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SYSREL Sample "Crash": Results Text Output Parts of SYSREL’s results file are printed here, first the stochastic model:
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Job name ............ : CRASH
Comment : Undefined
Transformation type : Rosenblatt
Optimization algorithm: NLPQL
SYSREL, (Version 9.0), (C) Copyright: RCP-GmbH 1989-1996
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************************************************
Check Stochastic Model for SYSREL
No.of basic variables: NBV = 8
************************************************
Variable: Speed0 ; No. on X-vector = 1
Comment : Initial vehicle velocity
Distribution Type.........= 3 : Lognormal (3)
Form of Input.............= 0 : Moments
Mean value................= 22.00 ( .220000000000000E+02)
Standard deviation........= 2.200 ( .220000000000000E+01)
Parameter VP(1 ) :xi = 21.89 ( .218908181846198E+02)
Parameter VP(2 ) :delta = .9975E-01 ( .997513451195939E-01)
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Variable: Mass ; No. on X-vector = 2
Comment : Vehicle mass
Distribution Type.........= 2 : Normal (2)
Form of Input.............= 0 : Moments
Mean value................= .1000E+05 ( .100000000000000E+05)
Standard deviation........= 5500. ( .550000000000000E+04)
Parameter VP(1 ) :m = .1000E+05 ( .100000000000000E+05)
Parameter VP(2 ) :sigma = 5500. ( .550000000000000E+04)
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Variable: Stiffnes; No. on X-vector = 3
Comment : Vehicle stiffness
Distribution Type.........= 3 : Lognormal (3)
Form of Input.............= 0 : Moments
Mean value................= .3000E+06 ( .300000000000000E+06)
Standard deviation........= .6000E+05 ( .600000000000000E+05)
Parameter VP(1 ) :xi = .2942E+06 ( .294174202707276E+06)
Parameter VP(2 ) :delta = .1980 ( .198042200435365E+00)
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Variable: Decelera; No. on X-vector = 4
Comment : Vehicle deceleration
Distribution Type.........= 3 : Lognormal (3)
Form of Input.............= 0 : Moments
Mean value................= 4.000 ( .400000000000000E+01)
Standard deviation........= 1.300 ( .130000000000000E+01)
Parameter VP(1 ) :xi = 3.804 ( .380413627492379E+01)
Parameter VP(2 ) :delta = .3169 ( .316876609947646E+00)
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Variable: Phi ; No. on X-vector = 5
Comment : angle [deg] between collision course and track direction
Distribution Type.........= 11 : Rayleigh (11)
Form of Input.............= 0 : Moments
Mean value................= 10.00 ( .100000000000000E+02)
Standard deviation........= 5.210 ( .521000000000000E+01)
Parameter VP(1 ) :alpha = 7.953 ( .795254267422614E+01)
Parameter VP(2 ) :tau = .3297E-01 ( .329658387875664E-01)
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Variable: Uaux ; No. on X-vector = 6
Comment : Auxiliary variable
Distribution Type.........= 2 : Normal (2)
Form of Input.............= 1 : Parameters
Mean value................= .0000 ( .000000000000000E+00)
Standard deviation........= 1.000 ( .100000000000000E+01)
Parameter VP(1 ) :m = .0000 ( .000000000000000E+00)
Parameter VP(2 ) :sigma = 1.000 ( .100000000000000E+01)
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Variable: kappa ; No. on X-vector = 7
Comment : Pay load factor
Distribution Type.........= 6 : Beta (6)
Form of Input.............= 0 : Moments
Mean value................= .7000 ( .700000000000000E+00)
Standard deviation........= .1000 ( .100000000000000E+00)
Parameter VP(1 ) :r = 6.286 ( .628571428571428E+01)
Parameter VP(2 ) :t = 4.714 ( .471428571428571E+01)
Parameter VP(3 ) :a = .3000 ( .300000000000000E+00)
Parameter VP(4 ) :b = 1.000 ( .100000000000000E+01)
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Variable: Fc ; No. on X-vector = 8
Comment : Maximum interaction force
Distribution Type.........= 3 : Lognormal (3)
Form of Input.............= 1 : Parameters
Mean value................= .2010E+07 ( .201002504171880E+07)
Standard deviation........= .2015E+06 ( .201506058892408E+06)
Parameter VP(1 ) is Const.Par.No. 5
Parameter VP(2 ) :delta = .1000 ( .100000000000000E+00)
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-- Constant (deterministic) Parameters --
Parameter :Dist ; No. on PVEC= 1 with value = 4.500
Comment : Distance from structural element to the road
Parameter :n ; No. on PVEC= 2 with value = 2500.
