Liqian Peng

Dynamic Data Driven Application System for Plume Estimation Using UAVs

In this article, a full dynamic data-driven application system (DDDAS) is proposed for dynamically estimating a concentration plume and planning optimal paths for unmanned aerial vehicles (UAVs) equipped with environmental sensors. The proposed DDDAS dynamically incorporates measured data from UAVs into an environmental simulation while simultaneously steering measurement processes. In order to assimilate incomplete and noisy state observations into this system in real-time, the proper orthogonal decomposition (POD) is used to estimate the plume concentration by matching partial observations with pre-computed dominant modes in a least-square sense. In order to maximize the information gain, UAVs are dynamically driven to hot spots chosen based on the POD modes. Smoothed particle hydrodynamics (SPH) techniques are used for UAV guidance with collision and obstacle avoidance. We demonstrate the efficacy of the data assimilation and control strategies in numerical simulations. Especially, a single UAV outperforms the ten static sensors in this scenario in terms of the mean square error over the full time interval. Additionally, the multi-vehicle data collection scenarios outperform the single vehicle scenarios for both static sensors at optimal positions and UAVs controlled by SPH.

Symplectic Model Reduction of Hamiltonian Systems

In this paper, a symplectic model reduction technique, proper symplectic decomposition (PSD) with symplectic Galerkin projection, is proposed to save the computational cost for the simplification of large-scale Hamiltonian systems while preserving the symplectic structure. As an analogy to the classical proper orthogonal decomposition (POD)-Galerkin approach, PSD is designed to build a symplectic subspace to fit empirical data, while the symplectic Galerkin projection constructs a reduced Hamiltonian system on the symplectic subspace. For practical use, we introduce three algorithms for PSD, which are based upon the cotangent lift, complex singular value decomposition, and nonlinear programming. The proposed technique has been proven to preserve system energy and stability. Moreover, PSD can be combined with the discrete empirical interpolation method to reduce the computational cost for nonlinear Hamiltonian systems. Owing to these properties, the proposed technique is better suited than the classical PO...

An Online Manifold Learning Approach for Model Reduction of Dynamical Systems

This article discusses a newly developed online manifold learning method, subspace iteration using reduced models (SIRM), for the dimensionality reduction of dynamical systems. This method may be viewed as subspace iteration combined with a model reduction procedure. Specifically, starting with a test solution, the method solves a reduced model to obtain a more precise solution, and it repeats this process until sufficient accuracy is achieved. The reduced model is obtained by projecting the full model onto a subspace that is spanned by the dominant modes of an extended data ensemble. The extended data ensemble in this article contains not only the state vectors of some snapshots of the approximate solution from the previous iteration but also the associated tangent vectors. Therefore, the proposed manifold learning method takes advantage of the information of the original dynamical system to reduce the dynamics. Moreover, the learning procedure is computed in the online stage, as opposed to being compute...

A DDDAS Plume Monitoring System with Reduced Kalman Filter

A new dynamic data-driven application system (DDDAS) is proposed in this article to dynamically estimate a concentration plume and to plan optimal paths for unmanned aerial vehicles (UAVs) equipped with environmental sensors. The proposed DDDAS dynamically incorporates measured data from UAVs into an environmental simulation while simultaneously steering measurement processes. The main idea is to employ a few time-evolving proper orthogonal decomposition (POD) modes to simulate a coupled linear system, and to simultaneously measure plume concentration and plume source distribution via a reduced Kalman filter. In order to maximize the information gain, UAVs are dynamically driven to hot spots chosen based on the POD modes using a greedy algorithm. We demonstrate the efficacy of the data assimilation and control strategies in a numerical simulation and a field test.

