Thermal investigations of microelectronic chip with non‐uniform power distribution: temperature prediction and thermal placement design optimization

2004 ◽  
Vol 21 (3) ◽  
pp. 29-43 ◽  
Author(s):  
Teck Joo Goh ◽  
K.N. Seetharamu ◽  
G.A. Quadir ◽  
Z.A. Zainal ◽  
K. Jeevan Ganeshamoorthy
Keyword(s):  
Power Distribution ◽  
Heat Dissipation ◽  
Thermal Analyses ◽  
Convection Heat Transfer ◽  
Multiple Linear Regression Model ◽  
Least Square Method ◽  
Least Square ◽  
Junction Temperature ◽  
Thermal Investigations ◽  
Placement Distance

This paper presents the thermal analyses carried out to predict the temperature distribution of the silicon chip with non‐uniform power dissipation patterns and to determine the optimal locations of power generating sources in silicon chip design layout that leads to the desired junction temperature, Tj. Key thermal parameters investigated are the heat source placement distance, level of heat dissipation, and magnitude of convection heat transfer coefficient. Finite element method (FEM) is used to investigate the effect of the key parameters. From the FEM results, a multiple linear regression model employing the least‐square method is developed that relates all three parameters into a single correlation which would predict the maximum junction temperature, Tj,max.

scholarly journals ANALISIS FAKTOR - FAKTOR YANG MEMPENGARUHI HARGA TANAH UNTUK PENGGUNAAN PERUMAHAN (STUDI KASUS: KECAMATAN BANYUMANIK)

2017 ◽  
Vol 5 (1) ◽  
pp. 57
Author(s):  
Triana Kurniwati ◽  
Bagio Mudakir
Keyword(s):  
Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Least Square Method ◽  
Research Area ◽  
Least Square ◽  
City Center ◽  
Land Price ◽  
Ordinary Least Square ◽  
The City

Semarang city is densely populated that demand of settlement will increase continually, but land in city center is very limited and even it is scarce, therefore the land price which is placed in city center is high. That is why many inhabitant of Semarang city prefer to live in outskirts of the city. The shifting of land demand to the outskirts is also followed by increasing of land price in outskirts, it causes the land price in outskirts is uncontrolled.The research takes location in Banyumanik area. This research area consists of 7 districts, that are Jabungan, Pudak Payung, Banyumanik, Srondol Kulon, Pedalangan, Ngesrep, and Gedawang district. The sample total is one hundred (100). The data is analyzed by using multiple linear regression model with ordinary least square method (OLS).

Thermal Analyses of LED Light Bars and Backlight Modules

2016 ◽  
Vol 33 (3) ◽  
pp. 331-339 ◽  
Author(s):  
M.-Y. Tsai ◽  
C.-Y. Tang ◽  
C.-E. Zheng ◽  
Y.-Y. Tsai ◽  
C.-H. Chen
Keyword(s):  
Heat Dissipation ◽  
Light Emitting Diode ◽  
Thermal Analyses ◽  
Heat Sinks ◽  
Junction Temperature ◽  
Thermal Interface Materials ◽  
Light Emitting ◽  
Led Light ◽  
The One ◽  
Interface Materials

AbstractThe effects of various parameters, such as thermal properties of substrates, thermal interface materials (TIMs) and heat sinks on the thermal performance of the light emitting diode (LED) light bars and backlight module are investigated experimentally and numerically in terms of junction temperature (Tj) and thermal resistances from junction to air (Rj-a). The results show that the measured Rj-a of the light bars by powering-on five LEDs in the test is different from one by powering-on only one LED, resulting from the extra heat coming from the adjacent LED packages affecting the Tj for the case of powering-on five LEDs. For the modules, Rj-a is significantly reduced by using the heat sinks for all backlight modules, and aluminum and iron heat sinks do not show any obvious difference in heat dissipation along with any substrates and TIMs. Furthermore, both experimental and simulation results show that the thermal conductivity of the substrates are more important and dominant than TIM and heat sink for the Rj-a of the backlight modules concerned, and also demonstrate that the thermal field for the local model can represent the one in full-scale backlight module.

Milling Force Modeling and Experimental Research of 300M Ultra High Strength Steel

2014 ◽  
Vol 800-801 ◽  
pp. 53-60 ◽  
Author(s):  
Hui Ping Zhang ◽  
Chong Xun Wang ◽  
Yi Nan Lai ◽  
Wen Juan Zheng
Keyword(s):  
High Strength Steel ◽  
Orthogonal Experiment ◽  
Multiple Linear Regression Model ◽  
High Strength ◽  
Least Square Method ◽  
Cutting Parameters ◽  
Least Square ◽  
Depth Of Cut ◽  
Milling Force ◽  
Ultra High Strength Steel

300M ultra high strength steel, a new type of steel with broad prospects for development, has good mechanical properties, and is widely used for manufacture of aircraft landing gear. In order to reveal influence law of cutting parameters on milling force of 300M ultra high strength steel, the influence law of feed rate, milling width, and depth of cut and spindle speed on milling force is firstly studied through the single factor experiments in this paper. Secondly, the influence level of experimental factors is compared by orthogonal experiment. Finally, combined with orthogonal test data and the least square method, the multiple linear regression model of milling force in 300M ultra high strength steel milling is built. The accuracy of the model has been verified well by experimental verification, which has the guiding significance to reveal the milling mechanism and actual production.

scholarly journals Multiple Linear Regression Model of Rice Production using Conjugate Gradient Methods

