Time-varying Speed Research Articles

New Cointegration-Based Feature Extraction Technique for Intelligent Bearing Fault Detection Under Time-Varying Speed

New Cointegration-Based Feature Extraction Technique for Intelligent Bearing Fault Detection Under Time-Varying Speed

Current-Aided Dynamic Time Warping for Planetary Gearbox Fault Detection at Time-Varying Speeds

Current-Aided Dynamic Time Warping for Planetary Gearbox Fault Detection at Time-Varying Speeds

Accurate and Efficient Instantaneous Angular Speed Estimation Method for Rolling Bearing Under Time-Varying Speed

Accurate and Efficient Instantaneous Angular Speed Estimation Method for Rolling Bearing Under Time-Varying Speed

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.

An electric vehicle routing model with charging stations consideration for sustainable logistics

PurposeRecently, electric vehicles have been widely used in the cold chain logistics sector to reduce the effects of excessive energy consumption and to support environmental friendliness. Considering the limited battery capacity of electric vehicles, it is vital to optimize battery charging during the distribution process.Design/methodology/approachThis study establishes an electric vehicle routing model for cold chain logistics with charging stations, which will integrate multiple distribution centers to achieve sustainable logistics. The suggested optimization model aimed at minimizing the overall cost of cold chain logistics, which incorporates fixed, damage, refrigeration, penalty, queuing, energy and carbon emission costs. In addition, the proposed model takes into accounts factors such as time-varying speed, time-varying electricity price, energy consumption and queuing at the charging station. In the proposed model, a hybrid crow search algorithm (CSA), which combines opposition-based learning (OBL) and taboo search (TS), is developed for optimization purposes. To evaluate the model, algorithms and model experiments are conducted based on a real case in Chongqing, China.FindingsThe result of algorithm experiments illustrate that hybrid CSA is effective in terms of both solution quality and speed compared to genetic algorithm (GA) and particle swarm optimization (PSO). In addition, the model experiments highlight the benefits of joint distribution over individual distribution in reducing costs and carbon emissions.Research limitations/implicationsThe optimization model of cold chain logistics routes based on electric vehicles provides a reference for managers to develop distribution plans, which contributes to the development of sustainable logistics.Originality/valueIn prior studies, many scholars have conducted related research on the subject of cold chain logistics vehicle routing problems and electric vehicle routing problems separately, but few have merged the above two subjects. In response, this study innovatively designs an electric vehicle routing model for cold chain logistics with consideration of time-varying speeds, time-varying electricity prices, energy consumption and queues at charging stations to make it consistent with the real world.

Rotating Machinery Fault Diagnosis Under Time-Varying Speeds: A Review

Rotating Machinery Fault Diagnosis Under Time-Varying Speeds: A Review

Time-frequency supervised contrastive learning via pseudo-labeling: An unsupervised domain adaptation network for rolling bearing fault diagnosis under time-varying speeds

The varying speed can cause the significant data distribution shift of bearings, making it difficult for deep learning-based bearing fault diagnosis models to ensure good generalization. Domain adaptation methods have been developed to address the domain shifts, while they struggle with the class-invariant features extraction under variable speed. Accordingly, a time–frequency supervised contrastive learning framework (TF-SupCon) is proposed for unsupervised cross-speed fault diagnosis of bearing. TF-SupCon adopts a pre-training-downstream task framework that aims to extract speed immune class-invariant features. During the pre-training phase, the physical consistency of the time-domain information and the frequency-domain information of bearing signal, a general feature applicable to different speed conditions, is learned in a targeted manner through supervised contrastive learning. Additionally, a K-Nearest Neighbor (KNN) algorithm based on cosine distance is designed to assign pseudo-labels to unlabeled target domain data, enabling cross-domain supervised contrastive pre-training. In the downstream task, unsupervised cross-domain fault diagnosis is performed using a KNN classifier and the speed immune time–frequency features by the trained encoders. It is worth noting that the same metric is maintained throughout both the pre-training phase and the downstream task, ensuring organic connection between the two stages. The superiority of TF-SupCon was demonstrated through a variety of fault diagnosis experiments conducted on both public and self-collected datasets. Lastly, the distances between time-domain and frequency-domain features of different categories were studied to verify the physical consistency between the features.

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.

Unbalanced Bearing Fault Diagnosis Under Various Speeds Based on Spectrum Alignment and Deep Transfer Convolution Neural Network

Bearing fault diagnosis plays a pivotal role in the safe and reliable operation of modern mechanical systems. However, the existing fault diagnosis methods rarely deal with the problem of category imbalance and various speeds concurrently, which cannot work effectively in practical scenarios. Considering the underlying similarities of data in frequency domain, data mining under various speeds can help to reduce the deviation of domain distribution. Therefore, a novel fault diagnosis method based on spectrum alignment (SA) and deep transfer convolution neural network (DTCNN) is proposed, where the SA and data augmentation module (DAM) are designed to extract spectrum alignment features from the unbalanced bearing data. The DTCNN model based on joint distribution adaptation (JDA) is built to facilitate learning reliable domain-invariant features. Different from the existing studies, a more general transfer task with time-varying speed is considered, even with complex faults. For 14 transfer tasks in two unbalanced fault diagnosis cases under variable speed, the average accuracy, F1-score, area under curve (AUC) of the proposed method can reach more than 97.76% 97.57% 98.75%. The results show that this method has superior diagnostic effect and better generalization ability than various state-of-the-art methods.

