TítuloProbabilismo explícito en la corrosión de armaduras en las estructuras de hormigón sometidas al ambiente marino de la costa gallega
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(2) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=4 cm.. -----------------------------------------------------------------------------Job name ............ : 2r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 13:31 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 4.000 ( 0.400000000000000E+01) = 0.8000 ( 0.800000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 4.000 ( 0.400000000000000E+01) = 0.8000 ( 0.800000000000000E+00). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(3) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=4 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 4.000 ) (cx ; 3; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 0.8144 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.517 Corresponding approximate prob.of failure = 0.3027 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.1338E-07 and Vector u-* (beta-point) : (x ; 1; -0.2466 ) (cx ; 2; -0.1148 ) (cs ; 3; 0.1097 ) (n ; 4; -0.3418 ) (T ; 5; 0.2533 ) Normalized U-space gradient (alfa-U) with norm = 2.059 : (x ; 1; 0.4772 ) (cx ; 2; 0.2221 ) (cs ; 3; -0.2124 ) (n ; 4; 0.6615 ) (T ; 5; -0.4902 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4772 ) (cx ; 2; 0.2221 ) (cs ; 3; -0.2124 ) (n ; 4; 0.6615 ) (T ; 5; -0.4902 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.803 ) (cx ; 2; 0.4885 ) (cs ; 3; 2.044 ) (n ; 4; 0.4192 ) (T ; 5; 18.91 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 1.228 ) (cx ; 2; 4.572 ) (cs ; 3; -1.093 ) (n ; 4; 15.13 ) (T ; 5; -0.2803 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(4) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=4 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 -----------------------------------------------------------------------------***************************************************** Report of an error by traceback facility (*YERR*) : Error in module :YSOMHO Warning from 2nd-order improvement: Absolute value of 1st-order beta(FORMBE) < 1 . 2nd-order improvement by Hohenbichlers formula might be inaccurate because it is based on asymptotic theory ! ----- Second-Order Improvement : ----radii of curvature in U-space : -10.802 -32.351 54.951. 13.558. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.528 Corresponding prob. of failure = 0.29870. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.986 0.997 1.00 0.998 1.00 1.00 1.01 1.02 1.02. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 3.02 2.19 1.89 1.58 1.49 1.49 1.60 1.45 1.35. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 0.517 Corresponding prob. of failure = 0.30248 Correction factor by simulation = 1.013 Coefficient of Variation in % = 1.344 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.79838 4.00000 0.950 (cx : 2) 0.488270 0.500000 0.977 (cs : 3) 2.04486 2.00000 1.022 (n : 4) 0.418558 0.450000 0.930 (T : 5) 18.9321 18.0000 1.052 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 1.729 4.19E-02 -1.106 -0.6317 1.250 1.486 6.86E-02 -0.8925 -0.7420 1.500 1.286 9.92E-02 -0.7478 -0.8632 1.750 1.116 0.13 -0.6434 -0.9997 2.000 0.9681 0.17 -0.5644 -1.157 2.250 0.8374 0.20 -0.5025 -1.342 2.500 0.7203 0.24 -0.4529 -1.565 2.750 0.6142 0.27 -0.4121 -1.842 3.000 0.5173 0.30 -0.3780 -2.195 3.250 0.4281 0.33 -0.3491 -2.664 3.500 0.3455 0.36 -0.3243 -3.320 3.750 0.2685 0.39 -0.3027 -4.307 4.000 0.1966 0.42 -0.2838 -5.966 4.250 0.1290 0.45 -0.2670 -9.298 4.500 0.6526E-01 0.47 -0.2521 -19.87 4.750 0.2287E-01 0.49 -0.2388 -264.1 5.000 -0.3423E-01 0.51 -0.2269 -18.14 5.250 -0.8852E-01 0.54 -0.2160 -9.618 5.500 -0.1402 0.56 -0.2061 -6.627 5.750 -0.1896 0.58 -0.1971 -5.117 6.000 -0.2369 0.59 -0.1888 -4.201 6.250 -0.2822 0.61 -0.1812 -3.584. Análisis Probabilista. E. Mosquera..
(5) Propuesta Probabilista a 50 años. 6.500 6.750 7.000 7.250 7.500 7.750 8.000 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. -0.3257 -0.3676 -0.4079 -0.4467 -0.4842 -0.5204 -0.5555 -0.5895 -0.6224 -0.6543 -0.6853 -0.7155 -0.7448 -0.7733 -0.8011 -0.8282 -0.8546 -0.8804 -0.9055 -0.9301 -0.9541 -0.9775 -1.001 -1.023 -1.045 -1.066 -1.088 -1.108 -1.129 -1.148 -1.168 -1.187 -1.206 -1.224 -1.243. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=4 cm.. 0.63 0.64 0.66 0.67 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.80 0.81 0.82 0.82 0.83 0.84 0.84 0.85 0.85 0.86 0.86 0.87 0.87 0.87 0.88 0.88 0.89 0.89 0.89. -0.1741 -0.1676 -0.1615 -0.1559 -0.1506 -0.1457 -0.1411 -0.1367 -0.1326 -0.1288 -0.1251 -0.1217 -0.1184 -0.1153 -0.1124 -0.1096 -0.1069 -0.1044 -0.1019 -0.9960E-01 -0.9738E-01 -0.9526E-01 -0.9322E-01 -0.9127E-01 -0.8939E-01 -0.8759E-01 -0.8586E-01 -0.8419E-01 -0.8259E-01 -0.8104E-01 -0.7955E-01 -0.7811E-01 -0.7672E-01 -0.7538E-01 -0.7408E-01. -3.141 -2.807 -2.546 -2.336 -2.164 -2.019 -1.897 -1.791 -1.699 -1.619 -1.547 -1.484 -1.426 -1.375 -1.328 -1.285 -1.246 -1.209 -1.176 -1.145 -1.116 -1.090 -1.065 -1.041 -1.019 -0.9985 -0.9790 -0.9605 -0.9431 -0.9265 -0.9108 -0.8959 -0.8816 -0.8681 -0.8551. Representative Alphas of Variables FLIM(1), 2r4.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.48 0.22 -0.21 0.66 -0.49 1.00. E. Mosquera..
