A Hybrid Particle Swarm Optimization and Genetic Algorithm for Model Updating of A Pier-Type Structure Using Experimental Modal Analysis
doi: 10.1007/s13344-020-0060-2
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Abstract: Conventional design of pier structures is based on the assumption of fully rigid joints. In practice, the real connections are semi-rigid that cause changes in dynamic characteristics. In this study, quality of the joints is investigated by considering changes in natural frequencies. For this purpose, numerical and experimental modal analyses are carried out on related physical model of a pier type structure. When numerical results are evaluated, natural frequencies generally do not match the expected experimental results. Uncertainties in different aspects of engineering problems are always a challenge for researchers. The numerical models which are constructed on the basis of highly idealized scheme may not be able to represent all of the physical aspects of the physical one. For this study, determination of percentage of semi-rigid joints is considered as an optimization problem based on the numerical and experimental frequencies. Probabilistic sensitivity analysis is also used to determine the search space. A new technique of optimization problem is solved by a combination of smart particle swarm optimization (PSO) and genetic algorithms, and a complicated and efficient system for model updating process is introduced. It is observed that the hybrid PSO-Genetic algorithm is applicable and appropriate in model updating process. It performs better than PSO algorithm, considering the good agreement between theoretical frequencies and experimental ones, before and after model updating.
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Figure 1. Experimental modal test: a) data acquisition system of the modal testing; b) fixing the accelerometers in considered joints.
Figure 2. (a) A sample of time series of recorded acceleration and (b) related coherence functions measured for the point in the vicinity of the shaker connection.
Figure 4. First and third mode shapes of the modal test gained by ME’scopeVES software (for the sake of clarity, only the outer columns have been considered).
Figure 6. Local directions of a space frame member (Weaver and Johnston, 1994).
Figure 7. Deformed semi rigid connection (Filho et al., 2004).
Figure 8. Variation of the first three natural frequencies for semi-rigidity in connection 3.
Figure 9. Variation of the first three natural frequencies for semi-rigidity in connection 5
Figure 10. Variation of the first four natural frequencies for simulation of semi rigid connection in all connections.
Figure 11. Coefficient of variations of predicted rigidity of connection in optimization process.
Figure 12. Coefficient of variations of first twelve frequencies gained by optimization process.
Figure 13. Objective function chart convergences for the HPSOGA and PSO algorithms versus iterations (scenario 8 of MCS).
Table 1. Physical and geometrical specifications of the empirical model
Piles specifications Deck specifications Parameter Value Parameter Value Length 400 mm Length 600 mm External diameter 400 mm External diameter 400 mm Thickness 10 mm Thickness 5 mm Mass density 7850 kg/m3 Mass density 7850 kg/m3 Poisson ratio 0.3 Poisson ratio 0.3 Young modulus 200 GPa Young modulus 200 GPa 
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Table 2. Coordinate of accelerometers joint and the stimulation points
Nodes SL1 SL4 SP1 SP2 F1 Locations (cm) (0, 5, 0) (0, 20, 0) (5, 20, 0) (30, 20, 5) (15, 5, 5)
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Table 3. Natural frequencies of the experimental model
Mode 1 2 3 4 5 Experimental frequency (Hz) 173 179.3 223.42 570.8 575.31
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Table 4. Initial natural frequencies from numerical modal analysis
Mode 1 2 3 4 5 Numerical frequency (Hz) 174.22 175.11 218.36 574.6 583.9
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Table 5. Best parameters for HPSO and basic PSO for model updating
Method Parameters Population/particle size Iteration C1 C2 w Pm Pc Basic PSO 50 140 2.1 1.9 0.7 − − HPSOGA 40 140 2.1 1.9 0.7 0.05 0.1
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Table 6. Rigidity percentages and springs stiffness calculated by optimization process
Method Connection number 1 2 3 4 5 6 7 8 9 PSO Ri (N·m/rad) 1.20×106 1.81×106 2.79×106 1.52×106 1.83×106 1.32×106 1.37×106 1.50×106 2.28×106 Pi (%) 87.3 91.2 94.1 89.7 91.3 88.3 88.7 89.6 92.9 PSO-GA Ri (N·m/rad) 1.27×106 1.77×106 1.27×106 1.59×106 2.06×106 1.54×106 1.34×106 1.57×106 2.36×106 Pi (%) 87.9 91.01 87.8 90.01 92.2 89.8 88.5 90 93.1
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Table 7. First five experimental and updated numerical frequencies
Frequency number f1 f2 f3 f4 f5 Experimental frequencies(Hz) 173 179.3 223.42 570.8 575.31 PSO Updated 173.2 180.93 220.68 569.86 571.45 Difference (%) 0.11 0.9 −1.22 −0.16 −0.67 HPSOGA Updated 173.15 180.23 219.87 571.2 572.60 Difference (%) 0.09 0.51 −1.58 0.08 −0.47
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