2. Training Manual 001419 15 Aug 2000 2.5-1 Probabilistic Design: Bringing FEA closer to REALITY! 2.5 Probabilistic Design Exploring randomness and scatter reveals a simple truth: It’s a part of reality - everywhere!

3. Training Manual 001419 15 Aug 2000 2.5-2 Probabilistic Design Introduction Probabilistic Design takes into account uncertainties (scatter) in input data and performs multiple runs to calculate scatter in output data. –Recognises the fact that input parameters do vary despite the best intentions. –Predicts variation in design performance. –Allows design for reliability.

4. Training Manual 001419 15 Aug 2000 2.5-3 Probabilistic Design … Introduction InputInput ANSYSANSYS OutputOutput Material properties Geometry Boundary Conditions Deformation Stresses, strains Fatigue, creep,... It’s a reality that input parameters are subjected to scatter => automatically the output parameters are uncertain as well!!

5. Training Manual 001419 15 Aug 2000 2.5-4 ANSYS PDS Probabilistic Design … Introduction Typical questions answered with probabilistic design: –How large is the scatter of the output parameters? –What is the probability that output parameters do not fulfil design criteria (failure probability)? –How much does the scatter of the input parameters contribute to the scatter of the output (sensitivities)?

6. Training Manual 001419 15 Aug 2000 2.5-5 Random Input Variables Random Output Parameters Finite-Element Model Material Strength Material Properties BC's Gaps Fixation Geometry/ Tolerances Loads Thermal Structural LCF lifetime Creep lifetime Corrosion lifetime Fracture mechanical lifetime … Probabilistic Design … Introduction The goal is to design more reliable products by estimating a component's lifetime.

7. Training Manual 001419 15 Aug 2000 2.5-6 Probabilistic Design … Introduction Probabilistic Design System (PDS) is useful in several industries and applications, e.g: –Aerospace –Gas Turbines (Rotating Machinery) –Automotive (Power Train)

8. Training Manual 001419 15 Aug 2000 2.5-7 Probabilistic Design … Introduction Deterministic Analysis Only provides a YES/NO answer. Safety margins are piled up “blindly” (worst material, maximum load, … worst case). Leads to costly over-design. Only “as planned,” “as is,” or the worst design. Sensitivities do not take interactions between input variables into account (second order cross terms). Probabilistic Analysis Provides a probability and reliability (design for reliability). Takes uncertainties into account in a realistic fashion. –Closer to reality –Over-design is avoided “Tolerance stack-up” taken into account Range/width of scatter is “built- in” into probabilistic sensitivities. Inherently takes into account interactions between input variables.

9. Training Manual 001419 15 Aug 2000 2.5-8 Probabilistic Design PDS Features Works with any ANSYS model. –Static, dynamic, linear, non-linear, thermal, Structural, Electro-magnetic, CFD … Allows large number random input and output parameters (max. total = input plus output is 5000). Ten statistical distributions for input parameters. Random input parameters can be correlated. Probabilistic methods: –Monte Carlo - Direct & Latin Hypercube Sampling –Response Surface - Central Composite & Box-Behnken Designs

10. Training Manual 001419 15 Aug 2000 2.5-9 Probabilistic Design … PDS Features Comprehensive probabilistic results, e.g: –Convergence plots –Histogram –Probabilities –Scatter plots –Sensitivities State-of-the art statistical procedures to analyze and visualize probabilistic results Use of distributed, parallel computing techniques for drastically reduced wall clock time of the analysis

11. Training Manual 001419 15 Aug 2000 2.5-10 Probabilistic Design GUI for PDS PDS menus are organized according to sequence of use, similar to design optimization menu: –Start by creating a loop file of any analysis –Define the problem –Specify methods and run options –Fit response surfaces –Postprocessing –Database handling

12. Training Manual 001419 15 Aug 2000 2.5-11 Probabilistic Design PDS Results Different types of results displays are available to answer typical PDS questions: –Statistics, histogram, sample diagrams These plots can be used to answer the question "How large is the scatter of the output parameters?" –Cumulative distribution function, probabilities "What is the probability that output parameters do not fulfil design criteria (failure probability)?" –Sensitivities, scatter diagram, response surface "How much does the scatter of the input parameters contribute to the scatter of the output?"

13. Training Manual 001419 15 Aug 2000 2.5-12 Simulation Value Sample Plot: Probabilistic Design Probabilistic Results

14. Training Manual 001419 15 Aug 2000 2.5-13 Mean Value Sample Plot Probabilistic Design Probabilistic Results

15. Training Manual 001419 15 Aug 2000 2.5-14 Standard Deviation Sample Plot: Probabilistic Design Probabilistic Results

16. Training Manual 001419 15 Aug 2000 2.5-15 Histogram Plot: Probabilistic Design Probabilistic Results For random input variablesFor random output parameters

17. Training Manual 001419 15 Aug 2000 2.5-16 Cumulative Distribution Function: Probabilistic Design Probabilistic Results

18. Training Manual 001419 15 Aug 2000 2.5-17 Sensitivities: Probabilistic Design Probabilistic Results Note: Sensitivity plot for Spearman rank order correlation coefficient Linear correlation coefficient Single parameter Sensitivity study

19. Training Manual 001419 15 Aug 2000 2.5-18 Scatter Plot: Probabilistic Design Probabilistic Results

20. Training Manual 001419 15 Aug 2000 2.5-19 Probabilistic Design Summary Probabilistic Design is a new feature at ANSYS 5.7 An easy-to-use tool for realistic prediction of reliability Based on widely accepted Monte Carlo simulation technique and Response Surface methods Allows for parallel / distributed processing of jobs