A Bayesian parameter estimation methodology for updating the distributions of the duration-based variables used in post-earthquake building recovery modeling is presented. The distributions of the recovery-related parameters specified in the resilience-based earthquake design initiative (REDi) and HAZUS are used as the basis of the priors. A data set of observed building damage and recovery following the 2014 South Napa earthquake is assembled and used to illustrate the proposed methodology. The recovery data set includes the permit acquisition and repair time for over 800 buildings affected by the earthquake. With this data, the conjugate prior (CP) and Markov Chain Monte Carlo (MCMC) methods are implemented to update the probability distribution parameters for the duration-based recovery variables. While the CP approach is easier to implement because it offers an analytical solution, the MCMC provides more flexibility in terms of the types of prior and sampling distributions that can be accommodated. Moreover, the results from a comparative implementation on the Napa data set shows that the MCMC method provides a reasonable approximation of the posterior marginal distribution of the duration-based recovery variables relative to the CP analytical solution.
A Bayesian Data Analytics Approach to Buildings' Thermal Parameter Estimation
Modeling buildings' heat dynamics is a complex process which depends on various factors including weather, building thermal capacity, insulation preservation, and residents' behavior. Gray-box models offer an explanation of those dynamics, as expressed in a few parameters specific to built environments that can provide compelling insights into the characteristics of building artifacts. In this paper, we present a systematic study of Bayesian approaches to modeling buildings' parameters, and hence their thermal characteristics. We build a Bayesian state-space model that can adapt and incorporate buildings' thermal equations and postulate a generalized solution that can easily adapt prior knowledge regarding the parameters. We then show that a faster approximate approach using Variational Inference for parameter estimation can posit similar parameters' quantification as that of a more time-consuming Markov Chain Monte Carlo (MCMC) approach. We perform extensive evaluations on two datasets to understand the generative process and attest that the Bayesian approach is more interpretable. We further study the effects of prior selection on the model parameters and transfer learning, where we learn parameters from one season and reuse them to fit the model in other seasons. We perform extensive evaluations on controlled and real data traces to enumerate buildings' parameters within a 95% credible interval.
more »
« less
- Award ID(s):
- 1544687
- NSF-PAR ID:
- 10113138
- Date Published:
- Journal Name:
- ACM e-Energy '19 Proceedings of the Tenth ACM International Conference on Future Energy Systems
- Page Range / eLocation ID:
- 89 to 99
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
-
In this paper, we propose MetaMobi, a novel spatio-temporal multi-dots connectivity-aware modeling and Meta model update approach for crowd Mobility learning. MetaMobi analyzes real-world Wi-Fi association data collected from our campus wireless infrastructure, with the goal towards enabling a smart connected campus. Specifically, MetaMobi aims at addressing the following two major challenges with existing crowd mobility sensing system designs: (a) how to handle the spatially, temporally, and contextually varying features in large-scale human crowd mobility distributions; and (b) how to adapt to the impacts of such crowd mobility patterns as well as the dynamic changes in crowd sensing infrastructures. To handle the first challenge, we design a novel multi-dots connectivity-aware learning approach, which jointly learns the crowd flow time series of multiple buildings with fusion of spatial graph connectivities and temporal attention mechanisms. Furthermore, to overcome the adaptivity issues due to changes in the crowd sensing infrastructures (e.g., installation of new ac- cess points), we further design a novel meta model update approach with Bernoulli dropout, which mitigates the over- fitting behaviors of the model given few-shot distributions of new crowd mobility datasets. Extensive experimental evaluations based on the real-world campus wireless dataset (including over 76 million Wi-Fi association and disassociation records) demonstrate the accuracy, effectiveness, and adaptivity of MetaMobi in forecasting the campus crowd flows, with 30% higher accuracy compared to the state-of-the-art approaches.more » « less
-
