Prediction of Transient Thermal Behavior of Planar Interconnect Architecture Using Proper Orthogonal Decomposition Method

2011 ◽  
Author(s):  
Banafsheh Barabadi ◽  
Yogendra K. Joshi ◽  
Satish Kumar
Keyword(s):  
Thermal Behavior ◽  
Proper Orthogonal Decomposition ◽  
Joule Heating ◽  
Computational Cost ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Fe Model ◽  
Inhomogeneous System ◽  
Transient Thermal ◽  
Proper Orthogonal

A major challenge in maintaining quality and reliability in today’s microelectronics devices comes from the ever increasing level of integration in the device fabrication as well as the high level of current densities that are carried through the microchip during operation. Cyclic thermal events during operation, stemming from Joule heating of the metal lines, can lead to fatigue failure due to the varying thermal expansion coefficients of the different materials that compose the microchip package. To aid in the avoidance of such device failures, it is imperative to develop a predictive capability for the thermal response of micro-electronic circuits. This work studied the problem of transient Joule heating in interconnects in a two-dimensional (2D) inhomogeneous system using a reduced order modeling approach of the Proper Orthogonal Decomposition (POD) method and Galerkin Projection Technique. This study considers an interconnect structure embedded in the bulk of a microelectronic device. The effect of different types of current pulses, pulse duration, and pulse amplitude were investigated. By using a representative step function as the heat source, the model predicted the exact transient thermal behavior of the system for all other cases without generating any new observations, using just a few POD modes. To validate this unique capability, the result of the POD model was compared with a finite element (FE) model developed in LS-DYNA®. The behaviors of the POD models were in good agreements with the corresponding FE models. This close correlation provides the capability of predicting other cases based on a smaller sample set which can significantly decrease the computational cost.

MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION

2005 ◽  
Vol 15 (03) ◽  
pp. 997-1013 ◽  
Author(s):  
C. W. ROWLEY
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Model Reduction ◽  
Projection Method ◽  
Computational Cost ◽  
Plane Channel ◽  
Orthogonal Decomposition ◽  
Inner Product ◽  
High Dimensional ◽  
Balanced Truncation ◽  
Proper Orthogonal

Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition (POD), balanced truncation, and a method called balanced POD. Balanced truncation produces better reduced-order models than POD, but is not computationally tractable for very large systems. Balanced POD is a tractable method for computing approximate balanced truncations, that has computational cost similar to that of POD. The method presented here is a variation of existing methods using empirical Gramians, and the main contributions of the present paper are a version of the method of snapshots that allows one to compute balancing transformations directly, without separate reduction of the Gramians; and an output projection method, which allows tractable computation even when the number of outputs is large. The output projection method requires minimal additional computation, and has a priori error bounds that can guide the choice of rank of the projection. Connections between POD and balanced truncation are also illuminated: in particular, balanced truncation may be viewed as POD of a particular dataset, using the observability Gramian as an inner product. The three methods are illustrated on a numerical example, the linearized flow in a plane channel.

scholarly journals Direct synthesis of equivalent circuits from reduced FE models using proper orthogonal decomposition

2016 ◽  
Vol 35 (6) ◽  
pp. 2035-2044 ◽  
Author(s):  
Toshihito Shimotani ◽  
Yuki Sato ◽  
Hajime Igarashi
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fe Analysis ◽  
Electric Machines ◽  
Orthogonal Decomposition ◽  
Computational Time ◽  
Equivalent Circuits ◽  
Fe Model ◽  
Content Type ◽  
Electromagnetic Devices ◽  
Proper Orthogonal

Purpose The purpose of this paper is to propose a fast synthesis method of the equivalent circuits of electromagnetic devices using model order reduction. Finite element method (FEM) has been widely used to design electromagnetic devices. For FE analysis of these devices connected to control and deriving circuits, FE equations coupled with the circuit equations have to be solved for many times in their design processes. If the FE models are replaced by equivalent circuit models, computational time could be drastically reduced. Design/methodology/approach In the proposed method, a reduced FE model is obtained using proper orthogonal decomposition (POD) in which the size of FE equation is effectively reduced so that the computational time for FE analysis is shortened. Then, the equivalent circuits are directly synthesized from the admittance function of the reduced system. Findings Accuracy and computational efficiency of the proposed method are compared with those of another POD-based method in which the equivalent circuits are synthesized from fitting of frequency characteristics using optimization algorithm. There are no significant differences in the accuracy of both methods, while the speedup ratio of the former method is found larger than that for the latter method for the same sampling points. Originality/value The equivalent circuits of electric machines and devices have been synthesized on the basis of physical insight of engineers. This paper proposes a novel method by which the equivalent circuits are automatically synthesized from FE model of the electric machines and devices using POD.

