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Physical Sciences and Mathematics Commons™
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Thermal Detection Of Inaccessible Corrosion, Matthew Charnley, Andrew Rzeznik
Thermal Detection Of Inaccessible Corrosion, Matthew Charnley, Andrew Rzeznik
Mathematical Sciences Technical Reports (MSTR)
In this paper, we explore the mathematical inverse problem of detecting corroded material on the reverse side of a partially accessible metal plate. We will show how a linearization can be used to simplify the initial problem and explain a regularization method used to obtain acceptable results for the corrosion profile. We will also state and perform some calculations for the full three-dimensional problem for possible future work.
Determining Properties Of Metal By Analyzing Changes In Impedance, Chase Mathison, Laura Booton
Determining Properties Of Metal By Analyzing Changes In Impedance, Chase Mathison, Laura Booton
Mathematical Sciences Technical Reports (MSTR)
In certain situations it is useful to identify an unknown sample of metal without contact or visual inspection. We wish to do this by inducing a current in a coil and placing the sample in the resulting magnetic field. For the special case in which the sample is an infinite slab, we have a model that gives the change in impedance of the coil based on the properties of the sample. In this paper we analyze the inverse problem of finding the metal properties from impedance measurements over a wide range of frequencies.
Nondestructive Electrothermal Detection Of Corrosion, Brittany Ambeau, Harris Enniss, Stefan Schnake
Nondestructive Electrothermal Detection Of Corrosion, Brittany Ambeau, Harris Enniss, Stefan Schnake
Mathematical Sciences Technical Reports (MSTR)
Nondestructive testing and imaging plays an important role in many industries, e.g., the monitoring and maintenance of corrosion in aircraft. The general technique is to input energy in some form into an object, observe the object’s response, and from this input-output information determine the internal structure. New techniques are always being explored, and recently there has been much interest in methods that use multiple forms of energy. In this vein, we examine a new technique for imaging corrosion or material loss in an object by combining electrical and thermal measurements on some accessible portion of the object’s outer boundary. The …
Electrical Impedance Imaging Of Corrosion On A Partially Accessible 2-Dimensional Region, Court Hoang, Katherine Osenbach
Electrical Impedance Imaging Of Corrosion On A Partially Accessible 2-Dimensional Region, Court Hoang, Katherine Osenbach
Mathematical Sciences Technical Reports (MSTR)
In this paper we examine the inverse problem of determining the amount of corrosion on an inaccessible surface of a two-dimensional region. Using numerical methods, we develop an algorithm for approximating corrosion profile using measurements of electrical potential along the accessible portion of the region. We also evaluate the effect of error on the problem, address the issue of ill-posedness, and develop a method of regularization to correct for this error. An examination of solution uniqueness is also presented.
Time-Dependent Thermal Imaging Of Circular Inclusions, Donald L. Brouwn, Mark Hubenthal
Time-Dependent Thermal Imaging Of Circular Inclusions, Donald L. Brouwn, Mark Hubenthal
Mathematical Sciences Technical Reports (MSTR)
This paper considers the inverse problem of locating one or more circular inclusions in a two-dimensional domain using thermal boundary data, specifically, the input heat flux and measured boundary temperature. The forward problem is governed by the heat equation. We show how the position and size of such defects can be recovered using the boundary data and various approximations of the solution to the forward problem. We also consider the stability of the algorithm involved to recover the defects.