Uncertain Flow Fields Research Articles

Optimizing measurement schemes to improve indoor airflow and temperature CFD–EnKF joint simulation

An ensemble Kalman filter (EnKF) effectively rectifies simulation inaccuracies arising from uncertain flow field boundary conditions. In this methodology, measurement data plays a pivotal and indispensable role. This study investigated the requirements for observation data in joint EnKF and computational fluid dynamics (CFD) simulation models to correct errors. It established guiding principles for measurement schemes and validated them using numerical experiments on the airflow and temperature fields in a small chamber. The optimized scheme significantly reduced simulation errors, enhancing assimilation accuracy. In addition, the influence of measurement noise was considered, revealing a positive correlation between assimilation and measurement errors, thus highlighting the significance of high-precision instruments. Additionally, this study confirmed that the optimal number of measurement points corresponds to the number of uncertain boundary condition variables. Fewer measurement points hinder accurate estimation, whereas increasing their number does not significantly improve the data assimilation accuracy, regardless of measurement noise. Overall, this study provides guidelines for implementing EnKF data assimilation to ensure reliable and precise results.

AUV Motion Planning in Uncertain Flow Fields Using Bayes Adaptive MDPs

This letter presents an uncertainty-aware motion planner for an autonomous underwater vehicle (AUV) which navigates in a cluttered scenario under an uncertain flow field. Safe and efficient navigation in such environments requires a precise motion model of an AUV. However, the motion of an AUV is difficult to be accurately predicted due to its nonlinear dynamics significantly affected by its surrounding fluids. To resolve this difficulty, we propose to use a Bayes Adaptive Markov Decision Process (BA-MDP) for robust decision making, which is able to hedge against errors in the AUV’s motion model through online learning. To construct the BA-MDP accurately, a Clustering Guided Explorative Tree (CGETree) is proposed to explore all the possible connectivities within the AUV’s state space in an offline manner. The CGETree’s nodes are clustered together to provide a discretization of the state space, and the tree edges, after being combined with a discrete noise model, provide a physics-based-prior for the transition model, which will be updated online along with the robot’s movement. The simulation results demonstrate that our proposed method achieves good performance in a seabed environment with a flow field whose uncertainty may not be known beforehand.

Strategy for Enhancing Fairing Air Conditioning Security Capacity in the On-Time Launch of Chinese Mars-1 Exploration

For the launch of Chinese Mars-1 exploration in a coastal spaceport at noon, summer, there are issues such as big fairing size, complex fairing layout and uncertain flow field of fairing. The author conducted analysis of fairing air conditioning security by thermodynamic modeling calculation and CFD simulation and proposed specific improvement measures to secure on-time launch according to the calculation analysis conclusions. Special test verification was conducted after the carrier rocket transfer. The improvement measures were proven to be effective. During mission launch, the fairing environment security is good. After fairing air conditioning decoupling, the fairing inside temperature rise is within the required scope, ensuring on-time launch of Mars exploration.

Path planning for autonomous underwater vehicles based on interval optimization in uncertain flow fields

The predictive uncertainty of ocean currents needs to be considered in the path planning of autonomous underwater vehicles (AUV) in oceanic environments. An interval optimization (IO) scheme is presented in this paper to plan time-optimal paths for AUVs operating in oceanic environments with dynamic and uncertain flow fields; interval currents are established to process the uncertainty of forecasted ocean flows, and the IO scheme is used to search for time-optimal paths in the interval current fields. The IO scheme is a two-layer framework: In the outer layer, quantum-behaved particle swarm optimization is used to generate and optimize candidate paths. In the inner layer, the interval response of the candidate path from the outer layer is calculated under interval current fields, and they are converted into a time-optimal fitness value in accordance with the possibility degree of interval numbers. The influence of predictive uncertainty is analyzed via simulation, and the robustness of the IO scheme is verified.

Moving source identification in an uncertain marine flow: Mediterranean Sea application

Identifying marine pollutant sources is essential to assess, contain and minimize their risk. We propose a Lagrangian Particle Tracking algorithm (LPT) to study the transport of passive tracers advected by an uncertain flow field described by an ensemble of realizations of the ocean currents, and to identify the source parameters of the release in backward mode. Starting from a probability map describing the distribution of a pollutant, reverse tracking is used to generate probabilistic inverse maps by integrating it with the ensemble of flow fields backward in time. An objective function based on the probability-weighted distance between the resulting inverse maps and the source trajectory is then minimized to identify the likely source of pollution. We conduct numerical experiments to demonstrate the efficiency of the proposed algorithm in the Mediterranean Sea. Passive tracers are released along the path of a ship and propagated with an ensemble of realistic flow fields to generate a probability map, which is then used for the inverse problem of source identification. Our results suggest that the proposed algorithm captures the release time and source of pollution, successfully pinpointing to the release parameters up to two weeks back in time in certain case studies.

