1.2. Reliability-Based Design Philosophy#
The video below introduces the reliability-based design philosophy of the unit, which relies heavily on reliability analysis to analyze structures, risk analysis and risk-based assessment criteria, all of which builds on what we covered in MUDE.
Download slides (PDF) from the video above.
Three Primary Topics#
There are three key points that are covered in this video that we want you to take with you throughout this unit.
Two topics were already introduced in MUDE: extreme value analysis and system reliability. The first is important because it is critical for properly assessing the variability in loads on hydraulic and offshore strucutres. It is especially important for extrapolating for very rare conditions that have never been observed before; for example, some dikes in the Netherlands are designed using the one-in-ten thousand year return period, but we really only have around 100 years of quality data! The extreme value distribution you select for design is often used for one of the random variables in a reliability analysis, described below.
System reliability is used when we have many components or failure mechanisms that play a role in the system we are designing. We will practice representing our physical system with simple representations like series and parallel systems in order to evaluate whether or not it’s safe and to improve our design. For this unit, you can think of a system analysis as the combination of many individual component reliability analysis.
Component reliability analysis is one of the primary probabilistic tools we will use for assessing our structures and systems. It is primarily focused on finding the probability of failure of one failure mechanism, or one component within a system. Key elements are a limit-state function, \(g(\textbf{x})\), which mathematically defines failure as a function of the variables of interest, and a multivariate probability density function, \(f_\textbf{x}(\textbf{x})\), where \(\textbf{x}\) is a vector of random variables. If we define the failure region as \(\Omega\) (it’s convenient if we define \(g(\textbf{x})\)) such that failure \(<0\)), our reliability problem becomes simply:
While the integral is simple and can be solved analytically for some cases, in practice this is must be solved with a variety of numerical methods due to a number of reasons, for example:
the limit-state function is non-linear
the marginal distributions (the distribution of each random variable) are diverse
there is dependence between the random variables
the limit-state function may not be possible to represent in a closed-form analytic expression (e.g., it’s based on a finite element model)
Although there are many methods to solve this problem, we will focus on two: Monte Carlo simulation (MCS) and the First-Order Reliability Method (FORM). By working through the process of completing a reliability-based design, it will be relatively straightforward for you to learn and apply different methods in the future.
Risk Analysis and Safety Standards#
Although this is not a primary topic of the unit, we will use some of the techniques covered in MUDE to derive risk-based satefy standards for our design projects. The level of detail and sophistication depends on the industry and regulations that govern it. We will cover this more throughout the quarter, but just to give you an idea:
the design of flood defences in the Netherlands is governed by one of the most detailed risk-based frameworks in the world. Satefy standards are derived based on a maximum allowable probability of flooding, which are then turned into a maximum allowable probaibility of failure for a specific failure mechanism of a structure (e.g., a dike) using system and component reliability analysis
the design of breakwaters is typically governed by a somewhat subjective maximum allowable failure probability over the structure design lifetime. This is most easily connected to the most dominant load and failure mechanism by choosing a hydraulic load with a return period corresponding to the failure
offshore renewable stuctures can be designed by optimizing expected economic damages (or minimizing losses). Although the procedure is relatively straightforward, it is not standardized in the industry
floating and submerged structures is a relatively new field, and the derivation of safety standards can be complex, not only because of the life safety issues involved, but perhaps due to societal perception of a submerged tunnel. Imagine if such a structure failed catastrophically—what would the public think? You might have a hard time convincing them to ever drive in such a structure! This can be taken into account by lowering your allowable system failure probability.
We hope these examples illustrate the challenges at hand for your design projects during the quarter, and will help you reflect on your design as you are evaluating it.