null (Ed.)A plethora of complex dynamical systems from disordered media to biological systems exhibit mathematical characteristics (e.g., long-range dependence, self-similar and power law magnitude increments) that are well-fitted by fractional partial differential equations (PDEs). For instance, some biological systems displaying an anomalous diffusion behavior, which is characterized by a non-linear mean-square displacement relation, can be mathematically described by fractional PDEs. In general, the PDEs represent various physical laws or rules governing complex dynamical systems. Since prior knowledge about the mathematical equations describing complex dynamical systems in biology, healthcare, disaster mitigation, transportation, or environmental sciences may not be available, we aim to provide algorithmic strategies to discover the integer or fractional PDEs and their parameters from system's evolution data. Toward deciphering non-trivial mechanisms driving a complex system, we propose a data-driven approach that estimates the parameters of a fractional PDE model. We study the space-time fractional diffusion model that describes a complex stochastic process, where the magnitude and the time increments are stable processes. Starting from limited time-series data recorded while the system is evolving, we develop a fractional-order moments-based approach to determine the parameters of a generalized fractional PDE. We formulate two optimization problems to allow us to estimate the arguments of the fractional PDE. Employing extensive simulation studies, we show that the proposed approach is effective at retrieving the relevant parameters of the space-time fractional PDE. The presented mathematical approach can be further enhanced and generalized to include additional operators that may help to identify the dominant rule governing the measurements or to determine the degree to which multiple physical laws contribute to the observed dynamics.more » « less
-
De Vico Fallani, Fabrizio (Ed.)The exponential family random graph modeling (ERGM) framework provides a highly flexible approach for the statistical analysis of networks (i.e., graphs). As ERGMs with dyadic dependence involve normalizing factors that are extremely costly to compute, practical strategies for ERGMs inference generally employ a variety of approximations or other workarounds. Markov Chain Monte Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the maximum likelihood estimator (MLE) of ERGM parameters, and is generally feasible for typical models on single networks with as many as a few thousand nodes. MCMC-based algorithms for Bayesian analysis are more expensive, and high-quality answers are challenging to obtain on large graphs. For both strategies, extension to the pooled case—in which we observe multiple networks from a common generative process—adds further computational cost, with both time and memory scaling linearly in the number of graphs. This becomes prohibitive for large networks, or cases in which large numbers of graph observations are available. Here, we exploit some basic properties of the discrete exponential families to develop an approach for ERGM inference in the pooled case that (where applicable) allows an arbitrarily large number of graph observations to be fit at no additional computational cost beyond preprocessing the data itself. Moreover, a variant of our approach can also be used to perform Bayesian inference under conjugate priors, again with no additional computational cost in the estimation phase. The latter can be employed either for single graph observations, or for observations from graph sets. As we show, the conjugate prior is easily specified, and is well-suited to applications such as regularization. Simulation studies show that the pooled method leads to estimates with good frequentist properties, and posterior estimates under the conjugate prior are well-behaved. We demonstrate the usefulness of our approach with applications to pooled analysis of brain functional connectivity networks and to replicated x-ray crystal structures of hen egg-white lysozyme.more » « less
-
The energy consumption of buildings at the city scale is highly influenced by the weather conditions where the buildings are located. Thus, having appropriate weather data is important for improving the accuracy of prediction of city-level energy consumption and demand. Typically, local weather station data from the nearest airport or military base is used as input into building energy models. However, the weather data at these locations often differs from the local weather conditions experienced by an urban building, particularly considering most ground-based weather stations are located far from many urban areas. The use of the Weather Research and Forecasting Model (WRF) coupled with an Urban Canopy Model (UCM) provides means to predict more localized variations in weather conditions. However, despite advances made in climate modeling, systematic differences in ground-based observations and model results are observed in these simulations. In this study, a comparison between WRF-UCM model results and data from 40 ground-based weather station in Austin, TX is conducted to assess existing systematic differences. Model validations was conducted through an iterative process in which input parameters were adjusted to obtain to best possible fit to the measured data. To account for the remaining systemic error, a statistical approach with spatial and temporal bias correction is implemented. This method improves the quality of the WRF-UCM model results by identifying the statistic properties of the systematic error and applying several bias correction techniques.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3307772.3328316
