Section: New Results

Semi and non-parametric methods

Post-Reflow Automated Optical Inspection of Lead Defects

Participants : Florence Forbes, Kai Qin, Huu Giao Nguyen, Darren Wraith, Ludovic Leau-mercier.

This is joint work with VI-Technology in the context of the IVP project.

Quality and throughput in printed circuit board (PCB) assembly lines constitute a continuous challenge, especially when placing smaller components on boards that are becoming increasingly dense. Automated optical inspection (AOI) technology allows PCB assembly lines to keep operating at a high throughput while visually inspecting production quality in term of paste deposits, mounted components and solder joints in an automatic and non-contact manner. In the AOI, high definition cameras precisely move in both X- and Y-direction to scan the device under test lit by special lighting techniques, e.g. light-emitting diode (LED) lighting. The captured images are then analyzed using specific inspection algorithms to identify defects. The AOI systems can be placed at several stages during the manufacturing process, such as bare board inspection, solder paste inspection, pre-reflow inspection and post-reflow inspection, which usually need some time to be programmed via offline learning of verified boards and expert expertise before online inspection starts. Vi TECHNOLOGY (VIT) offers a wide range of AOI solutions to increase productivity throughout electronics manufacturing lines while enhancing the quality of products. Post-reflow AOI is implemented after the reflow procedure in PCB assembly lines to enable inspection of the major post-reflow defects. This work focus on certain types of post-reflow defects occurring on leaded components, i.e. lifted lead, no solder, excess of solder, contamination on lead, insufficient solder, bad wedding and dry joint. We aim at developing efficient post-reflow lead defect detection approaches by synergizing image analysis, pattern recognition, machine learning, and statistics techniques to improve performance of VIT commercial post-reflow AOI solutions from two aspects: 1) Reducing both detection escape rate and false detection rate; 2) Minimizing programming efforts. The exact nature of the work is confidential.

An Improved CUDA-Based Implementation of Differential Evolution on GPU

Participants : Kai Qin, Florence Forbes.

Modern GPUs enable widely affordable personal computers to carry out massively parallel computation tasks. NVIDIA's CUDA technology provides a wieldy parallel computing platform. Many state-of-the-art algorithms arising from different fields have been redesigned based on CUDA to achieve computational speedup. Differential evolution (DE), as a very promising evolutionary algorithm, is highly suitable for parallelization owing to its data parallel algorithmic structure. However, most existing CUDA based DE implementations suffer from excessive low-throughput memory access and less efficient device utilization. This work presents an improved CUDA-based DE to optimize memory and device utilization: several logically-related kernels are combined into one composite kernel to reduce global memory access; kernel execution configuration parameters are automatically determined to maximize device occupancy; streams are employed to enable concurrent kernel execution to maximize device utilization. Experimental results on several numerical problems demonstrate superior computational time efficiency of the proposed method over two recent CUDA-based DE and the sequential DE across varying problem dimensions and algorithmic population sizes.

This work was nominated for the best paper award (finalist) in the Digital Entertainment Technologies and Arts / Parallel Evolutionary Systems session of the Genetic and Evolutionary Computation Conference 2012 (GECCO12) conference [33] .

Augmented cumulative distribution networks for multivariate extreme value modelling

Participants : Stéphane Girard, Gildas Mazo, Florence Forbes.

Max-stable distribution functions are theoretically grounded models for modelling multivariate extreme values. However they suffer from some striking limitations when applied to real data analysis due to the intractability of the likelihood when the number of variables becomes high. Cumulative Distribution Networks (CDN's) have been introduced recently in the machine learning community and allow the construction of max-stable distribution functions for which the density can be computed. Unfortunately, we show in this work that the dependence structure expected in the data may not be accurately reflected by max-stable CDN's. To face this limitation, we therefore propose to augment max-stable CDN's with the more standard Gumbel max-stable distribution function in order to enrich the dependence structure [32] .

Modelling extremal events

Participants : Stéphane Girard, Jonathan El-Methni, El-Hadji Deme.

Joint work with: Guillou, A. and Gardes, L. (Univ. Strasbourg).

We introduced a new model of tail distributions depending on two parameters $\tau \in [0,1]$ and $\theta >0$. This model includes very different distribution tail behaviors from Fréchet and Gumbel maximum domains of attraction. In the particular cases of Pareto type tails ($\tau =1$) or Weibull tails ($\tau =0$), our estimators coincide with classical ones proposed in the literature, thus permitting us to retrieve their asymptotic normality in an unified way. The first year of the PhD work of Jonathan El-methni has been dedicated to the definition of an estimator of the parameter $\tau$. This permits the construction of new estimators of extreme quantiles. The results are published in [17] . Our future work will consist in proposing a test procedure in order to discriminate between Pareto and Weibull tails.

We are also working on the estimation of the second order parameter $\rho$ (see paragraph  3.3.1 ). We proposed a new family of estimators encompassing the existing ones (see for instance  [64] , [63] ). This work is in collaboration with El-Hadji Deme, a PhD student from the Université de Saint-Louis (Sénégal). El-Hadji Deme obtained a one-year mobility grant to work within the Mistis team on extreme-value statistics. The results are submitted for publication [49] . We also proposed reduced-bias estimators of the Proportional Hazard Premium for heavy-tailed distributions. The results are submitted for publication [50] .

Conditional extremal events

Participants : Stéphane Girard, Gildas Mazo, Jonathan El-methni.

