Kalman Filter Method In The Analysis Of Vibrations Due To Water Waves

Andrzej Kozakiewicz, Piotr Wilde

• Publisher: World Scientific
• Year: 1993
• Print ISBN: 9789810212964, 9789810212964
• eBook ISBN: 9789812796479
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

The central theme of this book is the application of the linear filtering theory to the vibration of structures in a fluid. Emphasis is placed on the mathematical models which, in the theory of systems, characterize the state of a dynamic system. The mathematical models are in the form of linear Ito stochastic differential equations. Discretization of the models, which leads to straightforward computer applications, is also discussed. The book also presents an approach to nonlinear problems based on the expansion of random functions in a series. To elucidate the proposed approach, examples on the application of Kalman filters, which refer to the vibrations of cylinders in waves, are cited. This provides a practical orientation to complement the proposed theory and contributes to a clearer and deeper understanding of the subject matter.

Table of contents

• Contents
• Preface
• Chapter 1 Introduction
• Chapter 2 Mathematical models for random functions without dominant frequencies
• Chapter 3 Mathematical models for random functions with a dominant frequency
• Chapter 4 Expansion in a series of random functions with multiple dominant frequencies
• Chapter 5 Properties of a dynamic system
• Chapter 6 Free vibrations of structures in a fluid
• Chapter 7 Vibrations of structures due to water waves
• Chapter 8 Nonlinear problems of vibrations
• Appendix A Stochastic processes - definitions
• Appendix B Brownian motion process, Markov process, Wiener and Itô integrals
• Appendix C Stochastic difference equations
• Appendix D Itô stochastic differential equation
• Appendix E Stochastic differential equation for stationary processes
• Appendix F Kalman filters
• Bibliography
• Index