On advising to system operatorsM. Valečková, M. Kárný

System(with regulators)

Inputs

Outputs

Operator

Aim: advisory system as support for operators

Tool: modelling of block (system + operators)

Example: cold rolling mill

recorded hundreds of variables

relevant about 40 (possibly corelated)

• independent inputs

• operator’s settings

• generated by system regulators

• required

Choice of model

Requirements:

• simple

• respecting high-dimensional data

• multimodal

• data-based

• transparent construction of advice

Probabilistic mixtures

Mixture estimation

multidimensional data = samples from mixture

p(x1,x2,..,xn) = iN(iRi)

Estimation of unknown parameters (Bayesian approach)

quick, on-line, numeriaclly stable algorithm

strongly dependent on initialization

Result of mixture estimation

joint distribution of all variables

Result of mixture estimation

How to provide an advice

different operator + different “mood” = different behaviour

mode of behaviour ~ component of mixture

recommended component – the best quality marker

Simplification

one component used for advising

joint distribution – conditional distribution

p(operator’s settings | the rest) – time dependent

Open problems

• choice of model

• model estimation

• initialization

• construction of advice

Acknowledgement: EC Project ProdaCTool IST-1999-12058