Abstract
Complex engineering problems require simulations, which are computationally expensive in cases of inverse identification tasks since they commonly requires hundreds of thousands of simulations. This paper propose a method based on model reduction for crack size estimation, combining the proper orthogonal decomposition method with radial basis functions. The reduced model is validated by comparing the obtained boundary displacements with the corresponding results from a finite element model. This inverse procedure is formulated as the minimization of the difference between the measured and computed values of displacement at selected boundary nodes, called sensor points, using particle swarm optimization algorithm. Convex and a non-convex specimens have been considered for investigations of crack presence, and identification of its size, different crack sizes have been tested to demonstrate the efficiency of the proposed approach.
Highlights
Crack initiation and propagation is an omnipresent fact in all structures undergoing cyclic loads due to the fatigue phenomenon
The Particle Swarm Optimization (PSO) is a population based optimization method inspired from the behaviour of bird flocks that is characterized by distinct social and psychological principles
For the three levels of crack sizes, the maximum error value is found in the smallest crack (0.35mm), with a difference between the estimated and real crack equal to 0.02 mm, not the error is large because is calculated compared to a value which is near zero, the larger cracks (1.4 mm and 2.45 mm) have been identified with better precision, due their larger effect of the boundary displacement
Summary
Crack initiation and propagation is an omnipresent fact in all structures undergoing cyclic loads due to the fatigue phenomenon. To determine the boundary displacement field of a two dimensional elastic structure containing an unknown crack, RBF interpolation was used. This method can generate different sets of parameters, which were not included in the initial selection in the matrix P. Equation (7) can be expressed as an approximation of the snapshot u corresponding to a new parameter vector P : u(P) = Φ ⋅ a(P), This model will be referred as the trained POD-RBF network. It is capable of reproduce the unknown boundary displacement field of the structure that corresponds to any set of crack parameters P. The parameter c was chosen to be constant for all functions, and equal to the mean value of normalized parameters
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