Uncertainty Quantification of Stochastic Impact Dynamic Oscillator Using a Proper Orthogonal Decomposition-Polynomial Chaos Expansion Technique
| Autor: | Denis Brizard, Biswarup Bhattacharyya, Eric Jacquelin |
|---|---|
| Přispěvatelé: | Laboratoire de Biomécanique et Mécanique des Chocs (LBMC UMR T9406 ), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Gustave Eiffel |
| Rok vydání: | 2020 |
| Předmět: |
Polynomial chaos
Projectile Monte Carlo method 0211 other engineering and technologies General Engineering POLYNOMIAL CHAOS EXPANSION [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph] 02 engineering and technology 01 natural sciences Displacement (vector) Contact force 010101 applied mathematics PROPER ORTHOGONAL DECOMPOSITION Applied mathematics RANDOM VIBRATION Random vibration Time domain UNCERTAINTY QUANTIFICATION 0101 mathematics Uncertainty quantification 021106 design practice & management Mathematics |
| Zdroj: | Journal of Vibration and Acoustics Journal of Vibration and Acoustics, 2020, 142 (6), 19p. ⟨10.1115/1.4047359⟩ |
| ISSN: | 1528-8927 1048-9002 |
| DOI: | 10.1115/1.4047359 |
| Popis: | A proper orthogonal decomposition (POD)-based polynomial chaos expansion (PCE) is utilized in this article for the uncertainty quantification (UQ) of an impact dynamic oscillator. The time-dependent nonsmooth behavior and the uncertainties are decoupled using the POD approach. The uncertain response domain is reduced using the POD approach, and the dominant POD modes are utilized for the UQ of the response quantity. Furthermore, the PCE model is utilized for the propagation of the input uncertainties. Two different cases of impact oscillator are considered, namely, single impact and multiple impact. The contact between two bodies is modeled by Hertz’s law. For both the cases, UQ is performed on the projectile displacement, projectile velocity, and contact force. A highly nonsmooth behavior is noticed for the contact force. For that reason, most number of POD modes are required to assess the UQ of contact force. All the results are compared with the Monte Carlo simulation (MCS) and time domain PCE results. Very good accuracies are observed for the PCE and the POD-PCE predicted results using much less number of model evaluations compared to MCS. As the PCE coefficients are dependent on time, the PCE model is computed at each time step. On the contrary, for the POD-PCE model, the PCE coefficients are computed for the number of POD modes only: it is much less than the PCE model. |
| Databáze: | OpenAIRE |
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