(6) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=4 cm.. Reliability Index FLIM(1), 2r4.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 2r4.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(7) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=5 cm.. -----------------------------------------------------------------------------Job name ............ : 2r5 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 13:37 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 5.000 ( 0.500000000000000E+01) = 1.000 ( 0.100000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 5.000 ( 0.500000000000000E+01) = 1.000 ( 0.100000000000000E+01). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(8) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=5 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 5.000 ) (cx ; 3; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 1.814 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.022 Corresponding approximate prob.of failure = 0.1534 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= 0.1326E-08 and Vector u-* (beta-point) : (x ; 1; -0.5139 ) (cx ; 2; -0.2219 ) (cs ; 3; 0.2037 ) (n ; 4; -0.6722 ) (T ; 5; 0.4872 ) Normalized U-space gradient (alfa-U) with norm = 1.096 : (x ; 1; 0.5029 ) (cx ; 2; 0.2172 ) (cs ; 3; -0.1994 ) (n ; 4; 0.6579 ) (T ; 5; -0.4768 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5029 ) (cx ; 2; 0.2172 ) (cs ; 3; -0.1994 ) (n ; 4; 0.6579 ) (T ; 5; -0.4768 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 4.486 ) (cx ; 2; 0.4778 ) (cs ; 3; 2.081 ) (n ; 4; 0.3895 ) (T ; 5; 19.75 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.5511 ) (cx ; 2; 2.380 ) (cs ; 3; -0.5463 ) (n ; 4; 8.011 ) (T ; 5; -0.1452 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(9) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=5 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 4 Calls of state-function : 25 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -11.678 -34.561 54.853. 12.522. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.024 Corresponding prob. of failure = 0.15285. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.984 0.995 1.00 0.997 1.00 1.00 1.02 1.02 1.03. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 4.14 2.93 2.50 2.09 1.96 1.96 2.14 1.96 1.82. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.013 Corresponding prob. of failure = 0.15544 Correction factor by simulation = 1.017 Coefficient of Variation in % = 1.804 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 4.48487 5.00000 0.897 (cx : 2) 0.477757 0.500000 0.956 (cs : 3) 2.08169 2.00000 1.041 (n : 4) 0.389353 0.450000 0.865 (T : 5) 19.7584 18.0000 1.098 ---------- Parameter study for Parameter: D0 --------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.207 1.37E-02 -1.080 -0.4820 1.250 1.970 2.44E-02 -0.8756 -0.5480 1.500 1.773 3.81E-02 -0.7362 -0.6146 1.750 1.606 5.41E-02 -0.6350 -0.6835 2.000 1.460 7.21E-02 -0.5583 -0.7559 2.250 1.331 9.16E-02 -0.4980 -0.8329 2.500 1.215 0.11 -0.4494 -0.9157 2.750 1.110 0.13 -0.4095 -1.006 3.000 1.013 0.16 -0.3759 -1.104 3.250 0.9246 0.18 -0.3475 -1.213 3.500 0.8424 0.20 -0.3231 -1.334 3.750 0.7657 0.22 -0.3018 -1.471 4.000 0.6939 0.24 -0.2832 -1.626 4.250 0.6264 0.27 -0.2667 -1.805 4.500 0.5628 0.29 -0.2520 -2.014 4.750 0.5025 0.31 -0.2388 -2.261 5.000 0.4454 0.33 -0.2269 -2.558 5.250 0.3910 0.35 -0.2161 -2.923 5.500 0.3391 0.37 -0.2064 -3.384 5.750 0.2895 0.39 -0.1974 -3.984 6.000 0.2421 0.40 -0.1892 -4.797 6.250 0.1966 0.42 -0.1816 -5.956 6.500 0.1528 0.44 -0.1746 -7.773 6.750 0.1108 0.46 -0.1681 -11.00 7.000 0.7022E-01 0.47 -0.1621 -18.35 7.250 0.3111E-01 0.49 -0.1565 -51.54 7.500 0.1121E-01 0.50 -0.1513 -68.90 7.750 -0.2529E-01 0.51 -0.1464 -21.13 8.000 -0.6062E-01 0.52 -0.1418 -12.64. Análisis Probabilista. E. Mosquera..
(10) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. -0.9485E-01 -0.1281 -0.1603 -0.1916 -0.2220 -0.2516 -0.2804 -0.3085 -0.3359 -0.3626 -0.3887 -0.4142 -0.4390 -0.4634 -0.4871 -0.5104 -0.5332 -0.5555 -0.5774 -0.5988 -0.6198 -0.6404 -0.6606 -0.6804 -0.6999 -0.7190 -0.7378 -0.7563. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=5 cm.. 0.54 0.55 0.56 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.70 0.71 0.72 0.73 0.73 0.74 0.75 0.75 0.76 0.76 0.77 0.78. -0.1375 -0.1334 -0.1295 -0.1259 -0.1225 -0.1192 -0.1161 -0.1132 -0.1104 -0.1077 -0.1052 -0.1028 -0.1005 -0.9825E-01 -0.9613E-01 -0.9410E-01 -0.9215E-01 -0.9028E-01 -0.8848E-01 -0.8675E-01 -0.8508E-01 -0.8348E-01 -0.8193E-01 -0.8044E-01 -0.7900E-01 -0.7761E-01 -0.7627E-01 -0.7497E-01. -9.100 -7.155 -5.924 -5.076 -4.455 -3.979 -3.605 -3.303 -3.053 -2.843 -2.664 -2.509 -2.375 -2.256 -2.151 -2.057 -1.973 -1.897 -1.827 -1.764 -1.706 -1.653 -1.604 -1.558 -1.516 -1.476 -1.440 -1.405. Representative Alphas of Variables FLIM(1), 2r5.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.50 0.22 -0.20 0.66 -0.48 1.00. E. Mosquera..
