Posted: December 30th, 2022

ENM7005-B Modelling and Optimisation

Modelling is the process of creating a representation of a real-world system or process using mathematical or computational methods. The goal of modelling is to better understand the behavior and dynamics of the system or process being modeled, and to make predictions about how it will behave under different conditions.
Optimisation is the process of finding the optimal solution to a problem. In the context of modelling, optimisation involves finding the best possible solution to a given problem based on the model being used. This can involve finding the optimal values for certain variables, or identifying the optimal course of action to take in a given situation.
There are many different types of models and optimisation techniques that can be used, depending on the nature of the problem being addressed. Some common approaches include linear programming, integer programming, nonlinear programming, and dynamic programming. These techniques can be used to solve a wide range of problems, including resource allocation, scheduling, and design problems.
Modelling and optimisation are important tools in a variety of fields, including engineering, economics, and management. They can help companies and organizations make more informed decisions and improve their operations by providing a deeper understanding of the systems and processes they are working with.

ENM7005-B Modelling and Optimisation
Optimisation Coursework
1 Introduction
This course work is designed to test your understanding on optimisation
problems and optimisation algorithms, the detailed learning outcomes are
• L04: Critically evaluate the fundamental concepts of design Optimisation and
select, implement and assess a range of appropriate optimisation techniques.
• L05: Formulate and solve an optimisation problem related to engineering
design.
• L06: Collate and manage data, and apply scientific method, IT skills and
complex systematic problem-solving strategies.
2 Description
The expectation of this project are
(1) To select a system to study. Some suggestions are shown in the
following section. You can select one of the suggestions.
(2) To characterise the selected system, identifying important properties
(design objectives), select decision variable, and constraints. You can
obtain those information by proper literature review.
(3) To formulate the related optimisation problems and provide the matlab
code of the problem.
(4) Write a matlab codes for one of the following one-dimension
optimisation algorithm
• Equal Interval Algorithm
• Newton-Raphson Algorithm
• Fibonacci Algorithm
• Parabolic Interpolation Algorithm
(5) To solve the selected optimisation problem by applying appropriate
optimisation techniques including your algorithm. You can also
compare the efficiency of different optimsiation algorithms.
You should submit an individual report (about 5-10 pages).
The following section may be included in your report
• Introduction: the background of selected system.
• Literature review: briefly presents the state of research on selected
systems if needed.
• System description: the detail of the selected system should be
described in details, such as how the system works and how to
calculate their performances etc.
• Modelling: you should provide the optimisation models of the selected
system.
• Results: You can select some optimisation algorithms to solve the
problem and provide or compare your results. You should provide the
matlab codes for your problem.
• Conclusions and future work. You can summary your achievements or
experiences and provide some suggestion how to improve if you asked
re-do the project.
3 Parameters for your selected problem
𝑨, 𝑩, 𝑪, and 𝑫 to be used in the assessment questions are obtained from
the last four digits of your 8-digit UB number, 𝑿 𝑿 𝑿 𝑿 𝒂 𝒃 𝒄 𝒅, according
to
𝑨 = 1 + 𝒂, 𝑩 = 1 + 𝒃, 𝑪 = 1 + 𝒄, 𝑫 = 1 + 𝒅
It is your responsibility to ensure you use the correct parameter values in the
problem descriptions below. Illustration, if the last 4 digits of your UB
number are 9306 then YOUR parameter values would be 𝐴 = 10, 𝐵 = 4, 𝐶
= 1, 𝐷 = 7.
4 Suggestions of Problems
In this section, some suggestion systems are provided. You need to do some
research to obtain their important performances and to obtain the calculation
formula from references.
4.1 Water Tank
Design a cylindrical water tank of height 𝐻 and base radius 𝑅 so
that the leakage time 𝑇, through a hole (in the base) of fixed size
𝐴, is maximised. A primary constraint is that the total surface area
of the cylinder 𝑆 (side and base) is fixed where it is assumed that
the top surface is open. For a leakage speed 𝑢(𝑡), what is the
optimum value of 𝐻?
A good startis to acquire some information about Torricelli’s Law
(https://en.wikipedia.org/wiki/Torricelli%27s_law) , and assume that
𝑆 = (𝑨 + 𝑩)(𝑪 + 𝑫)
4.2 Machine Tool
A machine tool spindle is supported by two rolling bearings of
stiffness 𝑘1 = 𝑪 kN/µm and stiffness 𝑘2 = 𝑫 kN/µm (see diagram).
Data: spindle radius 𝑟 = (50 + 𝑩 ) mm, overhang ℎ = (100 + 𝑨)
mm, Young’s modulus for spindle material (steel) is 210 kN/mm2
.
Distance between bearing is 𝑥 and 𝛼 =
ℎ
𝑥
Deflection per unit load is given by
𝛿 =
ℎ
3
3𝐸𝐼 (1 +
1
𝛼
) +
(1 + 𝛼)
2
𝑘1
+
𝛼
2
𝑘2
Where 𝐼 =
𝜋𝑟
4
4
is the moment of inertia of the spindle section. Be
careful with units.
The design aims to make the deflection to be minimum.
5 Marking scheme
The group design report will be marked using the following schedule:
Item of Work Maximum
Mark Available
[%]
WRITTEN COMMUNICATION SKILLS (REPORT WRITING): (30%)
Abstract – quality and clarity of the summary of the report 5
Introduction – quality of description of Position, statement of
the Problem and link to main text
10
Main text – quality of links between concepts and sections 10
Conclusions – clear statement of Proposal which is related to
the stated Problem
5
TECHNICAL SKILLS: (70%)
Optimisation Model 20
Selection of Algorithm 20
Coding (Algorithms and Problems) 20
Analysis and Arguments 10
TOTAL 100
6 Contribution agreement
Contribution Aggreement
Group #: ___________________
Group Leader: ___________________
Module Code: _ENM7005B_______
Module Name: Modelling and Optimisation
Date : __ _______________
Members Contribution Ratio Signature