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Powered Air Purifying Respirator (PAPRs) are respirators that utilise a small centrifugal blower to aid in drawing air through a filter. If the dynamic behaviour of PAPRs with filters can be modelled, adaptive controllers can be made so that air is only supplied through the filter when a user inhales. This paper presents the identification of a Wiener model using a separable least squares method with experimental application to a PAPR. The linear dynamics are shown to fit to an output error model structure, with the nonlinearity being a quadratic function. The model structure is then validated on a PAPR constructed in open loop formation. The validation is furthered by altering the filter resistance to check the performance of the model.

In this paper, the Hammerstein identification problem with correlated inputs is studied in a prediction error framework using separable least squares methods. Thus, the identification is recast as an optimization over the parameters used to describe the nonlinearity. A sufficient condition is derived that guarantees that the identification problem is quasiconvex with respect to the parameters that describe the nonlinearity. Simulations using both IID and correlated inputs are used to illustrate the result.

International audience; This paper deals with the identification of Wiener models that involve backlash operators bordered by possibly noninvertible parametric lines. The latter are also allowed to cross each other making possible to account for general-shape static nonlinearities. The linear dynamic subsystem is not-necessarily parametric but is BIBO stable. A frequency identification method is developed that provides estimates of the nonlinear operator parameters as well as estimates of the linear subsystem frequency gain. The method involves standard and separable least squares estimators that all are shown to be consistent. Backlash operators and memoryless nonlinearities are handled within a unified framework.

Ph.D. Programs Foundation of Ministry of Education of China [20100121120020]; Major Science and Technology Special Project of Fujian Province, China [2009HZ0003-1]

The Hammerstein identification problem is studied using a prediction error method in a separable least squares framework. Thus, the identification is recast as an optimization over the parameters used to describe the nonlinearity. Under certain conditions the identification problem is quasiconvex. First, the identification problem is shown to be quasiconvex under certain assumptions, including the use of an IID input. Next, the IID requirement is relaxed, and a sufficient condition for quasiconvexity is derived. The results are illustrated using a series of simulations.

The stiction of control valve is one of main causes which make control loop instable in the process industry. Now a number of studies on the diagnosis of control valves are based on stiction. It needs developing a proper method which can detect, quantify, and compensate stiction. A non-invasive method has been used into the fault diagnosis for stiction of pneumatic control valve. Firstly, a two-parameter data-driven model about stiction has been established, and on the basis of separable least squares method, combined with the global search algorithm to deduce the model identification method. Secondly, ellipse fitting method has been adopt to confirm whether the stiction existed, thus the stiction could be quantified, and on this basis, the stiction was compensated. So it improved the performance of control system. Thirdly, the validity of the method was confirmed by simulation.

This note compares and contrasts the non-linear parameter varying (NLPV) and state-dependent parameter (SDP) model classes. It shows that, while they have similarities, the two-stage SDP modelling procedure, involving non-parametric identification, followed by parametric estimation, is quite different from the single stage NLPV procedure. In particular, the SDP procedure allows for the identification of the model structure and the nature of the non-linearities, prior to the estimation of the parameters that characterize this identified model structure. In contrast to NLPV modelling, therefore, SDP estimation opens up the ‘black box’ and reveals the inner nature of the non-linear system.

In this paper, the parametrization of state-space systems by data driven local coordinates as introduced by (McKelvey et al., 2003) is modified. This modification leads to an alternative analogous parametrization which can be used for a suitable concentrated likelihood-type criterion function, where the concentration step can be done by a generalized least squares step. An obvious consequence is the reduced number of parameters resulting in less computational burden, but, of course, the criterion function itself is changed by the concentration step. The resulting new parametrization is called slsDDLC, and its topological and geometrical properties are investigated in detail.

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.

In this paper, a sensitivity analysis is carried out for the problem of simultaneous estimation of induction motor's state and parameters. This is done using separable least squares formulation. It comes out that even in the presence of persistent excitations, the above problem is very sensitive to noises and/or uncertainties especially for one of the four possibly identifiable combinations of parameters. Numerical experiments are conducted that confirm the a priori sensitivity-based predictions.

Separable least squares are generally written in the form ‖y−A(q)c ‖2 = min where minimization has to be carried out with respect to the parameters q and c. The latter enter linearly into the expression of the objective function and this leads to considerable simplications. These simplifications are not possible if the functional to be minimized is of the form σ‖y−Aj(q)c‖2 = min In this communication we modify previous methods, so that they can deal with the more general case (2). We also show that the statistical properties of both linear and nonlinear estimates can be evaluated according to a procedure that enables us to keep the two classes of parameters separate. An important application is examined and its numerical solution worked out in detail.