(11) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=5 cm.. Reliability Index FLIM(1), 2r5.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 2r5.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(12) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=6 cm.. -----------------------------------------------------------------------------Job name ............ : 2r6 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 13:38 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 6.000 ( 0.600000000000000E+01) = 1.200 ( 0.120000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 6.000 ( 0.600000000000000E+01) = 1.200 ( 0.120000000000000E+01). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(13) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=6 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 6.000 ) (cx ; 3; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 2.814 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.431 Corresponding approximate prob.of failure = 7.6149E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.4360E-07 and Vector u-* (beta-point) : (x ; 1; -0.7540 ) (cx ; 2; -0.3045 ) (cs ; 3; 0.2713 ) (n ; 4; -0.9333 ) (T ; 5; 0.6657 ) Normalized U-space gradient (alfa-U) with norm = 0.8095 : (x ; 1; 0.5267 ) (cx ; 2; 0.2128 ) (cs ; 3; -0.1895 ) (n ; 4; 0.6520 ) (T ; 5; -0.4650 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5267 ) (cx ; 2; 0.2128 ) (cs ; 3; -0.1895 ) (n ; 4; 0.6520 ) (T ; 5; -0.4650 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 5.095 ) (cx ; 2; 0.4695 ) (cs ; 3; 2.109 ) (n ; 4; 0.3660 ) (T ; 5; 20.40 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.3553 ) (cx ; 2; 1.722 ) (cs ; 3; -0.3835 ) (n ; 4; 5.864 ) (T ; 5; -0.1046 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(14) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=6 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 4 Calls of state-function : 25 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -12.415 -36.454 54.956. 11.680. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.426 Corresponding prob. of failure = 7.68775E-02. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.983 0.993 1.00 0.996 1.00 0.998 1.02 1.02 1.03. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 5.24 3.64 3.07 2.56 2.38 2.37 2.66 2.46 2.28. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.415 Corresponding prob. of failure = 7.84733E-02 Correction factor by simulation = 1.021 Coefficient of Variation in % = 2.249 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 5.09839 6.00000 0.850 (cx : 2) 0.469653 0.500000 0.939 (cs : 3) 2.10812 2.00000 1.054 (n : 4) 0.366298 0.450000 0.814 (T : 5) 20.3879 18.0000 1.133 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 2.579 4.95E-03 -1.047 -0.3984 1.250 2.355 9.27E-03 -0.8546 -0.4466 1.500 2.163 1.53E-02 -0.7217 -0.4930 1.750 2.000 2.28E-02 -0.6244 -0.5388 2.000 1.856 3.17E-02 -0.5502 -0.5848 2.250 1.729 4.19E-02 -0.4917 -0.6316 2.500 1.615 5.32E-02 -0.4444 -0.6797 2.750 1.511 6.54E-02 -0.4054 -0.7293 3.000 1.415 7.85E-02 -0.3727 -0.7810 3.250 1.328 9.22E-02 -0.3448 -0.8351 3.500 1.246 0.11 -0.3208 -0.8920 3.750 1.170 0.12 -0.2999 -0.9521 4.000 1.099 0.14 -0.2815 -1.016 4.250 1.031 0.15 -0.2653 -1.084 4.500 0.9681 0.17 -0.2508 -1.157 4.750 0.9082 0.18 -0.2378 -1.235 5.000 0.8512 0.20 -0.2261 -1.320 5.250 0.7970 0.21 -0.2155 -1.412 5.500 0.7453 0.23 -0.2058 -1.512 5.750 0.6958 0.24 -0.1970 -1.621 6.000 0.6485 0.26 -0.1888 -1.742 6.250 0.6030 0.27 -0.1814 -1.877 6.500 0.5593 0.29 -0.1744 -2.026 6.750 0.5173 0.30 -0.1680 -2.195 7.000 0.4768 0.32 -0.1621 -2.386 7.250 0.4376 0.33 -0.1565 -2.604 7.500 0.3998 0.34 -0.1513 -2.857 7.750 0.3633 0.36 -0.1464 -3.152 8.000 0.3279 0.37 -0.1419 -3.503. Análisis Probabilista. E. Mosquera..
(15) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 0.2936 0.2603 0.2280 0.1966 0.1660 0.1363 0.1073 0.7910E-01 0.5158E-01 0.2473E-01 0.1638E-01 -0.9216E-02 -0.3423E-01 -0.5869E-01 -0.8261E-01 -0.1060 -0.1290 -0.1514 -0.1734 -0.1950 -0.2162 -0.2369 -0.2573 -0.2773 -0.2969 -0.3162 -0.3352 -0.3538. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=6 cm.. 0.38 0.40 0.41 0.42 0.43 0.45 0.46 0.47 0.48 0.49 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.59 0.60 0.61 0.62 0.62 0.63 0.64. -0.1376 -0.1335 -0.1297 -0.1261 -0.1227 -0.1195 -0.1164 -0.1135 -0.1107 -0.1081 -0.1055 -0.1031 -0.1008 -0.9863E-01 -0.9651E-01 -0.9449E-01 -0.9255E-01 -0.9068E-01 -0.8889E-01 -0.8717E-01 -0.8551E-01 -0.8391E-01 -0.8237E-01 -0.8089E-01 -0.7945E-01 -0.7807E-01 -0.7673E-01 -0.7544E-01. -3.927 -4.445 -5.104 -5.961 -7.125 -8.797 -11.40 -16.03 -26.54 -73.66 -100.4 -30.34 -18.04 -12.92 -10.11 -8.332 -7.109 -6.216 -5.534 -4.996 -4.561 -4.202 -3.901 -3.644 -3.422 -3.229 -3.060 -2.910. Representative Alphas of Variables FLIM(1), 2r6.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.53 0.21 -0.19 0.65 -0.47 1.00. E. Mosquera..
