Structure preserving approach to parametric dynamic compact thermal models of nonlinear heat conduction

In this paper it is shown how parametric dynamic compact thermal models can be exploited for the calibration of detailed thermal models of electronic components and packages. A constrained least square fit of the thermal response of a parametric dynamic compact thermal model, having as parameters the material thermal properties and geometrical details to be calibrated, onto the measured temperature response is performed. Numerical results show that the use of parametric dynamic compact thermal models instead of detailed compact thermal models, in conjunction with an optimization algorithm solving the constrained least square problem, can reduce the computational time for calibration by more than two orders of magnitude.

The goal of this research is to develop a Dynamic Compact Thermal Model (DCTM) of electronic packages. The general objectives of thermal modeling are to increase the accuracy of electrical analysis by taking the effect of temperature variation into consideration, predicting the reliability of the product, and acquiring the information which is necessary to design the cooling system in order to enhance the performance of the electronic systems. The project is focused on generating the dynamic compact thermal model of electronic packages so that the transient thermal behaviors of the package could be predicted fast and accurately. The approach proposed by DELPHI consortium (a collaborative European project) for static compact thermal model generation is extended in this work to generate the dynamic compact model of a BGA package represented by a RC network or admittance matrix. Two steps performed as the methodology of dynamic compact model generation in this work are: 1- A static compact thermal model of BGA package is generated and validated from the static thermal simulation and 2- A RC network is proposed as the contribution of this work and calculated by optimization as the dynamic compact thermal model of the package using the data of transient simualtion. The size of the proposed RC network then is optimized by eliminating some capacitors from the original RC network and validated by comparing its output to the ouptut of finite element simulation. COMSOL©, a Finite element analysis tool is used for thermal simulation and detailed steady state and transient model generation. The optimization algorithm implemented for both static and dynamic compact model generation is Nelder-Mead multidimensional optimization which is realized by MATLAB© programming. The obtained results from the compact models for both static and dynamic analysis of the BGA package are in agreement with the detailed thermal model results and with the available results in literature.

PurposeThe purpose of this paper is to develop a dynamic compact thermal model (DCTM) of electronic packages. This model is a necessary tool for rapid thermal analysis of the systems which we exposed to boundary condition variation and/or power switching mode such as mobile systems and battery powered systems.Design/methodology/approachThe methodology of compact model generation used was based on generating the transient dynamic detailed finite element thermal model of a package, designing a resistor/capacitor network topology representative of the dynamic detailed model, calculating the resistors'/capacitors' value by optimization method and validation efforts. The method is demonstrated for a ball grid array (BGA) package, a commonly used modern electronic package.FindingsBased on the obtained results, it can be concluded that the dynamic thermal behavior of a BGA package can be accurately described by a generated dynamic compact model in terms of predicted junction temperature response and heat flux of the desired locations of the package.Originality/valueThis model is capable of calculating the temperatures and heat fluxes at desired locations which can help the designer to perform the thermal analysis much faster and easier with the required accuracy.

Nanoscale electrothermal co-simulation: compact dynamic models of hyperbolic heat transport and self-consistent device Monte Carlo

ABSTRACTThis paper provides a method for estimating the parameters of a dynamic thermal rail vehicle model and reference values of these parameters. A linear dynamic discrete time system is used to model the thermal behaviour of the vehicle relevant for thermal comfort and air conditioning. The heat capacities and the heat transfer coefficients are stated for various vehicle classes. While dynamic thermal models are state of the art in buildings, cars and rail vehicles, no reference values can be found for these parameters. This paper shows how to estimate the heat capacity and the heat transfer coefficient from measured data for a given thermal model structure. Two different measurement data sources are used: special experiments and existing measurements. While specially designed experiments are only possible for new measurements, it is shown that satisfying results can be obtained with existing measurements. Measurement data from 13 vehicles are used to provide reference values for all passenger vehicles classes: tram, metro, regional and main-line. If all assumptions are satisfied, simulation results of the indoor air temperature agree well with measurements. Reference values for parameters of a dynamic thermal model are the basis for a wide application of such models in the rail vehicle industry.

