Optimization and reliability of complex systems

Optimization of mechanical structures aims to determine the best possible design in terms of cost and quality. In general, the designer considers an optimization criterion, restrictions and real or integer numerical design variables, and uses deterministic procedures. Examples include standard descent methods or stochastic or hybrid algorithms. However, this widespread approach can fall short when parameter variability or random phenomena need to be taken into account.

Because of errors in modeling the uncertainties inherent in mechanical characteristics, geometrical dimensions, manufacturing and assembly processes, design models for mechanical structures have to take account of uncertainties in design parameters right from the design phase, and subsequently during the optimization process. This raises the question of the robustness of optimization with regard to uncertainties in design parameters, and the questioning of solutions found by deterministic optimization methods.

A first approach, to take into account what are generally referred to as uncertainties, is to use safety coefficients, i.e. not to consider the result of the optimization as being the design to be proposed, but to modify it in such a way as to ensure greater reliability, generally by means of a multiplicative coefficient. This approach suffers from its lack of generality: safety coefficients, also known as safety factors, are closely linked to the particular situation studied and to the engineer's experience, and cannot therefore be extended to new situations, especially when accumulated experience is still weak and the history of observed faults is not sufficiently rich.

In response to these difficulties, analysis methods tending to take randomness into account have been developed. One of the first aspects of this approach was to check the level of reliability or, equivalently, the probability of failure of the solution to the optimization problem. In this way, it is customary to seek to determine an optimal design that satisfies a minimum level of reliability: this is known as reliability-aware optimization.