Time-varying Speed Conditions Research Articles

Rotating Machinery Fault Diagnosis under Time–Varying Speed Conditions Based on Adaptive Identification of Order Structure

Rotating machinery fault diagnosis is of key significance for ensuring safe and efficient operation of various industrial equipment. However, under nonstationary operating conditions, the fault–induced characteristic frequencies are often time–varying. Conventional Fourier spectrum analysis is not suitable for revealing time–varying details, and nonstationary fault feature extraction methods are still in desperate need. Order spectrum can reveal the rotational–speed–related time–varying frequency components as spectral peaks in order domain, thus facilitating fault feature extraction under time–varying speed conditions. However, the speed–unrelated frequency components are still nonstationary after angular–domain resampling, thus causing wide–band features and interferences in the order spectrum. To overcome such a drawback, this work proposes a rotating machinery fault diagnosis method based on adaptive separation of time–varying components and order feature extraction. Firstly, the rotational speed is estimated by the multi–order probabilistic approach (MOPA), thus eliminating the inconvenience of installing measurement equipment. Secondly, adaptive separation of the time–varying frequency component is achieved through time–varying filtering and surrogate test. It effectively eliminates interference from irrelevant components and noise. Finally, a high–resolution order spectrum is constructed based on the average amplitude envelope of each mono–component. It does not involve Fourier transform or angular–domain resampling, thus avoiding spectral leakage and resampling errors. By identifying the fault–related spectral peaks in the constructed order spectrum, accurate fault diagnosis can be achieved. The Rényi entropy values of the proposed order spectrum are significantly lower than those of the traditional order spectrum. This result verifies the effective energy concentration and high resolution of the proposed order spectrum. The results of both numerical simulation and lab experiments confirm the effectiveness of the proposed method in accurately presenting the time–varying frequency components for rotating machinery diagnosing faults.

Transient mixed thermal elastohydrodynamic lubrication under startup and shut down conditions

The transient mixed lubrication behaviors in thermal elastohydrodynamic lubrication (TEHL) contacts during startup and stop are investigated. A transient mixed TEHL model for point contacts under time-varying speed conditions is proposed with comprehensive consideration of surface roughness, thermal effect, and transient behavior. The model is validated by the comparison to available published data. Based on the developed model, significant differences have been found compared with transient EHL and steady TEHL models. In addition, the transient mixed TEHL performance during start–stop with different acceleration rates and surface roughness is investigated. It shows that the lubrication behaviors during start–stop have an irreversible process. The roughness can significantly enhance the transient behavior. The roughness effect has a remarkable impact on lubrication performance in mixed lubrication. The evolution of lubrication behaviors during start–stop is highly related to the acceleration rate and surface topography.

Enhanced fault diagnosis via stochastic resonance in a piecewise asymmetric bistable system.

Weak fault signals are often overwhelmed by strong noise or interference. The key issue in fault diagnosis is to accurately extract useful fault characteristics. Stochastic resonance is an important signal processing method that utilizes noise to enhance weak signals. In this paper, to address the issues of output saturation and imperfect optimization of potential structure models in classical bistable stochastic resonance (CBSR), we propose a piecewise asymmetric stochastic resonance system. A two-state model is used to theoretically derive the output signal-to-noise ratio (SNR) of the bistable system under harmonic excitations, which is compared with the SNR of CBSR to demonstrate the superiority of the method. The method is then applied to fault data. The results indicate that it can achieve a higher output SNR and higher spectral peaks at fault characteristic frequencies/orders, regardless of whether the system operates under fixed or time-varying speed conditions. This study provides new ideas and theoretical guidance for improving the accuracy and reliability of fault diagnosis technology.

RFIS-HI: a new health indicator for quantitative condition monitoring of the bearing under variable speed conditions

The health indicator (HI) plays a crucial role in the condition monitoring of the rolling bearing. However, most existing HIs exhibit significant fluctuations when the speed changes. To address the issue, this paper proposes a new HI namely reweighted fault impact strength (RFIS)-HI. First, sub-signals are obtained through a frequency division strategy, and corresponding resampled signals are derived using order tracking. Second, the average impact peak in the time domain is acquired to measure the impact of the signal. According to fault characteristic order (FCO), the ratio of FCOs summation to noise amplitude in the frequency domain is obtained to measure periodicity. Then, the FISgram is constructed for selecting the optimal frequency band. To better quantify the degradation degree of the bearing, different weights are assigned and optimized for constructing RFIS. Finally, the influence of rotational speed on RFIS is eliminated by utilizing prior knowledge. Taking the first 10% of the dataset as baseline data, RFIS-HI is constructed through relative similarity. In this paper, a bearing dataset under time-varying speed conditions and an XJTU-SY dataset are used for verification. Results show that the proposed HI can achieve better trendability, scale similarity, and stability.

