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Abstract Feature selection is a difficult but highly important preliminary step for bearings remaining useful life (RUL) estimation. To avoid the weights setting problem in hybrid metric, this work devotes to conduct feature selection by using a single metric. Due to noise and outliers, an existing feature selection metric, called monotonicity, used for estimating bearings RUL, requires data smoothing processing before adequate implementation. Such a smoothing process may remove significant part of meaningful information from data. To overcome this issue, a mixture distribution analysis-based feature selection metric is proposed. Moreover, based on this new metric, a feature selection approach for bearings RUL estimation is proposed. Numerical experiments benchmarking the proposed method and the existing metric monotonicity method on available real datasets highlight its effectiveness.

For all 2≤n∈N, the four vertices (00),(n0),(2nn),(nn) of the Pascal Triangle expanded from level 0 to level 2n 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 {(00),(n0),(nn)} and {(n+11),(2nn),(n+1n)}. 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.

Pooling different renewable energy sources (hydrogen, solar, wind, geothermal, etc.) enables developing a standalone energy micro-grid. The energy flows from these various sources are neither constant nor equivalent. Therefore, control and balancing mechanisms should be established for optimal energy utilization through an intelligent system based on interconnected microcontrollers networked with sensors. Our contribution addresses this issue by proposing an original architecture of an intelligent and distributed control system based on a sensor network and a strategy to share the electric power through the micro-grid. In our work we consider a micro-grid powered by sources of wind turbine, pv panels and battery which energy flows are controlled and balanced through our system depending on power demand of the loads. Alternating Current (AC) bus and Direct Current (DC) bus are tied together by an inverter. A set of microcontroller-sensor-actuators (which we named S.A.D for Sensor/Actuator Device) are deployed at strategic points in the micro-grid providing constantly data from power generated and consumed, equipment health and status. A control algorithm developed in relation to a network control strategy is implemented by combining the performance different microcontroller boards. Relying on existing literature works, a review of solution approaches to the challenging problem, of the power flows balancing between the different energy sources and storage batteries embedding appropriate IoT technologies and exploiting energy big-data platforms, is presented

Four noise-assisted empirical mode decomposition (EMD) algorithms, i.e., ensemble EMD (EEMD), complementary ensemble EMD (CEEMD), complete ensemble EMD with adaptive noise (CEEMDAN), and improved complete ensemble EMD with adaptive noise (ICEEMDAN), are noticeable improvements to EMD, aimed at alleviating mode mixing. However, the sampling frequency ratio (SFR), i.e., the ratio between the sampling frequency and the maximum signal frequency, may significantly impact their mode mixing alleviation performance. Aimed at this issue, we investigated and compared the influence of the SFR on the mode mixing alleviation performance of these four noise-assisted EMD algorithms. The results show that for a given signal, (1) SFR has an aperiodic influence on the mode mixing alleviation performance of four noise-assisted EMD algorithms, (2) a careful selection of SFRs can significantly improve the mode mixing alleviation performance and avoid decomposition instability, and (3) ICEEMDAN has the best mode mixing alleviation performance at the optimal SFR among the four noise-assisted EMD algorithms. The applications include, for instance, tool wear monitoring in machining as well as fault diagnosis and prognosis of complex systems that rely on signal decomposition to extract the components corresponding to specific behaviors.