Book Description

Inhaltsangabe:Introduction: In handling real-world optimization problems, it is often the case that the underlying decision variables and parameters cannot be controlled exactly as specified. For example, if a deterministic consideration of an optimization problem results in an optimal dimension of a cylindrical member to have a 50 mm diameter, there exists no manufacturing process which will guarantee the production of a cylinder having exactly a 50 mm diameter. Every manufacturing process has a finite machine precision and the dimensions are expected to vary around the specified value. Similarly, the strength of a material often does not remain fixed for the entire length of the material and is expected to vary from point to point. When such variations in decision variables and parameters are expected in practice, an obvious question arises: How reliable is the optimized design against failure when the suggested parameters cannot be adhered to? This question is important because in most optimization problems the deterministic optimum lies at the intersection of a number of constraint boundaries. Thus, if no uncertainties in parameters and variables are expected, the optimized solution is the best choice, but if uncertainties are expected, in most occasions, the optimized solution will be found to be infeasible, violating one or more constraints. These uncertainties, which are either controllable (e.g.imensions) or uncontrollable (e.g. material properties), are present and need to be accounted for in the design process. Assuming that the variables follow a probability distribution in practice, reliability-based design optimization (RBDO) methods find a reliable solution which is feasible with a pre-specified probability. In most RBDO problems, failure probability and costs are violating objectives, which means that when one is lowered, the other may rise. Therefore, it is important to identify the uncertain variables which have an impact on the problem and describe them with different probability distributions based on statistical calculations. Then, the ordinary deterministic constraint is replaced by a stochastic constraint which is only restricting the probability of failure for a solution, not the failure itself. This can be done for each constraint or for the complete set of constraints, for the complete structure. Different methods for evaluating the reliability of a solution exist. If the cumulative density function (CDF) with its [...]