Under the background of strong noise, it is difficult to detect and extract weak signals. To solve the above problems, a new combination model of power and exponential function in tri-stable system was proposed based on the classic bistable system model and the Gaussian Potential model. First of all, the tri-stable system model was constructed by combining power function and exponential function, then the stochastic resonance was generated by adjusting related parameters, which was validated by numerical simulations. Secondly, using the average Signal-to-Noise Ratio (SNR) of output as a measure index, the artificial fish swarm intelligence algorithm was used to optimize the corresponding parameters, which makes the tri-stable system combining the power function and the exponential function achieve the maximum output SNR, and the phenomenon stochastic resonance was generated. Finally, it was applied to the diagnosis of bearing faults. At the same condition that the output SNR is -25.8 dB, the output SNR of the bistable system and tri-stable system combining the power function and the exponential function is -13.1 dB and -8.59 dB respectively. Simulation results demonstrate that the performance of the proposed system is better than the bistable system, and it is effective in weak signal detection and extraction.

Aiming at the problem of the poor real-time performance of Inertial Navigation System (INS)/Global Positioning System (GPS) integrated navigation system caused by GPS information delay, a processing method which takes advantage of dealing with various asynchronous measurements at an information fusion time in factor graph algorithm was proposed. Before the system received GPS information, the factor nodes of the INS information were added to the factor graph model, and the integrated navigation results were obtained by incremental inference to ensure the real-time performance of the system. After the system received the GPS information, the factor nodes about the GPS information were added to the factor graph model to correct the INS error, thereby ensuring high-precision operation of the system for a long time. The simulation results show that, the navigation state that has just been updated by GPS information can correct the INS error effectively, when the correction effect of real-time navigation state on INS error becomes worse, as the time of GPS information delay becomes longer. The factor graph algorithm avoids the adverse effects of GPS information delay on the real-time performance of INS/GPS integrated navigation system, and ensures the accuracy of the system.

Aiming at the issue that chaotic attractor exists in Permanent Magnet Synchronous Motor (PMSM) and chaotic synchronous control of PMSM cannot be realized except on the cycle of the equilibrium point, a kind of zero error system algorithm based on automatic control theory and finite time control principle was proposed. Firstly, the error system was established by mathematical model of PMSM and a mathematical formula between each state variable and its expected value in PMSM. Secondly, synchronous controller and correction rate were designed for the error system model and the conclusion that the error system could quickly converge to zero in finite time was proved by using Lyapunov's stability criterion. Finally, interference was imposed on the error system and the robustness of the algorithm was analyzed. The theoretical analysis and simulation results show that the proposed algorithm can maitain in zero balance after reaching the zero point of the system, which can effectively restrain the chaotic attractor and adjust the input and output of PMSM flexibly; and the PMSM system has good robustness to the uncertainty parameter and external disturbance while ensuring the normal operation of PMSM.

Aiming at the characteristics of Synthetic Aperture Radar (SAR) images and the problem of the standard graph cut segmentation algorithm's high computational complexity, a method of strong scattering objects segmentation based on graph cut and Mean Shift algorithm was proposed. Firstly, the image was pre-processed with the Mean Shift algorithm to produce over-segmentation areas. Then, a graph was built with nodes responding to over-segmentation areas, and then the results of SAR strong scattering targets segmentation were obtained by using graph cut algorithm. Compared with nodes responding to pixels in the standard graph cut algorithm, the number of nodes and edges in the graph were reduced by two orders of magnitude and the computational efficiency was significantly improved. Furthermore, according to the strong scattering characteristics of the targets in SAR images, the “object” terminal and the “background” terminal were defined automatically to reduce human interaction. The experiments show that the proposed method combines the advantages of Mean Shift and graph cut effectively, and it can effectively extract SAR strong scattering targets from the background clutter.

Particle Swarm Optimization (PSO) algorithm is population-based and it is effective for multi-objective optimization problems. For the convergence of the swarm makes the classical algorithm easily converge to local pareto front, the convergence and diversity of the solution are not satisfactory. This paper proposed an independent dynamic inertia weights method for multi-objective particle swarm optimization (DWMOPSO). It changed each particle's inertia weight according to the evolution speed which was calculated by the value of each particle's best fitness in the history. It improved the probability to escape from the local optima. In comparison with Coello's MOPSO through five standard test functions, the solution of the new algorithm has great improvement both in the convergence to the true Pareto front and diversity.