Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

6.6 Conclusion: The Modelling Process and Open Statistical and Computing Challenges

Indirect modelling of the uncertain inputs is thought to have great potential for risk and uncertainty modelling: industrial samples often embrace varied degrees of freedom over the structures or systems under risk. There is thus quite a wealth of information to be retrieved in order to circumvent the variability of the systems and thus better control uncertain deviations from normal design. Amongst the various algorithms, a step-by-step approach is generally recommended starting with the less data-consuming framework of parameter identification and checking the residuals of such elementary model calibration before inferring intrinsic variability that requires full inversion techniques and more observations in order to converge. Linearisation around the best-estimate inputs is generally also a good starting point before going into non-linear formulations.

In this high-potential domain, considerable research is still needed. The existing methods mostly ignore the intrinsic variability of the model inputs through traditional calibration/assimilation or parameter estimation procedures. Only recently have the true inverse probabilistic methods been developed, mostly in the linearised Gaussian case. Non-linear and/or non Gaussian situations call for significant challenges to be overcome. This is obviously so on the computational side, as the integrals involved prove to be even more challenging than those ...