Joint work with: L. Gardes, Amblard, C. (TimB in TIMC laboratory, Univ. Grenoble I) and Daouia, A. (Univ. Toulouse I and Univ. Catholique de Louvain)

The goal of the PhD thesis of Alexandre Lekina was to contribute to the development of theoretical and algorithmic models to tackle conditional extreme value analysis, ie the situation where some covariate information $X$ is recorded simultaneously with a quantity of interest $Y$. In such a case, the tail heaviness of $Y$ depends on $X$, and thus the tail index as well as the extreme quantiles are also functions of the covariate. We combine nonparametric smoothing techniques  [59] with extreme-value methods in order to obtain efficient estimators of the conditional tail index and conditional extreme quantiles. When the covariate is functional and random (random design) and the tail of the distribution is heavy, we focus on kernel methods [18] . We extension to all kind of tails in investigated in [15] .

Conditional extremes are studied in climatology where one is interested in how climate change over years might affect extreme temperatures or rainfalls. In this case, the covariate is univariate (time). Bivariate examples include the study of extreme rainfalls as a function of the geographical location. The application part of the study is joint work with the LTHE (Laboratoire d'étude des Transferts en Hydrologie et Environnement) located in Grenoble.

More future work will include the study of multivariate and spatial extreme values. With this aim, a research on some particular copulas [1] has been initiated with Cécile Amblard, since they are the key tool for building multivariate distributions  [69] . The PhD theses of Jonathan El-methni and Gildas Mazo should address this issue too.

Level sets estimation

Participant : Stéphane Girard.

Joint work with: Guillou, A. and Gardes, L. (Univ. Strasbourg), Stupfler, G. (Univ. Strasbourg) and Daouia, A. (Univ. Toulouse I and Univ. Catholique de Louvain).

The boundary bounding the set of points is viewed as the larger level set of the points distribution. This is then an extreme quantile curve estimation problem. We proposed estimators based on projection as well as on kernel regression methods applied on the extreme values set, for particular set of points [10] .

In collaboration with A. Daouia, we investigate the application of such methods in econometrics [42] , [48] : A new characterization of partial boundaries of a free disposal multivariate support is introduced by making use of large quantiles of a simple transformation of the underlying multivariate distribution. Pointwise empirical and smoothed estimators of the full and partial support curves are built as extreme sample and smoothed quantiles. The extreme-value theory holds then automatically for the empirical frontiers and we show that some fundamental properties of extreme order statistics carry over to Nadaraya's estimates of upper quantile-based frontiers.

In the PhD thesis of Gilles Stupfler (co-directed by Armelle Guillou and Stéphane Girard), new estimators of the boundary are introduced. The regression is performed on the whole set of points, the selection of the “highest” points being automatically performed by the introduction of high order moments [19] , [20] , [21] .

Quantifying uncertainties on extreme rainfall estimations

Participant : Stéphane Girard.

Joint work with: Carreau, J. (Hydrosciences Montpellier), Gardes, L. (univ. Strasbourg) and Molinié, G. from Laboratoire d'Etude des Transferts en Hydrologie et Environnement (LTHE), France.

Extreme rainfalls are generally associated with two different precipitation regimes. Extreme cumulated rainfall over 24 hours results from stratiform clouds on which the relief forcing is of primary importance. Extreme rainfall rates are defined as rainfall rates with low probability of occurrence, typically with higher mean return-levels than the maximum observed level. For example Figure 2 presents the return levels for the Cévennes-Vivarais region that can be obtained. It is then of primary importance to study the sensitivity of the extreme rainfall estimation to the estimation method considered.

The obtained results are published in [12] .

Retrieval of Mars surface physical properties from OMEGA hyperspectral images.

Participant : Stéphane Girard.

Joint work with: Douté, S. from Laboratoire de Planétologie de Grenoble, France and Saracco, J (University Bordeaux).

Visible and near infrared imaging spectroscopy is one of the key techniques to detect, to map and to characterize mineral and volatile (eg. water-ice) species existing at the surface of planets. Indeed the chemical composition, granularity, texture, physical state, etc. of the materials determine the existence and morphology of the absorption bands. The resulting spectra contain therefore very useful information. Current imaging spectrometers provide data organized as three dimensional hyperspectral images: two spatial dimensions and one spectral dimension. Our goal is to estimate the functional relationship $F$ between some observed spectra and some physical parameters. To this end, a database of synthetic spectra is generated by a physical radiative transfer model and used to estimate $F$. The high dimension of spectra is reduced by Gaussian regularized sliced inverse regression (GRSIR) to overcome the curse of dimensionality and consequently the sensitivity of the inversion to noise (ill-conditioned problems) [47] . We have also defined an adaptive version of the method which is able to deal with block-wise evolving data streams [46] .

Statistical modelling development for low power processor.

Participant : Stéphane Girard.

Joint work with: A. Lombardot and S. Joshi (ST Crolles).

With scaling down technologies to the nanometer regime, the static power dissipation in semiconductor devices is becoming more and more important. Techniques to accurately estimate System On Chip static power dissipation are becoming essential. Traditionally, designers use a standard corner based approach to optimize and check their devices. However, this approach can drastically underestimate or over-estimate process variations impact and leads to important errors.

The need for an effective modeling of process variation for static power analysis has led to the introduction of Statistical static power analysis. Some publication state that it is possible to save up to 50% static power using statistical approach. However, most of the statistical approaches are based on Monte Carlo analysis, and such methods are not suited to large devices. It is thus necessary to develop solutions for large devices integrated in an industrial design flow. Our objective to model the total consumption of the circuit from the probability distribution of consumption of each individual gate. Our preliminary results are published in [23] .