scholarly journals Cluster-based reduced-order modelling of a mixing layer

2014 ◽  
Vol 754 ◽  
pp. 365-414 ◽  
Author(s):  
Eurika Kaiser ◽  
Bernd R. Noack ◽  
Laurent Cordier ◽  
Andreas Spohn ◽  
Marc Segond ◽  
...  
Keyword(s):  
Markov Process ◽  
State Space ◽  
Transition Matrix ◽  
Bluff Body ◽  
Mixing Layer ◽  
The State ◽  
Lorenz Attractor ◽  
Reduced Order ◽  
Physical Mechanisms ◽  
Reduced Order Modelling

AbstractWe propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger’s group (Burkardt, Gunzburger & Lee,Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337–355) and transition matrix models introduced in fluid dynamics in Eckhardt’s group (Schneider, Eckhardt & Vollmer,Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam–Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron–Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.

The harmonic functions of (At, Bt,)

1993 ◽  
Vol 114 (2) ◽  
pp. 369-377
Author(s):  
L. C. G. Rogers
Keyword(s):  
Markov Process ◽  
State Space ◽  
Harmonic Functions ◽  
Martin Boundary ◽  
The State ◽  
Process Yield ◽  
Reference Measure

The non-negative harmonic functions of a transient Markov process yield a great deal of information about the ‘behaviour at infinity’ of the process, and can be used to h-transform the process to behave in a certain way at infinity. The traditional analytic way of studying the non-negative harmonic functions is to construct the Martin boundary of the process (see, for example, Meyer [4], Kunita and T. Watanabe[3], and Kemeny, Snell & Knapp[2], Williams [7] for the chain case). However, certain conditions on the process need to be satisfied, one of the most basic of which is that there exists a reference measure η such that Uλ (x, ·) ≪ η for all λ > 0, all x ∈ E, the state space of the Markov process. (Here, (Uλ)λ>0 is the resolvent of the process.)

Reversibility and Acyclicity

1975 ◽  
Vol 12 (S1) ◽  
pp. 217-224 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Markov Process ◽  
State Space ◽  
Transition Matrix ◽  
Reversible Markov Process ◽  
Classical Definition ◽  
Dynamic Reversibility ◽  
Converse Assertion

It is well-known that the transition matrix of a reversible Markov process can have only real eigenvalues. An example is constructed which shows that the converse assertion does not hold. A generalised notion of reversibility is proposed, ‘dynamic reversibility’, which has many of the implications for the form of the transition matrix of the classical definition, but which does not exclude ‘circulation in state-space’ or, indeed, periodicity.

A Direct Approach to Order Reduction of Nonlinear Systems Subjected to External Periodic Excitations

2008 ◽  
Vol 3 (3) ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
Invariant Manifold ◽  
Large Scale ◽  
Reduction Process ◽  
Order Reduction ◽  
The State ◽  
Reduced Order Models ◽  
External Excitation ◽  
Reduced Order

In this work, the basic problem of order reduction of nonlinear systems subjected to an external periodic excitation is considered. This problem deserves special attention because modes that interact (linearly or nonlinearly) with external excitation dominate the response. These dominant modes are identified and chosen as the “master” modes to be retained in the reduction process. The simplest idea could be to use a linear approach such as the Guyan reduction and choose those modes whose natural frequencies are close to that of external excitation as the master modes. However, this technique does not guarantee accurate results when nonlinear interactions are strong and a nonlinear approach must be adopted. Recently, the invariant manifold technique has been extended to forced problems by “augmenting” the state space, i.e., forcing is treated as an additional state and an invariant manifold is constructed. However, this process does not provide a clear picture of possible resonances and conditions under which an order reduction is possible. In a direct innovative approach suggested here, a nonlinear time-dependent relationship between the dominant and nondominant states is assumed and the dimension of the state space remains the same. This methodology not only yields accurate reduced order models but also explains the consequences of various primary and secondary resonances present in the system. One obtains various reducibility conditions in a closed form, which show interactions among eigenvalues, nonlinearities and the external excitation. One can also recover all “resonance conditions” obtained via perturbation or averaging techniques. The “linear” as well as the “extended invariant manifold” techniques are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control of large-scale externally excited nonlinear systems.

State-Space Rotor Aeroelastic Modeling for Real-Time Helicopter Flight Simulation

2014 ◽  
Vol 1016 ◽  
pp. 451-459 ◽  
Author(s):  
Riccardo Gori ◽  
Francesca Pausilli ◽  
Marilena D. Pavel ◽  
Massimo Gennaretti
Keyword(s):  
State Space ◽  
Real Time ◽  
State Space Model ◽  
Flight Simulation ◽  
The State ◽  
Reduced Order ◽  
Helicopter Flight ◽  
Full State ◽  
Linear State ◽  
Real Time Simulations

This paper introduces a new approach for the identification of linear state-space models of dynamical systems of arbitrary complexity. The identification procedure is described and applied for modeling aeroelastic response of helicopter main rotors. With the aim of developing a tool that might be conveniently applied for real-time simulations of helicopter flight dynamics, the state-space model considered is a reduced-order description of loads transmitted to the airframe due to hub motion and blade pitch controls. In order to validate the proposed approach, loads from the state-space, reduced-order model are compared with those predicted by the complete full-state, nonlinear rotor model for prescribed helicopter maneuvers.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

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