Issue 28

B. Ye et alii, Frattura ed Integrità Strutturale, 28 (2014) 32-41; DOI: 10.3221/IGF-ESIS.28.04 36 The computation of FEM equations (step F) The step A to step E above is the solution procedure of the Ritz law finite element analysis for theEC detection forward problem. From the method, we can obtain the approximate solution of the vector [ A ] and then the probe impedance changes. Themulti-turn coil, if its density is n c and cross-section is dispersed to K unit element, the impedance of coil is: 2 1 1 2 2 A A K K c ck k ck ck k ck k k j n j J Z r r I I             (9) where, Δ k is triangular element area of the coil interface, r ck is distance from the element centroid to symmetric axis, A ck is the A at centroid, and J = n c I is current density of coil. In thisway, on the basis ofmagnetic vector potential of eachnode, we can compute the impedance changes of probe. I NVERSEPROBLEMAND IMPROVEDANTCOLONYALGORITHM uring the last decades, some optimization algorithms, such as artificial neural network, genetic algorithm and artificial immune algorithm, have been successfully applied to solve complex optimizationproblems inECNDT. Ant colony algorithm is another heuristic search algorithm succeeding artificial neural network, genetic algorithm and artificial immune algorithm. It is a bionic natural optimization algorithm based on research of foraging behaviors of a real ant colony. It has characteristics of probability seeking and adopts the catalytic mechanism of parallelism and positive feedback. Ant colony algorithm has strong robustness and an excellent distributed computing mechanism. It is easy to combine with artificial neural networks, genetic algorithm, artificial immune algorithm and particle swarm optimization algorithm. However, when solving the continuous domain optimization problems, Ant colony algorithm has the disadvantages of slow convergence and is time consuming in the process of evolution [13, 14]. This paper presents an improved ant colony algorithm (IACA) and proposes the use of IACA to quantitative estimate defect size from EC inspection signals. The IACA has more global search capability and robustness, and ease of implementation. Inorder to use IACA, the first step is object discretization as shown inFigure 4. Every vertical line represents a parameter variable. All vertical lines are divided intoN equal divisions. The discretization nodes represent the specific values of the parameter variable. Ants walk from the node “start” and pass through the node of every parameter variable. After reaching the node “end”, the IACA completes one cycle and gets a combinationof values of all parameter variables. Assuming ( r , i ) is the ithnode of parameter r, x r , j is the value of ( r , i ). ( r +1, j ) is the j th node of parameter r+1. [( r , 1) , ( r + 1) , j ] represents the line connecting node ( r , i ) and node ( r + 1, j ). The amount of ants is m . In the process of evolution, ant k ( k =1,2,…, m ) selects thewalk direction according to the pheromone of each path. At time t , the probability of ant k fromposition ( r , i ) toposition( r + 1, j ) is 1 1 1 0 [( , ),( , )] [( , ),( , )] argmax {[ ( )] [ ( )] } otherwise r j M r i r j r i r j t t q q s S               (10) where, M r +1 is the allowable range of the r + 1th parameter, 1 [( , ),( , )] ( ) r i r j t   is the intensity of pheromone trace on path [( r , i ), ( r + 1), j ] at time t . Initially, the intensity of pheromone of each path is equal. 1 0 [( , ),( , )] ( ) r i r j C    , C is constant. 1 [( , ),( , )] ( ) r i r j t   is visibility of pheromone trace onpath [( r , i ) , ( r + 1) , j ]. It’s is 1 1 1 1 1 [( , ),( , )] min ( ) ( , ) ( ) r i r j t J r j J r        (11) where, J ( r + 1, j ) is the heuristic function value of different node, J min ( r +1) is theminimum of J ( r + 1, j ) in j  M r +1 .When the ant selects the path, α is the important degree index of the intensity of pheromone trace, while β is the important degree index of the visibility of pheromone trace. α ≥0, β ≥ 0. q is random number, q  [0, 1 ]. q 0 is a parameter, 0≤ q 0 ≤1. S is the next node selected according to the probability shown inEq.12. D