Improving neural networks for mechanism kinematic chain isomorphism identification

Neural networks

Combinatorial optimization

Authors

Gloria Gálan-Marín

Enrique Mérida-Casermeiro

Domingo López Rodríguez

Published

1 October 2007

Publication details

Neural Processing Letters vol 26 (2), 133-143

Links

Abstract

Detection of isomorphism among kinematic chains is essential in mechanical design, but difficult and computationally expensive. It has been shown that both traditional methods and previously presented neural networks still have a lot to be desired in aspects such as simplifying procedure of identification and adapting automatic computation. Therefore, a new algorithm based on a competitive Hopfield network is developed for automatic computation in the kinematic chain isomorphism problem. The neural approach provides directly interpretable solutions and does not demand tuning of parameters. We have tested the algorithm by solving problems reported in the recent mechanical literature. Simulation results show the effectiveness of the network that rapidly identifies isomorphic kinematic chains.

Citation

Please, cite this work as:

[GML07] G. Galan-Marin, E. Merida-Casermeiro, and D. Lopez-Rodriguez. “Improving neural networks for mechanism kinematic chain isomorphism identification”. In: Neural processing letters 26.2 (2007), pp. 133-143.

BibTeX

@article{galan2007improving,
     title={Improving neural networks for mechanism kinematic chain isomorphism identification},
     author={Galan-Marin, Gloria and Merida-Casermeiro, Enrique and Lopez-Rodriguez, Domingo},
     journal={Neural processing letters},
     volume={26},
     number={2},
     pages={133–143},
     year={2007},
     publisher={Springer}
}

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Citations
CrossRef - Citation Indexes: 9
Scopus - Citation Indexes: 20

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Mendeley - Readers: 7

Cites

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] M. S. Alam and M. Suhaib. “A distinct matrix representation of the planar kinematic chains and isomorphism recognition”. In: Journal of Mechanical Engineering and Sciences 13.4 (Dec. 2019), p. 5717–5734. ISSN: 2289-4659. DOI: 10.15282/jmes.13.4.2019.01.0457. URL: http://dx.doi.org/10.15282/jmes.13.4.2019.01.0457.

[2] K. Dewangan and P. Prajapati. “Detection of Isomorphism and Inversions of Kinematic Chains Using an Evolutionary Approach”. In: Recent Advances in Machines, Mechanisms, Materials and Design. Springer Nature Singapore, 2024, p. 105–132. ISBN: 9789819754236. DOI: 10.1007/978-981-97-5423-6_9. URL: http://dx.doi.org/10.1007/978-981-97-5423-6_9.

[3] K. Dong, D. Li, and X. Kong. “Representation of planar kinematic chains with multiple joints based on a modified graph and isomorphism identification”. In: Mechanism and Machine Theory 172 (Jun. 2022), p. 104793. ISSN: 0094-114X. DOI: 10.1016/j.mechmachtheory.2022.104793. URL: http://dx.doi.org/10.1016/j.mechmachtheory.2022.104793.

[4] G. Galán-Marín, D. López-Rodríguez, and E. Mérida-Casermeiro. “A New Multivalued Neural Network for Isomorphism Identification of Kinematic Chains”. In: Journal of Computing and Information Science in Engineering 10.1 (Mar. 2010). ISSN: 1944-7078. DOI: 10.1115/1.3330427. URL: http://dx.doi.org/10.1115/1.3330427.

[5] M. Z. Ge, J. Y. Xiang, and Y. K. Zhang. “Research on Kinematic Chain Isomorphism Identification Method Based on the Standardization Adjacent Matrix”. In: Applied Mechanics and Materials 43 (Dec. 2010), p. 514–518. ISSN: 1662-7482. DOI: 10.4028/www.scientific.net/amm.43.514. URL: http://dx.doi.org/10.4028/www.scientific.net/amm.43.514.

[6] A. Geigel. “Machine learning AI systems and the virtue of inventiveness”. In: AI and Ethics 3.2 (Aug. 2022), p. 637–645. ISSN: 2730-5961. DOI: 10.1007/s43681-022-00197-x. URL: http://dx.doi.org/10.1007/s43681-022-00197-x.

[7] L. He, F. Liu, L. Sun, et al. “Isomorphic identification for kinematic chains using variable high-order adjacency link values”. In: Journal of Mechanical Science and Technology 33.10 (Oct. 2019), p. 4899–4907. ISSN: 1976-3824. DOI: 10.1007/s12206-019-0930-9. URL: http://dx.doi.org/10.1007/s12206-019-0930-9.

[8] H. Liu, S. Shi, P. Yang, et al. “An Improved Genetic Algorithm Approach on Mechanism Kinematic Structure Enumeration with Intelligent Manufacturing”. In: Journal of Intelligent & Robotic Systems 89.3–4 (May. 2017), p. 343–350. ISSN: 1573-0409. DOI: 10.1007/s10846-017-0564-z. URL: http://dx.doi.org/10.1007/s10846-017-0564-z.

[9] M. K. LOHUMI, A. MOHAMMAD, and I. A. KHAN. “A computerized loop based approach for identification of isomorphism and type of mobility in planar kinematic chains”. In: Sadhana 40.2 (Mar. 2015), p. 335–350. ISSN: 0973-7677. DOI: 10.1007/s12046-015-0344-z. URL: http://dx.doi.org/10.1007/s12046-015-0344-z.

[10] D. López-Rodríguez and E. Mérida-Casermeiro. “Shortest Common Superstring Problem with Discrete Neural Networks”. In: Adaptive and Natural Computing Algorithms. Springer Berlin Heidelberg, 2009, p. 62–71. ISBN: 9783642049217. DOI: 10.1007/978-3-642-04921-7_7. URL: http://dx.doi.org/10.1007/978-3-642-04921-7_7.