Computing the finite time Lyapunov exponent for flows with uncertainties

We propose an Eulerian approach to compute the expected finite time Lyapunov exponent (FTLE) of uncertain flow fields. The definition extends the usual FTLE for deterministic dynamical systems. Instead of performing Monte Carlo simulations as in typical Lagrangian computations, our approach associates each initial flow particle with a probability density function (PDF) which satisfies an advection-diffusion equation known as the Fokker-Planck (FP) equation. Numerically, we incorporate Strang's splitting scheme so that we can obtain a second-order accurate solution to the equation. To further improve the computational efficiency, we develop an adaptive approach to concentrate the computation of the FTLE near the ridge, where the so-called Lagrangian coherent structure (LCS) might exist. We will apply our proposed algorithm to several test examples including a real-life dataset to demonstrate the performance of the method.

Probabilistic solution to two-dimensional stochastic solute transport model by the Fokker-Planck equation approach

The study of solute transport in rivers is of environmental significance, since solute transported in river flows may affect the river water quality conditions. Solute transport in natural flows is a challenging process to be investigated, given natural flows usually indicate uncertainty in space and time. Two-dimensional models are more preferable to one-dimensional models, especially when the underlying flow field is complex. In this study, a stochastic horizontally two-dimensional solute transport model is developed. The proposed model can account for the effect of uncertain two-dimensional flow field and solute loading conditions on the uncertainty of the solute transport. The governing equation of the proposed model is in the form of Fokker-Planck equation, which characterizes the spatiotemporal evolution of the probability density function of the state variables of the solute transport process. Consequently, the mean and standard deviation behavior of the ensemble solute transport under uncertain conditions can be quantified. The numerical solutions of the proposed model are validated with the Monte Carlo simulations under uncertain flow fields. The comparison of the results by the two methods indicate the developed two-dimensional stochastic solute transport model can sufficiently express the spatial variability of the solute transport process and adequately capture the ensemble solute transport behavior by the complete probabilistic description of the solute transport process under uncertain conditions.

Extreme-Scale Stochastic Particle Tracing for Uncertain Unsteady Flow Visualization and Analysis.

We present an efficient and scalable solution to estimate uncertain transport behaviors-stochastic flow maps (SFMs)-for visualizing and analyzing uncertain unsteady flows. Computing flow maps from uncertain flow fields is extremely expensive because it requires many Monte Carlo runs to trace densely seeded particles in the flow. We reduce the computational cost by decoupling the time dependencies in SFMs so that we can process shorter sub time intervals independently and then compose them together for longer time periods. Adaptive refinement is also used to reduce the number of runs for each location. We parallelize over tasks-packets of particles in our design-to achieve high efficiency in MPI/thread hybrid programming. Such a task model also enables CPU/GPU coprocessing. We show the scalability on two supercomputers, Mira (up to 256K Blue Gene/Q cores) and Titan (up to 128K Opteron cores and 8K GPUs), that can trace billions of particles in seconds.

Robust Time-Optimal Guidance in a Partially Uncertain Time-Varying Flow-Field

In this paper, we address the problem of guiding an aerial or aquatic vehicle to a fixed target point in a partially uncertain flow-field. We assume that the motion of the vehicle is described by a point-mass linear kinematic model. In addition, the velocity of the flow-field, which is taken to be time varying, can be decomposed into two components: one which is known a priori and another one which is uncertain and only a bound on its magnitude is known. We show that the guidance problem can be reformulated as an equivalent pursuit evasion game with time-varying affine dynamics. To solve the latter game, we propose an extension of a specialized solution approach, which transforms the pursuit–evasion game (whose terminal time is free) via a special state transformation into a family of games with fixed terminal time. In addition, we provide a simple method to visualize the level sets of the value function of the game, along with the corresponding reachable sets. Furthermore, we compare our conservative game-theoretic solution with a pure optimal control solution, for the special case in which the flow-field is perfectly known a priori.

Path planning in uncertain flow fields using ensemble method

An ensemble-based approach is developed to conduct optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where an ensemble of deterministic predictions is used to model and quantify uncertainty. In an operational setting, much about dynamics, topography, and forcing of the ocean environment is uncertain. To address this uncertainty, the flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each of the resulting realizations of the uncertain current field, we predict the path that minimizes the travel time by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of the sampling strategy and to develop insight into extensions dealing with general circulation ocean models. In particular, the ensemble method enables us to perform a statistical analysis of travel times and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.

Reliability Evaluation of Groundwater Contamination Source Characterization under Uncertain Flow Field

Groundwater contamination is one of the serious environmental problems. Effective remediation strategies require accurate characteristics of contamination sources. Contamination source identification approaches need accurate flow and contaminant transport simulation models. In order to obtain reliable solutions, the simulation models need to be provided with reliable hydrogeologic information. In real life scenarios usually sparse and limited hydrogeologic information is available. In this study two hydraulic conductivity sampling networks are ranked based on their effectiveness in identifying reliable contamination source characteristics. Using multiple realizations of hydraulic conductivity fields, and the location and size of the contaminant plume at different monitoring stages, an index of reliability is estimated for each hydraulic conductivity sampling network. It is demonstrated that the source characteristics identified by utilizing the sampling network with higher index of reliability results in more accurate characterization of contamination sources. Therefore the developed methodology provides a tool to select an appropriate hydrogeologic sampling network for more efficient characterizing of contamination sources.

Feedback Navigation in an Uncertain Flowfield and Connections with Pursuit Strategies

Copyright ©2012 by E. Bakolas and P. Tsiotras. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.