A New Deterministic Approach in Probabilistic Design Optimization

In this paper, a simple and powerful formulation is presented for probabilistic design of engineering systems. The challenging task of optimum allocation of errors to design variables is transformed into a simple zero degree of difficulty geometric programming problem. This method is based on a known state of the design (the design values as well as the linear mapping between the input and output of the system). Uncertainties of design variables are assumed to be independent, and normally distributed. Failure is defined as a constraint in the optimization process, and has the form of the probability of divergence of outputs from their allowable bounds. Then, this constraint is simplified into a deterministic bound within six sigma spread. Having a zero DOD problem, the optimal solutions are readily available for any system regardless of the complexity. Several numerical experiments are conducted to assess the efficiency of the proposed formulation. The results are compared with more exhaustive searches using Monte Carlo simulation. For higher order and complex systems, it is demonstrated that this formulation will be %20 more conservative than the exact Monte Carlo simulation.