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Acta Optica Sinica, Volume. 40, Issue 11, 1122001(2020)

Application of Particle Swarm Annealing Optimization BVMD Method in Spatial Frequency Decomposition of Ultra-Precision Machined Surfaces

Weixiang Gao1,2, Xingzhan Li1、*, Hualin Zheng2, and Teng Hu2
Author Affiliations
  • 1Institute of Machinery Manufacturing Technology, China Academy of Engineering Physics, Mianyang, Sichuan 621900, China
  • 2College of Mechanical and Electrical Engineering, Southwest Petroleum University, Chengdu, Sichuan 610500, China
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    AbstractGet PDF(in Chinese)
    Figures&Tables (19)
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    References (28)
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    Figures & Tables(19)
    Flow chart of proposed method

    Fig. 1. Flow chart of proposed method

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    Quadrant inversion extension

    Fig. 2. Quadrant inversion extension

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    Step by step mirror extension

    Fig. 3. Step by step mirror extension

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    Flow chart of particle swarm annealing algorithm

    Fig. 4. Flow chart of particle swarm annealing algorithm

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    Three-dimensional image and one-dimensional PSD analysis of original morphology. (a) Original 3D shape; (b) PSD of original 3D shape

    Fig. 5. Three-dimensional image and one-dimensional PSD analysis of original morphology. (a) Original 3D shape; (b) PSD of original 3D shape

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    Extended 3D shape

    Fig. 6. Extended 3D shape

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    Processing results by 2D 1--4 Hanning windows. (a) 1-order; (b) 2-order; (c) 3-order; (d) 4-order

    Fig. 7. Processing results by 2D 1--4 Hanning windows. (a) 1-order; (b) 2-order; (c) 3-order; (d) 4-order

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    Amplitude frequency responses of 1--4 Hanning windows. (a) 1-order; (b) 2-order; (c) 3-order; (d) 4-order

    Fig. 8. Amplitude frequency responses of 1--4 Hanning windows. (a) 1-order; (b) 2-order; (c) 3-order; (d) 4-order

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    Optimization results of particle swarm annealing parameters. (a) Fitness; (b) decomposition level K; (c) penalty parameter α

    Fig. 9. Optimization results of particle swarm annealing parameters. (a) Fitness; (b) decomposition level K; (c) penalty parameter α

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    Decomposition results of data 1 and the corresponding one-dimensional PSD. (a) IMF 1; (b) IMF 2; (c) IMF 3; (d) IMF 4; (e) PSD of IMF 1; (f) PSD of IMF 2; (g) PSD of IMF 3; (h) PSD of IMF 4

    Fig. 10. Decomposition results of data 1 and the corresponding one-dimensional PSD. (a) IMF 1; (b) IMF 2; (c) IMF 3; (d) IMF 4; (e) PSD of IMF 1; (f) PSD of IMF 2; (g) PSD of IMF 3; (h) PSD of IMF 4

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    Measured data 2 and 3D and PSD figures of its decomposition. (a) Shape of data 2; (b) PSD of data 2; (c) IMF 1; (d) IMF 2; (e) IMF 3; (f) IMF 4; (g) IMF 5; (h) PSD of IMF 1; (i) PSD of IMF 2; (j) PSD of IMF 3; (k) PSD of IMF 4; (l) PSD of IMF 5

    Fig. 11. Measured data 2 and 3D and PSD figures of its decomposition. (a) Shape of data 2; (b) PSD of data 2; (c) IMF 1; (d) IMF 2; (e) IMF 3; (f) IMF 4; (g) IMF 5; (h) PSD of IMF 1; (i) PSD of IMF 2; (j) PSD of IMF 3; (k) PSD of IMF 4; (l) PSD of IMF 5

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    Measured data 3 and 3D and PSD figures of its decomposition. (a) Shape of data 3; (b) PSD of data 3; (c) IMF 1; (d) IMF 2; (e) IMF 3; (f) IMF 4; (g) IMF 5; (h) PSD of IMF 1; (i) PSD of IMF 2; (j) PSD of IMF 3; (k) PSD of IMF 4; (l) PSD of IMF 5

    Fig. 12. Measured data 3 and 3D and PSD figures of its decomposition. (a) Shape of data 3; (b) PSD of data 3; (c) IMF 1; (d) IMF 2; (e) IMF 3; (f) IMF 4; (g) IMF 5; (h) PSD of IMF 1; (i) PSD of IMF 2; (j) PSD of IMF 3; (k) PSD of IMF 4; (l) PSD of IMF 5

