Reconstruction of impact load on structures with limited measurements using dynamic hybrid adaptive differential search algorithm

Figures & data

Figure 1. General impact load.

Figure 2. Nelder-Mead algorithm.

Figure 3. The hybrid adaptive differential search algorithm (HADSA).

Figure 4. Dynamic hybrid adaptive differential search algorithm (DHADSA).

Figure 5. Simply supported plate with a midpoint loading.

Table 1. Properties of Lamina [22].

Youngs modulus,	Youngs modulus,	Shear modulus,	Poisson's ratio	Mass density
E1	E2	G12	ν	ρ
142 GPa	10.8 GPa	5.49 GPa	0.30	1600 kg/m^3

Figure 6. Identified and True Impact loading on a simply supported plate using DHADSA.

Figure 7. X-coordinate convergence plot for simply supported plate.

Figure 8. Y-coordinate convergence plot for simply supported plate.

Figure 9. Loading amplitude convergence plot for simply supported plate-DHADS algorithm.

Figure 10. Loading frequency convergence plot for simply supported plate-DHADS algorithm.

Figure 11. Unloading frequency convergence plot for simply supported plate-DHADS algorithm.

Figure 12. Convergence studies of various DSA implementations.

Figure 13. Percentage error in the reconstruction of impact load on a simply supported composite plate using DHADS algorithm.

Figure 14. Simply supported beam girder of span 10 m.

Figure 15. True and identified impact loading on simply supported beam.

Figure 16. Convergence plot related to the spatial location of the impact load-simply supported beam.

Figure 17. Convergence plot of impact load amplitude – simply supported beam.

Figure 18. Loading frequency convergence plot for simply supported beam.

Figure 19. Unloading frequency convergence plot for simply supported beam.

Figure 20. Convergence characteristics of the various differential search implementations- Simply supported beam.

Figure 21. Percentage error in the reconstruction of impact load on simply supported beam using DHADS algorithm.

Figure 22. Percentage average error in the reconstruction of the three impact loads on a simply supported beam using the proposed DHADS algorithm.

Figure 23. Identified and True Impact loading on the unknown system.

Figure 24. Convergence characteristics of the proposed DHADS algorithm.

Table 2. True and converged stiffness parameters of the simply supported beam using DHADS algorithm with constrained optimization formulations.

Element no.	1	2	3	4	5	6	7	8	9	10
True stiffness parameter	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Estimated stiffness parameter	1.0152	0.9638	0.9946	1.0273	0.9794	1.0167	0.9944	0.9946	0.9989	1.0442
Element no.	11	12	13	14	15	16	17	18	19	20
True stiffness parameter	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Estimated stiffness parameter	0.9869	1.0331	0.9927	1.0312	0.9941	0.9965	0.9889	0.9901	0.9994	0.9976

Figure 25. Error in the identification of stiffness parameters of the simply supported beam and with varied noise values using the variants of differential search implementations using constrained optimization formulations.

Figure 26. Error in the identification of stiffness parameters of the simply supported beam and with varied noise values using the variants of differential search implementations using unconstrained optimization formulations.

Figure 27. Error in the reconstruction of impact load on simply supported beam using with varied noise values using the variants of differential search implementations with simultaneous identification of system parameters using limited instrumentation using constrained and unconstrained optimization formulations.

Hu N, Fukunaga H, Matsumoto S, et al. An efficient approach for identifying impact force using embedded piezoelectric sensors. Int J Impact Eng. 2007;34(7):1258–1271.

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