Design Search and Optimisation (DSO) - Principles, Methods, Parameterizations and Case Studies

Learning Outcomes

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 basic elements of single and multi-variable optimizers;
• 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 CAD tools can be used to formulate design intent in DSO problems.
• the ways in which problem parameters can be used to formulate design intent in DSO problems;
• the issues confronting engineers as they seek usable DSO approaches;
• the ways in which these simple elements can be combined to provide solutions to DSO problems
• the issues confronting engineers as they seek practical DSO approaches.

Full CEng Programme Level Learning Outcomes

Having successfully completed this module you will be able to:

• 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.
• 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.
• 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.
• Coursework for the module is conducted in teams for some elements.
• 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.
• 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
• 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.

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.

• 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).

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.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

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.