Three-Dimensional Spatial–Temporal Cooperative Guidance Without Active Speed Control

This paper investigates the three-dimensional (3D) spatial–temporal cooperative guidance problem for multiple missiles with time-varying speeds, which is addressed by a progressive design strategy. First, the zero miss distance and desired impact directions are realized by a 3D vector impact angle control guidance (IACG) law whose time-to-go is predicted accurately and efficiently by a numerical algorithm. Then, by introducing an implicit trajectory-to-go function, the time-to-go control mechanism is clearly revealed under missile speed variation. Accordingly, a coordinated biased term is added to the 3D vector IACG law to ensure a simultaneous attack. Finally, considering the seeker’s field-of-view (FOV) limit, the resultant cooperative guidance law is further augmented by another biased term to prevent the lead angle from exceeding its upper bound. Unlike similar existing results, the proposed one can satisfy multiple complex spatial–temporal constraints without active speed control, thereby manifesting great practical significance. Several numerical simulations are provided to show the effectiveness and advantages of the proposed cooperative guidance law.

A spectral self-focusing fault diagnosis method for automotive transmissions under gear-shifting conditions

Transmissions are core components of automobiles in adjusting the speed. The time-varying operation conditions, particularly the frequent gear shifting, present significant challenges for condition monitoring and fault locating of transmissions. At present, most existing studies primarily focus on the issues arising from time-varying speed, but they do not consider the challenges introduced by gear shifting. Gear shifting changes the meshing gear pairs within the transmission, causing the monitoring indicator amplitude fluctuates greatly. Consequently, the indicator fails to reflect the overall degradation trend of the transmission. To address this problem, this paper proposes a fault diagnosis method for automotive transmissions with the consideration of gear shifting. Our contributions are as follows: Firstly, we propose a spectral variation sparsity indicator (SVSI) based on the order spectrum at each gear position. Secondly, we fuse SVSI from different gear positions and create a comprehensive indicator called weighted health indicator (WHI). Finally, a diagnosis method based on SVSI and WHI is proposed for automotive transmissions under gear-shifting conditions. The effectiveness of the proposed method is validated using datasets from four automotive transmissions. The results demonstrate that our method is capable of detecting faults prior to inspection and accurately identifying faulty gears. Moreover, the performance of WHI is compared with several existing indicators. The results demonstrate that WHI exhibits stronger correlation, monotonicity, and robustness. This indicates that WHI is able to effectively mitigate the influence of gear shifting, thereby better reflecting the overall degradation trend of the transmission. Consequently, our proposed method significantly contributes to the field of condition monitoring and fault locating for automotive transmissions.

Oscillatory time–frequency concentration for adaptive bearing fault diagnosis under nonstationary time-varying speed

Being a promising post-processing solution, application of time–frequency concentration (TFC) suffers in an adaptive fault diagnosis scenario due to non-adaptive extraction of bearing fault signature from noise-associated vibration signals under nonstationary time-varying speed. Aiming at solving this problem, a novel method called oscillatory time–frequency concentration (OTFC) is proposed by oscillation based adaptive extraction of time-varying bearing fault signature with the help of tunable Q factor wavelet transform (TQWT). OTFC can effectively suppress unwanted noise while adaptively reveals the time-varying fault characteristic frequency (FCF) and corresponding harmonics with excellent readability. Two distinct numerical simulations and experimental case studies have been utilized to verify the performance of the proposed OTFC. The results show that the proposed OTFC not only performs better than the conventional TFC method namely synchrosqueezing wavelet transform (SST) but also shows superior performance than traditional continuous wavelet transform (CWT) and advanced TFC method namely multitaper synchrosqueezing wavelet transform (MST).

Tracking and Transmission Design in Terahertz V2I Networks

This paper designs the vehicle tracking and resource allocation in the terahertz (THz) vehicle-to-infrastructure communications (V2I) networks, where roadside units (RSUs) equipped with leaky-wave antennas help to estimate the driving states of multiple vehicles and optimize the transmit power and bandwidth per vehicle after receiving the vehicles’ feedback. Different from the conventional phased arrays, the leaky-wave antenna has the potential of improving the sensing accuracy with lower system overhead thanks to its unique spatial-spectral coupling feature. The generalized mobile scenario is studied in which vehicles drive at time-varying speeds. A novel unscented Kalman filter (UKF) based solution is proposed to track the vehicles without requirement of addressing the Doppler effect. Based on the estimated states of multiple vehicles, a low-complexity resource allocation method is developed to maximize the sum rate under user fairness concern. Simulation results confirm that the proposed tracking solution can evaluate the propagation angle, vehicle’s states and inter-vehicle distance accurately, and the tailored resource allocation method strikes a delicate balance between the sum rate and user fairness in the multi-vehicle V2I scenario.

