In the fields of industrial production or safety monitoring, wireless sensor networks are often content with unreliable and time-varying channels that are susceptible to interference. Consequently, ensuring both transmission reliability and data accuracy has garnered substantial attention in recent years. Although multipath routing-based schemes can provide transmission reliability for wireless sensor networks, achieving high data accuracy simultaneously remains challenging. To address this issue, an Energy-efficient Multipath Routing algorithm balancing data Accuracy and transmission Reliability (EMRAR) is proposed to balance the reliability and accuracy of data transmission. The multipath routing problem is formulated into a multi-objective programming problem aimed at optimizing both reliability and power consumption while adhering to data accuracy constraints. To obtain the solution of the multi-objective programming, an adaptive artificial immune algorithm is employed, in which the antibody initialization method, antibody incentive calculation method, and immune operation are improved, especially for the multipath routing scheme. Simulation results show that the EMRAR algorithm effectively balances data accuracy and transmission reliability while also saving energy when compared to existing algorithms.

Aiming at non-stationary signals with complex components, the performance of a variational mode decomposition (VMD) algorithm is seriously affected by the key parameters such as the number of modes $K$, the quadratic penalty parameter $\alpha$ and the update step $\tau$. In order to solve this problem, an adaptive empirical variational mode decomposition (EVMD) method based on a binary tree model is proposed in this paper, which can not only effectively solve the problem of VMD parameter selection, but also effectively reduce the computational complexity of searching the optimal VMD parameters using intelligent optimization algorithm. Firstly, the signal noise ratio (SNR) and refined composite multi-scale dispersion entropy (RCMDE) of the decomposed signal are calculated. The RCMDE is used as the setting basis of the $\alpha$, and the SNR is used as the parameter value of the $\tau$. Then, the signal is decomposed into two components based on the binary tree mode. Before decomposing, the $\alpha$ and $\tau$ need to be reset according to the SNR and MDE of the new signal. Finally, the cycle iteration termination condition composed of the least squares mutual information and reconstruction error of the components determines whether to continue the decomposition. The components with large least squares mutual information (LSMI) are combined, and the LSMI threshold is set as 0.8. The simulation and experimental results indicate that the proposed empirical VMD algorithm can decompose the non-stationary signals adaptively, with lower complexity, which is O(n²), good decomposition effect and strong robustness.

Aiming at the problems of early weak fault feature extraction of bearings in rotating machinery, an improved stochastic resonance (SR) is proposed combined with the advantage of SR to enhance weak characteristic signals with noise energy. Firstly, according to the characteristics of the large parameters of the actual fault signal, the amplitude transform coefficient and frequency transform coefficient are introduced to convert the large parameter signal into small parameter signal which can be processed by SR, and the relationship of second-order parameters are introduced. Secondly, a comprehensive evaluation index (CEI) consisted of power spectrum kurtosis, correlation coefficient, structural similarity, root mean square error, and approximate entropy, is constructed through BP neural network. Moreover, this CEI is adopted as fitness function to search the optimal damping coefficient and amplitude transform coefficient with adaptive weight particle swarm optimization (PSO). Finally, according to the improved optimal SR system, the weak fault feature can be extracted. The simulation and experiment verify the effectiveness of the proposed method compared with traditional second-order general scale transform adaptive SR.

In the incipient fault vibration signals of rolling bearings, weak fault features are easily submerged in strong background noise and difficult to be extracted. The sparse decomposition method can perform well in the extraction of weak fault features, but the low signal-to-noise ratio (SNR) would cause excessive decomposition. To enhance the fault features and maintain the time–frequency structure of fault impulses, a novel incipient fault feature extraction of rolling bearing based on signal reconstruction is proposed. Firstly, the Teager energy operator (TEO) is used to obtain the envelope of the impulse components in the vibration signal, which is also sensitive to noise and would be seriously affected by strong noise. Secondly, a Savitzky–Golay (S–Golay) filter based on the particle swarm optimization (PSO) algorithm is adopted to suppress the noise in the TEO envelope and generate a smooth envelope signal. Finally, the fault signal is reconstructed by the multiplication of the filtered TEO envelope signal and the original signal. The reconstructed signal can maintain the structural characteristics of the original fault impact signal and can provide reliable feature enhancement signals for further sparse decomposition, multi-source vibration separation, and other operations. Simulation signals and experiments verify the effectiveness of this method in extracting early fault features under low SNRs.

In order to diagnose an incipient fault in rotating machinery under complicated conditions, a fast sparse decomposition based on the Teager energy operator (TEO) is proposed in this paper. In this proposed method, firstly, the TEO is employed to enhance the envelope of the impulses, which is more sensitive to frequency and can eliminate the low-frequency harmonic component and noise; secondly, a smoothing filtering algorithm was adopted to suppress the noise in the TEO envelope; thirdly, the fault signal was reconstructed by multiplication of the filtered TEO envelope and the original fault signal; finally, sparse decomposition was used based on a generalized S-transform (GST) to obtain the sparse representation of the signal. The proposed preprocessing method using the filtered TEO can overcome the interference of high-frequency noise while maintaining the structure of fault impulses, which helps the processed signal perform better on sparse decomposition; sparse decomposition based on GST was used to represent the fault signal more quickly and more accurately. Simulation and application prove that the proposed method has good accuracy and efficiency, especially in conditions of very low SNR, such as impulses with anSNR of −8.75 dB that are submerged by noise of the same amplitude.

For large rotating machinery with low speed and heavy load, the incipient fault characteristics of rolling bearings are particularly weak, making it difficult to identify them effectively by direct signal processing methods. To resolve this issue, we propose a novel approach to detecting incipient fault features that combines signal energy enhancement and signal decomposition. First, the structure of a conventional Teager algorithm is modified to further increase the energy of the micro-impact component and hence the impact amplitude. Then, a kind of composite chaotic mapping is constructed to extend the original fruit fly optimization algorithm (FOA) framework, improving the FOA’s randomness and search power. The effective intrinsic mode functions (IMFs) are determined by searching for the optimal combination values of the key parameters of the variational mode decomposition (VMD) with the improved chaotic FOA (ICFOA). The kurtosis index is then used to select the IMFs that are most relevant to the fault characteristics information. Finally, the sensitive components are analyzed to identify multiple early fault characteristics and determine detailed information about the faults. Moreover, the approach is evaluated by a simulation signal and a measured signal. The comprehensive evaluation indicates that the approach has clear advantages over other excellent methods in extracting the incipient fault feature information of the equipment and has great potential for application in engineering.