Bearing is one of the most important parts of rotating machinery with high failure rate, and its working state directly affects the performance of the entire equipment. Hence, it is of great significance to diagnose bearing faults, which can contribute to guaranteeing running stability and maintenance, thus promoting production efficiency and economic benefits. Usually, the bearing fault features are difficult to extract effectively, which results in low diagnosis performance. To solve the problem, this paper proposes a bearing fault feature extraction method and it establishes a bearing fault diagnosis method that is based on feature fusion. The basic idea of the method is as follows: firstly, the time-frequency feature of the bearing signal is extracted through Wavelet Packet Transform (WPT) to form the time-frequency characteristic matrix of the signal; secondly, the Multi-Weight Singular Value Decomposition (MWSVD) is constructed by singular value contribution rate and entropy weight. The features of the time-frequency feature matrix obtained by WPT are further extracted, and the features that are sensitive to fault in the time-frequency feature matrix are retained while the insensitive features are removed; finally, the extracted feature matrix is used as the input of the Support Vector Machine (SVM) classifier for bearing fault diagnosis. The proposed method is validated by data sets from the time-varying bearing data from the University of Ottawa and Case Western Reserve University Bearing Data Center. The results show that the algorithm can effectively diagnose the bearing under the steady-state and unsteady state. This paper proposes that the algorithm has better fault diagnosis capabilities and feature extraction capabilities when compared with methods that aree based on traditional feature technology.

As one of the most critical issues for target track, $\alpha$ -jerk model is an effective maneuver target track model. Non-Gaussian noises always exist in the track process, which usually lead to inconsistency and divergence of the track filter. A novel Kalman filter is derived and applied on $\alpha$ -jerk tracking model to handle non-Gaussian noise. The weighted least square solution is presented and the standard Kalman filter is deduced firstly. A novel Kalman filter with the weighted least square based on the maximum correntropy criterion is deduced. The robustness of the maximum correntropy criterion is also analyzed with the influence function and compared with the Huber-based filter, and, moreover, the kernel size of Gaussian kernel plays an important role in the filter algorithm. A new adaptive kernel method is proposed in this paper to adjust the parameter in real time. Finally, simulation results indicate the validity and the efficiency of the proposed filter. The comparison study shows that the proposed filter can significantly reduce the noise influence for $\alpha$ -jerk model.

Due to the influence of the complex underwater environment, the sound speed constantly changes, resulting in the acoustic signal propagation trajectory being curved, which greatly affects the positioning accuracy of the underwater long baseline (LBL) system. In this paper, an improved LBL positioning method based on a B-spline surface for fitting the effective sound speed table (ESST) is proposed. Firstly, according to the underwater sound speed profile, the discrete ESST of each measurement station is constructed before the positioning test, and then, the node position of the B-spline surface is optimized by particle swarm optimization (PSO) to accurately fit the discrete ESST. Based on this, the improved LBL positioning method is constructed. In the underwater positioning test, the effective sound speed can be quickly found by measuring the time of arrival (TOA) of the acoustic signal and the target depth, and moreover, the target position parameters can be quickly and accurately estimated. The numerical simulation results show that the improved positioning method proposed in this paper can effectively improve the LBL positioning accuracy and provide the theoretical basis and the technical support for the underwater navigation and positioning.

Underwater navigation practice shows that the long baseline survey has the characteristics of coplanar configuration, flat geometry, and large refraction error, which brings challenges to underwater positioning. To address this challenge, this paper proposes a high-precision real-time range-difference location algorithm based on underwater long baseline measurement. Firstly, the system error sources of long baseline positioning are analyzed in detail, the propagation models of different system errors are constructed, and the effects of system error sources on the rangefinder are described. Secondly, the limitations of traditional range iterative location algorithms and geometric analytic location algorithms in long baseline locations are analyzed. Then, using the strategy of converting the long baseline range information into the distance difference information, a high-precision real-time distance difference location algorithm based on long baseline measurement is presented. Finally, the feasibility of the algorithm is analyzed from the perspective of precision analysis. Numerical simulation results show that compared with the two traditional long-baseline positioning algorithms, the proposed algorithm has higher positioning accuracy and potential application value in the field of underwater real-time positioning.

The observation error model of the underwater acoustic positioning system is an important factor to influence the positioning accuracy of the underwater target. For the position inconsistency error caused by considering the underwater target as a mass point, as well as the observation system error, the traditional error model best estimation trajectory (EMBET) with little observed data and too many parameters can lead to the ill-condition of the parameter model. In this paper, a multi-station fusion system error model based on the optimal polynomial constraint is constructed, and the corresponding observation system error identification based on improved spectral clustering is designed. Firstly, the reduced parameter unified modeling for the underwater target position parameters and the system error is achieved through the polynomial optimization. Then a multi-station non-oriented graph network is established, which can address the problem of the inaccurate identification for the system errors. Moreover, the similarity matrix of the spectral clustering is improved, and the iterative identification for the system errors based on the improved spectral clustering is proposed. Finally, the comprehensive measured data of long baseline lake test and sea test show that the proposed method can accurately identify the system errors, and moreover can improve the positioning accuracy for the underwater target positioning.