Envelopment Analysis Research Articles

Use of Tach from Vibration to Estimate Bearing Spall Length

Vibration analysis is often used for bearing fault diagnostics. Envelope analysis or other cyclo-stationary processes can capture a fault feature or condition indicator that is correlated to the spall length. However, no study has defined a process for estimating spall length on real-world data. The problem is that the spall length is a time-domain property of the signal. This paper generates a synthetic tachometer signal from the fault itself. It is synchronous to the rolling element exit from the spall, allowing for a time-domain representation of waveform using the time synchronous average. From this, an estimate of the length of the bearing fault can be determined.

Adaptive Feature Extraction Using Sparrow Search Algorithm-Variational Mode Decomposition for Low-Speed Bearing Fault Diagnosis.

To address the challenge of extracting effective fault features at low speeds, where fault information is weak and heavily influenced by environmental noise, a parameter-adaptive variational mode decomposition (VMD) method is proposed. This method aims to overcome the limitations of traditional VMD, which relies on manually set parameters. The sparrow search algorithm is used to calculate the fitness function based on mean envelope entropy, enabling the adaptive determination of the number of mode decompositions and the penalty factor in VMD. Afterward, the optimised parameters are used to enhance traditional VMD, enabling the decomposition of the raw signal to obtain intrinsic mode function components. The kurtosis criterion is then used to select relevant intrinsic mode functions for signal reconstruction. Finally, envelope analysis is applied to the reconstructed signal, and the results reveal the relationship between fault characteristic frequencies and their harmonics. The experimental results demonstrate that compared with other advanced methods, the proposed approach effectively reduces noise interference and extracts fault features for diagnosing low-speed bearing faults.

Characterization of bearing health in a noisy environment using vibroacoustic approach

The bearing fault detection localized at outer race on a rotating machine operating in the same environment with another machine (whose wind tunnel generates a different noise) is investigated using acoustic and vibration analysis. The impact of increased acoustic and vibratory background noise on outer race defect detection is studied through spectral kurtogram representation and envelope analysis. The spectral power densities of these two types of noise clearly show that the nature of their associated radiation (airborne or solid-borne) has a different impact. The presence of a strongly amplified background noise demonstrates that the acoustic modality can detect the outer race defect peak at higher levels than the vibratory modality.

A Motion Planner Based on Mask-D3QN of Quadruped Robot Motion for Steam Generator.

Crawling robots are the focus of intelligent inspection research, and the main feature of this type of robot is the flexibility of in-plane attitude adjustment. The crawling robot HIT_Spibot is a new type of steam generator heat transfer tube inspection robot with a unique mobility capability different from traditional quadrupedal robots. This paper introduces a hierarchical motion planning approach for HIT_Spibot, aiming to achieve efficient and agile maneuverability. The proposed method integrates three distinct planners to handle complex motion tasks: a nonlinear optimization-based base motion planner, a TOPSIS-based base orientation planner, and a Mask-D3QN (MD3QN) algorithm-based gait motion planner. Initially, the robot's base and foot workspace were delineated through envelope analysis, followed by trajectory computation using Larangian methods. Subsequently, the TOPSIS algorithm was employed to establish an evaluation framework conducive to foundational turning planning. Finally, the MD3QN algorithm trained foot-points to facilitate robot movement along predefined paths. Experimental results demonstrated the method's adaptability across diverse tube structures, showcasing robust performance even in environments with random obstacles. Compared to the D3QN algorithm, MD3QN achieved a 100% success rate, enhanced average overall scores by 6.27%, reduced average stride lengths by 39.04%, and attained a stability rate of 58.02%. These results not only validate the effectiveness and practicality of the method but also showcase the significant potential of HIT_Spibot in the field of industrial inspection.

