Research On Blind Source Separation Method Of Multiple Faults Based On Adaptive Parallel Factor

With the support of the National Natural Science Fund(No.51675258),an adaptive blind source separation(BSS)method based on parallel factor(PARAFAC)is proposed to overcome the disadvantages of traditional BSS method,such as high complexity and long running time.The feasibility of the proposed method is verified by simulation analysis and experiments.The main research contents are as follows:1.The traditional blind source separation method based on PARAFAC-BSS is to decompose the PARAFAC model by batch alternating least squares(ALS)algorithm.It needs three pseudo-inverse operations in one iteration.It is difficult to process the collected data on-line in real time,because it is necessary to consider the computation of the whole new tensor decomposition at each sampling time.Aiming at the shortcomings of the traditional PARAFAC-BSS method,an adaptive PARAFAC-BSS method is proposed.The PARAFAC model is decomposed by using the weighted recursive least square tracing(RLST)algorithm.Firstly,the original PARAFAC model is decomposed by the traditional batch ALS algorithm,and the initial estimate of the loading matrix is obtained.Then,by adding new data slices to the original tensor along the direction of time dimension,and adding windows to the observation tensor,the new data slices have more weight.The loading matrix is updated using the previously calculated initial loading matrix.Compared with the repeated application of standard batch ALS,the proposed method does not need three pseudo-inverse operations,which can reduce the computational cost and improve the running speed.The proposed method is verified to be faster by the blind source separation of the two sets of simulated fault source signals.At last,the multi-fault signals of bearing are processed,which proves that this method has obvious advantages over the traditional method in running speed.2.Although the blind source separation method based on PARAFAC-RLST does not have to go through three pseudo-inverse operations in one iteration,it can process the data on-line with lower complexity and run faster,which greatly improves the efficiency of fault diagnosis.However,because this method uses the first-order gradient to optimize the exponential weighted least square cost function,the accuracy of the algorithm is reduced,and the wrong diagnosis result may be obtained.Therefore,this chapter improves the algorithm and proposes a blind source separation method based on second-order optimized adaptive PARAFAC(SOAP).The method uses the second-order stochastic gradient instead of the first-order gradient to optimize the exponential weighted least square cost function,which improves the accuracy of the algorithm.At the same time,in each step of the algorithm,the Kronecker product structure of the estimated subspace is approximately retained.The cyclic strategy is used to update each column of the subspace at each time,which can also reduce the complexity of the algorithm.The simulation and experimental results show that the proposed method has more practical engineering application value.3.The traditional under-determined BSS method mostly uses some mode decomposition methods to decompose the observed signal and obtain some sub-signal components.Then,using these signal components as new input signals,the new input signals are decomposed by independent component analysis(ICA)algorithm or its improved algorithm.The fault source signals are separated.ICA algorithm is based on matrix decomposition,and usually needs some constraints such as orthogonality,independence and constant modulus to guarantee the uniqueness of decomposition.In practical engineering,it is difficult to meet some harsh conditions,resulting in non-uniqueness of matrix decomposition,so it is difficult to guarantee the accuracy of the results of blind source separation.Therefore,we consider the combination of variable mode decomposition(VMD)and SOAP algorithm.Firstly,VMD algorithm is used to decompose multi-component signals into band-limited intrinsic mode function(BLIMF)by non-recursive decomposition.thus the under-determined problem is solved.Then,the appropriate mode functions is selected as new input signals,which is decomposed by SOAP algorithm to ensure the uniqueness of decomposition.In different noise environment,the separation effect is compared with traditional VMD-ICA method.Simulation and experimental results show that the proposed method can effectively solve the problem of under-determined blind source separation of bearing multi-fault signals in noisy environment.4.In order to solve blind source separation of nonlinear signals in practical engineering,Kernel function is combined with SOAP algorithm.Firstly,the nonlinear signals are mapped into the Kernel feature space by Kernel function method.Then,the source signals are separated by SOAP algorithm in the Kernel feature space.The KSOAP algorithm successfully separates the nonlinear mixed signals and compares with the traditional method.Finally,the proposed method is applied to multi-fault diagnosis of bearing.The experimental results further show the effectiveness of the proposed method.