Shell 2006

1
Shell 2006

• Advisor John R. Williams
• Research Assistant Ching-Huei Tsou

2
Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Next Steps

3
Summary of our Previous / Ongoing Work

• A generic framework for data management, data
  mining, and model building
• XML metadata tagging for easy searching,
  manipulating, and data integration and
  assimilation
• Web-Service based architecture which is secure,
  reliable, scalable, and platform independent
• Developing robust learning algorithms suitable
  for analyzing large volume of incomplete and
  inaccurate data.
• A high-performance machine learning library
  implementing the state-of-the-art learning
  algorithms
• Applied the methodology of optimization through
  measure-model-control loop to both simple and
  real-world systems
• Toy applications
• Standard benchmark problems
• Structural health monitoring
• Proactive stocking in retail stores

4
Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Next Steps

5
Focus of the 2006 Project

• We have been working on developing generic
  framework which helps identifying and optimizing
  systems through modeling, learning and
  simulation.
• We will focus on apply the techniques on specific
  system and types of data, possible directions
  are, as suggested by Dr. Jan Dirk Jansen,
• Production data management and criticality
• in a global system optimization context
• impact on maintenance
• Integration of maintenance and logistics in a
  total (producing) system optimization
• With the general objectives in mind, a natural
  extension of our previous work is to obtain real
  production data, build a realistic, dynamic
  updating model based on both domain knowledge and
  the data, and put the model in the optimization
  loop to help identifying critical processes and
  events.
• We have successfully applied this methodology to
  several systems and achieved promising results.
  How it works in a reservoir and how it compares
  to Shells existing approach is not yet studied,
  and thus one of the primary goal for next year.

6
Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Next Steps

7
Optimization through Measure-Model-Control Loop

• Shell Smart Well Technology
• Well with down-hole instrumentation, such as
  sensors, valves and inflow control devices
  installed on the production tubing
• A smart well management system can be modeled as
  a closed-loop Measure-Model-Control system
• Measure monitoring the fluid flow rates,
  temperature, and pressures of the well with
  down-hole sensors
• Model a mathematical model represents the
  current status of the well
• Control adjusting the valves and inflow control
  devices installed on the production tubing to
  optimize the production
• The goal is to achieve global system optimization

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Optimization through Measure-Model-Control Loop

• The loop can also be thought of as a
  learning-feedback loop
• In particular, we focused on building a realistic
  model of the system
• Robust against noisy, missing data
• Take advantages from both domain knowledge and
  data
• Dynamically updating when new measurements are
  available

9
Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Next Steps

10
Building Realistic Models

• Traditionally, two different approaches are
  commonly accepted in modeling
• Explicit Modeling
• Extensive domain knowledge is required
• Statistical Modeling
• Large amount of high quality data is required
• Proposed approach A hybrid model
• Synergy Combining Prior Knowledge and Data
• A Machine learning approach
• Prior knowledge is used to guide the learning
  process, when less data is available or the
  quality of data is suboptimal.
• When consistent data is abundant, it can override
  an incorrect assumption of prior knowledge

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Analytical vs. Inductive

• Perfect knowledge
• Given any Xi we can calculate Yi using the
  equation

• Data Knowledge
• Imperfect knowledge smooth curve
• Limited data

• Complete Data
• Given any Xi we can look-up Yi from the dataset

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What is New?

• Creating a parametric model and determining the
  values of the parameters using observed data,
  havent we been doing this for ages?
• True. But this is not the whole story
• In the simplest case perform a linear regression
  on a set of samples
• Data the set of samples
• Prior Knowledge the underlying distribution is
  linear
• Model linear function
• Parameters slope and offset of the line
• Cost function least square error

13
Training a Model

• Prior Distribution Linear
• Oversimplified model
• Large training error, cannot generalize well

• Prior Distribution Mixture Gaussian
• Overly complex model
• Overfitting, small training error, does not
  generalize well either

