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  Probabilistic stability analysis and optimisation for human-machine interactive systems using stochastic distribution shaping

   Faculty of Engineering & Digital Technologies

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  Dr Qichun Zhang  Applications accepted all year round  Self-Funded PhD Students Only

About the Project

Future industrial systems will be significantly different from their present states. The main factor we have to consider is the uncertainties. With the development of intelligent systems and AI, the stability analysis becomes more and more complex due to the increasing uncertainties within the system considering the human behaviours. For example, the network-based uncertainties, control-based uncertainties, human decision making, etc.

Traditionally, the performance of the human-machine interactive system needs to be analysed based on the system model while the interaction is considered as the disturbance. However, the accurate model is impossible to obtain with the uncertainties. As a result, the novel framework has to be established considering the uncertainties and the interactions of the system. In other words, we need to find an approach to describe the uncertainties within the system considering the human-machine interaction.

Motivated by the Monte Carlo method and probability theory, the probabilistic analysis should be developed combining the dynamics of the complex system, where the stochastic distribution modelling can be adopted to characterise the future industrial system. Following this idea, the uncertainties can be included into the modelling procedure even if the uncertainties have not been identified in advance. Based on the probabilistic description, the control, optimisation and fault diagnosis can be achieved to enhance the performance of the complex smart system.

To summarise the challenges mentioned above, the following tasks should be completed in this PhD programme:

  1. The complex system data-driven modelling: The accurate model cannot be obtained while the probability density function based modelling should be considered to reflect the complete properties of the uncertainties. Note that the dynamics of the industrial system might be very fast which results in the difficult for real-time probabilistic modelling.
  2. The probability density function shaping or shifting: It is difficult to change the probability density function shape even if the model has been established where the non-linearity and non-Gaussian distribution strongly affect the performance of the control design and optimisation.
  3. Since the experiments for smart industrial system are expensive, the simulation pilot system should be designed and developed based on the practical data, and the presented model can be trained as a benchmark while the novel control and optimisation algorithms can be validated before the practical implementation.

To solve the aforementioned problems, stochastic distribution control theory will be used firstly. In particular, the model structure should be confirmed for the smart system and the parameters should be obtained by the data-based learning. Once the probabilistic model has been established, the novel control, optimisation and fault diagnosis methods should be developed in terms of shaping the probability density function. However, which type of the system model can be properly achieve the probability density function based design requirement is still an open question.

The following 3-year schedule has been made for completing the project as a PhD research programme. In year one, the literature reviews for the existing power system analysis tools will be done while the stochastic distribution analysis should be overviewed. The novel probability density function based model should be established to describe the uncertainties of the system and the novel control/optimisation methods should be developed based on the probabilistic model in the second year. In the third year, the model and presented methods will be validated via simulation platform development and the final results will be tested in real experiment.

Computer Science (8) Mathematics (25)

Funding Notes

This is a self-funded project; applicants will be expected to pay their own fees or have access to suitable third-party funding, such as the Doctoral Loan from Student Finance.


Mifeng Ren, Qichun Zhang & Jianhua Zhang (2019) An introductory survey of probability density function control, Systems Science & Control Engineering, 7:1, 158-170
Milanović JV. 2017 Probabilistic stability analysis: the way forward for stability analysis of sustainable power systems. Phil. Trans. R. Soc. A 375: 20160296.

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