Double autocorrelation-based cyclicity evaluation for repetitive transients feature extraction

Abstract The vibration response caused by bearing local defects has impact and periodicity in waveform, which provides a standard for the frequency band selection in envelope analysis. However, most periodicity measurements without prior knowledge belong to sparsity evaluation, while the defects of sparsity index in nature are inevitable. Inspired by the periodic component extraction of autocorrelation function, a novel cyclicity measurement based on double autocorrelation calculation is proposed. With the help of normalization, this approach can distinguish periodic impulses from random impulses by using the periodic sub-maxima of the envelope autocorrelation. Considering the influence of the noise component on the autocorrelation of the periodic signal, the sub-maximums are maintained by threshold processing. On this basis, the re-autocorrelation is calculated to identify the periodic sub-maximum. Finally, as a non-prior index, a demodulation band selection is also proposed in combination with an impulsivity evaluation. The results of the proposed method are analyzed and verified by comparison with typical methods.

HTG transformation: an amplitude modulation method and its application in bearing fault diagnosis

Abstract Rolling bearings are critical components in modern mechanical equipment, and the health monitoring and predictive maintenance of bearings are crucial for the normal operation of machinery. Hence, there is a compelling need to delve into advanced methodologies for enhancing the detection of fault characteristics in bearings. Faulty bearings produce periodic impulses during constant-speed rotation, which can typically be detected through envelope analysis. However, in some complex conditions, the relevant fault frequencies may be hidden within interfering components. This paper presents an amplitude modulation technique called the hyperbolic tangent Gaussian (HTG) transformation, designed to extract weak fault components from signals. Firstly, a family of amplitude modulation functions, known as the HTG functions, is constructed. These functions modulate signals with normalized amplitudes to obtain a series of modulated signals. Simultaneously, a frequency domain amplitude ratio metric is used for the automatic selection of the optimal components. Finally, the HTGgram is introduced, a spectral decomposition method based on trend components, aiming to identify the best combination of filtering and modulation components. Simulations with multi-component bearing fault signals and experimental signals with composite bearing faults demonstrate that this method not only highlights fault features and suppresses noise interference but also adaptively selects frequency bands related to faults, enhancing fault information. This approach exhibits excellent adaptability and effectiveness in complex operating conditions with multiple interference components.

Multi-rolling element faults diagnosis of rolling bearing based on time-frequency analysis and multi-curves extraction

Abstract In industrial production, rolling bearings are widely used as key mechanical components in all types of rotating machinery. Fault diagnosis is essential for predicting bearing damage in advance, avoiding sudden equipment downtime and reducing economic losses. However, rolling element fault diagnosis of rolling bearings continues to be a challenge, especially with multi-rolling element faults. In view of the characteristics of randomness, weakness, and coupling in the vibration signal generated by multi-rolling element faults in rolling bearings, a multi-rolling element fault detection method is proposed by combination time-frequency (TF) analysis (TFA) with multi-curves extraction methods. The pre-processing method combined autoregressive model with maximum correlated kurtosis deconvolution is employed to enhance the weak periodic fault impulses in the raw vibration signals of the rolling bearing. Then an improved dynamic path multi-curves extraction method is proposed to extract multiple TF curves from the TF spectrogram (TFS) constructed via short-time Fourier transform. According to the proposed classification criteria, the TF curves are classified as homologous faults. The TF masking (TFM) method is employed to keep TF information closely associated with the fault impulse. Finally, the fault signals are reconstructed sequentially based on the TFS processed by TFM, and precise identification of multi-rolling element faults is achieved by envelope analysis. Experimental results demonstrate the effectiveness of the proposed method in extracting the weak fault features of multi-rolling elements and accomplishing fault separation and diagnosis.

Cross-correlation technique for phase error correction in reflection mode terahertz time-domain spectroscopy

