A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis

A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis

We consider the inverse sensitivity analysis problem of quantifying the uncertainty of inputs to a deterministic map given specified uncertainty in a linear functional of the output of the map. This is a version of the model calibration or parameter estimation problem for a deterministic map. We assume that the uncertainty in the quantity of interest is represented by a random variable with a g...

A Measure-Theoretic Computational Method for Inverse Sensitivity Problems III: Multiple Quantities of Interest

We consider inverse problems for a deterministic model in which the dimension of the output quantities of interest computed from the model is smaller than the dimension of the input quantities for the model. In this case, the inverse problem admits set-valued solutions (equivalence classes of solutions). We devise a method for approximating a representation of the set-valued solutions in the pa...

A Computational Measure Theoretic Approach to Inverse Sensitivity Problems II: A Posteriori Error Analysis

In part one of this paper [T. Butler and D. Estep, SIAM J. Numer. Anal., to appear], we develop and analyze a numerical method to solve a probabilistic inverse sensitivity analysis problem for a smooth deterministic map assuming that the map can be evaluated exactly. In this paper, we treat the situation in which the output of the map is determined implicitly and is difficult and/or expensive t...

A Sensitivity-Analysis Method for Inverse Simulation

semi-analytical solution for static and forced vibration problems of laminated beams through smooth fundamental functions method

در این پایان نامه روش جدیدی مبتنی بر روش حل معادلات دیفرانسیل پارهای بر اساس روش توابع پایه برای حل مسایل ارتعاش اجباری واستاتیک تیرها و صفحات لایه ای ارایه شده است که می توان تفاوت این روش با روش های متداول توابع پایه را در استفاده از توابع هموار در ارضاء معادلات حاکم و شرایط مرزی دانست. در روش ارایه شده در این پایاننامه از معادله تعادل به عنوان معادله حاکم بر رفتار سیستم استفاده شده است که مو...