2. Probabilistic Design Systems (PDS) Chapter Seven

3. Training Manual January 30, 2001 Inventory #001449 7-2 7. Probabilistic Design This module focuses on quantifying the quality and reliability of a design using Probabilistic Design Systems (PDS). The scope covered as part of this seminar is limited to highlighting the basic concepts of probabilistic design: A.Introduction – define probabilistic design and compare deterministic vs. probabilistic analysis B.Features – using ANSYS for probabilistic design C.Probabilistic Results – sample results displays

4. Training Manual January 30, 2001 Inventory #001449 7-3 Probabilistic Design A. Introduction Probabilistic Design takes into account uncertainties (scatter) in input data and performs multiple runs to calculate scatter in output data. –Recognizes the fact that input parameters do vary despite the best intentions. –Predicts variation in design performance. –Allows design for reliability.

5. Training Manual January 30, 2001 Inventory #001449 7-4 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!!

6. Training Manual January 30, 2001 Inventory #001449 7-5 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)?

7. Training Manual January 30, 2001 Inventory #001449 7-6 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.

8. Training Manual January 30, 2001 Inventory #001449 7-7 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 January 30, 2001 Inventory #001449 7-8 Probabilistic Design B. 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 January 30, 2001 Inventory #001449 7-9 Probabilistic Design … 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 January 30, 2001 Inventory #001449 7-10 Probabilistic Design … Features 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 January 30, 2001 Inventory #001449 7-11 Probabilistic Design C. Probabilistic 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 January 30, 2001 Inventory #001449 7-12 Simulation Value Sample Plot: Probabilistic Design … Probabilistic Results

14. Training Manual January 30, 2001 Inventory #001449 7-13 Mean Value Sample Plot Probabilistic Design … Probabilistic Results

15. Training Manual January 30, 2001 Inventory #001449 7-14 Standard Deviation Sample Plot: Probabilistic Design … Probabilistic Results

16. Training Manual January 30, 2001 Inventory #001449 7-15 Histogram Plot: Probabilistic Design … Probabilistic Results For random input variablesFor random output parameters

17. Training Manual January 30, 2001 Inventory #001449 7-16 Cumulative Distribution Function: Probabilistic Design … Probabilistic Results

18. Training Manual January 30, 2001 Inventory #001449 7-17 Sensitivities: Probabilistic Design … Probabilistic Results Note: Sensitivity plot for Spearman rank order correlation coefficient Linear correlation coefficient Single parameter Sensitivity study

19. Training Manual January 30, 2001 Inventory #001449 7-18 Scatter Plot: Probabilistic Design … Probabilistic Results

20. Training Manual January 30, 2001 Inventory #001449 7-19 Probabilistic Design D. Summary Probabilistic Design helps to design for reliability and quality Randomness and uncertainty is taken into account as it appears in real life Based on widely accepted Monte Carlo simulation technique and Response Surface methods Ideal for parallel / distributed processing of jobs