Stiffness identification and damage localization via differential evolution algorithms

Abstract

The goal of structural health monitoring is to identify which discrepancies between the actual behaviour of a structure and its reference undamaged state are indicative of damage. For this purpose, an objective function, which minimizes the difference between the measured and theoretical modal characteristics of the structure, is formulated. By selecting the stiffness parameters as optimization variables, a differential evolution algorithm is applied to create successive generations that better reflect the measured response, until a certain tolerance is met. At each step of the algorithm, the current modal parameters are recalculated from the new generation of stiffness matrices to estimate the value of the objective function. This procedure represents a favourable path to solve the so-called 'inverse problem'. Furthermore, the comparison of the identified stiffness matrix with the initial one allows for damage detection and localization. A numerical example, where a generic structure is discretized into finite elements, is provided.

On the application of modified cuckoo optimization algorithm to the crack detection problem of cantilever Euler–Bernoulli beam

“…Hence, in order to consider the natural frequencies of the lower modes involved in the cost function, weight coefficients, w i , are added to the cost function. w i is assumed 1 i in this study [25]. To solve the optimization problem defined above, the parameters depth (d c ) and location of crack (l c ) are defined in a range as follows: Table 1 The first four bending natural frequencies of an intact cantilever beam.…”

Damage detection on a three-storey steel frame using artificial neural networks and genetic algorithms

“…Crossover and mutation represent the two special features that make a genetic algorithm different from the traditional direct search methods and make it interesting for optimization and search problems. Being a robust search method, genetic algorithms have been extensively employed in civil engineering to cover several optimization problems starting from structural identification to damage detection and model updating [13][14][15][16][17][18][19][20][21]. Despite the increasing number of successful applications of GA based procedures in civil engineering, it must be anyway remembered that several limitations still exist.…”

“…The modal data, evaluated according to the output-only framework, are employed to build the objective functions to be used in the FE model updating process to assess the imposed damage. Many researchers have shown, in last decades, the efficiency of artificial intelligence algorithms such as the genetic algorithms (GA) in minimization problems [13][14][15]. Being the GA robust global optimization techniques, they have been successfully applied to solve a large class of structural problems in the engineering field.…”

Component mode synthesis techniques for finite element model updating

“…Stochastic optimization algorithms (e.g. [46][47][48]) are convenient tools for estimating the global optimum, avoiding premature convergence to a local one. These non-gradient based stochastic optimization algorithms require a significantly larger number of FE model re-analyses to be performed compared to the FE model analyses involved in gradient-based optimization algorithms, substantially increasing the computational demands.…”