stage of the project system. I ths paper, based o the dea of etropy, terval etropy measuremet method s put forward to evaluate the rsk of evets ad a geeralzed defto of etropy s defed further, whch s sutable for terval-valued etropy soluto. 3 ENTROPY AND INTERVAL ENTROPY MEASUREMENT METHOD 3. Etropy ad Rsk The dea of etropy s orgated from thermodyamcs, whch s a physcal quatty used to dcate that the process of thermal moto s rreversble. I 929, L. Szlard, a Hugary scetst proposed the ucertaty relatoshp betwee etropy ad formato, whch makes t possble to cte etropy formato scece. I 948, C. Shao created the formato theory Bell laboratory (Shao,949). I formato theory, the average formato quatty of formato source sgal commucato process s called etropy, whch made the formato etropy use practce. Accordg to the C. Shao theory, as for the dscrete memoryless formato source X, ts formato quatty.e. etropy H s defed as a fucto of the -dmesoal probablty vector P = p, p,, p ),.e.: ( 2 H ( X ) = p log = = H ( ) 2 p P () p = (2) = Etropy s the basc oto the formato theory feld. Iformally we ca defe etropy as the measure of ucertaty of a system that at a gve momet ca be oe of the states. Usually rsk s related to ucertaty of future evets. I other words, rsk s related to lack of kowledge about future evets. It would be atural to defe rsk as the amout of lackg formato. 3.2 Iterval-Valued Etropy If values of all p are kow, the etropy of a system ca be calculated accordg to the formula (). But fact, the probablty of the system th state s always dffcult to determe. m max Sometmes t s terval valued wth p, p rather tha sgle valued. If probabltes are terval-valued, how ca we calculate the etropy? Obvously, the etropy tself wll be terval. Accordg to formula (2), ther probabltes should satsfy wth equato (3) 658

3 m max p p (3) = = We caot use formula () drectly to calculate etropy, as the fucto h=-plogp s ot mootoc. Alexader Valshevsky proposed the calculato method of etropy for a system wth terval-valued The formula as follows (Aleksadrs, et.al, 2003): H max avg m = p log p = (4) H m avg max = p log p (5) = avg Here, p s defed as average probablty show equato (6), whch s obtaed from maxmum ad mmum probablty values. p p + p 2 m max avg = (6) From equato (4) ad (5), etropy for a system wth terval-valued probablty s terval etropy, whch s equal to (7) = (7) m max H H, H Thus, the terval-valued H = [H m, H max ] doates the probablty of occurrece of system evaluato dexes. After the potetal cosequece of evaluato dexes ad ther weghts are determed. The rsk value could be calculated fally. 3.3 Iterval Etropy Measuremet Method Rsk Aalyss I cty metro costructo stage, may ucertaty factor results much geotechcal rsk. As we kow that etropy s a measuremet method for future formato ucertaty ad rsk s related to ucertaty of future evet. I other words, rsk s related to lack of kowledge about future evets. Naturally, etropy would be used to measure rsk. As motoed above, terval etropy s a good way to measure geotechcal rsk metro costructo stage. The dea of t follows: () Frstly, accordg to the expert vestgato method, every probabltes of rsk dexes m max durg metro costructo stage are gve, whch are terval-valued wth pj, p j. (2) Supposg the mportace degree of every expert s equal, usg equato (4) ad equato m max (5), calculate the terval etropy of every rsk dex H = H, H. (3) Determe the etropy weght of every dex. As for the mult-dex makg decso problem, the relatve mportace degree s eeded to take to cosderato. Accordg to the cocept of etropy, the formato quatty ad qualty of every dex provded for evaluato scheme, decdes ts relatve weght decso makg. If the evaluato values of the j th dex are the same for every scheme, the etropy wll reach maxmum ut ad etropy weght s zero. That etropy weght s equal to zero meas the evaluato dex does t provde ay useful formato for decso maker ad decso maker would ot cosder t ay more. However, f the evaluato values of the j th dex for every scheme have much dfferece, the value of etropy wll be small ad etropy weght wll be large. I ths case, evaluato dex provdes useful formato for decso maker ad ths dex should be gve much emphass o. Here, the etropy weght s ot fxed for every evaluato dex, ad they would chage wth the chage of evaluato scheme. Therefore, usg etropy weght to descrbe the mportace of every dex s a reasoable rule 659