Rolling bearing fault diagnosis under time-varying speeds based on time-characteristic order spectrum and multi-scale domain adaptation network

In practical industrial applications, rolling bearing generally operates under variable conditions and its vibration signal significantly fluctuates in amplitude and frequency. This increases the feature distribution differences of the bearing fault samples and makes the health status identification of the bearing more difficult. To this end, a new intelligent fault diagnosis method for bearing under time-varying speed conditions is proposed based on time-characteristic order (TCO) spectrum and multi-scale domain adaptation network (MSDAN). Firstly, by using the good noise robustness and high time–frequency aggregation properties of the synchrosqueezed wave packet transform (SSWPT), the TCO spectrum method based on SSWPT is proposed to eliminate the impact of speed fluctuation, reducing the distribution shift of bearing data under time-varying speeds. Secondly, an MSDAN model based on global-local feature fusion is established to extract the domain-invariant features closely related to the bearing fault state from the TCO spectrum. Finally, the local maximum distribution discrepancy is introduced to capture the discriminative fine-grained features. The feasibility of the proposed method is verified in various transfer tasks on two different bearing datasets with time-varying speeds. Compared with some state-of-art methods, the proposed method can eliminate the sample distribution differences under time-varying speeds, significantly improving its accuracy and generalization performance in cross-domain fault diagnosis of rolling bearing.

Vibration amplitude normalization enhanced fault diagnosis under conditions of variable speed and extremely limited samples

Intelligent fault diagnosis of rotating equipment is increasingly reliant on algorithms that are driven by big data. By contrast, signal processing was once widely utilized for fault diagnosis in machinery as a classical tool for signal analysis due to its capability to investigate the fault-related mechanism and almost no demand on the number of data samples. This investigation was motivated by the notion that signal processing and data-driven algorithms are combined to exploit their respective characteristics and strengths. Furthermore, in engineering practice, numerous complex factors such as time-variable operating conditions of equipment, non-stationary properties of signals, and extremely limited samples available for model training, can make it difficult to learn discriminative features from input data, thereby diminishing the diagnostic accuracy. In this paper, a novel framework of vibration amplitude normalization (VAN) enhanced fault diagnosis is proposed. Firstly, after dissects deeply the effects of the time-varying speed conditions on vibration signal and its characteristics, VAN technique is proposed for non-stationary signal processing to obtain the approximate stationary signal, so as to facilitate the subsequent state characteristics mining from the vibration signal. Then, two VAN enhanced fault diagnosis methods—i.e. signal amplitude normalization integrated with shallow learning by cascade and VAN integrated with deep learning by embedding—are developed to capture discriminative features from approximate stationary signal for fault diagnosis under conditions of variable speed and extremely limited samples. Finally, the feasibility and effectiveness of the proposed methods are verified using actual vibration datasets measured on test rig and in-site wind turbines. The number of samples required to achieve the same diagnostic accuracy is reduced by an average of 60%, demonstrating the superiority.

Bearing Weak Fault Feature Extraction Under Time-Varying Speed Conditions Based on Frequency Matching Demodulation Transform

Bearing weak fault feature extraction under time-varying speed conditions is a challenging task. The classic time-frequency analysis (TFA) based ridge detection algorithms cannot work well for detecting time-varying fault characteristic frequency (FCF) harmonics of the bearing due to the limitation of time-frequency resolution and noise interference. As such, a novel frequency matching demodulation transform (FMDT) technique is developed by extending the generalized demodulation transform for bearing weak fault feature extraction and diagnosis under variable speeds. The main novelties of this article are concluded that: the FMDT can first estimate FCF under strong noise conditions by generating a series of demodulation parameters to match FCF with the criterion that the maximal peak can be captured at a specific frequency from the spectra of the demodulated signals, and then calculate rotational frequency (RF) harmonics; and the proposed FMDT-based method does not require the measured bearing RF, and can directly determine bearing fault type using the estimated FCF and RF harmonics. The effectiveness of the FMDT-based bearing fault diagnosis method is verified by both simulated and experimental results. Comparison analysis shows that the proposed method can generate much better results than the classic TFA-based ridge detection algorithms.

