In order to reduce fuel consumption and reduce the deviation between the final battery state-of-charge (SOC) value and the target value at the same time, a novel double-layer multi-objective optimization method is proposed, which adopts an improved ant colony optimization (ACO) algorithm and the equivalent fuel consumption minimization strategy (ECMS) considering mode switching. The proposed strategy adopts a two-layer structure. In the inner layer, the ECMS considering mode switching was adopted to optimize the working mode and working point, so as to achieve the goal of reducing fuel consumption. In the outer layer, aiming at the shortcomings of traditional ACO, the heuristic factor and adaptive volatilization factor were introduced. An improved ACO method was proposed to optimize the equivalent factor, so as to achieve the goal of reducing the deviation between the final value of SOC and the target value. In order to verify the effectiveness of the proposed algorithm, it is compared with the traditional ECMS strategy and the rule-based (RB) ECMS strategy. The simulation results show that the proposed energy management strategy combining an improved ACO algorithm with ECMS considering mode switching can reduce the energy consumption of the whole ship and control the battery power.

Bearing multi-fault detection from stochastic vibration signal is still a thorny task to dispose of because of the complex interplay between different fault components under severe noise interference. In such case, conventional techniques such as filter processing and envelope demodulation may cause undesired results. To overcome the limitation, this article explores a filtering-free technique combined probabilistic principal component analysis denoising with the Higuchi fractal dimension transformation to diagnose the bearing multi-faults. Fractal theory is used to optimize the model parameters and stabilize the random vibrational signal for fast Fourier transform spectrum analysis. Noise interference in the Higuchi transformation is capped using a probabilistic principal component analysis model whose parameters are optimized through embedding dimension Cao algorithm and correlation dimension Grassberger and Procaccia algorithm. The fault diagnostic scheme mainly falls into three steps. First, the original vibration signal is truncated into a series of sub-signal segments by moving window whose length is determined as twice the value of maximum time delay that is provided by examining the steady Higuchi fractal dimension value of a raw signal in a process of plotting the fractal dimension over a range of time delay. Then, the Higuchi approach is used to estimate the average fractal dimension for each segment to create a quasi-stationary Higuchi fractal dimension sequence on which, finally, the fault features are straightforwardly extracted by the fast Fourier transform algorithm. The effectiveness of the proposed method is validated using simulated and experimental compound bearing fault vibration signals. Some fault components may be clouded if applied Higuchi fractal dimension alone because of the noise interference, but using the probabilistic principal component analysis–Higuchi fractal dimension method leads to clear diagnostic results. It indicates that the proposed approach can be incorporated into bearing multi-fault extraction from raw vibration signals.

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