Development of a method to estimate the distribution of material properties using resolution-independent representation and its application

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K04571
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 22020:Structure engineering and earthquake engineering-related
• Research Institution: Hokkaido University (2020-2022); Tokyo Institute of Technology (2019)
• Principal Investigator: Furukawa Akira 北海道大学, 工学研究院, 准教授 (60724614)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: 多重解像度表現 / 弾性波トモグラフィ / マッチング追跡アルゴリズム / 周波数解析 / 基本解近似解法

Outline of Final Research Achievements

In this research, we have developed estimation methods that can flexibly set the resolution of solution according to the distribution of material properties, and checked their validity. We focused on the estimation of 1D permittivity distribution and 2D phase velocity distribution. Devising solution representations and solution methods, we obtained solutions whose resolution corresponds to the distribution representation to be estimated. In addition, new solution methods were proposed for frequency analysis and the method of fundamental solutions (MFS). The developed method for frequency analysis is able to flexibly set the frequency resolution which is typically determined by the original signal. Moreover, we confirmed the developed MFS enables to determine the location and number of the source points without prior setting.

Free Research Field

土木工学

Academic Significance and Societal Importance of the Research Achievements

本研究課題では，解の構成方法と求解方法に工夫を加えることで解像度の選択自由度を確保し，推定を行うことのできる手法の開発を行った．周波数解析や基本解近似解法を取り扱った研究例では，その有効性を示すことができた．これらの成果は，当該手法を用いた実用的な解析への展開が期待できる．さらに，本研究課題を通して得られた知見は，他の数値解析手法・数値シミュレーション手法の開発・改良に対しても貢献が期待できると考えられる．