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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 : [email protected] Introduction. Problem Definitions

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Tom musicka centre for process analytics and control technology university of newcastle

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 : [email protected]


Introduction

Introduction

  • Problem Definitions

  • Data Analysis

    • PreScreening

    • Data Validation

  • Neuro-Fuzzy Modelling

  • Model Comparison

    • Results

  • Bayesian Framework

    • Results

  • Conclusions

  • Future Work


Data mining

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

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

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

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

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

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

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

Data Analysis - Principal Component Analysis


Local principal component analysis

Local Principal Component Analysis


Data splitting

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 splitting1

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

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


Anfis structure

Input Data

S

Input Fuzzification

Normalised Rulebase

Local Models

Network Output

ANFIS Output

ANFIS Structure


Corus model comparison results

Corus - Model Comparison Results


Shell model comparison results

Shell - Model Comparison Results


Model comparison results corus and shell

Model Comparison Results - Corus and Shell


Bayesian methods

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 methods1

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 methods2

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

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


Banfis results comparison corus

BANFIS - Results Comparison - Corus


Banfis results comparison shell

BANFIS - Results Comparison - Shell


Banfis advantages and disadvantages

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

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

Acknowledgements

  • CPACT

  • TCD

  • Paul Kitson - Corus

  • Phil Jonathan, Paul Blackhurst - Shell


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