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    BDWT decomposition results of data 1 and corresponding PSD figures. (a) IMF 1; (b) IMF 2; (c) IMF 3; (d) IMF 4; (e) IMF 5; (f) PSD of IMF 1; (g) PSD of IMF 2; (h) PSD of IMF 3; (i) PSD of IMF 4; (j) PSD of IMF 5

    Fig. 13. BDWT decomposition results of data 1 and corresponding PSD figures. (a) IMF 1; (b) IMF 2; (c) IMF 3; (d) IMF 4; (e) IMF 5; (f) PSD of IMF 1; (g) PSD of IMF 2; (h) PSD of IMF 3; (i) PSD of IMF 4; (j) PSD of IMF 5

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    BDWT decomposition results of data 1 and corresponding PSD figures. (a) IMF 1; (b) IMF 2; (c) IMF 3; (d) IMF 4; (e) IMF 5; (f) IMF 6; (g) PSD of IMF 1; (h) PSD of IMF 2; (i) PSD of IMF 3; (j) PSD of IMF 4; (k) PSD of IMF 5; (l) PSD of IMF 6

    Fig. 14. BDWT decomposition results of data 1 and corresponding PSD figures. (a) IMF 1; (b) IMF 2; (c) IMF 3; (d) IMF 4; (e) IMF 5; (f) IMF 6; (g) PSD of IMF 1; (h) PSD of IMF 2; (i) PSD of IMF 3; (j) PSD of IMF 4; (k) PSD of IMF 5; (l) PSD of IMF 6

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    • Table 1. Main spatial frequency errors of data 1 and its decompositionmm-1

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      Table 1. Main spatial frequency errors of data 1 and its decompositionmm-1

      DataFrequency 1Frequency 2Frequency 3Frequency 4Frequency 5Frequency 6
      Data 10.16311.95804.40406.36208.809011.7500
      Layer 10.1631
      Layer 21.9580
      Layer 34.4040
      Layer 46.36208.809011.7500

    • Table 2. Reconstruction errors of BVMD and FFT & IFFT errors for different pretreatments

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      Table 2. Reconstruction errors of BVMD and FFT & IFFT errors for different pretreatments

      ErrorInitial dataContinuation dataWindow function data
      Error of FFT and IFFT /10-30.41763330.40357200.3387472
      Reconstruction error of BVMD /10-32.61632002.67073100.3554301

    • Table 3. Main spatial frequency errors of data 2 and its decompositionmm-1

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      Table 3. Main spatial frequency errors of data 2 and its decompositionmm-1

      DataFrequency 1Frequency 2Frequency 3Frequency 4Frequency 5Frequency 6
      Data 20.028850.115400.519300.778901.067001.55800
      Layer 10.02885
      Layer 20.11540
      Layer 30.51930
      Layer 40.77890
      Layer 51.067001.55800

    • Table 4. Main spatial frequency errors of data 3 and its decompositionmm-1

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      Table 4. Main spatial frequency errors of data 3 and its decompositionmm-1

      DataFrequency 1Frequency 2Frequency 3Frequency 4Frequency 5Frequency 6
      Data 30.081560.407800.734101.468002.365003.01800
      Layer 10.08156
      Layer 20.40780
      Layer 30.73410
      Layer 40.73410
      Layer 51.468002.365003.01800

    • Table 5. KL divergence contrast10-3

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      Table 5. KL divergence contrast10-3

      Data No.BDWTBEMDProposed algorithm
      Data 135.975418.670966318.6478
      Data 242.5655452.69506284.9310
      Data 318.718665.978433208.7450
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    Weixiang Gao, Xingzhan Li, Hualin Zheng, Teng Hu. Application of Particle Swarm Annealing Optimization BVMD Method in Spatial Frequency Decomposition of Ultra-Precision Machined Surfaces[J]. Acta Optica Sinica, 2020, 40(11): 1122001

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    Paper Information

    Category: Optical Design and Fabrication

    Received: Jan. 2, 2020

    Accepted: Mar. 10, 2020

    Published Online: Jun. 10, 2020

    The Author Email: Li Xingzhan (li_xingzhan@126.com)

    DOI:10.3788/AOS202040.1122001

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology