Inverse method for detection and sizing of cracks in thin sections using a hybrid genetic algorithm based signal parametrisation

A hybrid-GA method, based on signal parameterization, has been reported here for the improved detection and sizing of surface cracks of small sizes/depths in thin sections. The method relies on parameterizing the composite reference from the defect into its individual components i.e., the crack tip diffracted echo and the corner trap echo and subsequently use the relative arrival time technique (RATT). The phased array ultrasonic technique was employed in the investigation. Both experimental and simulated signals were used in the study. It is shown through both simulations and experiments that the hybrid-GA is successful in parameterizing both non-overlapping and overlapping echoes encountered in thin sections. It is additionally shown that the hybrid-GA improves the signal to noise ratio and correct for under-sampling of data.     

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.