Identifiability of discrete-time nonlinear systems: The local state isomorphism approach

A new theorem is provided to test the identifiability of discrete-time systems with polynomial nonlinearities. That extends to discrete-time systems the local state isomorphism approach for continuous-time systems. Two examples are provided to illustrate the approach.     

A sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs

In this paper, an original result in terms of a sufficient condition to test the identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system and a criterion for linear systems with constant delays is provided, from which the identifiability of the original nonlinear system can be proved. This result is obtained by combining a classical identifiability result for nonlinear ordinary differential systems due to Grewal and Glover (1976) with the identifiability of linear delayed-differential models developed by Orlov, Belkoura, Richard, and Dambrine (2002). This paper is a generalization of Denis-Vidal, Jauberthie, and Joly-Blanchard (2006), which deals with the specific case of nonlinear delayed-differential models with two delays and a single input.     

Difference algebra and system identification

The framework of differential algebra, especially Ritt’s algorithm, has turned out to be a useful tool when analyzing the identifiability of certain nonlinear continuous-time model structures. This framework provides conceptually interesting means to analyze complex nonlinear model structures via the much simpler linear regression models. One difficulty when working with continuous-time signals is dealing with white noise in nonlinear systems. In this paper, difference algebraic techniques, which mimic the differential-algebraic techniques, are presented. Besides making it possible to analyze discrete-time model structures, this opens up the possibility of dealing with noise. Unfortunately, the corresponding discrete-time identifiability results are not as conclusive as in continuous time. In addition, an alternative elimination scheme to Ritt’s algorithm will be formalized and the resulting algorithm is analyzed when applied to a special form of the nfir model structure.     

Identification of variable coefficients for vibrating systems by boundary control and observation

We consider the identification problem of coefficients for vibrating systems described by a Euler-Bernoulli beam eq~. ation Or a string equation, with one end clamped and with an input exerted on the other end. For the beam equation, the observations are the velocity and the angle velocity at the free end, while for the string equation, the observation is the velocity at the free end. In the framework of well-posed linear system theory, we show that both the density and the flexural rigidity of the beam, and the tension of the string, can be uniquely determined by the observations for all positive times. Moreover, a general constructive method is developed to show that the mass density and the elastic modulus of the string are not determined by the observation.     

Errors-in-variables methods in system identification

The paper gives a survey of errors-in-variables methods in system identification. Background and motivation are given, and examples illustrate why the identification problem can be difficult. Under general weak assumptions, the systems are not identifiable, but can be parameterized using one degree-of-freedom. Examples where identifiability is achieved under additional assumptions are also provided. A number of approaches for parameter estimation of errors-in-variables models are presented. The underlying assumptions and principles for each approach are highlighted.     

IDENTIFIABILITY AND DISTINGUISHABILITY TESTING FOR LINEAR MODELS IN HETEROGENEOUS CATALYSIS

If several values of the parameters of a model are associated with the same behavior, then the model is not identifiable and there is no hope of estimating a unique best value for the parameter vector from experimental data. Similarly, if several models with different structures correspond to the same behavior, then these models are not distinguishable and there is no hope of selecting a structure that best corresponds to the experimental data. Two methods for testing linear models for identifiability and distinguish ability are recalled and applied to types of catenary compartmental models encountered for instance when studying the isobutane-isobutene-hydrogen system by transient isotopic tracing.     

Mixture of two inverse Weibull distributions: Properties and estimation

The mixture model of two Inverse Weibull distributions (MTIWD) is investigated. First, some properties of the model with some graphs of the density and hazard function are discussed. Next, the identifiability property of the MTIWD is proved. In addition, the estimates of the unknown parameters via the EM Algorithm are obtained. The performance of the findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulations.     

Local identifiability of time-invariant linear systems by periodic test signals

This paper is concerned with the parameter local identifiability of dynamic systems operating in periodic regimes. The systems dealt with are time-invariant and discrete-time linear systems, with an output white gaussian disturbance. Sets of frequencies are characterized such that the parameter vector is identifiable if and only if the spectrum of the periodic test signal does not vanish over one of these sets. The analysis is developed by taking also into consideration measurement schedule sets which are scattered along the time axis.     

Linear and Integer Programming

Coordinate sensing systems have been widely used in various manufacturing processes to monitor product quality and automatically identify process faults. They play a crucial role in manufacturing quality improvement. For complex manufacturing processes, especially processes with multiple stages, typically not all process faults can be uniquely identified by a feasible sensing system. For these complex processes, a diagnosability study is an important issue for the evaluation and usage of coordinate sensing systems. This article conducts a diagnosability study of coordinate sensing systems based on matroid theory. The use of matroid theory improves understanding of existing results on diagnosability. In addition, new results and more efficient algorithms related to diagnosability study are investigated based on matroid theory. The developed theory and algorithms, which can be applied in a broad class of diagnosis problems, are demonstrated using a panel assembly process.