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PhD Opportunities

Condition-based maintenance using hidden semi-Markov models

School of Mathematics and Physics | PHD

Applications are now CLOSED
Funding
Unfunded
Reference Number
MAP/2021/006
Application Deadline
28 February 2021
Start Date
1 October 2021

Overview

Monitoring machines for the purpose of diagnostics and prognostics commonly referred to as condition-based maintenance (CBM) has the potential to improve efficiency and reduce costs. Diagnostics are used to determine the current health status of a machine/ component where as prognostics predicts the remaining useful life of the machine/component. By obtaining what the current health state of a machine is and then predicting when it will fail should not only save the company money but will also improve efficiency [1].

The hidden Markov model (HMM) has been used to describe the health states during a components degradation. These models are referred to as a doubly embedded stochastic process as they can be characterised as consisting of a stochastic process which is unobservable and can be inferred from another observable stochastic process. They have a rich mathematical structure however they can be restrictive in terms of the Markov assumption. The Markov property within the HMM can be seem as a possible disadvantage when using the HMM to model real-world situations as it assumes that the time spent within the hidden layer of the HMM follows a geometric distribution. The hidden semi-Markov model (HSMM) relaxes this assumption by allowing a variable duration or sojourn time for each of the hidden states [2].

This project proposes the investigation and development of HSMM’s within the application area of CBM taking into account non-constant machine use with the aim to increase the accuracy of predicting the remaining useful life and current health state of the component.

References
[1] Y. Peng, M. Dong, A prognosis method using age-dependent hidden semi-Markov model for equipment
health prediction, Mechanical Systems and Signal Processing, 25, 2011, 237-252.
[2] S. Yu, Hidden semi-Markov models, Artificial Intelligence, 174, 2010, 215-243.

Project Summary
Supervisor
Dr Hannah Mitchell
Mode of Study

Full-time: 3 years


Apply now Register your interest

Mathematics overview

The Mathematical Research Centre conducts world-class research in the following areas: Algebra, Analysis, Operator Algebras, Algebraic Topology, Topological Data Analysis, PDEs, Survival Analysis, Bayesian Networks, Data Analytics and Operational Research. It maintains vibrant international links with a large number of researchers around the globe and regularly hosts international conferences and research visitors.

List of researchers, their interests and upcoming PhD projects can be found at:
https://web.am.qub.ac.uk/wp/msrc/.


Mode of study / duration
Registration is on a full-time or part-time basis, under the direction of a supervisory team appointed by the University. You will be expected to submit your thesis at the end of three years of full-time registration for PhD, or two years for MPhil (or part-time equivalent).

Mathematics Highlights
Industry Links
  • The School has many industry links, some of which are with Seagate Technology R&D, Andor Technology and AVX Ltd. Many of our graduates take up positions with these companies in posts such as Statistical Analysis Programmer, Trainee Accountant, Financial Engineer and Business Analyst.
Career Development
  • Queen’s is ranked in the top 140 in the world for graduate prospects (QS Graduate Employability Rankings 2020). Graduates from the School take up employment through a number of companies such as Allstate, AquaQ Analytics, Citigroup, Deloitte, PwC, Randox, Seagate and UCAS.
World Class Facilities
  • Since 2014, the School has invested over £12 million in new world-class student and staff facilities. Maths and Physics students now have their own teaching centre that opened in 2016 housing experimental physics laboratories, two large computer rooms for mathematical simulations and student study plus a student interaction area.
    In addition, Northern Ireland has the lowest student cost of living in the UK (Which? University, 2018) being £5000 per year cheaper for students to live in Northern Ireland compared to London (Which? University 2018).
Key Facts

  • Students will have access to our facilities, resources and our dedicated staff. The School of Maths & Physics is one of the largest Schools in the University. Staff are involved in cutting-edge research that spans a multitude of fields.

Course content

Research Information

Research Themes
Information on the research interests and activities of academics in the Mathematical Science Research Centre can be found at https://web.am.qub.ac.uk/wp/msrc/. These interests fit into the themes: Algebra, Analysis, Data Science, Optimization and Operational Research, Partial Differential Equations, Statistics, Topology and Geometry.

Career Prospects

Introduction
Mathematical and statistical skills are in great demand in the economy, particularly the advanced skills developed at the PhD level.

Employment after the Course
As well as continuing in research careers, our PhD graduates have also gone on to work in finance, computing, data analysis, management and teaching. Our advisors will be happy to provide further information on the career prospects arising from your chosen research area. Further information on careers can be obtained from the School and the Faculty.

