Abstract
In the probabilistic analysis of engineering systems, the design point denotes a particular set of input parameters where the system response is most likely to take a given design value. It provides important information on the system behaviour and its sensitivity to input parameters. The design point is determined from the joint probability distribution function (pdf) of input parameters. Mathematically, the problem is equivalent to an isoperimetric problem: find a stationary point of the joint pdf subject to the given value of the system response. The proposed method depends on the response and the joint pdf being parallel at the stationary point. This requires the projection of the pdf gradient to be zero on the hyperplane orthogonal to the response gradient. Therefore, the design point is found by moving iteratively on the response surface in the direction of a non-zero projection vector until this vector vanishes. Convergence of this process is intuitively guaranteed. The method can be implemented for any number of input parameters. An example application is presented which demonstrates finding the most probable design metocean conditions for a floating structure. Such a problem is part of the response based analysis of offshore systems, which provided the initial motivation for this work. References H. O. Madsen, S. Krenk and N. C. Lind. Methods of structural safety . Dover, 1986. http://store.doverpublications.com/0486445976.html . S. R. Winterstein. An introduction to structural reliability, FORM, and LRFD design. Technical report , 2011. https://dl.dropboxusercontent.com/u/3121325/lrfd/lrfd.pdf . S. Winterstein, T. C. Ude, C. A. Cornell, P. Bjerager and S. Haver. Environmental parameters for extreme response: inverse FORM with omission sensitivity. Structural Safety and Reliability, Proc., ICOSSAR `93 , A. A. Balkema, 1994. R. G. Standing, R. Eichaker, H. D. Lawes, B. Campbell and R. B. Corr. Benefits of applying response based design methods to deepwater FPSOs. Offshore Tech. Conf. , 2002. doi:10.4043/14232-MS . P. S. Tromans and L. Vanderschuren. Response based design conditions in the North Sea: application of a new method. Offshore Tech. Conf. , 1995. doi:10.4043/7683-MS . I. M. Gefland and S. V. Fomin. Calculus of variations . Dover, 2000. http://store.doverpublications.com/0486414485.html . J. Mathews and R. L. Walkers. Mathematical Methods of Physics . W. A. Benjamin, 1964. E. M. Bitner-Gregersen. Joint probabilistic description of combined seas. ASME Proc., Safety and Reliability , OMAE2005–67382:169–180, 2005. doi:10.1115/OMAE2005-67382 . N. Morgan. Marine technology reference book . Butterworth–Heinemann, 1990.
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