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A Variety of Sensitivity Analysis

The analysis of uncertainty involves measuring the degree to which each random variable and its distribution parameters contribute to the uncertainty in the output quantities (limit-state function, failure probability and reliability index). UNIPASS™ provides a variety of important sensitivities results. These include the sensitivities of the reliability index and failure probability with respect to random variables and their distribution parameters. The distribution parameters include the means, standard deviations, and correlation coefficients of probability distributions.

 

In general, UNIPASS™ provides the following sensitivity information:

  • Sensitivity of limit-state function with respect to the random variables at the MPP in both the standard normal space and the original space

  • Sensitivity of failure probability and reliability index with respect to random variables

  • Sensitivity of failure probability and reliability index with respect to means and standard deviations

  • Sensitivity of failure probability and reliability index with respect to distribution parameters

  • Dimensionless sensitivity of failure probability and reliability index with respect to random variables, means and standard deviations

 

For CDF/PDF analysis, sensitivities values are available at different limit state function values as shown in Figure 1.  

  •  Up to 28 sensitivity measurement types
  • 3-D plot: (variables, sensitivity values, g levels)

 

sensitivity.jpg (107834 bytes)

 Figure 1. Example of a Sensitivity Plot in the CDF/PDF Analysis

 

This 3-D plot can be projected into a two dimensional view as shown in Figure 2. Click the button as Step A in Figure 1, one can plot this projected 2-D sensitivity plot.

  • Projected into 2-D plot: (g levels, sensitivity values)

  • Linear and curve fitting interpolation

  

sensitivity1.jpg (67839 bytes)

Figure 2. The cross sectional view of a sensitivity plot with curve fitting in CDF/PDF analysis

By fixing the limit state function level, one can plot a 2-D sensitivity measurement as  in the conventional probability analysis. This is shown in Step B in Figure 1 and the corresponding 2-D sensitivity plot is given in Figure 3.

sensitivity2.jpg (71485 bytes)

Figure 3. A sensitivity plot for a selected limit state function value in the CDF/PDF analysis

 

For a selected random variable, a 2-D sensitivity plot with coordinates of g values vs. sensitivity values can be obtained as shown in Figure 4 by following the Step C in Figure 1.

sensitivity3.jpg (70437 bytes)

Figure 4. A sensitivity plot for a selected random variable with curve fitting

 

Last Updated 11/12/08

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