A comparison of model order reduction methods for the simulation of wall heat transfer

In this paper, the potential of model order reduction for simulating building performance is assessed, via a case study of modelling heat transfer through a massive masonry wall. Two model order reduction techniques – proper orthogonal decomposition and proper generalized decomposition – are investigated and compared. Moreover, to illustrate the performance of model order reduction techniques, the accuracies of the two model order reduction techniques are respectively compared with a standard finite element method. The outcomes show that both of the two model order reduction techniques are able to provide an accurate result, and the proper generalized decomposition tends to be more versatile than the proper orthogonal decomposition method

Development of a Composite Technique for Preconditioning of 41Cr4 Steel Used as Gear Material: Examination of Its Microstructural Characteristics and Properties

Commercial 41Cr4 (ISO standard) steel was treated by a composite technique. An intermediate layer was introduced firstly at the 41Cr4 steel surface by traditional carburizing and nitriding. Then a hard Cr coating was brush-plated on the intermediate layer. Finally, the coating layer was modified by high current pulsed electron beam (HCPEB), followed by quenching and subsequent tempering treatment. The microstructure, mechanical properties, and fracture behavior were characterized. The results show that a nanocrystalline Cr coating is formed at the 41Cr4 steel surface by the treatment of the new composite technique. Such nanocrystalline Cr coating has acceptable hardness and high corrosion resistance performance, which satisfies the demands of the gears working under high speed and corrosive environment. The composite process proposed in this study is considered as a new prospect method due to the multifunction layer design on the gear surface

Study of Alloying Process on 40Cr Surface with Electron Beam after Electroplated Cr Layer

The electroplated hard chromium coat was selected as precoating to improve surface properties of 40Cr. Then electron beam alloying process was experimentalized. The relation rules were summarized between alloying process parameters and overall surface properties by surface morphology observation, surface energy spectrum analysis, EDX analysis in section, and XRD. Experiment results showed that the microcracks appeared on surface of electron beam alloying specimen. Microcracks could disappear when the orthogonal experimental optimum process was used. The matrix metal elements diffused into metal coating surface after electron beam treatment. The maximum depth of alloyed layer could reach 8 μm after electron beam alloying treatment, and electron beam alloying process generated new residual austenite phase

Efficient Probabilistic Assessment of Hygrothermal Performance: Sequential Monte Carlo and Decomposition Methods

In the my PhD project, we are going to improve the computational efficiency of probabilistic hygrothermal assessment mainly based on two approaches. The first approach focuses on the core model itself and aims at reducing the computation time for a single deterministic simulation. In this project these core simulation models are mainly about wall models which simulate the hygrothermal behavior of building materials and components in multi-layer walls. Several one-(1D) , two or three-(2 or 3D) dimensional models can be found in the literature. However, the application of these models is usually very time consuming due to the high degrees of freedom after the spatial and temporal discretization. Instead of these original models, Van Gelder et al used statistical surrogate models (such as polynomial regression model, Kriging etc.) to reduce the simulation time. However, since these statistical surrogate models can only deliver static results, surrogate models that allow mimicking the dynamic behavior (such as time evolution of temperatures, ...), need to be developed. In order to lower the computational complexity and obtain the dynamic behavior of the original model, model order reduction (MOR) methods are usually used. Through model order reduction, a large original model is approximated by a reduced model and the solution of the original system can be recovered from the solution of the reduced model. The second possible approach is going to restrict the number of needed repetitions of the core deterministic model in the framework of Monte Carlo method, which is the tool applied for estimating the probability distribution of the output parameters, and the current state-of-the-art in the Monte Carlo Method is based on a replicated optimized Latin hypercube sampling strategy. Optimized Latin hypercube sampling is a sampling strategy which divides each parameter into n intervals then makes sure that only a single sample is placed in each interval. Even though Optimized Latin hypercube sampling has a good convergence rate ( 1/n), since it is a variance-reduction method it becomes difficult to monitor it's convergence. In order to make convergence monitoring possible, replicated Latin hypercube sampling has been presented by Janssen, which uses permutated repetitions of smaller designs to reach the set number of runs n instead of single n-run Optimized Latin hypercube design. As a consequence, it allows evaluating the variances on the Monte Carlo outcomes which in turn permits halting the calculation when the desired accuracy levels are reached. However, the main drawback of this methods is, it does not converge as fast as normal optimal Latin hypercube designs. Another sampling design approach is to use low-discrepancy sampling designs to create the input variables of the Monte Carlo framework. Singhee [6] showed that low discrepancy sampling designs can often be a better choice compared to both simple random sampling and Latin Hypercube Sampling method due to it's lower variance, faster convergence and better accuracy. This result motivates us to study the application of sequential sampling method based on a low discrepancy design for improving the efficiency of Monte Carlo analysis.status: publishe

The use of proper orthogonal decomposition for the simulation of highly nonlinear hygrothermal performance

In this paper, the use of proper orthogonal decomposition for simulating nonlinear heat, air and moisture transfer is investigated via two applications: HAMSTAD benchmarks 2 and 3. Moreover, the potential of the reduced models constructed by proper orthogonal decomposition for simulating new problems with longer simulation periods is assessed. To illustrate the feasibilities of proper orthogonal decomposition method in the field of building physics, the accuracies of the reduced models are compared with the standard finite element method. The outcomes show that with a sufficient number of construction modes and a relatively large amount of snapshots, proper orthogonal decomposition method can deliver accurate results. In addition, guidelines on selecting an appropriate amount of simulation snapshot and construction modes are provided

The use of proper orthogonal decomposition for the simulation of highly nonlinear hygrothermal performance

status: publishe

A comparison of model order reduction methods for the simulation of wall heat transfer

status: publishe

Model order reduction for efficient deterministic and probabilistic assessment of building envelope thermal performance

status: Published onlin

Quasi-Monte-Carlo-based probabilistic assessment of wall heat loss

© 2017 The Authors. Published by Elsevier Ltd. In this paper, the potential of quasi-Monte Carlo methods for uncertainty propagation is assessed, via a case study of heat loss through a massive masonry wall. Four quasi-Monte Carlo sampling strategies-Optimized Latin hypercube, Sobol sequence, Niederreiter-Xing sequence and Good Lattice sequence-are applied and compared. Moreover, in order to terminate the quasi-Monte Carlo simulation when the desired accuracy is reached, an error estimation method is implemented. The outcomes show that all the four quasi-Monte Carlo methods outperform the standard Monte Carlo method; the Niederreiter-Xing sequence and Sobol sequence tend to be the best.status: publishe

POD–DEIM model order reduction for nonlinear heat and moisture transfer in building materials

status: publishe