Presentation at SIMS02, Oulu, Finland

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• On Emergent Models and Optimization of Parameters

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New view of models

• Keyword EMERGENCE
• When a large number of lower-level constructs are
  combined, new functionality pops up
• Qualitatively different approaches appropriate
• Static dependencies rather than dynamic
• High-dimensionality rather than SISO
• See Towards New Languages ...

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General Approach

• Higher-level adaptation scheme

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Notations

• Qualifiers
  (inputs)
• Qualities
  (outputs)

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Advantages

• Simplicity
  Dynamic models can be studied
  statically
• Generality
  All systems can be studied
  in the same framework
• Homogeneity
  Consistent level of
  abstraction, no matter what the physical system
  structure is like.

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About Structure

• Typically behavior is a continuous function of
  the parameters
• Sometimes the dependency is linear
• Generally a data mining problem
  Find patterns, apply multivariate statistical
  methods to substructures

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Unimodality assumption

• Now assume unimodality
• Applicable to simple subsystems
• A single local Gaussian distribution suffices
• Dependencies locally linear!

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New challenges

• Signals u and y more or less arbitrary
• Relationship between them is random
• Still, some dependency between Q and Q exists
• Use statistical tools
• MLR?
• PCA?

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Maximize correlation

• Good compromize PLS regression

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Visualization
If only one quality measure, only one
non-trivial direction exists
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Regression
Applying the latent variables the model
becomes and if the quality measure is scalar
, so that there holds
.
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Optimization

• Noticing that
• one can write the steepest descent algorithm as

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Example Heat exchanger
Typical partial differential equation model
plenty of adjustable parameters
when approximated
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Model parameter tuning
Quality measure
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PID optimization

• Cost criterion (quality measure)

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Further research
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Example Power plant