Advances in Statistical Monitoring of Complex Multivariate Processes: With Applications in Industrial Process Control / Edition 1

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Overview

The book summarises recent advances in statistical-based process monitoring of complex multivariate process systems.  It includes a broad range of applications of multivariate statistical techniques into the area of mechanical, manufacturing and power engineering, whilst traditionally such techniques are predominantly developed and applied in the chemical industry.

The content is aimed at presenting the theoretical foundation of multivariate statistical process control, outlining the drawbacks of this technology, describing improvements aimed at addressing such deficiencies and demonstrating the usefulness of these improvements using industrial examples that relate to applications in the chemical, mechanical, manufacturing and power industry as well as simple simulation studies.  The text also includes tutorial questions and worked examples.

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Product Details

  • ISBN-13: 9780470028193
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 10/16/2012
  • Series: Statistics in Practice Series
  • Edition number: 1
  • Pages: 480
  • Sales rank: 1,385,674
  • Product dimensions: 6.10 (w) x 9.30 (h) x 1.00 (d)

Meet the Author

Uwe Kruger, The Petroleum Institute, Abu Dhabi, United Arab Emirates

Lei Xie, Institute of Cyber-Systems & Control, Zhejiang University, China

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Table of Contents

Preface

Introduction

I Fundamentals of Multivariate Statistical Process Control

1 Motivation for Multivariate Statistical Process Control

1.1 Summary of Statistical Process Control

1.1.1 Roots and Evolution of Statistical Process Control

1.1.2 Principles of Statistical Process Control

1.1.3 Hypothesis Testing, Type I and II errors

1.2 Why Multivariate Statistical Process Control

1.2.1 Statistically Uncorrelated Variables

1.2.2 Perfectly Correlated Variables

1.2.3 Highly Correlated Variables

1.2.4 Type I and II Errors and Dimension Reduction

1.3 Tutorial Session

2 Multivariate Data Modeling Methods

2.1 Principal Component Analysis

2.1.1 Assumptions for Underlying Data Structure

2.1.2 Geometric Analysis of Data Structure

2.1.3 A Simulation Example

2.2 Partial Least Squares

2.2.1 Assumptions for Underlying Data Structure

2.2.2 Deflation Procedure for Estimating Data Models

2.2.3 A Simulation Example

2.3 Maximum Redundancy Partial Least Squares

2.3.1 Assumptions for Underlying Data Structure

2.3.2 Source Signal Estimation

2.3.3 Geometric Analysis of Data Structure

2.3.4 A Simulation Example

2.4 Estimating the Number of Source Signals

2.4.1 Stopping Rules for PCA Models

2.4.2 Stopping Rules for PLS Models

2.5 Tutorial Session

3 Process Monitoring Charts

3.1 Fault Detection

3.1.1 Scatter Diagrams

3.1.2 Nonnegative Quadratic Monitoring Statistics

3.2 Fault Isolation and Identification

3.2.1 Contribution Charts

3.2.2 Residual-Based Tests

3.2.3 Variable Reconstruction

3.3 Geometry of Variable Projections

3.3.1 Linear Dependency of Projection Residuals

3.3.2 Geometric Analysis of Variable Reconstruction

3.4 Tutorial Session

II Application Studies

4 Application to a Chemical Reaction Process

4.1 Process Description

4.2 Identification of a Monitoring Model

4.3 Diagnosis of a Fault Condition

5 Application to a Distillation Process

5.1 Process Description

5.2 Identification of a Monitoring Model

5.3 Diagnosis of a Fault Condition

III Advances in Multivariate Statistical Process Control

