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Example 1a: Robust Design for a Simple Cylinder with normal distributed design variables A simple cylinder as shown in the following figure is used to demon the Robust Design. This cylinder is designed as a constant volume and the standard deviations of design variables D (diameter) and H (height) are assumed to be constant value of 05. What are the robust Design of D and H if the volume of cylinder is held as 311?
Robust Design of a Simple Cylinder
Solution:
The design variables have constant standard deviation of 0.5 and their means are random variables (Hyper parameter distributions). It is noted that that the design variables re always entered after the variables of range.
The random variables are then set up as the first two random variables are the range of design variables and the two design variables are hyper parameter distribution as shown below. Variables : x1 = D Range: Uniform(4, 12) x2 = H Range: Uniform(4, 12) x3 = D: Normal(x1, 0.5) x4 = H: Normal(x2, 0.5)
The volume of the simple cylinder is held as constant of 311. therefore, the limit state function is defined as following equation. Limit State Function:
The final result is summarized as below: ***** ROBUST DESIGN ***** 1st-order standard dev. of g(x)......= 4.6235356E+01 value of limit-state function.....g(x) = 3.07430E-05 Robust Point
Example 1b: Robust Design for a Simple Cylinder with non-normal distributed design variables This example aims to study the effect of non-normality on the result of Robust Design. All the input is the same as in the previous example except that the design variables are exponential distributed. The random variables and limit state function are summarized as below.
Variables : x1 = D Range: Uniform(4, 12) x2 = H Range: Uniform(4, 12) x3 = D: Exponential(x1, 0.5) x4 = H: Exponential(x2, 0.5)
The volume of the simple cylinder is held as constant of 311. therefore, the limit state function is defined as following equation.
Limit State Function:
The final result is summarized as below: ***** ROBUST DESIGN ***** iteration number .................iter= 2 1st-order standard dev. of g(x)......= 2.8179883E+01 value of limit-state function.....g(x)=-3.73323E-05
variable Robust Point Directional names X-space U-space Cosine width 7.03435E+00 -5.37722E-01 0.11906 height 8.00244E+00 1.97217E-01 0.03728 The standard deviation of the volume is 28.17 vs. 46.23 in the previous example. This example shows the significant effect of design veritable’ distribution types on the standard deviation of limit state function.
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Last Updated 11/12/08
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