PSI - Issue 39

Nabam Teyi et al. / Procedia Structural Integrity 39 (2022) 608–623 Author name / Structural Integrity Procedia 00 (2019) 000–000

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the vibration characteristics of a broken cantilever beam with varying crack locations and depths. The diagnostic indices (natural frequencies, mode shapes) of the beam structure were determined using numerical and finite element methods. Through the implementation of an intelligent GA-based controller, the procedure for recognizing defects was automated. To acquire the optimal solution from the search space, a single point crossover and mutation technique was used. The created controller’s findings established that the system was capable of not only detecting cracks but also forecasting their locations and severity. Algorithms that follow laws of evolution are called EAs. GA is one class of EA that uses crossover; along with mutation as GA operators. Second, is evolutionary programming that uses only mutation as its operator. CEAs developed by Furukawa and Yagawa (1997) are a class of evolutionary algorithms that are optimised for continuous search spaces. CEAs’ reproductive operations are intended to be comparable to Gas’, as they make advantage of GAs' probabilistic properties. The primary distinction between CEAs and GAs is that the individual representation is provided by a search point, i.e. a true continuous vector. 4.4. Particle Swarm Optimization PSO is a population-based optimization technique inspired by the motions of bird flocks and schooling fish. The swarm selects the most advantageous options. It is a computer approach for optimizing a problem by iteratively enhancing a proposed solution (Fig. 9.). Based on a basic mathematical formula over the particle’s position and velocity, PSO moves a population of potential solutions around in the search space. Each particle’s mobility is governed by the known positions of the search-best space in addition to its local best known position. PSO although is similar to GA, crossover and mutation are two evolution operators that are missing. The system starts with a random population of solutions and iterates through generations until the best one emerges.

Fig. 9. PSO representation. Khatir et al. (2017) presented a non-destructive method for estimating the location and depth of a crack in beam like structures based on an inverse vibration issue. For damaged and undamaged beams, PSO–FEM was used. The change in the structure’s inherent frequencies caused by a crack was used as an objective function. They performed numerical examination of a cantilever beam and a 2-D frame structure. Jena et al. (2015) used a fuzzy adaptive PSO (APSO) to analytically determine local flexibility matrix of a single transverse open edge crack on a beam construction. The improved PSO reduced inertia weight nonlinearly from large to small. APSO added a dynamically variable inertia weight based on population fitness variance. The APSO algorithm’s integrity was confirmed both numerically and experimentally. Mohan et al. (2013) and Mohan et al. (2014) developed PSO algorithm using the FRF as an input response to locate and quantify cracks on simple cantilever beams and plane frame structures. The algorithm’s efficiency was tested for low level damage and noise detection. PSO outperformed GA in predicting damages due to its quick convergence, consistency and excellent local search capability. PSO with FRF was more accurate than PSO with frequencies. PSO using FRF reduced unnecessary false damage prediction compared to GA. 4.5. Continuous Wavelet Transform/ Discrete Wavelet Transform The Fourier Transform is used to breakdown a picture into sine and cosine components. The result of the transformation represents the image in the Fourier or frequency domain, whilst the input image represents the spatial domain counterpart. The Fourier Transform has the disadvantage of capturing global frequency information, which refers to frequencies that are present throughout a signal. Another alternative is the WT, which decomposes a function