A Challenge Problem on Uncertainty Quantification & Value of Information 1 Patrick Koch Dassault Systèmes SIMULIA 2013 NAFEMS World Congress Salzburg, Austria June 9-12 NAFEMS, Stochastic Working Group

Stochastics Working Group  Proactively represent the working group  Provide recommendations to advance the user community  Share breakthrough technology to the dedicated community  Assist with the development of publications Challenge Problem  Topic: Uncertainty Quantification (UQ) Challenge Problem  Promote effective use of engineering simulation methods  Showcase different approaches to UQ through presentations and/or publications  Showcase the use of software tool(s) to automate methodology  Selections will be featured in NAFEMS publications and presented at NAFEMS Americas’ Conference 2 Purpose Robust Design for improved reliability and reduced field issues 99% Customer Target Life Distribution (years) Lifecycle Field Issues

3 Challenge problem  A mathematical model of a typical electronic device as represented by a R-L-C network will be provided along with different levels of uncertainty estimates around the input parameters.  The challenge is to evaluate the reliability of the device using given criteria as well as quantify the value of information in each case.  Methods are not judged and this is not a competition to find the true solution

4 Problem Statement A typical electronic device is represented by R-L-C network in series as shown. Input signal is the step voltage source for a short duration. Output response is the voltage at the capacitor. The output response is sensitive to network parameters R, L and C. Uncertainty estimates regarding the R, L, C values are available. The challenge is to evaluate the reliability of the device using two criteria: a.Voltage at a particular time should be greater than a threshold b.Voltage rise time to be within a specified duration

5 Mathematical Model Uncertainty in RLC such that the voltage response across capacitor, Vc, may fall into: 1. Over damped 2. Critically damped 3. Under damped For each case above, the response Vc is expressed as Typical results A1 and A2 are solved using the initial conditions:

6 Parameter Information Uncertainty estimates of R, L, C parameters are available in different forms Case A: Intervals Case B: Multiple Intervals Case C: Sampled Points Case D: Incomplete Data Source 1: R=[40, 1000]  L = [1, 10]mH C = [1, 10]  F Source 2: R=[600, 1200]  L = [10, 100]mH C = [1, 10]  F Source 3: R=[10, 1500]  L = [4, 8]mH C = [0.5, 4]  F R=[40, 1000]  L = [1, 10]mHC = [1, 10]  F R=[40, R U ]  with nominal value of 650 , R u > 650 L = [1, L U ]mH with nominal value of 6 mH, L u > 6 C = [C L, 10]  F with nominal value of 7  F, C L < 7 R= {861, 87, 430, 798, 219, 152, 64, 361, 224, 614}  L={4.1, 8.8, 4.0, 7.6, 0.7, 3.9, 7.1, 5.9, 8.2, 5.1}mH C={9.0, 5.2, 3.8, 4.9, 2.9, 8.3, 7.7, 5.8, 10.0, 0.7}  F

7 Requirement Information 1. Assess reliability of the device using the two criteria: a.Voltage at a particular time should be greater than a threshold V C (t=10 ms) > 0.9 V b.Voltage rise time to be within a specified duration V C (t= t r ) =0.9 V, where t r < 8 ms c.Underdamped responses should be discarded. 2. Quantify the value of information in each case

Any tool or software may be used for the challenge problem. Saber from Synopsys is a tool used for analog/power electronics, electric power generation/conversion/distribution and mechatronics that may be used for this challenge problem.  Free Demo Version: Limited to 10 Monte Carlo runs and does not include Saber’s design optimization tool  Full Commercial Version (limited to 30 days) : Contact SWG member Jim Patton  Challenge Problem example available in Saber Resources

 Synopsys’ Saber team is sponsoring three giveaways*: JawBone JAMBOX Wireless Bluetooth Speakers  Recipients will be chosen randomly by the SWG from acceptable responses *Acceptance of the prize is an agreement with Synopsys to use your name, company name, and a photo in Saber Robust Design promotional material *Participation in the giveaways is optional 9 Giveaways

Contact Mary Fortier NAFEMS SWG Chair Phone: Timeline Selections will be featured in NAFEMS publications and presented at NAFEMS Americas Conference Spring 2014 Submit solutions for publication and presentations Nov. 29, 2013 Responses due by participants to accept challenge problem July Kick-off at NAFEMS World Congress June 2013