Terahertz time-domain spectroscopy in reflection mode geometry provides valuable surface and subsurface information, making it suitable for a layer analysis, coating, and non-destructive testing applications. The exchanging of the sample and reference’s position introduces a phase error when the position or alignment of the sample is not precisely maintained during measurements. This micrometer order of pitch error (Δx) between the reference and the sample could lead to an inherent error in the phase spectrum of the sample. In the present work, a novel approach, to the best of our knowledge, based on the cross-correlation with an envelope technique, has been demonstrated to reduce the uncertainty in the phase and reveal the hidden characteristic features of the given sample in THz TDS spectroscopy. In conjunction with experimental verification, we have employed a finite element analysis in COMSOL Multiphysics to simulate a misplacement error between a lossy dielectric medium (n=1.2 to 3.0 and k=0 to 0.9) and a reference. We have investigated the impact of varying properties of the lossy dielectric medium on delay measurements using a cross-correlation with an envelope analysis. We illustrated and demonstrated the advantage of our approach by measuring the optical properties of Teflon, quartz, and RDX by correcting the misalignment of the 15.75, 17.55, and 20.70 µm ranges, respectively.

Application of Salp Swarm Algorithm and Extended Repository Feature Selection Method in Bearing Fault Diagnosis

Motor fault diagnosis is an important task in the operational monitoring of electrical machines in manufacturing. This study proposes an effective bearing fault diagnosis model for electrical machinery based on machine learning techniques. The proposed model is a combination of three processes: feature extraction of signals collected from the motor based on multi-resolution analysis, fast Fourier transform, and envelope analysis. Next, redundant or irrelevant features are removed using the feature selection technique. A binary salps swarm algorithm combined with an extended repository is the proposed method to remove unnecessary features. As a result, an optimal feature subset is obtained to improve the performance of the classification model. Finally, two classifiers, k-nearest neighbor and support vector machine, are used to classify the fault of the electric motor. There are four input datasets used to evaluate the model performance, and UCI is the benchmark dataset to verify the effectiveness of the proposed feature selection technique. The remaining three datasets include the bearing dataset collected from experiments, with an average classification accuracy of 99.9%, as well as Case Western Reserve University (CWRU) and Machinery Failure Prevention Technology (MFPT), which are public datasets with average classification accuracies of 99.6% and 98.98%, respectively. The experimental results show that this method is more effective in diagnosing bearing faults than other traditional methods and prove its robustness.

A novel underwater weak signal detection method based on parameter optimized VMD and 3D chaotic system

Based on chaos theory, combined with improved variational mode decomposition, a novel method for underwater weak signal detection and frequency extraction is proposed. The aim of this research is to address the challenge of detecting underwater signals and extracting their frequencies under ultra-low Signal-to-Noise Ratio (SNR). A novel three-dimensional (3D) chaotic system with infinitely shrinking attractors is proposed, which incorporates a cosine function to achieve chaos control and enhancement. The nonlinear characteristics of the system, such as Lyapunov exponent and bifurcation, are analyzed in detail. Then, we design a frequency array and perform scale transformation on the chaotic system to construct a detection model that covering all frequencies. The model can transition from critical chaos to large period or intermittent chaos in the presence of external periodic signals by adjusting the parameters of the cosine function. Considering the relationship between the generation of intermittent chaos and the frequency of target signal, a frequency extraction algorithm based on chaos sparrow search algorithm optimization variational mode decomposition (CSSA-VMD) and Hilbert transform is designed. The algorithm can estimate the real frequency of underwater signals by performing noise reduction and envelope analysis on intermittent chaotic signals. The experimental results demonstrate that the proposed system can detect weak signals in complex marine backgrounds and extract their frequency features, with a detection SNR of -48 dB and a frequency error of less than 0.01%. Importantly, the circuit of the detection system has been implemented, verifying its feasibility for detecting and tracking underwater signals.

Assessment of Effects of Carbon Dioxide Exposure on Sleep Stability in Insomnia Using the Envelope Analysis

