Industrial Data Analytics for Diagnosis and Prognosis: A Random Effects Modelling Approach

✍ Scribed by Shiyu Zhou, Yong Chen

• Publisher: Wiley
• Year: 2021
• Tongue: English
• Leaves: 353
• Edition: 1
• Category: Library

✦ Synopsis

Discover data analytics methodologies for the diagnosis and prognosis of industrial systems under a unified random effects model  

In Industrial Data Analytics for Diagnosis and Prognosis - A Random Effects Modelling Approach, distinguished engineers Shiyu Zhou and Yong Chen deliver a rigorous and practical introduction to the random effects modeling approach for industrial system diagnosis and prognosis. In the book’s two parts, general statistical concepts and useful theory are described and explained, as are industrial diagnosis and prognosis methods. The accomplished authors describe and model fixed effects, random effects, and variation in univariate and multivariate datasets and cover the application of the random effects approach to diagnosis of variation sources in industrial processes. They offer a detailed performance comparison of different diagnosis methods before moving on to the application of the random effects approach to failure prognosis in industrial processes and systems. 

In addition to presenting the joint prognosis model, which integrates the survival regression model with the mixed effects regression model, the book also offers readers: 

• A thorough introduction to describing variation of industrial data, including univariate and multivariate random variables and probability distributions 
• Rigorous treatments of the diagnosis of variation sources using PCA pattern matching and the random effects model
• An exploration of extended mixed effects model, including mixture prior and Kalman filtering approach, for real time prognosis
• A detailed presentation of Gaussian process model as a flexible approach for the prediction of temporal degradation signals

Ideal for senior year undergraduate students and postgraduate students in industrial, manufacturing, mechanical, and electrical engineering, Industrial Data Analytics for Diagnosis and Prognosis is also an indispensable guide for researchers and engineers interested in data analytics methods for system diagnosis and prognosis. 