(16) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=6 cm.. Reliability Index FLIM(1), 2r6.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 2r6.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(17) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=7 cm.. -----------------------------------------------------------------------------Job name ............ : 2r7 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 13:39 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 7.000 ( 0.700000000000000E+01) = 1.400 ( 0.140000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 7.000 ( 0.700000000000000E+01) = 1.400 ( 0.140000000000000E+01). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(18) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=7 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 7.000 ) (cx ; 3; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 3.814 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 1.774 Corresponding approximate prob.of failure = 3.8004E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.1999E-07 and Vector u-* (beta-point) : (x ; 1; -0.9746 ) (cx ; 2; -0.3702 ) (cs ; 3; 0.3221 ) (n ; 4; -1.144 ) (T ; 5; 0.8058 ) Normalized U-space gradient (alfa-U) with norm = 0.6682 : (x ; 1; 0.5493 ) (cx ; 2; 0.2086 ) (cs ; 3; -0.1815 ) (n ; 4; 0.6446 ) (T ; 5; -0.4541 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5493 ) (cx ; 2; 0.2086 ) (cs ; 3; -0.1815 ) (n ; 4; 0.6446 ) (T ; 5; -0.4541 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 5.636 ) (cx ; 2; 0.4630 ) (cs ; 3; 2.129 ) (n ; 4; 0.3471 ) (T ; 5; 20.90 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.2622 ) (cx ; 2; 1.394 ) (cs ; 3; -0.3032 ) (n ; 4; 4.786 ) (T ; 5; -8.4291E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(19) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=7 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 5 Calls of state-function : 31 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -13.064 -38.142 55.232. 10.977. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 1.762 Corresponding prob. of failure = 3.89964E-02. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.983 0.991 0.998 0.994 0.999 0.995 1.02 1.03 1.04. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 6.33 4.33 3.62 3.02 2.78 2.76 3.17 2.98 2.75. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 1.751 Corresponding prob. of failure = 3.99343E-02 Correction factor by simulation = 1.024 Coefficient of Variation in % = 2.691 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 5.64466 7.00000 0.806 (cx : 2) 0.463228 0.500000 0.926 (cs : 3) 2.12796 2.00000 1.064 (n : 4) 0.347747 0.450000 0.773 (T : 5) 20.8814 18.0000 1.160 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas 1.000 2.885 1.96E-03 -1.008 -0.3424 1.250 2.665 3.85E-03 -0.8299 -0.3818 1.500 2.485 6.47E-03 -0.7045 -0.4184 1.750 2.325 1.00E-02 -0.6118 -0.4533 2.000 2.185 1.44E-02 -0.5405 -0.4874 2.250 2.060 1.97E-02 -0.4840 -0.5211 2.500 1.948 2.57E-02 -0.4382 -0.5547 2.750 1.845 3.25E-02 -0.4003 -0.5886 3.000 1.751 3.99E-02 -0.3684 -0.6230 3.250 1.665 4.80E-02 -0.3412 -0.6579 3.500 1.584 5.66E-02 -0.3178 -0.6937 3.750 1.509 6.57E-02 -0.2973 -0.7304 4.000 1.438 7.52E-02 -0.2793 -0.7682 4.250 1.372 8.51E-02 -0.2634 -0.8072 4.500 1.309 9.53E-02 -0.2491 -0.8475 4.750 1.249 0.11 -0.2363 -0.8896 5.000 1.193 0.12 -0.2248 -0.9333 5.250 1.139 0.13 -0.2143 -0.9790 5.500 1.087 0.14 -0.2048 -1.027 5.750 1.038 0.15 -0.1961 -1.077 6.000 0.9910 0.16 -0.1881 -1.129 6.250 0.9457 0.17 -0.1807 -1.185 6.500 0.9022 0.18 -0.1738 -1.244 6.750 0.8603 0.19 -0.1675 -1.306 7.000 0.8199 0.21 -0.1616 -1.371 7.250 0.7809 0.22 -0.1561 -1.441 7.500 0.7432 0.23 -0.1509 -1.516 7.750 0.7068 0.24 -0.1461 -1.596 8.000 0.6714 0.25 -0.1416 -1.682. Análisis Probabilista. E. Mosquera..
(20) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 0.6372 0.6039 0.5716 0.5403 0.5097 0.4800 0.4511 0.4228 0.3953 0.3684 0.3422 0.3166 0.2915 0.2670 0.2430 0.2196 0.1966 0.1740 0.1520 0.1303 0.1091 0.8824E-01 0.6778E-01 0.4770E-01 0.2798E-01 0.2646E-01 0.7431E-02 -0.1128E-01. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=7 cm.. 0.26 0.27 0.28 0.29 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.48 0.49 0.49 0.50 0.50. -0.1374 -0.1334 -0.1296 -0.1260 -0.1226 -0.1194 -0.1164 -0.1135 -0.1107 -0.1081 -0.1056 -0.1032 -0.1009 -0.9869E-01 -0.9659E-01 -0.9458E-01 -0.9265E-01 -0.9080E-01 -0.8902E-01 -0.8730E-01 -0.8565E-01 -0.8406E-01 -0.8253E-01 -0.8105E-01 -0.7963E-01 -0.7825E-01 -0.7692E-01 -0.7563E-01. -1.774 -1.874 -1.982 -2.099 -2.228 -2.369 -2.525 -2.698 -2.890 -3.107 -3.351 -3.631 -3.954 -4.331 -4.776 -5.310 -5.963 -6.780 -7.832 -9.236 -11.21 -14.18 -19.17 -29.28 -60.76 -1069. -55.45 -28.70. Representative Alphas of Variables FLIM(1), 2r7.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.55 0.21 -0.18 0.64 -0.45 1.00. E. Mosquera..