14
Generative vs. Discriminative (1/2)

• For a learning problem
• Y target function models which generate X
• X observed data
• We want to find a Y which maximize P(YX)
• The most probable model Y after we have seen data
  set X
• Generative approach
• Use Bayes rule P(YX) P(XY) P(Y) / P(X)
• P(XY) The probability of observing X,
  which is generated by a model Y
• P(Y) The probability of model Y is true (prior
  believe)
• P(X) constant when we maximize w.r.t. Y
• Discriminative approach
• Find a Y which maximize P(YX) directly (e.g.
  SVMs find a maximum margin hyperplane in the
  feature space)

15
Discriminative vs. Generative (2/2)

• Examples of generative learning approaches
• Naïve Baye
• Bayesian Belief Network
• Hidden Markov Model
• Graphical Model
• Examples of Discriminative approaches
• Nearest Neighbors
• Artificial Neural Networks
• Support Vector Machines
• The idea of guiding the learning process using
  prior knowledge is not new. In fact, it is the
  foundation of many generative learning
  approaches.
• On the other hand, discriminative approaches
  usually generalize better (more accurate) but the
  link between data and prior knowledge is not
  clear (ongoing research area)

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Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Handwriting Recognition
• Structural Health Monitoring
• Proactive Stocking
• Next Steps

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Example Handwriting Recognition

• MNIST
• Standard pattern recognition benchmark problem at
  ATT
• training set of 60,000 examples
• test set of 10,000 examples
• Classification Test Error
• Neural Network (NN)
• 1 Layer, No Hidden Unit (HU) 12 (LeCun et al.
  1998)
• 2 Layers, 800 HU 1.6 (Simard et al., ICDAR
  2003)
• Support Vector Machine (SVM), Gaussian Kernel
  1.4
• Record Low 0.4
• SVM Prior Knowledge
• Prior Knowledge invariant in small rotation
  and/or translation
• Test Error 0.56

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Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Handwriting Recognition
• Structural Health Monitoring
• Proactive Stocking
• Next Steps

19
Structural Health Monitoring

• Analytical Approach
• Finite element analysis
• Extensive domain knowledge is required
• Equations governing the vibration of the
  structure
• Dimensions, material, mass, external forces,
  damping
• Those information is usually not available in
  real-world problems
• Inductive Approach
• Statistical modeling (e.g. auto-regression model,
  Y. Lei, et al, 2003)
• Only the acceleration responses data is required
• However, the accuracy of auto-regression model is
  limited
• Last year we applied SVM to the problem and
  achieved better results
• Now, combining support vector machine with prior
  knowledge we can achieve much higher accuracy
• Prior knowledge used

ASCE Benchmark Problem
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Structural Health Monitoring

• Support vector regression without prior knowledge
• 20 features
• a1(t-1), a1(t-2), , a1(t-20)

• Support vector regression with prior knowledge
• 5 features
• a1(t-1), v1(t-1), a2(t-1), v2(t-1), P(t)-P(t-1)
• Smaller error indicates a more realistic model

21
Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Handwriting Recognition
• Structural Health Monitoring
• Proactive Stocking
• Next Steps

22
Example 3 Proactive Stocking

• Keeping products in-stock is one of the most
  important issues in retail stores
• Traditionally, a store manager / associate
  replenish a product when the quantity of the
  product on the sales floor is below the desired
  stock level
• Checking the stock level in sales floor is a time
  consuming manual process and is prone to error
• Often a low stock level is not observed until the
  product is completely out-of-stock, and the store
  has been losing sales

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Example 3 Proactive Stocking

• Based on the store process, data collected from
  point of sales, sales floor and backroom, a store
  model can be established.
• Knowing the daily sales, maximum shelf capacity
  and total on-hand product quantity, the model can
  infer the stock level in sales floor.
• Reduce the time consuming zoning work
• Replenish the product before it is out-of-stock
• Prioritize the replenishment
• Again a measure-model-control optimization problem

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Explicit Retail Store Model

• Given the complexity and the human-centric nature
  of operations in a chain store, statistical
  learning is necessary in addition to the explicit
  model.