Objectives: Insomnia is a common sleep disorder, and various strategies have been explored for its treatment. One of the methods involves the administration of carbon dioxide (CO<sub>2</sub>) at bedtime, as the CO<sub>2</sub> increment exerts a sedative effect on the central nervous system. We aimed to assess the effect of CO<sub>2</sub> on sleep quality in patients with insomnia using the coefficient of variation of the envelope (CVE) analysis, a novel analytical method. Methods: In this randomized, double-blind, sham-controlled crossover trial, 24 adults with sleeping difficulties underwent level 1 polysomnography. Two interventions involved exposure to either 2% low-concentration CO<sub>2</sub> gas or room air. CVE analysis was performed to assess the stability of the delta band. Morphological variations in delta waves can be quantitatively monitored using the envelope analysis, which assesses the effect of manipulations on sleep that may otherwise elude detection. Results: Exposure to CO<sub>2</sub> improved the total sleep time (TST) (<i>p</i>=0.010) and total arousal index (TAI) (<i>p</i>=0.011). The CVE analysis showed a distinct distribution between the experimental and sham-controlled groups. Moreover, correlations between the TST and CVE (r=0.41) and those between the TAI and CVE (r=0.40) were observed. Conclusions: This study is the first to evaluate the effects of CO<sub>2</sub> exposure on sleep stability in patients with insomnia. The CVE analysis implies the possibility of sleep stabilization by CO<sub>2</sub> administration and suggests a link between enhanced sleep maintenance and sleep stability.

Vibration-Based Detection of Axlebox Bearing Considering Inner and Outer Ring Raceway Defects

The occurrence of an axlebox bearing ring raceway defect is an inevitable and commonly observed phenomenon in railway wheels. It not only leads to surface damage but also poses the potential threat of further damage and degradation, thereby increasing the risks associated with running safety and maintenance costs. Hence, it becomes imperative to detect raceway defects at an early stage to mitigate safety hazards and reduce maintenance efforts. In this study, the focus lies in investigating the effectiveness of vibration-based detection techniques for identifying raceway defects in high-speed train axlebox bearing systems. To achieve this, a dynamic model that accurately represents the coupling dynamics between the vehicle and the track is developed. This model incorporates various dynamic factors, such as traction transmission, gear transmission, and track geometry irregularities. By using the comprehensive dynamic model, the dynamic responses of the axlebox can be accurately calculated. The proposed methodology primarily revolves around analysing the vertical vibrations of the axlebox caused by raceway defects in both the time and frequency domains. Additionally, an envelope analysis using a developed band-pass filter is also employed. The results obtained from this study clearly demonstrate the successful detection of raceway defects in a more realistic vehicle model, thereby providing an efficient approach for the detection of axlebox bearing raceway defects. Consequently, this research contributes significantly to the field of high-speed train systems and paves the way for enhanced safety and maintenance practices.

Methods of detection and localization of the sources of noise and vibration on car gearboxes: a review

One of the primary sources of noise and vibration in automobiles is gearboxes. Shafts, gears, and bearings are the main causes of noise and vibration in vehicle gearboxes. Various studies have reported that vibrations’ root cause is bearing excitation. Besides bearing fatal defects or extreme structure resonance amplification, gear mesh is the primary source of high-frequency vibration and noise, even in newly built units. Gear damage detection is frequently crucial in automotive gearboxes and vehicle safety. Furthermore, vibrations caused by shaft imbalances, shaft misalignments, and other factors can cause noise and vibrations in the drivetrain's transfer path. In addition, the vibration of an automobile gearbox is closely related to poor design, construction quality, and production accuracy. This paper reviewed previous research and methods on car gearboxes for conventional vehicles. It was obvious that frequency analysis and order analysis were commonly used in noise and vibration analysis on car gearboxes. Envelope analysis is usually used to analyze bearing faults. Finally, rolling-element bearing diagnostic techniques were also reviewed.

Early Fault Diagnosis of Bearings Based on Symplectic Geometry Mode Decomposition Guided by Optimal Weight Spectrum Index