Wheelset-Bearing Fault Feature Extraction From Multi-Impulsive Signals Under Time-Varying Speed Conditions

Wheelset-Bearing Fault Feature Extraction From Multi-Impulsive Signals Under Time-Varying Speed Conditions

Identification and separation of coupled vibration sources in multi-rotor gas turbines under time-varying speed conditions

Vibration sources in multi-rotor gas turbines under time-varying speed conditions are strongly coupled in the time–frequency domain, which prevents further mining of dynamic information from measured signals. Hence, a novel scheme of vibration source identification and separation is proposed to obtain individual source information. Firstly, the order and resonance components are identified by order analysis, and precise order numbers are further determined by computed order tracking. Then, in four typical vibration source coupling scenarios, the performances of Vold-Kalman filter (VKF), several typical adaptive mode decomposition methods and derivative methods are comparatively studied using Jeffcott rotor simulation system. Finally, the optimal source separation based on VKF and variational mode decomposition/extraction (VMD/VME) is determined. Furthermore, the settings of VKF filter bandwidth are studied quantitatively, and the effects of VMD and VME penalty factors are analyzed. In conclusion, the proposed scheme effectively identifies and accurately separates vibration sources from the test bed and gas turbine datasets, which provides important evidences for vibration monitoring and control as well as vibration transmission analysis of gas turbines.

Parallel adversarial feature learning and enhancement of feature discriminability for fault diagnosis of a planetary gearbox under time-varying speed conditions

The intelligent fault diagnosis of a planetary gearbox under variable speed is still a challenging topic. Due to the similar spectrum structure, overlapping features occur and result in decreasing diagnosis accuracy. Autoencoder-based methods can extract features adaptively but few studies have proposed approaches to enhance the discriminability of features from different classes under variable speeds. Besides, the adverse variability of encoder weights may result in an adverse effect on the decoder. Adversarially learned inference (ALI) trains the encoder and decoder independently, but it is time-consuming to reach Nash equilibrium. To address the issues, a parallel adversarial learning inference (PALI) model is proposed, which aims at validating the parallel training of encoder and decoder and enhancing the discriminability of features. Specifically, time-frequency analysis is utilized to reveal the time-varying characteristics of raw signals and obtain time-frequency images as input for the encoder. Then, an explicit multi-dimensional uniform distribution is used for the merit of a simple probability density function to construct visualized and well-classified samples as input for the decoder. After that, a parallel adversarial game is explored to train the encoder and decoder simultaneously and independently, which will reduce computing interference and make the extracted features similar to the well-classified samples and reconstruct the raw signals. Finally, a Softmax classifier is trained and tested by the features. This method and its generability are validated via a planetary gearbox data set and a public bearing data under variable speed. The results indicate that the proposed parallel adversarial game is valid for training encoder and decoder independently, and that PALI works as well as the adversarial autoencoder (AAE) and outperforms ALI, the variational autoencoder (VAE) in obtaining well-clustered features over different training data. Compared to Wigner–Ville distribution (WVD) and continuous wavelet transform (CWT), PALI based on short-time Fourier transformation (STFT) works better over different training data.

Bearing multi-fault diagnosis with iterative generalized demodulation guided by enhanced rotational frequency matching under time-varying speed conditions

The rotational frequency (RF) is an important information for multi-fault features detection of rolling bearing under varying speed conditions. In the traditional methods, such as the computed order analysis (COA) and the time–frequency analysis (TFA), the RF should be measured using an encoder or extracted by a complex algorithm, which bring challenge to bearing fault diagnosis. In order to address this issue, a novel iterative generalized demodulation (IGD) based method guided by the instantaneous fault characteristic frequency (IFCF) extraction and enhanced instantaneous rotational frequency (IRF) matching is proposed in this paper. Specifically, the resonance frequency band excited by bearing fault is first obtained by the band-pass filter, and its envelope time–frequency​ representation (TFR) is calculated using the Hilbert transform and the short-time Fourier transform (STFT). Second, the IFCF is extracted using the harmonic summation-based peak search algorithm from the envelope TFR. Third, the time-varying RF ridge is transformed into a line paralleling to the time axis using the IGD with the phase function (PF). The PF is calculated by the IFCF function and fault characteristic coefficient (FCC). Lastly, the iterative generalized demodulation spectrum (IGDS) is obtained using the fast Fourier transform (FFT) for identifying fault type corresponding to the extracted IFCF. Based on obtained fault type and FCC ratios, new PFs and frequency points (FPs) are calculated for detecting other faults. Both simulated and experimental results validate that multi-fault features of rolling bearing under time-varying rotational speeds can be effectively identified without RF measurement and extraction.

