On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment

2010 ◽  
Vol 83 (10) ◽  
pp. 1345-1375 ◽  
Author(s):  
I. Kalashnikova ◽  
M. F. Barone
Keyword(s):  
Compressible Flow ◽  
Solid Wall ◽  
Reduced Order Model ◽  
Stability And Convergence ◽  
Far Field ◽  
Order Model ◽  
Field Boundary ◽  
Reduced Order ◽  
Boundary Treatment ◽  
The Stability

Investigating the Stability Characteristics of Natural-Circulation Boiling Water Reactors Using Root Loci of a Reduced-Order Model

2001 ◽  
Vol 136 (3) ◽  
pp. 301-314 ◽  
Author(s):  
Robert Zboray ◽  
Wilhelmus J. M. de Kruijf ◽  
Tim H. J. J. van der Hagen ◽  
Hugo van Dam
Keyword(s):  
Natural Circulation ◽  
Reduced Order Model ◽  
Boiling Water ◽  
Boiling Water Reactors ◽  
Order Model ◽  
Reduced Order ◽  
Water Reactors ◽  
The Stability

Reduced-Order Model for Unsteady Compressible Flow Based on POD-Galerkin Projection

2012 ◽  
Vol 226-228 ◽  
pp. 835-839
Author(s):  
Yi Bin Dou ◽  
Min Xu
Keyword(s):  
Euler Equation ◽  
Compressible Flow ◽  
Calibration Method ◽  
Initial Guess ◽  
Reduced Order Model ◽  
Galerkin Projection ◽  
Numerical Dissipation ◽  
Test Case ◽  
Order Model ◽  
Reduced Order

Italic textIn this paper, the reduced-order model (ROM) of unsteady compressible flow based on POD-Galerkin projection has been investigated. The Euler equation formulated with the conservative variables for compressible flow has been reformulated using modified primitive variables. The POD modes are computed using snapshot method and then an explicit quadratic ROM is constructed by applying the Galerkin projection to the modified Euler equation. Because of lacking any dissipation in POD-Galerkin projection, the flow calibration method is introduced to account for the numerical dissipation to stabilize the ROM. At last, the NACA0012 airfoil undergoing pitch harmonic oscillating in Mach number Mach = 0.755 is calculated as a test case. For this flow configuration, the calibrated coefficients of the ROM are almost the same as the initial guess which comes from POD-Galerkin projection; the differences are mostly focused on the linear Lij coefficients and quadratic Qijk coefficients.

Semi-Active Control of Civil Structures With a Simultaneous Reduced-Order Modeling and a Tuning of the Control Law

2011 ◽  
Author(s):  
Kazuhiko Hiramoto ◽  
Taichi Matsuoka ◽  
Katsuaki Sunakoda
Keyword(s):  
Control Systems ◽  
Active Control ◽  
Closed Loop ◽  
Reduced Order Model ◽  
Control Law ◽  
Structural Damping ◽  
Order Model ◽  
Civil Structures ◽  
Reduced Order ◽  
The Stability

Various semi-active control methods have been proposed for vibration control of civil structures. In contrast to active vibration control systems, all semi-active control systems are essentially asymptotically stable because of the stability of the structural systems themselves (with structural damping) and the energy dissipating nature of the semi-active control law. In this study, by utilizing the above property on the stability of semi-active control systems, a reduced-order structural model and a semi-active control law are simultaneously obtained so that the performance of the resulting semi-active control system becomes good. Based on the above fact any semi-active control laws derived from some models stabilize all real-existing structural systems that have structural damping. It means that the difference of dynamic behaviors between the real structural system and the reduced-order mathematical model in the sense of the open-loop response is no longer an important issue. In other words, we do not have to consider the closed-loop stability, which is one of the most important constraints in active control, in the process of the reduced-order structural modeling and the semi-active control design. We can only focus on the control performance of the closed-loop system with the real structure with the (model-based) semi-active control law in obtaining the reduced-order model. The semi-active control law in the present study is based on the one step ahead prediction of the structural response. The Genetic Algorithm (GA) is adopted to obtain the reduced-order model and the semi-active control law based on the reduced order model.

