The purpose of this article is to present some recent applications of computer algebra to answer structural and numerical questions in applied sciences. A first example concerns identifiability which is a pre-condition for safely running parameter estimation algorithms and obtaining reliable results. Identifiability addresses the question whether it is possible to uniquely estimate the model parameters for a given choice of measurement data and experimental input. As discussed in this paper, symbolic computation offers an efficient way to do this identifiability study and to extract more information on the parameter properties. A second example addressed hereafter is the diagnosability in nonlinear dynamical systems. The diagnosability is a prior study before considering diagnosis. The diagnosis of a system is defined as the detection and the isolation of faults (or localization and identification) acting on the system. The diagnosability study determines whether faults can be discriminated by the mathematical model from observations. These last years, the diagnosability and diagnosis have been enhanced by exploitting new analytical redundancy relations obtained from differential algebra algorithms and by the exploitation of their properties through computer algebra techniques.

In this paper, an improvement of the bounded-error fault detection and identification method based on input-output polynomials of ([2]) is proposed. It is based on integro-differential polynomials used to estimate the fault values. The standard input-output polynomials are obtained from differential algebra elimination theory and can be used both for diagnosability analysis and fault estimation. Unfortunately, they may involve derivatives of high order whose estimation is a hard problem when system outputs are uncertain. Distribution theory allows us to transform them into integro-differential polynomials that involve lower order derivatives of the model outputs. In this paper, this method, extended to the set-membership (SM) framework, is used with the focus of achieving fault detection and identification. The original method and the new method are applied to a coupled water-tank model and compared. It is shown that the new method significantly improves the fault detection and identification results.