Grey box model | EPFL Graph Search

In mathematics, statistics, and computational modelling, a grey box model combines a partial theoretical structure with data to complete the model. The theoretical structure may vary from information on the smoothness of results, to models that need only parameter values from data or existing literature. Thus, almost all models are grey box models as opposed to black box where no model form is assumed or white box models that are purely theoretical. Some models assume a special form such as a linear regression or neural network. These have special analysis methods. In particular linear regression techniques are much more efficient than most non-linear techniques. The model can be deterministic or stochastic (i.e. containing random components) depending on its planned use. Model form The general case is a non-linear model with a partial theoretical structure and some unknown parts derived from data. Models with unlike theoretical structures need to be evaluated individuall

District heating and cooling systems to integrate renewable energy in urban areas

Francesca Belfiore

The building sector plays a crucial role in the ongoing energy transition due to its significant share of global energy consumption and carbon dioxide emissions, especially when combined with the estimation that 70% of the world's population will be living in urban areas by 2050.District heating and cooling (DHC) systems have been widely recognized among the viable options as an effective solution for achieving the challenging mid-century targets. In the context of decarbonizing and electrifying the thermal energy requirements in urban areas, this thesis provides a methodology for optimally designing district energy systems (DES).The thermal demand of existing non-residential buildings was first estimated through the development and calibration of grey-box models. Despite challenges and limitations of relying on measured data, doing so allows the definition of optimal operating temperatures for a future energy system. Comparing models calibrated with measurements obtained over different time resolutions revealed the poor performance of heating signature approaches when reconstructing hourly profiles and the potential of the clustering process of balancing modelling errors at the annual level. A flexible mixed-integer linear programming superstructure was then developed to systematically investigate optimal DHC configurations, including the sizing and operation of conversion technologies, as well as the type, layout, diameter, and operating temperatures of the thermal network. Comparing different solutions under economic, environmental and exergy-based key-performance indicators, demonstrated the potential of the anergy network to reduce investment costs without deteriorating systems performance. Additionally, a sensitivity analysis revealed that hybrid configurations with an intermediate degree of decentralization are the most robust to cost uncertainties.Finally, given that 90% of the existing DES worldwide are based on fossil fuels, the developed methods were further enhanced to address the optimal retrofit and expansion of existing systems. Particular focus was given to network expansion, replacing fossil-based technologies with more sustainable heat pumps, and synergies between heating and cooling requirements. Applying the developed methods to a case study further demonstrated both the sustainability and improved economics of the multi-temperature level configuration compared with the fossil-based, high temperature option.The work presented was carried out in collaboration with an international airport to assist their transition towards a fossil-free energy system based on a low temperature network.

EPFL2021

Spectroscopie mécanique de la relaxation des contraintes d'interface dans les composites à matrice métallique

Metal matrix composites are known for their excellent specific mechanical properties. Nevertheless, because of the thermal expansion mismatch between the matrix and the reinforcements, thermal stresses arise at the interfaces of such materials. In order to relax these stresses, dislocations are emitted from the interface and propagate in the matrix, which can influence the mechanical behavior of the composite material. Mechanical spectroscopy, which characterizes the ability of a solid to dissipate energy under an external excitation, was used to study the relaxation mechanisms occurring at the interface of MMCs. Indeed, the mobile matrix dislocations near the interface are the main sources of damping, making this technique very sensitive to these mechanisms. Composites studied here were processed by gas-pressure infiltration of the reinforcement preform by the molten metal. The processed composites were based on aluminum, magnesium and Mg-2%Si alloy, which is known for its high damping level. They were reinforced by short misorientated alumina fibers or long and aligned carbon and silicon carbide fibers. In the case of long fibers, two types of orientation were obtained: parallel or perpendicular to the composite axis. In order to modify the interface morphology, a heat treatment was carried out on aluminium matrix composites reinforced by alumina fibers during the infiltration process. By increasing the contact time between the molten matrix and the fibers, alumina crystals were formed on the surface of the fibers, whose size increased with time. The specific elastic moduli of the processed composites were clearly superior to those of matrix alone and their value agreed well with the existing theoretical models. Composites were submitted to thermal cycles from 120 K to 500 K and the internal friction and dynamical modulus were measured as a function of temperature. It was shown that the behavior of these two parameters, the large maximum at low temperatures and the modulus anomaly in the case of magnesium composites was driven by the motion of the dislocations activated in the matrix in order to relax thermal stresses. The internal friction was also characterized by a transient contribution, depending on the heating or cooling rate dT/dt and the excitation frequency ω. By using a model developed by Mayencourt and al., it was possible to determine two parameters C1 and C2 which were sensitive respectively to the mobile dislocation density relaxing the thermal stresses and the interface strength. The difference in the behavior of these two parameters as a function of temperature tended to show the great potential of the magnesium matrix composites. Indeed, the interface strength was decreasing at low temperature, allowing a better toughness whereas it was increasing at high temperature, improving the creep resistance. Finally, in the case of the aluminum matrix composites reinforced by short fibers with alumina crystals at the interface, it was observed that the elastic modulus was decreasing as crystal size increased. However, when the crystals exceeded a certain size, they were acting as pinning points between matrix and fibers, resulting in the increase of the modulus almost to its initial value. By determining the parameter C1 from the transient damping, it was shown that this parameter followed the same trend as the elastic modulus, which made it a good probe for the interface quality.

