Sequential experimental Design for Misspecified Nonlinear Models

International audienceIn design of experiments for nonlinear regression model identification, the design criterion depends on the unknown parameters to be identified. Classical strategies consist in designing sequentially the experiments by alternating the estimation and design stages. These strategies consider previous observations (collected data) only while estimating the unknown parameters during the estimation stages. This paper proposes to consider the previous observations not only during the estimation stages, but also by the criterion used during the design stages. Furthermore, the proposed criterion considers the robustness requirement: an unknown model error (misspecification) is supposed to exist and is modeled by a kernel-based representation (Gaussian process). Finally, the proposed sequential criterion is compared with a model-robust criterion which does not consider the previously collected data during the design stages, with the classical D-optimal and L-optimal criteria

Model-Robust Design of Experiments for Sequential Identification of ODE Parameters

International audienceThis paper presents the idea of sequential model-robust Design of Experiments (DOE) for the identification of dynamic systems modeled with an Ordinary Differential Equation (ODE). The studied DOE problem consists in selecting sequentially the instants where the measures will be done in order to best estimate the system's parameter. The robustness is achieved by considering a statistical representation of the model error defined as the difference between the true ODE and the ODE used in the model. The idea of modeling the model error with a statistical representation has been widely explored in the DOE literature for the identification of static systems. However, there have been little previous works that apply this idea for the identification of dynamic systems. This paper initiates an exploration of this idea in the context of first-order ODE. The model error is modeled by using a kernel-based representation (Gaussian process). A new criterion for the instant selection is constructed and tested on an illustrative example. The design reached with the proposed sequential robust criterion is compared with the design reached with the non-robust version of criterion and with the classical uniform design

MODEL-ROBUST SEQUENTIAL DESIGN OF EXPERIMENTS FOR IDENTIFICATION PROBLEMS

International audienceA new criterion for sequential design of experiments for linear regression model is developed. Considering the information provided by previous collected data is a well-known strategy to decide for the next design point in the case of nonlinear models. The paper applies this strategy for linear models. Besides, the problem is addressed in the context of robustness requirement: an unknown deviation from the linear regression model (called model error or misspecification) is supposed to exist and is modeled by a kernel-based representation (Gaussian process). The new approach is applied on a polynomial regression example and the obtained designs are compared with other designs obtained from other approaches that do not consider the information provided by previously collected data

Minimum-Entropy, PDF Approximation, and Kernel Selection for Measurement Estimation

The purpose of this paper is to investigate the selection of an appropriate kernel to be used in a recent robust approach called minimum-entropy estimator (MEE). This MEE estimator is extended to measurement estimation and pdf approximation when p(e) is unknown. The entropy criterion is constructed on the basis of a symmetrized kernel estimate p_hat (e) of p(e). The MEE performance is generally better than the Maximum Likelihood (ML) estimator. The bandwidth selection procedure is a crucial task to assure consistency of kernel estimates. Moreover, recent proposed Hilbert kernels avoid the use of bandwidth, improving the consistency of the kernel estimate. A comparison between results obtained with normal, cosine and Hilbert kernels is presented

Cross-Priming of Naive Cd8 T Cells against Melanoma Antigens Using Dendritic Cells Loaded with Killed Allogeneic Melanoma Cells

The goal of tumor immunotherapy is to elicit immune responses against autologous tumors. It would be highly desirable that such responses include multiple T cell clones against multiple tumor antigens. This could be obtained using the antigen presenting capacity of dendritic cells (DCs) and cross-priming. That is, one could load the DC with tumor lines of any human histocompatibility leukocyte antigen (HLA) type to elicit T cell responses against the autologous tumor. In this study, we show that human DCs derived from monocytes and loaded with killed melanoma cells prime naive CD45RA+CD27+CD8+ T cells against the four shared melanoma antigens: MAGE-3, gp100, tyrosinase, and MART-1. HLA-A201+ naive T cells primed by DCs loaded with HLA-A201− melanoma cells are able to kill several HLA-A201+ melanoma targets. Cytotoxic T lymphocyte priming towards melanoma antigens is also obtained with cells from metastatic melanoma patients. This demonstration of cross-priming against shared tumor antigens builds the basis for using allogeneic tumor cell lines to deliver tumor antigens to DCs for vaccination protocols

