A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network
Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and inte...
Ausführliche Beschreibung
Autor*in: |
Jianzhou Wang [verfasserIn] Chunying Wu [verfasserIn] Tong Niu [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2019 |
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Übergeordnetes Werk: |
In: Sustainability - MDPI AG, 2009, 11(2019), 2, p 526 |
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Übergeordnetes Werk: |
volume:11 ; year:2019 ; number:2, p 526 |
Links: |
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DOI / URN: |
10.3390/su11020526 |
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Katalog-ID: |
DOAJ018438091 |
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520 | |a Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. | ||
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10.3390/su11020526 doi (DE-627)DOAJ018438091 (DE-599)DOAJ4acbf34778d241edaf1006474d91cb08 DE-627 ger DE-627 rakwb eng TD194-195 TJ807-830 GE1-350 Jianzhou Wang verfasserin aut A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. wind speed forecasting echo state network forecasting accuracy, stability and practicality hybrid forecasting system interval prediction Environmental effects of industries and plants Renewable energy sources Environmental sciences Chunying Wu verfasserin aut Tong Niu verfasserin aut In Sustainability MDPI AG, 2009 11(2019), 2, p 526 (DE-627)610604120 (DE-600)2518383-7 20711050 nnns volume:11 year:2019 number:2, p 526 https://doi.org/10.3390/su11020526 kostenfrei https://doaj.org/article/4acbf34778d241edaf1006474d91cb08 kostenfrei http://www.mdpi.com/2071-1050/11/2/526 kostenfrei https://doaj.org/toc/2071-1050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4367 GBV_ILN_4700 AR 11 2019 2, p 526 |
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10.3390/su11020526 doi (DE-627)DOAJ018438091 (DE-599)DOAJ4acbf34778d241edaf1006474d91cb08 DE-627 ger DE-627 rakwb eng TD194-195 TJ807-830 GE1-350 Jianzhou Wang verfasserin aut A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. wind speed forecasting echo state network forecasting accuracy, stability and practicality hybrid forecasting system interval prediction Environmental effects of industries and plants Renewable energy sources Environmental sciences Chunying Wu verfasserin aut Tong Niu verfasserin aut In Sustainability MDPI AG, 2009 11(2019), 2, p 526 (DE-627)610604120 (DE-600)2518383-7 20711050 nnns volume:11 year:2019 number:2, p 526 https://doi.org/10.3390/su11020526 kostenfrei https://doaj.org/article/4acbf34778d241edaf1006474d91cb08 kostenfrei http://www.mdpi.com/2071-1050/11/2/526 kostenfrei https://doaj.org/toc/2071-1050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4367 GBV_ILN_4700 AR 11 2019 2, p 526 |
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10.3390/su11020526 doi (DE-627)DOAJ018438091 (DE-599)DOAJ4acbf34778d241edaf1006474d91cb08 DE-627 ger DE-627 rakwb eng TD194-195 TJ807-830 GE1-350 Jianzhou Wang verfasserin aut A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. wind speed forecasting echo state network forecasting accuracy, stability and practicality hybrid forecasting system interval prediction Environmental effects of industries and plants Renewable energy sources Environmental sciences Chunying Wu verfasserin aut Tong Niu verfasserin aut In Sustainability MDPI AG, 2009 11(2019), 2, p 526 (DE-627)610604120 (DE-600)2518383-7 20711050 nnns volume:11 year:2019 number:2, p 526 https://doi.org/10.3390/su11020526 kostenfrei https://doaj.org/article/4acbf34778d241edaf1006474d91cb08 kostenfrei http://www.mdpi.com/2071-1050/11/2/526 kostenfrei https://doaj.org/toc/2071-1050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4367 GBV_ILN_4700 AR 11 2019 2, p 526 |
