Abstract
This paper presents an innovative modeling strategy for the construction of efficient and compact surrogate models for the uncertainty quantification of time-domain responses of digital links. The proposed approach relies on a two-step methodology. First, the initial dataset of available training responses is compressed via principal component analysis (PCA). Then, the compressed dataset is used to train compact surrogate models for the reduced PCA variables using advanced techniques for uncertainty quantification and parametric macromodeling. Specifically, in this work sparse polynomial chaos expansion and least-square support-vector machine regression are used, although the proposed methodology is general and applicable to any surrogate modeling strategy. The preliminary compression allows limiting the number and complexity of the surrogate models, thus leading to a substantial improvement in the efficiency. The feasibility and performance of the proposed approach are investigated by means of two digital link designs with 54 and 115 uncertain parameters, respectively.
Highlights
The ever-growing demand for higher data rates in high-speed links, along with the increasing complexity and miniaturization, is making the effect of uncontrolled variations of design parameters on system performance far from being negligible.Among the several available approaches for uncertainty quantification, Monte Carlo (MC) simulation is undoubtedly the most straightforward method for assessing link performance with respect to parameter uncertainty
We introduce the two surrogate models that are used in the application examples in conjunction principal component analysis (PCA) compression, namely the sparse polynomial chaos expansion (PCE) [18] and the LS-support-vector machine (SVM) regression [22]
We use the UQLab toolbox [30] for calculating sparse PCE surrogate models and the LS-SVMlab toolbox [31] to carry out least-squares SVM (LS-SVM) regressions
Summary
The ever-growing demand for higher data rates in high-speed links, along with the increasing complexity and miniaturization, is making the effect of uncontrolled variations of design parameters (e.g., geometry, material parameters, and components tolerances) on system performance far from being negligible. A reasonable alternative is to build a different surrogate model for each output variable and time instant of interest (see, e.g., [9]) While this reduces the complexity of the single model, the overall number of models to be created is potentially huge, especially if a large number of time points is required, like for example when simulating eye diagrams. The feasibility and strength of the proposed technique are assessed by means of two high-speed links: a 16-bit Flash memory bus operating at 66 MHz (≈1 Gbps) and affected by 54 uncertain design parameters, and a single electronic link affected by 155 stochastic variables and driven by a DDR buffer transmitting at 133 Mbps For both test cases, PCA is applied to obtain a compressed representation of the training data. Throughout the paper, X , x, x, X, X denote a set, a scalar, a vector, a matrix, and a tensor, respectively
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