Sensor driven feedback for puff estimation using unmanned aerial vehicles

The puff (or the pollutant puff) represents an instantaneous pollution cloud released in the ambient atmosphere. This paper describes, and validates a complete dynamic data driven application system (DDDAS) for measuring and simulating a puff in a dynamic, urban environment. Unmanned aerial vehicles (UAVs) are used as mobile sensors to collect data from the concentration field which is then assimilated into a running advection diffusion simulation to predict the puff motion. In turn, the running simulation is used to determine desirable locations to place the sensors based on the previously collected data. We directly compare the error achieved in a real-time, low resolution simulation by using both static and mobile sensors in a the DDDAS. The scenario investigated here is analogous to a chemical puff that is released in an urban environment and travels downstream according to the advection diffusion equation. We find that a single mobile sensor in the DDDAS outperforms an array of several static sensors in this scenario. Additionally, groups of mobile sensors are able to further decrease the error levels in the simulation.

Cooperative control using data-driven feedback for mobile sensors

This article describes and validates a data-driven cooperative feedback control system for mobile sensors. The system can be used to guide resource constrained mobile sensors through a dynamically changing environment in order to obtain a path that results in data collection at important locations in the domain. A simulated chemical puff is used as a test application where small, resource constrained aerial vehicles provide mobile sensing capabilities. A fluid-based control scheme is used to guide the mobile sensors through the domain to collect data on the puff. The data is then used to update and improve a model of the puff concentration. Simulations are provided, demonstrating the decrease in error between the simulated and actual puffs over time. Additionally, the effect of using different numbers of mobile sensors as well as different schemes for guiding the mobile sensors is investigated. The feasibility of the technique using real sensors is demonstrated experimentally using a single UAV tracking a simulated puff.

Geometric model reduction of forced and dissipative Hamiltonian systems

In this paper, a geometric model reduction method, the proper symplectic decomposition (PSD) with structure-preserving projection, is proposed for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD)-Galerkin method, PSD is designed to build a symplectic subspace to fit empirical data, while the structure-preserving projection is developed to reconstruct reduced systems while simultaneously preserving the symplectic and forced structure. In a special case when the external force is described by the Rayleigh dissipative function, the proposed method automatically preserves the dissipativity of the original system. The stability, accuracy, and efficiency of the proposed method are illustrated through numerical simulations of a dissipative wave equation.

A localized symplectic model reduction technique for parameterized Hamiltonian systems

In this article, a localized symplectic model reduction technique, locally weighted proper symplectic decomposition (LWPSD), is proposed to simplify parameterized Hamiltonian systems. Our aim is two-fold. First, to achieve computational savings for large-scale Hamiltonian systems with parameter variation. Second, to preserve the symplectic structure of the original system. As an analogy to the proper orthogonal decomposition, the proper symplectic decomposition (PSD) can be used to construct a symplectic subspace to fit empirical data, and yield a low-order Hamiltonian system on the subspace. Instead of using a global basis to construct a global reduced model, the locally weighted approach approximates the original system by multiple lower-dimensional subspaces. Each local reduced basis is generated by the PSD of a weighted snapshot ensemble. Compared with the standard PSD, the LWPSD could yield a more accurate solution with a fixed subspace dimension. The stability, accuracy, and efficiency of the proposed technique are illustrated through the numerical simulation of the wave equation.

A Symplectic Technique for Model Reduction of Wave Equations

A symplectic model reduction technique, proper symplectic decomposition (PSD), is proposed to preserve the geometric structure and achieve computational saving for largescale wave equations. As an empirical model reduction approach, the PSD combines the idea of symplectic reduction with SVD-based projection. After rewriting the wave equation into a Hamiltonian form, the PSD can be applied to construct a low-order system that is suitable for the long-time integration. The stability, accuracy and efficiency of the reduced model are illustrated through the numerical simulations.

An Empirical Reduced Modeling Approach for Mobile, Distributed Sensor Platform Networks

In this paper, we present an efficient means for both modeling phenomena in a mobile sensor context and determining where the sensors should travel to collect meaningful information. Our approach is based on offline-online model reduction, which is performed via a snapshot-weighted proper orthogonal decomposition/discrete empirical interpolation. That is, through collected observations, we construct and reduce empirical dynamical systems that characterize the evolution of the phenomena and determine those locations that can be visited and sensed to improve the model quality. To showcase the effectiveness of our contributions, we apply them to the tasks of estimating the concentration and location of plumes in two-dimensional environments.