IPMM03, May 1823, 2003

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IPMM03

• Complexity and Emergence Towards a New
  Science of Industrial Automation

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... Ever Heard of ?
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A New Science ...

• Observation
• All nontrivial natural systems are
  computationally equivalent
  capable of universal computation
• Conclusion
• Almost all systems are unmodellable the best
  representation for system behaviour is the system
  itself
• Simulation is the only way to extract information
  about the system behaviour.
• Old Science is Out !?

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• Cellular Automata
• Simulation Model for Everything?

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... or End of Science?

• Science based exclusively on fancy analogies?
• Huge promises
• Complex Systems Theorists hope they can answer
  questions about the inevitability of life, or of
  the entire universe. They promise new laws of
  nature analogous to gravity or the second law of
  thermodynamics. They promise to make economics
  and other social sciences as rigorous as physics.
  They can find a cure for AIDS.
• Postmodern science / Ironic science (Horgan)

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Origin of Sciences

• Darwin Origin of Species (1859)
• In 1860, when theory was coming to Finland,
  Professor Fredrik Wilhelm Mäklin condemned the
  theory, and concluded that no scientist, perhaps
  excluding some sea shell collectors referring to
  local enthusiasts, could ever truly believe it!

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• Another key idea in Complex Systems Theory

EMERGENCE

• Simple underlying principles only are needed to
  implement complicated behaviors when they are
  iterated long enough

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Agenda now

• Try to rehabilitate the role of (more or less)
  traditional modeling
• Assume that finding abstractions still is
  possible
• Key observations
• There is infinite complexity in patterns only
  when seen on the surface level but the
  underlying functions are of importance
• One does not need models of infinite power one
  only needs constrained, non-universal model
  structures that are specific to application
  domain
• Now the application is modeling of dynamic
  processes

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Challenge How to utilize the explosion in
computing capacity for attacking the explosion of
process information? Goal Using the framework
of complex systems theory make models
automatically emerge from data!
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Contents

• Main issues in the rest of the presentation
• About Complex Systems
• About Complex Systems
• About simple complex data
• About complex complex data

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• Complex Systems Theory is science in the making
• Now is the transition period between paradigms
• Only afterwards one can see the shift between
  paradigms (Kuhn) and then it is too late
• How to predict the future to be there in time?

Where is this field going?
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Glue

• Theory

Application
Tools
Analogies
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• System is anything that can be seen as a system
• Systemic thinking tries to see dependencies and
  analogies among things
• For example, a system of humans is a system
• Research is a human endeavor How things evolve
  is dependent of individual human actors
• Practice is also highly human Process operators
  either approve of new tools and theories, or not.

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• Evolution in control engineering From classical
  through modern to postmodern theory
• Modern control theory never came to factory floor
  level
• PID control still rules!
• One reason for this was the resistance of
  operators
• If the methods are not understood, they are not
  used
• New approaches have to be mentally graspable with
  clever simplifications and abstractions to be
  employed
• Good models are needed!

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• How to find the borderline between order
  (mathematics) and chaos (nonmathematics)?
• How to reach analyzable emergence or holistic
  mathematics?

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• Experiences available from the fields of
  Artificial Intelligence and Cognitive Science

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• It is wise to learn from experiences.
• Complex Systems Theory and Artificial
  Intelligence are very analogous fields with some
  thirty years of difference
• Same kinds of problems
• AI Cognitive system intelligence /
  consciousness
• CS Complex system emergence
• Escaping goals?
• Same kinds of approaches
• AI Gap between numeric (NNs) and symbolic
  (ESs) approaches
• CS Chaos theory vs. complexity theory
• Same kinds of open-minded researchers and
  audience
• fluctuations in interest / financing

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... For example

• Compare to Turing test for intelligence
  Something is intelligent if it mimics
  intelligence -gt Shallow view of AI
• Wolframian test for complex systems
  Something is relevant if it only looks
  interesting -gt Shallow view of
  complex systems?
• Visual patterns emphasized more than underlying
  functions!

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• AI vs. automation systems
• Sensors / senses deliver data
• In both cases the same problem of mastering the
  high-dimensional universe of observations
• Artificial Intelligence can offer conceptual
  tools (making it difficult to ignore the nasty
  reality)
• Semantics
• Epistemology
• Ontology

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Semantics, Ontology ...