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Agenda

• Summery of Our Previous / Ongoing Work
• Focus of the 2006 Project
• Optimization through Measure-Model-Control Loop
• Building Realistic Models
• Examples
• Next Steps

26
Next Steps

• We have successfully applied this methodology to
  several systems and achieved promising results.
  How it works in a reservoir and how it compares
  to Shells existing approach is not yet studied,
  and thus the primary goal for next year.
• Input from Shell
• Processes involved in the production
• Production data
• Model Building
• Modeling the smart well system based on process
  analysis
• Learning the model / parameters from the
  production data
• Running the simulation / prediction on test sets
• Comparing predicted outputs with Shells existing
  system
• Optimization
• Given an accurate model, we can
• Evaluate new processes
• Predict feedbacks from the system (after
  influencing the system through certain control
  mechanisms)
• Identify critical events
• Data Management

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References

• Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner,
  "Gradient-Based Learning Applied to Document
  Recognition," Proceedings of the IEEE, vol. 86,
  no. 11, pp. 2278-2324, Nov. 1998.
• Patrice Y. Simard, Dave Steinkraus, John Platt,
  Best Practice for Convolutional Neural Networks
  Applied to Visual Document Analysis,
  International Conference on Document Analysis and
  Recogntion (ICDAR), IEEE Computer Society, Los
  Alamitos, pp. 958-962, 2003.
• Y. Lei, et al. An Enhanced Statistical Damage
  Detection Algorithm Using Time Series Analysis,
  in Proceedings of the 4th International Workshop
  on Structural Health Monitoring. 2003.
• Farrar, C.R., S.W. Doebling, and D.A. Nix,
  Vibration-Based Structural Damage
  Identification, Philosophical Transactions of
  the Royal Society Mathematical, Physical
  Engineering Sciences, 2001. 359(1778) p.
  131-149.
• T. Jaakkola and D. Haussler. Exploiting
  generative models in discriminative classifiers,
  In Advances in Neural Information Processing
  Systems 11, 1998.

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Additional Slides
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Probability Pre-requirement Bayes Rule

• P(A) A / World
• P(B) B / World
• P(AB) (AB) / World
• P(AB) (AB) / B P(AB) / P(B)
• the probability of A is true in a world where B
  is true
• P(BA) (AB) / A P(AB) / P(A)

• Bayes Rule
• P(BA) P(A) P(AB) P(AB) P(B)
• ? P(BA) P(AB) P(B) / P(A)

30
Generative vs. Discriminative (1/2)

• For a learning problem
• Y target function models which generate X
• X observed data
• We want to find a Y which maximize P(YX)
• The most probable model Y after we have seen data
  set X
• Generative approach
• Use Bayes rule P(YX) P(XY) P(Y) / P(X)
• P(XY) The probability of observing X,
  which is generated by a model Y
• P(Y) The probability of model Y is true (prior
  believe)
• P(X) constant when we maximize w.r.t. Y
• Discriminative approach
• Find a Y which maximize P(YX) directly (e.g.
  SVMs find a maximum margin hyperplane in the
  feature space)

31
Generative vs. Discriminative (2/2)

• Both approaches are popular in various fields,
  and each has its pros and cons
• Generative Model
• Prior Knowledge can be added
• Examples Naïve Bayes, Hidden Markov Model,
  Bayesian Network
• Pros prior knowledge, missing values, less data
  is required, variable attribute length
• Cons Computational inefficient
• Discriminative Model
• Make no attempts to model underlying
  distributions
• Examples Nearest Neighbors, Neural Networks,
  Support Vector Machine
• Pros more accurate than generative approach,
  performance is usually much better in large-scale
  problem
• Cons black-box, relationships between variables
  are not explicit, need more data

32
Bayesian Belief Network

• Bayes rule
• Naïve Bayes classifier
• Bayesian belief network
• Learning Bayesian belief network
• Missing data
• EM algorithm

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Support Vector Machine (1/2)

• Maximum margin classifier

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Support Vector Machine (2/2)

• Mapping to a higher dimension

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Solve / Train the Hybrid Model

• Design issues
• How to represent the arbitrary dynamics in terms
  of attribute values (parameters)
• How to estimate the probability required by the
  classifier
• Combine generative and discriminative learning
• New dot-product kernels derived from the system
  dynamics model
• Fisher kernels / Maximum entropy discrimination
• Not much has been done in this area