[11] R. Luque, D. López-Rodríguez, E. Mérida-Casermeiro, et al. “Video Object Segmentation with Multivalued Neural Networks”. In: 2008 Eighth International Conference on Hybrid Intelligent Systems. IEEE, Sep. 2008, p. 613–618. DOI: 10.1109/his.2008.130. URL: http://dx.doi.org/10.1109/his.2008.130.

[12] W. SUN, J. KONG, and L. SUN. “The improved hamming number method to detect isomorphism for kinematic chain with multiple joints”. In: Journal of Advanced Mechanical Design, Systems, and Manufacturing 11.5 (2017), p. JAMDSM0061–JAMDSM0061. ISSN: 1881-3054. DOI: 10.1299/jamdsm.2017jamdsm0061. URL: http://dx.doi.org/10.1299/jamdsm.2017jamdsm0061.

[13] V. Venkata Kamesh, K. Mallikarjuna Rao, and A. Balaji Srinivasa Rao. “An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory”. In: Journal of Mechanical Design 139.12 (Oct. 2017). ISSN: 1528-9001. DOI: 10.1115/1.4037628. URL: http://dx.doi.org/10.1115/1.4037628.

[14] H. Wang, A. Long, L. Yu, et al. “An efficient approach of graph isomorphism identification using loop theory and hopfield neural networks”. In: Multimedia Tools and Applications 83.8 (Aug. 2023), p. 22545–22566. ISSN: 1573-7721. DOI: 10.1007/s11042-023-16410-w. URL: http://dx.doi.org/10.1007/s11042-023-16410-w.

[15] S. Wei, K. Jianyi, W. Xingdong, et al. “Description and Isomorphism Judgment of the Kinematic Chain with Multiple Joints Based on Link-link Adjacency Matrix”. In: Journal of Mechanical Engineering 56.3 (2020), p. 41. ISSN: 0577-6686. DOI: 10.3901/jme.2020.03.041. URL: http://dx.doi.org/10.3901/jme.2020.03.041.

[16] P. Yang. “A review on graph isomorphism identification of mechanism kinematic chain for intelligent and digital manufacturing”. In: International Journal of Materials and Structural Integrity 4.1 (2010), p. 99. ISSN: 1745-0063. DOI: 10.1504/ijmsi.2010.032496. URL: http://dx.doi.org/10.1504/ijmsi.2010.032496.

[17] P. Yang and K. Zeng. “A high-performance approach on mechanism isomorphism identification based on an adaptive hybrid genetic algorithm for digital intelligent manufacturing”. In: Engineering with Computers 25.4 (Jul. 2009), p. 397–403. ISSN: 1435-5663. DOI: 10.1007/s00366-009-0132-7. URL: http://dx.doi.org/10.1007/s00366-009-0132-7.

[18] P. Yang, K. Zeng, C. Li, et al. “An improved hybrid immune algorithm for mechanism kinematic chain isomorphism identification in intelligent design”. In: Soft Computing 19.1 (Feb. 2014), p. 217–223. ISSN: 1433-7479. DOI: 10.1007/s00500-014-1244-6. URL: http://dx.doi.org/10.1007/s00500-014-1244-6.

[19] W. Yang, H. Ding, and A. Kecskeméthy. “Structural synthesis towards intelligent design of plane mechanisms: Current status and future research trend”. In: Mechanism and Machine Theory 171 (May. 2022), p. 104715. ISSN: 0094-114X. DOI: 10.1016/j.mechmachtheory.2021.104715. URL: http://dx.doi.org/10.1016/j.mechmachtheory.2021.104715.

[20] H. Yi, J. Wang, Y. Hu, et al. “Mechanism isomorphism identification based on artificial fish swarm algorithm”. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 235.21 (Jan. 2021), p. 5421–5433. ISSN: 2041-2983. DOI: 10.1177/0954406220977560. URL: http://dx.doi.org/10.1177/0954406220977560.

[21] L. Yu, C. Cai, J. Zhang, et al. “A simple and efficient method for isomorphism identification of planar kinematic chains”. In: Soft Computing 25.21 (Sep. 2021), p. 13263–13276. ISSN: 1433-7479. DOI: 10.1007/s00500-021-06187-1. URL: http://dx.doi.org/10.1007/s00500-021-06187-1.

[22] L. Yu, H. Wang, and S. Zhou. “Graph isomorphism identification based on link-assortment adjacency matrix”. In: Sādhanā 47.3 (Jul. 2022). ISSN: 0973-7677. DOI: 10.1007/s12046-022-01918-y. URL: http://dx.doi.org/10.1007/s12046-022-01918-y.

[23] L. Yu, S. Zhou, and H. Wang. “Mechanism Isomorphism Identification Based on Decision Tree Algorithm and Hybrid Particle Swarm Optimization Algorithm”. In: Neural Processing Letters 56.6 (Nov. 2024). ISSN: 1573-773X. DOI: 10.1007/s11063-024-11711-z. URL: http://dx.doi.org/10.1007/s11063-024-11711-z.

[24] K. Zeng, X. Fan, M. Dong, et al. “A fast algorithm for kinematic chain isomorphism identification based on dividing and matching vertices”. In: Mechanism and Machine Theory 72 (Feb. 2014), p. 25–38. ISSN: 0094-114X. DOI: 10.1016/j.mechmachtheory.2013.09.011. URL: http://dx.doi.org/10.1016/j.mechmachtheory.2013.09.011.