Marissa Condon

24-h electrical load data—a sequential or partitioned time series?

Variations in electrical load are, among other things, hour of the day dependent, introducing a dilemma for the forecaster: whether to partition the data and use a separate model for each hour of the day (the parallel approach), or use a single model (the sequential approach). This paper examines which approach is appropriate for forecasting hourly electrical load in Ireland. It is found that, with the exception of some hours of the day, the sequential approach is superior. The final solution however, uses a combination of linear sequential and parallel neural models in a multi-time scale formulation.

Empirical Balanced Truncation of Nonlinear Systems

Abstract Novel constructions of empirical controllability and observability gramians for nonlinear systems are proposed for subsequent use in a balanced truncation style of model reduction. The new gramians are based on a generalisation of the fundamental solution for a Linear Time-Varying system. Relationships between the given gramians for nonlinear systems and the standard gramians for both Linear Time-Invariant and Linear Time-Varying systems are established as well as relationships to prior constructions proposed for empirical gramians. Application of the new gramians is illustrated through a sample test-system.

On second-order differential equations with highly oscillatory forcing terms

We present a method to compute efficiently solutions of systems of ordinary differential equations (ODEs) that possess highly oscillatory forcing terms. This approach is based on asymptotic expansions in inverse powers of the oscillatory parameter, and features two fundamental advantages with respect to standard numerical ODE solvers: first, the construction of the numerical solution is more efficient when the system is highly oscillatory, and, second, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, featuring the Van der Pol and Duffing oscillators and motivated by problems in electronic engineering.

Nonlinear systems – algebraic gramians and model reduction

Purpose – Nonlinear dynamical systems may, under certain conditions, be represented by a bilinear system. The paper is concerned with the construction of the controllability and observability gramians for the corresponding bilinear system. Such gramians form the core of model reduction schemes involving balancing.Design/methodology/approach – The paper examines certain properties of the bilinear system and identifies parameters that capture important information relating to the behaviour of the system.Findings – Novel approaches for the determination of approximate constant gramians for use in balancing‐type model reduction techniques are presented. Numerical examples are given which indicate the efficacy of the proposed formulations.Research limitations/implications – The systems under consideration are restricted to the so‐called weakly nonlinear systems, i.e. those without strong nonlinearities where the essential type of behaviour of the system is determined by its linear part.Practical implications –...

An efficient nonlinear circuit simulation technique

This paper proposes a novel method for the analysis and simulation of integrated circuits (ICs) with the potential to greatly shorten the IC design cycle. The circuits are assumed to be subjected to input signals that have widely separated rates of variation, e.g., in communication systems, an RF carrier modulated by a low-frequency information signal. The proposed technique involves two stages. Initially, a particular order result for the circuit response is obtained using a multiresolution collocation scheme involving cubic spline wavelet decomposition. A more accurate solution is then obtained by adding another layer to the wavelet series approximation. However, the novel technique presented here enables the reuse of results acquired in the first stage to obtain the second-stage result. Therefore, vast gains in efficiency are obtained. Furthermore, a nonlinear model-order reduction technique can readily be used in both stages making the calculations even more efficient. Results will highlight the efficacy of the proposed approach

Krylov subspaces from bilinear representations of nonlinear systems

Purpose – The paper is aimed at the development of novel model reduction techniques for nonlinear systems.Design/methodology/approach – The analysis is based on the bilinear and polynomial representation of nonlinear systems and the exact solution of the bilinear system in terms of Volterra series. Two sets of Krylov subspaces are identified which capture the most essential part of the input‐output behaviour of the system.Findings – The paper proposes two novel model‐reduction strategies for nonlinear systems. The first involves the development, in a novel manner compared with previous approaches, of a reduced‐order model from a bilinear representation of the system, while the second involves reducing a polynomial approximation using Krylov subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example.Research limitations/implications – The proposed methodology is applicable to so‐called weakly nonlinear systems, where b...

On numerical methods for highly oscillatory problems in circuit simulation

Purpose – The purpose of this paper is to analyse a novel technique for an efficient numerical approximation of systems of highly oscillatory ordinary differential equations (ODEs) that arise in electronic systems subject to modulated signals.Design/methodology/approach – The paper combines a Filon‐type method with waveform relaxation techniques for nonlinear systems of ODEs.Findings – The analysis includes numerical examples to compare with traditional methods such as the trapezoidal rule and Runge‐Kutta methods. This comparison shows that the proposed approach can be very effective when dealing with systems of highly oscillatory differential equations.Research limitations/implications – The present paper constitutes a preliminary study of Filon‐type methods applied to highly oscillatory ODEs in the context of electronic systems, and it is a starting point for future research that will address more general cases.Originality/value – The proposed method makes use of novel and recent techniques in the area ...

On comparison of integral equation approaches for indoor wave propagation

Two integral equation formulations for the analysis of two-dimensional indoor EM wave propagation are discussed in this paper. The volume and the surface electric fleld integral equations are discretised by the Method of Moments, resulting in dense linear systems whose iterative solutions are accelerated by using acceleration techniques. Numerical results are presented to compare the performance of the two approaches when applied to the same indoor propagation problem.

Efficient Wideband Electromagnetic Scattering Computation for Frequency Dependent Lossy Dielectrics Using WCAWE

This paper presents a model order reduction algorithm for the volume electric field integral equation (EFIE) formulation, that achieves fast and accurate frequency sweep calculations of electromagnetic wave scattering. An inhomogeneous, two-dimensional, lossy dielectric object whose material is characterized by a complex permittivity which varies with frequency is considered. The variation in the dielectric properties of the ceramic BaxLa4Ti 2+xO 12+3x in the <1 GHz frequency range is investigated for various values of x in a frequency sweep analysis. We apply the well-conditioned asymptotic waveform evaluation (WCAWE) method to circumvent the computational complexity associated with the numerical solution of such formulations. A multipoint automatic WCAWE method is also demonstrated which can produce an accurate solution over a much broader bandwidth. Several numerical examples are given on order to illustrate the accuracy and robustness of the proposed methods.

Improved Forward Backward Method With Spectral Acceleration for Scattering From Randomly Rough Lossy Surfaces

An efficient and accurate iterative method is proposed for computing electromagnetic (EM) scattering from 1-D dielectric rough surfaces. The communication improves the convergence of forward backward method, applying it to the problem of 2D wave scattering from random lossy rough surfaces using a coupled surface integral equation formulation. A matrix splitting technique is introduced to reduce the number of matrix-vector multiplications required by the correction step and Spectral Acceleration (SA) is applied to reduce the computational complexity of each matrix-vector product from O(N2) to O(N). The proposed method is called the improved forward backward method with spectral acceleration (IFBM-SA). The numerical analysis demonstrates that IFBM-SA has a higher convergence rate than FBM-SA and a recent technique which is used as a reference method. Moreover, IFBM-SA is more robust than the reference method and has smaller storage requirements meaning that it can readily scale to larger problems. In addition an eigenvalue based analysis is provided illustrating how the improvement step works.