Rapid Transient Thermal Analysis of Three-Dimensional Interconnect Structures Using Proper Orthogonal Decomposition Method

2012 ◽  
Author(s):  
Banafsheh Barabadi ◽  
Satish Kumar ◽  
Yogendra K. Joshi
Keyword(s):  
Thermal Analysis ◽  
Proper Orthogonal Decomposition ◽  
Joule Heating ◽  
Hot Spot ◽  
Three Dimensional ◽  
Orthogonal Decomposition ◽  
Computational Time ◽  
Interconnect Architectures ◽  
High Level ◽  
Proper Orthogonal

The increase in the integration of interconnect wiring, as well as the high level of current densities are resulting in increased concerns about hot spot formation due to Joule heating in the metal lines of microprocessors. This temperature rise poses a major challenge in maintaining the quality and reliability of future devices, requiring a focus on physics based approaches for rapid and accurate thermal analysis of interconnect architectures. This work investigates the problem of transient Joule heating in a three-dimensional array of copper interconnects embedded in dielectric layers of SiO2 and Si3N4 using Proper Orthogonal Decomposition (POD) as the reduced order modeling approach. The case of natural convection was assumed on the boundaries. For validation, the results were compared with a three-dimensional finite volume model developed in Fluent and good agreements models were observed. While the Fluent model required hours of computational time, the POD based model predictions were achieved within seconds.

scholarly journals Enhancing the accuracy of deep learning based FE$^2$ algorithm using proper orthogonal decomposition

2021 ◽  
Author(s):  
Saumik Dana
Keyword(s):  
Deep Learning ◽  
Proper Orthogonal Decomposition ◽  
Computational Cost ◽  
Orthogonal Decomposition ◽  
Neural Nets ◽  
Neural Net ◽  
Input Output ◽  
Elastic Solids ◽  
Scale Modeling ◽  
Proper Orthogonal

The deep learning leveraged FE$^2$ algorithm for two-scale modeling of elastic solids eliminates the need to solve the RVE problem on-the-fly by replacing the effective input-output causality by a neural network. This potentially reduces the computational cost of the FE$^2$ algorithm significantly. In this work, we put forth the use of snapshot proper orthogonal decomposition to improve the accuracy of the machine learning leveraged algorithm. Instead of training one neural net, multiple neural nets are trained with the coefficients of the basis of the snapshot matrix as the target.

Nonlinear Modeling of Mechanical Gas Face Seal Systems Using Proper Orthogonal Decomposition

2006 ◽  
Vol 128 (4) ◽  
pp. 817-827 ◽  
Author(s):  
Haojiong Zhang ◽  
Brad A. Miller ◽  
Robert G. Landers
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Initial Conditions ◽  
Nonlinear Modeling ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Face Seal ◽  
Reduced Order ◽  
Wide Range ◽  
Gas Face Seal ◽  
Proper Orthogonal

An approach based on proper orthogonal decomposition and Galerkin projection is presented for developing low-order nonlinear models of the gas film pressure within mechanical gas face seals. A technique is developed for determining an optimal set of global basis functions for the pressure field using data measured experimentally or obtained numerically from simulations of the seal motion. The reduced-order gas film models are shown to be computationally efficient compared to full-order models developed using the conventional semidiscretization methods. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. Axial and tilt modes of stator motion are modeled, and simulation studies are conducted using different initial conditions and force inputs. The reduced-order models are shown to be applicable to seals operating within a wide range of compressibility numbers, and results are provided that demonstrate the global reduced-order model is capable of predicting the nonlinear gas film forces even with large deviations from the equilibrium clearance.

A Reduced-Order Model for Turbomachinery Flows Using Proper Orthogonal Decomposition

2013 ◽  
Author(s):  
Thomas A. Brenner ◽  
Forrest L. Carpenter ◽  
Brian A. Freno ◽  
Paul G. A. Cizmas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Computational Cost ◽  
Wheel Speed ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal

This paper presents the development of a reduced-order model based on the proper orthogonal decomposition (POD) method. The POD method has been developed to predict turbomachinery flows modeled by the Reynolds-averaged Navier–Stokes equations. The purpose of using a POD-based reduced-order model is to decrease the computational cost of turbomachinery flows. The POD model has been tested for two configurations: a canonical channel with a bump case and the transonic NASA Rotor 67 case. The Rotor 67 case has been simulated at design wheel speed and at three off-design conditions: 70, 80, and 90% of the wheel speed. The results of the POD-based reduced-order model where in excellent agreement with the full-order model results. The computational time of the reduced-order model was approximately one order of magnitude smaller than that of the full-order model.

Verification of Nonlinear Proper Orthogonal Decomposition Reduced Order Modeling for BWR Fuel Assemblies

2013 ◽  
Author(s):  
Dennis P. Prill ◽  
Andreas G. Class
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Power Distribution ◽  
Computational Cost ◽  
Orthogonal Decomposition ◽  
Low Flow ◽  
Reduced Order ◽  
Linear Character ◽  
Operation Conditions ◽  
Non Linear ◽  
Proper Orthogonal

Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. Studying potential power oscillations require focusing on BWR operation at high-power low-flow conditions interacting with unfavorable power distribution. Current design rules assure admissible operation conditions by exclusion regions determined by numerical calculations and analytical methods. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs) saving computational cost and improving the physical understanding. A general reduction technique is given by the proper orthogonal decomposition (POD). Model-specific options and aspects of the POD-ROM-methodology are considered. A first verification is illustrated by means of a chemical tubular reactor (TR) setup. Experimental and analytical results for natural convection in a closed circuit (NCC) [1, 2] serve as a second verification example. This setup shows a strongly non-linear character. The implemented model is validated by means of a linear stability map. Transient behavior of the NCC-POD-ROM can not only reproduce the input data but rather predict different states.

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