engs103p coursework no 4
TRANSCRIPT
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Abel NyamapfeneModule Coordinator ENGS103P Mathematical Modelling & AnalysisUniversity College London, Gower Street, London WC1E 6BTTel: +44 (0)20 7679 [email protected]
Mathematical Modelling & Analysis I ENGS103P
Coursework No 4
Topic Coverage: Topic 9: Engineering Uncertainty
Topic 10: Analysing Data
Date When Coursework Set 07 December 2015
Coursework Submission Deadline 11 January 2016
Date of Coursework Return 05 February 2016
Student Name:
Student UCL ID number:
Workgroup Number:
Workgroup Lead:
Department:
LONDONS GLOBAL UNIVERSITY
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Show all your workings
Engineering Unc ertainty
1. The water supply for a City C comes from two sources A and B through thewater supply network shown in the figure below.
F1 , F2 and F3 denote the failure of branch 1, 2, and 3 respectively. It is knownthat P(F1 ) = 0.1, P(F2 ) = 0.15, and P(F3) = 0.05.
Assuming the failures of the branches are independent. Determine the probabilityof failure of this water supply system to City C. [10%]
2. Consider two river streams flowing past an industrial plant. Let A denote the
event that stream a is polluted, and B denote that stream b is polluted. It is
determined from historical observations that
5
2)( AP ,
4
3)( BP ,
5
4)OR( BAP
a. Determine )( BAP and )A(BP . [10%]
b. Interpret the results. [5%]
c. Determine whether A and B are independent. [5%]
3. The bearing capacityX of the soil under a column-footing foundation is known tovary between 6-15 kips/sq ft. Its probability density function is given as
15
17.2
1)(
xxfX if 156 x
0)( xfX otherwise
If the column is designed to carry a load of 7.5 kips/sq ft, what is the probability
of failure of the foundation? [20%]
Source B
Source A
City CBranch 3
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Analysing Data
4. Table 1 shows measurements of current (mA) flowing in a sample of labelled
100 Ohms resistors at 1 V.
From Table 1 what is the systematic error from the sample to the nominalresistance value and what is the random error on the measurement. [10%]
Table 1: Measured current (mA) across sample of labelled 100 Ohms resistors at 1 V
10.10 9.85 9.93 10.01 9.82 9.99 10.16 10.03 9.89 9.97
5. Table 2 shows a range of voltage values applied across a given resistance
together with measurements of the corresponding value of current flowing
through the resistance.
a. By carrying out a linear regression in Matlab or Excel find the best fit straight line
for the given data. [10%]
b. Use linear interpolation to estimate the value of the current at 0.45 V. [10%]
Table 2: For a given resistance in the sample current as a function of voltage
Voltage(V)
0 0.1 0.2 0.3 0.4 0,.5 0.6 0.7 0.8 0.9 1
Current(mA)
0 0.99 2.00 3.01 4.1 4.85 5.99 7.02 7.98 9.00 10.03
6. Table 3 shows a range of voltage values applied across a diode together with
measurements of the corresponding value of current flowing through the diode.
Use regression techniques to find the ideality factor of the diode and calculatethe maximum error of a linear interpolation in the 0.9-1 V range compared tothe fitted value. [20%]
Table 3: Current as a function of voltage in a diode
Voltage
(V)
0 0.1 0.2 0.3 0.4 0,.5 0.6 0.7 0.8 0.9 1
Current(mA)
0 0 0 0 0 0 0 0.07 0.92 12.02 158.29
NB:Equation of a diode:
= exp( ) 1 Where I is in milli-amperes, V is in Volts, =ideality factor
= 38.68
=1.00 109