Homework 5 Solution

Homework 5 Solution - MEEN 260 Introduction to Engineering...

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MEEN 260 Introduction to Engineering Experimentation Homework 5: Regression and Strain Gauges Assigned: Thursday, 14 Feb. 2008 Due: Thursday, 21 Feb. 2008, 9:00am Homework Problems: Problem 1) Consider the data set given below: Measurement x y 1 0.1 5.5 2 0.3 7.4 3 0.6 9.1 4 1.2 16.4 5 1.5 22.1 6 1.6 24.4 7 1.7 26.9 8 1.9 32.8 Develop the least-squares fit to the following data using a linear regression b ax y + = , a 2 nd order regression 2 1 ya x =+ , and an exponential regression ax Ce y = . a) Determine the coefficients for all three regression models based on the summation formulas provided in the lecture notes. Derive your own summation formulas if necessary. Don’t use built-in functions of Excel to get the regressions directly; but you may use Excel to do the summations, generate the plots, etc. b) Determine the coefficients for all three regression models based on the matrix formulation of regression as presented in the lecture notes. You may use Matlab, Maple or similar software to do the matrix inversion, but show the values for all matrices and vectors in your homework. c) Do the coefficients obtained from both methods agree? (If they don’t, you’ve made a mistake)
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d) Calculate the correlation coefficients r and r’ . e) Plot the data and each regression model. Which regression represents the original measured data the most accurately? Justify your conclusion with plots and calculation of the correlation coefficients r and r’ . Problem 2) The Wheatstone Bridge (shown below) remains one of the most sensitive and accurate methods for precisely measuring resistance values. The fundamental concept of the Wheatstone Bridge is two voltage dividers, both fed by the same input. The circuit output is taken from both voltage divider outputs. Figure 1: Wheatstone Bridge a) Four Resistors are to be placed in the Wheatstone Bridge R 1 =1 and R 2 R 3 and R 4 can have resistance of 2, 3 or 4 ohms. Determine the configuration that will provide the
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This note was uploaded on 07/28/2010 for the course MEEN 260 taught by Professor Langari during the Fall '08 term at Texas A&M.

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Homework 5 Solution - MEEN 260 Introduction to Engineering...

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