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By J.M. Bruce

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A sample-based sensitivity analysis is a procedure in which the model is executed repeatedly for a set of input values. As described by Saltelli et al. [33] and illustrated in Fig. 18, the following steps can be identified in a sample-based sensitivity analysis: 1) Design of experiments: the question which the sensitivity analysis should answer is defined, and an appropriate strategy for sampling the input factors concerned with the analysis is decided. 2) Assign the probability distribution or range of variations to each input factor.

3 Final arrangement of the populated incidence matrix. {2}-Rule2, {3}-Rule3, {4}-Rule4, {5}-Rule3, and {6}-Rule4. Thus, the final data flow obtained by applying the incidence matrix method is as follows: model1 has Ws and q as input and CL as output, model2 has r and V as input and q as output, and finally model3 produces r as output. After performing the variable flow modeling, model1 has Ws and q as input and CL as output. However, the actual model1, as shown in Fig. 2a, has q and CL as input and Ws as output.

7a with X6 given as the independent variable. MDO AT PREDESIGN STAGE 2 144 6 144 6 6 144 P ¼ D1 þ D2 þ D3 þ D4 þ D5 þ D6 ¼ 6 6 0 6 4 88 88 0 63 0 0 63 0 35 232 138 0 169 138 63 232 138 0 0 6 0 81 94 63 144 94 0 3 232 169 7 7 232 7 7 0 7 7 81 5 144 The nonzero elements of the matrix are now replaced with 1. 2 1 61 6 61 P¼6 60 6 41 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 3 1 17 7 17 7 07 7 15 1 Now the Hadamard product of P and P T is 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 32 1 1 6 7 17 60 76 17 61 76 86 07 7 61 76 15 40 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 2 1 61 6 6 61 T P8P ¼ 6 60 6 6 41 2 1 60 6 6 61 ¼6 60 6 6 40 3 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 3 1 07 7 7 17 7 17 7 7 05 1 1 0 1 1 07 7 7 17 7 07 7 7 05 1 In the preceding matrix rows 1, 3, and 6 (and columns 1, 3, and 6) are equal and so are rows 2 and 5 (and columns 2 and 5).

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