Tools for fitting low-complexity nonlinear models based on experimental data are examined through the example problem of finding a reduced-order model suitable for control of a combustion instability operating in a limit cycle. This proceeds in four parts; physical modeling, linear system identification, nonlinear analysis, and validation test design. It is shown how the nonlinear tools of desc...

This work is concerned with L 1 data fitting for nonlinear inverse problems. This formulation is advantageous if the data is corrupted by impulsive noise. However, the problem is not differentiable and lacks local uniqueness, which makes its efficient solution challenging. By considering a regularized primal-dual formulation of this problem, local uniqueness can be shown under a second order su...

The functional form representation of input-output relationship through Volterra series provides a structured mathematical platform for the study of nonlinear systems. It employs multi-dimensional kernels, which upon convolution with the applied excitation forces, express system response in the form of a power series. Frequency domain transforms of these multi-dimensional kernels provide higher...

In this paper we consider the problem of estimating the parameters of a nonlinear dynamical system given a finite time series of observations that are contaminated by observational noise. The least squares method is a standard method for parameter estimation, but for nonlinear dynamical systems it is well known that the least squares method can result in biased estimates, especially when the no...

Many of the popular nonlinear time series models require a priori the choice of parametric functions which are assumed to be appropriate in specific applications. This approach is used mainly in financial applications, when sufficient knowledge is available about the nonlinear structure between the covariates and the response. One principal strategy to investigate a broader class on nonlinear t...

We use various nonlinear geometric partial differential equations to efficiently solve several surface modelling problems, including surface blending, N -sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows (mean curvature flow and average mean curvature flow), one fourth order flow (surface diffusion flow) and a sixth order flow. These n...

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co)variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The ana...

Background and Objectives: Efficient cost management in hospitals’ pharmaceutical inventories have the potential to remarkably contribute to optimization of overall hospital expenditures. To this end, reliable forecasting models for accurate prediction of future pharmaceutical demands are instrumental. While the linear methods are frequently used for forecasting purposes chiefly due to their si...

This paper deals with characterization of best approximations to vector-valued functions. The approximations are themselves vector-valued functions with components depending nonlinearly on the approximation parameters. The constraint is imposed that certain of the parameters should be identical for all components. An application to exponential approximation is discussed in some detail.

We study a nonlinear regression problem of fitting a circle (or a circular arc) to scattered data. We prove that under any standard assumptions on the statistical distribution of errors that are commonly adopted in the literature, the estimates of the circle center and radius have infinite moments. We also discuss methodological implications of this fact.