Stochastic occupancy modeling for spaces with irregular occupancy patterns using adaptive B-Spline-based inhomogeneous Markov Chains
张邯北，Christian Thilker, Henrik Madsen, Rongling Li, 肖赋，
马天佑，徐侃
摘要：
This paper presents a discrete time, discrete state-space in-homogeneous Markov Chains model for stochastic occupancy modeling in spaces with irregular occupancy patterns. The goal of the model is to provide accurate predictions of occupancy numbers, enabling appropriate actions to be taken for HVAC system to maintain optimal indoor environment. The proposed Markov Chain model incorporates time in-homogeneity by coupling the time-varying model parameters using a Periodic B-Spline expansion with adaptive knots, which effectively captures patterns in occupancy activity. This method optimizes the distribution of knots based on specific occupancy characteristics observed in different types of rooms. To evaluate the effectiveness of the proposed method, six months of occupancy data collected from a meeting room are utilized. A comprehensive comparison is conducted between the proposed adaptive B-Spline method and other approaches, including the counting method and uniform B-Spline method. The comparison considers both model accuracy and complexity, using metrics such as the Akaike Information Criterion and Bayesian Information Criterion. Results indicate that the proposed model achieves more accurate predictions with fewer model parameters compared to other methods. These forecasts are particularly useful in optimizing the control of HVAC systems, where accurate predictions of future occupancy numbers are essential.
论文绘图：
Figure 15. 自适应B样条和均匀B样条方法的对数似然、AIC的比较，随着缩放系数（𝑁）的数量变化，以及参数总数和相应的结点归一化分布的结果。
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