EPFL2004

High volume fraction particulate and interpenetrating phase composites (IPC)

Ghodratollah Roudini

The role of reinforcing phase contiguity in high volume fraction particulate composites is investigated using model composites of pure aluminium reinforced with α-Al2O3 particles. To produce the composites, alumina particle (5µm) preforms were either loosely packed or, alternatively, packed and CIPed; these were then sintered, varying the sintering time and temperature, and infiltrated with pure liquid aluminium using gas pressure infiltration. The microstructure of the resulting composites was characterized using image analysis in terms of reinforcement phase contiguity (β), defined as the ratio of particle surface that is in contact with other particles to that in contact with the matrix. The influence of this parameter on several characteristics of the composites and the preforms they were made from was then studied, using theoretical models in the literature to isolate the influence of this parameter from that of other variables, such as the volume fraction ceramic. To this end, the thermal conductivity of the sintered preforms, basic composite mechanical properties (hardness, tensile strength, and damage evolution during straining) and the thermal expansion of the composites were characterized and compared with theory; furthermore, quenching and neutron diffraction were used to probe in more depth the thermal expansion behaviour of the composites. The results show that the thermal conductivity of the preform increases, as expected, upon increasing the relative density (volume fraction) and the contiguity of alumina particle after sintering. Comparison of data with theory shows that, while experimental values for the CIPed samples agree with the prediction by Argento and Bouvard for the thermal conductivity of powder preforms as a function of densification, neither this model, nor that of Montes et al. , fits all experimental values. Rather, when pooled the data show that the thermal conductivity of powder preforms, normalized for relative density using the differential effective medium model, obeys relatively well a simple linear relation between contiguity and conductivity. The hardness of the composite increases with increasing relative density and increasing contiguity. Here again, after normalization for the dependence of hardness on ceramic volume fraction using current theory, a nearly linear relation is found between hardness and contiguity. Tensile testing results show that the strength of the composite increases with increasing fraction ceramic and increasing contiguity while the elongation decreases, composites with an interconnected ceramic phase rapidly becoming quite brittle, with elongations falling below half a percent. No clear relationship is found between contiguity and Young's modulus after normalization for the volume fraction ceramic. Measurements of internal damage evolution show that damage increases very rapidly with deformation in the present interconnected composites, in agreement with their brittle character. The thermal expansion results show that the CTE of the present composites often varies with temperature at a rate higher than that predicted to result from physical parameter variations by existing theoretical models. With regard to their thermal expansion, the composites can be separated into three classes that are characterized by the level of contiguity of the low expansion phase: low contiguity (i.e. β ≤ 0.045), medium contiguity (i.e. 0.05 ≤ β < 0.074) and high contiguity (i.e. β ≤ 0.074 ). The CTE values during heating for the low contiguity composites lie between Schapery's upper bound and the rule of mixtures, starting upon heat-up from the Schapery upper bound at low temperature and transiting above roughly 150°C to the rule of mixture prediction; upon cool-down the same behaviour is observed in reverse. The CTEs of the composites with medium contiguity at low temperatures are somewhat below the Schapery upper bound, increasing somewhat faster than predicted for this bound with increasing temperature to reach Shapery's upper bound at around 200°C. For the composites with high contiguity, the CTEs lie between elastic and plastic bounds predicted using the self-consistent model, the latter model being obtained by assigning a zero shear stiffness to the matrix. Physical reasoning and comparison of data with theory indicate that these transitions in expansivity of the composites are mostly a result of matrix yield following fully elastic deformation past a certain thermal excursion, this transition being prevented by increased ceramic phase contiguity. This interpretation is confirmed by neutron diffraction results. Increased reinforcement contiguity in the composites also affects the amplitude of strain hysteresis during thermal cycling, the magnitude of hysteresis decreasing in nearly linear fashion with increasing contiguity, reaching zero near β = 15%. Samples that were quenched into liquid nitrogen after a relaxation heat treatment and reheated to room temperature yielded data globally similar to those of as-processed samples. Nitrogen-quenched samples with higher contiguity (β ≥ 0.05) exhibit furthermore signs of ratcheting upon cycling, which was not observed in the composites with low contiguity.

EPFL2008