Yong Chen - Industrial Data Analytics for Diagnosis and Prognosis

12 Appendix: Basics of Vectors, Matrices, and Linear Vector Space

13 References

14 Index

1 Cover

2 Title page Industrial Data Analytics for Diagnosis and Prognosis A Random Effects Modelling Approach Shiyu Zhou University of Wisconsin – Madison Yong Chen University of Iowa

3 Copyright

4 Dedication

5 Table of Contents

6 Preface

7 Acknowledgments

8 Acronyms

9 Table of Notation

10 Begin Reading

11 Appendix: Basics of Vectors, Matrices, and Linear Vector Space

12 References

13 Index

14 End User License Agreement

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Today, we are facing a data rich world that is changing faster than ever before. The ubiquitous availability of data provides great opportunities for industrial enterprises to improve their process quality and productivity. Industrial data analytics is the process of collecting, exploring, and analyzing data generated from industrial operations and throughout the product life cycle in order to gain insights and improve decision-making. This book describes industrial data analytics approaches with an emphasis on diagnosis and prognosis of industrial processes and systems.

A large number of textbooks/research monographs exist on diagnosis and prognosis in the engineering field. Most of these engineering books focus on model-based diagnosis and prognosis problems in dynamic systems. The model-based approaches adopt a dynamic model for the system, often in the form of a state space model, as the basis for diagnosis and prognosis. Different from these existing books, this book focuses on the concept of random effects and its applications in system diagnosis and prognosis . The impetus for this book arose from the current digital revolution. In this digital age, the essential feature of a modern engineering system is that a large amount of data from multiple similar units/machines during their operations are collected in real time. This feature poses significant intellectual opportunities and challenges. As for opportunities, since we have observations from potentially a very large number of similar units, we can compare their operations, share the information, and extract common knowledge to enable accurate and tailored prediction and control at the individual level. As for challenges, because the data are collected in the field and not in a controlled environment, the data contain significant variation and heterogeneity due to the large variations in working/usage conditions for different units. This requires that the analytics approaches should be not only general (so that the common information can be learned and shared), but also flexible (so that the behavior of an individual unit can be captured and controlled). The random effects modeling approaches can exactly address these opportunities and challenges.