| The high-speed Renaissance Electric Multiple Units(EMUs)have received a series of technical effectiveness,which marks that China has already taken the leadership in the the field of high-speed trains world widely,and reflects the strength of national manufacturing.The reliability of the system determines the actual performance of the train.As a core unit to provide power for the whole train,traction system ensures the operation performance.Once faults are not detected timely,accidents occur,which will result in serious economic losses and even endangering the lives and property of passengers.With the increasing development of advanced sensors and computer technologies,data-driven based fault detection algorithms are widely used.Among them,neighborhood preserving embedding(NPE)method which stems from manifold learning has been widespreadly concerned,yet it still faces many challenges with the application to fault detection of high-speed trains.In this paper,the solutions to three problems are proposed as follows.(i)Now that the data set from sensors contains various frequency bands,an online fault detection algorithm based on wavelet packet(WTP)and neighborhood preserving embedding has been proposed to ameliorate the effectiveness of NPE.In this algorithm,the time-frequency signals have been reconstructed by wavelet packet,and the pre-processed signals have been used as the input of NPE.With the union of WTP and NPE,the off-line model has been established,which can detect the online faults promptly.Finally,by applying the proposed scheme to two different experimental platforms of high-speed railway traction system,the feasibility of this algorithm has been verified.(ii)A modified neighborhood preserving embedding(MNPE)algorithm has been proposed to deal with the singular problem,which may be encountered in the processing of high-dimensional data set.With the aid of matrix theory,the problem of solving a generalized eigenvector problem in NPE has been altered to an eigenvector problem and a generalized eigenvector problem.MNPE solves the singular problem effectively.It also improves the stability of the system and ensures the extraction of local information in the neighborhood of the sample.Finally,the developed algorithm has been applied to two experimental platforms of traction system successfully,which not only guarantees the rationality of fault detection,but also grabs considerable computing efficiency.(iii)Considering that NPE merely concerns the neighborhood information of a single manifold and a specified point,one multi-manifold regularization NPE(MMRNPE)method has been extracted.By fusing the paired point information from local preserving projection(LPP)algorithm,this newly method can take the reconstruction performance of the specified point and the paired point into account.Meanwhile,by combining diverse characteristics of multiple manifolds,the internal structure of data set is fully mined.Also,the introduction of information entropy is capable of avoiding the model degradation.The contained parameters in this algorithm may adjust the performance,and the proportion of different manifolds as well.By selecting the number of iterations,different detection accuracies have been obtained.Finally,the effectiveness of MMRNPE has been verified with the aid of two platforms,and when it comes to the influence of parameters selection,the detection results have been discussed.In addition,based on the voltage equation,flux equation and torque equation,as well as the coordinate transformation of the AC speed regulating system,a dynamic mathematical model of the electric traction experimental platform has been constructed,and the efficiency of basic control strategy of vector control has been analyzed. |