Numerical efficiency improvement
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Numerical efficiency is a decisive issue in uncertainty processing in view of making the respective analysis methods applicable in engineering practice. Subsequently, a selection of beneficial efficiency improving methods and procedures from the variety of developments are presented.
Reliability assessments, quantified with failure probablities, are usually performed with the aid of Monte Carlo simulations. Though for the determination of small failure probabilties especially in the case of complex nonlinear structures the Monte Carlo simulation meets their limits. A more advanced simulation method is subset sampling, which promises to compensate this drawback.
Neural Network-based Response Surface Approximation
This section deals with the application of the response surface method based on neural networks in the field of engineering. A multi-layer feedforward neural network is employed to replace the underlying structural analysis. It is trained on a data set from initial computations. The application of the backpropagation algorithm for training a neural network requires a decision for a particular training mode. For the examined examples it is shown that the incremental mode possesses different advantages compared to the batch mode. Furthermore, an approach to improve the approximation quality given by a neural network is introduced and demonstrated by means of a numerical example.