1. S9-1 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation SECTION 9 MONTE CARLO ANALYSIS, CORRELATION

2. S9-2 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation

3. S9-3 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation MONTE CARLO ANALYSIS, CORRELATION n This module includes: u Monte Carlo Analysis Overview u Factors: Distribution Types u Responses: Success (or Failure) Indicators u Correlation: Investigating Factor, Response Relationships

4. S9-4 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation MONTE CARLO ANALYSIS OVERVIEW n Overview: u The effect of random variable permutations on system response is being studied. n Typical Use: u Confidence analysis on mission-critical designs, ensuring that Factor variation does not significantly impact system performance. u Investigating Response + Factor relationships: which variations most influence system performance?

5. S9-5 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation MONTE CARLO ANALYSIS OVERVIEW n Example: Space Craft Separation Analysis u High-risk, one-time event. u Requirement stated as "tip-off rate less than 0.5 deg/sec, 3-sigma“. u In this context, 3-sigma means 99.7% probability of less than 0.5 deg/sec. u In ADAMS/Insight terms, at least 997 of 1000 runs have tip-off rate less than 0.5 deg/sec. u Consider also outliers: do factors combine in (un)expected ways to cause problems? Space Craft Payload

6. S9-6 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation FACTORS: DISTRIBUTION TYPES n Parameter values are specified via a Probability Density Function (PDF). n Several common PDF schemes are available in Insight. User-defined schemes are also possible:

7. S9-7 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation FACTORS: DISTRIBUTION TYPES n Most common distribution types: u Normal (the "bell curve") l Default factor value is the mean l Standard deviation is specified (how spread out values are) l Optional cutoff limits prevent unrealistic outliers u Uniform (even distribution of values) l Default factor value is midpoint of interval l User specifies limits n Sources of these values: u Vendor data u Physical Testing u Engineering experience

8. S9-8 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation RESPONSES: SUCCESS (OR FAILURE) INDICATORS n Quantify Response behavior by considering: u Mean Value u Variance u Standard Deviation u Coefficient of Variance u Gross totals (review Response values, sort by magnitude. Count number of trials having values larger than the design goal. Determine if the number of violators is less than the design criteria.)

9. S9-9 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation RESPONSES: SUCCESS (OR FAILURE) INDICATORS n Example: Response Review in Insight: u Mean tip-off rate for all trials is approximately 0.05 deg/s. u One Standard Deviation is approximately 0.1 deg/s. u Mean value plus 3 Std. Dev.’s is less than 0.5 deg/s design requirement (0.05 + 3 * 0.1 = 0.35). Design has been validated to 3-Sigma goal.

10. S9-10 ADM730, Section 9, September 2005 Copyright  2005 MSC.Software Corporation CORRELATION: INVESTIGATING FACTOR, RESPONSE RELATIONSHIPS n Investigate Factor and Response relationships via scatter plots and Correlation Matrix.