(21) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=7 cm.. Reliability Index FLIM(1), 2r7.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 2r7.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(22) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=8 cm.. -----------------------------------------------------------------------------Job name ............ : 2r8 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 13:41 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 8.000 ( 0.800000000000000E+01) = 1.600 ( 0.160000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 8.000 ( 0.800000000000000E+01) = 1.600 ( 0.160000000000000E+01). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 2.000 ( 0.200000000000000E+01) Standard deviation........ = 0.4000 ( 0.400000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.000 ( 0.200000000000000E+01) Distr.Param.no.2 : sigma = 0.4000 ( 0.400000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(23) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=8 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 8.000 ) (cx ; 3; 2.000 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 4.814 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 2.068 Corresponding approximate prob.of failure = 1.9336E-02 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.6982E-08 and Vector u-* (beta-point) : (x ; 1; -1.181 ) (cx ; 2; -0.4230 ) (cs ; 3; 0.3612 ) (n ; 4; -1.315 ) (T ; 5; 0.9176 ) Normalized U-space gradient (alfa-U) with norm = 0.5819 : (x ; 1; 0.5712 ) (cx ; 2; 0.2046 ) (cs ; 3; -0.1747 ) (n ; 4; 0.6360 ) (T ; 5; -0.4438 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.5712 ) (cx ; 2; 0.2046 ) (cs ; 3; -0.1747 ) (n ; 4; 0.6360 ) (T ; 5; -0.4438 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 6.110 ) (cx ; 2; 0.4577 ) (cs ; 3; 2.144 ) (n ; 4; 0.3317 ) (T ; 5; 21.30 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.2077 ) (cx ; 2; 1.190 ) (cs ; 3; -0.2541 ) (n ; 4; 4.112 ) (T ; 5; -7.1727E-02) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(24) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=8 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 6 Calls of state-function : 37 ---------------------------------------------------------------------------------- Second-Order Improvement : ----radii of curvature in U-space : -13.653 -39.695 55.669. 10.374. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 2.049 Corresponding prob. of failure = 2.02110E-02. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.982 0.988 0.995 0.992 0.994 0.990 1.02 1.03 1.04. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 7.42 5.01 4.16 3.47 3.17 3.12 3.69 3.51 3.22. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 2.038 Corresponding prob. of failure = 2.07536E-02 Correction factor by simulation = 1.027 Coefficient of Variation in % = 3.138 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 6.12715 8.00000 0.766 (cx : 2) 0.458070 0.500000 0.916 (cs : 3) 2.14319 2.00000 1.072 (n : 4) 0.332696 0.450000 0.739 (T : 5) 21.2742 18.0000 1.182 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 3.138 8.50E-04 -0.9631 -0.3002 1.250 2.928 1.71E-03 -0.8013 -0.3351 1.500 2.749 2.98E-03 -0.6847 -0.3663 1.750 2.595 4.73E-03 -0.5972 -0.3952 2.000 2.464 6.87E-03 -0.5294 -0.4228 2.250 2.342 9.59E-03 -0.4753 -0.4496 2.500 2.232 1.28E-02 -0.4311 -0.4757 2.750 2.131 1.65E-02 -0.3944 -0.5016 3.000 2.038 2.08E-02 -0.3635 -0.5274 3.250 1.953 2.54E-02 -0.3370 -0.5532 3.500 1.873 3.05E-02 -0.3142 -0.5791 3.750 1.799 3.60E-02 -0.2942 -0.6052 4.000 1.729 4.19E-02 -0.2766 -0.6316 4.250 1.663 4.81E-02 -0.2610 -0.6585 4.500 1.601 5.47E-02 -0.2470 -0.6858 4.750 1.542 6.15E-02 -0.2345 -0.7136 5.000 1.486 6.86E-02 -0.2231 -0.7421 5.250 1.433 7.60E-02 -0.2128 -0.7711 5.500 1.382 8.35E-02 -0.2034 -0.8009 5.750 1.333 9.13E-02 -0.1948 -0.8316 6.000 1.286 9.92E-02 -0.1869 -0.8631 6.250 1.241 0.11 -0.1797 -0.8956 6.500 1.198 0.12 -0.1729 -0.9292 6.750 1.156 0.12 -0.1667 -0.9638 7.000 1.116 0.13 -0.1608 -0.9996 7.250 1.077 0.14 -0.1554 -1.037 7.500 1.040 0.15 -0.1503 -1.075 7.750 1.003 0.16 -0.1456 -1.115 8.000 0.9681 0.17 -0.1411 -1.157. Análisis Probabilista. E. Mosquera..
