Optimization in a nutshell Introducing optislang to Master's students. Prof. Dr.-Ing. Frank Dienerowitz. EAH Jena Frank Dienerowitz Slide 1

Transcription

1 Optimization in a nutshell Introducing optislang to Master's students Prof. Dr.-Ing. Frank Dienerowitz EAH Jena Frank Dienerowitz Slide 1

2 Welcome to our university! Ernst-Abbe-Hochschule Jena University of Applied Sciences Health and Care Medical Eng. and Biotech. SciTec Students 400 employees 125 professors Social Work Business Admin. Mechanical Engineering Electrical Eng. and IT Fundamental Sciences Industrial Engineering source: EAH Jena EAH Jena Frank Dienerowitz Slide 2

3 My customers Master s Course Scientific Instrumentation Ba.Eng. / Ba.Sc.: Electrical, Mechanical, Physics, C&I fairly normal math and IT-skills source: EAH Jena They will most certainly encounter optimisation in their career! EAH Jena Frank Dienerowitz Slide 3

4 Typical Challenge Improve the design! P.1 P.2 electrode (+) P.5 electrode (-) P.6 P.3 P.4 MEMS actuator made of polysilicon blade length 3 mm thickness 50 μm source: Ansys WB 14.5 tutorial EAH Jena Frank Dienerowitz Slide 4

5 Typical Challenge Improve the design! Electrical Potential ΔU = 2 V Temperature Field 20 C 170 C Displacement Field Δy = 6 μm EAH Jena Frank Dienerowitz Slide 5

6 Typical Challenge Improve the design! Plan A: making in up as you go along Plan B: best practice 1. setup experiment and begin exploring a somewhat defined design space 2. realise: applying the typical full factorial DoE sampling restricts the number of parameters to be explored 3. conclude a rather limited optimisation 1. develop a parametric model of the problem; define design space, objective and constraints 2. setup experiment and interface with optimisation tool 3. explore and optimise the design in true 21 th century fashion conclusion: I need a bare-essentials optimisation course for my students! EAH Jena Frank Dienerowitz Slide 6

7 Course Outline Part 1 - Lecture Introduction 1 hour Models and Parameters Typical Workflow Motivation Sensitivity Analysis 2 hours Optimisation 1.5 hours Evaluating Sensitivity MOP Parallel Coordinates Plot Multiple Objective Optimisation Robust Design Advanced DoE Schemes Simple DoE Schemes Methods (Gradient, Simplex, ARSM, EA) Objective Function, Design Space & Constraints EAH Jena Frank Dienerowitz Slide 7

8 Course Outline Part 2 Computer Lab Session 1 Sensitivity Analysis Session 2 Optimisation Session 3 Solo Flight each session 1.5 hours EAH Jena Frank Dienerowitz Slide 8

9 Course Outline Part 2 Computer Lab The Solo Flight Railway Fuel Efficiency Cross Country Soaring Blue Riband of the Atlantic source: Wikipedia.de RMS Queen Mary EAH Jena Frank Dienerowitz Slide 9

10 Course Outline Topics we can t explore... for now! the contents of our bare-essentials course: a few parameters deterministic, continuous single objective optimisation solver: MS Excel stochastic and discrete parameters developing a good parametric model and many other topics... direct vs. model based optimisation robust design optimisation interfacing with ANSYS, Matlab, SimulationX etc loads of parameters EAH Jena Frank Dienerowitz Slide 10

11 Computational Landscape The model and the optimisation problem model: design space: objective: longitude latitude locate the deepest valley! source: Test functions for optimization needs MARCIN MOLGA, CZESŁAW SMUTNICKI, 2005 EAH Jena Frank Dienerowitz Slide 11

12 Computational Landscape Probing the Unknown: N = 9, 25, 81, 289 DoE scheme Full Factorial DoE scheme Adv. Latin Hypercube Sampling EAH Jena Frank Dienerowitz Slide 12

13 Computational Landscape Above the tree tops The M.O.P. optislang visualisation of the Meta-Model of Optimal Prognosis (MOP) EAH Jena Frank Dienerowitz Slide 13

14 Computational Landscape The optimisation methods visualised Gradient-based 33 designs Simplex 47 designs min min ARSM 120 designs Evol. Algorithm 250 designs min min - the global! EAH Jena Frank Dienerowitz Slide 14

15 Cycling Time Trial The model and the optimisation problem model: downward force road friction air drag propulsion force required human power rate of fatigue fatigue objective: maximise average velocity! constraint: total fatigue accumulated over all track sections less than 100%! v... velocity EAH Jena Frank Dienerowitz Slide 15

16 Cycling Time Trial Making sense of the design parameters 20 km Start 0.5% 4.0% 3.0% -6.0% 1.0% -1.8% Finish 100 designs Adv. LHS sampling v 1 v 2 v 3 v 4 v 5 v 6 v avg fatigue 17 km/h 14 km/h 25 km/h six design parameters: velocity for each section of the track 17 km/h 26 km/h 16 km/h 100% 8 km/h Parallel Coordinates Plot EAH Jena Frank Dienerowitz Slide 16

17 Cycling Time Trial Making sense of the design parameters 20 km Start 0.5% 4.0% 3.0% -6.0% 1.0% -1.8% Finish v 1 v 2 v 3 v 4 v 5 v 6 Importance of Parameters regarding average velocity 23% 3% 5% 6% 32% 27% Importance of Parameters regarding fatigue - 76% 20% based on MOP EAH Jena Frank Dienerowitz Slide 17

18 Cycling Time Trial The optimal race strategy 20 km Start 0.5% 4.0% 3.0% -6.0% 1.0% -1.8% Finish v 1 v 2 v 3 v 4 v 5 v 6 v avg fatigue % % % velocity in km/h by the way: 40 km/h is the limit of my comfort zone EAH Jena Frank Dienerowitz Slide 18

19 Farewell Get in touch. We do love optimisation! Ernst-Abbe-Hochschule Jena Department SciTec EAH Jena Frank Dienerowitz Slide 19