An enhanced fault diagnosis method for rolling element bearings using a combination of time-varying filtering for empirical mode decomposition (TVF-EMD) and a high-order energy operator (HO-EO) is proposed in this paper. Empirical mode decomposition (EMD), as a classical mode decomposition technique, has been widely used in quite a few fields. However, the separation problem and the intermittent problem, which can give rise to mode mixing, still remain unresolved. TVF-EMD is capable of improving mode mixing in comparison with EMD. In addition, TVF-EMD is more robust to noise than EMD. These improvements ensure that the vibration signal is decomposed into multiple meaningful empirical modes precisely, known as intrinsic mode functions (IMFs). Then, the meaningful IMFs are selected to be processed by HO-EO. HO-EO is very suitable for bearing fault diagnosis as a demodulation algorithm. Moreover, compared with traditional energy operators, it is more robust to strong noise and vibration interference, so it has a higher accuracy. With this proposed method, the weak bearing fault signature can be distinguished precisely in the energy spectrum. In order to verify the proposed method, single-and dual-fault bearings are used. The experimental results reveal that the proposed method is a powerful and effective tool for bearings fault diagnosis.

In this paper, a novel improved whale optimization algorithm (IWOA), based on the integrated approach, is presented for solving the flexible job shop scheduling problem (FJSP) with the objective of minimizing makespan. First of all, to make the whale optimization algorithm (WOA) adaptive to the FJSP, the conversion method between the whale individual position vector and the scheduling solution is firstly proposed. Secondly, a resultful initialization scheme with certain quality is obtained using chaotic reverse learning (CRL) strategies. Thirdly, a nonlinear convergence factor (NFC) and an adaptive weight (AW) are introduced to balance the abilities of exploitation and exploration of the algorithm. Furthermore, a variable neighborhood search (VNS) operation is performed on the current optimal individual to enhance the accuracy and effectiveness of the local exploration. Experimental results on various benchmark instances show that the proposed IWOA can obtain competitive results compared to the existing algorithms in a short time.

The Teager–Kaiser energy operator (TKEO) and Hilbert transform (HT) are widely used as conventional demodulation methods in the signal processing field; however, it is well known that they are sensitive to vibration interference and noise, and these limitations hamper their applications, especially in the presence of strong noise. A vibrating screen is a kind of screening equipment in the field of vibrating machinery, which differs greatly from the rotating machinery in terms of structural characteristics and operational principles. The vibration signal extracted from the vibrating screen is not only comprised of multiple constituents but also a great deal of background noise. Thus, TKEO and HT have a large limitation on bearing fault diagnosis of the vibrating screen. To overcome these shortcomings, an alternative energy operator method named the envelope-derivative operator (EDO) is proposed. The results of simulation and bearing fault diagnosis of the vibrating screen indicate that EDO can effectively extract fault characteristic frequency, certifying its feasibility and superiority in comparison with TKEO and EDO.

The flexible job shop scheduling problem (FJSP) is a difficult discrete combinatorial optimization problem, which has been widely studied due to its theoretical and practical significance. However, previous researchers mostly emphasized on the production efficiency criteria such as completion time, workload, flow time, etc. Recently, with considerations of sustainable development, low-carbon scheduling problems have received more and more attention. In this paper, a low-carbon FJSP model is proposed to minimize the sum of completion time cost and energy consumption cost in the workshop. A new bio-inspired metaheuristic algorithm called discrete whale optimization algorithm (DWOA) is developed to solve the problem efficiently. In the proposed DWOA, an innovative encoding mechanism is employed to represent two sub-problems: Machine assignment and job sequencing. Then, a hybrid variable neighborhood search method is adapted to generate a high quality and diverse population. According to the discrete characteristics of the problem, the modified updating approaches based on the crossover operator are applied to replace the original updating method in the exploration and exploitation phase. Simultaneously, in order to balance the ability of exploration and exploitation in the process of evolution, six adjustment curves of a are used to adjust the transition between exploration and exploitation of the algorithm. Finally, some well-known benchmark instances are tested to verify the effectiveness of the proposed algorithms for the low-carbon FJSP.

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