(25) Propuesta Probabilista a 50 años. 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. 0.9340 0.9009 0.8687 0.8374 0.8070 0.7773 0.7485 0.7203 0.6928 0.6660 0.6398 0.6142 0.5892 0.5647 0.5407 0.5173 0.4943 0.4718 0.4497 0.4281 0.4069 0.3860 0.3656 0.3455 0.3257 0.3063 0.2873 0.2685. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=8 cm.. 0.18 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.24 0.25 0.26 0.27 0.28 0.29 0.29 0.30 0.31 0.32 0.33 0.33 0.34 0.35 0.36 0.36 0.37 0.38 0.39 0.39. -0.1369 -0.1329 -0.1292 -0.1257 -0.1223 -0.1191 -0.1161 -0.1132 -0.1105 -0.1079 -0.1054 -0.1030 -0.1008 -0.9859E-01 -0.9651E-01 -0.9451E-01 -0.9260E-01 -0.9075E-01 -0.8898E-01 -0.8728E-01 -0.8563E-01 -0.8405E-01 -0.8253E-01 -0.8106E-01 -0.7964E-01 -0.7827E-01 -0.7695E-01 -0.7566E-01. -1.200 -1.245 -1.293 -1.342 -1.394 -1.448 -1.505 -1.565 -1.629 -1.696 -1.767 -1.842 -1.922 -2.007 -2.098 -2.195 -2.299 -2.411 -2.533 -2.664 -2.806 -2.961 -3.132 -3.319 -3.527 -3.757 -4.015 -4.306. Representative Alphas of Variables FLIM(1), 2r8.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.57 0.20 -0.17 0.64 -0.44 1.00. E. Mosquera..
(26) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIc‐ CEM I/II‐ Cs=2%‐ R=8 cm.. Reliability Index FLIM(1), 2r8.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.0. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. 13.0. 14.0. 15.0. 11.0. 12.0. 13.0. 14.0. 15.0. Failure Probability FLIM(1), 2r8.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. Análisis Probabilista. E. Mosquera..
(27) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2,5%‐ R=4 cm.. -----------------------------------------------------------------------------Job name ............ : 25r4 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 13:19 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 4.000 ( 0.400000000000000E+01) = 0.8000 ( 0.800000000000000E+00) = 0.2000 ( 0.200000000000000E+00) = 4.000 ( 0.400000000000000E+01) = 0.8000 ( 0.800000000000000E+00). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 2.500 ( 0.250000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.500 ( 0.250000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(28) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIc‐ CEM I/II‐ Cs=2,5%‐ R=4 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 4.000 ) (cx ; 3; 2.500 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 0.4781 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.294 Corresponding approximate prob.of failure = 0.3844 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.2171E-08 and Vector u-* (beta-point) : (x ; 1; -0.1397 ) (cx ; 2; -5.4457E-02) (cs ; 3; 5.3296E-02) (n ; 4; -0.1979 ) (T ; 5; 0.1482 ) Normalized U-space gradient (alfa-U) with norm = 3.523 : (x ; 1; 0.4750 ) (cx ; 2; 0.1852 ) (cs ; 3; -0.1812 ) (n ; 4; 0.6732 ) (T ; 5; -0.5041 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4750 ) (cx ; 2; 0.1852 ) (cs ; 3; -0.1812 ) (n ; 4; 0.6732 ) (T ; 5; -0.5041 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 3.888 ) (cx ; 2; 0.4946 ) (cs ; 3; 2.527 ) (n ; 4; 0.4322 ) (T ; 5; 18.53 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 2.092 ) (cx ; 2; 6.524 ) (cs ; 3; -1.277 ) (n ; 4; 26.35 ) (T ; 5; -0.4933 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
(29) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2,5%‐ R=4 cm.. Constant Parameters (PVEC): (t0 ; 1; 7.6700E-02) (t ; 2; 50.00 ) (ke ; 3; 2.400 ) (ka ; 4; 0.7000 ) (D0 ; 5; 3.000 ) -----------------------------------------------------------------------------Statistics after beta-point search Gradient evaluations : 3 Calls of state-function : 19 -----------------------------------------------------------------------------***************************************************** Report of an error by traceback facility (*YERR*) : Error in module :YSOMHO Warning from 2nd-order improvement: Absolute value of 1st-order beta(FORMBE) < 1 . 2nd-order improvement by Hohenbichlers formula might be inaccurate because it is based on asymptotic theory ! ----- Second-Order Improvement : ----radii of curvature in U-space : -12.970 -30.949 61.851. 13.852. ------------------ Results of Second-Order improvement-----------------Second-Order reliability index = 0.301 Corresponding prob. of failure = 0.38153. ----- Importance Sampling scheme based on SORM results ----Initialize Rand.Numb.Gen. with set no. 1 Importance sampling: Sample no. 10 E(Sim)= Importance sampling: Sample no. 20 E(Sim)= Importance sampling: Sample no. 30 E(Sim)= Importance sampling: Sample no. 40 E(Sim)= Importance sampling: Sample no. 50 E(Sim)= Importance sampling: Sample no. 60 E(Sim)= Importance sampling: Sample no. 70 E(Sim)= Importance sampling: Sample no. 80 E(Sim)= Importance sampling: Sample no. 90 E(Sim)=. 0.991 0.998 1.00 0.999 1.00 1.00 1.01 1.01 1.02. C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.= C.o.V.=. 2.46 1.74 1.49 1.24 1.16 1.20 1.25 1.13 1.06. (%) (%) (%) (%) (%) (%) (%) (%) (%). -------------------- Results of importance sampling -------------------Corrected reliability index = 0.292 Corresponding prob. of failure = 0.38523 Correction factor by simulation = 1.010 Coefficient of Variation in % = 1.066 100(=NSIMUL) samples generated; 0 samples failed. -----------------------------------------------------------------------------Partial Safety Factors: Equival. x-* / Characteristic Value Basic Variable, Equival. x-* , Charact. Value, Part.Safety Fact. (x : 1) 3.88545 4.00000 0.971 (cx : 2) 0.494417 0.500000 0.989 (cs : 3) 2.52732 2.50000 1.011 (n : 4) 0.431735 0.450000 0.959 (T : 5) 18.5471 18.0000 1.030 ---------- Parameter study for Parameter: D0 ---------Param. value, Reliab.index, Prob.(Failure), Param. Sens., Param. Elas. 1.000 1.528 6.32E-02 -1.127 -0.7269 1.250 1.280 0.10 -0.9089 -0.8750 1.500 1.076 0.14 -0.7613 -1.047 1.750 0.9023 0.18 -0.6548 -1.253 2.000 0.7516 0.23 -0.5743 -1.509 2.250 0.6183 0.27 -0.5115 -1.839 2.500 0.4988 0.31 -0.4609 -2.285 2.750 0.3906 0.35 -0.4194 -2.924 3.000 0.2918 0.39 -0.3847 -3.925 3.250 0.2008 0.42 -0.3553 -5.727 3.500 0.1165 0.45 -0.3300 -9.954 3.750 0.3802E-01 0.48 -0.3080 -31.12 4.000 -0.1983E-01 0.51 -0.2888 -30.78 4.250 -0.8883E-01 0.54 -0.2719 -10.67 4.500 -0.1539 0.56 -0.2567 -6.628 4.750 -0.2154 0.59 -0.2432 -4.879 5.000 -0.2737 0.61 -0.2310 -3.901 5.250 -0.3292 0.63 -0.2199 -3.277 5.500 -0.3820 0.65 -0.2099 -2.843 5.750 -0.4325 0.67 -0.2007 -2.523 6.000 -0.4809 0.68 -0.1923 -2.278 6.250 -0.5272 0.70 -0.1845 -2.083. Análisis Probabilista. E. Mosquera..
