Keywords: neural networks, uncertainty, imprecise probability, structural analysis, hybrid approaches, reliability assessment.

The chapter presents a review summarizing selected research results recently obtained by the authors. The main focus is on soft computing methods developed for the structural analysis. Artificial neural network approaches are highlighted, which can by applied for several tasks in engineering, e.g. numerical structural monitoring, lifetime prediction, reliability analysis and robustness assessment.

A significant task in computational engineering is to describe and predict numerically the structural behaviour in a realistic manner. Beside sophisticated numerical procedures to map physical phenomena and processes, an adequate description of available data covering the content of information provided is of prime importance.

Generally, the availability of information in engineering practice is limited. Incomplete, fragmentary, diffuse, and frequently expert specified knowledge leads to imprecision in data. In addition, engineers have to cope with the objective variability and fluctuations in material, geometry and loading. The traditional uncertainty model randomness can be used to describe uncertainty with an objective source. The reason is the frequentistic view on probability, which is the popular presupposition. A random event should be unlimited repeatable at constant reproduction conditions. by contrast, imprecision represents a subjective assessment, for which non-traditional uncertainty models like fuzziness are more appropriate. Applying imprecise probability concepts, objective components as well as subjective components of the uncertainty can be considered simultaneously.

The fuzzy stochastic structural analysis provides a rational framework to predict the structural behaviour under consideration of all significant nonlinearities and uncertain parameters assessed by imprecise probability. In this chapter, model-based, model-free and hybrid approaches are presented for the fuzzy stochastic structural analysis. Due to the complexity of the model-based methods, e.g. sophisticated finite element analyses of large nonlinear systems, a particularly efficient form of an approximation scheme is required. In this chapter, the improvement of the numerical efficiency is discussed utilizing neural network based response surface approximation schemes as hybrid approaches. Another hybrid approach is the combination of model-free material descriptions with neural networks and structural models. Artificial neural networks can be applied to predict the structural behaviour without using physical models. In this model-free approach, structural responses are computed based on results from structural monitoring.

The prediction of uncertain structural responses succeeds with the proposed soft computing methods. This is demonstrated by means of examples.

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