Reliability-Based Optimal Design of Complex Structures for Life-Cycle Performance under Uncertainty
Professor Emeritus A.H-S. Ang, University of California
Determining the proper reliability, in terms of the required safety index, remains an issue in the optimal design of a complex structural system for ensuring adequate life-cycle structural safety. This issue is addressed from the standpoint of the probabilistic reliability-based approach. As is well-known, the required safety indices for the design of structural components have been established (primarily through calibration) but not for the design of a complete structure as a system..
The main issue is how to handle uncertainties in design. In this regard, uncertainties in engineering can be classified into two broad types – the aleatory and epistemic types, known as “data-based” and “knowledge-based”, respectively. The aleatory type is the natural variability in information and its effect can be expressed in terms of probability; whereas the epistemic type may be represented by a range of possibilities and its effect may also be expressed in the same probability terms.
The effect of the aleatory uncertainty will result in the probability of failure of a structure. For a complex structural system, the PDEM is effective in its analysis and assessment, yielding the PDF of the ultimate system performance, Zmax. This result provides a convenient vehicle, and represents a rational basis for including the effect of the epistemic uncertainty, from which the real failure probability (and its associated safety index) becomes a random variable; any of its value may then be associated with a “statistical” confidence level.
For design, a high confidence level is desirable to ensure life-cycle structural safety.
The determination of the confidence level for the design of a complex system is discussed in light of good professional practice (including design standards) in the successful design of major existing critical systems.
The process for determining the proper safety index for the optimal design of a complex structure, as a complete system, is summarized in several steps.