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10.3390/su11020526 doi (DE-627)DOAJ018438091 (DE-599)DOAJ4acbf34778d241edaf1006474d91cb08 DE-627 ger DE-627 rakwb eng TD194-195 TJ807-830 GE1-350 Jianzhou Wang verfasserin aut A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. wind speed forecasting echo state network forecasting accuracy, stability and practicality hybrid forecasting system interval prediction Environmental effects of industries and plants Renewable energy sources Environmental sciences Chunying Wu verfasserin aut Tong Niu verfasserin aut In Sustainability MDPI AG, 2009 11(2019), 2, p 526 (DE-627)610604120 (DE-600)2518383-7 20711050 nnns volume:11 year:2019 number:2, p 526 https://doi.org/10.3390/su11020526 kostenfrei https://doaj.org/article/4acbf34778d241edaf1006474d91cb08 kostenfrei http://www.mdpi.com/2071-1050/11/2/526 kostenfrei https://doaj.org/toc/2071-1050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4367 GBV_ILN_4700 AR 11 2019 2, p 526 |
allfieldsSound |
10.3390/su11020526 doi (DE-627)DOAJ018438091 (DE-599)DOAJ4acbf34778d241edaf1006474d91cb08 DE-627 ger DE-627 rakwb eng TD194-195 TJ807-830 GE1-350 Jianzhou Wang verfasserin aut A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. wind speed forecasting echo state network forecasting accuracy, stability and practicality hybrid forecasting system interval prediction Environmental effects of industries and plants Renewable energy sources Environmental sciences Chunying Wu verfasserin aut Tong Niu verfasserin aut In Sustainability MDPI AG, 2009 11(2019), 2, p 526 (DE-627)610604120 (DE-600)2518383-7 20711050 nnns volume:11 year:2019 number:2, p 526 https://doi.org/10.3390/su11020526 kostenfrei https://doaj.org/article/4acbf34778d241edaf1006474d91cb08 kostenfrei http://www.mdpi.com/2071-1050/11/2/526 kostenfrei https://doaj.org/toc/2071-1050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4367 GBV_ILN_4700 AR 11 2019 2, p 526 |
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Jianzhou Wang misc TD194-195 misc TJ807-830 misc GE1-350 misc wind speed forecasting misc echo state network misc forecasting accuracy, stability and practicality misc hybrid forecasting system misc interval prediction misc Environmental effects of industries and plants misc Renewable energy sources misc Environmental sciences A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network |
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TD194-195 TJ807-830 GE1-350 A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network wind speed forecasting echo state network forecasting accuracy, stability and practicality hybrid forecasting system interval prediction |
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A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network |
abstract |
Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. |
abstractGer |
Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. |
abstract_unstemmed |
Given the rapid development and wide application of wind energy, reliable and stable wind speed forecasting is of great significance in keeping the stability and security of wind power systems. However, accurate wind speed forecasting remains a great challenge due to its inherent randomness and intermittency. Most previous researches merely devote to improving the forecasting accuracy or stability while ignoring the equal significance of improving the two aspects in application. Therefore, this paper proposes a novel hybrid forecasting system containing the modules of a modified data preprocessing, multi-objective optimization, forecasting, and evaluation to achieve the wind speed forecasting with high precision and stability. The modified data preprocessing method can obtain a smoother input by decomposing and reconstructing the original wind speed series in the module of data preprocessing. Further, echo state network optimized by a multi-objective optimization algorithm is developed as a predictor in the forecasting module. Finally, eight datasets with different features are used to validate the performance of the proposed system using the evaluation module. The mean absolute percentage errors of the proposed system are 3.1490%, 3.0051%, 3.0618%, and 2.6180% in spring, summer, autumn, and winter, respectively. Moreover, the interval prediction is complemented to quantitatively characterize the uncertainty as developing intervals, and the mean average width is below 0.2 at the 95% confidence level. The results demonstrate the proposed forecasting system outperforms other comparative models considered from the forecasting accuracy and stability, which has great potential in the application of wind power systems. |
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score |
7.400511 |