Laurent Le Brusquet

Robust estimation of flaw dimensions using remote field eddy current inspection

The remote field eddy current technique is used to inspect conductive pipes and to estimate the dimensions of flaws liable to exist in the conductive material. A data set which contains observations for calibrated flaws is used to learn the processing. This learning problem is addressed in the context of a small size data set in which the overfitting problem is often present. To obtain a robust estimation of flaw size, this problem is minimized as follows: the estimation of flaw size uses parameters whose number is chosen the smallest possible. To obtain this set of parameters, three approaches are proposed. A reduction of the data space dimension by means of principal component analysis and parametric modelling is carried out. Then, for both cases a bilinear regression is performed to estimate the flaw size. The third approach uses a neural network to learn the processing and to directly calculate an estimate of flaw size. An MDL (minimum description length) criterion is used in the learning step to choose the smallest number of required parameters and thus to avoid the overfitting risk. The three approaches are compared in terms of accuracy and robustness. A cross-validation test is carried out on noisy data.

Graph-constrained discriminant analysis of functional genomics data

Classification studies from microarray data have proved useful in tasks like predicting patient class. At the same time, more and more biological information about gene regulation networks has been gathered mainly in the form of graph. Incorporating the a priori biological information encoded by graphs turns out to be a very important issue to increase classification performance. We present a method to integrate information from a network topology into a classification algorithm: the graph-Constrained Discriminant Analysis (gCDA). We applied our algorithm to simulated and real data and show that it performs better than a linear Support Vector Machines classifier.

A criterion for model-robust design of experiments

The paper considers the design of experiments for linear models with misspecification, of the form t(x) = Sigmai = 1 p thetasiPhii(x) + r(x), where r(x) is an unknown deviation from the regression model. Considering a modeling of this misspecification, the goal is to obtain robust designs which minimize the integral quadratic risk. A kernel-based representation (Gaussian process) is chosen to model the misspecification and a new criterion is derived, composed of the classical L-criterion, plus a specific term. Robust designs are then given for polynomial regression, in the particular case of a Gaussian kernel for the Gaussian process. The benefits of this approach are finally demonstrated through comparison of the performance (in terms of integral quadratic error) of such designs versus L-optimal and uniform designs on a simple illustrative example

Robust moving horizon state estimation: Application to bioprocesses

In this paper, a robust nonlinear receding-horizon observer is proposed for the estimation of cellular concentration in a bioreactor. In the presence of uncertainties on the model parameter or on the initial state of the system, this estimation problem can lead to poor estimation performance. A min-max optimization solution can be used to increase the robustness of the observer in the presence of parameter uncertainties. This solution assumes that each model parameter belongs to an interval. The paper proposes an alternative modeling for these parameters: A Gaussian model is assumed in order to take into account the correlation between parameters. As the confidence region for the parameters is now an ellipsoid, the max step in the min-max problem is replaced by more tractable statistics. Expected value has been tested for its simplicity. For robustness requirements a statistic considering the variance of the estimation has also been developed. Numerical simulations illustrate the efficiency of the proposed estimation scheme.

Soft sensor design for power measurement and diagnosis in electrical furnace: A parametric estimation approach

In this paper, we propose as a first step a software solution to measure the electrical power consumed in an industrial furnace intended essentially for heat treatments. The soft sensor is constructed from the power physical measurement taken as the output of the set (dimmer + resistances), and the control signal measurement provided by a controller with an unknown structure. The second step consists in a detection of faults like a resistance disconnection, for instance. This phase requires the knowledge of the controller model and the furnace system. An overparametrization method was chosen for the controller estimation. An indirect closed-loop Input-Output (IO) identification approach was used for the furnace model estimation through a Tailor-Made and a decomposition of the closed-loop algorithms. A validation with two other experimental tests concludes the paper.

Development and assessment of a wake vortex characterization algorithm based on a hybrid lidar signal processing

Since air traffic is in constant expansion, a more efficient optimisation of the airports capacity is expected. In this context, the characterization of aircraft hazardous turbulences known as wake vortices with an operational vortex Lidar is one of the major issues for the dynamic distances separation. A study has been probed to develop a hybrid vortex algorithm , i.e that uses both the velocity envelopes and a parametric estimator in the interest of processing time as short as possible. The aim is to make this algorithm exploitable for operational projects. That is why a methodology has been set up to evaluate its precision and its robustness. The results of tests on simulated scenarios of different aircraft vortices and different weather conditions show that this algorithm is able to localize precisely wake vortices and to estimate accurately their circulation in a short time.

Discriminant Analysis for Multiway Data

A multiway Fisher Discriminant Analysis (MFDA) formulation is presented in this paper. The core of MFDA relies on the structural constraint imposed to the discriminant vectors in order to account for the multiway structure of the data. This results in a more parsimonious model than that of Fisher Discriminant Analysis (FDA) performed on the unfolded data table. Moreover, computational and overfitting issues that occur with high dimensional data are better controlled. MFDA is applied to predict the long term recovery of patients after traumatic brain injury from multi-modal brain Magnetic Resonance Imaging. As compared to FDA, MFDA clearly tracks down the discrimination areas within the white matter region of the brain and provides a ranking of the contribution of the neuroimaging modalities. Based on cross validation, the accuracy of MFDA is equal to 77 % against 75 % for FDA.

Sequential experimental design for misspecified nonlinear models

In 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 (already collected data) only while updating the estimated parameters. This paper proposes to consider the previous observations not only during the estimation stages, but also in 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 criterion and L-optimal criterion.