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The Incorporation of Prior Knowledge and Constraints through Bayesian Analysis into a Neuro-Fuzzy Inference System Framework. Tom Musicka Centre for Process Analytics and Control Technology University Of Newcastle Contact : tom.musicka@ncl.ac.uk. Introduction. Problem Definitions

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The Incorporation of Prior Knowledge and Constraints through Bayesian Analysis into a Neuro-Fuzzy Inference System Framework

Tom Musicka

Centre for Process Analytics and Control Technology

University Of Newcastle

Contact : tom.musicka@ncl.ac.uk


Introduction

  • Problem Definitions

  • Data Analysis

    • PreScreening

    • Data Validation

  • Neuro-Fuzzy Modelling

  • Model Comparison

    • Results

  • Bayesian Framework

    • Results

  • Conclusions

  • Future Work


Data Mining

  • Data Capture and Treatment

  • ‘Analysis of observational data sets to find unsuspecting relationships and to summarise the data in a number of understandable and useful ways’

    • Prediction

    • Classification

    • Detection of Relationships

    • Explicit Modelling

    • Clustering

    • Deviation Detection


Corus - Process and Scheduling Description

  • Hot Strip Steel Rolling - Corus

    • Multigrade Operation

    • Multistage Process

      • Reheating

      • Multi-Pass Reversing Rougher

      • Multi-Pass Finishing Rolling

      • Run Out Table (ROT) Cooling

      • Coiling

      • Testing


Corus - Problem Definition

  • Virtual Test House

  • Mechanical Property Prediction

    • Ultimate Tensile Strength

    • Yield Stress

    • Elongation

  • Project Description:

    • ‘To produce a modelling system capable of accurately and consistently predicting the the mechanical properties of Steel rolled at Hot Strip Mills within Corus UK.’


Shell - Process and Scheduling Description

  • Refinery High Viscosity Index (HVI) Operation - Shell

    • Multicrude Operation

    • Continuous and Batch Operations

    • Pressure to Minimise Working Capital

      • Statistical Visualisation

        • Masters Thesis

    • Four Unit Process

      • High Vacuum Unit (HVU)

      • Furfural Extraction Unit (FEU)

      • Propane De-Asphalting Unit (PDU)

      • MEK De-Waxing Unit (MDU)


Shell - Problem Definition

  • Slack Wax Oil Content (SWOC) Prediction

  • MDU Produces Lube Oil and Slack Wax

    • Slack Wax Contains Oil

    • Useful to know the % Oil Content

  • Project Description:

    • ‘To produce a model capable of accurately and consistently predicting the SWOC. This Model will be considered within the feasibility report for the purchase of an online physical measurement system’


Data Characteristics

  • Multiple Input, Single Output Models

  • Discrete and Continuous Variables

  • Missing Data

  • Process Noise

  • Outliers

  • Multiple Operating Regions

    • Strong Clustering

    • Overlapping Regions

    • Local Modelling Techniques

  • Non-Linear Relationships


Data Screening

  • Univariate Checks

  • Time Series Visualisation

  • Multivariate Statistics

    • Principal Component Analysis

    • Outlier Detection

    • Process Visualisation

  • Multi-Modal Data

    • Local PCA Models

      • Process Grades

      • Fuzzy Clustering

    • MixPCA


Data Analysis - Principal Component Analysis


Local Principal Component Analysis


Data Splitting

  • Data is Divided into 3 Data Sets

    • Training

      • Data to Build Model

    • Validation

      • Data used to Define Training Stopping Epoch

      • Improve Generalisation

    • Testing

      • Data Used to Quote Model Results

      • Unseen by Model in Training Phase

    • Ratio 70:15:15


Data Splitting

  • Outliers Removed

    • Fully Populated Data Set

  • Require Representation of Full Scope of Process Within Training Data

    • Random Selection

      • Sample from Data Distribution

      • With Respect to Operating Region

    • Kennard-Stone Selection

      • Sample from Flat Distribution

      • Mahalanobis Distance Metric for Selection

      • Analysis for Each Operating Region

      • Ensures Training Set Covers Full Scope


Advanced Modelling Studies

  • Projection to Latent Structures

    • Linear

    • Predictive Extension of PCA

  • Neural Networks

    • Non-linear

    • ‘Black-Box’

  • Neuro-Fuzzy Inference Systems

    • Adaptive Neuro-Fuzzy Inference System - ANFIS

    • Fuzzy Rulebase - Model Switching / Merging

    • Local Linear Models

  • Compromise between Accuracy, Interpretation and Simplicity


Input Data

S

Input Fuzzification

Normalised Rulebase

Local Models

Network Output

ANFIS Output

ANFIS Structure


Corus - Model Comparison Results


Shell - Model Comparison Results


Model Comparison Results - Corus and Shell


Bayesian Methods

  • Mathematical Foundation to Model Optimisation

  • Incorporates Use of Prior Knowledge

  • Advantage over Maximum Likelihood Models

    • Bayes Rule

      • Posterior = (Likelihood * Prior)/Evidence

    • Evidence is Constant for Given Model Structure


Bayesian Methods

  • Posterior - p(w|D,H)

    • Probability of Parameters, w, Representing Data, D, for Given Model, H

  • Likelihood - p(D|w,H)

    • Probability of the Model Fitting the Data

    • Accounts for Least Squares Modeling Power

  • Prior - p(w|H)

    • Incorporates Prior Knowledge into Training

    • Model Constraints

    • Independent of Data


Bayesian Methods

  • Bayesian Model Averaging

    • Accounts for Model Uncertainty

    • Avoids Use of Single Model

  • Prior Distribution

    • Incorporation of Process Knowledge

    • Favour Certain Characteristics

      • Model Interpretability

      • Model Accuracy


Bayesian ANFIS - BANFIS

  • Single ANFIS Structure

    • Process Knowledge

    • Cluster Analysis

  • Bayesian Model Averaging

    • Sample Rulebase Parameters

      • Markov Chain Monte Carlo

        • Rejection Sampling

      • Single Local Model Learning Stage

      • Cover Important Parameter Space


BANFIS - Results Comparison


BANFIS - Results Comparison - Corus


BANFIS - Results Comparison - Shell


BANFIS - Advantages and Disadvantages

  • Advantages

    • Improved results

    • Incorporates Parameter Uncertainty

    • Avoids Optimisation Training Problems

    • Avoids Single Network Solution

    • Incorporation of Prior Knowledge

  • Disadvantages

    • Complex Hierarchical Analysis

    • Network Interpretation Issues


Conclusions

  • Data Validation Methods

    • Screening

    • Local Models

    • Essential for Non-linear Modelling Methods

  • Compromise between:

    • Accuracy

    • Interpretation

    • Model Complexity

  • Results

    • Improvements in Accuracy and Data Analysis

    • Implementation of Bayesian Framework


Acknowledgements

  • CPACT

  • TCD

  • Paul Kitson - Corus

  • Phil Jonathan, Paul Blackhurst - Shell


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