Adaptive Multivariate Signal Decomposition Method And Its Application In Gear Fault Diagnosis

The health status of gears determines the operational quality of mechanical equipment.When gears develop subtle faults such as cracks and pitting that go unnoticed,the faults can further escalate during producti on.When the faults reach a certain stage,they can result in minor disruptions for repairs or even catastrophic consequences.Therefore,conducting research on gear fault diagnosis holds significant engineering practical significance.With the continuous development of technology,there is an increasing variety of fault diagnosis methods based on signal processing.Researchers have explored many methods for mechanical equipment fault diagnosis using single-channel signals,which is crucial for diagnosing faults in mechanical equipment.However,in cases where there is severe background noise or early-stage gear faults,the fault features captured from vibration signals are often not prominent enough,and the fault information contained in single-channel signals may be insufficient to determine if gears are faulty.Due to the comprehensive and rich fault information embedded in multi-channel signals,multi-channel signal processing has garnered attention from many researchers.With advancements in sensor technology,acquiring multi-channel vibration signals has become simple and feasible.Therefore,it is necessary to process the collected multi-channel signals as a multidimensional signal,extract more fault information,and achieve more comprehensive and accurate fault analysis.Therefore,supported by the National Natural Science Foundation of China(Project No.51975193,52275103),this paper focuses on the key component,gears,in gearboxes as the research object.Based on different application scenarios,the paper proposes the following methods: multi-signal information fusion and enhancement method,multi-signal denoising method,multi-signal decomposition method under various channel power imbalances,multi-signal decomposition method suitable for online monitoring,multi-signal decomposition method for improving mode aliasing performance,and multi-signal decomposition method for extracting subtle fault features in gears.The feasibility of applying the proposed methods and their theories in gear fault d iagnosis is discussed.The main research contents and innovation points of the paper are listed as follows.(1)A method for information fusion and fault feature enhancement of multivariate signals is proposed,which utilizes the multivariate local characteristic-scale decomposition(MLCD)and 1.5-Dimensional empirical envelope spectrum(1.5D EES).MLCD is based on the local characteristic-scale decomposition(LCD)and is used to analyze multivariate signals.An effective multi-channel information fusion method is proposed based on the analysis of the mod e alignment property of MLCD.After the fusion,the fault features in the fault signal components are significantly enhanced.Combining the advantages of the empirical envelope method and the 1.5D spectrum,the 1.5D EES is proposed to effectively reduce the noise of the envelope signal and further enhance the fault features of the signal.The MLCD-1.5D EES method is applied to gear fault simulation and experimental signals,and the results show that the MLCD-1.5D EES can effectively fuse signals from various channels,enhance gear fault features,and achieve gear fault diagnosis.(2)Adaptive quaternion multivariate local characteristic-scale decomposition(AQMLCD)method is proposed for the denoising of multi variate signals.First,a multivariate signal denoising method called quaternion singular value decomposition fault information spectrum(QSVDFIS)is defined.The core of QSVDFIS is the use of the cyclic modulation intensity(CMI)index to evaluate the gea r fault information in multivariate signals.The QSVDFIS selects the effective rank order of quaternion singular value decomposition by the CMI index to achieve the best denoising effect.QSVDFIS requires the correlation between the sub-signals of multivariate signals.The multivariate signal components obtained by MLCD have mod e alignment property,which ensures the correlation between the sub-signals of multivariate signals.Based on QSVDFIS and MLCD,AQMLCD is proposed to adaptively reduce noise and enhance fault feature components in multivariate signal components.The AQMLCD method is applied to experimental and simulated gear signals,and the results show that AQMLCD has excellent denoising effect and can effectively highlight the fault features in the signal.