[show abstract][hide abstract] ABSTRACT: 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.
Journal of Nondestructive Evaluation 01/2010; · 1.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: A 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.
[show abstract][hide abstract] ABSTRACT: A measurement can be defined as the best way to take advantage of the information given by the observed data. For this purpose, a natural formalism, based on a couple of fundamental equations, is presented. The model, which described the physical phenomenon, should in that sense be wisely built. The parameterization of the model structure is proved to have no effect on the statistical properties of the measurement. Then, a reparameterization of the model structure can be a way of optimizing the inversion process. An optimal reparameterization can be described. It leads to the inversion of a nonlinear system which cannot be solved in a closed form. So, to avoid such a problem, a new suboptimal method is proposed. The results are eventually exemplified on an eddy-current non-destructive testing problem.
[show abstract][hide abstract] ABSTRACT: This 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.
[show abstract][hide abstract] ABSTRACT: 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 (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.