Reliability Analysis and Optimization of Mechanical Structures
G.I. Schueller,M.A. Valdebenito2

A basic goal in engineering is designing and constructing systems which satisfy prescribed performance objectives. As an example, consider the design of a building in a seismic area: possible design objectives include limiting the amount of damage during minor seismic events and preventing collapse at major earthquakes. Besides fulfilling these design objectives, the final design of the building should also minimize the construction, maintenance and eventual collapse costs during the life time of the facility, as resources are always scarce. Thus, the design task may be interpreted as an optimization problem, i.e. the objective is to minimize overall costs, while ensuring that the structural performance is within acceptable limits.
A major challenge when designing any engineering system is that many relevant parameters are subject to unavoidable uncertainty. For example, precise characteristics of an earthquake (time history) are not known at the design stage. Another example refers to material properties, such as Young’s modulus, toughness, etc., which can not be characterized by precise (deterministic) values. The uncertainty in these parameters will propagate thus to the response of the system, e.g. due to random variations in loadings, properties, etc., the performance of the system will also vary randomly. Hence, these uncertainties should be reflected in the design process of a system. A possible means to quantify the effects of uncertainty in the system’s response is resorting to probability concepts, as they allow calculating reliability, i.e. the probability that the performance objectives will be fulfilled.
Reliability of a system and minimization of overall costs will be, in general, competing design objectives.
For example, a facility with a high level of reliability (which will be always desired by society) will most likely entail increased costs, as sophisticated construction and maintenance techniques can be required. On the contrary, reduced overall costs due to, e.g. poor construction and inefficient (or even nonexistent) maintenance, will be reflected in low levels of reliability, which can be unacceptable for society. Therefore, an optimal design solution should offer an appropriate trade off between safety and economical costs. Such an optimal solution can be achieved by explicitly incorporating the reliability measure in the optimization problem described above, i.e. by formulating a reliability-based optimization.

The objective of this presentation is introducing some of the most recently developed tools for performing RBO. The focus is on three key issues for solving any RBO problem, namely:

1. Assessment of the reliability of a system by means of Advanced Simulation Techniques (AST).
These techniques allow estimating probabilities of occurrence of rare events efficiently, e.g. for estimating a probability as low as p = 10−6, only a few hundred (or a few thousand) samples are required. AST include some well known sampling schemes such as Importance Sampling (IS) and the more recently developed Line Sampling (LS) [5] and Subset Simulation (SS) [1].

2. Introduction of approximation concepts, in order to simplify RBO problems. Such concepts include, e.g. approximate representations of the reliability of a system [2,3,4].

3. Application of parallel computing, which allows drastically reducing computation times associated with reliability assessment [8].

Theoretical as well as practical aspects on the application of tools for solving RBO problems will be discussed. Case studies will be also analyzed in order to show the applicability and efficiency of the tools introduced. Special emphasis will be given to applications involving damage accumulation during life time of a system, which are of significant relevance in a number of fields of engineering, such as civil, aeronautical, mechanical or offshore engineering, etc.