Industrial Data Analytics for Diagnosis and Prognosis: A Random Effects Modelling Approach
- Length: 352 pages
- Edition: 1
- Language: English
- Publisher: Wiley
- Publication Date: 2021-07-21
- ISBN-10: 1119666287
- ISBN-13: 9781119666288
- Sales Rank: #0 (See Top 100 Books)
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.
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
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