####################################################
### V6 Resource File                             ###
### generated on: Thu Feb 02 16:06:41 EST 2012   ###
###                                              ###
### This file is designed to be delivered to the ###
### translator.                                  ###
####################################################
7619=SENSITIVITIES
10205=Response
11112=Reliability Index (beta)
12208=Reliability Constraint results: 
27907=Adjusted Reliability Index (beta\')
35772=Reliability Constraint: 
37739=MPP in x-space
37746=Std. deviation
42341=MPP - Most Probable Point of failure
42862=Reliability Constraint
43464=Actual Reliability
45592=MVP - Mean Value Point
48961=Nominal Value
62615=Gradient at MVP in x-space
68527=Random Variable
70880=Responses at Mean Value Point: 
74993=Gradient at MPP in u-space
76178=Second order reliability could not be calculated. Ill-defined Hessian Matrix.
78813=Gradient at MPP in x-space
80763=Bound Value
85333=Bound Type
85443=Fractional Effect
88713=Mean
92148=FORM will be used for reliability calculation since only one random variable is defined
92149=Adjusted Reliability Index (beta\')
92150=Adjusted Reliability Index (beta\')
####################################################
###   Meta Model I18N string                       #
####################################################
desc=Second Order Reliability Method
dispname=Second Order Reliability Method (SORM)
longdesc=<b>SORM - Second Order Reliability Method</b><br><br> The <i>Second Order Reliability Method (SORM)</i> is a probabilistic method that comes from civil engineering, originally developed for performing structural reliability analysis. Given one or more identified random variables, the focus in structural reliability analysis is to assess the <i>probability of failure</i> - the probability of violating a constraint - of a structural component or system, resulting from performance (output) variation caused by the variation of uncertain, random (input) variables. The structural reliability is then defined as the probability of satisfying a constraint, and is equal to 1-probability of failure.\t<br><br> SORM takes advantage of the desirable properties of the standard normal probability distribution. Hasofer and Lind (1974) defined the reliability index as the shortest distance from the origin of the standard normal space (U-space) to a point on the failure surface. Mathematically, determining the reliability index is a minimization problem with one equality constraint(shortest distance such that the solution point is on the constraint, g(<b>X</b>)=g(<b>U</b>)=0). <br><br> A transformation is introduced to map the original random vector <b>X</b> (in X-space) to the standard, uncorrelated normal vector using <b>U</b>=T(<b>X</b>). The solution of the minimization problem in U-space, U*, is called the <i>Most Probable Point (MPP)</i>. <br><br> If the failure function g(<b>U</b>) is quadratic in terms of the normally distributed random variables U<sub>i</sub>, the failure probability is calculated as: <br><br> P<sub>f</sub> = \u03A6(-\u03B2) \u220F<sub>i=1</sub><sup>n-1</sup> (1+\u03B2 \u03BA<sub>i</sub>)<sup>(-1/2)</sup><br><br> where, \u03A6 is the standard normal distribution function, \u03B2 is the distance to the MPP and \u03BA<sub>i</sub> are the principal curvatures at MPP. 
prop.dispname.finitedifferencestepsize=Finite Difference Step Size
prop.dispname.minimumfinitedifferencestep=Minimum Finite Difference Step
prop.dispname.mppabsconvergence=MPP Absolute Convergence
prop.dispname.mppmaxiterations=MPP Maximum Iterations
prop.dispname.mpprelconvergence=MPP Relative Convergence
