Constructing Markov matrices for real-time transient contaminant transport analysis for indoor environments

Fontanini, Anthony D.; Vaidya, Umesh; Ganapathysubramanian, Baskar

doi:10.1016/j.buildenv.2015.07.020

Cited by 27 publications

(31 citation statements)

References 29 publications

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“…More recently, the discrete finite dimensional form of the PF operator, which takes the form of a Markov Matrix, has been used to identify optimal sensing locations [35,36]. Utilizing the finite dimensional PF operator has been shown to be a simple way to calculating real-time contaminant transport in buildings [37]. Additionally, such analysis also provides insight into the age of the air and where contaminants spend the most time [38].…”

Section: Sensor Placement Methodsmentioning

confidence: 99%

“…Utilizing the finite dimensional PF operator has been shown to be a simple way to calculating real-time contaminant transport in buildings [37]. Additionally, such analysis also provides insight into the age of the air and where contaminants spend the most time [38]. The critical advantage of this method is that the finite dimensional PF operator method is relatively computationally inexpensive, as they do not require solving the (direct or adjoint) advection-diffusion PDE or minimization of a complicated cost function.…”

Section: Sensor Placement Methodsmentioning

confidence: 99%

“…This paper is built upon previous work [35,37], of utilizing a dynamical systems approach to indoor air analysis. The main idea is determining sensor locations from velocity vector fields (acquired from analytical methods, CFD, particle imaging velocimetry, etc.).…”

Section: Sensor Placement Methodsmentioning

confidence: 99%

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A methodology for optimal placement of sensors in enclosed environments: A dynamical systems approach

Fontanini

Vaidya

Ganapathysubramanian

2016

Building and Environment

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Keywords:Sensor placement Markov matrix Set cover problem Indoor air quality Transmission of infectious diseases Chemical and biological warfare a b s t r a c t Air quality has been an important issue in public health for many years. Sensing the level and distributions of impurities help in the control of building systems and mitigate long term health risks. Rapid detection of infectious diseases in large public areas like airports and train stations may help limit exposure and aid in reducing the spread of the disease. Complete coverage by sensors to account for any release scenario of chemical or biological warfare agents may provide the opportunity to develop isolation and evacuation plans that mitigate the impact of the attack. All these scenarios involve strategic placement of sensors to promptly detect and rapidly respond.This paper presents a data driven sensor placement algorithm based on a dynamical systems approach. The approach utilizes the finite dimensional Perron-Frobenius (PF) concept. The PF operator (or the Markov matrix) is used to construct an observability gramian that naturally incorporates sensor accuracy, location constraints, and sensing constraints. The algorithm determines the response times, sensor coverage maps, and the number of sensors needed. The utility of the procedure is illustrated using four examples: a literature example of the flow field inside an aircraft cabin and three air flow fields in different geometries. The effect of the constraints on the response times for different sensor placement scenarios is investigated. Knowledge of the response time and coverage of the multiple sensors aides in the design of mechanical systems and response mechanisms. The methodology provides a simple process for place sensors in a building, analyze the sensor coverage maps and response time necessary during extreme events, as well as evaluate indoor air quality. The theory established in this paper also allows for future work in topics related to construction of classical estimator problems for the sensors, real-time contaminant transport, and development of agent dispersion, contaminant isolation/removal, and evacuation strategies.

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Section: Sensor Placement Methodsmentioning

confidence: 99%

Section: Sensor Placement Methodsmentioning

confidence: 99%

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A methodology for optimal placement of sensors in enclosed environments: A dynamical systems approach

Fontanini

Vaidya

Ganapathysubramanian

2016

Building and Environment

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“…(13) respectively. We refer the readers to [8] for more details on the numerical aspects of this approximation process.…”

Section: Definition 8 (Almost Everywhere (Ae) Uniform Stability) Fmentioning

confidence: 99%

“…The application of the proposed framework on a realistic building system model incorporating all the necessary physics and dynamics is currently being pursued [8,9]. The vector field that we use for the purpose of simulation is the average velocity field obtained from a detailed finite element-based simulation of Navier-Stokes equation.…”

Section: Placement Of Sensors In Building Systemmentioning

confidence: 99%

Operator theoretic framework for optimal placement of sensors and actuators for control of nonequilibrium dynamics

Sinha

Vaidya

Rajaram

2016

Journal of Mathematical Analysis and Applications

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In this paper, we present a novel operator theoretic framework for optimal placement of actuators and sensors in nonlinear systems. The problem is motivated by its application to control of nonequilibrium dynamics in the form of temperature in building systems and control of oil spill in oceanographic flow. The controlled evolution of a passive scalar field, modeling the temperature distribution or density of oil dispersant, is governed by a linear advection partial differential equation (PDE) with spatially located actuators and sensors. Spatial locations of actuators and sensors are optimized to maximize the controllability and observability regions of the linear advection PDE. Linear transfer Perron-Frobenius and Koopman operators, associated with the advective velocity field, are used to provide an analytical characterization for the controllable and observable spaces of the advection PDE. Set-oriented numerical methods are proposed for the finite dimensional approximation of the linear transfer operators. The finite dimensional approximation is shown to introduce weaker notion of controllability and observability, referred to as coarse controllability and observability. The finite dimensional approximation is used to formulate the optimization problem for the optimal placement of sensors and actuators. The optimal placement problem is a combinatorial optimization problem. However, the positivity property of the linear transfer operator is exploited to provide an exact solution to the optimal placement problem using greedy algorithm. Application of the framework is demonstrated for the placement of sensors in a building system for the detection of contaminants and for optimal release of dispersant location for control of contaminant in a Double Gyre velocity field. Simulation results reveal interesting connections between the optimal location of actuators and sensors, maximizing the controllability and observability regions respectively, and the coherent structures in the fluid flow.

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Modeling transient particle transport by fast fluid dynamics with the Markov chain method

2019

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Fast simulation tools for the prediction of transient particle transport are critical in designing the air distribution indoors to reduce the exposure to indoor particles and associated health risks. This investigation proposed a combined fast fluid dynamics (FFD) and Markov chain model for fast predicting transient particle transport indoors. The solver for FFD-Markov-chain model was programmed in OpenFOAM, an open-source CFD toolbox. This study used two cases from the literature to validate the developed model and found well agreement between the transient particle concentrations predicted by the FFD-Markov-chain model and the experimental data. This investigation further compared the FFD-Markov-chain model with the CFD-Eulerian model and CFD-Lagrangian model in terms of accuracy and efficiency. The accuracy of the FFD-Markov-chain model was similar to that of the other two models. For the two studied cases, the FFD-Markovchain model was 4.7 and 6.8 times faster, respectively, than the CFD-Eulerian model, and it was 137.4 and 53.3 times faster than the CFD-Lagrangian model in predicting the steady-state airflow and transient particle transport. Therefore, the FFD-Markov-chain model is able to greatly reduce the computing cost for predicting transient particle transport in indoor environments. Keywordscomputational fluid dynamics, indoor environment, Eulerian model, Lagrangian model, particle dispersion, aerosol dynamics Article History

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Constructing Markov matrices for real-time transient contaminant transport analysis for indoor environments

Cited by 27 publications

References 29 publications

A methodology for optimal placement of sensors in enclosed environments: A dynamical systems approach

A methodology for optimal placement of sensors in enclosed environments: A dynamical systems approach

Operator theoretic framework for optimal placement of sensors and actuators for control of nonequilibrium dynamics

Modeling transient particle transport by fast fluid dynamics with the Markov chain method

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