Our knowledge of physical phenomena guides both the models we build and the set of observations we make. Whilst we may have some knowledge of the generating mechanisms for various components of the phenomenon in question, the true system is unknown and we have the added effects of observational noise and external forcings. This Faraday Partnership project is developing novel methodologies for the fusion of physical knowledge with observations with the aim of providing (probabilistic) models which are compatible both with the underlying physics and expert human knowledge, and also with the data. The project focused on developing mathematical models with combined advances in nonlinear dynamics and statistical methods of estimation, while being sufficiently robust to deploy in the industrial contexts of grid frequency monitoring and the monitoring of rotating machinery. In short, the project aimed for Real-timE ModellIng of Nonlinear Data-streams (REMIND), while tracking sources of uncertainty both in the data and from the model structure.

In the context of grid frequency, the project has developed a structural model (based on estimated generation and its composition, estimated grid inertia, type of demand, and so on) and looks to contrast/combine such models with previously proven purely data based nonlinear models. The mathematical aims were to develop methods for useful real-time parameter estimation within the context of (1) datastreams (too much to store) and (2) model inadequacy (the mathematical structure of the class of models under consideration does not include a “correct” parameter set consistent with the data). This requires modelling model failure. During the project, models were applied in real-time trials by our industrial partners.

The project had the following objectives:

• Construct a consistent approach to the unification of structural and probabilistic modelling which is robust in the face of real-world constraints and applicable to unending data-streams.
• Advance ability to account for uncertainty in the derivation, estimation and verification of nonlinear models, with emphasis on employing ensembles over models of different mathematical structure.
• Provide a viable real-time monitoring framework for grid frequency, able to rapidly identify loss of generation, estimate impact of a given loss of generation, and provide estimates of time varying parameters.
• Provide more general methods for novelty detection in rotating machinery.

Further information may be found on the REMIND website at LSE.

Project staff and support

Liam Clarke (Postdoctoral Faraday associate, London School of Economics)
Lenny Smith (Principal Investigator, London School of Economics)
Melvin Brown (Technology translator, Smith Institute)

This project was carried out in the Department of Statistics at the London School of Economics, in conjunction with the National Grid Company and InterTec (UK). It was supported by earmarked EPSRC research funding through the Faraday Partnership for Industrial Mathematics, and had the working title Real-time modelling of nonlinear data-streams. Start date: November 2002; Duration: 2 years.

related resources:

»	Nonlinear data streams
	Project summary: Nonlinear data streams
	Industrial outcomes
	Further Reading

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