(3)The existing adaptive multivariate signal decomposition methods use the Hammersley projection strategy,which employs a uniform sampling strategy,resulting in projection vectors that remain unchanged throughout the decomposition process.As a result,the accuracy of the signal components obtained using the Hammersley projection strategy is not high enough.This phenomenon is particularly evident when the multivariate signal exhibits power imbalance.The Hammersley projection strategy requires multiple projections of the multivariate signal to obtain accurate signal components,which severely hinders the further improvement of the decomposition efficiency of the adaptive multivariate signal decomposition method.Therefore,it is necessary to propose new projection strategi es to address these issues.(1)To address the problem of low accuracy in decomposing multivariate signals with power imbalances in existing adaptive multivariate signal decomposition methods,a new method called completely adaptive projection multivariate local characteristicscale decomposition(CAPMLCD)is proposed.This method first introduces the completely adaptive projection(CAP)strategy,which evaluates the power distribution of the multivariate signal using the Gini coefficient and then re-clusters the projection vectors.The CAP projection strategy and the iterative update of the projection vectors are used to improve the MLCD method and propose the CAPMLCD.Unlike MEMD and MLCD,which use fixed and static projection vectors for decomposition,CAPMLCD uses continuously updated and dynamically changing projection vectors for decomposition.The effectiveness of CAPMLCD in improving the accuracy of multivariate signal decomposition in cases of power imbalances across channels is demonstrated using simulated and experimental signals of gear faults.(2)To address the problem of low efficiency in existing adaptive multivariate signal decomposition methods,a new method called fast multivariate local characteristicscale decomposition(FMLCD)is proposed,which can be used for online mon itoring.This method first introduces the fast projection(FP)strategy based on the CAP projection strategy,but with an added screening mechanism for the projection vectors.The FP sampling strategy and iterative update of the projection vectors are used to improve the MLCD method and propose the FMLCD.FMLCD adaptively and dynamically adjusts and screens the projection vectors based on the characteristics of the multivariate signal during the decomposition process as the iterations progress.The superiority of FMLCD in terms of noise robustness,decomposition accuracy,and efficiency is demonstrated using simulated and experimental signals of gear faults.Compared to other adaptive multivariate signal decomposition methods,FMLCD has a significant advantage in decomposition efficiency and is therefore expected to be applied to online fault monitoring.(4)Multivariate local fluctuation mode decomposition(MLFMD)is proposed to address the problem of serious mode mixing in existing adaptive multivariate sig nal decomposition methods.This method first introduces a new method for locating local extreme points,called second-order differential local extreme point localization(SDLEPL),which can effectively explore local hidden information in the signal.In addition,a new multivariate signal mean extraction method,multivariate periodic integral mean curve(MPIMC),is proposed,which adopts the idea of integral averaging to effectively characterize the local fluctuations of multivariate signals.Based on these methods,as well as the CAP projection strategy,MLFMD is proposed.The efficiency,accuracy,and anti-mode mixing ability of the MLFMD method are verified through gear fault simulation and experimental signals.(5)To address the difficulty in extracting fault features from weak gear faults,a novel approach called multivariate intrinsic wave-characteristic decomposition(MIWD)is proposed from the perspective of mean curve optimization.This method defines two new types of univariate mean curves and introduces six new methods for extracting multivariate mean curves.By combining the multivariate mean curve extraction methods defined in MEMD,MLCD,and MLFMD,as well as the six newly proposed methods,nine potential multivariate intrinsic wave componen ts are defined.Based on these nine components,MIWD is developed by incorporating the local optimality concept and CAP projection method.Unlike MEMD and MLCD,which use fixed multivariate mean curve extraction methods for decomposition,MIWD adapts the extraction method of multivariate mean curves to the characteristics of the multivariate signals by employing the local optimality concept during the decomposition process.Due to the optimal multivariate mean curve extraction at each stage of decomposition,MIWD outperforms other adaptive multivariate signal decomposition methods in extracting weak fault features from gears.The superiority of MIWD is demonstrated through simulations and experimental signals in terms of resistance to mode mixing,decomposit ion accuracy,decomposition capability,and orthogonality.