Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network
Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estima...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kitayama, Satoshi [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
Sequential approximate optimization |
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| Anmerkung: |
© Springer-Verlag London Limited 2011 |
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| Übergeordnetes Werk: |
Enthalten in: The international journal of advanced manufacturing technology - Springer-Verlag, 1985, 61(2011), 9-12 vom: 24. Nov., Seite 1067-1083 |
|---|---|
| Übergeordnetes Werk: |
volume:61 ; year:2011 ; number:9-12 ; day:24 ; month:11 ; pages:1067-1083 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00170-011-3755-y |
|---|
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OLC2026042268 |
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| 520 | |a Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. | ||
| 650 | 4 | |a Sequential approximate optimization | |
| 650 | 4 | |a Radial basis function network | |
| 650 | 4 | |a Variable blank holder force trajectory | |
| 650 | 4 | |a Deep drawing | |
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| 700 | 1 | |a Yamazaki, Koetsu |4 aut | |
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10.1007/s00170-011-3755-y doi (DE-627)OLC2026042268 (DE-He213)s00170-011-3755-y-p DE-627 ger DE-627 rakwb eng 670 VZ Kitayama, Satoshi verfasserin aut Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. Sequential approximate optimization Radial basis function network Variable blank holder force trajectory Deep drawing Kita, Kenta aut Yamazaki, Koetsu aut Enthalten in The international journal of advanced manufacturing technology Springer-Verlag, 1985 61(2011), 9-12 vom: 24. Nov., Seite 1067-1083 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:61 year:2011 number:9-12 day:24 month:11 pages:1067-1083 https://doi.org/10.1007/s00170-011-3755-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_21 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2241 GBV_ILN_2333 GBV_ILN_4046 AR 61 2011 9-12 24 11 1067-1083 |
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10.1007/s00170-011-3755-y doi (DE-627)OLC2026042268 (DE-He213)s00170-011-3755-y-p DE-627 ger DE-627 rakwb eng 670 VZ Kitayama, Satoshi verfasserin aut Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. Sequential approximate optimization Radial basis function network Variable blank holder force trajectory Deep drawing Kita, Kenta aut Yamazaki, Koetsu aut Enthalten in The international journal of advanced manufacturing technology Springer-Verlag, 1985 61(2011), 9-12 vom: 24. Nov., Seite 1067-1083 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:61 year:2011 number:9-12 day:24 month:11 pages:1067-1083 https://doi.org/10.1007/s00170-011-3755-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_21 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2241 GBV_ILN_2333 GBV_ILN_4046 AR 61 2011 9-12 24 11 1067-1083 |
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10.1007/s00170-011-3755-y doi (DE-627)OLC2026042268 (DE-He213)s00170-011-3755-y-p DE-627 ger DE-627 rakwb eng 670 VZ Kitayama, Satoshi verfasserin aut Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. Sequential approximate optimization Radial basis function network Variable blank holder force trajectory Deep drawing Kita, Kenta aut Yamazaki, Koetsu aut Enthalten in The international journal of advanced manufacturing technology Springer-Verlag, 1985 61(2011), 9-12 vom: 24. Nov., Seite 1067-1083 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:61 year:2011 number:9-12 day:24 month:11 pages:1067-1083 https://doi.org/10.1007/s00170-011-3755-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_21 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2241 GBV_ILN_2333 GBV_ILN_4046 AR 61 2011 9-12 24 11 1067-1083 |
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10.1007/s00170-011-3755-y doi (DE-627)OLC2026042268 (DE-He213)s00170-011-3755-y-p DE-627 ger DE-627 rakwb eng 670 VZ Kitayama, Satoshi verfasserin aut Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. Sequential approximate optimization Radial basis function network Variable blank holder force trajectory Deep drawing Kita, Kenta aut Yamazaki, Koetsu aut Enthalten in The international journal of advanced manufacturing technology Springer-Verlag, 1985 61(2011), 9-12 vom: 24. Nov., Seite 1067-1083 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:61 year:2011 number:9-12 day:24 month:11 pages:1067-1083 https://doi.org/10.1007/s00170-011-3755-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_21 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2241 GBV_ILN_2333 GBV_ILN_4046 AR 61 2011 9-12 24 11 1067-1083 |
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10.1007/s00170-011-3755-y doi (DE-627)OLC2026042268 (DE-He213)s00170-011-3755-y-p DE-627 ger DE-627 rakwb eng 670 VZ Kitayama, Satoshi verfasserin aut Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London Limited 2011 Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. Sequential approximate optimization Radial basis function network Variable blank holder force trajectory Deep drawing Kita, Kenta aut Yamazaki, Koetsu aut Enthalten in The international journal of advanced manufacturing technology Springer-Verlag, 1985 61(2011), 9-12 vom: 24. Nov., Seite 1067-1083 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:61 year:2011 number:9-12 day:24 month:11 pages:1067-1083 https://doi.org/10.1007/s00170-011-3755-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_21 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2241 GBV_ILN_2333 GBV_ILN_4046 AR 61 2011 9-12 24 11 1067-1083 |
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Kitayama, Satoshi Kita, Kenta Yamazaki, Koetsu |
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Kitayama, Satoshi |
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10.1007/s00170-011-3755-y |
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670 |
| title_sort |
optimization of variable blank holder force trajectory by sequential approximate optimization with rbf network |
| title_auth |
Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network |
| abstract |
Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. © Springer-Verlag London Limited 2011 |
| abstractGer |
Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. © Springer-Verlag London Limited 2011 |
| abstract_unstemmed |
Abstract Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed. © Springer-Verlag London Limited 2011 |
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| title_short |
Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network |
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