Many (mostly empirical) design formulae have been developed for the conceptual design of coastal structures. A number of these design formulae have been implemented in the software package BREAKWAT from WL / Delft Hydraulics. BREAKWAT is used by a large number of (inter)national parties such as (marine) contractors, engineering companies, universities, etc. The facility is widely applied as a tool to guide and assist in the design of many types of breakwaters.
The actual design formulae require several input parameters that describe the hydraulic environment (e.g. wave conditions) and the geometric properties of the structure. In practise, these input parameters are hardly ever known with a high degree of accuracy, and in design studies, decision-making and risk analysis, these uncertainties should be taken explicitly into account. So far this has not been done in a structured, quantitative, and statistically sound way, and in BREAKWAT applications little or no information is yet available about the uncertainty which must be assigned to the output parameters of design formulae.
In the present case an ensemble method was developed and implemented for uncertainty assessment for design formulae in BREAKWAT. The uncertainties in the input parameters must be specified by the user. This specification is based on elementary concepts of statistics which conveniently enable designers to take the effects of uncertainties into account, even if detailed information is missing. The user's input is translated into analytical probability distributions for the input parameters. For a large number of randomly generated samples of the input parameters, the design formula is used to construct a so-called empirical distribution of the output parameter. From this distribution several statistical quantities may be derived, such as the mean value, spread, and quantiles. In this way estimates for the output parameter and its uncertainty (in the form of confidence intervals) may be derived. Apart from the actual uncertainty assessment, the methodology can also be used for a sensitivity analysis to gain insight in the effect of variations of input parameters on the output parameter.
In this case a design formula to determine the dimensions of the rock material in the top-layers of a breakwater structure was selected. In practise this dimension of the rock material is an important parameter in the design of breakwaters. The output parameter, the nominal stone diameter Dn50, depends on 8 input parameters, and realistic estimates for their uncertainties were assigned to all these input parameters. |
