Principal Manifold Recognition Theory In Local Space And Its Application In Mechanical Fault Diagnosis

Rotating mechanical equipment is the first link of output movement after electric energy is transformed into mechanical energy.It is one of the most important equipment in industrial production.The research on the diagnosis technology of mechanical equipment is the key to ensure the smooth progress of production,reduce accidents and reduce economic losses.Usually,the signal of rotating equipment presents the characteristics of non-stationary and nonlinear.Manifold learning is widely used in nonlinear systems for feature fusion and dimensionality reduction in various fields.Its advantage is that using manifold learning can obtain the real manifold composition of the original data space,and can comprehensively describe the internal information and distribution characteristics of nonlinear system data while maintaining the spatial relationship and distance between data or samples.Based on manifold learning theory,aiming at the non-stationary and nonlinear characteristics of vibration signals of rotating equipment,this thesis puts forward some research methods in the key links of principal manifold recognition theory in local space.The specific contents are as follows:1.Aiming at the problems of low efficiency and large error of large sample set of local tangent space alignment(LTSA)method,an modified supervised local tangent space alignment(MS-LTSA)method is proposed.This method realizes the minimization of global error and dynamic feature extraction in the process of dimensionality reduction in high-dimensional data space.2.A locally tangent space aligned low rank embedded representation(LTSA-LRER)algorithm is proposed for subspace clustering and dimensionality reduction of data.Different from the existing Laplace regularized subspace representation method to describe the local structure,this method maps the original data to the local linear embedding space,and realizes the low rank subspace representation.These two goals restrict each other and are realized synchronously.The model retains the manifold structure of the sample well.Each cluster is located on its own manifold.It not only avoids the influence of neighborhood aliasing of samples on subspace representation and clustering,but also shows good robustness to noise.3.Aiming at the problem that the local tangent space alignment method is sensitive to noise and the limitation of noise reduction effect,a mainstream shape recognition method in local space is proposed.The proposed method takes advantage of the improved supervised local tangent space alignment in dimensionality reduction and error control,and embeds the local subspace projection method into the process of mainstream shape recognition.The reconstructed one-dimensional time series achieves ideal noise reduction effect.Then PE algorithm is applied to realize the effective classification of mechanical equipment faults.4.The principal manifold recognition and sparse enhanced signal decomposition method in local space are proposed for mechanical fault diagnosis.The proposed method shows a strong noise reduction ability for nonlinear and non-stationary signals.Through the analysis of measured data,the bearing fault signal is denoised,the clear characteristic frequency is extracted,and the fault diagnosis of Mechanical equipment is realized.