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 229-236
Author(s):  
Nur Idalisa Norddin ◽  
Mohd Rivaie Mohd Ali ◽  
Nurul Hafawati Fadhilah ◽  
Nur Atikah ◽  
Anis Shahida ◽  
...  
Keyword(s):  
Regression Model ◽  
Conjugate Gradient ◽  
Regression Models ◽  
Gradient Methods ◽  
Multiple Linear Regression Model ◽  
Least Square Method ◽  
Rice Production ◽  
Least Square ◽  
Basic Relationship ◽  
Least Square Problem

Regression is one of the basic relationship models in statistics. This paper focuses on the formation of regression models for the rice production in Malaysia by analysing the effects of paddy population, planted area, human population and domestic consumption. In this study, the data were collected from the year 1980 until 2014 from the website of the Department of Statistics Malaysia and Index Mundi. It is well known that the regression model can be solved using the least square method. Since least square problem is an unconstrained optimisation, the Conjugate Gradient (CG) was chosen to generate a solution for regression model and hence to obtain the coefficient value of independent variables.  Results show that the CG methods could produce a good regression equation with acceptable Root Mean-Square Error (RMSE) value.

scholarly journals Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method

2021 ◽  
Vol 1 (4 (109)) ◽  
pp. 64-73
Author(s):  
Serhii Zabolotnii ◽  
Vladyslav Khotunov ◽  
Anatolii Chepynoha ◽  
Olexandr Tkachenko
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Power Distribution ◽  
Maximum Likelihood Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Random Errors ◽  
Exponential Power Distribution ◽  
Exponential Power

This paper considers the application of a method for maximizing polynomials in order to find estimates of the parameters of a multifactorial linear regression provided the random errors of the regression model follow an exponential power distribution. The method used is conceptually close to a maximum likelihood method because it is based on the maximization of selective statistics in the neighborhood of the true values of the evaluated parameters. However, in contrast to the classical parametric approach, it employs a partial probabilistic description in the form of a limited number of statistics of higher orders. The adaptive algorithm of statistical estimation has been synthesized, which takes into consideration the properties of regression residues and makes it possible to find refined values for the estimates of the parameters of a linear multifactorial regression using the numerical Newton-Rafson iterative procedure. Based on the apparatus of the quantity of extracted information, the analytical expressions have been derived that make it possible to analyze the theoretical accuracy (asymptotic variances) of estimates for the method of maximizing polynomials depending on the magnitude of the exponential power distribution parameters. Statistical modeling was employed to perform a comparative analysis of the variance of estimates obtained using the method of maximizing polynomials with the accuracy of classical methods: the least squares and maximum likelihood. Regions of the greatest efficiency for each studied method have been constructed, depending on the magnitude of the parameter of the form of exponential power distribution and sample size. It has been shown that estimates from the polynomial maximization method may demonstrate a much lower variance compared to the estimates from a least-square method. And, in some cases (for flat-topped distributions and in the absence of a priori information), may exceed the estimates from the maximum likelihood method in terms of accuracy

Parametric Study in Thermal Optimization Design of Multi-Chip Module

2013 ◽  
Vol 432 ◽  
pp. 358-363
Author(s):  
Jian Zhang ◽  
Dong Lai Zhang
Keyword(s):  
Thermal Conductivity ◽  
Thermal Stress ◽  
Optimization Design ◽  
Heat Dissipation ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Junction Temperature ◽  
Design Parameters ◽  
Three Dimensional Model ◽  
Thermal Optimization

A three dimensional model of Multichip Module (MCM) is built with ANSYS. The temperature and thermal stress field distribution are studied. Taking into account the global heat dissipation and the local thermal stress, the effect of structure parameters and material properties on the maximum chip junction temperature and the maximum thermal stress of MCM are studied. The four design parameters are the thickness of the substrate, thermal conductivity of the substrate, thermal conductivity of the thermal grease and convection heat transfer coefficient. This paper gave the method to reduce the temperature, and the results provided an efficient basis for the compromising design of thermal stress, which is benefit for the thermal optimization of MCM.

Direct Assessment of Effective Renal Plasma Flow from Renoscintigraphy with a Gamma Camera and an On-Line Computer

1981 ◽  
Vol 20 (06) ◽  
pp. 274-278
Author(s):  
J. Liniecki ◽  
J. Bialobrzeski ◽  
Ewa Mlodkowska ◽  
M. J. Surma
Keyword(s):  
Count Rate ◽  
Renal Plasma Flow ◽  
Early Period ◽  
Least Square Method ◽  
Least Square ◽  
Uptake Coefficient ◽  
Positive Linear Correlation ◽  
On Line ◽  
Best Fit ◽  
Plasma Activity

A concept of a kidney uptake coefficient (UC) of 131I-o-hippurate was developed by analogy from the corresponding kidney clearance of blood plasma in the early period after injection of the hippurate. The UC for each kidney was defined as the count-rate over its ROI at a time shorter than the peak in the renoscintigraphic curve divided by the integral of the count-rate curve over the "blood"-ROI. A procedure for normalization of both curves against each other was also developed. The total kidney clearance of the hippurate was determined from the function of plasma activity concentration vs. time after a single injection; the determinations were made at 5, 10, 15, 20, 30, 45, 60, 75 and 90 min after intravenous administration of 131I-o-hippurate and the best-fit curve was obtained by means of the least-square method. When the UC was related to the absolute value of the clearance a positive linear correlation was found (r = 0.922, ρ > 0.99). Using this regression equation the clearance could be estimated in reverse from the uptake coefficient calculated solely on the basis of the renoscintigraphic curves without blood sampling. The errors of the estimate are compatible with the requirement of a fast appraisal of renal function for purposes of clinical diagknosis.

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