Efficient model order reduction via multi-node moment matching

Abstract

-The new concept of Multi-node Moment Matching (MMM) is introduced in this paper. The MMM technique simultaneously matches the moments at several nodes of a circuit using explicit moment matching around s=0. As compared to the well-known Single-point Moment Matching (SMM) techniques (such as AWE), MMM has several advantages. First, the number of moments required by MMM is significantly lower than SMM for a reduced order model of the same accuracy, which directly translates into computational efficiency. This higher computational efficiency of MMM as compared to SMM increases with the number of inputs to the circuit. Second, MMM has much better numerical stability as compared to SMM. This characteristic allows MMM to calculate an arbitrarily high order approximation of a linear system, achieving the required accuracy for systems with complex responses. Finally, MMM is highly suitable for parallel processing techniques especially for higher order approximations while SMM has to calculate the moments sequentially and cannot be adapted to parallel processing techniques.

Robust identification of continuous-time low-order models using moments of a single rectangular pulse response

“…Assume that the first N moments are equal. Then, for all t, the zero-state responses of S 1 and S 2 are equal provided that their common input is a polynomial in t of degree smaller than or equal to N. Ismail [16] explained the relationship between moments and real poles. Consider a proper transfer function, G (s), having n real poles that can be expressed as a partial fraction expansion:…”

“…For the four models in (13)- (16), namely, FOTD, SODF, SOTD, and SOZDF, their parameterizations can be determined by only the first three or four moments of a simple pulse response in which they are calculated numerically. Here, let the kth moment of a rectangular pulse response be m y k .…”

“…Using (11), the first four moments of the impulse response of the SOZDF model (16) can be determined by means of the moments of the pulse response as in (49). It means that m g k , k = 0, 1, 2, .…”

Large-Scale Battery System Development and User-Specific Driving Behavior Analysis for Emerging Electric-Drive Vehicles

“…The proposed solution builds upon the multi-node moment matching method [24]. Compared with conventional single-point moment matching techniques, such as the AWE method, the multi-node moment matching method offers a number of advantages, including requiring fewer number of moments under the same accuracy constraint, hence higher computation efficiency and better numerical stability.…”

Large-scale battery system modeling and analysis for emerging electric-drive vehicles

“…Frequency-Domain Analysis: A unified frequency-domain electric and thermal analysis solution that builds upon the multi-node moment matching method (MMM)[2] is proposed. Compared with conventional single-point moment matching techniques, such as the AWE method, MMM offers a number of advantages, including requiring fewer number of moments under the same accuracy constraint, hence higher computation efficiency and better numerical stability.Using the Laplace transformation, Equation 15-17 follow:sCe(s) − Ce(0) = K · I/s + Ce(t 0 ) · F · (KRI − Z 0 /s − Z 1 Ce(s)),(18)and sCtT (s) − G · T (s) = P/s + Ct · T (0).…”