Correct Model Structure Research Articles

Identification of non-linear rational systems using a prediction-error estimation algorithm

Identification of discrete–time non–linear stochastic systems which can be represented by a rational input–output model is considered. A prediction–error parameter estimation algorithm is developed and a criterion is derived using results from the theory of hypothesis testing to determine the correct model structure. The identification of a simulated system, and a heat exchanger are included to illustrate the algorithms.

Degeneracy in nonlinear least squares

As a result of random and/or systematic errors in the observations nonlinear least squares criteria may become degenerate in the sense that their structure essentially differs from that in the errorless case. The paper studies this degeneracy for models described by linear combinations of functions belonging to the same nonlinearly parametric family. For these models elementary types of degeneracy are theoretically explained and illustrated in a number of numerical examples. For practice, the most important conclusion is that degeneracy may preclude the computation of parameter values in the correct model structure.

Construction of more reliable complex metabolic models without repeated solution of their constituent differential equations

A method is described for constructing metabolic models composed of many nonlinear stiff differential equations. The system being modeled is divided into subunits (where such division is impractical, forcing functions are used), and algebraic relationships for their behavior at an instant in time are derived. Most of the usual searches for correct model structure and parameter sets are then done with the set of these algebraic relationships at different time points, relatively few expensive differential equation solutions being required. The software used, the application to several models of cardiac metabolism, and the significance of models of this type are discussed.

Model Order Testing Techniques in Parameter Estimation

A key problem in system identification is the determination of the correct model structure. For example, single-input/single output systems which are characterised by a discrete transfer function model (e.g. Astrom’s formulation) have a system structure which is determined by the respective orders of the regression polynomials. The various model order testing procedures are compared under the classification (i) Subjective methods with probability measure, (ii) Subjective methods with no probability measure, and (iii) Objective methods. In addition a distinction is made between methods derived for systems with dependent and independent observations. The merits of objective procedures are stressed by a number of numerical examples.

An order-testing criterion for mixed autoregressive moving average processes

Abstract In this paper an objective method is proposed for estimating the orders of Autoregressive Moving Average processes and single input/output systems. These methods are an extension of Akaike/s Final Prediction Error (FPE) criterion, which is based on the analysis of the estimated variance of the process. It is shown from extensive numerical examples that the modified FPE predicts the correct model structure with a greater degree of consistency than previous procedures.