Magalie Thomassin

New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models

The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example.

Tumor vascular responses to antivascular and antiangiogenic strategies: looking for suitable models

Antiangiogenic and vascular disrupting agents are in the current cancer therapeutic armamentarium. A better understanding of the intricate mechanisms ruling neovessel survival within tumors during or after treatment is needed. Refinement of imaging and a growing knowledge of molecular biology of tumor vascularization provide new insights. It is necessary to define suitable methods for monitoring tumor response and appropriate tools to analyze data. This review compares most commonly used preclinical models, considering their recent improvements, and describes promising new approaches such as microfluidics, real-time electrical impedance based technique and noninvasive imaging techniques. The advantages and limitations of the in vitro, ex vivo and in vivo models are discussed. This review also provides a critical summary of emerging approaches using mathematical modeling.

Proton MR Spectroscopy and Diffusion MR Imaging Monitoring to Predict Tumor Response to Interstitial Photodynamic Therapy for Glioblastoma

Despite recent progress in conventional therapeutic approaches, the vast majority of glioblastoma recur locally, indicating that a more aggressive local therapy is required. Interstitial photodynamic therapy (iPDT) appears as a very promising and complementary approach to conventional therapies. However, an optimal fractionation scheme for iPDT remains the indispensable requirement. To achieve that major goal, we suggested following iPDT tumor response by a non-invasive imaging monitoring. Nude rats bearing intracranial glioblastoma U87MG xenografts were treated by iPDT, just after intravenous injection of AGuIX® nanoparticles, encapsulating PDT and imaging agents. Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spectroscopy (MRS) allowed us an original longitudinal follow-up of post-treatment effects to discriminate early predictive markers. We successfully used conventional MRI, T2 star (T2*), Diffusion Weighted Imaging (DWI) and MRS to extract relevant profiles on tissue cytoarchitectural alterations, local vascular disruption and metabolic information on brain tumor biology, achieving earlier assessment of tumor response. From one day post-iPDT, DWI and MRS allowed us to identify promising markers such as the Apparent Diffusion Coefficient (ADC) values, lipids, choline and myoInositol levels that led us to distinguish iPDT responders from non-responders. All these responses give us warning signs well before the tumor escapes and that the growth would be appreciated.

EIV methods for system identification with fractional models

This paper deals with continuous-time system identification with fractional models in Errors-In-Variables context. Two estimators based on Higher-Order Statistics (third-order cumulants) are proposed. A State Variable Filter approach is extended to fractional orders to compute fractional derivatives of third-order cumulants estimates. The performance of the proposed algorithms is illustrated in a numerical example. Firstly, differentiation orders are fixed and differential equation coefficients are estimated. The consistency of the proposed estimators is evaluated through a study of the tuning parameter and Monte Carlo simulations. Then, the commensurate differentiation order is optimized along with the differential equation coefficients.

Differentiation similarities in fractional pseudo-state space representations and the subspace-based methods

The paper starts by presenting a new concept of differentiation similarity transformations for commensurate pseudo-states-space representations. It is proven that a pseudo-state-space representation with a commensurate differentiation order ν and a dimension of the transition matrix n can be similar to a pseudo-state-space representation with a commensurate order ν/k and a dimension of the transition matrix kn, where k is an integer number. A direct consequence of the aforementioned concept in fractional subspace-based identification methods for MIMO systems is that an overestimated pseudo-state-space representation has multiple minimums at commensurate differentiation orders over the integral number k. This result is especially visible when deterministic input/output signals are considered and less visible in the stochastic case due to overestimation.

Identifiability investigation of the aerodynamic coefficients from free flight tests

The identification of the aerodynamic coefficients, based on free flight measurements, remains a difficult task for flying vehicles like space vehicles, munitions, UAV. This is mainly due to the nonlinear structure of the mathematical model describing the behavior of the vehicle in flight, the absence of an input signal, the unknown initial conditions and the nonlinear dependence of the aerodynamic coefficients on several state variables. Under these conditions, the estimation of the model parameters must be processed with caution. In this paper, we propose a new procedure for the identification of the aerodynamic coefficients, and more precisely the pitch damping coefficient of a re-entry space vehicle. This approach is based on system identification techniques and several steps are required, like the polynomial description of the coefficient as a function of the Mach number and the total angle of attack, the a priori and a posteriori identifiability study, followed by the estimation of the parameters in question based on real experimental free flight measurements. This model-based method improves the accuracy of the estimated coefficient.

A Bayesian approach for time-delay estimation of a managed river reach in imposed experimental conditions

Abstract This article deals with the problem of estimating time-delays in the experimental modelling of river reaches managed by hydroelectric power plants. The purpose of the article is to estimate the reach time-delay from the data collected in imposed experimental conditions. The modelling of the managed river reach shows that the feedforward control performed by the operator “hides” the reach time-delay in the transfer function of the closed-loop system. So, classical time-delay estimation methods are inappropriate. The proposed solution considers the delay estimation as a problem of detecting a discontinuity in impulse response. A Bayesian approach is proposed to detect the delay and to estimate the impulse response from production data. This method is applied to one-day data sets supplied over one year in order to show its efficiency.

Third-order cumulants based method for continuous-time Errors-In-Variables system identification by fractional models

This paper deals with continuous-time system identification using fractional models in a noisy input/output context. The third-order cumulants based least squares method (tocls) is extended here to fractional models. The derivatives of the third-order cumulants are computed using a new fractional state variable filter. A numerical example is used to demonstrate the performance of the proposed method called ftocls (fractional third-order cumulants based least squares). The effect of the signal-to-noise ratio and the hyperparameter is studied.

Fourth-order cumulants based method for continuous-time EIV fractional model identification

The errors-in-variables (EIV) system identification problem concerns the dynamic systems whose discrete input and output are corrupted by additive noises, that can be white, colored and/or mutually correlated. In this paper, a new estimator based on Higher-Order Statistics (fourth-order cumulants) is proposed for continuous-time system identification with fractional models. Under some assumptions on the distributional properties of the noise and noisefree signals, the fractional fourth-order cumulants based least squares (ffocls) estimator gives consistent results. A numerical example illustrates the performance of the proposed method.

Aerodynamic coefficient identification of a space vehicle from multiple free-flight tests

The identification of aerodynamic coefficients, based on free-flight measurements, remains complex and challenging for vehicles such as space probes, unmanned aerial vehicles, or ammunition. In this paper, a detailed procedure for the identification of the drag, pitching moment slope, and pitch damping coefficients of a reentry space vehicle is presented. New models of these aerodynamic coefficients, based on polynomial functions of Mach numbers and incidence angles, are proposed, and an estimation strategy using multiple data series is applied. The free-flight data correspond to three-axis magnetometer and radar measurements for different experimental conditions. The resulting model is tested with new data sets to ascertain the model validity. The results show that the proposed description of the three aerodynamic coefficients and the estimation strategy are relevant.