Structural engineering from an inverse problems perspective

Abstract

The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural responses given data including external forces, geometry, member sizes, restraint, etc.—characterizing a forward problem (structural causalities → structural response). Shortly thereafter, junior engineers are introduced to structural design where they aim to, for example, select an appropriate structural form for members based on design criteria, which is the inverse of what they previously learned. Similar inverse realizations also hold true in structural health monitoring and a number of structural engineering sub-fields (response → structural causalities). In this light, we aim to demonstrate that many structural engineering sub-fields may be fundamentally or partially viewed as inverse problems and thus benefit via the rich and established methodologies from the inverse problems community. To this end, we conclude that the future of inverse problems in structural engineering is inexorably linked to engineering education and machine learning developments.

Distillation of non-locality in porous solids

“…The implicit trade-off in the size and resolution of the RVE ultimately forces existing models to demand computationally prohibitive resources when attempting to fully resolve the effect of the porous microstructure or lead to inaccurate numerical predictions [9]. The lack of a mathematical strategy to consistently characterize the underlying physics naturally prevents the development of a generalized well-posed inverse framework [25]. Consequently, only a handful of validated applications of classical frameworks, which are often restricted to the linear analysis of periodic porous solids, exist in the literature [10,24,26].…”

Optimal design of strain sensor placement for distributed static load determination

“…The present work seeks to provide guidance for designing sensor systems on beam-like structures. Methods for solving static inverse problems have been studied extensively [4]. Most of the current literature on static inverse problems focuses on structural health monitoring applications, where structural damage is measured indirectly from quasi-static response data [4][5][6][7][8][9][10][11][12].…”

“…Methods for solving static inverse problems have been studied extensively [4]. Most of the current literature on static inverse problems focuses on structural health monitoring applications, where structural damage is measured indirectly from quasi-static response data [4][5][6][7][8][9][10][11][12]. These structural health monitoring problems belong to the broad field of system identification, where the goal is to estimate-and identify changes to-system properties (e.g.…”

Blast wave kinematics: theory, experiments, and applications

“…Thus, the ability to determine this relationship a priori, from a known explosive yield, will provide vital information on the properties of the blast wave as it propagates. Further, a well-defined relationship that is valid for any distance permits the yield of an explosive to be determined through inverse analysis [6].…”