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This paper proposes an incipient chatter detection method to meet high dynamic applications' time and reliability constraints, such as high-speed milling involving heavy noise. The herein introduced method relies on a multiple sampling per revolution (MSPR) technique, coupled with two data preprocessing techniques, a modified adaptive cumulative chatter indicator, and a two-risk levels-based threshold. The MSPR technique enables collecting information-rich enough data to characterize the chatter dynamics thanks to a significant amount of data collected in each revolution. Therefore, the MSPR technique allows for acquiring the data using a short-time window, thus reducing the detection delay. Two data preprocessing techniques, i.e., Z-score normalization and mean-centered, are implemented for data integration and chatter information consolidation. The modified adaptive cumulative chatter indicator has three advantages: (a) it accumulates the information on the chatter feature and highlights the appearance of an incipient chatter; (b) it adapts to the variation of the environmental disturbance noises, resulting in enhanced detection reliability; (c) it is faster than the adaptive cumulative log-likelihood ratio (ACLLR) for decision-making statistically. The two-risk levels-based threshold overcomes the limitations of a unique threshold, and allows simultaneously assessing the two risk levels, thus improving detection reliability. We successfully applied the proposed method to detect incipient chatter in a digital high-speed milling process and assessed its effectiveness by comparing it with several existing chatter detection methods.

International audience; This paper addresses the problem of wireless sensor network (WSN) lifetime maximization, under limited available energy constraint. The investigations have shown that the valid amount of energy was not used by the existing disjoint set covers (DSC) based scheduling method for WSNs' lifetime maximization, because of the DSC constraints. Instead, we suggest in this paper to schedule non-disjoint sets covers (NDSC) for maximizing WSNs' lifetime. Thus, we have formulated this problem, using the integer linear programming (ILP) mathematical model, then we developed an approach based on genetic algorithm GA to find the maximal lifespan. As main contributions, we investigated and designed a new method using the NDSC instead of the DSC. This approach removes the latter's constraint and gives the opportunity to a sensor to participate in more than one cover, and thereby improves significantly the WSNs' lifetime. We proposed an exact method and a genetic algorithms (GA) for the NDSC efficient scheduling for the WSN lifetime maximization. The exact method lies on the integer linear programming (ILP). For the GA based heuristics, we used a specific arrangement of chromosomes combining several crossover and mutation strategies for encoding the solutions. We provided experimental results for different instances involving sensors with non-identical amount of initial energy and power consumption. In addition, we provided comparative analysis results between the solutions obtained by our both methods and the existing methods based on DSC. The comparisons of the run times and the solutions' quality revealed the dominance of the solutions yielded by our methods based on the NDSC compared to those based on the DSC.

For all 2 ≤ n ∈ N , the four vertices ( 0 0 ) , ( n 0 ) , ( 2 n n ) , ( n n ) of the Pascal Triangle expanded from level 0 to level 2 n define the greatest embedded rhomboid sub-block denoted n − GRSB in this paper. The n − GRSB is canonically partitioned into two triangular sub-blocks G and g , with respective vertex sets { ( 0 0 ) , ( n 0 ) , ( n n ) } and { ( n + 1 1 ) , ( 2 n n ) , ( n + 1 n ) } . The G -sub-block (resp. g -sub-block) has twelve distinct triangular matrix arrangements, numbered from 1 to 12 and designated here G -matrix set (resp. g -matrix set): three northeast, three northwest, three southwest and three distinct triangular southeast arrangements. From the n − GRSB we define thirty-six full matrix forms of the Pascal triangle (FP-matrices for short) simply adding pairwise complementary subblocks of the G - and g -matrices. We then identify and present the invariant groups underlying two significant partitions of the FP-matrix set. The insight gained from a previous study of the twelve G-matrices led us to derive the 36 full matrix forms presented in this paper. Several papers in the literature have dealt with some matrix forms of the Pascal Triangle. Only two of these are so far encountered in the literature. Our work is the first to focus on the hitherto little known 36 full matrix forms as mathematical objects in their own right. As novelty, this paper presents, for the first time, the set of the thirty-six full Pascal matrices. This work focuses on a systematic study of matrix forms derived from the Pascal Triangle, on the individual properties of these forms, their applications, and on the groups of transformations that structure their relations.

