Source of Uncertainty and Bayesian Updating

This example demonstrates that even for a deterministic system without any external loading, the response appears to be uncertain. In the real world, there are many types of unmodeled behavior/dynamics of complex physical phenomena (e.g., chaotic systems) and one possible approach is to treat them as random variables or random processes. Then, statistical moments are used to represent the overall behavior. This type of error is regarded hereafter as a modeling error. Another main source of uncertainty is due to the finite amount of information carried by the data. Due to the finite amount of the measurement, and hence the finite amount of information, identification results can be determined up to finite precision so uncertainty gets into the picture. Finally, due to the finite precision of data acquisition, measurement error is induced, including electrical noise and quantization error. 

George Soros also recognized in financial markets and economics that uncertainty is due to lack of information [251]. In the context of social sciences, it is more appropriate to regard incomplete information as incomplete knowledge. Of course, in financial markets or 

There are several important questions the author attempts to address in this book  

In order to address these questions, this book proceeds with six chapters. Chapter 1 gives the general introduction and literature review of applications in different disciplines of engineering. The purpose for model updating is discussed and the types of uncertainty considered in this book are also exploited. 

Chapters 3 and 4 introduce two recently developed Bayesian methods for updating the mathematical models of dynamical systems. Chapter 3 presents the Bayesian spectral density approach. The spectral density estimator is defined to take into account of the aliasing and leakage effect. The statistical properties of the spectral density estimator are examined and 

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