Hans Janssen

Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence

Monte Carlo analysis has become nearly ubiquitous since its introduction, now over 65 years ago. It is an important tool in many assessments of the reliability and robustness of systems, structures or solutions. As the deterministic core simulation can be lengthy, the computational costs of Monte Carlo can be a limiting factor. To reduce that computational expense as much as possible, sampling efficiency and convergence for Monte Carlo are investigated in this paper. The first section shows that non-collapsing space-filling sampling strategies, illustrated here with the maximin and uniform Latin hypercube designs, highly enhance the sampling efficiency, and render a desired level of accuracy of the outcomes attainable with far lesser runs. In the second section it is demonstrated that standard sampling statistics are inapplicable for Latin hypercube strategies. A sample-splitting approach is put forward, which in combination with a replicated Latin hypercube sampling allows assessing the accuracy of Monte Carlo outcomes. The assessment in turn permits halting the Monte Carlo simulation when the desired levels of accuracy are reached. Both measures form fairly noncomplex upgrades of the current state-of-the-art in Monte-Carlo based uncertainty analysis but give a substantial further progress with respect to its applicability.

Comparative study of metamodelling techniques in building energy simulation: guidelines for practitioners

Computer simulation of real system behaviour is increasingly used in research and development. As simulation models become more reliable, they also often become more complex to capture the progressive complexity of the real system. Calculation time can be a limiting factor for using simulation models in optimisation studies, for example, which generally require multiple simulations. Instead of using these timeconsuming simulation models, the use of metamodels can be considered. A metamodel approximates the original simulation model with high condence via a simplied mathematical model. A series of simulations then only takes a fraction of the original simulation time, hence allowing signicant computational savings. In this paper, a strategy that is both reliable and time-ecient is provided in order to guide users in their metamodelling problems. Furthermore, polynomial regression (PR), multivariate adaptive regression splines (MARS), kriging (KR), radial basis function networks (RBF), and neural networks (NN) are compared on a building energy simulation problem. We nd that for the outputs of this example and based on Root Mean Squared Error (RMSE), coecient of determination (R 2 ), and Maximal Absolute Error (MAE), KR

Simulation efficiency and accuracy of different moisture transfer potentials

Simulation models for moisture transfer in building materials are highly incongruent with respect to the moisture potential used. Often the relatively better numerical efficiency and accuracy of a certain moisture potential is put forward as motivation. Various claims are made in that respect, but factual evidence is typically lacking. This paper aims at providing such support by assessing simulation efficiency and accuracy for capillary pressure, relative humidity and -log(-capillary pressure). To that goal, a suite of benchmark simulations are performed with those three potentials and performances are compared, based on deviations from reference solutions and on numbers of iterations required. The study initially reveals mixed results, showing no consistent advantages for either potential. Further analysis uncovers though that -log(-capillary pressure) suffers from a strongly nonlinear moisture capacity near saturation. This finally results in a decision in favour of capillary pressure and relative humidity, at least for general-purpose moisture transfer simulation.

Evaluation of Sub-Zonal Airflow Models for the Prediction of Local Interior Boundary Conditions – Natural and Forced Convection Cases

Currently, researchers are striving to advance the possibilities to calculate the integrated phenomena of heat, air and moisture flows in buildings, with specific focus on the interactions between the building zones and building components. This paper presents an investigation of the capability and applicability of the sub-zonal airflow model to predict the local indoor environmental conditions, as well as the local surface transfer coefficients near building components. Two test cases were analyzed for, respectively, natural and forced convection in a room. The simulation results predicted from the sub-zonal airflow models are compared to experimental data and numerical computational fluid dynamics (CFD) results. The study shows that sub-zonal models combined with an appropriate surface transfer coefficient model are able to give reliable predictions of the local indoor environmental conditions and surface transfer coefficients near the building component for the analyzed cases. The relatively short computation time and flexibility of the sub-zonal model makes the application attractive for transient simulation of heat, air and moisture transport in buildings. However, the availability of appropriate reference conditions, for example experimental or numerical results, is a prerequisite for the development of a reliable sub-zonal model.

Adaptive integration of element matrices in finite-element moisture transfer simulations

While serving different purposes, numerical simulations of moisture and heat transfer in soils and in building components are very similar in methodology: in both cases, spatially and temporally discretised equations for transfer of moisture and heat in porous materials are solved subject to (atmospheric) boundary conditions. The strongly non-linear transfer equations and boundary conditions however render such hygrothermal simulations computationally very expensive, and an efficient numerical solution algorithm is required. Such increasingly efficient numerical solution schemes allow for more, larger, longer or more precise simulations, widening the application capabilities of hygrothermal simulations. The computational cost of hygrothermal simulations revolves around the serial iterative com-position and decomposition of the coefficient matrix of the system of algebraic equations de-scribing the discretised moisture and heat transfer, and is thus determined by the cost of one (de)composition, and the number of required (de)compositions. This article presents two op-timisation measures for simulations of moisture and heat transfer in building components un-der atmospherical excitation: adaptive integration and variations on the Newton-Raphson iterative scheme. Adaptive integration targets the cost of one (de)composition, while the varia-tions on Newton-Raphson aims at the number of required (de)compositions. While exempli-fied by building physical simulations, the presented optimisation measures are equally valid for simulations of moisture and heat transfer in soils. It will be demonstrated that the common preference for low-order numerical integration of the finite element matrices has an adverse effect on the required spatial discretisation: a fine dis-cretisation throughout is needed for accurate simulation of the moving moisture fronts typical of infiltration problems. Adaptive integration allows to merge low-order numerical integration with rougher spatial discretisations, reducing the number of required integration points and of discretisation nodes. A second section of the article investigates the efficiency of (variations on) the Newton-Raphson scheme. It will be demonstrated that appropriate application of Newton-Raphson on the boundary conditions, of modified iteration and of separate convergence criteria can drastically diminish the number of required (de) compositions.

A determination methodology for the spatial profile of the convective heat transfer coefficient on building components

Several experimental procedures have been established to determine the convective heat transfer coefficient, a frequently used parameter in many engineering disciplines. Almost all of these methodologies focus on point or spatially averaged values. Yet, in many studies the spatial profile of the local convective heat transfer is of importance. In this paper, a methodology to determine such spatial profile is proposed. In this method, experiments are combined with Monte Carlo simulations. Such an approach makes it possible to account for inaccuracies in the input data. As an example, the methodology is applied to determine the spatial profile of the local convective heat transfer coefficient near a corner for two thermal bridge configurations. The temperature difference between interior surface and indoor air is found to restrict the applicability of the method. Nonetheless, for the case with a sufficient temperature difference, the order of magnitude of the convective heat transfer coefficients further away from the corner is in line with literature data. An important limitation of the technique at this stage of its development is, however, its requirement for prior knowledge of the equation that describes the spatial profile of the convective heat transfer coefficient. Despite these drawbacks, the methodology shows much potential and can be valuable for other applications as well.