Full Description
This book organizes and explains, in a systematic and pedagogically effective manner, recent advances in path integral solution techniques with applications in stochastic engineering dynamics. It fills a gap in the literature by introducing to the engineering mechanics community, for the first time in the form of a book, the Wiener path integral as a potent uncertainty quantification tool. Since the path integral flourished within the realm of quantum mechanics and theoretical physics applications, most books on the topic have focused on the complex-valued Feynman integral with only few exceptions, which present path integrals from a stochastic processes perspective. Remarkably, there are only few papers, and no books, dedicated to path integral as a solution technique in stochastic engineering dynamics. Summarizing recently developed techniques, this volume is ideal for engineering analysts interested in further establishing path integrals as an alternative potent conceptual and computational vehicle in stochastic engineering dynamics.
Contents
Introduction.- Wiener path integral formalism.- Linear
systems under Gaussian white noise excitation: exact closed form solutions.- Nonlinear
systems under Gaussian white noise excitation.- Nonlinear systems under
non-white, non-Gaussian and non-stationary excitation.- Nonlinear systems with singular
diffusion matrices: a broad perspective including hysteresis modeling.- High-dimensional
nonlinear systems: circumventing the curse of dimensionality via a
reduced-order formulation.- Efficient numerical implementation strategies via
sparse representations and compressive sampling.- An enhanced quadratic Wiener
path integral approximation with applications to nonlinear system reliability
assessment.- Epilogue.