Explainable 1DCNN with demodulated frequency features method for fault diagnosis of rolling bearing under time-varying speed conditions

Intelligent fault diagnosis of rolling bearings under non-stationary and time-varying speed conditions is still a challenging task. At the same time, a reasonable explanation for an intelligent diagnosis model based on features is currently lacking. Therefore, we exploit an explainable one-dimensional convolutional neural network (1DCNN) model by combining with the demodulated frequency features of vibration signals and apply it to the fault classification of rolling bearings under time-varying speed conditions. First, the speed signals obtained by the speed encoder were transformed into generalized demodulation operator (GDO). Second, combined with the sensitive frequency band and GDO, the generalized demodulation algorithm was used to extract the frequency features from the amplitude envelope of the vibration signal. Subsequently, the proposed lightweight 1DCNN was trained to classify the frequency features and identify the health states of the rolling bearing. Finally, the local interpretable model-agnostic explanations model was utilized to explain the proposed model based on the features which own weight. It is found that the internal classification mechanism of the lightweight 1DCNN is realized according to the distribution of fault features, which is consistent with the process of human brain analysis. Two kinds of time-varying speed datasets which come from the University of Ottawa and XJTU are tested and verified. The results show that compared with other intelligent fault diagnosis methods, the identification error of the proposed method is lower and the diagnosis stability is better. The average diagnostic accuracy was 96.26% and 99.82%, respectively.

Vibration analysis of a deep groove ball bearing with localized and distributed faults subject to waviness based on an improved model under time-varying speed condition

In this paper, a six-degree-of-freedom (6-DOF) comprehensive dynamic model of bearing-pedestal having waviness on its inner race and different sized surface damages has been presented to investigate the vibration response under time-varying speed conditions. It can provide a good solution to further analyze rotor systems with unfixed or elastic-supported pedestals, where vibrations in both horizontal and vertical directions are crucial. A signal processing method for fault feature extraction and enhancement of rolling element bearing in varying speed conditions is proposed. Vibration patterns with different raceway waviness and different sized surface damages are specifically studied. Characteristic frequencies are observed, which can be used for diagnosis of different sized waviness and faults under time-varying speed process. The present study will provide new insights into dynamic behavior of bearing system,

Bearing Fault Diagnosis under Time-Varying Speed and Load Conditions via Observer-Based Load Torque Analysis

Bearing fault is the most common failure in rotating machines, and bearing fault diagnosis (BFD) has been investigated using vibration, current, or acoustic signals. However, there are still challenges in some existing approaches. This study proposes a novel BFD method based on natural observer. Based on the analysis of the effects on the load torque signal caused by bearing faults in the permanent magnetic synchronous machine (PMSM), a modified natural observer was designed to reconstruct the load torque signal from electrical signals, acquiring a novel indicator without the additional sensor installed. Angular resampling was implemented to convert the non-stationary load torque signal into a stationary one to reduce the computational complexity. For full-auto diagnosis without human involvement, a threshold determination algorithm was also modified. Experimental validations were carried out under speed-varying and torque-varying conditions and were compared with phase current and q-axis current signals. The average signal-to-noise ratio (SNR) of the estimated load torque is about 8.65 times compared with the SNR of the traditional q-axis current. The effectiveness of the proposed method prior to the traditional PMSM bearing fault indicators is demonstrated by the order spectrum results.

Convolution enabled transformer via random contrastive regularization for rotating machinery diagnosis under time-varying working conditions

Mechanical equipment such as wind turbines often operates under time-varying working conditions (TVWC). The vibration signals collected from their key rotating components, such as bearings and gears, are often affected by TVWC. In this situation, eliminating the influence of working conditions is the key to effectively implementing end-to-end intelligent diagnosis of rotating machinery (RM). This paper first introduces the transformer encoder architecture to construct a diagnostic model. Then an improved self-attentive module based on a depth-separable convolution operation is built to encode better condition-independent depth diagnostic features and reduce the number of model parameters. Thus, a convolution enabled Transformer (Con-eT) is constructed as a deep encoder for the diagnostic model. Subsequently, a random contrastive regularization (RCR) method inspired by recently proposed contrastive learning is proposed to incentivize the model to learn working-condition-independent features and to improve the model's working condition generalization performance. A publicly available dataset of bearings at time-varying speeds is adopted to verify the effectiveness of the proposed method. Meanwhile, a specific experiment with a wind turbine gearbox designed explicitly for time-varying speed conditions further demonstrates the advantage of the proposed method over the comparative method in terms of the model’s working condition generalization.