6 Further Modeling Issues

6.1 Accuracy of Estimating PCA Models

6.1.1 Revisiting the Eigendecomposition of Sz0z0

6.1.2 Two Illustrative Examples

6.1.3 Maximum Likelihood PCA for Known Sgg

6.1.4 Maximum Likelihood PCA for Unknown Sgg

6.1.5 A Simulation Example

6.1.6 A Stopping Rule for Maximum Likelihood PCA Models

6.1.7 Properties of Model and Residual Subspace Estimates

6.1.8 Application to a Chemical Reaction Process - Revisited

6.2 Accuracy of Estimating PLS Models

6.2.1 Bias and Variance of Parameter Estimation

6.2.2 Comparing Accuracy of PLS and OLS Regression Models

6.2.3 Impact of Error-in-Variables Structure upon PLS Models

6.2.4 Error-in-Variable Estimate for Known See

6.2.5 Error-in-Variable Estimate for Unknown See

6.2.6 Application to a Distillation Process - Revisited

6.3 Robust Model Estimation

6.3.1 Robust Parameter Estimation

6.3.2 Trimming Approaches

6.4 Small Sample Sets

6.5 Tutorial Session

7 Monitoring Multivariate Time-Varying Processes

7.1 Problem Analysis

7.2 Recursive Principal Component Analysis

7.3 MovingWindow Principal Component Analysis

7.3.1 Adapting the Data Correlation Matrix

7.3.2 Adapting the Eigendecomposition

7.3.3 Computational Analysis of the Adaptation Procedure

7.3.4 Adaptation of Control Limits

7.3.5 Process Monitoring using an Application Delay

7.3.6 MinimumWindow Length

7.4 A Simulation Example

7.4.1 Data Generation

7.4.2 Application of PCA

7.4.3 Utilizing MWPCA based on an Application Delay

7.5 Application to a Fluid Catalytic Cracking Unit

7.5.1 Process Description

7.5.2 Data Generation

7.5.3 Pre-analysis of Simulated Data

7.5.4 Application of PCA

7.5.5 Application of MWPCA

7.6 Application to a Furnace Process

7.6.1 Process Description

7.6.2 Description of Sensor Bias

7.6.3 Application of PCA

7.6.4 Utilizing MWPCA based on an Application Delay

7.7 Adaptive Partial Least Squares

7.7.1 Recursive Adaptation of Sx0x0 and Sx0y0

7.7.2 MovingWindow Adaptation of Sv0v0 and Sv0y0

7.7.3 Adapting The Number of Source Signals

7.7.4 Adaptation of the PLS Model

7.8 Tutorial Session

8 Monitoring Changes in Covariance Structure

8.1 Problem Analysis

8.1.1 First Intuitive Example

8.1.2 Generic Statistical Analysis

8.1.3 Second Intuitive Example

8.2 Preliminary Discussion of Related Techniques

8.3 Definition of Primary and Improved Residuals

8.3.1 Primary Residuals for Eigenvectors

8.3.2 Primary Residuals for Eigenvalues

8.3.3 Comparing both Types of Primary Residuals

8.3.4 Statistical Properties of Primary Residuals

8.3.5 Improved Residuals for Eigenvalues

8.4 Revisiting the Simulation Examples in Section 8.1

8.4.1 First Simulation Example

8.4.2 Second Simulation Example

8.5 Fault Isolation and Identification

8.5.1 Diagnosis of Step-Type Fault Conditions

8.5.2 Diagnosis of General Deterministic Fault Conditions

8.5.3 A Simulation Example

8.6 Application Study to a Gearbox System

8.6.1 Process Description

8.6.2 Fault Description

8.6.3 Identification of a Monitoring Model

8.6.4 Detecting a Fault Condition

8.7 Analysis of Primary and Improved Residuals

8.7.1 Central Limit Theorem

8.7.2 Further Statistical Properties of Primary Residuals

8.7.3 Sensitivity of Statistics based on Improved Residuals

8.8 Tutorial Session

IV Description of Modeling Methods

9 Principal Component Analysis

9.1 The Core Algorithm

9.2 Summary of the PCA Algorithm

9.3 Properties of a PCA Model

10 Partial Least Squares

10.1 Preliminaries

10.2 The Core Algorithm

10.3 Summary of the PLS Algorithm10.4 Properties of PLS

10.5 Properties of Maximum Redundancy PLS

References

Index

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