Indoor physical field estimation from sparse sensor observations
Date of Issue2017-08-29
School of Electrical and Electronic Engineering
Indoor physical fields (e.g. thermal map, pressure field, air velocity field, etc.) are very useful information for energy efficient air-conditioning system design. Computational fluid dynamics (CFD) simulation is the most popular tool to estimate indoor physical fields. But the simulation is computationally expensive and time-consuming. The simulation results are also inaccurate compared with sensor observations. Therefore, a new method to rapidly find the accurate estimation of indoor physical fields is very interesting. In this work, we show how sparse sensor observations can be effectively used for indoor physical fields estimation by solving the three research problems: 1. Calibration of simulated physical fields using sparse sensor observations; 2. Reconstruction of physical fields from sparse sensor observations; 3. Sensor placement for the optimal physical field reconstruction. Current CFD calibration work has mainly focused on the calibration of input parameters of CFD simulation. No reported publication has considered the calibration of the simulation results. We took inspiration from the image editing problem and developed a methodology to calibrate the simulated physical fields based on sparse sensor observations. We formulated the calibration work to be an optimization problem. The cost function consists of two terms. One term guarantees a good local adjustment of the simulated physical fields. The other term transmits the adjustment from local regions around sensing locations to the global domain. The proposed method can enhance the simulated physical field while preserving the overall original profile. An experiment was implemented in an air-conditioned room to demonstrate the feasibility of the method. Four sensor observations were used to calibrate a simulated thermal map with 167x365 data points. The experimental results show the effectiveness of the proposed method. We then provided a two-stage physical field reconstruction approach to rapidly reconstruct a physical field from the observed input parameters of the CFD simulation and sparse observations of the physical field. With a physical field database obtained from CFD simulations, we can find the principal component analysis (PCA) modes of the physical fields. In the first stage, we built a regression model between the input parameters and the PCA coefficients. To find this model, we provided a scaled extreme learning machine (sELM) algorithm. With the regression model, we can obtain the PCA coefficients and reconstruct an approximated physical field. In the second stage, we estimated the error of the approximated physical field from sparse sensor observations, with which we can correct the physical field estimated in the first stage. The proposed method is shown better than current methods even using fewer sensor observations. With the above results, we noted that sensor placement is a critical problem for physical field reconstruction. To address the problem, we develop a new greedy algorithm, named maximal projection on minimum eigenspace (MPME). In this algorithm, we select the sensing locations one-by-one. The least number of required sensors can be determined by checking whether the estimation accuracy is satisfied after each sensing location is determined. The minimum eigenspace is defined as the eigenspace associated with the minimum eigenvalue of the dual observation matrix. For each sensing location, the projection of its observation vector onto the minimum eigenspace is shown to be monotonically decreasing w.r.t. the worst case error variance (WCEV) of the estimated parameters. We select the sensing location whose observation vector has the maximum projection onto the minimum eigenspace of the current dual observation matrix. The proposed MPME is shown to be one of the most computationally efficient algorithms. Our Monte-Carlo simulations show that MPME outperforms the state of the art, especially when the number of available sensors is very limited. The MPME algorithm can be easily used for the indoor physical field reconstruction, but the current methods cannot because of their high storage requirement and high computation cost.