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•Regression terms
•Regression coefficients
•Goodness-of-fit measures
The goodness-of-fit measures provide a means to verify the quality of the response surface and whether it is a good representation of the underlying data (in other words, the sample points).
You can request a print out of this data at any time.
Command(s): RSPRNT
GUI: Main Menu> Prob Design> Response Surf> Prn Resp Surf
1.3.10.5. Generating Monte Carlo Simulation Samples on the Response Surfaces
After you have generated a response surface set that includes one or more response surfaces for one
or more random output parameters then you also need to perform Monte Carlo Simulations using these response surfaces to generate probabilistic results. This is where the PDS generates sampling values for the random input variables in the same way it did for the simulation looping performed using your analysis file. But instead of using the random input variable values in the analysis file and running through the analysis file, it uses the approximation function derived for the response surfaces to calculate approximated response values. The process of calculating an explicitly known equation is much faster than running through the analysis file and performing a finite element analysis, so you can run a large number of simulation loops in a relatively short time. Usually, several thousand simulation loops are performed if you utilize the response surfaces.
After you have generated the Monte Carlo Simulation loops on the response surfaces, you can begin probabilistic postprocessing and review the probabilistic results the same way as you would for Monte Carlo Simulations. However, there is one difference for postprocessing between Monte Carlo results and Monte Carlo results derived from response surface approximations. For Monte Carlo simulation
results, the accuracy of the results is determined by the number of simulation loops that are performed. The PDS can visualize the accuracy of Monte Carlo results by means of confidence limits or confidence bounds. For Monte Carlo results derived from response surface approximations, the confidence bounds are suppressed. This is necessary because the accuracy is not determined by the number of simulation loops (as mentioned above, you typically perform a large number of these) but by the goodness-of-fit
or the response surface model itself. With increasing numbers of simulation loops the confidence bounds tend to merge with the result curve you are plotting (the width of the confidence band shrinks to zero). This could lead you to conclude that the results are very, very accurate. However, the underlying response surface approximation could have been completely inadequate (for example, using a linear approximation function for a highly nonlinear problem).
Command(s): RSSIMS
GUI: Main Menu> Prob Design> Response Surf> RS Simulation
1.3.11. Review Results Data
After probabilistic design looping is complete, you can review the results sets in a variety of ways using the commands described in this section. These commands can be applied to the results from any probabilistic design method or tool.
•Statistics
–Sample History
–Histogram
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–Cumulative Distribution Function
–Probabilities
–Inverse Probabilities
•Trends
–Scatter Plot
–Sensitivities
–Correlation Matrix
•Report
–Print HTML Report
1.3.11.1. Viewing Statistics
To postprocess one particular design variable, select this option. The statistics options are described below.
Plot Sample History
Use the PDSHIS command to request a sample history plot.
Command(s): PDSHIS
GUI: Main Menu> Prob Design> Prob Results> Statistics> Sampl History
You must specify the results set you want to use, the design variable you want to review, the plot type to use, and the confidence level.
Plot Histogram
Use the PDHIST command to request a histogram plot of a design variable.
Command(s): PDHIST
GUI: Main Menu> Prob Design> Prob Results> Statistics> Histogram
You must specify the results set you want to use, the design variable you want to review, the number of classes/points to use, and the type of histogram.
CumulativeDF
Use the PDCDF command to request a histogram plot of a design variable.
Command(s): PDCDF
GUI: Main Menu> Prob Design> Prob Results> Statistics> CumulativeDF
You must specify the results set you want to use, the design variable you want to review, and the confidence level.
The confidence level is a probability expressing the confidence that the values for the cumulative distribution function are in fact between the confidence bounds. The larger the confidence level, the wider the confidence bounds. Plotting of the confidence bounds only makes sense for the postprocessing of Monte Carlo simulation results. Here, the confidence bounds represent the accuracy of the results and with increasing sample size the width of the confidence bounds gets smaller for the same confidence level. For response surface methods the number of simulations done on the response surface is usually
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Using Probabilistic Design |
very large. Therefore, the accuracy of the results is determined by the goodness of the response surface fit and not by the confidence level.
Probabilities
Use the PDPROB command to request the value of a design variable at a specific point on the cumulative distribution curve.
Command(s): PDPROB
GUI: Main Menu> Prob Design> Prob Results> Statistics> Probabilities
You must specify the results set you want to use, the design variable you want to review, the relation (greater than, less than), the limit value, and the confidence level.
Inverse Probabilities
Use the PDPINV command to request the value of a design variable at a specific point on the cumulative distribution curve.
Command(s): PDPINV
GUI: Main Menu> Prob Design> Prob Results> Statistics> Inverse Prob
You must specify the results set you want to use, the design variable you want to review, the relation (greater than, less than), the limit value, and the confidence level.
1.3.11.2. Viewing Trends
To postprocess one particular design variable as it relates to another, select this option. The trend options are described below.
Scatter Plot
Use the PDSCAT command to request a scatter plot showing the correlation between two design variables.
Command(s): PDSCAT
GUI: Main Menu> Prob Design> Prob Results> Trends> Scatter Plot
You must select the results set that you want to use, the design variables that you want to review, the type of trendline curve to use (and if plotted, the polynomial order), and the maximum number of point to include in the scatter plot.
Sensitivities
Use the PDSENS command to request the sensitivities of an output parameter to the input variables.
Command(s): PDSENS
GUI: Main Menu> Prob Design> Prob Results> Trends> Sensitivities
You must specify the results set and output parameter you want to use, the type of chart to plot, the type of correlation coefficient, and the sensitivity level.
Correlation Matrix
Use the PDCMAT command to calculate the correlation coefficient matrix.
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of ANSYS, Inc. and its subsidiaries and affiliates. |
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