Under-determined Blind Source Separation And Its Applications Based On Potential Function And Compressive Sensing

Blind Source Separation has received much concern for a long time since it was introduced because of its wide applications. The well-determined and over-determined blind source separation has been much maturely studied, but for the under-determined blind source separation problem that the number of measured signal is less than the source signal, there are still some technical bottlenecks of its theory and algorithm to be explored further.Signal sparsity is the premise of under-determined blind source separation algorithm, but in practice, only very few signals are sparse in the time domain, so the majority of the signals must be sparsely decomposed to make sure the single with sparsity before under-determined sparse decomposition. There are some deficiencies such as slow operation rate and low arithmetic precision in traditional matching pursuit sparse decomposition algorithm based on over-complete atomic dictionary, in view of the above, an improved Particle Swarm Optimization algorithm with gradient information was put forward in this paper to find the best atom during the MP sparse decomposition process, which can get higher convergence rate and decomposition rate, and also can improve the algorithm accuracy in some degree. Under the same precision requirement, the required time of the proposed algorithm is only one fifth of the classic sparse decomposition algorithm. This improved MP algorithm was used in signal de-noising, the de-nosing efficiency of the proposed algorithm is7.5519dB higher than the wavelet de-noising for the signal with the signal to noise ratio of5dB, which shows much advantages of the algorithm in this paper.Under-determined blind source separation algorithm is divided into two steps: estimated mixing matrix and source signal reconstruction. There are some deficiencies in traditional two-step algorithm for under-determined blind source separation, such as the value of K is difficult to be determined, the algorithm is sensitive to the initial value, noises and singular points are difficult to be excluded, the algorithm is lacking theory basis, etcetera. In order to solve these problems, a new two-step algorithm based on the potential function algorithm and compressive sensing theory was proposed. Firstly, the mixing matrix was estimated by improved potential function algorithm based on multi-peak value particle swarm optimization algorithm, after the sensing matrix was constructed by the estimated mixing matrix, the sensing compressive algorithm based on orthogonal matching pursuit was introduced in the process of under-determined blind source separation to realize the signal reconstruction. The under-determined blind source separation experiments of mixed sinusoidal signal and mixed voice signals were done in this paper, the simulation results show that the highest estimation precision of the mixing matrix can reach99.13%, and all the signal reconstruction interference ratios can be higher than10dB, which meets the reconstruction accuracy requirements well and confirms the effectiveness of the proposed algorithm. This algorithm is of good universality and high accuracy for under-determined blind source separation of one-dimensional mixing signals.Combining with the actual engineering applications, the proposed algorithm was applied to the analysis and fault diagnosis of wind turbine gearbox vibration signals. First, in the premise of retaining the fault feature, the collected wind turbine gearbox vibration signals were made sparse composition and de-noising process by the improved matching pursuit in this paper. Secondly, the signals after de-noising process were made under-determined blind source separation by the proposed algorithm, compared with the results under normal operating state, the location of fault point could be initially determined. Finally, the spectrum analysis of the separated wind turbine gearbox vibration signals was done, according to the fault diagnosis knowledge, the fault reason could be ultimately determined. After the disassemble and repair of the wind turbine gearbox, the location of fault point and the fault reason were consistent with the inference, which proved the feasibility of the proposed algorithm in this paper in practice.At last, the advantages and disadvantages of the proposed algorithm were summarized, at same time, combining with wireless sensor networks, a blueprint was sketched out for a better state of wireless real-time monitoring of wind turbines, and the prospect of the proposed algorithm was forecasted.