Response Surface Approximation for Reliability-Based Optimization
For the present work, response surface approximation of two types was created.
The first type is analysis response surface (ARS), which is fitted to the strains in the
laminate in terms of both design variables and random variables. Using the ARS, the
probability of failure at every design point can be calculated inexpensively by Monte
Carlo simulation based on the fitted polynomials. The second type of response surface is
design response surface (DRS) that is fitted to probability of failure as a function of
design variables. The DRS is created in order to filter out noise induced by the Monte
Carlo simulation and is used to calculate the reliability constraint in the design
optimization. The details of the ARS/DRS approach are given in chapter three.
Analysis Response Surfaces
Besides the design and random variables described in the problem formulation, the
service temperature was treated as a variable ranging from 770F to -4230F in order to
avoid constructing analysis response surfaces at each selected temperature. Therefore, the
total number of variables was seventeen. However, the strains in the laminate do not
depend on the Hyve strain allowables, so the ARS were fitted to the strains in terms of
twelve variables, which included four design variables, four elastic properties, two
coefficients of thermal expansion, the stress-free temperature and the service temperature.
The range of the design variables (Table 5-3) for the ARS was chosen based on the
values of the optimal deterministic design. Ranges for random variables are automatically
handled and explained below. Using the ARS and five strain allowables, probabilities of
failure are calculated by Monte Carlo simulations, while the strain constraints were
evaluated at 21 uniformly distributed service temperatures between 770F and -4230F.