4 whch embodes the relatve mportace of every dex. The etropy weght should be determed accordg to equato (8): ω = m H m = H (8) (4) Accordg to equato (9) ad the etropy weght of every dex, the rsk of all rsk factors costructo stage s: m H (9) = R = ω where, ω s expert weght value of the th rsk factor, whch could be determed by expert vestgato method accordg to equato (8). H s the etropy of the th rsk factor, whch could be gve through the equato (7), ad m s the umber of rsk factors. The rsk value obtaed form equato (9) has the followg propertes: ) R [0,], whch could be proved by the feature of ω = ad 0 H. 2) Whe R s lttle (or ear zero), t meas that the rsk assessmet system s almost deftve ad there s o rsk. 3) Whe R reaches up to maxmum ut, t meas that the rsk assessmet s carred out wth mmum formato. At ths codto, the etropy of all H are equal to. Ths meas that the rsk factor values of all system are the same ad ay sequece sheld costructo wll take rsks. At ths tme, t s ecessary to get much more the formato, such as addtoal explorato survey, evrometal vestgato, trag sheld drver ad specto sheld mache aga etc.. 4) The etropy ca measure the quatty of useful formato from avalable formato. 4 CASE STUDY I geotechcal rsk aalyss, a proposed way of assessg frequecy s to have a rsk assessmet team, cosstg of expereced tuel egeers to formulate ther ow gudeles for frequecy classes. These could be related to the umber of evets expereced by the partcpats, the umber of evets they have heard of, the umber of expereced ear-msses ad the umber of ear-msses they have heard of; all relato to the umber of projects they have bee volved or are aware of. It would be of great beeft for a rsk aalyss (Aleksadrs, et.al, 2003). Ths aalyss method s called expert vestgato method. If the classfcatos of frequecy of occurrece wth terval values have bee gve, how we ca determe the global rsk level of the sheld tuelg costructo system s the focus of ths paper. I urba areas, tuel works costructo of s ofte assocated wth rsk that ca arse from dfferet factors. The ma categorses of rsk cludes geologcal ad hydrogeologcal rsk, desg rsks, costructo rsks ad the thrd party rsk. The followg tems are the ma rsk sources urba sheld tuellg costructo: ) Geologcal caver ahead of sheld tuellg mache 2) Ecoutered barrer or solated grate durg sheld tuellg 3) Sheld tuellg through rver or lake 4) Sheld equpmet falure tuellg toward workg-well 5) Excavato face falure 6) Leakage of water or slurry betwee segmets coecto 7) Axal devato of sheld tuellg 8) Ifluece of sheld tuellg costructo o rug metro les 9) Sheld tuellg through/across brdge ples, buldg ples or mportat buldgs/utltes 660

