Inverse problems and parameter estimation: integration of measurements and analysis

Abstract

The main purpose of this paper is to introduce the five following papers on inverse problems, and to relate the field of inverse problems to measurements. Inverse techniques are an emerging suite of methods which, when fully embraced, promise to provide better experiments and improved understanding of physical processes. This paper provides an overview of the general procedure and concepts related to identification of parameters or functions by inverse techniques. A discussion of errors and their implication for an appropriate function for minimization in inverse procedures is presented, and two methods for achieving this minimization are discussed. Some sequential concepts for parameter estimation are presented, along with a discussion of residuals and confidence intervals. Experiment design and optimization are reviewed, and a discussion of residuals and their relation to model building is presented.

Inverse finite element method for large‐displacement beams

“…to determine the undeformed (reference) configuration knowing the deformed shape of the body and the applied loads. Beck and Woodburry [1] classified it as an inverse design problem, in contrast to classical inverse (measurement) problems that consist in determining material data knowing both the deformed and undeformed configurations, as well as the service loads.…”

Magnetic Material Characterization Using an Inverse Problem Approach

“…This sCRB offers the lower bound of the error within a rather small computational time compared to the well-know time-demanding techniques such as Monte Carlo simulations applied in e.g. (Leach et al, 2009), stochastic finite element method (Beck & Woodbury, 1998), polynomial chaos decomposition (Gaignaire et al, 2010).…”

Nonparametric Monitoring for Geotechnical Structures Subject to Long-Term Environmental Change

“…Some examples of the application of LSE in geomechanical applications include the work of Gioda and Maier [44], Cividini et al [45], Cividini et al [46], Arai et al [47], Arai et al [48], Arai et al [49], Gioda and Sakurai [50], Shoji et al [51], Shoji et al [52], Anandarajah and Agarwal [53], Murakami et al [54], Beck and Woodbury [55], and Xiang et al [56].…”