arXiv subjects

Piyush Grover

Publications and source records attributed to Piyush Grover.

22 records · Page 2Linked to original sources

arXiv2016

Sparse sensing and DMD based identification of flow regimes and bifurcations in complex flows

We present a sparse sensing framework based on Dynamic Mode Decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermo-fluid systems. Motivated by real-time sensing and control of thermal-fluid flows in buildings and equipment, we apply this method to a Direct Numerical Simulation (DNS) data set of a 2D laterally heated cavity. The resulting flow solutions can be divided into several regimes, ranging from steady to chaotic flow. The DMD modes and eigenvalues capture the main temporal and spatial scales in the dynamics belonging to different regimes. Our proposed classification method is data-driven, robust w.r.t measurement noise, and exploits the dynamics extracted from the DMD method. Namely, we construct an augmented DMD basis, with "built-in" dynamics, given by the DMD eigenvalues. This allows us to employ a short time-series of data from sensors, to more robustly classify flow regimes, particularly in the presence of measurement noise. We also exploit the incoherence exhibited among the data generated by different regimes, which persists even if the number of measurements is small compared to the dimension of the DNS data. The data-driven regime identification algorithm can enable robust low-order modeling of flows for state estimation and control.

math.DS↗

arXiv2015

Learning-based Reduced Order Model Stabilization for Partial Differential Equations: Application to the Coupled Burgers Equation

We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure models for ROMs, where we use a model-free extremum seeking (ES) dither-based algorithm to learn the best closure models' parameters, for optimal ROM stabilization. We first propose to auto-tune linear closure models using ES, and then extend the results to a closure model combining linear and nonlinear terms, for better stabilization performance. The coupled Burgers' equation is employed as a test-bed for the proposed tuning method.

eess.SY↗

arXiv2015

Model-free control framework for multi-limb soft robots

The deformable and continuum nature of soft robots promises versatility and adaptability. However, control of modular, multi-limbed soft robots for terrestrial locomotion is challenging due to the complex robot structure, actuator mechanics and robot-environment interaction. Traditionally, soft robot control is performed by modeling kinematics using exact geometric equations and finite element analysis. The research presents an alternative, model-free, data-driven, reinforcement learning inspired approach, for controlling multi-limbed soft material robots. This control approach can be summarized as a four-step process of discretization, visualization, learning and optimization. The first step involves identification and subsequent discretization of key factors that dominate robot-environment, in turn, the robot control. Graph theory is used to visualize relationships and transitions between the discretized states. The graph representation facilitates mathematical definition of periodic control patterns (simple cycles) and locomotion gaits. Rewards corresponding to individual arcs of the graph are weighted displacement and orientation change for robot state-to-state transitions. These rewards are specific to surface of locomotion and are learned. Finally, the control patterns result from optimization of reward dependent locomotion task (e.g. translation) cost function. The optimization problem is an Integer Linear Programming problem which can be quickly solved using standard solvers. The framework is generic and independent of type of actuator, soft material properties or the type of friction mechanism, as the control exists in the robot's task space. Furthermore, the data-driven nature of the framework imparts adaptability to the framework toward different locomotion surfaces by re-learning rewards.

cs.RO↗

arXiv2012

Topological chaos, braiding and bifurcation of almost-cyclic sets

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler, Ross, Grover, Kumar, Topological chaos and periodic braiding of almost-cyclic sets. Physical Review Letters 106 (2011), 114101]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or `ghost rods' around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

nlin.CD↗