Fig. 1. Schematic diagram of chaos algorithm
Fig. 2. Waveform decomposition flowchart combined with MDE algorithm
Fig. 3. The first set of waveform fitting results (a) non-optimization, (b) LM optimization based on GGM, (c) L-BFGS optimization based on GGM, (d) DE optimization based on GGM, (e) MDE optimization based on GM, (f) MDE optimization based on GGM
Fig. 4. The second set of waveform fitting result (a) non-optimization, (b) LM optimization based on GGM, (c) L-BFGS optimization based on GGM, (d) DE optimization based on GGM, (e) MDE optimization based on GM, (f) MDE optimization based on GGM
Fig. 5. The third set of waveform fitting results (a) non-optimization, (b) LM optimization based on GGM, (c) L-BFGS optimization based on GGM, (d) DE optimization based on GGM, (e) MDE optimization based on GM, (f) MDE optimization based on GGM
Fig. 6. Study area
Fig. 7. Point cloud of waveform decomposition
Fig. 8. Comparison of system and decomposed point cloud (a) system point cloud(red) and decomposed point cloud(white), (b) new point cloud after decomposition
Fig. 9. Point cloud of flat roof (a)system, (b) LM, (c) L-BFGS, (d) DE, (e) MDE
Fig. 10. Point cloud of gabled roof (a)system, (b) LM, (c) L-BFGS, (d) DE, (e) MDE
优化算法 | 不优化 | LM | L-BFGS | GA | PSO | DE | MDE |
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误差 | 160.462 1 | 68.968 5 | 66.076 1 | 101.773 6 | 98.054 9 | 65.562 5 | 59.867 1 | 时间/s | 0.857 2 | 319.355 6 | 129.689 0 | 320.503 0 | 265.888 0 | 237.773 0 | 293.809 0 |
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Table 1. Fitting accuracy and running time of different optimization algorithms
| 系统 | LM | L-BFGS | DE | MDE |
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平顶/cm | 6.668 9 | 8.779 3 | 7.261 2 | 6.874 2 | 6.627 1 | 人字形屋顶/cm | 8.855 1 | 9.582 0 | 8.682 9 | 8.352 6 | 8.531 1 |
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Table 2. Roof fitting error of each algorithm