Calibration of detailed thermal models by parametric dynamic compact thermal models

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.

A novel model order reduction method for the construction of parametric dynamic compact thermal models of nonlinear heat diffusion problems is proposed. The method extends a previous method, recently proposed by the Authors, for the construction of parametric dynamic compact thermal models of linear heat diffusion problems. The method has been validated through the analysis of a simple die in which high levels of non-linearities and large variations of parameters occur.

The paper presents a compact thermal model of an electronic component enclosed in a D2Pak case.The model includes convection cooling and is compared to a linear model with isothermal boundary condition.The model presented is a static model.

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.

The construction and usage of compact thermal models (CTMs), for the thermal analysis as well as the design of cooling devices for electronic systems, are reviewed. These models have many advantages over the so called detailed models based on 3D simulations, mainly being a convenient and simple quantitative description of the modeled object, when constructional details are either unavailable or too detailed to be of use at the desired level of analysis. However, CTMs have manifested some deficiencies in many cases, in particular, multiple chip modules (MCM) and stacked dies. The opposite approach, detailed modeling, is more reliable, although extremely heavy. A new approach is proposed that solves this dilemma by bridging the gap between compact and detailed models. While retaining all advantages of CTMs, i.e., having a limited number of degrees of freedom and not requiring detailed constructional features, it can attain any required precision level depending on the degree of complexity adopted. It gives reliable results covering all operating conditions including MCM and stacked dies. Moreover, it gives access to data on surface temperature gradients that were never obtained before by compact models and are highly important for reliability issues.

Compact thermal models (CTM) of LED packages enable suppliers to provide thermal representations of their products, without divulging any proprietary information about their construction, so that their customers may simulate the LED's thermal performance within their end operating environment. Such CTMs are extracted from the simulated thermal response of so called ‘detailed’ LED models. These models are detailed to the extent where the 3D construction of the model, both geometry and material properties, are included. The accuracy of the CTM will only be as accurate as that of the originating detailed 3D model. The accuracy of the 3D detailed model is best assured by calibrating it against a measurement of a physical sample. This paper presents a methodology whereby the 3D detailed model parameters can be determined so as to match a transient thermal measurement.

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.

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.

Thermal analysis of lithium-ion batteries

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

The current work presents a comparative study of industry-wide practice of modeling opto-electronic packages for their thermal analysis, with a focus on the DELPHI-type model. A single opto-electronic package that has a representative construction of other types of opto-electronic packages is chosen for this study. This package is Small-Form Factor Pluggable device, commonly referred to as the SFP. Based on the required level of accuracy and computational resources consumed, the SFP is modeled using one of the following techniques; a lumped system of fixed thermal conductivity, a two-resistor network model, a multi-resistor DELPHI-type network model and a detailed geometrical model. In the current study, these modeling techniques are studied in a comparative mode. The performances of the different models are compared to a validated detailed model. Boundary conditions used for comparing the different models with the detailed model is decided based on practical situations commonly encountered by SFPs in system-level models. The practical situations also include cage-level installation of the SFPs. In addition to presenting the performance of each modeling technique with respect to the detailed model, discussion on their advantages and limitations are also included in this paper.

Dynamic parametric modeling-based model updating strategy of aeroengine casings

In this article, we propose a new behavioral thermal modeling method for fast building performance analysis, which is critical for energy-efficient smart building control and management. The new approach is based on two recurrent neutral network architecture to obtain the compact nonlinear thermal models for complicated building. We start with a more realistic building simulation program, EnergyPlus, from Department of Energy, to model some practical buildings such as office buildings and data centers. EnergyPlus can model the various time-series inputs to a building such as ambient temperature, heating, ventilation, and air-conditioning (HVAC) inputs, power consumption of electronic equipment, lighting and number of occupants in a room sampled in each hour and produce resulting temperature traces of zones (rooms). In this work, we apply two recurrent neural network (RNN) architectures to build the non-linear compact thermal model of the building: one is non-linear state-space RNN architecture (NLSS), which has global feedbacks, and the other one is Elman's RNN architecture (ELNN), which has local feedbacks in each layer. We give a simple formula to calculate the RNN layer number, layer size to configure RNN architecture to avoid overfitting and underfitting problems. A cross-validation based training technique is further applied to improve predictable accuracy of models. Experimental results from a case study of three buildings show that ELNN and NLSS can both build very accurate building thermal models for the 2-zone and 5-zone building cases: both of them have average errors from around 1% to 1.5% for the two buildings. For the more complex 6-zone building case, ELNN outperforms NLSS with maximum errors 16% against 23%. But both methods have 2.2% average errors.

Temperature control of the new-generation integrated multicore system is challenging. This is because the leakage power, which is significant in modern systems, is nonlinearly related to temperature, resulting in a complex nonlinear control problem in thermal management. In this article, a new dynamic thermal management (DTM) method with compact piecewise linear (PWL) model based predictive control is proposed to solve the nonlinear control problem. First, a compact PWL thermal model, which takes dynamic power as input, is built by combining multiple local compact linear thermal models expanded at several Taylor expansion points. These local compact linear thermal models are obtained by sampling-based model order reduction with high accuracy. Their Taylor expansion points are selected by a systematic scheme, which exploits the thermal behavior property of the multicore chips. Based on the compact PWL thermal model, a new predictive control method is proposed to compute the future power recommendation for DTM. By approximating the nonlinearity accurately with the compact PWL thermal model and being equipped with predictive control technique, the new DTM achieves an overall high quality temperature management with smooth and accurate temperature tracking. Experimental results show that the new method outperforms the linear model predictive control based method and the echo state network based predictive thermal management method in temperature management quality with lower computing overhead.