Feature Sparse Representation Of Mechanical Signal Based On Overcomplete Fourier Dictionary

Dynamic test is an important method of equipment condition monitoring,which can reflect the dynamic characteristics and health status effectively.As a common component,harmonics need to be focused in mechanical test signal analysis and processing.In this study,the over complete Fourier dictionary(OFD)for signal decomposition was constructed.Based on the theory of basis pursuit(BP)in sparse representation(SR),the main lobe width of harmonic components in the feature domain is compressed.Meanwhile,the Split Augmented Lagrangian Shrinkage Algorithm(SALSA)is used to ensure the efficiency of BP in highly over complete Fourier dictionary.For the specific mechanical signal model,numerical simulation examples show that the method can achieve the super-resolution analysis of harmonic components effectively.Combined with other decomposition methods,the ability of separating aberrant components and extracting transient characteristics is improved.The proposed method was applied to sense undersampled signal from high-speed milling and diagnose vibration fault of mechanical equipment.Good results were obtained.The main research contents and achievements are as follows:(1)Study on recovery of under-sampled force measurement from high-speed milling process using sparsity in frequency domain.Aiming at a problem that the data of a cutting force model verification experiment was undersampled,the correction principle of aliasing harmonics was discussed by constructing simulation signals.Meanwhile,high-resolution representation of undersampled force measurement was realized by SALSA.Compared with the fast Fourier transform(FFT)spectrum,the representation on overcomplete Fourier dictionary was sparse,and each harmonic was only represented by several spectral lines.The correction principle was used to identify aliased components and correct sparse spectrum.Finally,the time domain waveform of force signal was reconstructed.Experiments based on simulation signals and sampled data from high speed milling aluminum alloy verify that the relative amplitude error is less than 1%,and the correlation coefficient is higher than 0.999.(2)Study on feature enhancement of rub impact fault based on sparse denoising of wavelet subspace.Rub-impact fault is one of main failure in rotor system.Therefore,research on that is of great significance.The preprocessed vibration signal was decomposed by composite wavelet packet to extract the optimal feature component with significant impulse characteristic.However,the residual noise in wavelet subspace seriously affects modulation feature recognition and instantaneous information extraction.OFD was constructed and SALSA was used for denoising of feature components,according to the characteristic that the main components of the characteristic component were harmonic components.After denoising,the instantaneous frequency curve of the optimal feature scale component changed smoothly and the periodic feature was obviously enhanced,which made fault information be extracted easily and accurately.Effect of the proposed method was verified by simulation signal and experimental data of simulated rub-impact.Compared with ensemble empirical mode decomposition,the ability for extracting fault information of the proposed method is better.(3)Study on fault diagnosis for gearbox of air separation unit based on sparse identification of harmonics.In order to meet the pursuit of high efficiency in engineering application and improve the processing speed of sparse denoising,a fast algorithm of SALSA was constructed based on harmonics sparse recognition.Combining fast algorithm and composite wavelet packet decomposition,the vibration signal analysis of a gearbox fault with abnormal noise in a large air separation compressor unit is carried out.The analysis results captured the transient characteristics(abrupt changes in instantaneous frequency and instantaneous amplitude)that characterize the sequential friction between the thrust splints on the left and right sides of the pinion gear and the large gear.However,the current mainstream diagnosis methods cannot effectively suppress the complex noise in the subspace,and can only partially extract the fault features.In addition,compared with the basis pursuit algorithm,the improved method studied avoids iterative calculation during program execution,and the calculation efficiency increased about 1.3 times than SALSA.