Fault diagnosis of rolling bearing under time-varying speed conditions based on EfficientNetv2

The rolling bearing is a widely-used component in engineering. The fault diagnosis of rolling bearings is key to ensuring the normal operation of equipment. At present, research into the fault diagnosis of rolling bearings mainly focuses on the analysis of vibration data under constant working conditions. However, when dealing with practical engineering problems, equipment frequently operates at variable speed. To analyse the vibration data in the case of frequency conversion and accurately extract the fault characteristic frequency is a challenge, especially when the fault characteristics are weak. In addition, traditional vibration characteristic analysis requires professional technicians to supervise the operation of the equipment, which requires a certain professional ability of the staff. Based on the above two problems, this paper proposes a rolling bearing fault diagnosis model under time-varying speed working conditions, based on the EfficientNetv2 network. This method uses a short-time Fourier transform to convert a one-dimensional vibration signal into a two-dimensional image signal, and uses the advantages of an image recognition network to realize the fault diagnosis under time-varying speed conditions. After training the network, based on transfer learning, the experimental data verify that the accuracy of the results reaches 99.9 ± 0.1%, even in the case of weak fault characteristics, and there is no need for professional technicians to supervise and diagnose once the model is trained, which is conducive to practical application.

Noise source localization in permanent magnet synchronous motors under time-varying speed working conditions

Noise source localization of rotating machinery plays an important role in machinery noise diagnosis and control. Various beamforming methods have been developed for stationary sound source localization. However, for rotating machinery working under time-varying speed conditions, the radiated acoustic signals are typically nonstationary. Under these conditions, characterizing and localizing nonstationary sound sources remains a challenge. Permanent magnet synchronous motors are one of the most widely used rotating machinery in modern industries and often work under variable speed conditions. Herein, the noise source localization problem of motors under time-varying speed conditions was studied. A nonstationary noise source localization method based on the Vold-Kalman filter and time-domain beamforming is proposed to restore the spatial acoustic maps of permanent magnet synchronous motors(PMSMs) at a characteristic order. First, the Vold-Kalman filter is adopted to extract acoustic signals at a characteristic order from the nonstationary measurements using a microphone array. Then, the filtered multichannel acoustic signals are fed into the time-domain beamforming algorithm to obtain the noise source localization result in a characteristic order. Combining Vold-Kalman filter with time-domain beamforming enables the characterization of non-stationary sound sources in the time, spatial, and order domains. The experimental results verify the effectiveness of the proposed method in noise source localization for motors under time-varying speed conditions. In addition, the experimental case with two motors further proves that the proposed method can simultaneously realize noise source separation at different characteristic orders.

Detection and Diagnosis of Bearing Faults Under Fixed and Time-Varying Speed Conditions Using Persistence Spectrum and Multi-Scale Structural Similarity Index

With the widespread use of variable speed drives, a robust scheme that can detect and diagnose bearing faults under fixed and variable speed conditions becomes essential for reliable operation. Unfortunately, most of the reported methods in the literature are dedicated to working under fixed speed and will face challenges under variable speed conditions. Besides, most of them require detailed bearing information that may be unavailable in the real world. Therefore, in this paper, a new scheme is proposed for bearing faults detection and diagnosis under fixed and time-varying speed conditions. The proposed scheme is based on the analysis of vibration signals using the persistence spectrum that can provide images rich with health-related features largely independent from rotating speed. Then, the produced image is compared with priorly stored images of the persistence spectrum of a healthy case. This comparison is performed using the multi-scale structural similarity index, which is a robust basis for images comparison without the need for training or expert knowledge. The obtained index is compared against an adaptive threshold for fault detection. Upon detecting a fault, the persistence spectrum image is compared with that of stored different fault types for fault diagnosis. The proposed scheme is extensively validated using three experimental datasets under different speed conditions. The results show that it can detect bearing faults in an earlier stage without the need for bearing specifications or shaft speed. Moreover, it can successfully diagnose bearing faults severity with accuracy reaching 100% with the minimum required data.

Unknown bearing fault diagnosis under time-varying speed conditions and strong noise background

Unknown bearing fault diagnosis under time-varying speed conditions and strong noise background

A novel tacholess order analysis method for bearings operating under time-varying speed conditions

Order tracking (OT) of vibration envelope signal based on instantaneous frequency (IF) estimated from a time-frequency representation (TFR) is generally applied to detect bearing defects under time-varying speed conditions. However, these TFR based OT approaches require a high resolution for accurate estimation of the IF. To overcome these issues, a tacholess OT technique based on the fast dynamic time warping (FDTW) algorithm is applied to detect bearing defects for the first time in this paper. FDTW based signal transformation is initially applied to align a filtered shaft signal to a reference signal of constant frequency, followed by reconstructing the bearing envelope signal. The resulting envelope signal is able to provide a richer fault indication than the original signal. The efficacy of the developed OT method is established using a simulation analysis followed by experimental validation using measurements obtained from a laboratory test-rig and a wind turbine bearing.