When the rotating machinery fails, the signal generated by the faulty component often no longer maintains the original symmetry, which makes the vibration signal with nonlinear and non-stationary characteristics, and is easily affected by background noise and other equipment excitation sources. In the early stage of fault occurrence, the fault signal is weak and difficult to extract. Traditional fault diagnosis methods are not able to easily diagnose fault information. To address this issue, this paper proposes an early fault diagnosis method for symplectic geometry mode decomposition (SGMD) based on the optimal weight spectrum index (OWSI). Firstly, using normal and fault signals, the optimal weight spectrum is derived through convex optimization. Secondly, SGMD is used to decompose the fault signal, obtaining a series of symplectic geometric modal components (SGCs) and calculating the optimal weight index of each component signal. Finally, using the principle of maximizing the OWSI, sensitive components reflecting fault characteristics are selected, and the signal is reconstructed based on this index. Then, envelope analysis is performed on the sensitive components to extract early fault characteristics of rolling bearings. OWSI can effectively distinguish the interference components in fault signals using normal signals, while SGMD has the characteristic of unchanged phase space structure, which can effectively ensure the integrity of internal features in data. Using actual fault data of rolling bearings for verification, the results show that the proposed method can effectively extract sensitive components that reflect fault characteristics. Compared with existing methods such as Variational Mode Decomposition (VMD), Feature Mode Decomposition (FMD), and Spectral Kurtosis (SK), this method has better performance.

DTMSgram: a novel optimal demodulation frequency band selection method for wheelset bearings fault diagnosis under wheel-rail excitation

Due to the influence of the wheel-rail excitation and complex transmission path, the fault signature of wheelset bearings is often obscured by complex background noise, which brings great challenges to the adaptive determination of the informative frequency band (IFB) in envelope analysis. In this paper, the vibration response characteristics of the axle box under wheel–rail excitation are revealed through full-scale bench tests. The experimental results show that tread damage will provoke periodic transient impacts and it has an obvious sparsity in the frequency domain. Inspired by this feature, a DTMSgram method is proposed to enhance the fault feature components of vibration signals through time-domain and frequency-domain noise reduction technology, and improve the accuracy of demodulation frequency band selection. Firstly, the amplitude spectrum of different weight coefficients is used to preprocess the vibration signal and adjust the full band component of the vibration signal. Then, the autocorrelation process is performed on each layer’s narrowband filtered signal envelope in kurtogram to further reduce noise interference from a time-domain perspective. Moreover, a two-dimensional color map is constructed showing the normalized squared envelope spectrum of the IFBs determined simultaneously from the modified signal. Finally, the effectiveness of the proposed method is verified by simulated signal and experimental data of three sets of full-size wheelset bearing systems. The analysis results indicate this proposed method can effectively overcome the influence of complex wheel–rail excitation interference and can diagnose multi-source faults simultaneously.

Automatic Feature Extraction Based on Envelope Analysis and its Application in Rolling-Element Bearing Fault Detection

Bearing fault diagnosis is essential for the maintenance, durability, and reliability of rotating machines. It can minimize economic losses by removing unplanned downtime in the industry due to the failure of rotary machines. In bearing fault detection, developing fault features extraction techniques that can successfully applicable for various fault severity and different operating conditions is still a critical issue. In the current work, the feature extraction technique is a combination between pre-processing algorithms and envelope analysis method. In the pre-processing stage, the autoregressive (AR) model is used to filter the original signal and remove the deterministic vibration sources, as well as maintain the signal representing the condition of the bearing without contaminating noises. Then, the most suitable frequency band is selected based on the spectral kurtosis (SK) analysis. This band contains the signature frequencies of the roller bearing. After that, envelope analysis is employed for detecting faults at different severity. Finally, the features represented the peaks at fundamental fault frequencies are automatically selected from the envelope spectrum. By analyzing all diagnoses results, it is found that the presented method effectively extracts the features at calculated resonance bearing frequencies and proves the significance of the enhancements in a pre-filtering stage in the overall detection performance. Also, it can benefit from these features in the fault classification fields at different speeds because it is independent of speed variation.

Advantages of periodic non-stationary random process model in vibration signal processing

The use of two different techniques for the analysis of vibration signals, whose carrier harmo¬nics are modulated by high-frequency narrow-band random processes is discussed. Periodically non-stationary random processes (PNRP) are suitable models for description of vibration signals of damaged mechanism. A proposed processing technique can be considered as an alternative to squared envelope analysis, kurtosis techniques, squared envelope spectrum (SES) and its use in the analysis of a vibration signal is discussed. It is shown that the spectral estimates obtained by the envelope square method are biased and inconsistent. The possibility of obtaining of the unbiased estimates by the PNVP method even for a signal/noise ratio equal to 0.07 has been demonstrated.

