代写BENG0091、代做Stochastic Calculus、代写Matlab编程语言、代做Matlab代写

日期：2019-03-25 10:25

Department of Biochemical Engineering

BENG0091 Stochastic Calculus & Uncertainty Analysis

Coursework 2

To be submitted on Moodle by 22-March-2019 (23:55)

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.

Department of Biochemical Engineering

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 2.5

ΔP Pa 80 Triangular 5 Half-Normal 2

ρ kg/m3 1000 Uniform 2 Triangular 1

Q m3

/s 0.003 Normal 3 Half-Normal 3

L m 0.2 Uniform 8 Half-Normal 2

μ Pa·s 8.9·10-4 Normal 8 Triangular 2

1. 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.

[10 marks]

2. 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. [10 marks]

3. 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. [10 marks]

4. 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.

Department of Biochemical Engineering

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.

[10 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. [10 marks]

Guidelines:

- You need to provide all Matlab (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 @ alex.kiparissides@ucl.ac.uk

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-

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