scholarly journals An efficient Bayesian neural network surrogate algorithm for shape detection

2022 ◽  
Vol 62 ◽  
pp. C112-C127
Author(s):  
Mahadevan Ganesh ◽  
Stuart Collin Hawkins ◽  
Nino Kordzakhia ◽  
Stefanie Unicomb
Keyword(s):  
Neural Network ◽  
Light Scattering ◽  
Inverse Problems ◽  
Inverse Scattering ◽  
Obstacle Detection ◽  
Reduced Order Model ◽  
Far Field ◽  
Order Model ◽  
Reduced Order ◽  
Comput Phys

We present an efficient Bayesian algorithm for identifying the shape of an object from noisy far field data. The data is obtained by illuminating the object with one or more incident waves. Bayes' theorem provides a framework to find a posterior distribution of the parameters that determine the shape of the scatterer. We compute the distribution using the Markov Chain Monte Carlo (MCMC) method with a Gibbs sampler. The principal novelty of this work is to replace the forward far-field-ansatz wave model (in an unbounded region) in the MCMC sampling with a neural-network-based surrogate that is hundreds of times faster to evaluate. We demonstrate the accuracy and efficiency of our algorithm by constructing the distributions, medians and confidence intervals of non-convex shapes using a Gaussian random circle prior. References Y. Chen. Inverse scattering via Heisenberg’s uncertainty principle. Inv. Prob. 13 (1997), pp. 253–282. doi: 10.1088/0266-5611/13/2/005 D. Colton and R. Kress. Inverse acoustic and electromagnetic scattering theory. 4th Edition. Vol. 93. Applied Mathematical Sciences. References C112 Springer, 2019. doi: 10.1007/978-3-030-30351-8 R. DeVore, B. Hanin, and G. Petrova. Neural Network Approximation. Acta Num. 30 (2021), pp. 327–444. doi: 10.1017/S0962492921000052 M. Ganesh and S. C. Hawkins. A reduced-order-model Bayesian obstacle detection algorithm. 2018 MATRIX Annals. Ed. by J. de Gier et al. Springer, 2020, pp. 17–27. doi: 10.1007/978-3-030-38230-8_2 M. Ganesh and S. C. Hawkins. Algorithm 975: TMATROM—A T-matrix reduced order model software. ACM Trans. Math. Softw. 44.9 (2017), pp. 1–18. doi: 10.1145/3054945 M. Ganesh and S. C. Hawkins. Scattering by stochastic boundaries: hybrid low- and high-order quantification algorithms. ANZIAM J. 56 (2016), pp. C312–C338. doi: 10.21914/anziamj.v56i0.9313 M. Ganesh, S. C. Hawkins, and D. Volkov. An efficient algorithm for a class of stochastic forward and inverse Maxwell models in R3. J. Comput. Phys. 398 (2019), p. 108881. doi: 10.1016/j.jcp.2019.108881 L. Lamberg, K. Muinonen, J. Ylönen, and K. Lumme. Spectral estimation of Gaussian random circles and spheres. J. Comput. Appl. Math. 136 (2001), pp. 109–121. doi: 10.1016/S0377-0427(00)00578-1 T. Nousiainen and G. M. McFarquhar. Light scattering by quasi-spherical ice crystals. J. Atmos. Sci. 61 (2004), pp. 2229–2248. doi: 10.1175/1520-0469(2004)061<2229:LSBQIC>2.0.CO;2 A. Palafox, M. A. Capistrán, and J. A. Christen. Point cloud-based scatterer approximation and affine invariant sampling in the inverse scattering problem. Math. Meth. Appl. Sci. 40 (2017), pp. 3393–3403. doi: 10.1002/mma.4056 M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378 (2019), pp. 686–707. doi: 10.1016/j.jcp.2018.10.045 A. C. Stuart. Inverse problems: A Bayesian perspective. Acta Numer. 19 (2010), pp. 451–559. doi: 10.1017/S0962492910000061 B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande. Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry. J. Quant. Spectro. Rad. Trans. 100 (2006), pp. 393–405. doi: 10.1016/j.jqsrt.2005.11.053

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