Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
复制标题
DOI：
10.1002/nme.6606
复制
发表时间：
2020-01
影响因子：
2.9
通讯作者：
B. A. Wilson;P. Ledger
中科院分区：
文献类型：
--
作者：
B. A. Wilson;P. Ledger
在金属探测中，通过测量低频范围内的扰动磁场来识别隐藏的导电可渗透物体是很重要的。应用包括在运输枢纽的安全检查中确定威胁物品、未爆弹药的位置和前冲突地区的杀伤人员地雷、搜索具有考古意义的物品和回收有价值的金属。最近，利用极化张量来解决反问题，或者更一般地定位和分类目标，引起了人们的极大关注。磁极化率张量(MPT)使用少量的系数来描述导电的可渗透物体，它有一个明确的公式来计算它们的系数，并有一个众所周知的频率行为，我们称之为它的频谱特征。然而，要计算这样的特征并建立它们的库以用于对象分类，需要重复解决传输问题，这通常使用有限元离散化近似完成。为了减少运算量，我们提出了一种高效的降阶模型(ROM)，该模型利用适当的正交分解来快速计算MPT谱签名，从而进一步降低了问题的复杂性。我们的只读存储器受益于预测的MPT系数相对于用有限元解获得的系数的精度的后验误差估计。这些估计可以在只读存储器的在线阶段被廉价地计算，从而允许只读存储器预测得到验证。为了进一步提高MPT谱特征的计算效率，我们提供了缩放结果，这使得能够在物体大小或电导率变化的情况下立即计算特征。我们通过对一系列均匀和非均匀导电可渗透物体的应用来说明我们的方法。
The identification of hidden conducting permeable objects from measurements of the perturbed magnetic field taken over a range of low frequencies is important in metal detection. Applications include identifying threat items in security screening at transport hubs, location of unexploded ordnance, and antipersonnel landmines in areas of former conflict, searching for items of archeological significance and recycling of valuable metals. The solution of the inverse problem, or more generally locating and classifying objects, has attracted considerable attention recently using polarizability tensors. The magnetic polarizability tensor (MPT) provides a characterization of a conducting permeable object using a small number of coefficients, has an explicit formula for the calculation of their coefficients, and a well understood frequency behavior, which we call its spectral signature. However, to compute such signatures, and build a library of them for object classification, requires the repeated solution of a transmission problem, which is typically accomplished approximately using a finite element discretization. To reduce the computational cost, we propose an efficient reduced order model (ROM) that further reduces the problem using a proper orthogonal decomposition for the rapid computation of MPT spectral signatures. Our ROM benefits from a posteriori error estimates of the accuracy of the predicted MPT coefficients with respect to those obtained with finite element solutions. These estimates can be computed cheaply during the online stage of the ROM allowing the ROM prediction to be certified. To further increase the efficiency of the computation of the MPT spectral signature, we provide scaling results, which enable an immediate calculation of the signature under changes in the object size or conductivity. We illustrate our approach by application to a range of homogenous and inhomogeneous conducting permeable objects.