通过电子信息技术中的被动测量识别多层介质中的主动异常

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Youjun Deng, Hongyu Liu, Yajuan Wang
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引用次数: 0

摘要

SIAM 应用数学杂志》,第 84 卷第 4 期,第 1362-1384 页,2024 年 8 月。 摘要我们建议研究一个反问题,即通过电阻抗断层扫描(EIT)中出现的相关电测量来确定嵌入多层背景介质中的多个异常点。我们的研究有几个显著特点。首先,我们研究中考虑的异常点非常普遍,其特征包括位置、支撑、不同大小、电导率参数以及随身携带的源强度。其次,我们利用主动异常点产生的电场进行测量。这相当于一次被动测量。第三,背景介质具有多层和片状恒定结构,可用于模拟实际应用中更普遍的情况,例如人体。在异常点较小,但考虑到其大小不一,仍有多个尺度的异常点的条件下,我们推导出了极化张量方面的电场尖锐公式,这使我们在确定不同情况下主动异常点的特征参数时,能够建立全面独特的可识别性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Identifying Active Anomalies in a Multilayered Medium by Passive Measurement in EIT
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1362-1384, August 2024.
Abstract. We propose to study an inverse problem of determining multiple anomalies embedded in a multilayered background medium by the associated electric measurement which arises in Electrical Impedance Tomography (EIT). There are several salient features of our study. First, the anomaly considered in our study is extremely general which is characterized by its location, support, varying size, conductivity parameter, as well as a carry-on source intensity. Second, we make use of the measurement of the electric field generated by the active anomalies. This corresponds to a single passive measurement. Third, the background medium is of a multilayered and piecewise-constant structure and can be used to model a more general scenario from practical applications; say, e.g., the human body. Under the condition that the anomalies are small, but still in multiple scales considering their varying sizes, we derive a sharp formula of the electric field in terms of the polarization tensors, which enables us to establish comprehensive unique identifiability results in determining the characteristic parameters of the active anomalies in different situations.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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