5 0) Ifluece of sheld tuellg costructo o mportat ppeles or mucpal road. I the followg secto, based o these rsk sources metoed above, combg wth expert vestgato method, the terval etropy rsk measuremet method would be troduced detals. The step follows: ) Usg expert vestgato method, accordg to the frequecy classfcato Gudeles of Rsk Maagemet for the Costructo of Subway ad Udergroud Works publshed by Cha Cvl Egeerg Socety (CCES, Togj Uversty, 2007), the probablty of rsk s dvded to fve classes show Table. At the same tme separato to 5 classes or tervals s geerally recommeded as a practcal way of classfyg frequecy by Iteratoal Tuel Assocato (ITA) (ITA, 2004). Table Classfcato of frequecy of occurrece Class/grade Descrptve Very Very ulkely ulkely occasoal lkely frequecy class lkely Iterval P<0.0% 0.0% P<0.% 0.% P<% % P<0% P 0% probablty Note: P s the frequecy of occurrece. Assume that above metoed te rsk factors are composed of a rsk scheme of sheld tuellg costructo system. I ths system, seve expereced sheld tuellg egeerg experts are composed of a rsk assessmet team. Accordg to the rule of expert vestgato method, we carred out rsk assessmet of ths system. The evaluato matrx descrbed by terval probablty value of te rsk factors gve by seve experts s obtaed: P = p p m max [ j ~ j ] m 0.0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0.00 = 0.00 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0. Here, m s the umber of rsk factor, s the umber of expert. 2) Accordg to equato (4) ad equato (5), f the expert weght s assumed equally, the terval etropy value of te evaluato dex (.e. te rsk sources) could be expressed wth max m maxmum etropy ad mmum etropy : H H 66

6 m max H = H, H = ) Usg formula (8), the etropy weght of te dexesω (=, 2, 3 0) are: ω H = ω H = m max ( ), ( ) 4) Submt the ω ad expressed by: H ( =,2,3 0) to equato (9), the rsk terval value could be m max R R R [ ] =, = 0.086,0.042 I ths evaluato project system, the rsk of sheld tuellg costructo s betwee.986% ad 4.2%. It meas the probablty of occurrece of hazards sheld tuellg costructo les terval value [.986%, 4.2%]. Accordg to ths rsk rato, the costructo ower or cotractors have a quattatve rsk value for the whole costructo. Ad the ower could use t to apply for surace. 5 CONCLUSIONS I ths paper we preseted the dea of usg etropy as a measuremet of rsk, ad based o the metro costructo rsk assessmet practce ad the dffculty, a terval-etropy measuremet approach towards rsk aalyss s put forward. I ths paper, we propose several heurstc approaches towards etropy geeralzato ad exteso, whch are sutable to carry o quattatve rsk assessmet metro costructo system. Combed wth the commo assessmet method, whch s expert vestgato method, t s beleved that proposed quattatve measuremet method s good way to measure the rsk metro costructo. It should be poted that, there are may kds of rsk measuremet methods. How to evaluate ad aalyze the rsk much more effectvely, feasbly s stll a problem to be researched further. REFERENCE 662

7 Aleksadrs Valševsks, Arkady Borsov, (2003) Usg Iterval-Valued Etropy for Rsk Assessmet, Proceedgs of Modellg ad Smulato of Busess Systems, Kauas Uversty of Techology Press Techologja, Lthuaa, 2003, pp Cheg Log, (2004) Rsk aalyss ad assessmet durg costructo of soft sol sheld tuel urba area, [D], Togj Uversty, , Shagha, Cha. Cha Cvl Egeerg Socety (CCES), Togj Uversty (2007), Gudeles of rsk maagemet for the costructo of subway ad udergroud works.p5. Este.H.H, Vck.S.G, (974) Geologcal model for tuel cost model. Proceedg of Rapd Excavato ad Tuellg Coferece, 2d, 974, pp: ITA, (2004)Gudeles for Tuelg Rsk Maagemet. P.Grasso, E.Chrott, S.Xu, et., (2007) Use of rsk maagemet pla for urba mechazed tuellg projects: From the establshmet of the method to the successful practce, ITA-AITES Word Tuel Cogress 2007 ad the 33rd ITA-AITES Geeral Assembly, 2007,5, Prague, Taylor & Fracs Group, Lodo, pp: Qufag Hu, (2006) Rsk Aalyss ad Its Applcato for Tuel Works based o Research of Stratum ad Sol Spatal Varablty, [D], Togj Uversty, , Shagha, Cha. Shao C., Weaver W. (949), The mathematcal theory of commucato, Urbaa: Uversty of Illos Press. 663

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