Solution of the direct and inverse problems in NDE: the MADEND project

The \u201cMADEND\u201d project (Methods and Applications of Non-Destructive Electromagnetic Diagnostics) has been a joint research project shared among a group of researchers belonging to some Italian universities, aiming to develop and improve tools of interest for Non Destructive Evaluation (NDE) via electromagnetic methods. The project received in 2001 a 2-years Italian Research Ministry grant, and terminated in 2003. This paper proposes to highlight some of the results achieved thanks to the complementary theoretical and experimental competencies developed by the various units forming the project team. Section 2 is dedicated to the direct problem resolution techniques. Some approaches will be discussed, belonging to two very different categories: a) model based (i.e. based on the underlying physics) numerical methods; b) Soft Computing methods, including also Artificial Intelligence methods (e.g. neuro-fuzzy systems). Section 3 is dedicated to the methods and algorithms for solving the inverse problem, presenting: a) a non-iterative imaging method for Electric Impedance Tomography (EIT), b) a method for ECT based on the \u201cTime of Flight\u201d concept and c) Statistical treatment of system parameters uncertainties in the measurement systems used in ECT. Finally Section 4 reports some technical applications which can benefit from the theoretical and experimental procedures; in addition, the benchmarks will be briefly described