MITESD_77S10_soln02 (1)

# MITESD_77S10_soln02 (1) - 16.888/ESD 77 Multidisciplinary...

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16.888/ESD 77 Multidisciplinary System Design Optimization: Assignment 2 Part a) Solution a1) Design of Experiments a1-a) Experiment # Mean (ft) Variance (ft^2) 1 13.9 10.9 2 12.6 6.5 3 12.9 5.4 4 12.9 7.8 5 12.4 5.3 6 17.7 26.8 7 12.1 6.1 8 13.3 18.7 9 15.1 24.5 Overall mean range, R = 13.6 ft. The variance is calculated using the unbiased ( J J ) 2 estimate (i.e., variance = s n 2 1 = n where ‘n’ is the number of n 1 experiments). a1-b) The design variable settings and their main effects table is shown below: Setting Effects A1 -0.5 A2 0.7 A3 -0.1 B1 -0.7 B2 -0.9 B3 1.6 C1 1.3 C2 -0.1 C3 -1.2 D1 0.2 D2 0.5 D3 -0.6 a1-c) 1

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From the above table, the optimal airplane has settings (A2, B3, C1, D2) and corresponds to experiment #6. It has the highest mean range of 17.7 ft but also has a high variance of 26.8 ft^2. a1-d) The overall average range (average across all experiments) is J mean = 13.6 ft. Now adding the effects of the variable settings for the optimal airplane, the predicted range is J = J mean + (0.7 + 1.6 + 1.3 +0.5) ft = 17.7 ft. This corresponds to the mean of experiment #6. a1-e) Flight: 12345 M e a n V a r i a n c e Distance (ft): 16.5 19.75 22.5 18.6 17.9 19.05 5.105 The mean of the test flights is 19.05 ft with a variance of 5.1ft and the prediction was 17.7 feet. With a variance that large the mean of the test flight and the prediction can be considered the same or at least similar. There was considerable experimental variation during the tests as some airplanes flew straight, others flew curved paths. Therefore, with the large amount of experimental variation the prediction seems supported by experiment a1-f) The optimal airplane setting becomes the baseline design for conducting further parameter study. In a parameter study, only one factor is changed at a time, keeping all other variables at the baseline setting. The number of experimental points = 1+n*(l-1) =1+4*2=9. Experiment # A B C D 1 (baseline) A2 B3 C1 D2 2 A1 B3 C1 D2 3 A3 B3 C1 D2 4 A2 B1 C1 D2 5 A2 B2 C1 D2 6 A2 B3 C2 D2 7 A2 B3 C3 D2 8 A2 B3 C1 D1 9 A2 B3 C1 D3 Except the base design, none of the previous designs is included in this table. Therefore each of the 8 new experiments would potentially lead to enhanced understanding of the design space, including possible interactions. This might lead to improved estimate on mean and reduce the variability. a1-g) A larger variance indicates a wider spread of results about a mean value and reduces the confidence one has in the mean value as a predictor. This 2
essentially means that the mean is not a good enough predicted of the expected performance. Standard deviation, which is the square root of the variance, can be used to define confidence bounds on the expected range and would serve as an indicator while selecting an optimal design setting for further exploration.

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## This note was uploaded on 11/08/2011 for the course AERO 16.851 taught by Professor Ldavidmiller during the Fall '03 term at MIT.

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MITESD_77S10_soln02 (1) - 16.888/ESD 77 Multidisciplinary...

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