Comment : number of vehicles per day
Parameter :lamda ; No. on PVEC= 3 with value = .1000E-09
Comment : rate for leaving the track
Parameter :t ; No. on PVEC= 4 with value = .3650E+05
Comment : reference time in days
Parameter :xsi ; No. on PVEC= 5 with value = .2000E+07
Comment : Maximum interaction force
Parameter :b ; No. on PVEC= 6 with value = 2.500
Comment : width of the truck (or obstacle)
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----- Correlations of normal/lognormal variables on input -----
1.000
.000 1.000
.000 .300 1.000
.000 .000 .000 1.000
.000 .000 .000 .000 1.000
.000 .000 .000 .000 .000 1.000
.000 .000 .000 .000 .000 .000 1.000
.000 .000 .000 .000 .000 .000 .000 1.000
Next, the echo of the logical model is provided:Assignment of sequential Constraint numbers in SYSREL
to JLIM-numbers in LIMIT:
Constraint no.= 1; JLIM no.in LIMIT = 1 :
Conditional failure event of column
Constraint no.= 2; JLIM no.in LIMIT = 2 :
Condition of braking before hit
Constraint no.= 3; JLIM no.in LIMIT = 3 :
Auxiliary limit for event probabilities
Input: K M A T (Cols.=Constraints; Lines=Cut-Sets):
1 2 3
1: I I I
Occurrence of Basic-(X-)Variables in the state functions (LIMIT).
Names of all ( 8) Basic Variables, followed by JLIM-numbers
denoting Constraints where they are used.
Speed0 : 1, 2,
Mass : 1,
Stiffnes: 1,
Decelera: 1, 2,
Phi : 1, 2, 3,
Uaux : 3,
kappa : 1,
Fc : 1, 2,
Finally, the results from the parameter study on the median of Fc are given:---------- Parameter study for Parameter: xsi ------------ Par.Value , Lower Bound Pf, L.B.-beta , Upper Bound Pf, U.B.-beta .1500E+07 .1718E-02 2.926 .1718E-02 2.926 ---------------------------------------------------------------------------- .1750E+07 .3905E-03 3.359 .3905E-03 3.359 .1878E-05 .9783 ---------------------------------------------------------------------------- .2000E+07 .8221E-04 3.768 .8221E-04 3.768 .1753E-05 .9304 ---------------------------------------------------------------------------- .2250E+07 .1644E-04 4.153 .1644E-04 4.153 .1633E-05 .8848 ---------------------------------------------------------------------------- .2500E+07 .3159E-05 4.516 .3159E-05 4.516 .1521E-05 .8420 ---------------------------------------------------------------------------- Statistics in SYSREL: No.of state-function calls= 1104 gradient calls= 120 (Estimated REAL-storage= 1328) Needed REAL-storage= 1118 Needed INTEGER-storage= 1136 CPU-time overall : 14.13 seconds CPU-time in *LIMIT* : 1.45 seconds The error indicator (IER) at the end of SYSREL was = 0 Graphical Output Finally, some results in graphical form demonstrate some of the post-processing capabilities of SYSREL. Reliability index of the parallel system for a parameter run on the median of the resistance Fc
Influence of the Basic Variables on system reliability (so called a-values)
Influence of the mean values of the Basic Variables on system reliability
Influence of the standard deviations of the Basic Variables on system reliability
Influence of the constant parameters on system reliability
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