• How to make mindless data processing make
  something relevant automatically emerge?
• Some understanding is necessary
• How to automate this understanding?
• How to formulate meaning?
• How to couple semantics in manipulations?
• How to assure that the data contains the
  necessary atoms of information?

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• Domain area semantics differs in different fields
• It seems that there cannot exist General Theory
  of All Possible Complex Systems
• How about General Theory of Complex
  Automation Systems?
• Can one automatically capture
  the semantics of process data?

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First, study the modeling of gases on different
levels, having different time scales / numbers of
constituents

• Elementary particles (orbitals) stochastics
• Atoms (ideal gas model) determinism
• Atom groups (statistical mechanics) stochastics
  
• Gas volumes (press. and temp.) determinism
• Real gases (turbulence) stochastics
• Ideal mixer (concentrations) determinism

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• The last level above is the level of todays
  automation system models
• When there are dozens of such ideal mixers, the
  overall plant structure is no more easy to master
• How to reach the next (statistical!?) level of
  abstraction? How to make relevant phenomena
  emerge on that next level?

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• In dynamic systems, semantics can be defined
  contextually, in terms of systems connections to
  the environment (inputs and outputs)
• In dynamic systems, interpretation of behaviors
  can be explicitly defined
• This means that
• Information atoms are captured in simulations
• Semantics is captured in mathematical formulas

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General approach

• Higher-level view of a process
• Monte Carlo simulations deliver statistical
  information
• Individual signal realizations forgotten!

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Advantages

• Simplicity
  Dynamic models can be studied
  statically (but the dimensionality
  typically grows)
• Generality Homogeneity
  All systems
  can be studied in the same framework Level of
  abstraction remains consistent, no matter what
  the physical system structure is like.

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Simple complex data

• First assume unimodality
• Applicable to subsystems with simple structure
• A single Gaussian distribution suffices
• Dependencies locally linear!

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Applications

• Exploratory analyses
• Optimization
• Self-organization
• New approaches to controller construction, etc.
• Theoretical benefits From dynamic to static
  models
• New framework for multi-model adaptive control
• Closer connection between model and actual
  process data
• Hardware-in-a-loop
• Self-adapting models

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Example Adaptive control

• Typically, adaptive control structures are
  bilinear
• Now, however, there are two separate linear
  models on different levels

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Higher-level adaptation scheme
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Notations

• Qualifiers
  (inputs)
• Qualities
  (outputs)

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• 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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Model between qualifiers and qualities 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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Further research
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Controller Optimization
Cost criterion (quality measure)
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Better PIDs!

• Proportional action
• Integrative action
• Derivative action
• Accuracy action
• Robustness action
• Speed action

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• Tuning of higher-level system behavior

Not too much changes here!?
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Complex complex data

• If the data is multimodal, the linearity
  assumptions do no more hold
• Modeling the data is, in general, a data mining
  task
• Are there any general
  guidelines?

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Classes of natural data
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• It turns out that all models have locally linear
  substructures
• Piecewise linear
  models can be used
• Modeling by
  clusterwise PCA

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Application Trajectory learning
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Further experiments

• Life-Like control
• Apply natural dynamics for moving limbs

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Further example

• Study the process
• where

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Hierarchic modeling

• Connection of mixtures

Mixture model
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Mixtures of Mixtures

• At different scales of time or size, different
  mixture models become relevant

Connection of mixtures
Mixture models
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• How to master the complicated AND/OR graphs?
• Wittgenstein Whatever you cannot express in a
  language, you cannot think about
• A formalism is needed to
  capture the data structures!

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New languages?

• Structure of the language
• Numeric rather than crisp classes and methods
• Two-way inheritance
• Compilation of the language
• Static pattern matching and associative
  regression
• Based on mathematics and linear algebra
• Programming of the language
• Numeric weights can adapt to match measurements
• Framework for agents Independent actors can
  deliver the data.

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Conclusion

• Hooray models!

• However, models should never be mixed with the
  objective reality
• But good models can be the same as the subjective
  reality!

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• The contribution from AI to modeling is not in
  one-way direction only
• Note that the mind constructs the model of the
  environment onto the tabula rasa and the model
  just might be based on the mixtures of mixtures
• If the truly same modeling principles are
  applied
• Optimized data structures represent mental
  representations (assuming that the senses and
  sensors are interchangeable)
• Real knowledge mining (rather than data mining)
  possible

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• Physical model
• Conceptual model

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Wish you no complexes!