The Research And Application Of Dimensionality Reduction Characteristic Of Vibration Signal Based On Sparse Manifold Learning

With the development of science and technology，high-dimensional data which is hard tounderstand，represent and process exists in many fields. There are still a lot of difficulties toprocess high-dimensional data. Therefore, how to extract the essence characteristics from theobtained high dimensional data is an important problem to be solved. However, the high-dimensional data obtained in reality are most nonlinear. It’s hard to explore the structure andcorrelation of high dimensional data through traditional linear method, and also difficult to revealthe manifold distribution.Aiming at the shortcomings of linear methods, many nonlinear dimensionality reductionmethods have been proposed, and these methods break the traditional framework of lineardimension reduction methods. In fact, the vibration signals collected are nonlinear, so locally linearembedding algorithm is conducted to discover features of vibration signals. But LLE algorithm issensitive to the data noise, when the noise is larger the stability will become poor. Aiming at theshortcomings of traditional algorithm, sparse constraint is introduced to improve the algorithm.Aiming at the shortcoming of the classical RDT, a multi-secant method of the improved RDT isproposed in this paper. At last the effectiveness of algorithms is verified in practical engineeringapplication.The sparse constraint LLE algorithm makes the reconstruction error function the optimalreconstruction weight matrix is sparser by adding L1norm punitive constraint. And the effect ofnoise points is excluded better. Simulation experimental results of the typical high dimensionaldata set dimensionality reduction show that the dimensionality reduction results of the LLEalgorithm in sparse constraint is significantly better than the classic LLE algorithm under theinfluence of different noise, and has a stronger ability in resisting noise.Multi-secant RDT makes the number of averaged sub-sample increased, which eliminates theeffects of noise. Therefore better free response signals can be obtained and providing good basicsignals for the algorithm. Then the sparse constrained local linear embedding algorithm is combined with wavelet packettransform to extract WPE energy manifold flow characteristics of vibration signal collected fromthe cable of Qing Shuipu bridge which is processed by multi-secant RDT. Finally support vectormachine achieve fault classification based on WPE energy manifold flow characteristics, andcomparative analysis is made with WPE vector, WPE matrix, wavelet time entropy, experimentaltests show that the algorithm has high accuracy, stability and reliability.In summary, sparse constraint is introduced to improve the robustness and noise immunity ofLLE algorithm. But when the number of sample data points is relatively large, L1norm willconduct multiple iterations to find the global optimal solution, and lead to computing time of LLE-L1algorithm becomes very long. In practical engineering application, fault condition vibrationsignal is not collected due to the limit conditions, so we add noise to healthy vibration signals tosimulate fault signals. It will make some limitations for the algorithm applied to the actual project.