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.

Bearing failure diagnosis at time-varying speed based on adaptive clustered fractional Gabor transform

For bearing fault diagnosis at time-varying speed with tachometer-free and non-resampling, the crucial process is to obtain a high-resolution time-frequency representation and extract fault features. However, current multi-component non-stationary signal feature extraction methods based on time-frequency transform suffer from fixed parameter settings and insufficient resolution for low signal-to-noise ratio signals. To address these issues, a novel adaptive clustered fractional Gabor transform is proposed and applied to extract bearing fault features at time-varying speed. Firstly, the grey wolf optimization is utilized to adaptively search for the optimal fractional order and Gauss window length based on the maximum spectral kurtosis and the generalized time-bandwidth product to achieve the most adequate fractional Gabor spectrum (FrGS). Then, the Clustering by Fast Search and Find of Density Peaks algorithm reconstructs the sparse representation of the FrGS, remapping multi-component signals into single-component clusters. Bearing fault diagnosis is achieved by matching the relative order of each cluster with the bearing fault characteristic coefficients. Simulation signals validate the superiority of the feature extraction method, and experimental signals validate the feasibility of the bearing fault diagnosis method.

Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized Intersections

To improve the driving efficiency and energy-saving characteristics for large-scale mixed traffic flows under different market penetration rates (MPRs) of intelligent and connected vehicles (ICVs) at unsignalized intersections, considering the cooperative eco-driving performance between ICVs and human-driven vehicles (HDVs) with time-varying speed characteristics, the hierarchical and distributed cooperative eco-driving architecture is first established in this paper, consisting of a cloud decision layer and a vehicle control layer. For the cloud decision layer, the multivehicle model-free adaptive predictive cooperative driving (MFAPCD) method is designed by using only the driving data of the HDVs and ICVs formation based on compact form dynamic linearization (CFDL) technique, thereby improving traffic efficiency. Furthermore, the CFDL integral terminal sliding mode predictive control (CFDL-ITSMPC) scheme is utilized to predict the time-varying driving speed of HDVs, and then, the CFDL predictive control (CFDL-PC) scheme is utilized to predict the expected control variables of ICVs formation. For the vehicle control layer, based on the anticipated driving speed obtained from the cloud decision layer, the nonlinear distributed model predictive control (NDMPC) method is utilized for distributed optimal control of each vehicle formation, to achieve optimization in terms of energy saving. Simulation results show that, compared with the signal time assignment strategy, the method can increase the average velocity by about 15.22% and decrease the average fuel consumption by about 36.43% under different MPRs and traffic volumes.

Generalized Synchroextracting-Based Stepwise Demodulation Transform and Its Application to Fault Diagnosis of Rotating Machinery

The nonstationary characteristics of time-varying signals can be characterized by time–frequency analysis (TFA) accurately, which has been widely used in fault diagnosis of rotating machinery. However, some practical signals contain complex multicomponent modes and noise interference, which will pose challenges to traditional TFA methods. In this article, a novel technique called generalized synchroextracting-based stepwise demodulation (GSET-SD) transform is proposed. GSET-SD introduces a strategy that combines synchroextracting transform (SET) with a stepwise demodulation procedure, thereby solving the problem of detecting and retrieving the amplitude- and frequency-modulated (AM-FM) components of a multicomponent signal from the time–frequency representation (TFR), while allowing the signal to be reconstructed from the TFR. Furthermore, to increase the estimation accuracy of the initial instantaneous frequency (IF) in processing the strong modulation signals, SET is extended to the second-order or higher order domain, and the IF is accurately estimated by the higher order polynomial method, which can obtain higher resolution TFR. The proposed approach has been applied to numerical simulations and application research. The experimental results verify the effectiveness and superiority of GSET-SD in processing strong modulation signals and demonstrate its promise in the field of fault diagnosis of rotating machinery under time-varying speeds.

The long-time behavior of solitary waves for the weakly damped KdV equation

In this paper, we first introduce the long-time behavior stability of solitary waves for the weakly damped Korteweg–de Vries equation. More concretely, solutions of the dissipative system with the initial values near a c_{0}-speed solitary wave, are approximated by a long curve on the family of solitary waves with the time-varying speed |c(t)-c_{0}| being small, in the long-time period (i.e., 0leqslant tleqslant O(frac{1}{epsilon ^{tau}})). Meanwhile, the approximation difference in a suitably weighted space H^{1}_{a}(mathbb{R}) is of the order of the damping coefficient and of some kind of exponential weight form. As a comparison, we also study the long-time behavior stability, i.e., for 0leqslant t<+infty , the solutions are approximated by a long curve on the family of solitary waves with the exponential decay speed c(t)= c_{0}e^{-beta t} (0<beta leqslant 1), when the initial values are near a c_{0}-speed solitary wave. However, here, the approximation difference merely defined in H^{1}(mathbb{R}) depends on the damping coefficient ϵ and the exponential decay coefficient β.