Research On The Intelligent Methods For Fault Diagnosis Of Rotating Machinery Under Non-stationary Conditions

Bearings and gears are the key components of engineering machinery,rail traffic vehicle,agricultural machinery and aero-engine,etc.Thus,it is critical to ensure the normal and stable operation of mechanical equipment by studying the fault diagnosis of rotating machinery.Many deep learning approaches have been widely researched in the intelligent fault diagnosis of rotating machinery.Due to the complex working cases of mechanical equipment,such as variable rotating speeds,variable loads,time-varing rotating speeds and other non-stationary conditions,the performance of traditional deep learning approaches may drop dramatically.Domain adaptation（DA）approaches can realize the cross-domain fault diagnosis between the two different but related datasets.However,when the discrepancy between different domains is rather large,the performance of DA may also decrease.Considering the effect of the large distribution discrepancy between different domains which caused by the insufficient target domain samples,class-imbalanced samples and other practical application cases,the intelligent fault diagnosis approaches of rotating machinery under non-stationary conditions are studied based on the deep learning and DA techniques.Moreover,the performance of the methods in dealing with different working conditions is analyzed.The key points of the paper are as follow:（1）To overcome the weakness which lacks the ability to extract representative features under non-stationary condition with variable rotating speeds of the traditional sparse filtering approach,a method named STFT-FS is proposed by taking the advantages of time-frequency analysis method in variable rotating speeds condition.Then,time-frequency features are taken as the input data for sparse filtering model,and the fault features are unsupervised extracted.Through the visual operation of time-frequency features,the results show that time-frequency features contain more representative information,and the features of different faults are more discriminative.As a result,the ability of extracting the representative features of the traditional sparse filtering under the condition of variable rotating speeds is improved.（2）In practical application,there are often insufficient samples in the target domain,which results in the large distribution difference across different domains and the degradation of fault diagnosis performance.To this end,the time-frequency data under normal conditions are adopted as the target domain data,and the geodesic flow kernel approach is applied for mapping the data in different domains into the Grassmann manifold space.Then,the distance along the geodesic flow between different domains is reduced,and the similarity of different domians is improved by the subspace distribution alignment approach.Finally,the domain-invariant features with high transferrable are extracted and the prediction of all fault types in the target domain under the condition of variable rotating speeds and variable loads is achieved.（3）In practical engineering application,the situation of class imbalance is common.The class-imbalanced situation mainly caused by the large amount of samples under normal conditions,few samples under fault conditions,and different number of samples under different health conditions.Due to the imbalanced calsses,large distribution discrepancy across different domains is obtained,which results in the under-adaptation problem for traditional joint matching methods.The degradation of distribution adaptation performance will lead to the low accuracy of fault classification.In view of the large difference of data distribution under the condition of class imbalance,a new distance measurement method,maximum variance difference,is proposed and introduced into the joint matching model,which further reduces the difference of cross domain distribution and improves the ability of distribution adaptation under the condition of class imbalance.Meanwhile,l₂-norm is used to preprocess the data in frequency domain,which improves the generalization ability of the proposed model.（4）Considering the class imbalance problem in practical application,the manifold regularization based on manifold learning is combined with joint matching to improve the manifold consistency between source and target domain.Meanwhile,the discrepancy of marginal distribution and the geometric structure between different domains are reduced,and the transferrable of domain-invariant features are further improved by reweighting the instances of source domain.The effectiveness and robustness of the proposed approach are demonstrated by the cross domain fault diagnosis experiments of bearing and gear datasets under the condition of variable rotating speeds and variable loads.（5）Under time-varying conditions,fault features will change with the variable rotating speeds or loads,which make the extraction of effective fault features difficult.Taking time-frequency data as input data,the sparse balanced distribution adaptation is introduced into the sparse filtering model which owns strong ability in feature extraction.According to the actual situation,different weights are given to the marginal and condition distribution adaptation methods to reduce the difference between source and target domain.As a result,the fault diagnosis under the condition of time-varying rotating speeds is realized.The experimental results demonstrate the validity and the high calculation efficiency of the proposed approach.（6）Aiming at the problem that it is difficult to realize the rotating machinery fault diagnosis under the condition of time-varying rotating speeds in practical application,the samples under constant rotating speeds are taken as the source domain data to predict the fault types of the samples under the time-varying rotating speeds.A deep domain adaptive model based on DNN is proposed,which takes time-frequency domain data as input data.MMD and manifold regularization are applied to reduce the discrepancy of marginal distribution and geometric structure between different domains based on deep characterization features.Meanwhile,weight regularization is employed to strengthen the representativeness for specific features of original data.Finally,subspace alignment is adopted for further improving the similarity of cross domain deep features.Furthermore,to enhance the transferability and representativeness of the domain-invariant features,the deep network structure is applied to reinforce the weight of the invariant part in the feature distribution and extract the deep characterization features.The experimental results verify the superior performance of the deep domain adaptive method under the condition of time-varying rotating speeds.