The vibration response of faulty bearing is always characterized by periodic transient impulses in the signal. Generally, these fault-related features are inevitably submerged in noise and harmonic ...components. Mathematical morphology is an excellent method of noise reduction, which can retain the detail information of impulses in the time domain. However, the filtering effect of traditional morphological operator (MO) might be easily affected by random impulses, and the proper selection of the structure element (SE) depends heavily on the experience of researchers. In order to effectively remove these interferences and extract the fault features accurately, an improved method, named adaptive morphological filter (AMF), is proposed in this article. This method utilizes autocorrelation to lift MO in time domain to enhance periodic components, and the scale of SE can, therefore, be calculated with the local maximum of the autocorrelation spectrum. Since the selection of the optimal SE scale is adaptive, researchers' experience is no longer needed, and there is also no need to calculate the fault characteristic frequency (FCF) for the determination of maximum scale of SE. The vibration and acoustical signals of faulty locomotive wheel set bearing are analyzed with this method, and the results verify its effectiveness and ability.
In a planetary gear set with an elastic ring gear, there are several pairs of flexible internal meshing simultaneously. The interactions between them are often ignored when considering their mesh ...stiffness. This study is devoted to investigating the effect of the number of equally spaced planets and the number of fixed supports of ring gear on mesh force and loaded-static transmission error (LSTE) as well as related mesh stiffness through a 2D system-level finite element model. This model is first validated by the comparison with the traditional potential energy method (PEM) when the ring gear is fully fixed. Then taking the number of planets and fixed supports as variables, 16 sets of analyses are conducted. Mesh force and LSTE extracted from the model, together with the mesh stiffness derived by them, are analyzed and concluded in the time domain and/or frequency domain. It is demonstrated that the number of planets has a certain impact on the ring-planet mesh stiffness. In terms of the number of planets and fixed supports, planetary gear systems can be classified into three categories according to the distinctive behaviors of mesh force and LSTE in the time domain and frequency domain.
How to accurately extract the fault related periodical impulses is the key to bearing fault diagnosis. The blind deconvolution (BD) method has been positively affirmed its ability in this field. ...However, the experience dependent parameter-setting and vulnerable to interference under complex working condition are two main problems that seriously limit its application. To address these issues, an improved BD method, named adaptive morphological BD, is proposed in this article. A new indicator, the morphological frequency negentropy, is first constructed through morphological analysis and adopted as the objective function for deconvolution. With its robustness to random impact and noise being verified, the optimal Morlet wavelet filter is selected with morphological frequency negentropy (MFN) and used as the initial filter. The sampling matrix is enhanced with varying morphological filtering and its size is adaptively determined by power spectral density. Through adaptive setting of the length of the filter, the dependence of prior knowledge for parameter setting is therefore reduced. Finally, the diagonal slice spectrum is applied on the filtered signal to remove in-band and residual noise. The effectiveness of the proposed method is validated by simulation signal and real datasets. Comparison analysis with other typical filter methods further shows its superiority.
The singular spectrum decomposition (SSD) is an effective signal denoising tool and has been attracted much attention in fault diagnosis. However, the filtering effect and calculation efficiency of ...SSD are seriously affected by the embedding dimension of trajectory matrix. To overcome these disadvantages, the improved SSD (ISSD) is proposed in this paper. A length factor is designed to optimize the construction of trajectory matrix, which considers the fault information in both time-domain and frequency-domain. A series of analysis, including impulse response analysis and multi-components signal decomposition, demonstrate the ISSD lifts the performance of SSD. After that, a new indicator, named singular Gini index, is applied to select the optimal singular spectrum components (SSCs) decomposed by the ISSD. To further supplement the impulses extraction effect of the ISSD, the sparsity operation is improved by combing the morphological analysis to process the vibration and sound signals. The sparsity factor is updated in each iteration and the structure element in morphological analysis is determined adaptively. Benefiting from the virtues of ISSD and sparsity analysis, the fault impulses in the processed signal are more prominent. Finally, according to the information of bearing characteristic frequencies in the spectrum, the fault type of bearing is determined. The reliability and feasibility of the proposed method is identified by analyzing the different simulation and experimental cases.
The condition monitoring of rolling element bearings (REBs) is essential to maintain the reliable operation of rotating machinery, and the difficulty lies in how to estimate fault information from ...the raw signal that is always overwhelmed by severe background noise and other interferences. The method based on a sparse model has attracted increasing attention because it can capture deep-level fault features. However, when processing a signal with complex components and weak fault features, the performance of sparse model-based methods is often not ideal. In this work, the fault information-based sparse low-rank algorithm (FISLRA) is proposed to abstract the fault information from a noisy signal interfered with by background noise and external interference. Concretely, a sparse and low-rank model is formulated in the time-frequency domain. Then, a fast-converging algorithm is derived based on the alternating direction method of multipliers (ADMM) to solve the formulated model. Moreover, to further highlight the periodical transients, a correlated kurtosis-based thresholding (CKT) scheme proposed in this paper is also incorporated to solve the proposed low-rank spares model. The superiority of the proposed FISLRA over the traditional sparse low-rank model (TSLRM) and spectral kurtosis (SK) is proved by simulation analysis. In addition, two experimental signals collected from a bearing test rig are utilized to demonstrate the efficiency of the proposed FISLRA in fault detection. The results illustrate that compared to the TSLRM method, FISLRA can effectively extract periodical fault transients even when harmonic components (HCs) are present in the noisy signal.
