Application of stochastic inverse theory to marine hydrodynamics

The objective of this article is to give an overview about the stochastic inverse method and its application to an ill-posed inverse problem in marine hydrodynamics. In stochastic inversion, it is possible to take into account inherent measurement and system uncertainties in the solution of an inverse problem in a very simple manner. The stochastic inverse method transforms the original inverse problem into the problem of a probabilistic question. Thus, the solution to an inverse problem is described by a distribution of the unknown parameters. These are some main differences with the deterministic inverse method. Stochastic inversion also provides lots of advantages over deterministic inverse methods such as quantitative parameter estimates, determination of confidence intervals, treatments of arbitrary forward maps, error estimates, or parameter estimates given noisy measurement data. In this work, the robust solution procedure from the perspective of the stochastic inverse method is discussed with two different ill-posed inverse problems in marine hydrodynamics.

[1]  Takeshi Kinoshita,et al.  Solution of an unstable inverse problem: wave source evaluation from observation of velocity distribution , 2000 .

[2]  Hal R. Varian,et al.  Economic and financial modeling with Mathematica , 1993, TELOS The electronic library of science.

[3]  Bangti Jin,et al.  Hierarchical Bayesian inference for Ill-posed problems via variational method , 2010, J. Comput. Phys..

[4]  A. Kirsch.  An Introduction to the Mathematical Theory of Inverse Problems , 1996, Applied Mathematical Sciences.

[5]  Takayuki Morikawa,et al.  REVIEW AND PERSPECTIVE OF INCORPORATING STATED PREFERENCE DATA IN TRAVEL DEMAND ANALYSIS , 1990 .

[6]  William R B Lionheart,et al.  Forward and Inverse Problems in Towed Cable Hydrodynamics , 2008 .

[7]  C. W. Groetsch,et al.  Inverse Problems in the Mathematical Sciences , 1993 .

[8]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[9]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[10]  M. Ben-Akiva,et al.  Discrete choice analysis , 1989 .

[11]  Nicholas Zabaras,et al.  A Bayesian inference approach to the inverse heat conduction problem , 2004 .

[12]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[13]  Imma Curiel,et al.  Cooperative game theory and applications , 1997 .

[14]  K. Button.  DOES THE THEORY OF THE 'CORE' EXPLAIN WHY AIRLINES FAIL TO COVER THEIR LONG-RUN COSTS OF CAPITAL? , 2003 .

[15]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[16]  Feng-Yeu Shyr,et al.  Applying game theory on strategic planning of freeway buses in competing with high speed rail , 2008 .

[17]  Takeshi Kinoshita,et al.  Numerical experiments on an ill-posed inverse problem for a given velocity around a hydrofoil by iterative and noniterative regularizations , 2000 .

[18]  S. L. Han,et al.  A numerical investigation of the inverse problem of the wavemaker , 2009 .

[19]  Takeshi Kinoshita,et al.  An ill-posed inverse problem of a wing with locally given velocity data and its analysis , 2000 .

[20]  Nando de Freitas,et al.  An Introduction to MCMC for Machine Learning , 2004, Machine Learning.

[21]  E. Somersalo,et al.  Statistical and computational inverse problems , 2004 .