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Introduction Lecture 1 ME EN 575 Andrew Ning aning@byu.edu - PDF document

Introduction Lecture 1 ME EN 575 Andrew Ning aning@byu.edu Outline Syllabus Optimization Basics Project Examples (from past students) Syllabus Course Website: http://flow.byu.edu/me575/ Syllabus: Please Read! Make sure your email is


  1. Introduction Lecture 1 ME EN 575 Andrew Ning aning@byu.edu Outline Syllabus Optimization Basics Project Examples (from past students)

  2. Syllabus Course Website: http://flow.byu.edu/me575/

  3. Syllabus: Please Read! • Make sure your email is current on Learning Suite • Prerequisites/undergraduates • Must not refer to homeworks/exams from prior students • Homework • Project • Weekly Quizzes • Piazza • Ask Questions! Optimization Basics

  4. What is Optimization? Optimal Conventional Baseline Baseline Specifications Specifications design design Analyze or Analyze experiment Evaluate Change Evaluate Change objective and design performance design constraints Is the Is the design design No No good? optimal? Yes Yes Final design Final design Design Variables x (array)

  5. Objective Function J ( x ) or f ( x ) (scalar)

  6. Multidisciplinary Optimization Simultaneous: Sequential: Aerodynamic Optimization Optimizer Structural Optimization Aerodynamic Structural Analysis Analysis Constraints c ( x ) ≤ 0 (array)

  7. Bound constraints Linear constraints Nonlinear constraints Optimization Problem Statement J ( x ) minimize x ∈ R n with respect to subject to c j ( x ) ≤ 0 , j = 1 , 2 , . . . , m

  8. Smooth Discontinuous Linear Continuity Linearity Nonlinear Static Continuous Dynamic Quantitative Discrete Optimization Design Problem Time Variables Classification Qualitative Deterministic Data Constraints Convexity Unconstrained Stochastic Constrained Non- Convex Convex • Nonlinear • Constrained • Differentiable

  9. Optimization Methods • Gradient-based • Gradient-free • Response surfaces • Convex • Integer or Mixed Integer Project Examples (from past students)

  10. Cylindrical surface with tailored stiffness L 2 k 2 Kerf k 1 θ 1 (b) θ 2 L 3 k 3 L 1 θ 3 L 4 y 2 y 1 y 3 F F L t,2 L t,3 L t,4 L t,1 w 2 w 3 w 1 w 4 L 1 L 3 L 4 L 2 L 5 k 1 k 2 k 3 k 4 L 3 L 1 L 2 L 4 L 5 Todd Nelson and Jared Bruton System evolvability of a cookstove Jeff Allen and Kendall Thacker

  11. Wind farm power and acoustics Jared Thomas and Eric Tingey Optimized schedule simulator for students Sam McDonald and Dallin Swiss

  12. Shape optimization of turbine geometry in pulsing flow conditions Mark Fernelius UAV Path Planning 100 80 60 40 20 0 0 20 40 60 80 100 Kyle Ingersoll, Patrick DeFranco, and Bryce Ingersoll

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