Markov chain Monte Carlo (MCMC) methods require a large number of samples to approximate a posterior distribution, which can be costly when the likelihood or prior is expensive to evaluate. The number of samples can be reduced if we can avoid repeated samples and those that are close to each other. This is the idea behind deterministic sampling methods such as Quasi-Monte Carlo (QMC). However, the existing QMC methods aim at sampling from a uniform hypercube, which can miss the high probability regions of the posterior distribution and thus the approximation can be poor. Minimum energy design (MED) is a recently proposed deterministic sampling method, which makes use of the posterior evaluations to obtain a weighted space-filling design in the region of interest. However, the existing implementation of MED is inefficient because it requires several global optimizations and thus numerous evaluations of the posterior. In this article, we develop an efficient algorithm that can generate MED with few posterior evaluations. We also make several improvements to the MED criterion to make it perform better in high dimensions. The advantages of MED over MCMC and QMC are illustrated using an example of calibrating a friction drilling process.

To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of accurately estimating the control-by-noise interactions. Moreover, the existing space-filling designs focus on uniformly distributing the points in the design space, which are not suitable for noise factors because they usually follow nonuniform distributions such as normal distribution. This would suggest placing more points in the regions with high probability mass. However, noise factors also tend to have a smooth relationship with the response and therefore, placing more points toward the tails of the distribution is also useful for accurately estimating the relationship. These two opposing effects make the experimental design methodology a challenging problem. We propose optimal and computationally efficient solutions to this problem and demonstrate their advantages using simulated examples and a real industry example involving a manufacturing packing line. Supplementary materials for the article are available online.

Occupants interact with buildings in various ways via their presence (passive effects) and control actions (active effects). Therefore, understanding the influence of occupants is essential if we are to evaluate the performance of a building. In this paper, we model the mean profiles and variability of occupancy variables (presence and actions) separately. We will use a multi-variate Gaussian distribution to generate mean profiles of occupancy variables, while the variability will be represented by a multi-dimensional time series model, within a framework for a meta-analysis that synthesizes occupancy data gathered from a pool of buildings. We then discuss variants of occupancy models with respect to various outcomes of interest such as HVAC energy consumption and peak demand behavior via a sensitivity analysis. Results show that our approach is able to generate stochastic occupancy profiles, requiring minimum additional input from the energy modeler other than standard diversity profiles. Along with the meta analysis, we enable the generalization of previous research results and statistical inferences to choose occupancy variables for future buildings. The sensitivity analysis shows that for aggregated building energy consumption, occupant presence has a smaller impact compared to lighting and appliance usage. Specifically, being accumulatively 55% wrong with regard to presence, only translates to 2% error in aggregated cooling energy in July and 3.6% error in heating energy in January. Such a finding redirects focus to the accurate estimation of lighting and appliance usage for a better prediction of aggregated energy consumption. Furthermore, it proves that accurate knowledge of the mean profiles is sufficient, that is, stochastic occupancy models do not play a significant role in the prediction of aggregated consumption in a conventional office building where the interaction between the operation of building systems and the spatial and temporal variability of occupancy is weak. When it comes to peak demand behavior, occupancy variability should be taken into account, as static profiles are not able to produce adequate estimates of power duration probabilities close to the power peak. (C) 2016 Elsevier Ltd. All rights reserved.

This paper proposes a lightweight Bayesian calibration of dynamic models that accounts for model parameter uncertainties. A regression model was built to represent the dynamic model using parameter screening and multiple linear regression. Given this regression model and prior probability distributions of its input parameters, a Bayesian calibration method is developed to provide their posterior distributions. A case study is presented and the result shows considerable alignment between model prediction and measurement after calibration. This indicates its capability to perform fast risk-conscious calibration for most current retrofit practice where only monthly consumption and demand data are available.

This paper proposes a generic Bayesian approach for calibrating building energy models. It employs sampling algorithms and parameter screening techniques to select influential model parameters on multiple types of model outputs, and uses Bayesian inference to generate the calibrated, probabilistic estimates of these parameters by incorporating human knowledge and considering parameter uncertainty and model discrepancy. Depending on model complexity and fidelity, it either calibrates the model directly, or uses a linear regression model as the meta-model and uses it to estimate the parameters in the original model. A case study involving both dynamic and reduced-order building energy models demonstrates the proposed approach and the result shows considerable agreement between prediction and measurement.

Computational models have found wide applications in simulating physical systems. Uncertainties in input parameters of the system can greatly influence the outputs, which are studied by Uncertainty Analysis (UA) and Sensitivity Analysis (SA). As the system becomes more complex, the number of input parameters can be large and existing methods for UA and SA are computationally intensive or prohibitive. We propose a unified framework by using a hierarchical variable selection approach to connect UA and SA with one design. By incorporating the effect hierarchy principle and the effect heredity principle, the method works well especially when the number of input parameters is large. Since the procedure requires only one design, it is economical in run size and computationally efficient. Keywords–Uncertainty analysis; Sensitivity analysis; Screening; Effect hierarchy principle; Effect heredity principle; Polynomial chaos expansions.

In current practice, HVAC systems are sized based on standardized procedures that were mostly developed by ASHRAE. The standard approach only implicitly deals with uncertainty in peak system demand through the selection of an appropriate design day and the choice of a safety factor. Although this method works satisfactorily in most cases, it offers no support to a system designer who wants to track the risk associated with an undersized system. The opposite, i.e. avoiding that the system is needlessly oversized deserves even more attention given the fact that current practice of "defensive sizing" leads to oversized systems which leads to wasted capital investment and systems that operate far away from the optimum efficiency loads. This paper explores a new framework to guide the use of uncertainty analysis (UA) and sensitivity analysis (SA) in HVAC system sizing. UA will replace the safety factor with quantified margins based on comprehensive quantification of different sources of uncertainty. A probabilistic-based SA is then used to identify the important individual factors or groups of factors that contribute to uncertainty, providing means of risk management by applying better quality assurance methods or negotiating performance contracts. (C) 2014 Elsevier B.V. All rights reserved.