International audience; This study introduced an investigation to evaluate spatial and temporal variations of the wind potential for the techno-economic feasibility analysis of the energy production in Northwest Africa (a case of Mauritania). The present research was introduced as the first attempt to appraise the spatio-temporal influence of the wind energy production in Mauritania, and particularly focused on analyzing seasonal, daily, and turbulence index on the available wind potential in this region. Data measured every 10 min over one-year period were collected from eight sites (with three different height levels) located mainly on the west coast of Mauritania, and the annual average of the wind characteristics were determined. Power density, Weibull parameters, turbulence indices, and power-law exponents were estimated based on seasonal and daily wind analyses. Comparative studies of the power density potential of the wind on different sites were also conducted while investigating the influence of seasons, height of the wind turbines, wind directional distributions, and daily characteristics. Investigations regarding the generated energy from the wind turbine and the related capacity factor were performed based on eight particular wind turbines (Ecotècnia-44, Ecotècnia-48, Nordex-N50, Neg-Micon, Vestas-V66, Power-Wind-90, Bonus-2MW, and Vestas-V90). Results showed that the power-law exponent was higher where the turbulence index was low. The analysis of the power distribution allowed concluding on the energy availability according to the influent variables. Findings of the present techno-economic analysis (for electricity generation from the planned wind energy systems) revealed that the best cost of energy (ranging from 0.0187 €/kWh to 0.0596 €/kWh) was observed for the wind turbine Ecotècnia-48 on all sites.

International audience; This paper investigates the preventive age replacement policy (ARP) for a system subject to random failures. Unlike most maintenance models in the literature, our model considers a system that is exploited under different operating environments each characterized by its own degree of severity. The system lifetimes follow a different distribution depending on the environment it is operating under. Furthermore, the system lifetimes distribution is assumed unknown and therefore estimated from field reliability data. The reliability of the system is calculated using two kernel estimators. This method offers the advantage of non-parametric estimation methods and completely determined by two parameters, namely the smoothing parameter and the kernel function. First, a probability maintenance cost model is derived and conditions under which an optimal preventive maintenance age exists are provided. Then, a statistical maintenance cost model is developed using two kernel estimators. The impact of the variability of the kernel smoothing parameter on the cost model is also investigated. Numerical experiments are provided to illustrate the proposed approach. Results obtained demonstrate the accuracy of the proposed statistical maintenance cost model.

International audience; This paper proposes a genetic algorithm (GA) with a benchmarking study for optimizing the wireless sensor network (WSN) lifespan. Four crossover operators combined with four mutation operators were developed to enhance the GA efficiency, and thus the performance of the lifespan optimization algorithm. The traditional one-point crossover operator, referred to as the "simple crossover," is used to evaluate the modified "partially matched" and the "order" crossovers. Also, a new crossover operator referred to as "rotated" crossover is also proposed and evaluated. Different combinations of these crossover operators with the one-point and two-points deterministic and random mutations allowed to optimize the WSNs lifespan. The algorithms were coded in the C programming language and applied to different instances of WSNs initial configurations. The optimization software tool developed based on the combinatorial operators allows selecting the best solution among 16 through smart decision making. For illustration, among all the investigated algorithms, the modified partially matched crossover associated with the random two-points mutation has shown the best performances on the studied instance due to its capability to reach closer to the optimal solution.

International audience; This work initiates a systematic investigation into the matrix forms of the Pascal triangle as mathematical objects in their own right. The present paper is especially devoted to the so-called G-matrices, i.e. the set of the twelve (n+1)×(n+1) triangular matrix forms that can be derived from the Pascal triangle expanded to the level View the MathML source. For n=1, the G-matrix set reduces to a set of four distinct matrices. The twelve G-matrices are defined and the classic Pascal recursion is reformulated for each of the twelve G-matrices. Three sets of matrix transformations are then introduced to highlight different relations between the twelve G-matrices and for generating them from appropriately chosen subsets.