Dynamic parametric modeling-based model updating strategy of aeroengine casings

Innovative methodology to extract dynamic compact thermal models: Application to power devices

We address the problem of generating Dynamic Compact Thermal Models for non-linear and non-homogeneous heat diffusion problems. We propose a novel Model Order Reduction technique that is based on i) a specifically designed discretization that properly models the non-linear behaviour of different materials, and ii) the introduction of an improved Hyper Reduction method that dramatically reduces the problem dimension. Our experiments show that our method performs similarly to full Finite Volume simulation in terms of accuracy, while being much more computationally efficient.

Compared with other harmonic source models, the dynamic parameter model (DPM) has the advantage of accuracy and good application prospects. Previous studies on the DPM have been carried out under ideal conditions. In order to improve the practicability of the DPM, for the first time, this paper studied the influence of some factors in practical system on the DPM, the corresponding solutions and suggestions were put forward. Firstly, the DPM was briefly introduced and the concept of nonlinear characteristic curve of harmonic source was put forward. Secondly, in order to deal with the time-varying of harmonic source in practical system, a method of dividing each working state and modeling separately was developed. Thirdly, the influence of the sampling quantity, range and error on the accuracy and parameters of the DPM were analyzed, the guidance on sampling for different kinds of harmonic sources were obtained. Finally, the practical research direction of the DPM in the future were discussed.

In this paper a novel approach is proposed for generating dynamic compact models of nonlinear heat diffusion problems for electronics components. The method is very efficient and leads to accurate approximations of the space-time distribution of temperature rise within the component for all waveforms of the injected powers.

A novel approach for extracting dynamic compact thermal models from nonlinear heat diffusion equations, which take into account the temperature dependence of thermal properties, is presented. In such Model Order Reduction method, the nonlinear heat diffusion equation is projected onto the space spanned by a few terms in the Volterra's series expansion of the solution. Such projection is performed by a novel structure-preserving hyper-reduction algorithm. The resulting method is very efficient, and can lead to very accurate compact thermal models, with unprecedented levels of simplicity. Moreover such models can be extracted for practically any regular temperature dependence of heat capacity, thermal conductivity and heat exchange coefficients. The method has been validated through the analysis of a complex ultra thin stacked chip module.

This work presents the application of mathematical methods of parametric model order reduction (pMOR) for automatic generation of the highly accurate, parametric compact models of radio-frequency micro-devices. More specifically, the miniaturized Faraday-induction-based magnetic resonance sensor is considered. Unlike conventional approaches, when magnetic resonance sensor is represented by a lumped-element-based compact model, mathematical pMOR methods are formal, robust and can be performed in an automated way. The introduced parametrization allows producing compact models that are valid over the range of desired parameter's values without the need to repeat the reduction.

This paper investigates the influence of boundary conditions on the validation of a dynamic compact thermal model. The applied boundary conditions are used to consider the effect of the non-modelled parts of the microthruster. The values obtained through different optimization processes show the presence of local minima. This effect is overcome through a design of experiments, based on a central composite design. With the response surface fitted to the model error surface, a Monte-Carlo simulation is made, in order to obtain statistical information on the input parameters. Finally, the influence of the selected input parameters on the evolution of some relevant nodes is plotted. The thermal dynamics of these nodes, is to be predicted with a dynamic multiport compact thermal model.

Dynamic compact thermal model of high power light emitting diode

Detailed kinetic models at the network reaction level are usually constructed using enzymatic mechanistic rate equations and the associated kinetic parameters. However, during the cellular life cycle thousands of different reactions occur, which makes it very difficult to build a detailed large-scale ldnetic model. In this work, we provide a critical overview of specific limitations found during the reconstruction of the central carbon metabolism dynamic model from E. coli (based on kinetic data available). In addition, we provide clues that will hopefully allow the systems biology community to more accurately construct metabolic dynamic models in the future. The difficulties faced during the construction of dynamic models are due not only to the lack of kinetic information but also to the fact that some data are still not curated. We hope that in the future, with the standardization of the in vitro enzyme protocols the approximation of in vitro conditions to the in vivo ones, it will be possible to integrate the available kinetic data into a complete large scale model. We also expect that collaborative projects between modellers and biologists will provide valuable kinetic data and permit the exchange of important information to solve most of these issues.