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Effect of load-generation variability on power grid cascading failures
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
R. Rocchetta, E. Patelli, L. Bing, G. Sansavini
This section proposes a concise introduction to uncertainty quantification and methods for global sensitivity analysis. Traditionally, uncertainty quantification and analysis consist in the assignment of probability distributions to the model input factors (variables and parameters). Once the uncertainty has been characterized, it is propagated into the simulation code via Monte Carlo method. First, uncertain factors are characterised by assigning probability distributions. This is an important step which has to be performed adequately to assure high quality and consistency of results (Patelli, Pradlwarter, & Schuller 2010). Then, samples are obtained from the joint probability distribution of the input factors, e.g. by Latin hypercube sampling, quasi-random sequences or crude Monte Carlo inverse transform sampling (Patelli, Broggi, Angelis, & Beer 2014). Once the ith input realisation is obtained Xi = [Xi(0),..,Xi(m)], the sample is forwarded to the computational model M(X). This allows obtaining information about the input-output mapping defined by the computational model as follows: () M:X→Y,X→Y=M(X)
Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models
Published in Nuclear Science and Engineering, 2023
For physics-based computational models, VVUQ has been very widely investigated, and many methodologies have been developed.17 In brief, verification aims to identify, quantify, and reduce errors during the mapping from a mathematical model to a computational model; validation aims to determine the degree of accuracy of the model in representing real physics. In physics-based modeling and simulation, estimating the uncertainties in output responses is an essential step in model validation, and it can establish confidence in the model predictions. Uncertainty quantification methods for physical models provide an estimate of output uncertainties by propagating uncertainties from random input parameters, with methods such as Monte Carlo sampling, stochastic spectral methods and surrogate-based methods, etc. Uncertainty quantification of ML models is equally important but is relatively less studied, especially in nuclear engineering. The focus of this paper is on UQ of ML models, more specifically neural networks because they are the most widely used supervised ML algorithm for both regression and classification tasks.
Knowledge transfer using Bayesian learning for predicting the process-property relationship of Inconel alloys obtained by laser powder bed fusion
Published in Virtual and Physical Prototyping, 2022
Cuiyuan Lu, Xiaodong Jia, Jay Lee, Jing Shi
As mentioned previously, significant efforts have been made on using machine learning approaches to study the challenging issues related to metal additive manufacturing (Sing et al. 2021) as well as other manufacturing processes (Gong et al. 2022). The Bayesian learning model is favoured in this problem setting for the following reasons. First, uncertainty quantification is important for engineering applications because it can be used to calibrate the model confidence under given input, and also it can be considered in the process parameter optimisation for robust solutions. Second, the majority of the transfer learning algorithms are focused on the classification problems. Transfer learning of prediction tasks related to the process-property relationship for metal additive manufacturing is uncharted to the best of our knowledge. Third, the Bayesian approach has rigorous mathematical derivations, and the associated sensitivity tests can be used to validate and verify the model performance.
Shape optimization and uncertainty assessment of a centrifugal pump
Published in Engineering Optimization, 2022
Alessia Fracassi, Remo De Donno, Antonio Ghidoni, Pietro Marco Congedo
In an uncertain environment, the objective function and the constraint depend not only on the design variables , as shown above, but also on a random vector of the uncertainties that impact on the pump performance. The uncertainty quantification refers to the assessment of the effect of the input uncertainties on model outputs or results. Given , these uncertainties are propagated through a computational model, and statistical or interval assessments are evaluated on the resulting responses.