In modern electronic circuits, the density of packages and interconnections is so high that the analysis of signal propagation and power distribution in printed circuit boards is becoming challenging in terms of computer resources and simulation time. Additional requirements are introduced to assess the impact of tolerances or parameter variability on system performance, since a large number of deterministic simulations are required either to optimize the design or to determine the risk of non-compliance with speciﬁcations. Parameter uncertainties arise from temperature variations, intrinsic characteristics of materials, geometrical and electrical tolerances, etc., that can generate large variability of output signals.
To address these challenges, Georgia Tech C3PS is collaborating with researchers from Politecnico di Torino, Italy in the areas of “Machine Learning to Improve the Reliability of Complex Systems”. This collaboration is a result of a European Union (EU) Project under the category “Internationalization of Research” awarded to Politecnico di Torino, Italy.
Recently, the keyword “Machine Learning” has gained widespread reputation in the above scenario. Machine learning methods are general purposes techniques which have been successfully applied in different research areas as an alternative to the state-of-the-art approaches. However, the benefits of the application of such techniques to realistic structures in terms of both dimension of the parameter space and range of variability of the input parameters still has to be proven. Our research approach focuses exactly on the above issues. The goal is to develop an innovative framework for the black-box modeling of real-life problems. The underlying idea is to combine the flexibility of the support vector machine regression with the powerful and sophisticated sampling schemes such as the adaptive controlled stratification. The interest in this type of approach is to evaluate an extreme quantile of a response of an expensive numerical model through the use of a surrogate model which is developed for free in computational time. The surrogate model, which is generated from a limited number of simulations, allows the estimation of the variability of a system response and its sensitivity analysis in quantifying the impact of the uncertain input parameters. The chosen surrogate model is developed in such a way that it can reproduce a similar trend in terms of sensitivity to the input parameters when the output tends toward an extreme value. The main advantage of this technique is in its ability to provide a data set adapted to the research of the quantile to be estimated. This data set is provided by the surrogate model which has to be well developed. In particular, the surrogate model has to be well correlated with the complex numerical model in the areas of extreme response values of the latter. This correlation relies on the magnitude of the responses of the surrogate and the complex models. In other words, the two responses must have similar trends with respect to the uncertain input variables. The feasibility of the proposed approach will be investigated on realistic challenging-to-solve problems with emphasis on reliability analysis.
The scientific area of collaboration between the two universities will be focused on the development of a modeling framework for the black-box modeling of complex systems with specific emphasis to reliability analysis. The goal of this project is to develop an innovative modeling framework for the black-box modeling of complex systems with specific emphasis on reliability analysis. The underlying idea is to combine the flexibility of the machine learning regressions with advanced techniques for the adaptive sampling to provide a compact and accurate model of the system responses. The model is obtained by training the machine learning regression with a small set of possible noisy system responses. The accuracy of the obtained model is improved according to the information on the sampling patterns provided by the adaptive sampling techniques.