Ignacio Rubio Scola

Input Optimization for Observability of State Affine Systems

In this paper a method for designing the input of a state affine system in order to guarantee a pre-specified degree of observability is proposed. It consists of an off-line algorithm to build an optimal, and so-called regularly persistent, input for the system. Optimality is defined with respect to the minimization of the input energy, and observability through a lower bound for the observability Gramian of the system, which is known to allow for an exponential observer design. The approach is presented for discrete-time systems, and is illustrated in simulation by an application example corresponding to a problem of fault detection in pipelines.

Online observability optimization for state affine systems with output injection and observer design

Observability being in general subject to the applied input for a nonlinear system, the aim of the present work is to propose an input selection strategy for a special class of systems, so as to make them observable. The considered systems are those admitting a state-affine structure with output injection. For such systems, an online algorithm is proposed to compute an appropriate input in real time. It guarantees observability by ensuring a lower bound on the related Gramian, and minimizes at the same time the input variations with respect to some reference value required for the system operation. This computation is updated at each time with the new output measurements becoming available. The proposed methodology is illustrated on a piping system example, for which an exponential observer is finally obtained.

Input selection in observer design for non-uniformly observable systems

Abstract In this paper the problem of inputs in observer design for systems which are not uniformly observable is considered. It is emphasized how it amounts to a control problem , which can be solved in a general way by some appropriate optimization approach. This is illustrated on the basis of a quite general Kalman-like observer form – possibly with high gain , as well as related simulation results on an application example.

Leak detection and location based on improved pipe model and nonlinear observer

This paper proposes a new contribution to observer-based approaches for detection and location of leaks in pipelines. In previous studies for such approaches, the observer is most of the time designed for a model obtained from hydraulic dynamical equations and finite difference techniques, using pressures at both ends of the pipe as boundary conditions; in the present work, the finite difference model is modified by using other boundary conditions, which are the pressure in the inlet pump and the pressure at the end of the pipe system. This modification provides a better representation of the pipeline dynamics, as illustrated by comparing the behavior simulated in this way with real data. It is then emphasized that this improved model may be used for an observer-based direct estimation of a possible leak flow in the pipe - together with its position, only using two measured variables (instead of four in former studies): one pressure at one end of the pipe, and one flow at the other pipe side. The other two variables, to be known by the observer - related to the boundary conditions, can indeed be taken here as constant values, since they correspond to the inlet pump pressure and the atmospheric pressure respectively. Results obtained with an Extended Kalman observer designed on this basis are finally presented, both in simulation and with real data.

Blockage and Leak Detection and Location in Pipelines Using Frequency Response Optimization

This paper proposes a new approach based on the frequency response for fault identification in pipelines. The method focuses on extended blockage detection and location, and a case of simultaneous punctual blockage and leak identification. The proposed approach is based on a frequency modeling of pipeline dynamics including the effect of faults under study, by means of transfer matrix representation, and a related optimization: using measurements at both ends of the pipeline, together with an appropriate excitation, the parameters of the faults are directly identified from the frequency response. This methodology is shown to be very efficient based on the simulation results, even in the presence of additive measurement noise.

Improving Kalman filtering by input selection for nonuniformly observable state-affine systems

In this paper, a problem of persistent input design for the application of a Kalman-like observer to a class of systems which are not uniformly observable is considered. The class of systems is that of state-affine ones, for which Kalman filtering theory can be applied as soon as the input is defined as a function of time. In fact, it is first highlighted how an appropriate choice of the system input can improve the performance of the Kalman filter in this case. It is then emphasized how this input selection amounts to a control problem, which can be solved by an appropriate optimization approach. This input design is finally illustrated with some simulation results on an application example.

Optimizing Kalman optimal observer for state affine systems by input selection

In this paper, a new algorithm to build an optimal input for state reconstruction in the class of state-affine systems is proposed, in the sense that it enhances the performances of a Kalman-like observer, as well as it guarantees the system observability. The approach relies on the fact that for a state-affine system, as soon as the input is defined as a function of time, Kalman filtering theory can be applied. In fact, it is first highlighted how an appropriate choice of the system input can improve the Kalman filtering performance in this case. It is then emphasized how this input selection amounts to a control problem, which can be solved by an appropriate optimization algorithm. Finally, the algorithm is applied to a case of fault detection in a pipeline as an illustrative example, with some simulation results showing the observer performance improvement with the proposed input.

Pipeline partial blockage modeling and identification

Abstract This paper proposes an extension of former finite-difference-based models for pipelines dynamics to a case including possible partial blockages in the pipe. Model equations are first established, and a simple application to the detection – and location – of such faults is then presented via an identification-like procedure. Simulation results finally illustrate the proposed methodology.