✦ Table of Contents

Industrial Data Analytics for Diagnosis and Prognosis
Contents
Preface
Acknowledgments
Acronyms
Table of Notation
1 Introduction
1.1 Background and Motivation
1.2 Scope and Organization of the Book
1.3 How to Use This Book
Bibliographic Note
Part 1 Statistical Methods and Foundation for Industrial
Data Analytics
2 Introduction to Data Visualization and Characterization
2.1 Data Visualization
2.1.1 Distribution Plots for a Single Variable
2.1.2 Plots for Relationship Between Two Variables
2.1.3 Plots for More than Two Variables
2.2 Summary Statistics
2.2.1 Sample Mean, Variance, and Covariance
2.2.2 Sample Mean Vector and Sample Covariance Matrix
2.2.3 Linear Combination of Variables
Bibliographic Notes
Exercises
3 Random Vectors and the Multivariate Normal Distribution
3.1 Random Vectors
3.2 Density Function and Properties of Multivariate Normal
Distribution
3.3 Maximum Likelihood Estimation for Multivariate Normal
Distribution
3.4 Hypothesis Testing on Mean Vectors
3.5 Bayesian Inference for Normal Distribution
Bibliographic Notes
Exercises
4 Explaining Covariance Structure: Principal Components
4.1 Introduction to Principal Component Analysis
4.1.1 Principal Components for More Than Two Variables
4.1.2 PCA with Data Normalization
4.1.3 Visualization of Principal Components
4.1.4 Number of Principal Components to Retain
4.2 Mathematical Formulation of Principal Components
4.2.1 Proportion of Variance Explained
4.2.2 Principal Components Obtained from the Correlation Matrix
4.3 Geometric Interpretation of Principal Components
4.3.1 Interpretation Based on Rotation
4.3.2 Interpretation Based on Low-Dimensional Approximation
Bibliographic Notes
Exercises
5 Linear Model for Numerical and Categorical
Response Variables
5.1 Numerical Response – Linear Regression Models
5.1.1 General Formulation of Linear Regression Model
5.1.2 Significance and Interpretation of Regression Coefficients
5.1.3 Other Types of Predictors in Linear Models
5.2 Estimation and Inferences of Model Parameters for Linear
Regression
5.2.1 Least Squares Estimation
5.2.2 Maximum Likelihood Estimation
5.2.3 Variable Selection in Linear Regression
5.2.4 Hypothesis Testing
5.3 Categorical Response – Logistic Regression Model
5.3.1 General Formulation of Logistic Regression Model
5.3.2 Significance and Interpretation of Model Coefficients
5.3.3 Maximum Likelihood Estimation for Logistic Regression
Bibliographic Notes
Exercises
6 Linear Mixed Effects Model
6.1 Model Structure
6.2 Parameter Estimation for LME Model
6.2.1 Maximum Likelihood Estimation Method
6.2.2 Distribution-Free Estimation Methods
6.3 Hypothesis Testing
6.3.1 Testing for Fixed Effects
6.3.2 Testing for Variance–Covariance Parameters
Bibliographic Notes
Exercises
Part 2 Random Effects Approaches for Diagnosis and
Prognosis
7 Diagnosis of Variation Source Using PCA
7.1 Linking Variation Sources to PCA
7.2 Diagnosis of Single Variation Source
7.3 Diagnosis of Multiple Variation Sources
7.4 Data Driven Method for Diagnosing Variation Sources
Bibliographic Notes
Exercises
8 Diagnosis of Variation Sources Through
Random Effects Estimation
8.1 Estimation of Variance Components
8.2 Properties of Variation Source Estimators
8.3 Performance Comparison of Variance Component Estimators
Bibliographic Notes
Exercises
9 Analysis of System Diagnosability
9.1 Diagnosability of Linear Mixed Effects Model
9.2 Minimal Diagnosable Class
9.3 Measurement System Evaluation Based on System
Diagnosability
Bibliographic Notes
Exercises
Appendix
10 Prognosis Through Mixed Effects Models for Longitudinal Data
10.1 Mixed Effects Model for Longitudinal Data
10.2 Random Effects Estimation and Prediction for an Individual Unit
10.3 Estimation of Time-to-Failure Distribution
10.4 Mixed Effects Model with Mixture Prior Distribution
10.4.1 Mixture Distribution
10.4.2 Mixed Effects Model with Mixture Prior for Longitudinal Data
10.5 Recursive Estimation of Random Effects Using Kalman Filter
10.5.1 Introduction to the Kalman Filter
10.5.2 Random Effects Estimation Using the Kalman Filter
Biographical Notes
Exercises
Appendix
11 Prognosis Using Gaussian Process Model
11.1 Introduction to Gaussian Process Model
11.2 GP Parameter Estimation and GP Based Prediction
11.3 Pairwise Gaussian Process Model
11.3.1 Introduction to Multi-output Gaussian Process
11.3.2 Pairwise GP Modeling Through Convolution Process
11.4 Multiple Output Gaussian Process for Multiple Signals
11.4.1 Model Structure
11.4.2 Model Parameter Estimation and Prediction
11.4.3 Time-to-Failure Distribution Based on GP Predictions
Bibliographical Notes
Exercises
12 Prognosis Through Mixed Effects Models for
Time-to-Event Data
12.1 Models for Time-to-Event Data Without Covariates
12.1.1 Parametric Models for Time-to-Event Data
12.1.2 Non-parametric Models for Time-to-Event Data
12.2 Survival Regression Models
12.2.1 Cox PH Model with Fixed Covariates
12.2.2 Cox PH Model with Time Varying Covariates
12.2.3 Assessing Goodness of Fit
12.3 Joint Modeling of Time-to-Event Data and Longitudinal Data
12.3.1 Structure of Joint Model and Parameter Estimation
12.3.2 Online Event Prediction for a New Unit
12.4 Cox PH Model with Frailty Term for Recurrent Events
Bibliographical Notes
Exercises
Appendix
Appendix: Basics of Vectors, Matrices, and Linear Vector Space
References
Index