Multidimensional Uncertainty Quantification of Microwave/RF Networks Using Linear Regression and Optimal Design of Experiments

Prasad, Aditi Krishna; Ahadi, Majid; Roy, Sourajeet

doi:10.1109/tmtt.2016.2584608

Cited by 37 publications

(24 citation statements)

References 46 publications

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“…As mentioned in Section 4.2.1, the frequency response is typically approximated using one PCE per frequency point, equivalently, per time step in time-domain approaches. 37,53 This can be computationally expensive in cases where a large number of frequency points must be examined. For high-frequency models where the frequency dependence is also a relatively smooth functional, eg, no sharp resonances exist in the examined frequency range, one can extend the presented surrogate modeling approach, such that it includes the frequency dependence as well.…”

Section: Broadband Surrogate Modelingmentioning

confidence: 99%

“…In the context of this work, a further reason for investigating and improving the LS-PCE method is its popularity in the setting of EM simulations. [33][34][35][36][37] The approximation accuracy of the PCE is crucially affected by the choice of the polynomial space P M . This is especially relevant in high-dimensional approximations because of the fact that the dimension of P M grows very fast with the number of RVs, which constitutes a manifestation of the so-called curse of dimensionality.…”

Section: Introductionmentioning

confidence: 99%

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Robust adaptive least squares polynomial chaos expansions in high‐frequency applications

Loukrezis

Galetzka

Gersem

2020

Int J Numerical Modelling

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We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic high-frequency electromagnetic models in a black-box way, in particular, given only a dataset of random parameter realizations and the corresponding observations regarding a quantity of interest, typically a scattering parameter. The construction of the polynomial basis is based on a greedy, adaptive, sensitivity-related method. The sequential expansion of the experimental design employs different optimality criteria, with respect to the algebraic form of the least squares problem. We investigate how different conditions affect the robustness of the derived surrogate models, that is, how much the approximation accuracy varies given different experimental designs. It is found that relatively optimistic criteria perform on average better than stricter ones, yielding superior approximation accuracies for equal dataset sizes. However, the results of strict criteria are significantly more robust, as reduced variations regarding the approximation accuracy are obtained, over a range of experimental designs. Two criteria are proposed for a good accuracy-robustness trade-off.keywordspolynomial chaos, surrogate modeling, high-frequency electromagnetic devices, least squares regression, adaptive basis, sequential experimental design

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Section: Broadband Surrogate Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust adaptive least squares polynomial chaos expansions in high‐frequency applications

Loukrezis

Galetzka

Gersem

2020

Int J Numerical Modelling

View full text Add to dashboard Cite

show abstract

“…Moreover, a sparse linear regression method for high-speed circuits based on the modified Fedorov search algorithm is described in [70], which utilizes comparatively few regression nodes for the PC coefficient computation. Linear regression has been used with optimal regression nodes based on D-optimal design for microwave/RF networks in a multi-dimensional UQ framework [71]. In [72], the regression nodes are selected by a non-adaptive quasi-optimal technique (for least squares linear regression), which maximizes a parameter based on the mutual column orthogonality and the determinant of the model matrix.…”

Section: Pc-based Applications In Electronicsmentioning

confidence: 99%

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

2018

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Advances in manufacturing process technology are key ensembles for the production of integrated circuits in the sub-micrometer region. It is of paramount importance to assess the effects of tolerances in the manufacturing process on the performance of modern integrated circuits. The polynomial chaos expansion has emerged as a suitable alternative to standard Monte Carlo-based methods that are accurate, but computationally cumbersome. This paper provides an overview of the most recent developments and challenges in the application of polynomial chaos-based techniques for uncertainty quantification in integrated circuits, with particular focus on high-dimensional problems.

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“…Consequently, quantification of such effects and, eventually, reducing them already at the design stage is essential to ensure the structure robustness. 3,4 The latter normally means diminishing statistical moments of the system outputs, especially their variance. 5 However, for microwave components, design specifications are often expressed in a minimax form, that is, using upper/lower bounds for the selected figures of interest (eg, maximum acceptable level of reflection, minimum acceptable bandwidth, maximum acceptable power split error, etc.)…”

Section: Introductionmentioning

confidence: 99%

Rapidtolerance‐awaredesign of miniaturized microwave passives by means ofconfined‐domainsurrogates

Pietrenko‐Dabrowska

2020

Int J Numerical Modelling

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The effects of uncertainties, primarily manufacturing tolerances but also incomplete information about operating conditions or material parameters, can be detrimental to the performance of microwave components. Quantification of such effects is essential to ensure a meaningful evaluation of the structure, in particular, its reliability under imperfect fabrication procedures. The improvement of the circuit robustness can be achieved by reducing sensitivity to geometry/material parameter deviations, which requires optimization of suitably chosen statistical performance metrics such as the yield. The prerequisite for the latter is statistical analysis. In the case of compact circuits, it is executed through full-wave electromagnetic (EM) analysis. The fundamental difficulty, that is, the high CPU cost, can be alleviated by the employment of fast surrogate models, which is the method of choice for the majority of contemporary approaches. Despite its advantages, a practical challenge of surrogate-assisted design is the initial computational overhead related to metamodel construction. As a workaround, this work proposes the employment of a recently introduced concept of constrained modelling, where the surrogate domain is confined only to contain the essential subsets of the parameter space. In the context of yield optimization, the domain needs to correspond to directions featuring maximum variability of the circuit responses (particularly the parts thereof that affect the yield value in the most significant way) with respect to its geometry parameters. The small volume of the domain spanned by such directions permits setting up an accurate model using a fraction of training data samples required by conventional methods. The proposed technique is demonstrated using a miniaturized microstrip rat-race coupler with its yield optimized at the cost of just a few dozen of EM simulations of the circuit. EM-based Monte Carlo simulations corroborate the reliability of the approach.

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Multidimensional Uncertainty Quantification of Microwave/RF Networks Using Linear Regression and Optimal Design of Experiments

Cited by 37 publications

References 46 publications

Robust adaptive least squares polynomial chaos expansions in high‐frequency applications

Robust adaptive least squares polynomial chaos expansions in high‐frequency applications

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

Rapidtolerance‐awaredesign of miniaturized microwave passives by means ofconfined‐domainsurrogates

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