Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows
The content of this paper shows the first outcomes of a supplementary method to simulate the behavior of a simple design formed by two rectangular leaflets under a pulsatile flow condition. These problems are commonly handled by using Fluid-Structure Interaction (FSI) simulations; however, one of it...
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| Format: | Article |
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MDPI AG
2020-11-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/10/22/8228 |
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| author | Carlos Duran-Hernandez Rene Ledesma-Alonso Gibran Etcheverry |
| author_facet | Carlos Duran-Hernandez Rene Ledesma-Alonso Gibran Etcheverry |
| author_sort | Carlos Duran-Hernandez |
| collection | DOAJ |
| description | The content of this paper shows the first outcomes of a supplementary method to simulate the behavior of a simple design formed by two rectangular leaflets under a pulsatile flow condition. These problems are commonly handled by using Fluid-Structure Interaction (FSI) simulations; however, one of its main limitations are the high computational cost required to conduct short time simulations and the vast number of parameter adjustments to simulate different scenarios. In order to overcome these disadvantages, we propose a system identification method with hereditary computation—AutoRegressive with eXogenous (ARX) input method—to train a model with FSI simulation outcomes and then use this model to simulate the outputs that are commonly measured from this kind of simulation, such as the pressure difference and the opening area of the leaflets. Numerical results of the presented methodology show that our model is able to follow the trend with significant agreement with the FSI results, with an average correlation coefficient <i>R</i> of <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>t</mi><mi>r</mi></mrow></msub><mo>=</mo><mn>90.14</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>t</mi><mi>r</mi></mrow></msub><mo>=</mo><mn>92.27</mn><mo>%</mo></mrow></semantics></math></inline-formula> in training; whereas for validation, the average <i>R</i> is <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>v</mi><mi>a</mi><mi>l</mi></mrow></msub><mo>=</mo><mn>93.31</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>v</mi><mi>a</mi><mi>l</mi></mrow></msub><mo>=</mo><mn>83.08</mn><mo>%</mo></mrow></semantics></math></inline-formula> for opening area and pressure difference, respectively. The system identification model is efficiently capable of estimating the outputs of the FSI approach; however, it is not intended to substitute FSI simulations, but to complement them when the requirement is to conduct many repetitions of the phenomena with similar conditions. |
| first_indexed | 2024-03-10T14:42:27Z |
| format | Article |
| id | doaj.art-e8136ba23d2f4a0491b510b9b774351f |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T14:42:27Z |
| publishDate | 2020-11-01 |
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| spelling | doaj.art-e8136ba23d2f4a0491b510b9b774351f2023-11-20T21:41:23ZengMDPI AGApplied Sciences2076-34172020-11-011022822810.3390/app10228228Using Autoregressive with Exogenous Input Models to Study Pulsatile FlowsCarlos Duran-Hernandez0Rene Ledesma-Alonso1Gibran Etcheverry2Department of Computing, Electronics and Mechatronics, Universidad de las Americas Puebla, San Andres Cholula, Puebla 72810, MexicoDepartment of Industrial and Mechanical Engineering, Universidad de las Americas Puebla, San Andres Cholula, Puebla 72810, MexicoDepartment of Computing, Electronics and Mechatronics, Universidad de las Americas Puebla, San Andres Cholula, Puebla 72810, MexicoThe content of this paper shows the first outcomes of a supplementary method to simulate the behavior of a simple design formed by two rectangular leaflets under a pulsatile flow condition. These problems are commonly handled by using Fluid-Structure Interaction (FSI) simulations; however, one of its main limitations are the high computational cost required to conduct short time simulations and the vast number of parameter adjustments to simulate different scenarios. In order to overcome these disadvantages, we propose a system identification method with hereditary computation—AutoRegressive with eXogenous (ARX) input method—to train a model with FSI simulation outcomes and then use this model to simulate the outputs that are commonly measured from this kind of simulation, such as the pressure difference and the opening area of the leaflets. Numerical results of the presented methodology show that our model is able to follow the trend with significant agreement with the FSI results, with an average correlation coefficient <i>R</i> of <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>t</mi><mi>r</mi></mrow></msub><mo>=</mo><mn>90.14</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>t</mi><mi>r</mi></mrow></msub><mo>=</mo><mn>92.27</mn><mo>%</mo></mrow></semantics></math></inline-formula> in training; whereas for validation, the average <i>R</i> is <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>v</mi><mi>a</mi><mi>l</mi></mrow></msub><mo>=</mo><mn>93.31</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>v</mi><mi>a</mi><mi>l</mi></mrow></msub><mo>=</mo><mn>83.08</mn><mo>%</mo></mrow></semantics></math></inline-formula> for opening area and pressure difference, respectively. The system identification model is efficiently capable of estimating the outputs of the FSI approach; however, it is not intended to substitute FSI simulations, but to complement them when the requirement is to conduct many repetitions of the phenomena with similar conditions.https://www.mdpi.com/2076-3417/10/22/8228autoregressive exogenous inputfluid-structure interactioncomputational fluid dynamicssystem identificationleafletshereditary computation |
| spellingShingle | Carlos Duran-Hernandez Rene Ledesma-Alonso Gibran Etcheverry Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows Applied Sciences autoregressive exogenous input fluid-structure interaction computational fluid dynamics system identification leaflets hereditary computation |
| title | Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows |
| title_full | Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows |
| title_fullStr | Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows |
| title_full_unstemmed | Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows |
| title_short | Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows |
| title_sort | using autoregressive with exogenous input models to study pulsatile flows |
| topic | autoregressive exogenous input fluid-structure interaction computational fluid dynamics system identification leaflets hereditary computation |
| url | https://www.mdpi.com/2076-3417/10/22/8228 |
| work_keys_str_mv | AT carlosduranhernandez usingautoregressivewithexogenousinputmodelstostudypulsatileflows AT reneledesmaalonso usingautoregressivewithexogenousinputmodelstostudypulsatileflows AT gibranetcheverry usingautoregressivewithexogenousinputmodelstostudypulsatileflows |