(30) Propuesta Probabilista a 50 años. 6.500 6.750 7.000 7.250 7.500 7.750 8.000 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75 12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00. -0.5717 -0.6145 -0.6557 -0.6955 -0.7338 -0.7709 -0.8068 -0.8416 -0.8754 -0.9081 -0.9399 -0.9708 -1.001 -1.030 -1.059 -1.086 -1.113 -1.140 -1.166 -1.191 -1.216 -1.240 -1.263 -1.286 -1.309 -1.331 -1.353 -1.374 -1.395 -1.415 -1.435 -1.455 -1.475 -1.494 -1.512. Ambiente IIIc‐ CEM I/II‐ Cs=2,5%‐ R=4 cm.. 0.72 0.73 0.74 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.83 0.84 0.85 0.86 0.86 0.87 0.87 0.88 0.88 0.89 0.89 0.90 0.90 0.90 0.91 0.91 0.92 0.92 0.92 0.92 0.93 0.93 0.93 0.93. -0.1774 -0.1707 -0.1646 -0.1588 -0.1535 -0.1485 -0.1438 -0.1394 -0.1352 -0.1313 -0.1276 -0.1241 -0.1207 -0.1176 -0.1146 -0.1118 -0.1090 -0.1065 -0.1040 -0.1016 -0.9938E-01 -0.9722E-01 -0.9515E-01 -0.9317E-01 -0.9126E-01 -0.8943E-01 -0.8767E-01 -0.8598E-01 -0.8434E-01 -0.8277E-01 -0.8126E-01 -0.7979E-01 -0.7838E-01 -0.7702E-01 -0.7570E-01. -1.925 -1.794 -1.684 -1.589 -1.507 -1.436 -1.373 -1.316 -1.266 -1.221 -1.180 -1.142 -1.108 -1.076 -1.047 -1.021 -0.9956 -0.9723 -0.9506 -0.9303 -0.9113 -0.8933 -0.8764 -0.8605 -0.8454 -0.8311 -0.8175 -0.8046 -0.7923 -0.7806 -0.7694 -0.7587 -0.7485 -0.7387 -0.7293. Representative Alphas of Variables FLIM(1), 25r4.pti. x cx cs n T Sum of a². Análisis Probabilista. 0.47 0.19 -0.18 0.67 -0.50 1.00. E. Mosquera..
(31) Propuesta Probabilista a 50 años. 3.00. Ambiente IIIc‐ CEM I/II‐ Cs=2,5%‐ R=4 cm.. Reliability Index FLIM(1), 25r4.pti. Beta. 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00. 0.0. 1.5. Failure Probability 0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 1.0. 3.0. 4.5. 6.0. 7.5 D0. 9.0. 10.5. 12.0. 13.5. 15.0. Failure Probability FLIM(1), 25r4.pti. 2.0. 3.0. 4.0. 5.0. 6.0. 7.0. D0. 8.0. 9.0. 10.0. 11.0. 12.0. Análisis Probabilista. 13.0. 14.0. 15.0. E. Mosquera..
