Section: New Results

Classical engineering: Monitoring and control of complex systems

Modeling, signal analysis and control with medical applications

Participants : Alexandre Guerrini, Lisa Guigue, Claire Médigue, Michel Sorine, Serge Steer.

Reduced order cardiac modeling and applications. See Section 4.3 for complements. We consider two topics:

- Personalized medecine: a first validation on clinical data of our model of controlled contraction of cardiac muscle has been obtained [55] .

- Heart Failure with preserved Ejection Fraction (HFpEF): this work is done in collaboration with Bijan Gahleh (INSERM U955). Our objective is to define markers of HFpEF identifiable from noninvasive measurements. After having assembled a high precision ECG acquisition and post-processing system, we have measured multi-lead ECG on pigs treated to induce HFpEF, cf. B. Gahleh et al [109] . The analysis of the diastolic electric interval (e.g. P-wave, PR interval etc.) is ongoing.

Semiclassical analysis of cardiovascular signals. A summary of the theory is now published [51] .

CGAO-REA : Computerized Glucose Control in Critically Ill Patients. The version CGAO_v1 of our controller (see Sections 4.3 ), has been used in a large multi-center study, CGAO-REA (35 active ICUs, more than 3500 included patients). Mortality has not been changed [70] , [48] but the protocol is now formalized and tunable. CGAO-REA has proved that our controller is robust in the real life context and comparable to human control with its present tuning. Improving the tuning (in particular the glycemic target) seems possible.

Diagnosis of inhomogeneous insulation degradation in electric cables by distributed shunt conductance estimation

Participant : Qinghua Zhang.

For the diagnosis of inhomogeneous insulation degradation in electric cables, the estimation of distributed shunt conductance is studied in this work. Gradual growth of the shunt conductance is a consequence of degradation of the dielectric properties of the insulator. The proposed estimation method is based on voltage and current measurements at a single end of the cable. After the linearization of the bilinear term of the telegrapher's equations through a perturbation approach, the Kalman filter is applied to transform the problem of dynamic system parameter estimation to a simple linear regression problem. Numerical simulations are made to demonstrate the feasibility of the proposed method. In particular, it is shown that the weak sensitivity of the available measurements to the shunt conductance can be compensated by long time data samples. See [61] for more details.

Feasibility of reflectometry techniques for non destructive evaluation of external post-tensioned cables

Participants : Michel Sorine, Qinghua Zhang.

Nowadays a considerable number of bridges is reaching an age when renovating operations become necessary. For some bridges, external post-tension is realized with cables protected in ducts, with the residual internal space imperfectly filled with a fluid cement grout. Detecting the problems of injection in the ducts is visually impossible from the outside. In collaboration with IFSTTAR (Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux) through the I4S team common to Inria and IFSTTAR, the feasibility of reflectometry techniques for cable health monitoring is investigated via numerical simulations and laboratory experiments. The main idea consists in adding electrically conductive tapes along a duct so that the duct and the added tapes can be treated as an electrical transmission line. It is then possible to apply advanced reflectometry methods developed by the SISYPHE project-team, initially for true electric cables.

Nonlinear system identification

Participants : Boyi Ni, Michel Sorine, Qinghua Zhang.

In the framework of the joint Franco-Chinese ANR-NSFC EBONSI project (see Section 8.1.1 ), the topics studied this year on nonlinear system identification are mainly on the detection of asymmetric control valve stiction from oscillatory data based on a method for extended Hammerstein system identification, and on the identification of Wiener systems.

The study on control valve stiction is motivated by the detection of control valves with asymmetric stiction resulting in oscillations in feedback control loops. The joint characterization of the control valve and the controlled process is formulated as the identification of a class of extended Hammerstein systems. The input nonlinearity is described by a point-slope-based hysteretic model with two possibly asymmetric ascent and descent paths. An iterative identification method is proposed, based on the idea of separating the ascent and descent paths subject to the oscillatory input and output. The structure of the formulated extended Hammerstein system is shown to be identifiable, and the oscillatory signals in feedback control loops are proved to be informative by exploiting the cyclo-stationarity of these oscillatory signals. Numerical, experimental and industrial examples confirm the effectiveness of the proposed identification method.

Wiener system identification has been investigated this year by focusing on the estimation of the finite impulse response (FIR) of the linear subsystem. Under the assumption of Gaussian input distribution, this work mainly aims at addressing a deficiency of the well-known correlation-based method for Wiener system identification: it fails when the nonlinearity of the Wiener system is an even function. This method is, in the considered Gaussian input case, equivalent to the best linear approximation (BLA), which exhibits the same deficiency. A new method is developed this year, based on a weighted principal component analysis (wPCA). Its consistency is proved for Wiener systems with either even or non even nonlinearities. Its computational cost is almost the same as that of a standard PCA. Numerical simulations are made to compare the new wPCA-based method to the correlation-based method for different Wiener systems with nonlinearities more or less close to an even function.

Model-based fault diagnosis for descriptor systems

Participants : Abdouramane Moussa Ali, Qinghua Zhang.

This work is about fault diagnosis for linear time varying descriptor systems, the discrete time counterpart of dynamic systems described by differential-algebraic equations. The Kalman filter for descriptor systems is first revisited by completing existing results about its properties that are essential for the purpose of fault diagnosis. Based on the analysis of the effects of the considered actuator and sensor faults on the innovation of the Kalman filter, it is shown that the considered fault diagnosis problem in linear time varying descriptor systems can be transformed to a classical linear regression problem formulated by appropriately filtering the input-output data. Following this result, algorithms for fault diagnosis through maximum likelihood estimation are then developed.

In the framework of the ITEA2 MODRIO project (see Section  8.2.1 ), this work is in preparation for studying hybrid system monitoring, aiming at extending existing results from state-space systems to descriptor systems in the modes of a hybrid system.

Analysis of the Behavior of Networks of Dynamical Systems

Participant : Pierre-Alexandre Bliman.

We have established convergence results for some continuous-time dynamics which are analogs to ant colony optimization algorithms that solve shortest path problems. Global asymptotic stability has been shown, and the speed of convergence has been calculated explicitly and shown to be proportional to the difference between the reciprocals of the second shortest and the shortest paths. Such precise results are missing in the context of ant colony optimization algorithms (which are discrete-time dynamical systems). The systems studied are special instances of networks of dynamical systems which represent the evolution of some state variable on each path, coupled in a competitive way through global macroscopic quantity. Such models are related to simple forms of models studied in mathematical epidemiology, which will be the subject of further work. This work is done in cooperation with Amit Bhaya from COPPE, Universidade Federal de Rio de Janeiro. Papers have been submitted [77] .