Application of Short Time Fourier Transform (STFT) For Diagnosing Rolling Bearing Faults

A fan is crucial for maintaining airflow in industries. Bearings in fans prevent friction and must be robust to function effectively. Damage to the bearings can diminish machine performance. Predictive maintenance is essential for early detection of faults. One way to analyze bearing faults is by using the Short Time Fourier Transform (STFT), as it excels in analyzing non-stationary signals. Experiments were conducted under normal conditions and with inner race faults in bearings at a shaft speed of 1162.5 Hz. Vibration detection was done using an accelerometer sensor, and Matlab analysis was employed. The data was processed using the Fourier Transform (FT) method through both time and frequency domains, as well as the STFT through spectrograms. In the spectrum plot, there is still a significant amount of noise present. This high amplitude of noise from other frequencies obscures the bearing fault amplitudes. Furthermore, the Fourier Transform (FT) is only suitable for analyzing stationary signals. To address this, an envelope analysis was used to filter out the noise. The STFT analysis method provides simultaneous frequency and time information. This reveals that the spectrogram results for inner race faults depict three high amplitude peaks at harmonic frequencies. This indicates that the signal is non-stationary due to fluctuating amplitudes, making bearing fault analysis more accessible.

The LESGIRgram: A New Method to Select the Optimal Demodulation Frequency Band for Rolling Bearing Faults

Resonance demodulation of vibration signals is a common method for extracting fault information from rolling bearings. Nonetheless, demodulation quality is dependent on frequency band location. Established methods such as the Fast Kurtogram, Autogram, SKRgram, etc. have achieved satisfactory results in some cases, but the results are not good in the presence of strong white Gaussian noise and random impulses. To solve these issues, an algorithm that selects the optimal demodulation frequency band (ODFB) based on the ratio of the logarithmic envelope spectrum Gini coefficient (LESGIRgram) is proposed. The core idea of this paper is to capture the difference between the LESGIgrams of health and fault signals and accordingly locate the frequency bands that contain the most fault information. Initially, the baseline is constructed by calculating the logarithmic envelope spectrum Gini coefficient matrix of the health bearing (LESGIbaseline). Next, the LESGI matrix of the fault bearing (LESGImeasured) is computed. The ratio of LESGImeasured to LESGIbaseline is calculated, and the ODFB can be selected with the maximum LESGIR. The fault signal is then filtered using this derived ODFB, and envelope analysis is performed to extract fault features. The proposed algorithm for detecting rolling bearing faults has been verified for accuracy and effectiveness through simulation and experimental data.

Fault feature detection of planet gear in multi-stage planetary gearbox based on angle compensation synchronous averaging

Planetary gearboxes are often used for power transmission in wind turbines. It makes the gear fault detection of planetary gearboxes very useful and necessary. Generally, windowed synchronous averaging (WSA) is a widely used method to detect planet gear failure in planetary gearboxes. However, the WSA is not directly suitable for the multi-stage planetary gearbox since different planetary stages are working together and vibrations from different stages are coupled to each other. The coupled interference is the synchronous interference, which cannot be reduced by the WSA. It makes the faulty planet gear of interest difficult to detect. To address this issue, an angle compensation synchronous averaging (ACSA) scheme is proposed. The equi-angle resampling is applied to the obtained vibration first. Then, the synchronous interference can be constructed by applying the synchronous averaging-based angle compensation strategy, and removed by subtracting it from the resampled vibration. Subsequently, the fast spectral kurtosis is utilized on the residual vibration to obtain the envelope signal. Next, the WSA is further applied to the residual vibration and envelope signal for constructing the synthetic vibration and synthetic envelope signal corresponding to the planet gear of interest. Finally, the narrowband demodulation and envelope analysis are used to detect planet gear failure. Experiments on a two-stage planetary gearbox positively support the ACSA scheme.