Robust artificial neural network for reliability and sensitivity analysis of complex non-linear systems

Uchenna Bright Oparaji, Sheu Rong-Jiun, Mark Bankhead, Jonathan Austin, Edoardo Patelli

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
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Artificial Neural Networks (ANNs) are commonly used in place of expensive models to reduce the computational burden required for uncertainty quantifcation, reliability and sensitivity analysis. ANN with selected architecture is trained with the back-propagation algorithm from few data representatives of the input/output relationship of the underlying model of interest. However, different performing ANNs might be obtained with the same training data as a result of the random initialization of the weight parameters in each of the network, leading to an uncertainty in selecting the best performing ANN. On the other hand, using cross-validation to select the best performing ANN based on the ANN with the highest R2 value can lead to biassing in the prediction. This is as a result of the fact that the use of R2 cannot determine if the prediction made by ANN is biased. Additionally, R2 does not indicate if a model is adequate, as it is possible to have a low R2 for a good model and a high R2 for a bad model. Hence in this paper, we propose an approach to improve the robustness of a prediction made by ANN. The approach is based on a systematic combination of identical trained ANNs, by coupling the Bayesian framework and model averaging. Additionally, the uncertainties of the robust prediction derived from the approach are quantified in terms of condence intervals. To demonstrate the applicability of the proposed approach, two synthetic numerical examples are presented. Finally, the proposed approach is used to perform a reliability and sensitivity analysis on a process simulation model of a UK nuclear effluent treatment plant developed by National Nuclear Laboratory (NNL) and treated in this study as a black-box employing a set of training data as a test case. This model has been extensively validated against plant and experimental data and used to support the UK effluent discharge strategy.
Original languageEnglish
Pages (from-to)80-90
Number of pages11
JournalNeural Networks
Early online date17 Sep 2017
Publication statusPublished - 1 Dec 2017


  • Monte-Carlo simulation
  • global sensitivity analysis
  • reliability analysis
  • artificial neural network
  • uncertainty quantification


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