An Investigation of Particle Swarm Optimization Topologies in Structural Damage Detection
Abstract
:1. Introduction
2. Structural Damage Detection
2.1. Problem Formulation
2.2. Fitness Function
3. Particle Swarm Optimization
3.1. Basic Model
- (1)
- Initialize the position and velocity of the particles.
- (2)
- Calculate the fitness value using Equation (7).
- (3)
- For each particle , compare its fitness value with the local best location that it has experienced. If , update it as the current personal best position.
- (4)
- For each particle , compare its personal best fitness value with the global best fitness value . If , update it as the current global best position.
- (5)
- (6)
- If the algorithm reaches the maximum number of iterations or the minimum value of the fitness function, stop the algorithm, and output the result; if not, go to step (2).
3.2. PSO Topologies
4. Numerical Simulations for SDD of the Cantilever Beam
- Initialization: the positions of the initial population are randomly created in the search space, and the initial velocities of the population are set to zero to prevent the swarm explosion at the beginning of the algorithm [26].
- , , , N, and : the population size N is set to 100 and the maximum number of iterations is ; the inertia weight is linearly decreasing with the number of iterations from to ; the time-varying acceleration coefficient strategy for and is formulated as [12]:
- Calculation accuracy: in view of the limitation of measurement accuracy in the experiment, the calculation accuracy of the algorithm adopts 1 × 10.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Young Modulus E (Pa) | Poisson Ratio ν | Density ρ (Kg·m−3) | Width w (m) | Thickness d (m) |
---|---|---|---|---|
N/m | 0.33 | 7850 | m | m |
Damage Scenarios | Types | Elements | Severity |
---|---|---|---|
1 | I | 8 (Front) | 20% |
2 | 15 (Middle) | 30% | |
3 | 25 (End) | 50% | |
4 | II | 5, 6 (Neighbor) | 10%, 10% |
5 | 13, 18 (Symmetrical) | 20%, 50% | |
6 | 15, 25 | 20%, 30% | |
7 | III | 5, 6, 25 | 30%, 30%, 20% |
8 | 10, 16, 22 | 30%, 30%, 30% | |
9 | 15, 19, 20 | 10%, 10%, 10% |
Types | Damage Scenarios | Global | Local | Von Neumann | Wheel | Four Clusters | Clan Global | Clan Local | Multi-Ring |
---|---|---|---|---|---|---|---|---|---|
I | 1 | 0.98 | 1 | 1 | 0.96 | 1 | 1 | 1 | 1 |
2 | 0.7 | 0.96 | 0.98 | 0.54 | 0.93 | 0.93 | 0.93 | 0.99 | |
3 | 0.79 | 1 | 1 | 0.80 | 1 | 0.97 | 0.97 | 1 | |
II | 4 | 0.92 | 1 | 1 | 0.76 | 1 | 0.98 | 0.98 | 1 |
5 | 0.88 | 1 | 1 | 0.8 | 0.99 | 0.97 | 0.96 | 1 | |
6 | 0.38 | 0.86 | 0.73 | 0.23 | 0.7 | 0.56 | 0.55 | 0.74 | |
III | 7 | 0.42 | 0.62 | 0.71 | 0.28 | 0.6 | 0.47 | 0.5 | 0.71 |
8 | 0.24 | 0.38 | 0.28 | 0.23 | 0.36 | 0.23 | 0.27 | 0.32 | |
9 | 0.29 | 0.55 | 0.47 | 0.15 | 0.38 | 0.35 | 0.31 | 0.47 |
Types | Damage Scenarios | Global | Local | Von Neumann | Wheel | Four Clusters | Clan Global | Clan Local | Multi-Ring |
---|---|---|---|---|---|---|---|---|---|
I | 1 | 44.4796 | 89.72 | 66.33 | 69.1771 | 45.8 | 39.15 | 40.04 | 67.03 |
2 | 55.0857 | 97.7917 | 77.4592 | 85.6481 | 57.1828 | 51.5484 | 49.4839 | 80.2727 | |
3 | 46.5443 | 91.28 | 65.12 | 74.0625 | 47.65 | 40.4639 | 42.7320 | 68.28 | |
II | 4 | 77.3913 | 124.49 | 99.42 | 104.0395 | 80.15 | 67.9796 | 70.2551 | 104.41 |
5 | 81.1136 | 141.02 | 110.97 | 113.6750 | 88.8081 | 81.0103 | 79.5938 | 117.1100 | |
6 | 86.2895 | 137.9419 | 111.3151 | 106.7826 | 93.9 | 88.0714 | 84.9818 | 117.7027 | |
III | 7 | 97.6667 | 166.6452 | 131.6901 | 120.2857 | 106.5833 | 94.4468 | 98.48 | 140.2254 |
8 | 102.375 | 169.2368 | 147.5714 | 127.6087 | 113.3611 | 105.4783 | 112.7037 | 153.3438 | |
9 | 93.1034 | 166.0727 | 132.4043 | 132.3333 | 111.3684 | 97.2857 | 115.6774 | 137.3617 |
Damage Type | Global | Local | Von Neuman | Wheel | Four Cluster | Clan Global | Clan Local | Multi-Ring |
---|---|---|---|---|---|---|---|---|
I | 7.3333 | 3 | 2.6667 | 7.6667 | 3.6667 | 4.6667 | 4.6667 | 2.3333 |
II | 7 | 1.8333 | 2.5 | 8 | 3.5 | 5.1667 | 5.8333 | 2.1667 |
III | 6.6667 | 1.6667 | 2.6667 | 7.8333 | 3.3333 | 6.1667 | 5.3333 | 2.3333 |
Overall | 7 | 2.1667 | 2.6111 | 7.8333 | 3.5 | 5.3333 | 5.2778 | 2.2778 |
Damage Type | Local | Von Neuman | Four Cluster | Multi-Ring |
---|---|---|---|---|
I | 4 | 2 | 1 | 3 |
II | 4 | 2 | 1 | 3 |
III | 4 | 2 | 1 | 3 |
Overall | 4 | 2 | 1 | 3 |
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Li, X.-L.; Serra, R.; Olivier, J. An Investigation of Particle Swarm Optimization Topologies in Structural Damage Detection. Appl. Sci. 2021, 11, 5144. https://doi.org/10.3390/app11115144
Li X-L, Serra R, Olivier J. An Investigation of Particle Swarm Optimization Topologies in Structural Damage Detection. Applied Sciences. 2021; 11(11):5144. https://doi.org/10.3390/app11115144
Chicago/Turabian StyleLi, Xiao-Lin, Roger Serra, and Julien Olivier. 2021. "An Investigation of Particle Swarm Optimization Topologies in Structural Damage Detection" Applied Sciences 11, no. 11: 5144. https://doi.org/10.3390/app11115144