Bearing plays an important role in industrial equipment and it may operate under varying conditions. When the speed of shaft changes, whether monotonous or non-monotonous speed, common diagnostic ...approaches cannot effectively extract fault features. But encoders and tachometers are not always available. Therefore, tacholess order tracking methods which can directly extract the instantaneous rotating frequency (IRF) from vibration signal are very useful in bearing fault diagnosis under varying speed. Among these methods, the generalized linear chirplet transform (GLCT) can produce time–frequency representation without constructing any mathematical model, but there are two parameters must be set in advance. The parameters have great influence on the analysis result. To reduce the dependence on the prior knowledge of presetting the parameters in varying conditions, two different improved GLCT methods are proposed in this paper. To do with the situation where the trend of speed changes is monotonous, the scale-space is introduced to lift GLCT which can adaptively set a vital parameter, and the other parameter is set to default value. When faced with non-monotonous speed, the second method is proposed which the grey wolf optimizer (GWO) and Gini index are introduced to search the optimal parameters of GLCT without any prior knowledge. With the help of the proposed methods, the IRF can be extracted directly from vibration signal. Then, the raw signal can be resampled based on the IRF to eliminate the influences of speed. The morphological filtering is adopted to remove the noise and extract the fault characteristics order (FCO). Another two typical time–frequency analysis methods are used for comparisons. Three different signals are used for analysis to demonstrate the superiority of the proposed methods.
•Two tacholess order tracking methods are proposed based on GLCT to extract the instantaneous rotation frequency directly.•Scale-space is introduced into GLCT to adaptively determines the value of N.•Grey wolf algorithm and Gini index are adopted to lift GLCT.
With the continuous innovation of science and technology, the mathematical modeling and analysis of bodily injury in the process of exercise have always been a hot and difficult point in the research ...field of scholars. Although there are many research results on the nonlinear classification of the basketball sports neural network model, usually only one model is used, which has certain defects. The combination forecasting model based on the ARIMA model and neural network based on LSTM can make up for this defect. In the process of the experiment, the most important is the construction of the combination model and the acquisition of volunteer data in the process of the ball game. In this experiment, the ARIMA model is used as the linear part of the data, and LSTM neural network model is used to get the sequence of body injury. The results of the empirical study show that: it is reasonable to divide the injury of thigh and calf in the process of basketball sports, which is very consistent with the force point of the human body in the process of sports. The results of the two models predicting the average degree of bodily injury for many times are about 0.32 and 0.38 respectively, which are far less than 1. The execution time of the program for simultaneous prediction on the computer is about 1 minute, which is extremely effective.
With the increasing requirements for the reliability and safety of high-end equipment, the predictive maintenance of high-end equipment has been indispensable. The remaining useful life (RUL) ...prediction is a key part of predictive maintenance. Most existing studies regard the process of health degradation as a single-stage process, which demands the RUL prediction model to have high adaptability and generalization performance. However, current RUL prediction models cannot meet this requirement and predict accurately therefore cannot be achieved as expected. In view of that, this paper proposes a stage division method and constructs a powerful RUL prediction model to solve this problem. Firstly, a novel continuous gradient recognition algorithm is developed to identify the degradation initial time, and then the whole health degradation process is divided into two stages, called the normal operation stage and the accelerated degradation stage. Secondly, a bidirectional recursive gated dual attention unit is proposed to predict the RUL during the accelerated degradation stage. It introduces two attention gates into the classical gated recurrent unit and constructs a bidirectional structure to fully learn the forward and backward degradation law of time series as well as the initial hidden state of the forward network is corrected by the final hidden state of the backward network. Two real bearing datasets are analyzed to verify the effectiveness and capability of the proposed method. Finally, the comparative analysis is implemented and the results further show that the proposed method has better performance both in prediction accuracy and robustness.
Extracting the fault-related repetitive impulses from the observed signal disturbed by deterministic components, random impulses and background noise are a critical problem in diagnosing the bearing ...fault. This article proposes a maximum squared-enveloped multipoint kurtosis morphological deconvolution (MSEMKMD) method to tackle this issue. First, an unbiased-autocorrelation double-scale morphological filter (MF) is designed to preserve the repetitive-impulse characteristic of the observed signal and filter out these noises from different sources. The minimum entropy deconvolution (MED) method is then used to enhance recovering the repetitive impulses disturbed by these noises. In this method, the squared-enveloped multipoint kurtosis (SEMK) indicator is developed to select the optimal structural element (SE) scale and filtered result. Finally, the results of analyses with simulation and experimental data show the superiority of the MSEMKMD in fault-related impulse recovery for bearing fault diagnosis.
•Minimum entropy deconvolution is introduced into multiscale morphological filtering.•The influence of random impulses is eliminated.•Maximum scale of structure element in MMF can be determined ...adaptively.•Diagonal slice spectrum is introduced to choose the optimal morphological filter.
The bearing fault signal can be seen as convolution of periodical impulses and interference components. The minimum entropy deconvolution (MED) is effective approach for the deconvolution of signal. However, the MED is vulnerable to random impulse and interference components. To solve the problem, an improved method, named minimum entropy morphological deconvolution (MEMD), is proposed in this paper. Firstly, the amplitude frequency response of two typical morphological operators (MOs) are discussed. These operators are then introduced into MED to filter the sample matrix. The optimal MO is selected based on the amplitude ratio of diagonal slice spectrum (DSS). Eventually, the filtered result is analyzed by DSS to identify the fault type. In MEMD, the influence of random shocks is eliminated and the scale of SE can be determined adaptively. The MEMD is verified by simulation and experimental signals. Comparison study is implemented and the analysis results verify its effectiveness and feasibility.
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