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In order to take into account the uncertainties linked to the variables in the evaluation of the statistical properties of structural response, a reliability approach with probabilistic aspect was considered. This is called the Probabilistic Transformation Method (PTM). This method is readily applicable when the function between the input and the output of the system is explicit. However, the situation is much more involved when it is necessary to perform the evaluation of implicit function between the input and the output of the system through numerical models. In this work, we propose a technique that combines Finite Element Analysis (FEA) and Probabilistic Transformation Method (PTM) to evaluate the Probability Density Function (PDF) of response where the function between the input and the output of the system is implicit. This technique is based on the numerical simulations of the Finite Element Analysis (FEA) and the Probabilistic Transformation Method (PTM) using an interface between Finite Element software and Matlab. Some problems of structures are treated in order to prove the applicability of the proposed technique. Moreover, the obtained results are compared to those obtained by the reference method of Monte Carlo. A second aim of this work is to develop an algorithm of global optimization using the local method SQP, because of its effectiveness and its rapidity of convergence. For this reason, we have combined the method SQP with the Multi start method. This developed algorithm is tested on test functions comparing with other methods such as the method of Particle Swarm Optimization (PSO). In order to test the applicability of the proposed approach, a structure is optimized under reliability constraints.
Background: Phototherapy is the most commonly used modality in the treatment of vitiligo. Oral PUVA is the classical treatment and the NB-UVB is a recently introduced form excluding the shorter erythemogenic wavelengths. Aims: This study was designed to compare the effects of PUVA and NB-UVB clinically and immuno-pathologically in managing non segmental vitiligo. Patients/Methods: Thirty vitiligo patients were divided randomly into two groups and treated either by oral PUVA or by narrow band UVB for 4 months, and evaluation was done clinically and immuno-pathologically. Results: One patient in PUVA group (3.3%) failed to respond to therapy while 29 patients (93.3%) improved including all NB-UVB cases. Excellent repigmentation was achieved in 6.7% in PUVA group and 66.6% in NB-UVB group; good repigmentation was achieved in 60% in PUVA and 20% in NB-UVB while 26.7% in PUVA and 13.3% in NB-UVB showed mild repigmentation. The color matching was excellent in all NB-UVB patients. Recurrence and activation of vitiligo were demonstrated in some NB-UVB cases and were less in PUVA treated cases. Microscopic examination revealed persistence of dermal lympho-histiocytic infiltrate and the interface changes in biopsies from vitiliginous lesions treated with NB-UVB more than with PUVA. Conclusions: NB-UVB provides significant better results than oral PUVA in managing non-segmental vitiligo. Although NB-UVB therapy gives a rapid effect, yet the observation of