Towards Parameter Identification of a Behavioral Model from a Virtual Reality Experiment
In this paper, we investigate the calibration of a mathematical model describing different behaviors occurring during a natural, a societal, or a technological catastrophe. This model was developed in collaboration with geographers and psychologists. To collect information on the level of stress, ps...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3175 |
| _version_ | 1797502658965143552 |
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| author | Nathalie Verdière Oscar Navarro Aude Naud Alexandre Berred Damienne Provitolo |
| author_facet | Nathalie Verdière Oscar Navarro Aude Naud Alexandre Berred Damienne Provitolo |
| author_sort | Nathalie Verdière |
| collection | DOAJ |
| description | In this paper, we investigate the calibration of a mathematical model describing different behaviors occurring during a natural, a societal, or a technological catastrophe. This model was developed in collaboration with geographers and psychologists. To collect information on the level of stress, psychologists of the LPPL laboratory of Nantes (France) led virtual reality experiments. These experiments consisted in immersing individuals in a situation of catastrophe and measuring their electrocardiogram. From the physical and biological data collected, we present the methodology to calibrate the behavioral model. First, a theoretical analysis is carried out to determine (i) if the parameters can be uniquely estimated, (ii) the minimal number of discrete measurements required for the estimation. Then, from these analyses, an estimation procedure is performed to calibrate the mathematical model or at least to have an order magnitude of the model parameters. Through this work, we will show from simulations that the proposed system makes it possible to apprehend non observable human processes. |
| first_indexed | 2024-03-10T03:38:17Z |
| format | Article |
| id | doaj.art-8f9b2e83cada4d87963183f07b8d6eb9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:38:17Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8f9b2e83cada4d87963183f07b8d6eb92023-11-23T09:25:22ZengMDPI AGMathematics2227-73902021-12-01924317510.3390/math9243175Towards Parameter Identification of a Behavioral Model from a Virtual Reality ExperimentNathalie Verdière0Oscar Navarro1Aude Naud2Alexandre Berred3Damienne Provitolo4Laboratoire de Mathématiques Appliquées, FR-CNRS-3335, 25, Rue Philippe Lebon, 76063 Le Havre, FranceLaboratoire de Psychologie des Pays de la Loire—UPRES EA 4638, University of Nantes, 44312 Nantes, FranceLaboratoire de Psychologie des Pays de la Loire—UPRES EA 4638, University of Nantes, 44312 Nantes, FranceLaboratoire de Mathématiques Appliquées, FR-CNRS-3335, 25, Rue Philippe Lebon, 76063 Le Havre, FranceCampus Azur 250, Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, IRD, Géoazur, Rue Albert Einstein, CEDEX, 06905 Sophia Antipolis, FranceIn this paper, we investigate the calibration of a mathematical model describing different behaviors occurring during a natural, a societal, or a technological catastrophe. This model was developed in collaboration with geographers and psychologists. To collect information on the level of stress, psychologists of the LPPL laboratory of Nantes (France) led virtual reality experiments. These experiments consisted in immersing individuals in a situation of catastrophe and measuring their electrocardiogram. From the physical and biological data collected, we present the methodology to calibrate the behavioral model. First, a theoretical analysis is carried out to determine (i) if the parameters can be uniquely estimated, (ii) the minimal number of discrete measurements required for the estimation. Then, from these analyses, an estimation procedure is performed to calibrate the mathematical model or at least to have an order magnitude of the model parameters. Through this work, we will show from simulations that the proposed system makes it possible to apprehend non observable human processes.https://www.mdpi.com/2227-7390/9/24/3175parameter estimationvirtual realityidentifiabilitybehavioral model |
| spellingShingle | Nathalie Verdière Oscar Navarro Aude Naud Alexandre Berred Damienne Provitolo Towards Parameter Identification of a Behavioral Model from a Virtual Reality Experiment Mathematics parameter estimation virtual reality identifiability behavioral model |
| title | Towards Parameter Identification of a Behavioral Model from a Virtual Reality Experiment |
| title_full | Towards Parameter Identification of a Behavioral Model from a Virtual Reality Experiment |
| title_fullStr | Towards Parameter Identification of a Behavioral Model from a Virtual Reality Experiment |
| title_full_unstemmed | Towards Parameter Identification of a Behavioral Model from a Virtual Reality Experiment |
| title_short | Towards Parameter Identification of a Behavioral Model from a Virtual Reality Experiment |
| title_sort | towards parameter identification of a behavioral model from a virtual reality experiment |
| topic | parameter estimation virtual reality identifiability behavioral model |
| url | https://www.mdpi.com/2227-7390/9/24/3175 |
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