Last modified: 31 May 2022 13:05
Ever wondered how Excel is able to draw an optimal line through a set of points? This course looks at how typical engineering problems that cannot be described mathematically (or are difficult to do so) can be solved so that the optimal solution is found. The course contains a range of examples to show how the techniques are applied to real world problems in different engineering disciplines. The course will show how to develop computational algorithms from scratch, with a fundamental understanding of how the algorithms function, both mathematically and then in real time on a computer.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
To provide MEng students with a range of advanced engineering analysis techniques in terms of mathematical optimisation and software development, applicable over a range of engineering disciplines.
Main Learning Outcomes
A range of advanced mathematical optimisation techniques used in engineering analysis, applicable over a range of engineering disciplines, is studied. Techniques of mathematical optimisation are used as the basis for much engineering synthesis and the solution of inverse problems. In addition, the student will learn general techniques for the analysis of a given problem and how to break this down into its component parts. Students carry out practical exercises using MATLAB
By the end of the course students should:
A) have knowledge and understanding of:
• general techniques of mathematical optimisation
• methods of mathematical minimisation
• optimisation problems arising in engineering applications
• optimisation algorithms for 1-dimensional problems
• gradient methods for multi-dimensional optimisation
• optimisation methods for constrained and unconstrained problems
• methods of problem analysis
B) have gained intellectual skills so that they are able to:
• distinguish local and global optimisation schemes and their applicability
• describe how optimisation problems arise in engineering applications
• formulate optimisation algorithms for 1-dimensional problems
• derive and apply gradient methods to multi-dimensional optimisation
• apply optimisation methods to constrained and unconstrained problems
• solve specific engineering problems of some complexity
• approach any given problem and break it down for solving through software
C) have gained practical skills so that they are able to:
• use MATLAB to solve advanced engineering problems
• use flowcharts and pseudo code to solve or describe a given problem
D) have gained or improved transferable skills so that they are able to:
• write technical reports dealing with difficult engineering problems
General techniques of mathematical optimisation and minimisation. Methods for one variable: Newton's method; Fibonacci search; Golden-section search; Curve fitting approaches using Quadratic interpolation, Cubic interpolation; Brent's method. Methods for many variables: Direct search methods using Hooke and Jeeves' method, Downhill simplex (Nelder and Mead's) method; Gradient methods using the method of steepest descent, Quadratic functions, Newton-Raphson method, Conjugate directions, Fletcher-Reeves method, Davidson-Fletcher-Powell method. Constrained Optimisation: Equality constrains, Inequality constrains, Convexity and Concavity.
Discipline specific applications. Modelling data using Non-linear least squares, Levenberg-Marquardt algorithm. Local and global optimisation using Simulated annealing, Genetic algorithms; Inverse problems; Regularisation; Applications of Local and global optimisation: simulated annealing and genetic algorithms in engineering problem solving procedures. Other Applications specific to engineering disciplines.
Information on contact teaching time is available from the course guide.
Open book timed exam (30%)
Open book timed exam (70%)
Re-sit of only the failed assessment component(s)
There are no assessments for this course.
|Knowledge Level||Thinking Skill||Outcome|
|Factual||Remember||ILO’s for this course are available in the course guide.|