Nondestructive Evaluation Laboratory: Electromagnetic Imaging and Inverse Problems
Antonello Tamburrino | tamburr1@egr.msu.edu | www.egr.msu.edu/ndel/
Imaging is the science, technique and process of creating visual representations of the interior of a body from nondestructive measurements taken from the outside. Imaging relies onto the ability of classical fields to penetrate and interact with the interior of a body. Examples include medical and industrial imaging systems where thermal, ultra-sound, X-rays or electromagnetic fields are employed to obtain an image of the interior of the object. Electromagnetic Imaging refers to the use of electromagnetic fields (from static to microwave and higher frequencies) for providing and image of an object.
The problem of obtaining an image of the interior of an object from a set of noisy measurements is usually ill-posed, that is either does not admit a solution, or the solution is not unique or it does not depend continuously upon the data. Moreover, the problem is typically non-linear thus posing difficult challenges.
Imaging is multidisciplinary field involving inversion methods and algorithms, numerical modelling, sensor system design and material science. Inversion algorithms, the key “component” form an image of the interior of a body. They can be iterative or non-iterative and relies on a model of the probe-specimen interaction. Numerical modelling is required to model the aforementioned probe-specimen interaction. Other than for imaging algorithms, numerical modeling is crucial for understanding the physics of the probe-specimen interaction in view of the optimization of the design of the probe, virtual prototyping and training. Material science plays a key role in characterizing some features of the material property to be imaged and in indirect measurements as for micromagnetic measurements.
In the following a brief description of the most recent research activities carried out by this research group is provided. The methods described in the following refer to some selected industrial applications. However, these methods can be applied to a broader area of problems including medical imaging, geophysical prospection, aeronautical and aerospace testing, gas and oil pipelines inspection, nuclear power plant inspection, etc.
Non Iterative Imaging Methods
This new class of imaging algorithm has been recently introduced as alternative to iterative imaging methods. Specifically, Non Iterative Imaging Methods have been developed for real-time nondestructive evaluation of materials, where one is interested in imaging anomalies inside a homogeneous body.
Iterative methods form an image of the interior of a body by iteratively minimizing the distance between numerically computed data and the experimental measurements (objective function). At each step of the procedure the solution of at least one numerical model is required. These methods are time-consuming and , moreover, can be trapped in false solution (local minima of the objective function). Non iterative imaging methods are based on a simple local test to evaluate if a point of the body is part or not of an anomalous region. The local test does not require the solution of a numerical model at run-time and it is suitable for real-time imaging.
These methods have been successfully applied to Electrical Resistance or Capacitance Tomography, Eddy Current Testing and extension to microwave tomography is ongoing. From a general perspective, they can be applied when the underlying physics is governed by an elliptic PDE, a parabolic PDE and a hyperbolic PDE. Applications have been mainly devoted to imaging of cracks in conducting structures of interest in aeronautical and nuclear power plants.
Numerical Modelling
Computational models provide a phenomenological tool for studying the underlying physics for accurate prediction of the probe-specimen interaction. As a matter of fact, numerical modeling is recognized as a key component for developing fast imaging/detection procedures, for understanding the physical behavior exhibited by materials under testing, for understanding the signatures provided by a specific probe and measurement protocol, for an optimized probe design and virtual prototyping, for training, etc.
Despite the availability of general purpose numerical simulators for computational electromagnetics, the specialized nature of NDE calls for the development of custom designed simulation software because of the specific features/requirements for Electromagnetic Imaging: (i) the multiscale nature of the physical problem, (ii) low computational time in view of (a) probe design and optimization and (b) automated inspection, (iii) proper (great) accuracy because of the ill-posedness of the inverse problem. As matter of fact, there are very few commercial examples of such custom numerical softwares.
In the past years we have developed advanced numerical models for a fast and efficient modelling of the Eddy Current Imaging of conductive materials, even in the presence of an anisotropy conductivity tensor. Recent numerical models concerns the inspection of ferromagnetic specimens where the magnetic constitutive relationship is hysteretic and the electrical conductivity is non vanishing. This class of materials has attracted considerable interest in application such as material characterization in steel industry, or material degradation in nuclear power plants.