People teaching you

Dr David Barnes
Postgraduate Advisor - Mathematical Sciences Research Centre

Email: d.barnes@qub.ac.uk

Dr Salissou Moutari
Director of Research - Mathematical Sciences Research Centre

Email: s.moutari@qub.ac.uk

Learning Outcomes

Course structure

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Assessment

Assessment processes for the Research Degree differ from taught degrees. Students will be expected to present drafts of their work at regular intervals to their supervisor who will provide written and oral feedback; a formal assessment process takes place annually.

This Annual Progress Review requires students to present their work in writing and orally to a panel of academics from within the School. Successful completion of this process will allow students to register for the next academic year.

The final assessment of the doctoral degree is both oral and written. Students will submit their thesis to an internal and external examining team who will review the written thesis before inviting the student to orally defend their work at a Viva Voce.

Feedback

Supervisors will offer feedback on draft work at regular intervals throughout the period of registration on the degree.

Facilities
Students will enjoy the benefits of modern practical laboratories, extensive computer facilities and interactive spaces.

Entrance requirements

Graduate
The minimum academic requirement for admission to a research degree programme is normally an Upper Second Class Honours degree from a UK or ROI HE provider, or an equivalent qualification acceptable to the University. Further information can be obtained by contacting the School.

International Students

For information on international qualification equivalents, please check the specific information for your country.

English Language Requirements

Evidence of an IELTS* score of 6.0, with not less than 5.5 in any component, or an equivalent qualification acceptable to the University is required. *Taken within the last 2 years.

International students wishing to apply to Queen's University Belfast (and for whom English is not their first language), must be able to demonstrate their proficiency in English in order to benefit fully from their course of study or research. Non-EEA nationals must also satisfy UK Visas and Immigration (UKVI) immigration requirements for English language for visa purposes.

For more information on English Language requirements for EEA and non-EEA nationals see: www.qub.ac.uk/EnglishLanguageReqs.

If you need to improve your English language skills before you enter this degree programme, INTO Queen's University Belfast offers a range of English language courses. These intensive and flexible courses are designed to improve your English ability for admission to this degree.

As a result of the COVID-19 pandemic, we will be offering Academic English and Pre-sessional courses online only from June to September 2020.

  • Academic English: an intensive English language and study skills course for successful university study at degree level
  • Pre-sessional English: a short intensive academic English course for students starting a degree programme at Queen's University Belfast and who need to improve their English.

Tuition Fees

Northern Ireland (NI) 1 £4,500
Republic of Ireland (ROI) 2 £4,500
England, Scotland or Wales (GB) 1 £4,500
EU Other 3 £17,460
International £17,460

1 EU citizens in the EU Settlement Scheme, with settled or pre-settled status, are expected to be charged the NI or GB tuition fee based on where they are ordinarily resident, however this is provisional and subject to the publication of the Northern Ireland Assembly Student Fees Regulations. Students who are ROI nationals resident in GB are expected to be charged the GB fee, however this is provisional and subject to the publication of the Northern Ireland Assembly student fees Regulations.

2 It is expected that EU students who are ROI nationals resident in ROI will be eligible for NI tuition fees, in line with the Common Travel Agreement arrangements. The tuition fee set out above is provisional and subject to the publication of the Northern Ireland Assembly student fees Regulations.

3 EU Other students (excludes Republic of Ireland nationals living in GB, NI or ROI) are charged tuition fees in line with international fees.

All tuition fees quoted are for the academic year 2021-22, and relate to a single year of study unless stated otherwise. Tuition fees will be subject to an annual inflationary increase, unless explicitly stated otherwise.

For further information please refer to www.qub.ac.uk/brexit-advice/information-for-students.

More information on postgraduate tuition fees.

Mathematics costs

There are no specific additional course costs associated with this programme.

Additional course costs

All Students

Depending on the programme of study, there may also be other extra costs which are not covered by tuition fees, which students will need to consider when planning their studies . Students can borrow books and access online learning resources from any Queen's library. If students wish to purchase recommended texts, rather than borrow them from the University Library, prices per text can range from £30 to £100. Students should also budget between £30 to £100 per year for photocopying, memory sticks and printing charges. Students may wish to consider purchasing an electronic device; costs will vary depending on the specification of the model chosen. There are also additional charges for graduation ceremonies, and library fines. In undertaking a research project students may incur costs associated with transport and/or materials, and there will also be additional costs for printing and binding the thesis. There may also be individually tailored research project expenses and students should consult directly with the School for further information.

How do I fund my study?
1.PhD Opportunities

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Information on Postgraduate Research scholarships for international students.

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Find a supervisor

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To find a potential supervisor aligned with your area of interest, or if you are unsure of who to contact, look through the staff profiles linked here.

You might be asked to provide a short outline of your proposal to help us identify potential supervisors.