Robust Estimation of Hidden Corrosion Parameters using an Eddy Current Technique

An eddy current technique is used to inspect the interface between air and a conductive material such as aluminum, which can be covered with a non-conductive material. Hidden corrosion may appear inside the conductive material. This corrosion leads to flaws whose shape varies greatly depending of the flaw. The proposed methodology addresses this problem by considering the potential shapes as realizations of a random process. The goal of the proposed approach is not to find the exact shape of the corrosion flaw but to estimate some of its dimensional parameters. The area and the dimension ratio of the shape have been chosen because they depict the importance of the corrosion damage. The estimation of the area and the dimension ratio is achieved in a Nondestructive Evaluation context: An alternating magnetic field is created in the air above the inspected material and the magnetic field near the air-aluminum interface is measured. It is a typical inverse measurement problem. Due to the complexity of the shape and of the physical phenomena, no algebraic model exists to solve this inverse problem. That is why a machine learning approach has been carried out: A database of observed signals for reference flaws is created (by using FEM tool) and used to calibrate a relationship giving the estimated area and the estimated dimension ratio from the observed signal. As the number of flaws in the database cannot be very large, the proposed approach overcomes the over fitting risk by performing a reduction of the data dimension

Nonlinear model selection - Application to an indirect inductive measurement of conductivity

International audienceAn efficient method and algorithm for experimental data processing based on parametric inversion is proposed. This method is applied to a metallic rod conductivity measurement based on induced secondary voltage technique. Firstly, the case of an ideal excitation circuit is studied. For this case, when the excitation signal is a current step, a model of the data can be obtained in a closed-form as an infinite sum of exponential functions whose relaxation times are related to the physical properties of the inspected material. Therefore, for time points greater than the largest relaxation constant, only one term is sufficient; but, for these times, the signal-to-noise ratio is smaller, so the variance of the estimated conductivity is larger. When taking into account some data at earlier time points, N terms are necessary to minimize the residual modelling error. The conductivity variance is then smaller but the identification process is more complex. A trade-off has been achieved between these two aspects. Finally, the choice of an L1 norm criterion upon the identification error is used to reject outliers from experimental data. Secondly, a more realistic circuit is considered (the primary time constant is taken into account). In that case, two steps are necessary to calculate the direct model. A nonlinear equation is solved and the results are put into a closed-form expression (an infinite sum of exponential functions)

Apport du filtrage particulaire au recalage altimétrique dans un contexte de navigation hybridée

Un système de navigation hybridé associe plusieurs moyens de positionnement afin d'augmenter la précision, la disponibilité, et la fiabilité de l'information délivrée. Cette thèse se focalise sur l'association d'une centrale inertielle et de mesures radio-altimétriques pour la navigation des aéronefs (drones, missiles). La problématique consiste à fusionner de manière optimale les informations inertielles et les mesures du radio-altimètre. Ce problème se formule comme une opération de filtrage non-linéaire, la non-linéarité résultant du profil arbitraire du terrain survolé. On se propose dans le cadre de la thèse d'évaluer les performances de l'algorithme de filtrage particulaire. Cet algorithme, bien qu'encore très peu utilisé pour des applications industrielles à cause de la lourdeur des calculs qu'il engendre, suscite un intérêt croissant avec l'augmentation constante des capacités de calcul des processeurs. Cette étude s'est concentrée à la fois sur le contexte applicatif (principe de la navigation inertielle, modélisation des imperfections des senseurs inertiels, description des algorithmes actuellement utilisés, principe de la mesure radio-altimétrique) et sur la théorie du filtrage particulaire. Ceci a permis de préciser les apports potentiels du filtrage particulaire par rapport aux autres algorithmes plus classiques (filtre à grille, filtre de Kalman étendu, unscented Kalman filter). L'expérience acquise sur les différentes variantes de filtre particulaire a permis de proposer des solutions satisfaisant au mieux le cahier des charges imposé par le contexte applicatif.A hybrid navigation system combines several positioning means so as to achieve a greater accuracy, availability, and reliability. This study focuses on the association of an inertial navigation system, an on-board radar-altimeter and a digital terrain elevation model. The target application is autonomous aircrafts (UAVs, long-range missiles). The problem consists in combining the inertial data and radio-altimeter measurements in an optimal way. The problem can be expressed as a non-linear filtering operation. The non-linearity is due to the arbitrary shape of the terrain. In this thesis, we propose to assess the performances of the particle filtering algorithm. Although particle filtering is still little used in industrial application because of its heavy computation requirements, it arouses a growing interest as the processors constantly rise in performance. This study describes both the application context (principle of inertial navigation, model of inertial sensor errors, description of commonly used algorithms, principle of radar-altimeter measurements) and the theoretical aspects of particle filtering. It highlights the potential advantages of particle filtering algorithm over the classical ones (grid filtering, extended Kalman filter, unscented Kalman filter). The knowledge acquired on several variants of the particle filter (Rao-blackwellized particle filter, Gaussian particle filter) leads to solutions that meet at best the application constraints.ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF