Real-Time Reconstruction of Contaminant Dispersion from Sparse Sensor Observations with Gappy POD Method

Abstract

Real-time estimation of three-dimensional field data for enclosed spaces is critical to HVAC control. This task is challenging, especially for large enclosed spaces with complex geometry, due to the nonuniform distribution and nonlinear variations of many environmental variables. Moreover, constructing and maintaining a network of sensors to fully cover the entire space is very costly, and insufficient sensor data might deteriorate system performance. Facing such a dilemma, gappy proper orthogonal decomposition (POD) offers a solution to provide three-dimensional field data with a limited number of sensor measurements. In this study, a gappy POD method for real-time reconstruction of contaminant distribution in an enclosed space is proposed by combining the POD method with a limited number of sensor measurements. To evaluate the gappy POD method, a computational fluid dynamics (CFD) model is utilized to perform a numerical simulation to validate the effectiveness of the gappy POD method in reconstructing contaminant distributions. In addition, the optimal sensor placement is given based on a quantitative metric to maximize the reconstruction accuracy, and the sensor placement constraints are also considered during the sensor design process. The gappy POD method is found to yield accurate reconstruction results. Further works will include the implementation of real-time control based on the POD method.Energies 2020, 13, 1956 2 of 12 dynamics (FFD) [17][18][19][20][21][22], and zonal models [23][24][25] can provide three-dimensional field data for an indoor environment with only a small number of boundary conditions that are, however often difficult to obtain in real applications. Even though CFD have been widely employed for predicting the spatial variation of indoor environmental variables [26], the large amount of computational time makes real-time prediction extremely difficult and, thereby, unlikely to achieve real-time control. To overcome the large computational cost, the FFD model is proposed by solving the continuity equation and unsteady Navier-Stokes equations with a time-splitting approach [21]. In addition, the computational speed of FFD could be further accelerated by using parallel and GPU computing [19]. Considering its reasonable accuracy and high computational efficiency, the FFD method has been extensively studied for fast simulation of transient flow [18,19] and for inverse design of the ventilation parameters [20]. Although the reduction in computing time is significant, it is still computationally costly to implement, especially for real-time control. Different from CFD and FFD models, the zonal models are easily incorporated into the control system [25] and require very little computation time, because they only solve energy and mass balance equations at each thermal zone. However, based on the assumption that all quantities are uniform at each zone, zonal models are unable to provide detailed spatial information for a room space [23]. The third category is the data-driven approach. The artif...

Investigating the Performance of a Super High-head Francis Turbine under Variable Discharge Conditions Using Numerical and Experimental Approach

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