The aim of this paper is to develop a novel method to determine the severity of a damage in a thin plate. This paper presents a novel fault detection and diagnosis approach employing a new electromagnetic acoustic transducer, called EMAT, together with a complex signal processing method. The method consists in the recognition of a fault that exists within the structure, the fault location, i.e. the identification of the geometric position of damage, and the determining the significance of the damage, which indicates the importance or severity of the defect. The main scientific novelties presented in this paper is: to develop of a new type of electromagnetic acoustic transducer; to incorporate wavelet transforms for signal representation enhancements; to investigate multi-parametric analysis for noise identification and defect classification; to study attenuation curves properties for defect localization improvement; flaw sizing and location algorithm development.

We go to a nutritionist and she recommends that our diet contains not less than 150 calories, not more than 10g of protein, not less than 10g of carbohydrates and not less than 8g of fat. Also, we decide that our diet should have minimal cost. In addition we conclude that our diet should include at least 0.5g of fish and not more than 1 cups of milk. Again this is an allocation of recourses problem where we want the optimal diet at minimum cost. We have six unknown variables that define weight of the food. There is a lower bound for Fish as 0.5 g. There is an upper bound for Milk as 1 cup. To model and solve this problem, we can use linear programming. Modern linear programming was the result of a research project undertaken by the US Department of Air Force under the title of Project SCOOP (Scientific Computation of Optimum Programs). As the number of fronts in the Second World War increased, it became more and more difficult to coordinate troop supplies effectively. Mathematicians looked for ways to use the new computers being developed to perform calculations quickly. One of the SCOOP team members, George Dantzig, developed the simplex algorithm for solving simultaneous linear programming problems. The simplex method has several advantageous properties: it is very efficient, allowing its use for solving problems with many variables; it uses methods from linear algebra, which are readily solvable.