(32) Propuesta Probabilista a 50 años. Ambiente IIIc‐ CEM I/II‐ Cs=2,5%‐ R=5 cm.. -----------------------------------------------------------------------------Job name ............ : 25r5 Failure criterion no. : 1 Comment : No commen Transformation type : Rosenblatt Optimization algorithm: RFLS Date(dd.mm.yyyy) .... : 25.02.2011 Time(hh:mm) ........ : 13:20 Comrel-TI, (Version 8), (c) Copyright: RCP GmbH (1989-2009) ----------------------------------------------------------------------------------------------------------------------------------------------------------Defined in State Functions Window for Symbolic Processor: DEFFUNC(1)()=D0*(t0/t)^n DEFFUNC(2)()=5725*(1/293-1/(T+273)) DEFFUNC(3)()=(T/20)*exp(FUNC(2)) FLIM(1)=x-2*(1-sqrt(cx/cs))*sqrt(3*0.315*FUNC(1)*FUNC(3)*t*ke*ka) -----------------------------------------------------------------------------************************************************ Check Stochastic Model for COMREL-TI No.of basic variables: NBV = 5 ************************************************. Variable: x ; No. on Comment : Recubrimiento en Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector = 1 cm : Normal (2) : Mean & Std.Dev. (0) = 5.000 ( 0.500000000000000E+01) = 1.000 ( 0.100000000000000E+01) = 0.2000 ( 0.200000000000000E+00) = 5.000 ( 0.500000000000000E+01) = 1.000 ( 0.100000000000000E+01). Variable: cx ; No. on X-vector = 2 Comment : Conc. Critica Cloruros en % cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 0.5000 ( 0.500000000000000E+00) Standard deviation........ = 0.1000 ( 0.100000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 0.5000 ( 0.500000000000000E+00) Distr.Param.no.2 : sigma = 0.1000 ( 0.100000000000000E+00) ------------------------Variable: cs ; No. on X-vector = 3 Comment : Conc. Super. Cloruros en% cemento Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev. (0) Mean value................ = 2.500 ( 0.250000000000000E+01) Standard deviation........ = 0.5000 ( 0.500000000000000E+00) Coefficient of Variation.. = 0.2000 ( 0.200000000000000E+00) Distr.Param.no.1 : m = 2.500 ( 0.250000000000000E+01) Distr.Param.no.2 : sigma = 0.5000 ( 0.500000000000000E+00) ------------------------Variable: n ; No. on Comment : Factor de edad Distribution Type......... Form of Input............. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. X-vector =. 4. : Normal (2) : Mean & Std.Dev. (0) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01) = 0.2000 ( 0.200000000000000E+00) = 0.4500 ( 0.450000000000000E+00) = 9.0000E-02 ( 0.900000000000000E-01). Variable: T ; No. on X-vector = 5 Comment : Temperatura en ºC Distribution Type......... : Normal (2) Form of Input............. : Mean & Std.Dev.. (0). Análisis Probabilista. E. Mosquera..
(33) Propuesta Probabilista a 50 años. Mean value................ Standard deviation........ Coefficient of Variation.. Distr.Param.no.1 : m Distr.Param.no.2 : sigma -------------------------. = = = = =. Ambiente IIIc‐ CEM I/II‐ Cs=2,5%‐ R=5 cm.. 18.00 3.600 0.2000 18.00 3.600. ( 0.180000000000000E+02) ( 0.360000000000000E+01) ( 0.200000000000000E+00) ( 0.180000000000000E+02) ( 0.360000000000000E+01). -- Constant (deterministic) Parameters -Parameter :t0 ; No. on PVEC= Comment : tiempo inicial en años. 1 with value =. Parameter :t ; No. on PVEC= Comment : tiempo final en años. 2 with value =. 50.00. Parameter :ke ; No. on PVEC= 3 with value = Comment : Param de Ejecución y curado. 2.400. Parameter :ka ; No. on PVEC= Comment : Param de microclima. 0.7670E-01. 4 with value =. 0.7000. Parameter :D0 ; No. on PVEC= 5 with value = Comment : Coef. de Difusión en m2/s 10^-12 -------------------------. 3.000. (x (cs (T. ; ; ;. (Lower bounds on U-space variables) 1; -36.69 ) (cx ; 2; 3; -36.69 ) (n ; 4; 5; -36.69 ). -36.69 -36.69. ) ). (x (cs (T. ----- Default U-start = Origin (U=0) ---; 1; 0.000 ) (cx ; 2; 0.000 ; 3; 0.000 ) (n ; 4; 0.000 ; 5; 0.000 ). ) ). (x (cs (T. --; ; ;. ) ). X-start: Median values from U=0 1; 5.000 ) (cx ; 3; 2.500 ) (n ; 5; 18.00 ). ---2; 0.5000 4; 0.4500. (Upper bounds on U-space variables) (x ; 1; 36.69 ) (cx ; 2; 36.69 ) (cs ; 3; 36.69 ) (n ; 4; 36.69 ) (T ; 5; 36.69 ) -----------------------------------------------------------------------------Echo of Control Switches (integer parameters) for this run : IMETH , IALFA , NSIMUL, IUDEF , IGRFL ,MAXIT1, MAXIT2 2 0 100 0 0 50 50 Echo of Control Constants (real parameters) for this run : EPSCON=1.00E-03, SMU=0.10, SIMSTA=1.000000 SCALing constant (set by COMREL) = 1.478 ********************************** RESULTS: ********************************** First-Order reliability index : (FORMBE) = 0.808 Corresponding approximate prob.of failure = 0.2095 -----------------------------------------------------------------------------Scaled State-Function value at x-*(u-*)= -0.9489E-08 and Vector u-* (beta-point) : (x ; 1; -0.4036 ) (cx ; 2; -0.1469 ) (cs ; 3; 0.1388 ) (n ; 4; -0.5410 ) (T ; 5; 0.3955 ) Normalized U-space gradient (alfa-U) with norm = 1.354 : (x ; 1; 0.4995 ) (cx ; 2; 0.1819 ) (cs ; 3; -0.1718 ) (n ; 4; 0.6696 ) (T ; 5; -0.4895 ) Normalized Representative alfa-values with norm = 1.000 : (x ; 1; 0.4995 ) (cx ; 2; 0.1819 ) (cs ; 3; -0.1718 ) (n ; 4; 0.6696 ) (T ; 5; -0.4895 ) -----------------------------------------------------------------------------Solution in Basic- (X-) space (x-*): (x ; 1; 4.596 ) (cx ; 2; 0.4853 ) (cs ; 3; 2.569 ) (n ; 4; 0.4013 ) (T ; 5; 19.42 ) Gradient in Basic- (X-) space (scaled by 1/SCAL, see above): (x ; 1; 0.6765 ) (cx ; 2; 2.463 ) (cs ; 3; -0.4653 ) (n ; 4; 10.08 ) (T ; 5; -0.1842 ) ------------------------------------------------------------------------------. Análisis Probabilista. E. Mosquera..
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