BENG0091 Stochastic Calculus & Uncertainty Analysis
matlab代做 | angular代做 | lab代写 – 该题目是一个常规的matlab的练习题目代写, 是比较有代表性的matlab/angular等代写方向, 这是值得参考的lab代写的题目
Coursework 2
The company you work for ( Pipes and Tubing for All, PTFA ) has tasked you with assessing the characteristics of the latest piping material that has come out of the R&D labs under the code name Poly-Uber-Oxyside (PUO). To do that you need to evaluate the friction factor ( f ) and the Reynolds number ( Re ) of water flowing through a segment of PUO pipe of known length ( L ). The standardised test set-up (Figure 1) that has been approved by your QA department consists of a known section (L) of tubing, a flowmeter, a variable speed pump and a pressure monitor.
Figure 1 Experimental determination of resistance characteristics
The QA department has also summarised the random and systematic standard errors associated with the measurement of each variable in Table 1. Both the random and systematic uncertainty ranges are given in % values based on the nominal value of each variable. You are confident that absolutely no correlation exists between the standard and random errors of all measured variables.
Table 1 Summary of random and standard systematic errors
Variable Units Nominal Value
Distribution
of random
errors
Random
Uncertainty
( sr ) % value
Distribution
of systematic
errors
Systematic
Uncertainty
(br) % value
d m 0.05 Uniform 10 Normal 2.
P Pa 80 Tri angular 5 Half-Normal 2
kg/m^3 1000 Uniform 2 Triangular 1
Q m^3 /s 0.003 Normal 3 Half-Normal 3
L m 0.2 Uniform 8 Half-Normal 2
Pas 8.910-^4 Normal 8 Triangular 2
- Using the Taylor Series Method (TSM) for uncertainty propagation, determine the expanded uncertainty of the result both for the calculation of the friction factor (f) and the calculation of the Reynolds number (Re). Discuss and justify your assumptions. [ 1 0 marks]
- Using the Monte Carlo Method (MCM) for uncertainty propagation, determine the expanded uncertainty of the result both for the calculation of the friction factor (f) and the calculation of the Reynolds number (Re). Discuss and justify your assumptions. Using appropriate graphs, prove that your calculation of the expanded uncertainty has converged. [ 1 0 marks]
- Did the values for the expanded uncertainties calculated in (Q1) differ from those calculated in (Q2)? If so, explain why this may be the case. Prove your hypothesis/justification by presenting an appropriate MCM simulation. [ 1 0 marks]
- Your company is considering refurbishing your QA laboratories and wishes to prioritise expenditure in purchasing high-fidelity equipment for the measurement of the variables with the largest impact on the determination of the friction factor (f) and the Reynolds number (Re). For this question only (i.e. all of question 4 ), assume that all variables follow a uniform distribution. Perform a Sensitivity Analysis using the Elementary Effects Method for each of the two equations, assuming a range of variation of 50% around the nominal value.
a. Apply the Elementary Effects Method using the original sampling strategy
proposed by Morris [1] and justify/prove convergence [ 15 marks]
b. Apply the Elementary Effects Method using a latin hypercube sampling
strategy and justify/prove convergence [ 20 marks]
c. Apply the Elementary Effects Method using a low discrepancy sequence for
sampling and justify/prove convergence [ 15 marks]
d. Discuss any limitations of the EET method you have discovered during its
implementation and what steps you have taken to alleviate those limitations.
[ 1 0 marks]
e. Recommend the priority in which expenditure should be distributed in order
to ensure that the best equipment is purchased for the most impactful
variables. Justify you answer based on your results from steps (3a, 3b and 3c)
and discuss the most appropriate choice of sampling strategy in the context of
the present example. [ 1 0 marks]
Guidelines:
- You need to provide all mat lab (or equivalent) code that you have used as part of your submission. The code needs to be in a state where we can copy it off your submission and execute it locally reaching the same results as those in your report.
- Your submission (excluding the space taken up by your code) should be no more than 10 pages and contain no more than 10 Figures.
- You need to develop your own code and are not allowed to use pre-existing toolboxes.
- For any questions ask me directly @ [email protected]
References:
[1] Saltelli A., Ratto M., Andres T., Campolongo F., Cariboni J., Gatelli D., Saisana M. and
Tarantola S. (2008) Global Sensitivity Analysis. The Primer , John Wiley & Sons, Ltd.
ISBN: 978- 0 - 470 - 05997 - 5
[2] Coleman H.W. and Steele W.G. (2009) Experimentation, Validation, and Uncertainty
Analysis for Engineers, Third Edition , John Wiley & Sons, Inc. ISBN: 978- 0 - 470 - 16888 -
2