Inverse-free second moment method for electrical systems with uncertain parameters

• Published in: International journal of circuit theory and applications 2005-03, Vol.33 (2), p.135-145
• Main Authors: Shakshuki, E., Ponnambalam, K., Vlach, J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Electric, optical and optoelectronic circuits; Electronics; Exact sciences and technology; random algebraic equations; reliability; second moment methods; sparse matrices; Theoretical study. Circuits analysis and design
• ISSN: 0098-9886; 1097-007X
• DOI: 10.1002/cta.308

Engineering systems are usually designed deterministically, but if there are uncertainties in parameters, an appropriate approach is to use probabilistic methods. For reliability estimation it is necessary to have at least the first two moments including means and covariances of the output variables. Most of the existing methods applied to problems involving linear systems need inverses of matrices. There are two problems with these approaches. First, for large sparse linear systems (for example, a tri‐diagonal system) the inverse is fully dense. Second, the mean of the random matrix has to be non‐singular. In this paper, we present a new method to automatically formulate the moment equations that aims to overcome the drawbacks of these methods and apply it on electrical networks. This method does not require an inverse and able to solve problems when the mean matrix of a system is singular. In addition, it takes advantage of both sparsity (zero elements) and deterministic coefficients. This method can be used to solve both uncorrelated and correlated cases. To demonstrate the feasibility of this method, a quantitative comparison with another existing method requiring the inverse and with Monte Carlo results is done. Copyright © 2005 John Wiley & Sons, Ltd.