Module overview
This module introduces students to formal design search and optimization (DSO) approaches using a mixture of lectures covering theory and practice and a series of worked case studies with student participation.
Aims and Objectives
Learning Outcomes
Full CEng Programme Level Learning Outcomes
Having successfully completed this module you will be able to:
- The role of multiple aspects of product and process performance in the design stage are emphasized and used to balance and trade off requirements in a variety of ways and are assessed in the coursework tasks.
- Coursework for the module is conducted in teams for some elements.
- Methods for browsing and presenting complex data structures are taught along with tools to analyze such structures so as to draw out important aspects in the data and are assessed in the coursework tasks.
- Methods for evaluating the impact uncertainty on product and process performance are covered as are methods to reduce and manage risk to produce robust products and processes and are assessed in the final online exam.
- A fundamental aspect of the course is covering methods to select appropriate design processes given the sophistication of design methods, reliability of data sources and importance of outcomes and are assessed in the coursework tasks.
- The use of the most appropriate algorithms in optimization and machine learning given the design problem at hand and the data available is a central thread of the course and are assessed in the coursework tasks.
- The fundamental theory of optimization and machine learning using a range of surrogate approaches are taught, and are assessed in the final online exam.
- Advanced methods for trading off performance during the design phase using optimization and machine learning form the core of the module and are assessed in the final online exam
- Design problems are investigated to study issues such as uncertainty in product and operational characteristics, and are assessed in the coursework tasks. These are used to assess the most appropriate ways to tackle design improvement methods.
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- evaluate the utility and robustness of DSO produced designs.
- make intelligent choices among the available DSO approaches;
- more fully understand the components of a successful DSO approaches to design;
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- the ways in which various tools can be brought together to tackle realistic DSO problems via the use of bespoke workflows;
- the ways in which these simple elements can be combined to provide solutions to DSO problems
- the basic elements of single and multi-variable optimizers;
- the issues confronting engineers as they seek usable DSO approaches;
- the issues confronting engineers as they seek practical DSO approaches.
- the ways in which problem parameters can be used to formulate design intent in DSO problems;
- the ways in which CAD tools can be used to formulate design intent in DSO problems.
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- set-up and solve simple DSO problems using a range of software tools including FEA codes and Excel.
Syllabus
- Design Search and Optimization (DSO) (2 lectures)
Beginnings
A Taxonomy of Optimization
A Brief History of Optimization Methods
The Place of Optimization in Design – Commercial Tools
Geometry Modelling & Design Parameterization
The Role of Parameterization in Design
Discrete and Domain Element Parameterizations
NACA Airfoils
Spline Based Approaches
Partial Differential Equation and Other Analytical Approaches
Basis Function Representation
Morphing
Shape Grammars
Mesh Based Evolutionary Encodings
CAD Tools v's Dedicated Parameterization Methods
- Single Variable Optimizers – Line Search (1 lecture)
Unconstrained Optimization with a Single Real Variable
Optimization with a Single Discrete Variable
Optimization with a Single Non-Numeric Variable
- Multi-Variable Optimizers (3 lectures)
Population versus Single Point Methods
Gradient-based Methods
Newton's Method
Conjugate Gradient Methods
Quasi-Newton or Variable Metric Methods
Noisy/Approximate Function Values
Non-Gradient Algorithms
Pattern or Direct Search
Stochastic and Evolutionary Algorithms
Termination and Convergence Aspects
- Constrained Optimization (2 lectures)
Problem Transformations
Lagrangian Multipliers
Feasible Directions Method
Penalty Function Methods
Combined Lagrangian and Penalty Function Methods
Sequential Quadratic Programming
Chromosome Repair
- Meta-models and Response Surface Methods (2 lectures)
Global versus Local Meta-models
Meta-modelling Tools
Simple RSM Examples
Combined Approaches – Hybrid Searches, Meta-heuristics
Meta-heuristics – Search Workflows
Visualization – understanding the results of DSO
- Multi-objective Optimization (1 lecture)
Multi-objective Weight Assignment Techniques
Methods for Combining Goal Functions, Fuzzy Logic & Physical Programming
Pareto Set Algorithms
Nash Equilibria
- Robustness in Optimization and Uncertainty Quantification (UQ) (3 lectures)
Robustness versus Nominal Performance
Evolutionary Algorithms for Robust Design
Robustness Metrics
Noisy Phenotype One -- Tsutusi and Ghosh's Method (NP)
Noisy Phenotype Two -- Modified Tsutusi and Ghosh Method (NP2)
Design of Experiment One -- One-at-a-time Experiments (OAT)
Design of Experiments Two and Three -- Orthogonal Arrays (L64 & L81)
Comparison of Metrics
Using Surrogates in robustness studies
Krigs
Co-Krigs
Combined Krigs
- Problem Classification and Getting Started (1 lecture)
Run-time
Deterministic v's Probabilistic Analyses
Number of Variables to be explored
Goals and Constraints
- Initial Search Process Choice (1 lecture)
Case studies from industry - possible case studies include the following:
- Case study 1: The design of an encastre cantilever beam:
This is based around simple Euler-Bernoulli beam theory and Excel to set up and solve a simple structures DSO problem. Each student pairing tackles a different set of boundary conditions and the
whole class’s studies then allow a Pareto Front to be constructed illustrating which pairings have produced Pareto optimal designs and which have produced sub-optimal designs. This is a very simple
case study just to get students used to the whole idea of DSO approaches.
- Case study 2: Multi-objective design problem:
For this case study, a multi-objective design problem will be described, which will have to be solved and presented during the course of the laboratory sessions. The problem will involve optimizing for more than one objective and constraints and takes significant time to calculate. This renders conventional optimization strategies inefficient and the use of surrogate models will be essential. Students will be free to employ any method(s) learnt earlier in the course, laboratory sessions or from elsewhere.
- Case study 3: Global versus local search methods:
An airplane wing design problem will be used to demonstrate the differences between local and global search methods. A key element of this study concerns the fixed computational budget often faced in real engineering problems. It is not necessary to have to have an aerodynamics background to follow this design study.
- Case study 4: Adjoint aerodynamic shape optimisation of transonic airfoils:
Aerodynamic shape optimisation is a powerful tool for airfoil design. In such an approach, numerical optimisation algorithms are coupled with CFD tools to find the best airfoil shape for, e.g., minimum drag subject to lift, pitching moment, and airfoil thickness constraints. Medium and long-range transport aircraft usually fly in the transonic regime, where the creation of shock waves on the airfoil can result in significant wave drag. However, using careful shape optimisation, a shock-free airfoil can be designed. Such design optimisation requires a suitable airfoil shape parameterization technique and a computationally efficient approach to calculate the derivatives of the objective function and constraints for gradient-based optimisation.
- Revision (2 lectures).
Learning and Teaching
Teaching and learning methods
Teaching methods include
- Lectures.
- Talks by invited speakers from industry.
- Computer sessions.
Learning activities include
- Using the DSO capabilities of the Excel spreadsheet system.
- Using a commercial parametric CAD system to prepare a model for FEA based DSO.
- Using MATLAB based workflows and optimization toolkits.
Type | Hours |
---|---|
Lecture | 17 |
Wider reading or practice | 10 |
Seminar | 2 |
Practical classes and workshops | 17 |
Preparation for scheduled sessions | 18 |
Revision | 20 |
Completion of assessment task | 48 |
Follow-up work | 18 |
Total study time | 150 |
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Final Assessment | 50% |
Continuous Assessment | 50% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Set Task | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Method | Percentage contribution |
---|---|
Set Task | 100% |
Repeat Information
Repeat type: Internal & External